WorldWideScience

Sample records for topological partition function

  1. Topological string partition functions as polynomials

    International Nuclear Information System (INIS)

    Yamaguchi, Satoshi; Yau Shingtung

    2004-01-01

    We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)

  2. The wave function behavior of the open topological string partition function on the conifold

    International Nuclear Information System (INIS)

    Kashani-Poor, Amir-Kian

    2007-01-01

    We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C 3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator

  3. Gate-tunable current partition in graphene-based topological zero lines

    Science.gov (United States)

    Wang, Ke; Ren, Yafei; Deng, Xinzhou; Yang, Shengyuan A.; Jung, Jeil; Qiao, Zhenhua

    2017-06-01

    We demonstrate new mechanisms for gate-tunable current partition at topological zero-line intersections in a graphene-based current splitter. Based on numerical calculations of the nonequilibrium Green's functions and Landauer-Büttiker formula, we show that the presence of a perpendicular magnetic field on the order of a few Teslas allows for carrier sign dependent current routing. In the zero-field limit the control on current routing and partition can be achieved within a range of 10-90 % of the total incoming current by tuning the carrier density at tilted intersections or by modifying the relative magnitude of the bulk band gaps via gate voltage. We discuss the implications of our findings in the design of topological zero-line networks where finite orbital magnetic moments are expected when the current partition is asymmetric.

  4. Compactified webs and domain wall partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)

    2017-04-15

    In this paper we use the topological vertex formalism to calculate a generalization of the ''domain wall'' partition function of M-strings. This generalization allows calculation of partition function of certain compactified webs using a simple gluing algorithm similar to M-strings case. (orig.)

  5. Dual little strings and their partition functions

    Science.gov (United States)

    Bastian, Brice; Hohenegger, Stefan; Iqbal, Amer; Rey, Soo-Jong

    2018-05-01

    We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds XN ,M at a generic point in the Kähler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows us to compute the topological string partition function of XN ,M as a series expansion in different Kähler parameters. Using this result, we give further explicit proof for a duality found previously in the literature, which relates XN ,M˜XN',M' for N M =N'M' and gcd (N ,M )=gcd (N',M') .

  6. Supersymmetric partition functions and the three-dimensional A-twist

    Energy Technology Data Exchange (ETDEWEB)

    Closset, Cyril [Theory Department, CERN,CH-1211, Geneva 23 (Switzerland); Kim, Heeyeon [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada); Willett, Brian [Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States)

    2017-03-14

    We study three-dimensional N=2 supersymmetric gauge theories on M{sub g,p}, an oriented circle bundle of degree p over a closed Riemann surface, Σ{sub g}. We compute the M{sub g,p} supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round S{sup 3} can be understood as the expectation value of a so-called “fibering operator” on S{sup 2}×S{sup 1} with a topological twist. More generally, we show that the 3d N=2 supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on M{sub g,p} are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimensional supersymmetric dualities.

  7. Partition functions of web diagrams with an O7{sup −}-plane

    Energy Technology Data Exchange (ETDEWEB)

    Hayashi, Hirotaka [Tokai University, 4-1-1 Kitakaname,Hiratsuka, Kanagawa 259-1292 (Japan); Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Zoccarato, Gianluca [Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain)

    2017-03-22

    We consider the computation of the topological string partition function for 5-brane web diagrams with an O7{sup −}-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the orientifold we are able to apply the topological vertex to obtain the Nekrasov partition function of the corresponding 5d theory. We apply this procedure to the case of 5d SU(N) theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure USp(2N) theories. For these cases we discuss the dictionary between parameters and moduli of the 5d gauge theory and lengths of 5-branes in the web diagram and moreover we perform comparison of the results obtained via application of the topological vertex and the one obtained via localisation techniques, finding in all instances we consider perfect agreement.

  8. Consequences of Common Topological Rearrangements for Partition Trees in Phylogenomic Inference.

    Science.gov (United States)

    Chernomor, Olga; Minh, Bui Quang; von Haeseler, Arndt

    2015-12-01

    In phylogenomic analysis the collection of trees with identical score (maximum likelihood or parsimony score) may hamper tree search algorithms. Such collections are coined phylogenetic terraces. For sparse supermatrices with a lot of missing data, the number of terraces and the number of trees on the terraces can be very large. If terraces are not taken into account, a lot of computation time might be unnecessarily spent to evaluate many trees that in fact have identical score. To save computation time during the tree search, it is worthwhile to quickly identify such cases. The score of a species tree is the sum of scores for all the so-called induced partition trees. Therefore, if the topological rearrangement applied to a species tree does not change the induced partition trees, the score of these partition trees is unchanged. Here, we provide the conditions under which the three most widely used topological rearrangements (nearest neighbor interchange, subtree pruning and regrafting, and tree bisection and reconnection) change the topologies of induced partition trees. During the tree search, these conditions allow us to quickly identify whether we can save computation time on the evaluation of newly encountered trees. We also introduce the concept of partial terraces and demonstrate that they occur more frequently than the original "full" terrace. Hence, partial terrace is the more important factor of timesaving compared to full terrace. Therefore, taking into account the above conditions and the partial terrace concept will help to speed up the tree search in phylogenomic inference.

  9. Application of radial basis function neural network to predict soil sorption partition coefficient using topological descriptors.

    Science.gov (United States)

    Sabour, Mohammad Reza; Moftakhari Anasori Movahed, Saman

    2017-02-01

    The soil sorption partition coefficient logK oc is an indispensable parameter that can be used in assessing the environmental risk of organic chemicals. In order to predict soil sorption partition coefficient for different and even unknown compounds in a fast and accurate manner, a radial basis function neural network (RBFNN) model was developed. Eight topological descriptors of 800 organic compounds were used as inputs of the model. These 800 organic compounds were chosen from a large and very diverse data set. Generalized Regression Neural Network (GRNN) was utilized as the function in this neural network model due to its capability to adapt very quickly. Hence, it can be used to predict logK oc for new chemicals, as well. Out of total data set, 560 organic compounds were used for training and 240 to test efficiency of the model. The obtained results indicate that the model performance is very well. The correlation coefficients (R2) for training and test sets were 0.995 and 0.933, respectively. The root-mean square errors (RMSE) were 0.2321 for training set and 0.413 for test set. As the results for both training and test set are extremely satisfactory, the proposed neural network model can be employed not only to predict logK oc of known compounds, but also to be adaptive for prediction of this value precisely for new products that enter the market each year. Copyright © 2016 Elsevier Ltd. All rights reserved.

  10. Toda 3-point functions from topological strings

    International Nuclear Information System (INIS)

    Mitev, Vladimir; Pomoni, Elli; National Technical Univ. of Athens

    2014-09-01

    We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In (L. Bao, V. Mitev, E. Pomoni, M. Taki, and F. Yagi, JHEP 1401 (2014), 175) we computed the partition function of 5D T N theories on S 4 x S 1 and suggested that they should be interpreted as the three-point structure constants of q-deformed Toda. In this paper, we provide the exact AGT-W dictionary for this relation and rewrite the 5D T N partition function in a form that makes taking the 4D limit possible. Thus, we obtain a prescription for the computation of the partition function of the 4D T N theories on S 4 , or equivalently the undeformed 3-point Toda structure constants. Our formula, has the correct symmetry properties, the zeros that it should and, for N=2, gives the known answer for Liouville CFT.

  11. Toda 3-point functions from topological strings

    Energy Technology Data Exchange (ETDEWEB)

    Mitev, Vladimir [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)

    2015-06-08

    We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In http://dx.doi.org/10.1007/JHEP01(2014)175 we computed the partition function of 5D T{sub N} theories on S{sup 4}×S{sup 1} and suggested that they should be interpreted as the three-point structure constants of q-deformed Toda. In this paper, we provide the exact AGT-W dictionary for this relation and rewrite the 5D T{sub N} partition function in a form that makes taking the 4D limit possible. Thus, we obtain a prescription for the computation of the partition function of the 4D T{sub N} theories on S{sup 4}, or equivalently the undeformed 3-point Toda structure constants. Our formula, has the correct symmetry properties, the zeros that it should and, for N=2, gives the known answer for Liouville CFT.

  12. Toda 3-point functions from topological strings

    Energy Technology Data Exchange (ETDEWEB)

    Mitev, Vladimir [Humboldt-Univ., Berlin (Germany). Inst. fuer Mathematik und Inst. fuer Physik; Pomoni, Elli [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; National Technical Univ. of Athens (Greece). Physics Div.

    2014-09-15

    We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In (L. Bao, V. Mitev, E. Pomoni, M. Taki, and F. Yagi, JHEP 1401 (2014), 175) we computed the partition function of 5D T{sub N} theories on S{sup 4} x S{sup 1} and suggested that they should be interpreted as the three-point structure constants of q-deformed Toda. In this paper, we provide the exact AGT-W dictionary for this relation and rewrite the 5D T{sub N} partition function in a form that makes taking the 4D limit possible. Thus, we obtain a prescription for the computation of the partition function of the 4D T{sub N} theories on S{sup 4}, or equivalently the undeformed 3-point Toda structure constants. Our formula, has the correct symmetry properties, the zeros that it should and, for N=2, gives the known answer for Liouville CFT.

  13. Topological anomalies for Seifert 3-manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)

    2015-07-14

    We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

  14. Generating functional for Donaldson invariants and operator algebra in topological D=4 Yang-Mills theory

    International Nuclear Information System (INIS)

    Johansen, A.A.

    1992-01-01

    It is shown, that under the certain constraints the generating functional for the Donaldson invariants in the D=4 topological Yang-Mills theory can be interpreted as a partition function for the renormalizable theory. 20 refs

  15. Periodic Schur process, cylindric partitions and N=2* theory

    International Nuclear Information System (INIS)

    Iqbal, Amer; Kozcaz, Can; Sohail, Tanweer

    2011-01-01

    Type IIA string theory compactified on an elliptic CY3-fold gives rise to N=2U(1) gauge theory with an adjoint hypermultiplet. We study the refined open and closed topological string partition functions of this geometry using the refined topological vertex. We show that these partition functions, open and closed, are examples of periodic Schur process and are related to the generating function of the cylindric partitions if the Kaehler parameters are quantized in units of string coupling. The level-rank duality appears as the exchange symmetry of the two Kaehler parameters of the elliptic CY3-fold.

  16. From topological strings to minimal models

    International Nuclear Information System (INIS)

    Foda, Omar; Wu, Jian-Feng

    2015-01-01

    We glue four refined topological vertices to obtain the building block of 5D U(2) quiver instanton partition functions. We take the 4D limit of the result to obtain the building block of 4D instanton partition functions which, using the AGT correspondence, are identified with Virasoro conformal blocks. We show that there is a choice of the parameters of the topological vertices that we start with, as well as the parameters and the intermediate states involved in the gluing procedure, such that we obtain Virasoro minimal model conformal blocks.

  17. From topological strings to minimal models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, Omar [School of Mathematics and Statistics, University of Melbourne,Royal Parade, Parkville, VIC 3010 (Australia); Wu, Jian-Feng [Department of Mathematics and Statistics, Henan University,Minglun Street, Kaifeng city, Henan (China); Beijing Institute of Theoretical Physics and Mathematics,3rd Shangdi Street, Beijing (China)

    2015-07-24

    We glue four refined topological vertices to obtain the building block of 5D U(2) quiver instanton partition functions. We take the 4D limit of the result to obtain the building block of 4D instanton partition functions which, using the AGT correspondence, are identified with Virasoro conformal blocks. We show that there is a choice of the parameters of the topological vertices that we start with, as well as the parameters and the intermediate states involved in the gluing procedure, such that we obtain Virasoro minimal model conformal blocks.

  18. Insulator function and topological domain border strength scale with architectural protein occupancy

    Science.gov (United States)

    2014-01-01

    Background Chromosome conformation capture studies suggest that eukaryotic genomes are organized into structures called topologically associating domains. The borders of these domains are highly enriched for architectural proteins with characterized roles in insulator function. However, a majority of architectural protein binding sites localize within topological domains, suggesting sites associated with domain borders represent a functionally different subclass of these regulatory elements. How topologically associating domains are established and what differentiates border-associated from non-border architectural protein binding sites remain unanswered questions. Results By mapping the genome-wide target sites for several Drosophila architectural proteins, including previously uncharacterized profiles for TFIIIC and SMC-containing condensin complexes, we uncover an extensive pattern of colocalization in which architectural proteins establish dense clusters at the borders of topological domains. Reporter-based enhancer-blocking insulator activity as well as endogenous domain border strength scale with the occupancy level of architectural protein binding sites, suggesting co-binding by architectural proteins underlies the functional potential of these loci. Analyses in mouse and human stem cells suggest that clustering of architectural proteins is a general feature of genome organization, and conserved architectural protein binding sites may underlie the tissue-invariant nature of topologically associating domains observed in mammals. Conclusions We identify a spectrum of architectural protein occupancy that scales with the topological structure of chromosomes and the regulatory potential of these elements. Whereas high occupancy architectural protein binding sites associate with robust partitioning of topologically associating domains and robust insulator function, low occupancy sites appear reserved for gene-specific regulation within topological domains. PMID

  19. Toda 3-point functions from topological strings II

    Energy Technology Data Exchange (ETDEWEB)

    Isachenkov, Mikhail [DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mitev, Vladimir [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)

    2016-08-09

    In http://dx.doi.org/10.1007/JHEP06(2015)049 we proposed a formula for the 3-point structure constants of generic primary fields in the Toda field theory, derived using topological strings and the AGT-W correspondence from the partition functions of the non-Lagrangian T{sub N} theories on S{sup 4}. In this article, we obtain from it the well-known formula by Fateev and Litvinov and show that the degeneration on a first level of one of the three primary fields on the Toda side corresponds to a particular Higgsing of the T{sub N} theories.

  20. Towards Lax Formulation of Integrable Hierarchies of Topological Type

    NARCIS (Netherlands)

    Carlet, G.; van de Leur, J.; Posthuma, H.; Shadrin, S.

    2014-01-01

    To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider the Hirota and Lax formulations of the

  1. Towards Lax Formulation of Integrable Hierarchies of Topological Type

    NARCIS (Netherlands)

    van de Leur, Johannes; Carlet, Guido; Shadrin, Sergey; Posthuma, Hessel

    2014-01-01

    To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider theHirota and Lax formulations of the

  2. A Macdonald refined topological vertex

    Science.gov (United States)

    Foda, Omar; Wu, Jian-Feng

    2017-07-01

    We consider the refined topological vertex of Iqbal et al (2009 J. High Energy Phys. JHEP10(2009)069), as a function of two parameters ≤ft\\lgroup x, y \\right\\rgroup , and deform it by introducing the Macdonald parameters ≤ft\\lgroup q, t \\right\\rgroup , as in the work of Vuletić on plane partitions (Vuletić M 2009 Trans. Am. Math. Soc. 361 2789-804), to obtain ‘a Macdonald refined topological vertex’. In the limit q → t , we recover the refined topological vertex of Iqbal et al and in the limit x → y , we obtain a qt-deformation of the original topological vertex of Aganagic et al (2005 Commun. Math. Phys. 25 425-78). Copies of the vertex can be glued to obtain qt-deformed 5D instanton partition functions that have well-defined 4D limits and, for generic values of ≤ft\\lgroup q, t\\right\\rgroup , contain infinite-towers of poles for every pole present in the limit q → t .

  3. Service task partition and distribution in star topology computer grid subject to data security constraints

    Energy Technology Data Exchange (ETDEWEB)

    Xiang Yanping [Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China (China); Levitin, Gregory, E-mail: levitin@iec.co.il [Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China (China); Israel electric corporation, P. O. Box 10, Haifa 31000 (Israel)

    2011-11-15

    The paper considers grid computing systems in which the resource management systems (RMS) can divide service tasks into execution blocks (EBs) and send these blocks to different resources. In order to provide a desired level of service reliability the RMS can assign the same blocks to several independent resources for parallel execution. The data security is a crucial issue in distributed computing that affects the execution policy. By the optimal service task partition into the EBs and their distribution among resources, one can achieve the greatest possible service reliability and/or expected performance subject to data security constraints. The paper suggests an algorithm for solving this optimization problem. The algorithm is based on the universal generating function technique and on the evolutionary optimization approach. Illustrative examples are presented. - Highlights: > Grid service with star topology is considered. > An algorithm for evaluating service reliability and data security is presented. > A tradeoff between the service reliability and data security is analyzed. > A procedure for optimal service task partition and distribution is suggested.

  4. Service task partition and distribution in star topology computer grid subject to data security constraints

    International Nuclear Information System (INIS)

    Xiang Yanping; Levitin, Gregory

    2011-01-01

    The paper considers grid computing systems in which the resource management systems (RMS) can divide service tasks into execution blocks (EBs) and send these blocks to different resources. In order to provide a desired level of service reliability the RMS can assign the same blocks to several independent resources for parallel execution. The data security is a crucial issue in distributed computing that affects the execution policy. By the optimal service task partition into the EBs and their distribution among resources, one can achieve the greatest possible service reliability and/or expected performance subject to data security constraints. The paper suggests an algorithm for solving this optimization problem. The algorithm is based on the universal generating function technique and on the evolutionary optimization approach. Illustrative examples are presented. - Highlights: → Grid service with star topology is considered. → An algorithm for evaluating service reliability and data security is presented. → A tradeoff between the service reliability and data security is analyzed. → A procedure for optimal service task partition and distribution is suggested.

  5. Finite volume QCD at fixed topological charge

    OpenAIRE

    Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya

    2007-01-01

    In finite volume the partition function of QCD with a given $\\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of...

  6. A 250 plastome phylogeny of the grass family (Poaceae): topological support under different data partitions

    Science.gov (United States)

    Burke, Sean V.; Wysocki, William P.; Clark, Lynn G.

    2018-01-01

    The systematics of grasses has advanced through applications of plastome phylogenomics, although studies have been largely limited to subfamilies or other subgroups of Poaceae. Here we present a plastome phylogenomic analysis of 250 complete plastomes (179 genera) sampled from 44 of the 52 tribes of Poaceae. Plastome sequences were determined from high throughput sequencing libraries and the assemblies represent over 28.7 Mbases of sequence data. Phylogenetic signal was characterized in 14 partitions, including (1) complete plastomes; (2) protein coding regions; (3) noncoding regions; and (4) three loci commonly used in single and multi-gene studies of grasses. Each of the four main partitions was further refined, alternatively including or excluding positively selected codons and also the gaps introduced by the alignment. All 76 protein coding plastome loci were found to be predominantly under purifying selection, but specific codons were found to be under positive selection in 65 loci. The loci that have been widely used in multi-gene phylogenetic studies had among the highest proportions of positively selected codons, suggesting caution in the interpretation of these earlier results. Plastome phylogenomic analyses confirmed the backbone topology for Poaceae with maximum bootstrap support (BP). Among the 14 analyses, 82 clades out of 309 resolved were maximally supported in all trees. Analyses of newly sequenced plastomes were in agreement with current classifications. Five of seven partitions in which alignment gaps were removed retrieved Panicoideae as sister to the remaining PACMAD subfamilies. Alternative topologies were recovered in trees from partitions that included alignment gaps. This suggests that ambiguities in aligning these uncertain regions might introduce a false signal. Resolution of these and other critical branch points in the phylogeny of Poaceae will help to better understand the selective forces that drove the radiation of the BOP and PACMAD

  7. The dispersionless Lax equations and topological minimal models

    International Nuclear Information System (INIS)

    Krichever, I.

    1992-01-01

    It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)

  8. A statistical mechanical approach to restricted integer partition functions

    Science.gov (United States)

    Zhou, Chi-Chun; Dai, Wu-Sheng

    2018-05-01

    The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

  9. Topological Properties of Spatial Coherence Function

    International Nuclear Information System (INIS)

    Ji-Rong, Ren; Tao, Zhu; Yi-Shi, Duan

    2008-01-01

    The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures (coherence vortices) of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function

  10. The ABCD of topological recursion

    DEFF Research Database (Denmark)

    Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.

    Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial data a quantum Airy structure...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....

  11. Partition functions for supersymmetric black holes

    NARCIS (Netherlands)

    Manschot, J.

    2008-01-01

    This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a

  12. Topology-function conservation in protein-protein interaction networks.

    Science.gov (United States)

    Davis, Darren; Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Stojmirovic, Aleksandar; Pržulj, Nataša

    2015-05-15

    Proteins underlay the functioning of a cell and the wiring of proteins in protein-protein interaction network (PIN) relates to their biological functions. Proteins with similar wiring in the PIN (topology around them) have been shown to have similar functions. This property has been successfully exploited for predicting protein functions. Topological similarity is also used to guide network alignment algorithms that find similarly wired proteins between PINs of different species; these similarities are used to transfer annotation across PINs, e.g. from model organisms to human. To refine these functional predictions and annotation transfers, we need to gain insight into the variability of the topology-function relationships. For example, a function may be significantly associated with specific topologies, while another function may be weakly associated with several different topologies. Also, the topology-function relationships may differ between different species. To improve our understanding of topology-function relationships and of their conservation among species, we develop a statistical framework that is built upon canonical correlation analysis. Using the graphlet degrees to represent the wiring around proteins in PINs and gene ontology (GO) annotations to describe their functions, our framework: (i) characterizes statistically significant topology-function relationships in a given species, and (ii) uncovers the functions that have conserved topology in PINs of different species, which we term topologically orthologous functions. We apply our framework to PINs of yeast and human, identifying seven biological process and two cellular component GO terms to be topologically orthologous for the two organisms. © The Author 2015. Published by Oxford University Press.

  13. Lectures on 2d gauge theories. Topological aspects and path integral techniques

    International Nuclear Information System (INIS)

    Blau, M.; Thompson, G.

    1993-10-01

    In these lectures are discussed two classes of two-dimensional field theories which are not obviously topological, but which nevertheless exhibit an intriguing equivalence with certain topological theories. These classes are two-dimensional Yang-Mills theory and the so-called G/G gauged Wess-Zumino-Witten model. The aim is to exhibit and extract the topological information contained in these theories and to present a technique which allows to calculate directly their partition functions and topological correlation functions on arbitrary closed surfaces. 34 refs

  14. Topological setting of Bessel functions

    International Nuclear Information System (INIS)

    Mekhfi, M.

    1995-11-01

    We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs

  15. EXTENSION OF FORMULAS FOR PARTITION FUNCTIONS

    African Journals Online (AJOL)

    Ladan et al.

    2Department of Mathematics, Ahmadu Bello University, Zaria. ... 2 + 1 + 1. = 1 + 1 + 1 + 1. Partition function ( ). Andrew and Erikson (2004) stated that the ..... Andrews, G.E., 1984, The Theory of Partitions, Cambridge ... Pure Appl. Math.

  16. 1992 Trieste lectures on topological gauge theory and Yang-Mills theory

    International Nuclear Information System (INIS)

    Thompson, G.

    1993-05-01

    In these lecture notes we explain a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called BF and cohomological theories. The quantum Yang-Mills theory is solved exactly using path integral techniques. Explicit expressions, in terms of group representation theory, are obtained for the partition function and various correlation functions. In a particular limit the Yang-Mills theory devolves to the topological models and the previously determined correlation functions give topological information about the moduli spaces of flat connections. In particular, the partition function yields the volume of the moduli space for which an explicit expression is derived. These notes are self contained, with a basic introduction to the various ideas underlying the topological field theories. This includes some relatively new work on handling problems that arise in the presence of reducible connections, which in turn, forms the bridge between the various models under consideration. These notes are identical to those made available to participants of the 1992 summer school in Trieste, except for one or two additions added circa January 1993. (author). 52 refs, 6 figs

  17. Combinatorics and complexity of partition functions

    CERN Document Server

    Barvinok, Alexander

    2016-01-01

    Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. .

  18. Partition function of a chiral boson on a 2-torus from the Floreanini–Jackiw Lagrangian

    International Nuclear Information System (INIS)

    Chen, Wei-Ming; Ho, Pei-Ming; Kao, Hsien-chung; Khoo, Fech Scen; Matsuo, Yutaka

    2014-01-01

    We revisit the problem of quantizing a chiral boson on a torus. The conventional approach is to extract the partition function of a chiral boson from the path integral of a non-chiral boson. Instead we compute it directly from the chiral boson Lagrangian of Floreanini and Jackiw modified by topological terms involving an auxiliary field. A careful analysis of the gauge-fixing condition for the extra gauge symmetry reproduces the correct results for the free chiral boson, and has the advantage of being applicable to a wider class of interacting chiral boson theories

  19. Matrix string partition function

    CERN Document Server

    Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre

    1998-01-01

    We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.

  20. String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups

    International Nuclear Information System (INIS)

    Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio

    2012-01-01

    This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)

  1. Off-diagonal series expansion for quantum partition functions

    Science.gov (United States)

    Hen, Itay

    2018-05-01

    We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.

  2. Three-dimensional topological insulators and bosonization

    Energy Technology Data Exchange (ETDEWEB)

    Cappelli, Andrea [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Randellini, Enrico [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Dipartimento di Fisica e Astronomia, Università di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Sisti, Jacopo [Scuola Internazionale Superiore di Studi Avanzati (SISSA),Via Bonomea 265, 34136 Trieste (Italy)

    2017-05-25

    Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

  3. Three-dimensional low-energy topological invariants

    International Nuclear Information System (INIS)

    Bakalarska, M.; Broda, B.

    2000-01-01

    A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion τ R and Betti numbers. (orig.)

  4. A topologically twisted index for three-dimensional supersymmetric theories

    International Nuclear Information System (INIS)

    Benini, Francesco; Zaffaroni, Alberto

    2015-01-01

    We provide a general formula for the partition function of three-dimensional N=2 gauge theories placed on S 2 ×S 1 with a topological twist along S 2 , which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S 2 and four-dimensional theories on S 2 ×T 2 . In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.

  5. The topological B model as a twisted spinning particle

    International Nuclear Information System (INIS)

    Marcus, Neil; Yankielowicz, Shimon

    1994-01-01

    The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a particle theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on any Kaehler manifold - it does not require the Calabi-Yau condition - so it may provide a more generalized setting for the B model than the topological sigma model.The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, and agrees with that of the original B model. After showing how to deform the Kaehler and complex structures in the particle, we prove the independence of this partition function on the Kaehler structure, and investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories. ((orig.))

  6. Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

    Directory of Open Access Journals (Sweden)

    Zhong Wang

    2014-01-01

    Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

  7. A partition function approximation using elementary symmetric functions.

    Directory of Open Access Journals (Sweden)

    Ramu Anandakrishnan

    Full Text Available In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm - the direct interaction algorithm (DIA - for approximating the canonical partition function [Formula: see text] in [Formula: see text] operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs, which can be computed in [Formula: see text] operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.

  8. Zeta Function Expression of Spin Partition Functions on Thermal AdS3

    Directory of Open Access Journals (Sweden)

    Floyd L.Williams

    2015-07-01

    Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

  9. Topological terms induced by finite temperature and density fluctuations

    International Nuclear Information System (INIS)

    Niemi, A.J.; Department of Physics, The Ohio State University, Columbus, Ohio 43210)

    1986-01-01

    In (3+1)-dimensional finite-temperature and -density SU(2) gauge theories with left-handed fermions, the three-dimensional Chern-Simons term (topological mass) can be induced by radiative corrections. This result is derived by use of a family's index theorem which also implies that in many other quantum field theories various additional lower-dimensional topological terms can be induced. In the high-temperature limit these terms dominate the partition function, which suggests applications to early-Universe cosmology

  10. Descriptive Topology in Selected Topics of Functional Analysis

    CERN Document Server

    Kakol, J; Pellicer, Manuel Lopez

    2011-01-01

    "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set

  11. The position value for partition function form network games

    NARCIS (Netherlands)

    Nouweland, van den C.G.A.M.; Slikker, M.

    We use the axiomatization of the position value for network situations in van den Nouweland and Slikker (2012) to define a position value for partition function form network situations. We do this by generalizing the axioms to the partition function form value function setting as studied in Navarro

  12. ABCD of Beta Ensembles and Topological Strings

    CERN Document Server

    Krefl, Daniel

    2012-01-01

    We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.

  13. Non-perturbative effects and the refined topological string

    Energy Technology Data Exchange (ETDEWEB)

    Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

    2013-06-15

    The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

  14. Disk partition function and oscillatory rolling tachyons

    International Nuclear Information System (INIS)

    Jokela, Niko; Jaervinen, Matti; Keski-Vakkuri, Esko; Majumder, Jaydeep

    2008-01-01

    An exact cubic open string field theory rolling tachyon solution was recently found by Kiermaier et al and Schnabl. This oscillatory solution has been argued to be related by a field redefinition to the simple exponential rolling tachyon deformation of boundary conformal theory. In the latter approach, the disk partition function takes a simple form. Out of curiosity, we compute the disk partition function for an oscillatory tachyon profile, and find that the result is nevertheless almost the same

  15. Factorisations for partition functions of random Hermitian matrix models

    International Nuclear Information System (INIS)

    Jackson, D.M.; Visentin, T.I.

    1996-01-01

    The partition function Z N , for Hermitian-complex matrix models can be expressed as an explicit integral over R N , where N is a positive integer. Such an integral also occurs in connection with random surfaces and models of two dimensional quantum gravity. We show that Z N can be expressed as the product of two partition functions, evaluated at translated arguments, for another model, giving an explicit connection between the two models. We also give an alternative computation of the partition function for the φ 4 -model.The approach is an algebraic one and holds for the functions regarded as formal power series in the appropriate ring. (orig.)

  16. First Meeting in Topology and Functional Analysis

    CERN Document Server

    López-Pellicer, Manuel

    2014-01-01

    Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.

  17. Phylogenetic relationships in Asarum: Effect of data partitioning and a revised classification.

    Science.gov (United States)

    Sinn, Brandon T; Kelly, Lawrence M; Freudenstein, John V

    2015-05-01

    Generic boundaries and infrageneric relationships among the charismatic temperate magnoliid Asarum sensu lato (Aristolochiaceae) have long been uncertain. Previous molecular phylogenetic analyses used either plastid or nuclear loci alone and varied greatly in their taxonomic implications for the genus. We analyzed additional molecular markers from the nuclear and plastid genomes, reevaluated the possibility of a derived loss of autonomous self-pollination, and investigated the topological effects of matrix-partitioning-scheme choice. We sequenced seven plastid regions and the nuclear ITS1-ITS2 region of 58 individuals representing all previously recognized Asarum s.l. segregate genera and the monotypic genus Saruma. Matrices were partitioned using common a priori partitioning schemes and PartitionFinder. Topologies that were recovered using a priori partitioning of matrices differed from those recovered using a PartitionFinder-selected scheme, and by analysis method. We recovered six monophyletic groups that we circumscribed into three subgenera and six sections. Putative fungal mimic characters served as synapomorphies only for subgenus Heterotropa. Subgenus Geotaenium, a new subgenus, was recovered as sister to the remainder of Asarum by ML analyses of highly partitioned datasets. Section Longistylis, also newly named, is sister to section Hexastylis. Our analyses do not unambiguously support a single origin for all fungal-mimicry characters. Topologies recovered through the analysis of PartitionFinder-optimized matrices can differ drastically from those inferred from a priori partitioned matrices, and by analytical method. We recommend that investigators evaluate the topological effects of matrix partitioning using multiple methods of phylogenetic reconstruction. © 2015 Botanical Society of America, Inc.

  18. Topological string in harmonic space and correlation functions in S3 stringy cosmology

    International Nuclear Information System (INIS)

    Saidi, El Hassan; Sedra, Moulay Brahim

    2006-01-01

    We develop the harmonic space method for conifold and use it to study local complex deformations of T*S 3 preserving manifestly SL(2,C) isometry. We derive the perturbative manifestly SL(2,C) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c=1 noncritical theory are described by highest υ (n,0) and lowest components υ (0,n) of SL(2,C) spin s=n2 multiplets (υ (n-k,k) ), 0= α + and V α - . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T*S 1 (S 1 ) to the harmonic method on T*S 3 (S 3 ). The manifestly SU(2,C) covariant correlation functions of the S 3 quantum cosmology model of Gukov-Saraikin-Vafa are also studied

  19. Domain wall partition functions and KP

    International Nuclear Information System (INIS)

    Foda, O; Wheeler, M; Zuparic, M

    2009-01-01

    We observe that the partition function of the six-vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP τ function and express it as an expectation value of charged free fermions (up to an overall normalization)

  20. Exact partition functions for gauge theories on Rλ3

    Directory of Open Access Journals (Sweden)

    Jean-Christophe Wallet

    2016-11-01

    Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

  1. A brief history of partitions of numbers, partition functions and their modern applications

    Science.gov (United States)

    Debnath, Lokenath

    2016-04-01

    'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

  2. Partition functions. I. Improved partition functions and thermodynamic quantities for normal, equilibrium, and ortho and para molecular hydrogen

    Science.gov (United States)

    Popovas, A.; Jørgensen, U. G.

    2016-11-01

    Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims: We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods: Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H2. Both equilibrium and normal hydrogen was taken into consideration. Results: Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H2 are also reported. Conclusions: For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when

  3. Genus two partition functions of extremal conformal field theories

    International Nuclear Information System (INIS)

    Gaiotto, Davide; Yin Xi

    2007-01-01

    Recently Witten conjectured the existence of a family of 'extremal' conformal field theories (ECFTs) of central charge c = 24k, which are supposed to be dual to three-dimensional pure quantum gravity in AdS 3 . Assuming their existence, we determine explicitly the genus two partition functions of k = 2 and k = 3 ECFTs, using modular invariance and the behavior of the partition function in degenerating limits of the Riemann surface. The result passes highly nontrivial tests and in particular provides a piece of evidence for the existence of the k = 3 ECFT. We also argue that the genus two partition function of ECFTs with k ≤ 10 are uniquely fixed (if they exist)

  4. Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

    International Nuclear Information System (INIS)

    Dubrovin, B.A.

    1992-01-01

    We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (for A n -Series): The Casimirs for the first P.B. give the correct coupling parameters for the perturbed topological minimal model; the correspondence {coupling parameters}→{primary fields} is determined by the second P.B. The partition function (at the tree level) and the chiral algebra for LG minimal models are calculated for any genus g. (orig.)

  5. Solving topological field theories on mapping tori

    International Nuclear Information System (INIS)

    Blau, M.; Jermyn, I.; Thompson, G.

    1996-05-01

    Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs

  6. Approximation methods for the partition functions of anharmonic systems

    International Nuclear Information System (INIS)

    Lew, P.; Ishida, T.

    1979-07-01

    The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations

  7. Lattice topological field theory on nonorientable surfaces

    International Nuclear Information System (INIS)

    Karimipour, V.; Mostafazadeh, A.

    1997-01-01

    The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary *-algebras in general, and for the group ring A=R[G] of discrete groups G, in particular. copyright 1997 American Institute of Physics

  8. SO(N) reformulated link invariants from topological strings

    International Nuclear Information System (INIS)

    Borhade, Pravina; Ramadevi, P.

    2005-01-01

    Large N duality conjecture between U(N) Chern-Simons gauge theory on S 3 and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background

  9. Hemisphere partition function and monodromy

    Energy Technology Data Exchange (ETDEWEB)

    Erkinger, David; Knapp, Johanna [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10, 1040 Vienna (Austria)

    2017-05-29

    We discuss D-brane monodromies from the point of view of the gauged linear sigma model. We give a prescription on how to extract monodromy matrices directly from the hemisphere partition function. We illustrate this procedure by recomputing the monodromy matrices associated to one-parameter Calabi-Yau hypersurfaces in weighted projected space.

  10. Generalised twisted partition functions

    CERN Document Server

    Petkova, V B

    2001-01-01

    We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.

  11. LOCAL ENTROPY FUNCTION OF DYNAMICAL SYSTEM

    Directory of Open Access Journals (Sweden)

    İsmail TOK

    2013-05-01

    Full Text Available In this work, we first,define the entropy function of the topological dynamical system and investigate basic properties of this function without going into details. Let (X,A,T be a probability measure space and consider P = { pl5p2,...,pn} a finite measurable partition of all sub-sets of topological dynamical system (X,T.Then,the quantity H (P = ^ zpt is called the i=1 entropy function of finite measurable partition P.Where f-1 log t if 0 0.If diam(P < s,then the quantity L^ (T = h^ (T - h^ (T,P is called a local entropy function of topological dynamical system (X,T . In conclusion, Let (X,T and (Y,S be two topological dynamical system. If TxS is a transformation defined on the product space (XxY,TxS with (TxS(x , y = (Tx,Sy for all (x,y X x Y.Then L ^^ (TxS = L^d(T + L (S .and, we prove some fundamental properties of this function.

  12. Rotational partition functions for linear molecules

    International Nuclear Information System (INIS)

    McDowell, R.S.

    1988-01-01

    An accurate closed-form expression for the rotational partition function of linear polyatomic molecules in 1 summation electronic states is derived, including the effect of nuclear spin (significant at very low temperatures) and of quartic and sextic centrifugal distortion terms (significant at moderate and high temperatures). The proper first-order quantum correction to the classical rigid-rotator partition function is shown to yield Q/sub r/ ≅β -1 exp(β/3), where βequivalenthcB/kT and B is the rotational constant in cm -1 ; for β≥0.2 additional power-series terms in β are necessary. Comparison between the results of this treatment and exact summations are made for HCN and C 2 H 2 at temperatures from 2 to 5000 K, including separate evaluation of the contributions of nuclear spin and centrifugal distortion

  13. Statistical mechanics of polymer networks of any topology

    International Nuclear Information System (INIS)

    Duplantier, B.

    1989-01-01

    The statistical mechanics is considered of any polymer network with a prescribed topology, in dimension d, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made to O(ε 2 ), where d = 4 -ε, of the basic critical dimensions σ L associated with any L=leg vertex (L ≥ 1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent γ G of any network G to O(ε 2 ), including L-leg star polymers. The infinite sets of contact critical exponents θ between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents θ 0 , θ 1 , θ 2 calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimension d = 4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the Θ-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constituting L-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents σ L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled

  14. Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory.

    Science.gov (United States)

    Delgado-Friedrichs, Olaf; Robins, Vanessa; Sheppard, Adrian

    2015-03-01

    We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical complex with a real-valued function defined on its vertices (the voxel values). This function is extended to a discrete gradient vector field using the algorithm presented in Robins, Wood, Sheppard TPAMI 33:1646 (2011). In the current paper we define basins (the building blocks of a partition) and segments of the skeleton using the stable and unstable sets associated with critical cells. The natural connection between Morse theory and homology allows us to prove the topological validity of these constructions; for example, that the skeleton is homotopic to the initial object. We simplify the basins and skeletons via Morse-theoretic cancellation of critical cells in the discrete gradient vector field using a strategy informed by persistent homology. Simple working Python code for our algorithms for efficient vector field traversal is included. Example data are taken from micro-CT images of porous materials, an application area where accurate topological models of pore connectivity are vital for fluid-flow modelling.

  15. Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings.

    Science.gov (United States)

    Werner, Tomás

    2015-07-01

    Many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring. By generalizing max-sum diffusion (one of convergent message passing algorithms for approximate MAP inference in graphical models), we propose an iterative algorithm to upper bound such partition functions over commutative semirings. The iteration of the algorithm is remarkably simple: change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal. In many commutative semirings, repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide. We call this state marginal consistency. During that, an upper bound on the partition function monotonically decreases. This abstract algorithm unifies several existing algorithms, including max-sum diffusion and basic constraint propagation (or local consistency) algorithms in constraint programming. We further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity (order). Finally, we discuss instances of the framework for several semirings, including the distributive lattice and the max-sum and sum-product semirings.

  16. The calculation of isotopic partition function ratios by a perturbation theory technique

    International Nuclear Information System (INIS)

    Singh, G.; Wolfsberg, M.

    1975-01-01

    The vibrational Hamiltonian of a molecule in the harmonic approximation, H = (1/2) Σ (g/subi/jp/subi/p/subj/ + f/subi/jq/subi/q/subj/), has been divided into a diagonal part (terms with i=j) and an off-diagonal part (inot-equalj), which is regarded as the perturbation. The vibrational partition function of the molecule is then calculated by Schwinger perturbation theory as the partition function of the unperturbed problem, corresponding to a collection of oscillators with frequencies 2πν/subi/' = (f/subi/ig/subi/i)/sup 1 / 2 /, plus perturbation correction terms which are calculated to second order. With the usual assumptions of isotope effect calculations that the molecular translations and rotations are classical and separable from the vibrations, the perturbation formulation of the vibrational partition function is easily transformed into a perturbation theory formulation of (reduced) isotopic partition function ratios. If, for example, the molecular potential function is expressed in terms of the displacements of bond stretches and bond angle bends from their respective equilibrium values, the unperturbed partition function ratio corresponds to the isotope effect expected for noninteracting bond-stretch and bond-angle-bend oscillators. Detailed comparison is made for a number of molecular systems of perturbation theory calculations of partition functions and isotopic partition function ratios with exact calculations carried out by actually obtaining the normal mode vibrational frequencies of the vibrational Hamiltonian. Good agreement is found. The utility of the perturbation theory formulation resides in the fact that it permits one to look at isotope effects in a very simple manner; some demonstrations are given

  17. Modular invariant partition functions for toroidally compactified bosonic string

    International Nuclear Information System (INIS)

    Ardalan, F.; Arfaei, H.

    1988-06-01

    We systematically find all the modular invariant partition functions for the toroidally compactified closed bosonic string defined on a subset of a simply laced simple Lie algebra lattice, or equivalently for the closed bosonic string moving on a group manifold with the WZW coefficient k=1. We examine the relation between modular invariance of partition function and the possibility of describing it by an even Lorentzian self dual lattice in our context. (author). 23 refs

  18. One-loop partition functions of 3D gravity

    International Nuclear Information System (INIS)

    Giombi, Simone; Yin Xi; Maloney, Alexander

    2008-01-01

    We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over 'boundary excitations' of AdS 3 , which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.

  19. Function spaces with uniform, fine and graph topologies

    CERN Document Server

    McCoy, Robert A; Jindal, Varun

    2018-01-01

    This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.

  20. 1-loop partition function in AdS{sub 3}/CFT{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Wu, Jie-qiang [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China)

    2015-12-16

    The 1-loop partition function of the handlebody solutions in the AdS{sub 3} gravity have been derived some years ago using the heat kernel techniques and the method of images. In the semiclassical limit, such partition function should correspond to the order O(c{sup 0}) part in the partition function of dual conformal field theory(CFT) on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, the CFT is effectively free in the sense that to the leading order of c the multi-point function is further simplified to be a summation over the products of two-point functions of single-particle states. Correspondingly in the bulk, the graviton is freely propagating without interaction. Furthermore the product of the two-point functions may define the links, each of which is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the multiplier of the element in the conjugacy class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity and its dual CFT.

  1. Quantum corrections to Bekenstein–Hawking black hole entropy and gravity partition functions

    International Nuclear Information System (INIS)

    Bytsenko, A.A.; Tureanu, A.

    2013-01-01

    Algebraic aspects of the computation of partition functions for quantum gravity and black holes in AdS 3 are discussed. We compute the sub-leading quantum corrections to the Bekenstein–Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the AdS 3 /CFT 2 correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson–Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states

  2. Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

    Science.gov (United States)

    Zhou, Chi-Chun; Dai, Wu-Sheng

    2018-02-01

    In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

  3. Lattice formulation of a two-dimensional topological field theory

    International Nuclear Information System (INIS)

    Ohta, Kazutoshi; Takimi, Tomohisa

    2007-01-01

    We investigate an integrable property and the observables of 2-dimensional N=(4,4) topological field theory defined on a discrete lattice by using the 'orbifolding' and 'deconstruction' methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the N=(4,4) theory. (author)

  4. Two-loop superstring partition function

    International Nuclear Information System (INIS)

    Morozov, A.Y.

    1988-01-01

    Is it possible to choose the odd moduli on super-Riemann surfaces of genus p≥2 in such a way that the corresponding contributions to the superstring partition function vanish before the integration over the space of the moduli? It is shown that, at least for p = 2, the answer to this question is affirmative, and in this case the odd moduli should be localized at branch points

  5. The SOS model partition function and the elliptic weight functions

    International Nuclear Information System (INIS)

    Pakuliak, S; Silantyev, A; Rubtsov, V

    2008-01-01

    We generalized a recent observation (Khoroshkin and Pakuliak 2005 Theor. Math. Phys. 145 1373) that the partition function of the six-vertex model with domain wall boundary conditions can be obtained from a calculation of projections of the product of total currents in the quantum affine algebra U q (sl 2 -hat) in its current realization. A generalization is done for the elliptic current algebra (Enriquez and Felder 1998 Commun. Math. Phys. 195 651, Enriquez and Rubtsov 1997 Ann. Sci. Ecole Norm. Sup. 30 821). The projections of the product of total currents in this case are calculated explicitly and are presented as integral transforms of a product of the total currents. It is proved that the integral kernel of this transform is proportional to the partition function of the SOS model with domain wall boundary conditions

  6. Topological defect clustering and plastic deformation mechanisms in functionalized graphene

    Science.gov (United States)

    Nunes, Ricardo; Araujo, Joice; Chacham, Helio

    2011-03-01

    We present ab initio results suggesting that strain plays a central role in the clustering of topological defects in strained and functionalized graphene models. We apply strain onto the topological-defect graphene networks from our previous work, and obtain topological-defect clustering patterns which are in excellent agreement with recent observations in samples of reduced graphene oxide. In our models, the graphene layer, containing an initial concentration of isolated topological defects, is covered by hydrogen or hydroxyl groups. Our results also suggest a rich variety of plastic deformation mechanism in functionalized graphene systems. We acknowledge support from the Brazilian agencies: CNPq, Fapemig, and INCT-Materiais de Carbono.

  7. Pure spinor partition function and the massive superstring spectrum

    International Nuclear Information System (INIS)

    Aisaka, Yuri; Arroyo, E. Aldo; Berkovits, Nathan; Nekrasov, Nikita

    2008-01-01

    We explicitly compute up to the fifth mass-level the partition function of ten-dimensional pure spinor worldsheet variables including the spin dependence. After adding the contribution from the (x μ , θ α , p α ) matter variables, we reproduce the massive superstring spectrum. Even though pure spinor variables are bosonic, the pure spinor partition function contains fermionic states which first appear at the second mass-level. These fermionic states come from functions which are not globally defined in pure spinor space, and are related to the b ghost in the pure spinor formalism. This result clarifies the proper definition of the Hilbert space for pure spinor variables.

  8. Dominant partition method. [based on a wave function formalism

    Science.gov (United States)

    Dixon, R. M.; Redish, E. F.

    1979-01-01

    By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.

  9. A GLOBAL SOLUTION TO TOPOLOGICAL RECONSTRUCTION OF BUILDING ROOF MODELS FROM AIRBORNE LIDAR POINT CLOUDS

    Directory of Open Access Journals (Sweden)

    J. Yan

    2016-06-01

    Full Text Available This paper presents a global solution to building roof topological reconstruction from LiDAR point clouds. Starting with segmented roof planes from building LiDAR points, a BSP (binary space partitioning algorithm is used to partition the bounding box of the building into volumetric cells, whose geometric features and their topology are simultaneously determined. To resolve the inside/outside labelling problem of cells, a global energy function considering surface visibility and spatial regularization between adjacent cells is constructed and minimized via graph cuts. As a result, the cells are labelled as either inside or outside, where the planar surfaces between the inside and outside form the reconstructed building model. Two LiDAR data sets of Yangjiang (China and Wuhan University (China are used in the study. Experimental results show that the completeness of reconstructed roof planes is 87.5%. Comparing with existing data-driven approaches, the proposed approach is global. Roof faces and edges as well as their topology can be determined at one time via minimization of an energy function. Besides, this approach is robust to partial absence of roof planes and tends to reconstruct roof models with visibility-consistent surfaces.

  10. Aperiodic topological order in the domain configurations of functional materials

    Science.gov (United States)

    Huang, Fei-Ting; Cheong, Sang-Wook

    2017-03-01

    In numerous functional materials, such as steels, ferroelectrics and magnets, new functionalities can be achieved through the engineering of the domain structures, which are associated with the ordering of certain parameters within the material. The recent progress in technologies that enable imaging at atomic-scale spatial resolution has transformed our understanding of domain topology, revealing that, along with simple stripe-like or irregularly shaped domains, intriguing vortex-type topological domain configurations also exist. In this Review, we present a new classification scheme of 'Zm Zn domains with Zl vortices' for 2D macroscopic domain structures with m directional variants and n translational antiphases. This classification, together with the concepts of topological protection and topological charge conservation, can be applied to a wide range of materials, such as multiferroics, improper ferroelectrics, layered transition metal dichalcogenides and magnetic superconductors, as we discuss using selected examples. The resulting topological considerations provide a new basis for the understanding of the formation, kinetics, manipulation and property optimization of domains and domain boundaries in functional materials.

  11. Commuting quantum circuits and complexity of Ising partition functions

    International Nuclear Information System (INIS)

    Fujii, Keisuke; Morimae, Tomoyuki

    2017-01-01

    Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy collapses to the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of calculating the imaginary-valued partition functions of Ising models. We apply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising partition functions with imaginary coupling constants. Specifically, we show that a multiplicative approximation of Ising partition functions is #P-hard for almost all imaginary coupling constants even on planar lattices of a bounded degree. (paper)

  12. Many-body formalism for fermions: The partition function

    Science.gov (United States)

    Watson, D. K.

    2017-09-01

    The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the N particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done "on paper" by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli

  13. Coexistence via resource partitioning fails to generate an increase in community function.

    Directory of Open Access Journals (Sweden)

    John P DeLong

    Full Text Available Classic ecological theory suggests that resource partitioning facilitates the coexistence of species by reducing inter-specific competition. A byproduct of this process is an increase in overall community function, because a greater spectrum of resources can be used. In contrast, coexistence facilitated by neutral mechanisms is not expected to increase function. We studied coexistence in laboratory microcosms of the bactivorous ciliates Paramecium aurelia and Colpidium striatum to understand the relationship between function and coexistence mechanism. We quantified population and community-level function (biomass and oxygen consumption, competitive interactions, and resource partitioning. The two ciliates partitioned their bacterial resource along a size axis, with the larger ciliate consuming larger bacteria than the smaller ciliate. Despite this, there was no gain in function at the community level for either biomass or oxygen consumption, and competitive effects were symmetrical within and between species. Because other potential coexistence mechanisms can be ruled out, it is likely that inter-specific interference competition diminished the expected gain in function generated by resource partitioning, leading to a system that appeared competitively neutral even when structured by niche partitioning. We also analyzed several previous studies where two species of protists coexisted and found that the two-species communities showed a broad range of biomass levels relative to the single-species states.

  14. Estimating the Partition Function Zeros by Using the Wang-Landau Monte Carlo Algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Seung-Yeon [Korea National University of Transportation, Chungju (Korea, Republic of)

    2017-03-15

    The concept of the partition function zeros is one of the most efficient methods for investigating the phase transitions and the critical phenomena in various physical systems. Estimating the partition function zeros requires information on the density of states Ω(E) as a function of the energy E. Currently, the Wang-Landau Monte Carlo algorithm is one of the best methods for calculating Ω(E). The partition function zeros in the complex temperature plane of the Ising model on an L × L square lattice (L = 10 ∼ 80) with a periodic boundary condition have been estimated by using the Wang-Landau Monte Carlo algorithm. The efficiency of the Wang-Landau Monte Carlo algorithm and the accuracies of the partition function zeros have been evaluated for three different, 5%, 10%, and 20%, flatness criteria for the histogram H(E).

  15. Calculation of the octanol-water partition coefficient of armchair polyhex BN nanotubes

    Science.gov (United States)

    Mohammadinasab, E.; Pérez-Sánchez, H.; Goodarzi, M.

    2017-12-01

    A predictive model for determination partition coefficient (log P) of armchair polyhex BN nanotubes by using simple descriptors was built. The relationship between the octanol-water log P and quantum chemical descriptors, electric moments, and topological indices of some armchair polyhex BN nanotubes with various lengths and fixed circumference are represented. Based on density functional theory electric moments and physico-chemical properties of those nanotubes are calculated.

  16. Partition function zeros of the one-dimensional Potts model: the recursive method

    International Nuclear Information System (INIS)

    Ghulghazaryan, R G; Ananikian, N S

    2003-01-01

    The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition function may be associated with neutral fixed points of the recurrence relation. Further, a general equation for zeros of the partition function is found and a classification of the Yang-Lee, Fisher and Potts zeros is given. It is shown that the Fisher zeros in a nonzero magnetic field are located on several lines in the complex temperature plane and that the number of these lines depends on the value of the magnetic field. Analytical expressions for the densities of the Yang-Lee, Fisher and Potts zeros are derived. It is shown that densities of all types of zeros of the partition function are singular at the edge singularity points with the same critical exponent

  17. Random trees between two walls: exact partition function

    International Nuclear Information System (INIS)

    Bouttier, J; Di Francesco, P; Guitter, E

    2003-01-01

    We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labelled by integers representing their position in the target space, with the solid-on-solid constraint that adjacent vertices have labels differing by ±1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p function with constrained periods. These results are used to analyse the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs

  18. $\\mathcal{N}=2^\\star$ from Topological Amplitudes in String Theory

    CERN Document Server

    Florakis, Ioannis

    2016-01-01

    In this paper, we explicitly construct string theory backgrounds that realise the so-called $\\mathcal N=2^\\star$ gauge theory. We prove the consistency of our models by calculating their partition function and obtaining the correct gauge theory spectrum. We further provide arguments in favour of the universality of our construction which covers a wide class of models all of which engineer the same gauge theory. We reproduce the corresponding Nekrasov partition function once the $\\Omega$-deformation is included and the appropriate field theory limit taken. This is achieved by calculating the topological amplitudes $F_g$ in the string models. In addition to heterotic and type II constructions, we also realise the mass deformation in type I theory, thus leading to a natural way of uplifting the result to the instanton sector.

  19. RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology.

    Directory of Open Access Journals (Sweden)

    Namhee Kim

    Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs

  20. Plurisubharmonic and holomorphic functions relative to the plurifine topology

    DEFF Research Database (Denmark)

    El Kadiri, M.; Fuglede, Bent; Wiegerinck, J.

    2011-01-01

    topology and f∘h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak...

  1. Unique Path Partitions

    DEFF Research Database (Denmark)

    Bessenrodt, Christine; Olsson, Jørn Børling; Sellers, James A.

    2013-01-01

    We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.......We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions....

  2. Superfluid Kubo formulas from partition function

    International Nuclear Information System (INIS)

    Chapman, Shira; Hoyos, Carlos; Oz, Yaron

    2014-01-01

    Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stress-energy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are non-dissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems

  3. Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian

    2006-10-01

    An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.

  4. Partition Function and Configurational Entropy in Non-Equilibrium States: A New Theoretical Model

    Directory of Open Access Journals (Sweden)

    Akira Takada

    2018-03-01

    Full Text Available A new model of non-equilibrium thermodynamic states has been investigated on the basis of the fact that all thermodynamic variables can be derived from partition functions. We have thus attempted to define partition functions for non-equilibrium conditions by introducing the concept of pseudo-temperature distributions. These pseudo-temperatures are configurational in origin and distinct from kinetic (phonon temperatures because they refer to the particular fragments of the system with specific energies. This definition allows thermodynamic states to be described either for equilibrium or non-equilibrium conditions. In addition; a new formulation of an extended canonical partition function; internal energy and entropy are derived from this new temperature definition. With this new model; computational experiments are performed on simple non-interacting systems to investigate cooling and two distinct relaxational effects in terms of the time profiles of the partition function; internal energy and configurational entropy.

  5. Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

    Science.gov (United States)

    Zylka, Christian; Vojta, Guenter

    1993-01-01

    The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

  6. On entire functions restricted to intervals, partition of unities, and dual Gabor frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

    2014-01-01

    Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the enti...

  7. Generalised partition functions: inferences on phase space distributions

    Directory of Open Access Journals (Sweden)

    R. A. Treumann

    2016-06-01

    Full Text Available It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the

  8. Topological entropy of continuous functions on topological spaces

    International Nuclear Information System (INIS)

    Liu Lei; Wang Yangeng; Wei Guo

    2009-01-01

    Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems

  9. Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

    Science.gov (United States)

    Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

    2018-03-01

    We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

  10. Minimal models on Riemann surfaces: The partition functions

    International Nuclear Information System (INIS)

    Foda, O.

    1990-01-01

    The Coulomb gas representation of the A n series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius) 2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)

  11. Minimal models on Riemann surfaces: The partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)

    1990-06-04

    The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).

  12. Restoring canonical partition functions from imaginary chemical potential

    Science.gov (United States)

    Bornyakov, V. G.; Boyda, D.; Goy, V.; Molochkov, A.; Nakamura, A.; Nikolaev, A.; Zakharov, V. I.

    2018-03-01

    Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Zn(T) are coefficients of this expansion. Using various methods we study properties of Zn(T). At the last step we perform cubic spline for temperature dependence of Zn(T) at fixed n and compute baryon number susceptibility χB/T2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 163 × 4 lattice with mπ/mρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line Tc(µ2B) = Tc(C-ĸµ2B/T2c) with ĸ = -0.0453 ± 0.0099.

  13. Instanton counting, Macdonald function and the moduli space of D-branes

    International Nuclear Information System (INIS)

    Awata, Hidetoshi; Kanno, Hiroaki

    2005-01-01

    We argue the connection of Nekrasov's partition function in the Ω background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N = 2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters ε 1 ,ε 2 of toric action on C 2 factorizes correctly as the character of SU(2) L x SU(2) R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F 0 . We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T 2 action allows us to obtain the generating functions of equivariant χ y and elliptic genera of the Hilbert scheme of n points on C 2 by the method of topological vertex

  14. Entanglement entropy of gapped phase and topological order in three dimensions

    NARCIS (Netherlands)

    Grover, T.; Turner, A.M.; Vishwanath, A.

    2011-01-01

    We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by integrating an ‘entropy density’ over the partition boundary that

  15. Topological amplitudes in heterotic superstring theory

    International Nuclear Information System (INIS)

    Antoniadis, I.; Taylor, T.R.

    1996-06-01

    We show that certain heterotic string amplitudes are given in terms of correlators of the twisted topological (2,0) SCFT, corresponding to the internal sector of the N = 1 spacetime supersymmetric background. The genus g topological partition function F g corresponds to a term in the effective action of the form W 2g , where W is the gauge or gravitational superfield. We study also recursion relations related to holomorphic anomalies, showing that, contrary to the type II case, they involve correlators of anti-chiral superfields. The corresponding terms in the effective action are of the form W 2g II n , where II is a chiral superfield obtained by chiral projection of a general superfield. We observe that the structure of the recursion relations is that of N = 1 spacetime supersymmetry Ward identity. We give also a solution of the tree level recursion relations and discuss orbifold examples. (author). 23 refs, 2 figs

  16. Hamiltonian thermodynamics of d-dimensional (d≥4) Reissner-Nordstroem-anti-de Sitter black holes with spherical, planar, and hyperbolic topology

    International Nuclear Information System (INIS)

    Dias, Goncalo A. S.; Lemos, Jose P. S.

    2009-01-01

    The Hamiltonian thermodynamics formalism is applied to the general d-dimensional Reissner-Nordstroem-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology. After writing its action and performing a Legendre transformation, surface terms are added in order to guarantee a well-defined variational principle with which to obtain sensible equations of motion, and also to allow later on the thermodynamical analysis. Then a Kuchar canonical transformation is done, which changes from the metric canonical coordinates to the physical parameters coordinates. Again, a well-defined variational principle is guaranteed through boundary terms. These terms influence the falloff conditions of the variables and at the same time the form of the new Lagrange multipliers. Reduction to the true degrees of freedom is performed, which are the conserved mass and charge of the black hole. Upon quantization a Lorentzian partition function Z is written for the grand canonical ensemble, where the temperature T and the electric potential φ are fixed at infinity. After imposing Euclidean boundary conditions on the partition function, the respective effective action I * , and thus the thermodynamical partition function, is determined for any dimension d and topology k. This is a quite general action. Several previous results can be then condensed in our single general formula for the effective action I * . Phase transitions are studied for the spherical case, and it is shown that all the other topologies have no phase transitions. A parallel with the Bose-Einstein condensation can be established. Finally, the expected values of energy, charge, and entropy are determined for the black hole solution.

  17. Linearization of non-commuting operators in the partition function

    International Nuclear Information System (INIS)

    Ahmed, M.

    1983-06-01

    A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)

  18. Revealing topological organization of human brain functional networks with resting-state functional near infrared spectroscopy.

    Science.gov (United States)

    Niu, Haijing; Wang, Jinhui; Zhao, Tengda; Shu, Ni; He, Yong

    2012-01-01

    The human brain is a highly complex system that can be represented as a structurally interconnected and functionally synchronized network, which assures both the segregation and integration of information processing. Recent studies have demonstrated that a variety of neuroimaging and neurophysiological techniques such as functional magnetic resonance imaging (MRI), diffusion MRI and electroencephalography/magnetoencephalography can be employed to explore the topological organization of human brain networks. However, little is known about whether functional near infrared spectroscopy (fNIRS), a relatively new optical imaging technology, can be used to map functional connectome of the human brain and reveal meaningful and reproducible topological characteristics. We utilized resting-state fNIRS (R-fNIRS) to investigate the topological organization of human brain functional networks in 15 healthy adults. Brain networks were constructed by thresholding the temporal correlation matrices of 46 channels and analyzed using graph-theory approaches. We found that the functional brain network derived from R-fNIRS data had efficient small-world properties, significant hierarchical modular structure and highly connected hubs. These results were highly reproducible both across participants and over time and were consistent with previous findings based on other functional imaging techniques. Our results confirmed the feasibility and validity of using graph-theory approaches in conjunction with optical imaging techniques to explore the topological organization of human brain networks. These results may expand a methodological framework for utilizing fNIRS to study functional network changes that occur in association with development, aging and neurological and psychiatric disorders.

  19. Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end

    International Nuclear Information System (INIS)

    Yang Wenli; Chen Xi; Feng Jun; Hao Kun; Shi Kangjie; Sun Chengyi; Yang Zhanying; Zhang Yaozhong

    2011-01-01

    With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we derive the recursion relations of the partition function for the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Solving the recursion relations, we obtain the explicit determinant expression of the partition function. Our result shows that, contrary to the eight-vertex model without a reflecting end, the partition function can be expressed as a single determinant.

  20. Characterization of topological phases of dimerized Kitaev chain via edge correlation functions

    Science.gov (United States)

    Wang, Yucheng; Miao, Jian-Jian; Jin, Hui-Ke; Chen, Shu

    2017-11-01

    We study analytically topological properties of a noninteracting modified dimerized Kitaev chain and an exactly solvable interacting dimerized Kitaev chain under open boundary conditions by analyzing two introduced edge correlation functions. The interacting dimerized Kitaev chain at the symmetry point Δ =t and the chemical potential μ =0 can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation, which permits us to calculate the edge correlation functions analytically. We demonstrate that the two edge correlation functions can be used to characterize the trivial, Su-Schrieffer-Heeger-like topological and topological superconductor phases of both the noninteracting and interacting systems and give their phase diagrams.

  1. Inflation and Topological Phase Transition Driven by Exotic Smoothness

    Directory of Open Access Journals (Sweden)

    Torsten Asselmeyer-Maluga

    2014-01-01

    Full Text Available We will discuss a model which describes the cause of inflation by a topological transition. The guiding principle is the choice of an exotic smoothness structure for the space-time. Here we consider a space-time with topology S3×ℝ. In case of an exotic S3×ℝ, there is a change in the spatial topology from a 3-sphere to a homology 3-sphere which can carry a hyperbolic structure. From the physical point of view, we will discuss the path integral for the Einstein-Hilbert action with respect to a decomposition of the space-time. The inclusion of the boundary terms produces fermionic contributions to the partition function. The expectation value of an area (with respect to some surface shows an exponential increase; that is, we obtain inflationary behavior. We will calculate the amount of this increase to be a topological invariant. Then we will describe this transition by an effective model, the Starobinski or R2 model which is consistent with the current measurement of the Planck satellite. The spectral index and other observables are also calculated.

  2. Topological vertex, string amplitudes and spectral functions of hyperbolic geometry

    Energy Technology Data Exchange (ETDEWEB)

    Guimaraes, M.E.X.; Rosa, T.O. [Universidade Federal Fluminense, Instituto de Fisica, Av. Gal. Milton Tavares de Souza, s/n, CEP 24210-346, Niteroi, RJ (Brazil); Luna, R.M. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil)

    2014-05-15

    We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of a hyperbolic three-geometry associated with q-series in the computation of the string amplitudes. (orig.)

  3. Partition function for a singular background

    International Nuclear Information System (INIS)

    McKenzie-Smith, J.J.; Naylor, W.

    2005-01-01

    We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)

  4. Partition function for a singular background

    Energy Technology Data Exchange (ETDEWEB)

    McKenzie-Smith, J.J. [Financial Risk Management Ltd, 15 Adam Street, London WC2N 6AH (United Kingdom)]. E-mail: julian.mckenzie-smith@frmhedge.com; Naylor, W. [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)]. E-mail: naylor@yukawa.kyoto-u.ac.jp

    2005-03-17

    We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)

  5. Further Stable methods for the calculation of partition functions

    International Nuclear Information System (INIS)

    Wilson, B G; Gilleron, F; Pain, J

    2007-01-01

    The extension to recursion over holes of the Gilleron and Pain method for calculating partition functions of a canonical ensemble of non-interacting bound electrons is presented as well as a generalization for the efficient computation of collisional line broadening

  6. Invertebrate diversity classification using self-organizing map neural network: with some special topological functions

    Directory of Open Access Journals (Sweden)

    WenJun Zhang

    2014-06-01

    Full Text Available In present study we used self-organizing map (SOM neural network to conduct the non-supervisory clustering of invertebrate orders in rice field. Four topological functions, i.e., cossintopf, sincostopf, acossintopf, and expsintopf, established on the template in toolbox of Matlab, were used in SOM neural network learning. Results showed that clusters were different when using different topological functions because different topological functions will generate different spatial structure of neurons in neural network. We may chose these functions and results based on comparison with the practical situation.

  7. Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

    Science.gov (United States)

    Göschl, Daniel

    2018-03-01

    We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

  8. Generalized finite polynomial approximation (WINIMAX) to the reduced partition function of isotopic molecules

    International Nuclear Information System (INIS)

    Lee, M.W.; Bigeleisen, J.

    1978-01-01

    The MINIMAX finite polynomial approximation to an arbitrary function has been generalized to include a weighting function (WINIMAX). It is suggested that an exponential is a reasonable weighting function for the logarithm of the reduced partition function of a harmonic oscillator. Comparison of the error function for finite orthogonal polynomial (FOP), MINIMAX, and WINIMAX expansions of the logarithm of the reduced vibrational partition function show WINIMAX to be the best of the three approximations. A condensed table of WINIMAX coefficients is presented. The FOP, MINIMAX, and WINIMAX approximations are compared with exact calculations of the logarithm of the reduced partition function ratios for isotopic substitution in H 2 O, CH 4 , CH 2 O, C 2 H 4 , and C 2 H 6 at 300 0 K. Both deuterium and heavy atom isotope substitution are studied. Except for a third order expansion involving deuterium substitution, the WINIMAX method is superior to FOP and MINIMAX. At the level of a second order expansion WINIMAX approximations to ln(s/s')f are good to 2.5% and 6.5% for deuterium and heavy atom substitution, respectively

  9. Characterisations of Partition of Unities Generated by Entire Functions in Cd

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

    2017-01-01

    Collections of functions forming a partition of unity play an important role in analysis. In this paper we characterise for any N∈N the entire functions P for which the partition of unity condition ∑n∈ZdP(x+n)χ[0,N]d(x+n)=1 holds for all x∈Rd. The general characterisation leads to various easy wa...

  10. The volume conjecture and topological strings

    NARCIS (Netherlands)

    Dijkgraaf, R.; Fuji, H.

    2009-01-01

    In this paper, we discuss a relation between Jones-Witten theory of knot invariants and topological open string theory on the basis of the volume conjecture. We find a similar Hamiltonian structure for both theories, and interpret the AJ conjecture as the D-module structure for a D-brane partition

  11. Topological properties and functionalities in oxide thin films and interfaces

    Science.gov (United States)

    Uchida, Masaki; Kawasaki, Masashi

    2018-04-01

    As symbolized by the Nobel Prize in Physics 2016, ‘topology’ has been recognized as an essential standpoint to understand and control the physics of condensed matter. This concept may be spreading even into application areas such as novel electronics. In this trend, there has been reported a number of studies for oxide films and heterostructures with topologically non-trivial electronic or magnetic states. In this review, we overview the trends of new topological properties and functionalities in oxide materials by sorting out a number of examples. The technological advances in oxide film growth achieved over the last few decades are now opening the door for harnessing novel topological properties.

  12. Higher genus partition functions of meromorphic conformal field theories

    International Nuclear Information System (INIS)

    Gaberdiel, Matthias R.; Volpato, Roberto

    2009-01-01

    It is shown that the higher genus vacuum amplitudes of a meromorphic conformal field theory determine the affine symmetry of the theory uniquely, and we give arguments that suggest that also the representation content with respect to this affine symmetry is specified, up to automorphisms of the finite Lie algebra. We illustrate our findings with the self-dual theories at c = 16 and c = 24; in particular, we give an elementary argument that shows that the vacuum amplitudes of the E 8 x E 8 theory and the Spin(32)/Z 2 theory differ at genus g = 5. The fact that the discrepancy only arises at rather high genus is a consequence of the modular properties of higher genus amplitudes at small central charges. In fact, we show that for c ≤ 24 the genus one partition function specifies already the partition functions up to g ≤ 4 uniquely. Finally we explain how our results generalise to non-meromorphic conformal field theories.

  13. A paradox in the electronic partition function or how to be cautious with mathematics

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, E.N. [CRICYT - CONICET, Mendoza (Argentina); Departamento de Fisica, Universidad Nacional de San Luis, San Luis (Argentina)

    2001-09-01

    When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)

  14. A paradox in the electronic partition function or how to be cautious with mathematics

    International Nuclear Information System (INIS)

    Miranda, E.N.

    2001-01-01

    When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)

  15. Open string topological amplitudes and gaugino masses

    International Nuclear Information System (INIS)

    Antoniadis, I.; Narain, K.S.; Taylor, T.R.

    2005-09-01

    We discuss the moduli-dependent couplings of the higher derivative F-terms (TrW 2 ) h-1 , where W is the gauge N =1 chiral superfield. They are determined by the genus zero topological partition function F (0,h) , on a world-sheet with h boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal N =(2,0) superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form Π n (TrW 2 ) h-2 , where Π's represent chiral projections of non-holomorphic functions of chiral superfields. An important property of these couplings is that they violate R-symmetry for h ≥ 3. As a result, once supersymmetry is broken by D-term expectation values, (TrW 2 ) 2 generates gaugino masses that can be hierarchically smaller than the scalar masses, behaving as m 1/2 ∼ m 0 4 in string units. Similarly, ΠTrW 2 generates Dirac masses for non-chiral brane fermions, of the same order of magnitude. This mechanism can be used for instance to obtain fermion masses at the TeV scale for scalar masses as high as m 0 ∼ O (10 13 ) GeV. We present explicit examples in toroidal string compactifications with intersecting D-branes. (author)

  16. On the analytical evaluation of the partition function for unit hypercubes in four dimensions

    International Nuclear Information System (INIS)

    Hari Dass, N.D.

    1984-10-01

    The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU 2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)

  17. Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

    NARCIS (Netherlands)

    Marcolli, Matilde; Cornelissen, Gunther

    2014-01-01

    The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory. We introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium

  18. A novel partitioning method for block-structured adaptive meshes

    Science.gov (United States)

    Fu, Lin; Litvinov, Sergej; Hu, Xiangyu Y.; Adams, Nikolaus A.

    2017-07-01

    We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

  19. A novel partitioning method for block-structured adaptive meshes

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Lin, E-mail: lin.fu@tum.de; Litvinov, Sergej, E-mail: sergej.litvinov@aer.mw.tum.de; Hu, Xiangyu Y., E-mail: xiangyu.hu@tum.de; Adams, Nikolaus A., E-mail: nikolaus.adams@tum.de

    2017-07-15

    We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

  20. The Euler–Riemann gases, and partition identities

    International Nuclear Information System (INIS)

    Chair, Noureddine

    2013-01-01

    The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ 4 , and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t) 2 ) . Finally, we propose two formulas which brings

  1. Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

    International Nuclear Information System (INIS)

    Roumeliotis, J.; Smith, E.R.

    1992-01-01

    The authors consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity ζ in an applied electric field E with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the ζ plane occupy the imaginary axis from -i∞ to -iζ c and iζ c to i∞ for some ζ c . They also occupy the diamond shape of four straight lines from ±iζ c to ζ c and from ±iζ c to -ζ c . The fugacity ζ acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric field E. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented

  2. Fuzzy weakly preopen (preclosed) function in Kubiak-Sostak fuzzy topological spaces

    International Nuclear Information System (INIS)

    Zahran, A.M.; Abd-Allah, M. Azab.; Abd El-Rahman, Abd El-Nasser G.

    2009-01-01

    In this paper, we introduce and characterize fuzzy weakly preopen and fuzzy weakly preclosed functions between L-fuzzy topological spaces in Kubiak-Sostak sense and also study these functions in relation to some other types of already known functions.

  3. The partition function of the supersymmetric two-dimensional black hole and little string theory

    International Nuclear Information System (INIS)

    Israel, Dan; Kounnas, Costas; Troost, Jan; Pakman, Ari

    2004-01-01

    We compute the partition function of the supersymmetric two-dimensional euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N = 2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N = 2 minimal model factor of the correct central charge and projecting on integral N = 2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry. (author)

  4. Colour-independent partition functions in coloured vertex models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O., E-mail: omar.foda@unimelb.edu.au [Dept. of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 (Australia); Wheeler, M., E-mail: mwheeler@lpthe.jussieu.fr [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 (France); Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 Paris cedex 05 (France)

    2013-06-11

    We study lattice configurations related to S{sub n}, the scalar product of an off-shell state and an on-shell state in rational A{sub n} integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A{sub n} models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S{sub 2} (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S{sub 2}, which depends on two sets of Bethe roots, {b_1} and {b_2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b_1}→∞, and/or {b_2}→∞, into a product of determinants, 2. Each of the latter determinants is an A{sub 1} vertex-model partition function.

  5. Colour-independent partition functions in coloured vertex models

    International Nuclear Information System (INIS)

    Foda, O.; Wheeler, M.

    2013-01-01

    We study lattice configurations related to S n , the scalar product of an off-shell state and an on-shell state in rational A n integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S 2 (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S 2 , which depends on two sets of Bethe roots, {b 1 } and {b 2 }, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b 1 }→∞, and/or {b 2 }→∞, into a product of determinants, 2. Each of the latter determinants is an A 1 vertex-model partition function

  6. A discrete transition zone organizes the topological and regulatory autonomy of the adjacent tfap2c and bmp7 genes.

    Directory of Open Access Journals (Sweden)

    Taro Tsujimura

    2015-01-01

    Full Text Available Despite the well-documented role of remote enhancers in controlling developmental gene expression, the mechanisms that allocate enhancers to genes are poorly characterized. Here, we investigate the cis-regulatory organization of the locus containing the Tfap2c and Bmp7 genes in vivo, using a series of engineered chromosomal rearrangements. While these genes lie adjacent to one another, we demonstrate that they are independently regulated by distinct sets of enhancers, which in turn define non-overlapping regulatory domains. Chromosome conformation capture experiments reveal a corresponding partition of the locus in two distinct structural entities, demarcated by a discrete transition zone. The impact of engineered chromosomal rearrangements on the topology of the locus and the resultant gene expression changes indicate that this transition zone functionally organizes the structural partition of the locus, thereby defining enhancer-target gene allocation. This partition is, however, not absolute: we show that it allows competing interactions across it that may be non-productive for the competing gene, but modulate expression of the competed one. Altogether, these data highlight the prime role of the topological organization of the genome in long-distance regulation of gene expression.

  7. Splittings of free groups, normal forms and partitions of ends

    Indian Academy of Sciences (India)

    geodesic laminations and show that this space is compact. Many of the ... determined by the partition of ends of ˜M associated to the spheres. In §4, we recall ... As is well-known we can associate to a graph a topological space. Geometrically ...

  8. On the partition function of d+1 dimensional kink-bearing systems

    International Nuclear Information System (INIS)

    Radosz, A.; Salejda, W.

    1987-01-01

    It is suggested that the problem of finding a partition function of d+1 dimensional kink-bearing system in the classical approximation may be formulated as an eigenvalue problem of an appropriate d dimensional quantum

  9. Positron Emission Tomography Reveals Abnormal Topological Organization in Functional Brain Network in Diabetic Patients.

    Science.gov (United States)

    Qiu, Xiangzhe; Zhang, Yanjun; Feng, Hongbo; Jiang, Donglang

    2016-01-01

    Recent studies have demonstrated alterations in the topological organization of structural brain networks in diabetes mellitus (DM). However, the DM-related changes in the topological properties in functional brain networks are unexplored so far. We therefore used fluoro-D-glucose positron emission tomography (FDG-PET) data to construct functional brain networks of 73 DM patients and 91 sex- and age-matched normal controls (NCs), followed by a graph theoretical analysis. We found that both DM patients and NCs had a small-world topology in functional brain network. In comparison to the NC group, the DM group was found to have significantly lower small-world index, lower normalized clustering coefficients and higher normalized characteristic path length. Moreover, for diabetic patients, the nodal centrality was significantly reduced in the right rectus, the right cuneus, the left middle occipital gyrus, and the left postcentral gyrus, and it was significantly increased in the orbitofrontal region of the left middle frontal gyrus, the left olfactory region, and the right paracentral lobule. Our results demonstrated that the diabetic brain was associated with disrupted topological organization in the functional PET network, thus providing functional evidence for the abnormalities of brain networks in DM.

  10. BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters

    Science.gov (United States)

    Nekrasov, Nikita

    2018-03-01

    We study generalized gauge theories engineered by taking the low energy limit of the Dp branes wrapping {X × {T}^{p-3}}, with X a possibly singular surface in a Calabi-Yau fourfold Z. For toric Z and X the partition function can be computed by localization, making it a statistical mechanical model, called the gauge origami. The random variables are the ensembles of Young diagrams. The building block of the gauge origami is associated with a tetrahedron, whose edges are colored by vector spaces. We show the properly normalized partition function is an entire function of the Coulomb moduli, for generic values of the {Ω} -background parameters. The orbifold version of the theory defines the qq-character operators, with and without the surface defects. The analytic properties are the consequence of a relative compactness of the moduli spaces M({ěc n}, k) of crossed and spiked instantons, demonstrated in "BPS/CFT correspondence II: instantons at crossroads, moduli and compactness theorem".

  11. Asymptotic expansion of a partition function related to the sinh-model

    CERN Document Server

    Borot, Gaëtan; Kozlowski, Karol K

    2016-01-01

    This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...

  12. Robust extrapolation scheme for fast estimation of 3D Ising field partition functions: application to within subject fMRI data

    Energy Technology Data Exchange (ETDEWEB)

    Risser, L.; Vincent, T.; Ciuciu, Ph. [NeuroSpin CEA, F-91191 Gif sur Yvette (France); Risser, L.; Vincent, T. [Laboratoire de Neuroimagerie Assistee par Ordinateur (LNAO) CEA - DSV/I2BM/NEUROSPIN (France); Risser, L. [Institut de mecanique des fluides de Toulouse (IMFT), CNRS: UMR5502 - Universite Paul Sabatier - Toulouse III - Institut National Polytechnique de Toulouse - INPT (France); Idier, J. [Institut de Recherche en Communications et en Cybernetique de Nantes (IRCCyN) CNRS - UMR6597 - Universite de Nantes - ecole Centrale de Nantes - Ecole des Mines de Nantes - Ecole Polytechnique de l' Universite de Nantes (France)

    2009-07-01

    In this paper, we present a first numerical scheme to estimate Partition Functions (PF) of 3D Ising fields. Our strategy is applied to the context of the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate region-dependent, hemodynamic filters. For any region, a specific binary Markov random field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make this spatial regularization fully adaptive, our approach is first based upon it, classical path-sampling method to approximate a small subset of reference PFs corresponding to pre-specified regions. Then, file proposed extrapolation method allows its to approximate the PFs associated with the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust; to topological inhomogeneities in the definition of the reference regions. As a result, it strongly alleviates the computational burden and makes spatially adaptive regularization of whole brain fMRI datasets feasible. (authors)

  13. General topology

    CERN Document Server

    Willard, Stephen

    2004-01-01

    Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: ""continuous topology,"" represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and ""geometric topology,"" covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340

  14. Accounting for the contributions of topological excitations in phase transitions through dual actions

    International Nuclear Information System (INIS)

    Ramos, Rudnei O.

    2006-01-01

    Topological excitations are believed to play an important role in different areas of physics. For example, cases of topical interest are the study of contributions of nonhomogeneous field configurations, in particular those of topological nature (like kinks, vortices and monopoles) in phase transitions associated to spontaneous symmetry breaking, the use of topological excitations in dual models of QCD to understand properties of its vacuum and confinement through the condensation of magnetic monopoles and vortices and also the relevance of these nonhomogeneous type of configurations in cosmology, again associated to possible phase transitions that are expected to have happened in the early universe. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The contribution of these nontrivial vacuum excitations in the phase transition for the scalar Abelian Higgs model in a thermal background is then studied and the results interpreted from the computation of the partition function taking into account the vortice-strings in the functional integration. This is made possible from the derived dual action. The relevance of the obtained results in cosmology, the analogy with phase transitions in superconductors, the relevance also for the study of confinement and other extensions of our calculations are briefly discussed here. (author)

  15. Topology

    CERN Document Server

    Manetti, Marco

    2015-01-01

    This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

  16. One loop partition function of six dimensional conformal gravity using heat kernel on AdS

    Energy Technology Data Exchange (ETDEWEB)

    Lovreković, Iva [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)

    2016-10-13

    We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach introduced in http://dx.doi.org/10.1007/JHEP11(2011)010 and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass.

  17. Topological and functional properties of the small GTPases protein interaction network.

    Directory of Open Access Journals (Sweden)

    Anna Delprato

    Full Text Available Small GTP binding proteins of the Ras superfamily (Ras, Rho, Rab, Arf, and Ran regulate key cellular processes such as signal transduction, cell proliferation, cell motility, and vesicle transport. A great deal of experimental evidence supports the existence of signaling cascades and feedback loops within and among the small GTPase subfamilies suggesting that these proteins function in a coordinated and cooperative manner. The interplay occurs largely through association with bi-partite regulatory and effector proteins but can also occur through the active form of the small GTPases themselves. In order to understand the connectivity of the small GTPases signaling routes, a systems-level approach that analyzes data describing direct and indirect interactions was used to construct the small GTPases protein interaction network. The data were curated from the Search Tool for the Retrieval of Interacting Genes (STRING database and include only experimentally validated interactions. The network method enables the conceptualization of the overall structure as well as the underlying organization of the protein-protein interactions. The interaction network described here is comprised of 778 nodes and 1943 edges and has a scale-free topology. Rac1, Cdc42, RhoA, and HRas are identified as the hubs. Ten sub-network motifs are also identified in this study with themes in apoptosis, cell growth/proliferation, vesicle traffic, cell adhesion/junction dynamics, the nicotinamide adenine dinucleotide phosphate (NADPH oxidase response, transcription regulation, receptor-mediated endocytosis, gene silencing, and growth factor signaling. Bottleneck proteins that bridge signaling paths and proteins that overlap in multiple small GTPase networks are described along with the functional annotation of all proteins in the network.

  18. Use of JANAF Tables in Equilibrium Calculations and Partition Function Calculations for an Undergraduate Physical Chemistry Course

    Science.gov (United States)

    Cleary, David A.

    2014-01-01

    The usefulness of the JANAF tables is demonstrated with specific equilibrium calculations. An emphasis is placed on the nature of standard chemical potential calculations. Also, the use of the JANAF tables for calculating partition functions is examined. In the partition function calculations, the importance of the zero of energy is highlighted.

  19. Ranking beta sheet topologies of proteins

    DEFF Research Database (Denmark)

    Fonseca, Rasmus; Helles, Glennie; Winter, Pawel

    2010-01-01

    One of the challenges of protein structure prediction is to identify long-range interactions between amino acids. To reliably predict such interactions, we enumerate, score and rank all beta-topologies (partitions of beta-strands into sheets, orderings of strands within sheets and orientations...... of paired strands) of a given protein. We show that the beta-topology corresponding to the native structure is, with high probability, among the top-ranked. Since full enumeration is very time-consuming, we also suggest a method to deal with proteins with many beta-strands. The results reported...... in this paper are highly relevant for ab initio protein structure prediction methods based on decoy generation. The top-ranked beta-topologies can be used to find initial conformations from which conformational searches can be started. They can also be used to filter decoys by removing those with poorly...

  20. Positron Emission Tomography Reveals Abnormal Topological Organization in Functional Brain Network in Diabetic Patients

    Directory of Open Access Journals (Sweden)

    Qiu eXiangzhe

    2016-05-01

    Full Text Available Recent studies have demonstrated alterations in the topological organization of structural brain networks in diabetes mellitus (DM. However, the DM-related changes in the topological properties in functional brain networks are almost unexplored so far. We therefore used fluoro-D-glucose positron emission tomography (FDG-PET data to construct functional brain networks of 73 DM patients and 91 sex- and age-matched normal controls (NCs, followed by a graph theoretical analysis. We found that both DM patients and NCs had a small-world topology in functional brain network. In comparison to the NC group, the DM group was found to have significantly lower small-world index, lower normalized clustering coefficients and higher normalized shortest path length. Moreover, for diabetic patients, the nodal centrality was significantly reduced in the right rectus, the right cuneus, the left middle occipital gyrus, and the left postcentral gyrus, and it was significantly increased in the orbitofrontal region of the left middle frontal gyrus, the left olfactory region, and the right paracentral lobule. Our results demonstrated that the diabetic brain was associated with disrupted topological organization in the functional PET network, thus providing the functional evidence for the abnormalities of brain networks in DM.

  1. Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies

    Energy Technology Data Exchange (ETDEWEB)

    Bonora, L., E-mail: bonora@sissa.it [International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A., E-mail: abyts@uel.br [Departamento de Fisica, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina (Brazil)

    2011-11-11

    There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS{sub 3}, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.

  2. Mirror of the refined topological vertex from a matrix model

    CERN Document Server

    Eynard, B

    2011-01-01

    We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined vertex. With the same method we also find a matrix model for the strip geometry, and we find its mirror curve. The fact that there is a matrix model shows that the refined topological string amplitudes also satisfy the remodeling the B-model construction.

  3. On the definition of the partition function in quantum Regge calculus

    International Nuclear Information System (INIS)

    Nishimura, Jun

    1995-01-01

    We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results. (author)

  4. Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

    Directory of Open Access Journals (Sweden)

    Apu Kumar Saha

    2015-06-01

    Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.

  5. Do motifs reflect evolved function?--No convergent evolution of genetic regulatory network subgraph topologies.

    Science.gov (United States)

    Knabe, Johannes F; Nehaniv, Chrystopher L; Schilstra, Maria J

    2008-01-01

    Methods that analyse the topological structure of networks have recently become quite popular. Whether motifs (subgraph patterns that occur more often than in randomized networks) have specific functions as elementary computational circuits has been cause for debate. As the question is difficult to resolve with currently available biological data, we approach the issue using networks that abstractly model natural genetic regulatory networks (GRNs) which are evolved to show dynamical behaviors. Specifically one group of networks was evolved to be capable of exhibiting two different behaviors ("differentiation") in contrast to a group with a single target behavior. In both groups we find motif distribution differences within the groups to be larger than differences between them, indicating that evolutionary niches (target functions) do not necessarily mold network structure uniquely. These results show that variability operators can have a stronger influence on network topologies than selection pressures, especially when many topologies can create similar dynamics. Moreover, analysis of motif functional relevance by lesioning did not suggest that motifs were of greater importance to the functioning of the network than arbitrary subgraph patterns. Only when drastically restricting network size, so that one motif corresponds to a whole functionally evolved network, was preference for particular connection patterns found. This suggests that in non-restricted, bigger networks, entanglement with the rest of the network hinders topological subgraph analysis.

  6. Finite volume gauge theory partition functions in three dimensions

    International Nuclear Information System (INIS)

    Szabo, Richard J.

    2005-01-01

    We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ε-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules

  7. Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

    Science.gov (United States)

    Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

    2015-01-23

    The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

  8. Graph topologies on closed multifunctions

    Directory of Open Access Journals (Sweden)

    Giuseppe Di Maio

    2003-10-01

    Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.

  9. On the relativistic partition function of ideal gases

    International Nuclear Information System (INIS)

    Sinyukov, Yu.M.

    1983-01-01

    The covariant partition function method for ideal Boltzmann and Bose gases is developed within quantum field theory. This method is a basis to describe the statistical and thermodynamical properties of the gases in canonical, grand canonical and pressure ensembles in an arbitrary inertial system. It is shown that when statistical systems are described relativistically it is very important to take into account the boundary conditions. This is due to the fact that an equilibrium system is not closed mechanically. The results may find application in hadron physics. (orig.)

  10. Instantons: Dynamical mass generation, chiral ward identities and the topological charge correlation function

    International Nuclear Information System (INIS)

    McDougall, N.A.

    1983-01-01

    When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the eta' to the topological charge correlation function, a relationship is derived in which msub(eta') 2 fsub(eta') 2 is proportional to the vacuum energy density. (orig.)

  11. Zeros of the partition function for some generalized Ising models

    International Nuclear Information System (INIS)

    Dunlop, F.

    1981-01-01

    The author considers generalized Ising Models with two and four body interactions in a complex external field h such that Re h>=mod(Im h) + C, where C is an explicit function of the interaction parameters. The partition function Z(h) is then shown to satisfy mod(Z(h))>=Z(c), so that the pressure is analytic in h inside the given region. The method is applied to specific examples: the gauge invariant Ising Model, and the Widom Rowlinson model on the lattice. (Auth.)

  12. On πgp-continuous functions in topological spaces

    International Nuclear Information System (INIS)

    Park, Jin Han; Park, Jin Keun

    2004-01-01

    The concept of πgp-closed sets was introduced by Park [On πgp-closed sets in topological spaces, Indian J. Pure Appl. Math., in press]. The aim of this paper is to consider and characterize πgp-irresolute and πgp-continuous functions via the concept of πgp-closed sets and to relate these concepts to the classes of πGPO-compact spaces and πGP-connected spaces

  13. Two-dimensional ferroelectric topological insulators in functionalized atomically thin bismuth layers

    Science.gov (United States)

    Kou, Liangzhi; Fu, Huixia; Ma, Yandong; Yan, Binghai; Liao, Ting; Du, Aijun; Chen, Changfeng

    2018-02-01

    We introduce a class of two-dimensional (2D) materials that possess coexisting ferroelectric and topologically insulating orders. Such ferroelectric topological insulators (FETIs) occur in noncentrosymmetric atomic layer structures with strong spin-orbit coupling (SOC). We showcase a prototype 2D FETI in an atomically thin bismuth layer functionalized by C H2OH , which exhibits a large ferroelectric polarization that is switchable by a ligand molecule rotation mechanism and a strong SOC that drives a band inversion leading to the topologically insulating state. An external electric field that switches the ferroelectric polarization also tunes the spin texture in the underlying atomic lattice. Moreover, the functionalized bismuth layer exhibits an additional quantum order driven by the valley splitting at the K and K' points in the Brillouin zone stemming from the symmetry breaking and strong SOC in the system, resulting in a remarkable state of matter with the simultaneous presence of the quantum spin Hall and quantum valley Hall effect. These phenomena are predicted to exist in other similarly constructed 2D FETIs, thereby offering a unique quantum material platform for discovering novel physics and exploring innovative applications.

  14. Partition function as a Laplace transform of a positive measure in the strength parameter

    International Nuclear Information System (INIS)

    Bessis, D.

    1980-01-01

    We shall consider the partition function Z(lambda), of an N-body system whose Hamiltonian reads: H = H/sub O/ + lambdaH/sub I/. H/sub O/ is an exactly solvable Hamiltonian, one for which, for example all thermodynamical quantities can be calculated. H/sub I/ is the perturbation. We are interested in the analytic properties in the strength parameter lambda of the partition function Z(lambda) = Tr e/sup -ν[H 0 + lambdaH/sub I/]/ where for convenience the volume V and inverse temperature ν dependence has been suppressed on the left hand side. The representation for Z(lambda) is given and discussed, and applications are described

  15. How Incorrect Is the Classical Partition Function for the Ideal Gas?

    Science.gov (United States)

    Kroemer, Herbert

    1980-01-01

    Discussed is the classical partition function for the ideal gas and how it differs from the exact value for bosons or fermions in the classical regime. The differences in the two values are negligible hence the classical treatment leads in the end to correct answers for all observables. (Author/DS)

  16. Functional integral representation of the nuclear many-body grand partition function

    International Nuclear Information System (INIS)

    Kerman, A.K.; Troudet, T.

    1984-01-01

    A local functional integral formulation of the nuclear many-body problem is proposed which is a generalization of the method previously developed. Its most interesting feature is that it allows an expansion of the many-body evolution operator around any arbitrary mean-field which takes into account the pairing correlations between the nucleons. This is explicitly illustrated for the nuclear many-body grand partition function for which special attention is paid to the static temperature-dependent Hartree-Fock-Bogolyubov (H.F.B.) approximation. Indeed, the temperature-dependent H.F.B. configuration appears to be the optimal choice from a variational point of view among all the possible independent quasi-particle motion approximations. An analytic approximation of the energy level density rho (E,A) is given using explicitly the arbitrariness in the choice of the mean-field and a possible numerical application is proposed. Finally, a new compact formulation of our functional integral that might be useful for future Monte Carlo calculations is proposed

  17. Anyonic partition functions and windings of planar Brownian motion

    International Nuclear Information System (INIS)

    Desbois, J.; Heinemann, C.; Ouvry, S.

    1995-01-01

    The computation of the N-cycle Brownian paths contribution F N (α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that F N 0 (α)=product k=1 N-1 [1-(N/k)α]. In the paramount three-anyon case, one can show that F 3 (α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S 3

  18. Topological variation in the evolution of new reactions in functionally diverse enzyme superfamilies.

    Science.gov (United States)

    Meng, Elaine C; Babbitt, Patricia C

    2011-06-01

    In functionally diverse enzyme superfamilies (SFs), conserved structural and active site features reflect catalytic capabilities 'hard-wired' in each SF architecture. Overlaid on this foundation, evolutionary changes in active site machinery, structural topology and other aspects of structural organization and interactions support the emergence of new reactions, mechanisms, and substrate specificity. This review connects topological with functional variation in each of the haloalkanoic acid dehalogenase (HAD) and vicinal oxygen chelate fold (VOC) SFs and a set of redox-active thioredoxin (Trx)-fold SFs to illustrate a few of the varied themes nature has used to evolve new functions from a limited set of structural scaffolds. Copyright © 2011 Elsevier Ltd. All rights reserved.

  19. Instantons: Dynamical mass generation, chiral ward identities and the topological charge correlation function

    Energy Technology Data Exchange (ETDEWEB)

    McDougall, N.A. (Oxford Univ. (UK). Dept. of Theoretical Physics)

    1983-01-10

    When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the eta' to the topological charge correlation function, a relationship is derived in which msub(eta')/sup 2/fsub(eta')/sup 2/ is proportional to the vacuum energy density.

  20. Partition functions with spin in AdS2 via quasinormal mode methods

    International Nuclear Information System (INIS)

    Keeler, Cynthia; Lisbão, Pedro; Ng, Gim Seng

    2016-01-01

    We extend the results of http://dx.doi.org/10.1007/JHEP06(2014)099, computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev http://dx.doi.org/10.1088/0264-9381/27/12/125001. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |h〉 and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins.

  1. Topological organization of the human brain functional connectome across the lifespan

    Directory of Open Access Journals (Sweden)

    Miao Cao

    2014-01-01

    Full Text Available Human brain function undergoes complex transformations across the lifespan. We employed resting-state functional MRI and graph-theory approaches to systematically chart the lifespan trajectory of the topological organization of human whole-brain functional networks in 126 healthy individuals ranging in age from 7 to 85 years. Brain networks were constructed by computing Pearson's correlations in blood-oxygenation-level-dependent temporal fluctuations among 1024 parcellation units followed by graph-based network analyses. We observed that the human brain functional connectome exhibited highly preserved non-random modular and rich club organization over the entire age range studied. Further quantitative analyses revealed linear decreases in modularity and inverted-U shaped trajectories of local efficiency and rich club architecture. Regionally heterogeneous age effects were mainly located in several hubs (e.g., default network, dorsal attention regions. Finally, we observed inverse trajectories of long- and short-distance functional connections, indicating that the reorganization of connectivity concentrates and distributes the brain's functional networks. Our results demonstrate topological changes in the whole-brain functional connectome across nearly the entire human lifespan, providing insights into the neural substrates underlying individual variations in behavior and cognition. These results have important implications for disease connectomics because they provide a baseline for evaluating network impairments in age-related neuropsychiatric disorders.

  2. Natural Microbial Assemblages Reflect Distinct Organismal and Functional Partitioning

    Science.gov (United States)

    Wilmes, P.; Andersson, A.; Kalnejais, L. H.; Verberkmoes, N. C.; Lefsrud, M. G.; Wexler, M.; Singer, S. W.; Shah, M.; Bond, P. L.; Thelen, M. P.; Hettich, R. L.; Banfield, J. F.

    2007-12-01

    The ability to link microbial community structure to function has long been a primary focus of environmental microbiology. With the advent of community genomic and proteomic techniques, along with advances in microscopic imaging techniques, it is now possible to gain insights into the organismal and functional makeup of microbial communities. Biofilms growing within highly acidic solutions inside the Richmond Mine (Iron Mountain, Redding, California) exhibit distinct macro- and microscopic morphologies. They are composed of microorganisms belonging to the three domains of life, including archaea, bacteria and eukarya. The proportion of each organismal type depends on sampling location and developmental stage. For example, mature biofilms floating on top of acid mine drainage (AMD) pools exhibit layers consisting of a densely packed bottom layer of the chemoautolithotroph Leptospirillum group II, a less dense top layer composed mainly of archaea, and fungal filaments spanning across the entire biofilm. The expression of cytochrome 579 (the most highly abundant protein in the biofilm, believed to be central to iron oxidation and encoded by Leptospirillum group II) is localized at the interface of the biofilm with the AMD solution, highlighting that biofilm architecture is reflected at the functional gene expression level. Distinct functional partitioning is also apparent in a biological wastewater treatment system that selects for distinct polyphosphate accumulating organisms. Community genomic data from " Candidatus Accumulibacter phosphatis" dominated activated sludge has enabled high mass-accuracy shotgun proteomics for identification of key metabolic pathways. Comprehensive genome-wide alignment of orthologous proteins suggests distinct partitioning of protein variants involved in both core-metabolism and specific metabolic pathways among the dominant population and closely related species. In addition, strain- resolved proteogenomic analysis of the AMD biofilms

  3. Axiomatic method of partitions in the theory of Noebeling spaces. I. Improvement of partition connectivity

    International Nuclear Information System (INIS)

    Ageev, S M

    2007-01-01

    The Noebeling space N k 2k+1 , a k-dimensional analogue of the Hilbert space, is considered; this is a topologically complete separable (that is, Polish) k-dimensional absolute extensor in dimension k (that is, AE(k)) and a strongly k-universal space. The conjecture that the above-listed properties characterize the Noebeling space N k 2k+1 in an arbitrary finite dimension k is proved. In the first part of the paper a full axiom system of the Noebeling spaces is presented and the problem of the improvement of a partition connectivity is solved on its basis. Bibliography: 29 titles.

  4. Alteration of long-distance functional connectivity and network topology in patients with supratentorial gliomas

    Energy Technology Data Exchange (ETDEWEB)

    Park, Ji Eun; Kim, Ho Sung; Kim, Sang Joon; Shim, Woo Hyun [University of Ulsan College of Medicine, Department of Radiology and Research Institute of Radiology, Asan Medical Center, Songpa-Gu, Seoul (Korea, Republic of); Kim, Jeong Hoon [University of Ulsan College of Medicine, Department of Neurosurgery, Asan Medical Center, Seoul (Korea, Republic of)

    2016-03-15

    The need for information regarding functional alterations in patients with brain gliomas is increasing, but little is known about the functional consequences of focal brain tumors throughout the entire brain. Using resting-state functional MR imaging (rs-fMRI), this study assessed functional connectivity in patients with supratentorial brain gliomas with possible alterations in long-distance connectivity and network topology. Data from 36 patients with supratentorial brain gliomas and 12 healthy subjects were acquired using rs-fMRI. The functional connectivity matrix (FCM) was created using 32 pairs of cortical seeds on Talairach coordinates in each individual subject. Local and distant connectivity were calculated using z-scores in the individual patient's FCM, and the averaged FCM of patients was compared with that of healthy subjects. Weighted network analysis was performed by calculating local efficiency, global efficiency, clustering coefficient, and small-world topology, and compared between patients and healthy controls. When comparing the averaged FCM of patients with that of healthy controls, the patients showed decreased long-distance, inter-hemispheric connectivity (0.32 ± 0.16 in patients vs. 0. 42 ± 0.15 in healthy controls, p = 0.04). In network analysis, patients showed increased local efficiency (p < 0.05), but global efficiency, clustering coefficient, and small-world topology were relatively preserved compared to healthy subjects. Patients with supratentorial brain gliomas showed decreased long-distance connectivity while increased local efficiency and preserved small-world topology. The results of this small case series may provide a better understanding of the alterations of functional connectivity in patients with brain gliomas across the whole brain scale. (orig.)

  5. Spectral zeta function and non-perturbative effects in ABJM Fermi-gas

    International Nuclear Information System (INIS)

    Hatsuda, Yasuyuki

    2015-03-01

    The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of ''non-perturbative'' poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.

  6. Lagrangian statistics and flow topology in forced two-dimensional turbulence.

    Science.gov (United States)

    Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

    2011-03-01

    A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

  7. Spin glass: thermal properties and characterization of the ± J Sherrington-Kirkpatrick model partition function zeros

    International Nuclear Information System (INIS)

    Faria, A.C. de.

    1990-01-01

    A detailed study of the S-K model through the analysis of the zeros of the partition function in the complex temperature plane is performed. By the exact way, the notable thermodynamical properties of the system to a variety of the length (N=5→25 spins) are calculated, using only standards concepts (without the use of tricks like that of replicas). Dilute models had been also considered. The principal result of this work is the characterization of the zeros of the partition function of the S-K model. (author)

  8. Gentile statistics and restricted partitions

    Indian Academy of Sciences (India)

    The partition function of Gentile statistics also has the property that it nicely interpolates between the ... We now construct the partition function for such a system which also incorporates the property of interpolation ... As in [4], we however keep s arbitrary even though for s > 2 there are no quadratic. Hamiltonian systems.

  9. Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

    Energy Technology Data Exchange (ETDEWEB)

    Solbrig, Stefan

    2008-07-01

    In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

  10. Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

    International Nuclear Information System (INIS)

    Solbrig, Stefan

    2008-01-01

    In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

  11. Schwinger's formula and the partition function for the bosonic and fermionic harmonic oscillators

    International Nuclear Information System (INIS)

    Albuquerque, L.C. de; Farina, C.; Rabello, S.J.

    1994-01-01

    We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for Qed, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillators. (author)

  12. Tunable Electronic and Topological Properties of Germanene by Functional Group Modification

    Directory of Open Access Journals (Sweden)

    Ceng-Ceng Ren

    2018-03-01

    Full Text Available Electronic and topological properties of two-dimensional germanene modified by functional group X (X = H, F, OH, CH3 at full coverage are studied with first-principles calculation. Without considering the effect of spin-orbit coupling (SOC, all functionalized configurations become semiconductors, removing the Dirac cone at K point in pristine germanene. We also find that their band gaps can be especially well tuned by an external strain. When the SOC is switched on, GeX (X = H, CH3 is a normal insulator and strain leads to a phase transition to a topological insulator (TI phase. However, GeX (X = F, OH becomes a TI with a large gap of 0.19 eV for X = F and 0.24 eV for X = OH, even without external strains. More interestingly, when all these functionalized monolayers form a bilayer structure, semiconductor-metal states are observed. All these results suggest a possible route of modulating the electronic properties of germanene and promote applications in nanoelectronics.

  13. An advanced complex analysis problem book topological vector spaces, functional analysis, and Hilbert spaces of analytic functions

    CERN Document Server

    Alpay, Daniel

    2015-01-01

    This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

  14. Topological Hausdorff dimension and level sets of generic continuous functions on fractals

    International Nuclear Information System (INIS)

    Balka, Richárd; Buczolich, Zoltán; Elekes, Márton

    2012-01-01

    Highlights: ► We examine a new fractal dimension, the so called topological Hausdorff dimension. ► The generic continuous function has a level set of maximal Hausdorff dimension. ► This maximal dimension is the topological Hausdorff dimension minus one. ► Homogeneity implies that “most” level sets are of this dimension. ► We calculate the various dimensions of the graph of the generic function. - Abstract: In an earlier paper we introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. For a compact metric space K let dim H K and dim tH K denote its Hausdorff and topological Hausdorff dimension, respectively. We proved that this new dimension describes the Hausdorff dimension of the level sets of the generic continuous function on K, namely sup{ dim H f -1 (y):y∈R} =dim tH K-1 for the generic f ∈ C(K), provided that K is not totally disconnected, otherwise every non-empty level set is a singleton. We also proved that if K is not totally disconnected and sufficiently homogeneous then dim H f −1 (y) = dim tH K − 1 for the generic f ∈ C(K) and the generic y ∈ f(K). The most important goal of this paper is to make these theorems more precise. As for the first result, we prove that the supremum is actually attained on the left hand side of the first equation above, and also show that there may only be a unique level set of maximal Hausdorff dimension. As for the second result, we characterize those compact metric spaces for which for the generic f ∈ C(K) and the generic y ∈ f(K) we have dim H f −1 (y) = dim tH K − 1. We also generalize a result of B. Kirchheim by showing that if K is self-similar then for the generic f ∈ C(K) for every y∈intf(K) we have dim H f −1 (y) = dim tH K − 1. Finally, we prove that the graph of the generic f ∈ C(K) has the same Hausdorff and topological Hausdorff dimension as K.

  15. Topology of helical fluid flow

    DEFF Research Database (Denmark)

    Andersen, Morten; Brøns, Morten

    2014-01-01

    function for the topology of the streamline pattern in incompressible flows. On this basis, we perform a comprehensive study of the topology of the flow field generated by a helical vortex filament in an ideal fluid. The classical expression for the stream function obtained by Hardin (Hardin, J. C. 1982...... the zeroes of a single real function of one variable, and we show that three different flow topologies can occur, depending on a single dimensionless parameter. By including the self-induced velocity on the vortex filament by a localised induction approximation, the stream function is slightly modified...... and an extra parameter is introduced. In this setting two new flow topologies arise, but not more than two critical points occur for any combination of parameters....

  16. Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

    Energy Technology Data Exchange (ETDEWEB)

    Solbrig, Stefan

    2008-07-01

    In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

  17. PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape.

    Directory of Open Access Journals (Sweden)

    Yong Wang

    2014-07-01

    Full Text Available Ubiquitin (Ub can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.

  18. PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape.

    Science.gov (United States)

    Wang, Yong; Tang, Chun; Wang, Erkang; Wang, Jin

    2014-07-01

    Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.

  19. Partition functions with spin in AdS{sub 2} via quasinormal mode methods

    Energy Technology Data Exchange (ETDEWEB)

    Keeler, Cynthia [Niels Bohr International Academy, Niels Bohr Institute,University of Copenhagen, Blegdamsvej 17, DK 2100, Copenhagen (Denmark); Lisbão, Pedro [Department of Physics, University of Michigan,Ann Arbor, MI-48109 (United States); Ng, Gim Seng [Department of Physics, McGill University,Montréal, QC H3A 2T8 (Canada)

    2016-10-12

    We extend the results of http://dx.doi.org/10.1007/JHEP06(2014)099, computing one loop partition functions for massive fields with spin half in AdS{sub 2} using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev http://dx.doi.org/10.1088/0264-9381/27/12/125001. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |h〉 and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS{sub 2n} and higher spins.

  20. Donaldson-Witten theory and indefinite theta functions

    Science.gov (United States)

    Korpas, Georgios; Manschot, Jan

    2017-11-01

    We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

  1. Topology with applications topological spaces via near and far

    CERN Document Server

    Naimpally, Somashekhar A

    2013-01-01

    The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces. This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising. It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and...

  2. A topological derivative method for topology optimization

    DEFF Research Database (Denmark)

    Norato, J.; Bendsøe, Martin P.; Haber, RB

    2007-01-01

    resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void......We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...... regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures....

  3. [Aberrant topological properties of whole-brain functional network in chronic right-sided sensorineural hearing loss: a resting-state functional MRI study].

    Science.gov (United States)

    Zhang, Lingling; Liu, Bin; Xu, Yangwen; Yang, Ming; Feng, Yuan; Huang, Yaqing; Huan, Zhichun; Hou, Zhaorui

    2015-02-03

    To investigate the topological properties of the functional brain network in unilateral sensorineural hearing loss patients. In this study, we acquired resting-state BOLD- fMRI data from 19 right-sided SNHL patients and 31 healthy controls with normal hearing and constructed their whole brain functional networks. Two-sample two-tailed t-tests were performed to investigate group differences in topological parameters between the USNHL patients and the controls. Partial correlation analysis was conducted to determine the relationships between the network metrics and USNHL-related variables. Both USNHL patients and controls exhibited small-word architecture in their brain functional networks within the range 0. 1 - 0. 2 of sparsity. Compared to the controls, USNHL patients showed significant increase in characteristic path length and normalized characteristic path length, but significant decrease in global efficiency. Clustering coefficient, local efficiency and normalized clustering coefficient demonstrated no significant difference. Furthermore, USNHL patients exhibited no significant association between the altered network metrics and the duration of USNHL or the severity of hearing loss. Our results indicated the altered topological properties of whole brain functional networks in USNHL patients, which may help us to understand pathophysiologic mechanism of USNHL patients.

  4. Functional representation for the grand partition function of a multicomponent system of charged particles: Correlation functions of the reference system

    Directory of Open Access Journals (Sweden)

    O.V.Patsahan

    2006-01-01

    Full Text Available Based on the method of collective variables (CV with a reference system, the exact expression for the functional of the grand partition function of a m-component ionic model with charge and size asymmetry is found. Particular attention is paid to the n-th particle correlation functions of the reference system which is presented as a m-component system of "colour" hard spheres of the same diameter. A two-component model is considered in more detail. In this case the recurrence formulas for the correlation functions are found. A general case of a m-component inhomogeneous system of the "colour" hard spheres is also analysed.

  5. The Cardy limit of the topologically twisted index and black strings in AdS{sub 5}

    Energy Technology Data Exchange (ETDEWEB)

    Hosseini, Seyed Morteza; Nedelin, Anton; Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,I-20126 Milano (Italy)

    2017-04-04

    We evaluate the topologically twisted index of a general four-dimensional N=1 gauge theory in the “high-temperature' limit. The index is the partition function for N=1 theories on S{sup 2}×T{sup 2}, with a partial topological twist along S{sup 2}, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional N=(0,2) SCFTs obtained from the compactification on S{sup 2}. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS{sub 5}×SE{sub 5}, where SE{sub 5} are five-dimensional Sasaki-Einstein spaces.

  6. Mirror symmetry, toric branes and topological string amplitudes as polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Alim, Murad

    2009-07-13

    The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

  7. Mirror symmetry, toric branes and topological string amplitudes as polynomials

    International Nuclear Information System (INIS)

    Alim, Murad

    2009-01-01

    The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

  8. The Perspective on Data and Control Flow Analysis in Topological Functioning Models by Petri Nets

    Directory of Open Access Journals (Sweden)

    Asnina Erika

    2014-12-01

    Full Text Available The perspective on integration of two mathematical formalisms, i.e., Colored Petri Nets (CPNs and Topological Functioning Model (TFM, is discussed in the paper. The roots of CPNs are in modeling system functionality. The TFM joins principles of system theory and algebraic topology, and formally bridges the solution domain with the problem domain. It is a base for further automated construction of software design models. The paper discusses a perspective on check of control and data flows in the TFM by CPNs formalism. The research result is definition of mappings from TFMs to CPNs.

  9. Construction of Scaling Partitions of Unity

    Directory of Open Access Journals (Sweden)

    Ole Christensen

    2017-11-01

    Full Text Available Partitions of unity in ℝd formed by (matrix scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the functions and matrices yielding such a partition of unity. For expanding matrices, the characterization leads to easy ways of constructing appropriate functions with attractive properties like high regularity and small support. We also discuss a class of integral transforms that map functions having the partition of unity property to functions with the same property. The one-dimensional version of the transform allows a direct definition of a class of nonuniform splines with properties that are parallel to those of the classical B-splines. The results are illustrated with the construction of dual pairs of wavelet frames.

  10. Topological nearly entropy

    Science.gov (United States)

    Gulamsarwar, Syazwani; Salleh, Zabidin

    2017-08-01

    The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

  11. Large scale genomic reorganization of topological domains at the HoxD locus.

    Science.gov (United States)

    Fabre, Pierre J; Leleu, Marion; Mormann, Benjamin H; Lopez-Delisle, Lucille; Noordermeer, Daan; Beccari, Leonardo; Duboule, Denis

    2017-08-07

    The transcriptional activation of HoxD genes during mammalian limb development involves dynamic interactions with two topologically associating domains (TADs) flanking the HoxD cluster. In particular, the activation of the most posterior HoxD genes in developing digits is controlled by regulatory elements located in the centromeric TAD (C-DOM) through long-range contacts. To assess the structure-function relationships underlying such interactions, we measured compaction levels and TAD discreteness using a combination of chromosome conformation capture (4C-seq) and DNA FISH. We assessed the robustness of the TAD architecture by using a series of genomic deletions and inversions that impact the integrity of this chromatin domain and that remodel long-range contacts. We report multi-partite associations between HoxD genes and up to three enhancers. We find that the loss of native chromatin topology leads to the remodeling of TAD structure following distinct parameters. Our results reveal that the recomposition of TAD architectures after large genomic re-arrangements is dependent on a boundary-selection mechanism in which CTCF mediates the gating of long-range contacts in combination with genomic distance and sequence specificity. Accordingly, the building of a recomposed TAD at this locus depends on distinct functional and constitutive parameters.

  12. Self-similar structure in the distribution and density of the partition function zeros

    International Nuclear Information System (INIS)

    Huang, M.-C.; Luo, Y.-P.; Liaw, T.-M.

    2003-01-01

    Based on the knowledge of the partition function zeros for the cell-decorated triangular Ising model, we analyze the similar structures contained in the distribution pattern and density function of the zeros. The two own the same symmetries, and the arising of the similar structure in the road toward the infinite decoration-level is exhibited explicitly. The distinct features of the formation of the self-similar structure revealed from this model may be quite general

  13. Effect of video server topology on contingency capacity requirements

    Science.gov (United States)

    Kienzle, Martin G.; Dan, Asit; Sitaram, Dinkar; Tetzlaff, William H.

    1996-03-01

    Video servers need to assign a fixed set of resources to each video stream in order to guarantee on-time delivery of the video data. If a server has insufficient resources to guarantee the delivery, it must reject the stream request rather than slowing down all existing streams. Large scale video servers are being built as clusters of smaller components, so as to be economical, scalable, and highly available. This paper uses a blocking model developed for telephone systems to evaluate video server cluster topologies. The goal is to achieve high utilization of the components and low per-stream cost combined with low blocking probability and high user satisfaction. The analysis shows substantial economies of scale achieved by larger server images. Simple distributed server architectures can result in partitioning of resources with low achievable resource utilization. By comparing achievable resource utilization of partitioned and monolithic servers, we quantify the cost of partitioning. Next, we present an architecture for a distributed server system that avoids resource partitioning and results in highly efficient server clusters. Finally, we show how, in these server clusters, further optimizations can be achieved through caching and batching of video streams.

  14. N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

    International Nuclear Information System (INIS)

    Blau, M.; Thompson, G.

    1991-11-01

    Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number χ (M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number χ (M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs

  15. Analyzing Dynamic Probabilistic Risk Assessment Data through Topology-Based Clustering

    Energy Technology Data Exchange (ETDEWEB)

    Diego Mandelli; Dan Maljovec; BeiWang; Valerio Pascucci; Peer-Timo Bremer

    2013-09-01

    We investigate the use of a topology-based clustering technique on the data generated by dynamic event tree methodologies. The clustering technique we utilizes focuses on a domain-partitioning algorithm based on topological structures known as the Morse-Smale complex, which partitions the data points into clusters based on their uniform gradient flow behavior. We perform both end state analysis and transient analysis to classify the set of nuclear scenarios. We demonstrate our methodology on a dataset generated for a sodium-cooled fast reactor during an aircraft crash scenario. The simulation tracks the temperature of the reactor as well as the time for a recovery team to fix the passive cooling system. Combined with clustering results obtained previously through mean shift methodology, we present the user with complementary views of the data that help illuminate key features that may be otherwise hidden using a single methodology. By clustering the data, the number of relevant test cases to be selected for further analysis can be drastically reduced by selecting a representative from each cluster. Identifying the similarities of simulations within a cluster can also aid in the drawing of important conclusions with respect to safety analysis.

  16. Conformal partition functions of critical percolation from D 3 thermodynamic Bethe Ansatz equations

    Science.gov (United States)

    Morin-Duchesne, Alexi; Klümper, Andreas; Pearce, Paul A.

    2017-08-01

    Using the planar Temperley-Lieb algebra, critical bond percolation on the square lattice can be reformulated as a loop model. In this form, it is incorporated as {{ L}}{{ M}}(2, 3) in the Yang-Baxter integrable family of logarithmic minimal models {{ L}}{{ M}}( p, p\\prime) . We consider this model of percolation in the presence of boundaries and with periodic boundary conditions. Inspired by Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite Y-system of functional equations. In this way, we obtain nonlinear integral equations in the form of a closed finite set of TBA equations described by a D 3 Dynkin diagram. Following the methods of Klümper and Pearce, we solve the TBA equations for the conformal finite-size corrections. For the ground states of the standard modules on the strip, these agree with the known central charge c  =  0 and conformal weights Δ1, s for \\renewcommand≥≥slant} s\\in {{ Z}≥slant 1} with Δr, s=\\big((3r-2s){\\hspace{0pt}}^2-1\\big)/24 . For the periodic case, the finite-size corrections agree with the conformal weights Δ0, s , Δ1, s with \\renewcommand{≥{≥slant} s\\in\\frac{1}{2}{{ Z}≥slant 0} . These are obtained analytically using Rogers dilogarithm identities. We incorporate all finite excitations by formulating empirical selection rules for the patterns of zeros of all the eigenvalues of the standard modules. We thus obtain the conformal partition functions on the cylinder and the modular invariant partition function (MIPF) on the torus. By applying q-binomial and q-Narayana identities, it is shown that our refined finitized characters on the strip agree with those of Pearce, Rasmussen and Zuber. For percolation on the torus, the MIPF is a non-diagonal sesquilinear form in affine u(1) characters given by the u(1) partition function Z2, 3(q)=Z2, 3{Circ}(q) . The u(1) operator content is {{ N}}Δ, \\barΔ=1 for Δ=\\barΔ=-\\frac{1}{24}, \\frac{35}{24} and {{ N}}Δ, \\barΔ=2 for

  17. Graph theoretical analysis reveals disrupted topological properties of whole brain functional networks in temporal lobe epilepsy.

    Science.gov (United States)

    Wang, Junjing; Qiu, Shijun; Xu, Yong; Liu, Zhenyin; Wen, Xue; Hu, Xiangshu; Zhang, Ruibin; Li, Meng; Wang, Wensheng; Huang, Ruiwang

    2014-09-01

    Temporal lobe epilepsy (TLE) is one of the most common forms of drug-resistant epilepsy. Previous studies have indicated that the TLE-related impairments existed in extensive local functional networks. However, little is known about the alterations in the topological properties of whole brain functional networks. In this study, we acquired resting-state BOLD-fMRI (rsfMRI) data from 26 TLE patients and 25 healthy controls, constructed their whole brain functional networks, compared the differences in topological parameters between the TLE patients and the controls, and analyzed the correlation between the altered topological properties and the epilepsy duration. The TLE patients showed significant increases in clustering coefficient and characteristic path length, but significant decrease in global efficiency compared to the controls. We also found altered nodal parameters in several regions in the TLE patients, such as the bilateral angular gyri, left middle temporal gyrus, right hippocampus, triangular part of left inferior frontal gyrus, left inferior parietal but supramarginal and angular gyri, and left parahippocampus gyrus. Further correlation analysis showed that the local efficiency of the TLE patients correlated positively with the epilepsy duration. Our results indicated the disrupted topological properties of whole brain functional networks in TLE patients. Our findings indicated the TLE-related impairments in the whole brain functional networks, which may help us to understand the clinical symptoms of TLE patients and offer a clue for the diagnosis and treatment of the TLE patients. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

  18. Topological gravity with minimal matter

    International Nuclear Information System (INIS)

    Li Keke

    1991-01-01

    Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)

  19. Grand partition function in field theory with applications to sine-Gordon field theory

    International Nuclear Information System (INIS)

    Samuel, S.

    1978-01-01

    Certain relativistic field theories are shown to be equivalent to the grand partition function of an interacting gas. Using the physical insight given by this analogy many field-theoretic results are obtained, particularly for the sine-Gordon field theory. The main results are enumerated in the summary to which the reader is referred

  20. Comparing Transformation Possibilities of Topological Functioning Model and BPMN in the Context of Model Driven Architecture

    Directory of Open Access Journals (Sweden)

    Solomencevs Artūrs

    2016-05-01

    Full Text Available The approach called “Topological Functioning Model for Software Engineering” (TFM4SE applies the Topological Functioning Model (TFM for modelling the business system in the context of Model Driven Architecture. TFM is a mathematically formal computation independent model (CIM. TFM4SE is compared to an approach that uses BPMN as a CIM. The comparison focuses on CIM modelling and on transformation to UML Sequence diagram on the platform independent (PIM level. The results show the advantages and drawbacks the formalism of TFM brings into the development.

  1. Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Kaiwen [Department of Mathematics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China); Wang, Xin; Huang, Min-xin [Interdisciplinary Center for Theoretical Study,Department of Modern Physics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China)

    2017-01-16

    We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant ℏ and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ℂ{sup 3}/ℤ{sub 5} orbifold and several SU(N) geometries. We also give a proof for some models at ℏ=2π/k.

  2. Acoustic inverse scattering using topological derivative of far-field measurements-based L2 cost functionals

    International Nuclear Information System (INIS)

    Bellis, Cédric; Bonnet, Marc; Cakoni, Fioralba

    2013-01-01

    Originally formulated in the context of topology optimization, the concept of topological derivative has also proved effective as a qualitative inversion tool for a wave-based identification of finite-sized objects. This approach remains, however, largely based on a heuristic interpretation of the topological derivative, whereas most other qualitative approaches to inverse scattering are backed by a mathematical justification. As an effort toward bridging this gap, this study focuses on a topological derivative approach applied to the L 2 -norm of the misfit between far-field measurements. Either an inhomogeneous medium or a finite number of point-like scatterers are considered, using either the Born approximation or a full-scattering model. Topological derivative-based imaging functionals are analyzed using a suitable factorization of the far-field operator, for each of the considered cases, in order to characterize their behavior and assess their ability to reconstruct the unknown scatterer(s). Results include the justification of the usual sign heuristic underpinning the method for (i) the Born approximation and (ii) full-scattering models limited to moderately strong scatterers. Semi-analytical and numerical examples are presented. Within the chosen framework, the topological derivative approach is finally discussed and compared to other well-known qualitative methods. (paper)

  3. Topologies on the algebra of test functions in quantum field theory

    International Nuclear Information System (INIS)

    Hofmann, G.

    1982-01-01

    The algebraic structure of the tensor algebra over the Schwartz spce defines two topologies. The properties of the locally convex topologies situated between the topologies defined above are studied and the families of topologies for which the positive cone is normal or non-normal are constructed

  4. Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

    International Nuclear Information System (INIS)

    Rubio, Wilfredo Montealegre; Paulino, Glaucio H; Silva, Emilio Carlos Nelli

    2011-01-01

    Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures—FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method

  5. Partition functions in even dimensional AdS via quasinormal mode methods

    International Nuclear Information System (INIS)

    Keeler, Cynthia; Ng, Gim Seng

    2014-01-01

    In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension Δ) in even-dimensional AdS d+1 space, using the quasinormal mode method developed in http://dx.doi.org/10.1088/0264-9381/27/12/125001 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane H 2 , we find a series of zero modes for negative real values of Δ whose presence indicates a series of poles in the one-loop partition function Z(Δ) in the Δ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in http://dx.doi.org/10.1088/0264-9381/27/12/125001. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. http://dx.doi.org/10.1007/JHEP11(2011)010 and Banerjee et al. http://dx.doi.org/10.1007/JHEP03(2011)147. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS 2 black hole. They are also interpretable as matrix elements of the discrete series representations of SO(2,1) in the space of smooth functions on S 1 . We generalize our results to general even dimensional AdS 2n , again finding a series of zero modes which are related to discrete series representations of SO(2n,1), the motion group of H 2n .

  6. The Application of the Weighted k-Partite Graph Problem to the Multiple Alignment for Metabolic Pathways.

    Science.gov (United States)

    Chen, Wenbin; Hendrix, William; Samatova, Nagiza F

    2017-12-01

    The problem of aligning multiple metabolic pathways is one of very challenging problems in computational biology. A metabolic pathway consists of three types of entities: reactions, compounds, and enzymes. Based on similarities between enzymes, Tohsato et al. gave an algorithm for aligning multiple metabolic pathways. However, the algorithm given by Tohsato et al. neglects the similarities among reactions, compounds, enzymes, and pathway topology. How to design algorithms for the alignment problem of multiple metabolic pathways based on the similarity of reactions, compounds, and enzymes? It is a difficult computational problem. In this article, we propose an algorithm for the problem of aligning multiple metabolic pathways based on the similarities among reactions, compounds, enzymes, and pathway topology. First, we compute a weight between each pair of like entities in different input pathways based on the entities' similarity score and topological structure using Ay et al.'s methods. We then construct a weighted k-partite graph for the reactions, compounds, and enzymes. We extract a mapping between these entities by solving the maximum-weighted k-partite matching problem by applying a novel heuristic algorithm. By analyzing the alignment results of multiple pathways in different organisms, we show that the alignments found by our algorithm correctly identify common subnetworks among multiple pathways.

  7. Topological amplitudes in string theory

    International Nuclear Information System (INIS)

    Antoniadis, I.; Taylor, T.R.

    1993-07-01

    We show that certain type II string amplitudes at genus g are given by the topological partition F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form Σ g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings. (author). 22 refs, 2 figs

  8. Topological characteristics of multi-valued maps and Lipschitzian functionals

    International Nuclear Information System (INIS)

    Klimov, V S

    2008-01-01

    This paper deals with the operator inclusion O element of F(x)+N Q (x), where F is a multi-valued map of monotonic type from a reflexive space V to its conjugate V * and N Q is the cone normal to the closed set Q, which, generally speaking, is not convex. To estimate the number of solutions of this inclusion we introduce topological characteristics of multi-valued maps and Lipschitzian functionals that have the properties of additivity and homotopy invariance. We prove some infinite-dimensional versions of the Poincare-Hopf theorem

  9. The role of a topologically conserved isoleucine in glutathione transferase structure, stability and function

    International Nuclear Information System (INIS)

    Achilonu, Ikechukwu; Gildenhuys, Samantha; Fisher, Loren; Burke, Jonathan; Fanucchi, Sylvia; Sewell, B. Trevor; Fernandes, Manuel; Dirr, Heini W.

    2010-01-01

    The role of a topologically conserved isoleucine in the structure of glutathione transferase was investigated by replacing the Ile71 residue in human GSTA1-1 by alanine or valine. The common fold shared by members of the glutathione-transferase (GST) family has a topologically conserved isoleucine residue at the N-terminus of helix 3 which is involved in the packing of helix 3 against two β-strands in domain 1. The role of the isoleucine residue in the structure, function and stability of GST was investigated by replacing the Ile71 residue in human GSTA1-1 by alanine or valine. The X-ray structures of the I71A and I71V mutants resolved at 1.75 and 2.51 Å, respectively, revealed that the mutations do not alter the overall structure of the protein compared with the wild type. Urea-induced equilibrium unfolding studies using circular dichroism and tryptophan fluorescence suggest that the mutation of Ile71 to alanine or valine reduces the stability of the protein. A functional assay with 1-chloro-2,4-dinitrobenzene shows that the mutation does not significantly alter the function of the protein relative to the wild type. Overall, the results suggest that conservation of the topologically conserved Ile71 maintains the structural stability of the protein but does not play a significant role in catalysis and substrate binding

  10. Finiteness of Lorentzian 10j symbols and partition functions

    International Nuclear Information System (INIS)

    Christensen, J Daniel

    2006-01-01

    We give a short and simple proof that the Lorentzian 10j symbol, which forms a key part of the Barrett-Crane model of Lorentzian quantum gravity, is finite. The argument is very general, and applies to other integrals. For example, we show that the Lorentzian and Riemannian causal 10j symbols are finite, despite their singularities. Moreover, we show that integrals that arise in Cherrington's work are finite. Cherrington has shown that this implies that the Lorentzian partition function for a single triangulation is finite, even for degenerate triangulations. Finally, we also show how to use these methods to prove finiteness of integrals based on other graphs and other homogeneous domains

  11. Classification algorithms using adaptive partitioning

    KAUST Repository

    Binev, Peter; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald

    2014-01-01

    © 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.

  12. Classification algorithms using adaptive partitioning

    KAUST Repository

    Binev, Peter

    2014-12-01

    © 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.

  13. Disrupted topological organization of resting-state functional brain network in subcortical vascular mild cognitive impairment.

    Science.gov (United States)

    Yi, Li-Ye; Liang, Xia; Liu, Da-Ming; Sun, Bo; Ying, Sun; Yang, Dong-Bo; Li, Qing-Bin; Jiang, Chuan-Lu; Han, Ying

    2015-10-01

    Neuroimaging studies have demonstrated both structural and functional abnormalities in widespread brain regions in patients with subcortical vascular mild cognitive impairment (svMCI). However, whether and how these changes alter functional brain network organization remains largely unknown. We recruited 21 patients with svMCI and 26 healthy control (HC) subjects who underwent resting-state functional magnetic resonance imaging scans. Graph theory-based network analyses were used to investigate alterations in the topological organization of functional brain networks. Compared with the HC individuals, the patients with svMCI showed disrupted global network topology with significantly increased path length and modularity. Modular structure was also impaired in the svMCI patients with a notable rearrangement of the executive control module, where the parietal regions were split out and grouped as a separate module. The svMCI patients also revealed deficits in the intra- and/or intermodule connectivity of several brain regions. Specifically, the within-module degree was decreased in the middle cingulate gyrus while it was increased in the left anterior insula, medial prefrontal cortex and cuneus. Additionally, increased intermodule connectivity was observed in the inferior and superior parietal gyrus, which was associated with worse cognitive performance in the svMCI patients. Together, our results indicate that svMCI patients exhibit dysregulation of the topological organization of functional brain networks, which has important implications for understanding the pathophysiological mechanism of svMCI. © 2015 John Wiley & Sons Ltd.

  14. Replica analysis of partition-function zeros in spin-glass models

    International Nuclear Information System (INIS)

    Takahashi, Kazutaka

    2011-01-01

    We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distributions of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.

  15. Different alterations in brain functional networks according to direct and indirect topological connections in patients with schizophrenia.

    Science.gov (United States)

    Park, Chang-Hyun; Lee, Seungyup; Kim, Taewon; Won, Wang Yeon; Lee, Kyoung-Uk

    2017-10-01

    Schizophrenia displays connectivity deficits in the brain, but the literature has shown inconsistent findings about alterations in global efficiency of brain functional networks. We supposed that such inconsistency at the whole brain level may be due to a mixture of different portions of global efficiency at sub-brain levels. Accordingly, we considered measuring portions of global efficiency in two aspects: spatial portions by considering sub-brain networks and topological portions by considering contributions to global efficiency according to direct and indirect topological connections. We proposed adjacency and indirect adjacency as new network parameters attributable to direct and indirect topological connections, respectively, and applied them to graph-theoretical analysis of brain functional networks constructed from resting state fMRI data of 22 patients with schizophrenia and 22 healthy controls. Group differences in the network parameters were observed not for whole brain and hemispheric networks, but for regional networks. Alterations in adjacency and indirect adjacency were in opposite directions, such that adjacency increased, but indirect adjacency decreased in patients with schizophrenia. Furthermore, over connections in frontal and parietal regions, increased adjacency was associated with more severe negative symptoms, while decreased adjacency was associated with more severe positive symptoms of schizophrenia. This finding indicates that connectivity deficits associated with positive and negative symptoms of schizophrenia may involve topologically different paths in the brain. In patients with schizophrenia, although changes in global efficiency may not be clearly shown, different alterations in brain functional networks according to direct and indirect topological connections could be revealed at the regional level. Copyright © 2017 Elsevier B.V. All rights reserved.

  16. Partitioning of functional and taxonomic diversity in surface-associated microbial communities.

    Science.gov (United States)

    Roth-Schulze, Alexandra J; Zozaya-Valdés, Enrique; Steinberg, Peter D; Thomas, Torsten

    2016-12-01

    Surfaces, including those submerged in the marine environment, are subjected to constant interactions and colonisation by surrounding microorganisms. The principles that determine the assembly of those epibiotic communities are however poorly understood. In this study, we employed a hierarchical design to assess the functionality and diversity of microbial communities on different types of host surfaces (e.g. macroalgae, seagrasses). We found that taxonomic diversity was unique to each type of host, but that the majority of functions (> 95%) could be found in any given surface community, suggesting a high degree of functional redundancy. However, some community functions were enriched on certain surfaces and were related to host-specific properties (e.g. the degradation of specific polysaccharides). Together these observations support a model, whereby communities on surfaces are assembled from guilds of microorganisms with a functionality that is partitioned into general properties for a surface-associated life-style, but also specific features that mediate host-specificity. © 2016 Society for Applied Microbiology and John Wiley & Sons Ltd.

  17. Chamber identity programs drive early functional partitioning of the heart.

    Science.gov (United States)

    Mosimann, Christian; Panáková, Daniela; Werdich, Andreas A; Musso, Gabriel; Burger, Alexa; Lawson, Katy L; Carr, Logan A; Nevis, Kathleen R; Sabeh, M Khaled; Zhou, Yi; Davidson, Alan J; DiBiase, Anthony; Burns, Caroline E; Burns, C Geoffrey; MacRae, Calum A; Zon, Leonard I

    2015-08-26

    The vertebrate heart muscle (myocardium) develops from the first heart field (FHF) and expands by adding second heart field (SHF) cells. While both lineages exist already in teleosts, the primordial contributions of FHF and SHF to heart structure and function remain incompletely understood. Here we delineate the functional contribution of the FHF and SHF to the zebrafish heart using the cis-regulatory elements of the draculin (drl) gene. The drl reporters initially delineate the lateral plate mesoderm, including heart progenitors. Subsequent myocardial drl reporter expression restricts to FHF descendants. We harnessed this unique feature to uncover that loss of tbx5a and pitx2 affect relative FHF versus SHF contributions to the heart. High-resolution physiology reveals distinctive electrical properties of each heart field territory that define a functional boundary within the single zebrafish ventricle. Our data establish that the transcriptional program driving cardiac septation regulates physiologic ventricle partitioning, which successively provides mechanical advantages of sequential contraction.

  18. Plane partition vesicles

    International Nuclear Information System (INIS)

    Rensburg, E J Janse van; Ma, J

    2006-01-01

    We examine partitions and their natural three-dimensional generalizations, plane partitions, as models of vesicles undergoing an inflation-deflation transition. The phase diagrams of these models include a critical point corresponding to an inflation-deflation transition, and exhibits multicritical scaling in the vicinity of a multicritical point located elsewhere on the critical curve. We determine the locations of the multicritical points by analysing the generating functions using analytic and numerical means. In addition, we determine the numerical values of the multicritical scaling exponents associated with the multicritical scaling regimes in these models

  19. An introduction to topological Yang-Mills theory

    International Nuclear Information System (INIS)

    Baal, P. van; Rijksuniversiteit Utrecht

    1990-01-01

    In these lecture notes I give a ''historical'' introduction to topological gauge theories. My main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. I show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the infinite dimensional space of gauge connections, with the Chern-Simons functional as the appriopriate Morse function(al). I therefore discuss the De Rham cohomology, Hodge theory, Morse theory, Floer homology, Witten's construction of the Lagrangian for topological gauge theory, the subsequent BRST formulation of topological quantum field theory and finally Witten's construction of the Donaldson polynomials. (author)

  20. Topology optimization based on spline-based meshfree method using topological derivatives

    International Nuclear Information System (INIS)

    Hur, Junyoung; Youn, Sung-Kie; Kang, Pilseong

    2017-01-01

    Spline-based meshfree method (SBMFM) is originated from the Isogeometric analysis (IGA) which integrates design and analysis through Non-uniform rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.

  1. Topology optimization based on spline-based meshfree method using topological derivatives

    Energy Technology Data Exchange (ETDEWEB)

    Hur, Junyoung; Youn, Sung-Kie [KAIST, Daejeon (Korea, Republic of); Kang, Pilseong [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)

    2017-05-15

    Spline-based meshfree method (SBMFM) is originated from the Isogeometric analysis (IGA) which integrates design and analysis through Non-uniform rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.

  2. Topological phase transitions of (BixSb1-x)2Se3 alloys by density functional theory.

    Science.gov (United States)

    Abdalla, L B; Padilha José, E; Schmidt, T M; Miwa, R H; Fazzio, A

    2015-07-01

    We have performed an ab initio total energy investigation of the topological phase transition, and the electronic properties of topologically protected surface states of (BixSb1-x)2Se3 alloys. In order to provide an accurate alloy concentration for the phase transition, we have considered the special quasirandom structures to describe the alloy system. The trivial → topological transition concentration was obtained by (i) the calculation of the band gap closing as a function of Bi concentration (x), and (ii) the calculation of the Z2 topological invariant number. We show that there is a topological phase transition, for x around 0.4, verified for both procedures (i) and (ii). We also show that in the concentration range 0.4 x < 0.7, the alloy does not present any other band at the Fermi level besides the Dirac cone, where the Dirac point is far from the bulk states. This indicates that a possible suppression of the scattering process due to bulk states will occur.

  3. Off-critical local height probabilities on a plane and critical partition functions on a cylinder

    Directory of Open Access Journals (Sweden)

    Omar Foda

    2018-03-01

    Full Text Available We compute off-critical local height probabilities in regime-III restricted solid-on-solid models in a 4N-quadrant spiral geometry, with periodic boundary conditions in the angular direction, and fixed boundary conditions in the radial direction, as a function of N, the winding number of the spiral, and τ, the departure from criticality of the model, and observe that the result depends only on the product Nτ. In the limit N→1, τ→τ0, such that τ0 is finite, we recover the off-critical local height probability on a plane, τ0-away from criticality. In the limit N→∞, τ→0, such that Nτ=τ0 is finite, and following a conformal transformation, we obtain a critical partition function on a cylinder of aspect-ratio τ0. We conclude that the off-critical local height probability on a plane, τ0-away from criticality, is equal to a critical partition function on a cylinder of aspect-ratio τ0, in agreement with a result of Saleur and Bauer.

  4. Correlation functions in topological Yang-Mills theory with two fermionic charges

    International Nuclear Information System (INIS)

    Marculescu, S.

    1997-01-01

    The solution of the Donaldson cohomology problem for the topological Yang-Mills theory with two fermionic symmetries needs besides the gauge field and its descendants additional fields, hereafter called ascendants of the gauge field. It is shown that the dependence of the ascendants disappears in the all the correlation functions. This property allows one for the usual interpretation of the Donaldson invariants as cocycles of the instanton moduli space. (orig.)

  5. Partition functions of classical Heisenberg spin chains with arbitrary and different exchange

    International Nuclear Information System (INIS)

    Cregg, P J; GarcIa-Palacios, J L; Svedlindh, P

    2008-01-01

    The classical Heisenberg model has been effective in modelling exchange interactions in molecular magnets. In this model, the partition function is important as it allows the calculation of the magnetization and susceptibility. For an ensemble of N-spin sites, this typically involves integrals in 2N dimensions. Here, for two-, three- and four-spin nearest neighbour open linear Heisenberg chains these integrals are reduced to sums of known functions, using a result due to Gegenbauer. For the case of the three- and four-spin chains, the sums are equivalent in form to the results of Joyce. The general result for an N-spin chain is also obtained

  6. Topologically convergent and divergent functional connectivity patterns in unmedicated unipolar depression and bipolar disorder.

    Science.gov (United States)

    Wang, Y; Wang, J; Jia, Y; Zhong, S; Zhong, M; Sun, Y; Niu, M; Zhao, L; Zhao, L; Pan, J; Huang, L; Huang, R

    2017-07-04

    Bipolar disorder (BD), particularly BD II, is frequently misdiagnosed as unipolar depression (UD), leading to inappropriate treatment and poor clinical outcomes. Although depressive symptoms may be expressed similarly in UD and BD, the similarities and differences in the architecture of brain functional networks between the two disorders are still unknown. In this study, we hypothesized that UD and BD II patients would show convergent and divergent patterns of disrupted topological organization of the functional connectome, especially in the default mode network (DMN) and the limbic network. Brain resting-state functional magnetic resonance imaging (fMRI) data were acquired from 32 UD-unmedicated patients, 31 unmedicated BD II patients (current episode depressed) and 43 healthy subjects. Using graph theory, we systematically studied the topological organization of their whole-brain functional networks at the following three levels: whole brain, modularity and node. First, both the UD and BD II patients showed increased characteristic path length and decreased global efficiency compared with the controls. Second, both the UD and BD II patients showed disrupted intramodular connectivity within the DMN and limbic system network. Third, decreased nodal characteristics (nodal strength and nodal efficiency) were found predominantly in brain regions in the DMN, limbic network and cerebellum of both the UD and BD II patients, whereas differences between the UD and BD II patients in the nodal characteristics were also observed in the precuneus and temporal pole. Convergent deficits in the topological organization of the whole brain, DMN and limbic networks may reflect overlapping pathophysiological processes in unipolar and bipolar depression. Our discovery of divergent regional connectivity that supports emotion processing could help to identify biomarkers that will aid in differentiating these disorders.

  7. Transfer functions for solid solution partitioning of cadmium for Australian soils

    NARCIS (Netherlands)

    Vries, de W.; Mc Laughlin, M.J.; Groenenberg, J.E.

    2011-01-01

    To assess transport and ecotoxicological risks of metals, such as cadmium (Cd) in soils, models are needed for partitioning and speciation. We derived regression-based “partition-relations” based on adsorption and desorption experiments for main Australian soil types. First, batch adsorption

  8. Partitioning taxonomic diversity of aquatic insect assemblages and functional feeding groups in Neotropical Savanna headwater streams

    Science.gov (United States)

    Biological diversity can be divided into: alpha (α, local), beta (β, difference in assemblage composition among locals), and gamma (γ, total diversity). We assessed the partitioning of taxonomic diversity of Ephemeroptera, Plecoptera and Trichoptera (EPT) and of functional feedin...

  9. Coding Partitions

    Directory of Open Access Journals (Sweden)

    Fabio Burderi

    2007-05-01

    Full Text Available Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD, we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ``unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguouscomponent and other (if any totally ambiguouscomponents. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes.

  10. Real topological string amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Narain, K.S. [The Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Piazzalunga, N. [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794-3636 (United States); International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy); Tanzini, A. [International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy)

    2017-03-15

    We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G{sub χ}, at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g{sup ′}=−χ+1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F{sub g}.

  11. Topological phases of topological-insulator thin films

    Science.gov (United States)

    Asmar, Mahmoud M.; Sheehy, Daniel E.; Vekhter, Ilya

    2018-02-01

    We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as a function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3 . As a result, while the magnitude of the matrix element at the center of the surface Brillouin zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and nontopological phases, separated by semimetallic states, as the film thickness varies. In the topological phase, the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3 , making Bi2Te3 , where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.

  12. Topological rings

    CERN Document Server

    Warner, S

    1993-01-01

    This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.

  13. Partition function expansion on region graphs and message-passing equations

    International Nuclear Information System (INIS)

    Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong

    2011-01-01

    Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

  14. Modular relations for the Rogers-Ramanujan-Slater type functions of order fifteen and its applications to partitions

    Directory of Open Access Journals (Sweden)

    Chandrashekar Adiga

    2013-10-01

    Full Text Available In a manuscript of Ramanujan, published with his Lost Notebook [20] there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers-Ramanujan-Slater type functions of order fifteen which are analogues to Ramanujan’s well known forty identities. Furthermore, we give partition theoretic interpretations of two modular relations.

  15. Duality in twisted N=4 supersymmetric gauge theories in four dimensions

    CERN Document Server

    Labastida, J.M.F.; Lozano, Carlos

    1999-01-01

    We consider a twisted version of the four-dimensional N=4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N=4 down to N=2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin four-manifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformations. The partition function transforms in the same way as the one first presented by Vafa and Witten for another twist of the N=4 supersymmetric theory in their strong coupling test of S-duality. Both partition functions coincide on K3. The topological correlation functions turn out to transform covariantly under duality, following a simple pattern which seems to be inherent in a general type of topological quantum field ...

  16. Topological Aspects of Solitons in Ferromagnets

    International Nuclear Information System (INIS)

    Ren Jirong; Wang Jibiao; Li Ran; Xu Donghui; Duan Yishi

    2008-01-01

    Two kinds of topological soliton (skyrmion and magnetic vortex ring) in ferromagnets are studied. They have the common topological origin, a tensor H αβ = n-vector · (∂ α n-vector x ∂ β n-vector ), which describes the non-trivial distribution of local orientation of magnetization n-vector at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings

  17. Cylindric partitions, {{\\boldsymbol{ W }}}_{r} characters and the Andrews-Gordon-Bressoud identities

    Science.gov (United States)

    Foda, O.; Welsh, T. A.

    2016-04-01

    We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin’s product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of {\\hat{{sl}}}r algebras, the {{\\boldsymbol{ M }}}r r,r+d minimal model characters of {{\\boldsymbol{ W }}}r algebras, and the r-string abaci generating functions, providing simple proofs for each. We then set r = 2, and use two-cylindric partitions to re-derive the AGB identities as follows. Firstly, we use Borodin’s product expression for the generating functions of the two-cylindric partitions with infinitely long parts, to obtain the product sides of the AGB identities, times a factor {(q;q)}∞ -1, which is the generating function of ordinary partitions. Next, we obtain a bijection from the two-cylindric partitions, via two-string abaci, into decorated versions of Bressoud’s restricted lattice paths. Extending Bressoud’s method of transforming between restricted paths that obey different restrictions, we obtain sum expressions with manifestly non-negative coefficients for the generating functions of the two-cylindric partitions which contains a factor {(q;q)}∞ -1. Equating the product and sum expressions of the same two-cylindric partitions, and canceling a factor of {(q;q)}∞ -1 on each side, we obtain the AGB identities.

  18. Quark-parton model from dual topological unitarization

    International Nuclear Information System (INIS)

    Cohen-Tannoudji, G.; El Hassouni, A.; Kalinowski, J.; Peschanski, R.

    1979-01-01

    Topology, which occurs in the topological expansion of quantum chromodynamics (QCD) and in the dual topological unitarization (DTU) schemes, allows us to establish a quantitative correspondence between QCD and the dual S-matrix approaches. This topological correspondence, proposed by Veneziano and made more explicit in a recent paper for current-induced reactions, provides a clarifying and unifying quark-parton interpretation of soft inclusive processes. Precise predictions for inclusive cross sections in hadron-hadron collisions, structure functions of hadrons, and quark fragmentation functions including absolute normalizations are shown to agree with data. On a more theoretical ground the proposed scheme suggests a new approach to the confinement problem

  19. Comparative evaluation of community detection algorithms: a topological approach

    International Nuclear Information System (INIS)

    Orman, Günce Keziban; Labatut, Vincent; Cherifi, Hocine

    2012-01-01

    Community detection is one of the most active fields in complex network analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing the network structure in such cohesive subgroups to be revealed. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand index, normalized mutual information, etc). However, this type of comparison neglects the topological properties of the communities. In this paper, we present a comprehensive comparative study of a representative set of community detection methods, in which we adopt both types of evaluation. Community-oriented topological measures are used to qualify the communities and evaluate their deviation from the reference structure. In order to mimic real-world systems, we use artificially generated realistic networks. It turns out there is no equivalence between the two approaches: a high performance does not necessarily correspond to correct topological properties, and vice versa. They can therefore be considered as complementary, and we recommend applying both of them in order to perform a complete and accurate assessment. (paper)

  20. Network topology and functional connectivity disturbances precede the onset of Huntington's disease.

    Science.gov (United States)

    Harrington, Deborah L; Rubinov, Mikail; Durgerian, Sally; Mourany, Lyla; Reece, Christine; Koenig, Katherine; Bullmore, Ed; Long, Jeffrey D; Paulsen, Jane S; Rao, Stephen M

    2015-08-01

    Cognitive, motor and psychiatric changes in prodromal Huntington's disease have nurtured the emergent need for early interventions. Preventive clinical trials for Huntington's disease, however, are limited by a shortage of suitable measures that could serve as surrogate outcomes. Measures of intrinsic functional connectivity from resting-state functional magnetic resonance imaging are of keen interest. Yet recent studies suggest circumscribed abnormalities in resting-state functional magnetic resonance imaging connectivity in prodromal Huntington's disease, despite the spectrum of behavioural changes preceding a manifest diagnosis. The present study used two complementary analytical approaches to examine whole-brain resting-state functional magnetic resonance imaging connectivity in prodromal Huntington's disease. Network topology was studied using graph theory and simple functional connectivity amongst brain regions was explored using the network-based statistic. Participants consisted of gene-negative controls (n = 16) and prodromal Huntington's disease individuals (n = 48) with various stages of disease progression to examine the influence of disease burden on intrinsic connectivity. Graph theory analyses showed that global network interconnectivity approximated a random network topology as proximity to diagnosis neared and this was associated with decreased connectivity amongst highly-connected rich-club network hubs, which integrate processing from diverse brain regions. However, functional segregation within the global network (average clustering) was preserved. Functional segregation was also largely maintained at the local level, except for the notable decrease in the diversity of anterior insula intermodular-interconnections (participation coefficient), irrespective of disease burden. In contrast, network-based statistic analyses revealed patterns of weakened frontostriatal connections and strengthened frontal-posterior connections that evolved as disease

  1. Topological interpretation of Luttinger theorem

    OpenAIRE

    Seki, Kazuhiro; Yunoki, Seiji

    2017-01-01

    Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...

  2. Development of partitioning method : cold experiment with partitioning test facility in NUCEF (I)

    International Nuclear Information System (INIS)

    Yamaguchi, Isoo; Morita, Yasuji; Kondo, Yasuo

    1996-03-01

    A test facility in which about 1.85 x 10 14 Bq of high-level liquid waste can be treated has been completed in 1994 at Nuclear Fuel Cycle Safety Engineering Research Facility (NUCEF) for research and development of Partitioning Method. The outline of the partitioning test facility and support equipments for it which were design terms, constructions, arrangements, functions and inspections were given in JAERI-Tech 94-030. The present report describes the results of the water transfer test and partitioning tests, which are methods of precipitation by denitration, oxalate precipitation, solvent extraction, and adsorption with inorganic ion exchanger, using nitric acid to master operation method of the test facility. As often as issues related to equipments occurred during the tests, they were improved. As to issues related to processes such as being stopped up of columns, their measures of solution were found by testing in laboratories. They were reflected in operation of the Partitioning Test Facility. Their particulars and improving points were described in this report. (author)

  3. Asymmetry of Hemispheric Network Topology Reveals Dissociable Processes between Functional and Structural Brain Connectome in Community-Living Elders

    Directory of Open Access Journals (Sweden)

    Yu Sun

    2017-11-01

    Full Text Available Human brain is structurally and functionally asymmetrical and the asymmetries of brain phenotypes have been shown to change in normal aging. Recent advances in graph theoretical analysis have showed topological lateralization between hemispheric networks in the human brain throughout the lifespan. Nevertheless, apparent discrepancies of hemispheric asymmetry were reported between the structural and functional brain networks, indicating the potentially complex asymmetry patterns between structural and functional networks in aging population. In this study, using multimodal neuroimaging (resting-state fMRI and structural diffusion tensor imaging, we investigated the characteristics of hemispheric network topology in 76 (male/female = 15/61, age = 70.08 ± 5.30 years community-dwelling older adults. Hemispheric functional and structural brain networks were obtained for each participant. Graph theoretical approaches were then employed to estimate the hemispheric topological properties. We found that the optimal small-world properties were preserved in both structural and functional hemispheric networks in older adults. Moreover, a leftward asymmetry in both global and local levels were observed in structural brain networks in comparison with a symmetric pattern in functional brain network, suggesting a dissociable process of hemispheric asymmetry between structural and functional connectome in healthy older adults. Finally, the scores of hemispheric asymmetry in both structural and functional networks were associated with behavioral performance in various cognitive domains. Taken together, these findings provide new insights into the lateralized nature of multimodal brain connectivity, highlight the potentially complex relationship between structural and functional brain network alterations, and augment our understanding of asymmetric structural and functional specializations in normal aging.

  4. Painlevé equations, topological type property and reconstruction by the topological recursion

    Science.gov (United States)

    Iwaki, K.; Marchal, O.; Saenz, A.

    2018-01-01

    In this article we prove that Lax pairs associated with ħ-dependent six Painlevé equations satisfy the topological type property proposed by Bergère, Borot and Eynard for any generic choice of the monodromy parameters. Consequently we show that one can reconstruct the formal ħ-expansion of the isomonodromic τ-function and of the determinantal formulas by applying the so-called topological recursion to the spectral curve attached to the Lax pair in all six Painlevé cases. Finally we illustrate the former results with the explicit computations of the first orders of the six τ-functions.

  5. The H0 function, a new index for detecting structural/topological complexity information in undirected graphs

    Science.gov (United States)

    Buscema, Massimo; Asadi-Zeydabadi, Masoud; Lodwick, Weldon; Breda, Marco

    2016-04-01

    Significant applications such as the analysis of Alzheimer's disease differentiated from dementia, or in data mining of social media, or in extracting information of drug cartel structural composition, are often modeled as graphs. The structural or topological complexity or lack of it in a graph is quite often useful in understanding and more importantly, resolving the problem. We are proposing a new index we call the H0function to measure the structural/topological complexity of a graph. To do this, we introduce the concept of graph pruning and its associated algorithm that is used in the development of our measure. We illustrate the behavior of our measure, the H0 function, through different examples found in the appendix. These examples indicate that the H0 function contains information that is useful and important characteristics of a graph. Here, we restrict ourselves to undirected.

  6. DTN routing in body sensor networks with dynamic postural partitioning.

    Science.gov (United States)

    Quwaider, Muhannad; Biswas, Subir

    2010-11-01

    This paper presents novel store-and-forward packet routing algorithms for Wireless Body Area Networks ( WBAN ) with frequent postural partitioning. A prototype WBAN has been constructed for experimentally characterizing on-body topology disconnections in the presence of ultra short range radio links, unpredictable RF attenuation, and human postural mobility. On-body DTN routing protocols are then developed using a stochastic link cost formulation, capturing multi-scale topological localities in human postural movements. Performance of the proposed protocols are evaluated experimentally and via simulation, and are compared with a number of existing single-copy DTN routing protocols and an on-body packet flooding mechanism that serves as a performance benchmark with delay lower-bound. It is shown that via multi-scale modeling of the spatio-temporal locality of on-body link disconnection patterns, the proposed algorithms can provide better routing performance compared to a number of existing probabilistic, opportunistic, and utility-based DTN routing protocols in the literature.

  7. Synchronization in complex networks with switching topology

    International Nuclear Information System (INIS)

    Wang, Lei; Wang, Qing-guo

    2011-01-01

    This Letter investigates synchronization issues of complex dynamical networks with switching topology. By constructing a common Lyapunov function, we show that local and global synchronization for a linearly coupled network with switching topology can be evaluated by the time average of second smallest eigenvalues corresponding to the Laplacians of switching topology. This result is quite powerful and can be further used to explore various switching cases for complex dynamical networks. Numerical simulations illustrate the effectiveness of the obtained results in the end. -- Highlights: → Synchronization of complex networks with switching topology is investigated. → A common Lyapunov function is established for synchronization of switching network. → The common Lyapunov function is not necessary to monotonically decrease with time. → Synchronization is determined by the second smallest eigenvalue of its Laplacian. → Synchronization criterion can be used to investigate various switching cases.

  8. Topological insulators and topological superconductors

    CERN Document Server

    Bernevig, Andrei B

    2013-01-01

    This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...

  9. Topological Classification of Morse Functions and Generalisations of Hilbert's 16-th Problem

    International Nuclear Information System (INIS)

    Arnold, Vladimir I.

    2007-01-01

    The topological structures of the generic smooth functions on a smooth manifold belong to the small quantity of the most fundamental objects of study both in pure and applied mathematics. The problem of their study has been formulated by A. Cayley in 1868, who required the classification of the possible configurations of the horizontal lines on the topographical maps of mountain regions, and created the first elements of what is called today 'Morse Theory' and 'Catastrophes Theory'. In the paper we describe this problem, and in particular describe the classification of Morse functions on the 2 sphere and on the torus

  10. Topology Optimization

    DEFF Research Database (Denmark)

    A. Kristensen, Anders Schmidt; Damkilde, Lars

    2007-01-01

    . A way to solve the initial design problem namely finding a form can be solved by so-called topology optimization. The idea is to define a design region and an amount of material. The loads and supports are also fidefined, and the algorithm finds the optimal material distribution. The objective function...... dictates the form, and the designer can choose e.g. maximum stiness, maximum allowable stresses or maximum lowest eigenfrequency. The result of the topology optimization is a relatively coarse map of material layout. This design can be transferred to a CAD system and given the necessary geometrically...... refinements, and then remeshed and reanalysed in other to secure that the design requirements are met correctly. The output of standard topology optimization has seldom well-defined, sharp contours leaving the designer with a tedious interpretation, which often results in less optimal structures. In the paper...

  11. Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces

    Directory of Open Access Journals (Sweden)

    A. A. Salama

    2014-03-01

    Full Text Available In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.

  12. Monolayer group-III monochalcogenides by oxygen functionalization: a promising class of two-dimensional topological insulators

    Science.gov (United States)

    Zhou, Si; Liu, Cheng-Cheng; Zhao, Jijun; Yao, Yugui

    2018-03-01

    Monolayer group-III monochalcogenides (MX, M = Ga, In; X = S, Se, Te), an emerging category of two-dimensional (2D) semiconductors, hold great promise for electronics, optoelectronics and catalysts. By first-principles calculations, we show that the phonon dispersion and Raman spectra, as well as the electronic and topological properties of monolayer MX can be tuned by oxygen functionalization. Chemisorption of oxygen atoms on one side or both sides of the MX sheet narrows or even closes the band gap, enlarges work function, and significantly reduces the carrier effective mass. More excitingly, InS, InSe, and InTe monolayers with double-side oxygen functionalization are 2D topological insulators with sizeable bulk gap up to 0.21 eV. Their low-energy bands near the Fermi level are dominated by the px and py orbitals of atoms, allowing band engineering via in-plane strains. Our studies provide viable strategy for realizing quantum spin Hall effect in monolayer group-III monochalcogenides at room temperature, and utilizing these novel 2D materials for high-speed and dissipationless transport devices.

  13. Voxel Scale Complex Networks of Functional Connectivity in the Rat Brain: Neurochemical State Dependence of Global and Local Topological Properties

    Directory of Open Access Journals (Sweden)

    Adam J. Schwarz

    2012-01-01

    Full Text Available Network analysis of functional imaging data reveals emergent features of the brain as a function of its topological properties. However, the brain is not a homogeneous network, and the dependence of functional connectivity parameters on neuroanatomical substrate and parcellation scale is a key issue. Moreover, the extent to which these topological properties depend on underlying neurochemical changes remains unclear. In the present study, we investigated both global statistical properties and the local, voxel-scale distribution of connectivity parameters of the rat brain. Different neurotransmitter systems were stimulated by pharmacological challenge (d-amphetamine, fluoxetine, and nicotine to discriminate between stimulus-specific functional connectivity and more general features of the rat brain architecture. Although global connectivity parameters were similar, mapping of local connectivity parameters at high spatial resolution revealed strong neuroanatomical dependence of functional connectivity in the rat brain, with clear differentiation between the neocortex and older brain regions. Localized foci of high functional connectivity independent of drug challenge were found in the sensorimotor cortices, consistent with the high neuronal connectivity in these regions. Conversely, the topological properties and node roles in subcortical regions varied with neurochemical state and were dependent on the specific dynamics of the different functional processes elicited.

  14. Yang-Lee zeros for a Potts model of helix-coil transition with nontrivial topology

    International Nuclear Information System (INIS)

    Ananikian, N.; Ananikyan, L.; Artuso, R.; Sargsyan, K.

    2007-07-01

    The Yang-Lee partition function zeros of the Q-state Potts model on a zigzag ladder are studied by a transfer-matrix approach. This Q-state model has a non-trivial topology induced by three-site interactions on a zigzag ladder and is proposed as a description of helix-coil transition in homo-polymers. The Yang-Lee zeros are associated to complex values of the solvent-related coupling constant K (magnetic field) and they are exactly derived for arbitrary values of the system parameters: Q, J (coupling constant of hydrogen binding) and temperature. It is shown that there is only a quasi-phase transition for all temperatures. The densities of the Yang-Lee zeros are singular at the edge singularity points and the critical exponent σ = -1/2. (author)

  15. Weakly interacting topological insulators: Quantum criticality and the renormalization group approach

    Science.gov (United States)

    Chen, Wei

    2018-03-01

    For D -dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D - or (D +1 ) -dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.

  16. Topological orbifold models and quantum cohomology rings

    International Nuclear Information System (INIS)

    Zaslow, E.

    1993-01-01

    We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of CP 1 by the dihedral group D 4 , how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral CP 1 orbifolds. We then consider CP 2 /D 4 , and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds. (orig.)

  17. Hashing for Statistics over K-Partitions

    DEFF Research Database (Denmark)

    Dahlgaard, Soren; Knudsen, Mathias Baek Tejs; Rotenberg, Eva

    2015-01-01

    In this paper we analyze a hash function for k-partitioning a set into bins, obtaining strong concentration bounds for standard algorithms combining statistics from each bin. This generic method was originally introduced by Flajolet and Martin [FOCS'83] in order to save a factor Ω(k) of time per...... concentration bounds on the most popular applications of k-partitioning similar to those we would get using a truly random hash function. The analysis is very involved and implies several new results of independent interest for both simple and double tabulation, e.g. A simple and efficient construction...

  18. Renormalization of topological field theory

    International Nuclear Information System (INIS)

    Birmingham, D.; Rakowski, M.; Thompson, G.

    1988-11-01

    One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs

  19. 2D CFT partition functions at late times

    Science.gov (United States)

    Dyer, Ethan; Gur-Ari, Guy

    2017-08-01

    We consider the late time behavior of the analytically continued partition function Z( β + it) Z( β - it) in holographic 2 d CFTs. This is a probe of information loss in such theories and in their holographic duals. We show that each Virasoro character decays in time, and so information is not restored at the level of individual characters. We identify a universal decaying contribution at late times, and conjecture that it describes the behavior of generic chaotic 2 d CFTs out to times that are exponentially large in the central charge. It was recently suggested that at sufficiently late times one expects a crossover to random matrix behavior. We estimate an upper bound on the crossover time, which suggests that the decay is followed by a parametrically long period of late time growth. Finally, we discuss gravitationally-motivated integrable theories and show how information is restored at late times by a series of characters. This hints at a possible bulk mechanism, where information is restored by an infinite sum over non-perturbative saddles.

  20. Partitioning inter annual variability in net ecosystem exchange between climatic variability and functional change

    International Nuclear Information System (INIS)

    Hui, D.; Luo, Y.; Katul, G.

    2003-01-01

    Inter annual variability in net ecosystem exchange of carbon is investigated using a homogeneity-of-slopes model to identify the function change contributing to inter annual variability, net ecosystem carbon exchange, and night-time ecosystem respiration. Results of employing this statistical approach to a data set collected at the Duke Forest AmeriFlux site from August 1997 to December 2001 are discussed. The results demonstrate that it is feasible to partition the variation in ecosystem carbon fluxes into direct effects of seasonal and inter annual climatic variability and functional change. 51 refs., 4 tabs., 5 figs

  1. A Quality-Aware Relay Node Placement Algorithm to Connect Disjoint WSN Segments with Topology Reorganized

    Directory of Open Access Journals (Sweden)

    Zheng Zimu

    2014-05-01

    Full Text Available Connecting numerous separate parts can be indispensable to simply WSNs that operate autonomously or partitions of a single segmented WSN. Linking them is subject to different intersegment quality of communication and service (QoC and QoS while relay nodes are deployed with their exact number and positions left to define, which is the problem that we focus on. Finding the optimal number and position of relays is NP-hard and therefore heuristics and approximation are pursued. This paper presents an effective approach to deploy appropriate relays to satisfy both the QoC and QoS requirements by introducing probabilistic topology control. The key idea is to regulate a new parallel rule and cost function for segments, which eventually maximizes the utilization of deployed node and avoids the deployment of additional relays as much as possible. The optimization problem is then mapped to finding the path that fulfills the both requirements together with least overheads. The experimental result is validated that although the number of relays is slightly increased to meet extra requirements, the network connectivity can be improved by up to 289.5 % with reorganized topology.

  2. Artificial Epigenetic Networks: Automatic Decomposition of Dynamical Control Tasks Using Topological Self-Modification.

    Science.gov (United States)

    Turner, Alexander P; Caves, Leo S D; Stepney, Susan; Tyrrell, Andy M; Lones, Michael A

    2017-01-01

    This paper describes the artificial epigenetic network, a recurrent connectionist architecture that is able to dynamically modify its topology in order to automatically decompose and solve dynamical problems. The approach is motivated by the behavior of gene regulatory networks, particularly the epigenetic process of chromatin remodeling that leads to topological change and which underlies the differentiation of cells within complex biological organisms. We expected this approach to be useful in situations where there is a need to switch between different dynamical behaviors, and do so in a sensitive and robust manner in the absence of a priori information about problem structure. This hypothesis was tested using a series of dynamical control tasks, each requiring solutions that could express different dynamical behaviors at different stages within the task. In each case, the addition of topological self-modification was shown to improve the performance and robustness of controllers. We believe this is due to the ability of topological changes to stabilize attractors, promoting stability within a dynamical regime while allowing rapid switching between different regimes. Post hoc analysis of the controllers also demonstrated how the partitioning of the networks could provide new insights into problem structure.

  3. Analytical model for macromolecular partitioning during yeast cell division

    International Nuclear Information System (INIS)

    Kinkhabwala, Ali; Khmelinskii, Anton; Knop, Michael

    2014-01-01

    Asymmetric cell division, whereby a parent cell generates two sibling cells with unequal content and thereby distinct fates, is central to cell differentiation, organism development and ageing. Unequal partitioning of the macromolecular content of the parent cell — which includes proteins, DNA, RNA, large proteinaceous assemblies and organelles — can be achieved by both passive (e.g. diffusion, localized retention sites) and active (e.g. motor-driven transport) processes operating in the presence of external polarity cues, internal asymmetries, spontaneous symmetry breaking, or stochastic effects. However, the quantitative contribution of different processes to the partitioning of macromolecular content is difficult to evaluate. Here we developed an analytical model that allows rapid quantitative assessment of partitioning as a function of various parameters in the budding yeast Saccharomyces cerevisiae. This model exposes quantitative degeneracies among the physical parameters that govern macromolecular partitioning, and reveals regions of the solution space where diffusion is sufficient to drive asymmetric partitioning and regions where asymmetric partitioning can only be achieved through additional processes such as motor-driven transport. Application of the model to different macromolecular assemblies suggests that partitioning of protein aggregates and episomes, but not prions, is diffusion-limited in yeast, consistent with previous reports. In contrast to computationally intensive stochastic simulations of particular scenarios, our analytical model provides an efficient and comprehensive overview of partitioning as a function of global and macromolecule-specific parameters. Identification of quantitative degeneracies among these parameters highlights the importance of their careful measurement for a given macromolecular species in order to understand the dominant processes responsible for its observed partitioning

  4. The part-frequency matrices of a partition

    Directory of Open Access Journals (Sweden)

    William J. Keith

    2016-09-01

    Full Text Available A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, whichis elementary to describe and is naturally motivated by Glaisher’s bijection. We prove results thatsuggest surprising usefulness for such a simple tool, including the existence of a related statistic thatrealizes every possible Ramanujan-type congruence for the partition function. To further exhibit itsresearch utility, we give an easy generalization of a theorem of Andrews, Dixit and Yee [1] on the mocktheta functions. Throughout, we state a number of observations and questions that can motivate anarray of investigations.

  5. Chern-Simons Theory, Matrix Models, and Topological Strings

    International Nuclear Information System (INIS)

    Walcher, J

    2006-01-01

    This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U (∞) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the beginner may

  6. The partition function of an interacting many body system

    International Nuclear Information System (INIS)

    Rummel, C.; Ankerhold, J.

    2002-01-01

    Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuation and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e. g. for gap fluctuations in nano-scale superconducting devices previously studied within a PSPA type of approximation. (author)

  7. Quantum topological entropy: First steps of a 'pedestrian' approach

    International Nuclear Information System (INIS)

    Hudetz, T.

    1991-01-01

    We introduce a notion of topological entropy for automorphisms of arbitrary (noncommutative, but unital) nuclear C * -algebras A, generalizing the 'classical' topological entropy for a homeomorphism T: X → X of an arbitrary (possibly connected) compact Hausdorff space X, where the generalization is of course understood in the sense that the latter topological dynamical system (with Z-action) is equivalently viewed as the C * -dynamical system given by the T-induced automorphism of the Abelian C * -algebra A = C(X) of (complex-valued) continuous functions on X. As a simple but basic example, we calculate our quantum topological entropy for shift automorphisms on AF algebras A associated with topological Markov chains (i.e. 'quantum topological' Markov chains); and also a real physical interpretation of our simple 'quantum probabilistic' entropy functionals is discussed (already in the introduction, anticipating the later definitions and results). (author)

  8. On effective theories of topological strings

    International Nuclear Information System (INIS)

    Elitzur, S.; Forge, A.; Rabinovici, E.

    1992-01-01

    We study the construction of effective target-space theories of topological string theories. The example of the CP1 topological sigma model is analysed in detail. An effective target-space theory whose correlation functions are defined by the sum over connected Riemann surfaces of all genera is found to be itself topological. The values of the couplings of this effective theory are expressed in terms of those of the world-sheet theory for a general CP1-like world-sheet model. Any model of this type can be obtained as an effective theory. The definition of the effective theory's expectation values as a sum over disconnected surfaces as well, is shown not to be compatible with those of a topological theory, at least as long as the connectivity of the target space is kept fixed. Dilaton-type couplings emerge in the full lagrangian realization of the moduli space of topological theories with n observables. En route, we encounter a nonperturbative duality, an equivalence of theories with different world-sheets and discuss the relation between the cosmological constant in these finite theories and the zero-point function. (orig.)

  9. Basic algebraic topology and its applications

    CERN Document Server

    Adhikari, Mahima Ranjan

    2016-01-01

    This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...

  10. Entanglement entropy of ABJM theory and entropy of topological black hole

    Science.gov (United States)

    Nian, Jun; Zhang, Xinyu

    2017-07-01

    In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

  11. Topological strings from quantum mechanics

    International Nuclear Information System (INIS)

    Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

    2014-12-01

    We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

  12. Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds

    International Nuclear Information System (INIS)

    Rusokov, B.Y.

    1990-01-01

    Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including non-orientable one. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities' point of view, non-orientability of the manifold is equivalent to its non-compactness

  13. Photoinduced Topological Phase Transitions in Topological Magnon Insulators.

    Science.gov (United States)

    Owerre, S A

    2018-03-13

    Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1-3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.

  14. Proximity effects in topological insulator heterostructures

    International Nuclear Information System (INIS)

    Li Xiao-Guang; Wu Guang-Fen; Zhang Gu-Feng; Culcer Dimitrie; Zhang Zhen-Yu; Chen Hua

    2013-01-01

    Topological insulators (TIs) are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to Tl-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topological helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath. These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI-based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications. (topical review - low-dimensional nanostructures and devices)

  15. Mesh Partitioning Algorithm Based on Parallel Finite Element Analysis and Its Actualization

    Directory of Open Access Journals (Sweden)

    Lei Zhang

    2013-01-01

    Full Text Available In parallel computing based on finite element analysis, domain decomposition is a key technique for its preprocessing. Generally, a domain decomposition of a mesh can be realized through partitioning of a graph which is converted from a finite element mesh. This paper discusses the method for graph partitioning and the way to actualize mesh partitioning. Relevant softwares are introduced, and the data structure and key functions of Metis and ParMetis are introduced. The writing, compiling, and testing of the mesh partitioning interface program based on these key functions are performed. The results indicate some objective law and characteristics to guide the users who use the graph partitioning algorithm and software to write PFEM program, and ideal partitioning effects can be achieved by actualizing mesh partitioning through the program. The interface program can also be used directly by the engineering researchers as a module of the PFEM software. So that it can reduce the application of the threshold of graph partitioning algorithm, improve the calculation efficiency, and promote the application of graph theory and parallel computing.

  16. Topological Organization of Functional Brain Networks in Healthy Children: Differences in Relation to Age, Sex, and Intelligence

    OpenAIRE

    Wu, Kai; Taki, Yasuyuki; Sato, Kazunori; Hashizume, Hiroshi; Sassa, Yuko; Takeuchi, Hikaru; Thyreau, Benjamin; He, Yong; Evans, Alan C.; Li, Xiaobo; Kawashima, Ryuta; Fukuda, Hiroshi

    2013-01-01

    Recent studies have demonstrated developmental changes of functional brain networks derived from functional connectivity using graph theoretical analysis, which has been rapidly translated to studies of brain network organization. However, little is known about sex- and IQ-related differences in the topological organization of functional brain networks during development. In this study, resting-state fMRI (rs-fMRI) was used to map the functional brain networks in 51 healthy children. We then ...

  17. The topological entropy of iterated piecewise affine maps is uncomputable

    Directory of Open Access Journals (Sweden)

    Pascal Koiran

    2001-12-01

    Full Text Available We show that it is impossible to compute (or even to approximate the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real number can be obtained as the topological entropy of a piecewise affine function. It seems that these two questions are also open for cellular automata.

  18. A partitioned correlation function interaction approach for describing electron correlation in atoms

    International Nuclear Information System (INIS)

    Verdebout, S; Godefroid, M; Rynkun, P; Jönsson, P; Gaigalas, G; Fischer, C Froese

    2013-01-01

    The traditional multiconfiguration Hartree–Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core–valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the

  19. A partitioned correlation function interaction approach for describing electron correlation in atoms

    Science.gov (United States)

    Verdebout, S.; Rynkun, P.; Jönsson, P.; Gaigalas, G.; Froese Fischer, C.; Godefroid, M.

    2013-04-01

    The traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core-valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the MR

  20. Topology

    CERN Document Server

    Hocking, John G

    1988-01-01

    ""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t

  1. Topological hierarchy matters — topological matters with superlattices of defects

    International Nuclear Information System (INIS)

    He Jing; Kou Su-Peng

    2016-01-01

    Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states. In this paper, we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters. We find that both topological defects (quantized vortices) and non topological defects (vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects. These topological mid-gap states have nontrivial topological properties, including the nonzero Chern number and the gapless edge states. Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters. (topical review)

  2. The star-triangle relation, lens partition function, and hypergeometric sum/integrals

    Energy Technology Data Exchange (ETDEWEB)

    Gahramanov, Ilmar [Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Radiation Problems ANAS,B. Vahabzade 9, AZ1143 Baku (Azerbaijan); Department of Mathematics, Khazar University,Mehseti St. 41, AZ1096 Baku (Azerbaijan); Kels, Andrew P. [Institute of Physics, University of Tokyo,Komaba, Tokyo 153-8902 (Japan)

    2017-02-08

    The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S{sub b}{sup 3}/ℤ{sub r}) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.

  3. The star-triangle relation, lens partition function, and hypergeometric sum/integrals

    International Nuclear Information System (INIS)

    Gahramanov, Ilmar; Kels, Andrew P.

    2017-01-01

    The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S b 3 /ℤ r ) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.

  4. Interaction effects and quantum phase transitions in topological insulators

    International Nuclear Information System (INIS)

    Varney, Christopher N.; Sun Kai; Galitski, Victor; Rigol, Marcos

    2010-01-01

    We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

  5. Localization and diagonalization. A review of functional integral techniques for low-dimensional gauge theories and topological field theories

    International Nuclear Information System (INIS)

    Blau, M.; Thompson, G.

    1995-01-01

    We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs

  6. Acoustic design by topology optimization

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard; Jensen, Jakob Søndergaard; Sigmund, Ole

    2008-01-01

    To bring down noise levels in human surroundings is an important issue and a method to reduce noise by means of topology optimization is presented here. The acoustic field is modeled by Helmholtz equation and the topology optimization method is based on continuous material interpolation functions...... in the density and bulk modulus. The objective function is the squared sound pressure amplitude. First, room acoustic problems are considered and it is shown that the sound level can be reduced in a certain part of the room by an optimized distribution of reflecting material in a design domain along the ceiling...

  7. Trivial topological phase of CaAgP and the topological nodal-line transition in CaAg (P1 -xA sx)

    Science.gov (United States)

    Xu, N.; Qian, Y. T.; Wu, Q. S.; Autès, G.; Matt, C. E.; Lv, B. Q.; Yao, M. Y.; Strocov, V. N.; Pomjakushina, E.; Conder, K.; Plumb, N. C.; Radovic, M.; Yazyev, O. V.; Qian, T.; Ding, H.; Mesot, J.; Shi, M.

    2018-04-01

    By performing angle-resolved photoemission spectroscopy and first-principles calculations, we address the topological phase of CaAgP and investigate the topological phase transition in CaAg (P1 -xA sx) . We reveal that in CaAgP, the bulk band gap and surface states with a large bandwidth are topologically trivial, in agreement with hybrid density functional theory calculations. The calculations also indicate that application of "negative" hydrostatic pressure can transform trivial semiconducting CaAgP into an ideal topological nodal-line semimetal phase. The topological transition can be realized by partial isovalent P/As substitution at x =0.38 .

  8. Boundary Hamiltonian Theory for Gapped Topological Orders

    Science.gov (United States)

    Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

    2017-06-01

    We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

  9. The Benefits of Adaptive Partitioning for Parallel AMR Applications

    Energy Technology Data Exchange (ETDEWEB)

    Steensland, Johan [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Advanced Software Research and Development

    2008-07-01

    Parallel adaptive mesh refinement methods potentially lead to realistic modeling of complex three-dimensional physical phenomena. However, the dynamics inherent in these methods present significant challenges in data partitioning and load balancing. Significant human resources, including time, effort, experience, and knowledge, are required for determining the optimal partitioning technique for each new simulation. In reality, scientists resort to using the on-board partitioner of the computational framework, or to using the partitioning industry standard, ParMetis. Adaptive partitioning refers to repeatedly selecting, configuring and invoking the optimal partitioning technique at run-time, based on the current state of the computer and application. In theory, adaptive partitioning automatically delivers superior performance and eliminates the need for repeatedly spending valuable human resources for determining the optimal static partitioning technique. In practice, however, enabling frameworks are non-existent due to the inherent significant inter-disciplinary research challenges. This paper presents a study of a simple implementation of adaptive partitioning and discusses implied potential benefits from the perspective of common groups of users within computational science. The study is based on a large set of data derived from experiments including six real-life, multi-time-step adaptive applications from various scientific domains, five complementing and fundamentally different partitioning techniques, a large set of parameters corresponding to a wide spectrum of computing environments, and a flexible cost function that considers the relative impact of multiple partitioning metrics and diverse partitioning objectives. The results show that even a simple implementation of adaptive partitioning can automatically generate results statistically equivalent to the best static partitioning. Thus, it is possible to effectively eliminate the problem of determining the

  10. TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

    Science.gov (United States)

    2017-01-01

    Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

  11. An improved genetic algorithm with dynamic topology

    International Nuclear Information System (INIS)

    Cai Kai-Quan; Tang Yan-Wu; Zhang Xue-Jun; Guan Xiang-Min

    2016-01-01

    The genetic algorithm (GA) is a nature-inspired evolutionary algorithm to find optima in search space via the interaction of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topologies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence. (paper)

  12. Rethinking Sensitivity Analysis of Nuclear Simulations with Topology

    Energy Technology Data Exchange (ETDEWEB)

    Dan Maljovec; Bei Wang; Paul Rosen; Andrea Alfonsi; Giovanni Pastore; Cristian Rabiti; Valerio Pascucci

    2016-01-01

    In nuclear engineering, understanding the safety margins of the nuclear reactor via simulations is arguably of paramount importance in predicting and preventing nuclear accidents. It is therefore crucial to perform sensitivity analysis to understand how changes in the model inputs affect the outputs. Modern nuclear simulation tools rely on numerical representations of the sensitivity information -- inherently lacking in visual encodings -- offering limited effectiveness in communicating and exploring the generated data. In this paper, we design a framework for sensitivity analysis and visualization of multidimensional nuclear simulation data using partition-based, topology-inspired regression models and report on its efficacy. We rely on the established Morse-Smale regression technique, which allows us to partition the domain into monotonic regions where easily interpretable linear models can be used to assess the influence of inputs on the output variability. The underlying computation is augmented with an intuitive and interactive visual design to effectively communicate sensitivity information to the nuclear scientists. Our framework is being deployed into the multi-purpose probabilistic risk assessment and uncertainty quantification framework RAVEN (Reactor Analysis and Virtual Control Environment). We evaluate our framework using an simulation dataset studying nuclear fuel performance.

  13. BKP plane partitions

    International Nuclear Information System (INIS)

    Foda, Omar; Wheeler, Michael

    2007-01-01

    Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another

  14. BKP plane partitions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, Omar; Wheeler, Michael [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)

    2007-01-15

    Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.

  15. Topological wave functions and the 4D-5D lift

    OpenAIRE

    Gao, Peng; Pioline, Boris

    2008-01-01

    We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ''magic'' N=2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the t...

  16. Inferring network topology from complex dynamics

    International Nuclear Information System (INIS)

    Shandilya, Srinivas Gorur; Timme, Marc

    2011-01-01

    Inferring the network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method for inferring the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is hardly restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology from observing a time series of state variables only. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstructing both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of external noise that distorts the original dynamics substantially. The method provides a conceptually new step towards reconstructing a variety of real-world networks, including gene and protein interaction networks and neuronal circuits.

  17. Induced topological pressure for topological dynamical systems

    International Nuclear Information System (INIS)

    Xing, Zhitao; Chen, Ercai

    2015-01-01

    In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure

  18. Inducing magneto-electric response in topological insulator

    International Nuclear Information System (INIS)

    Zeng, Lunwu; Song, Runxia; Zeng, Jing

    2013-01-01

    Utilizing electric potential and magnetic scalar potential formulas, which contain zero-order Bessel functions of the first kind and the constitutive relations of topological insulators, we obtained the induced magnetic scalar potentials and induced magnetic monopole charges which are induced by a point charge in topological insulators. The results show that infinite image magnetic monopole charges are generated by a point electric charge. The magnitude of the induced magnetic monopole charges are determined not only by the point electric charge, but also by the material parameters. - Highlights: ► Electric potential and magnetic scalar potential which contain zero-order Bessel function of the first kind were derived. ► Boundary conditions of topological insulator were built. ► Induced monopole charges were worked out.

  19. Topological superconductivity, topological confinement, and the vortex quantum Hall effect

    International Nuclear Information System (INIS)

    Diamantini, M. Cristina; Trugenberger, Carlo A.

    2011-01-01

    Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.

  20. Uncertain Henry's law constants compromise equilibrium partitioning calculations of atmospheric oxidation products

    Directory of Open Access Journals (Sweden)

    C. Wang

    2017-06-01

    Full Text Available Gas–particle partitioning governs the distribution, removal, and transport of organic compounds in the atmosphere and the formation of secondary organic aerosol (SOA. The large variety of atmospheric species and their wide range of properties make predicting this partitioning equilibrium challenging. Here we expand on earlier work and predict gas–organic and gas–aqueous phase partitioning coefficients for 3414 atmospherically relevant molecules using COSMOtherm, SPARC Performs Automated Reasoning in Chemistry (SPARC, and poly-parameter linear free-energy relationships. The Master Chemical Mechanism generated the structures by oxidizing primary emitted volatile organic compounds. Predictions for gas–organic phase partitioning coefficients (KWIOM/G by different methods are on average within 1 order of magnitude of each other, irrespective of the numbers of functional groups, except for predictions by COSMOtherm and SPARC for compounds with more than three functional groups, which have a slightly higher discrepancy. Discrepancies between predictions of gas–aqueous partitioning (KW/G are much larger and increase with the number of functional groups in the molecule. In particular, COSMOtherm often predicts much lower KW/G for highly functionalized compounds than the other methods. While the quantum-chemistry-based COSMOtherm accounts for the influence of intra-molecular interactions on conformation, highly functionalized molecules likely fall outside of the applicability domain of the other techniques, which at least in part rely on empirical data for calibration. Further analysis suggests that atmospheric phase distribution calculations are sensitive to the partitioning coefficient estimation method, in particular to the estimated value of KW/G. The large uncertainty in KW/G predictions for highly functionalized organic compounds needs to be resolved to improve the quantitative treatment of SOA formation.

  1. Disrupted Topological Organization in Whole-Brain Functional Networks of Heroin-Dependent Individuals: A Resting-State fMRI Study

    OpenAIRE

    Jiang, Guihua; Wen, Xue; Qiu, Yingwei; Zhang, Ruibin; Wang, Junjing; Li, Meng; Ma, Xiaofen; Tian, Junzhang; Huang, Ruiwang

    2013-01-01

    Neuroimaging studies have shown that heroin addiction is related to abnormalities in widespread local regions and in the functional connectivity of the brain. However, little is known about whether heroin addiction changes the topological organization of whole-brain functional networks. Seventeen heroin-dependent individuals (HDIs) and 15 age-, gender-matched normal controls (NCs) were enrolled, and the resting-state functional magnetic resonance images (RS-fMRI) were acquired from these subj...

  2. Topological protection of multiparticle dissipative transport

    Science.gov (United States)

    Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de Las Heras, Daniel; Fischer, Thomas M.

    2016-06-01

    Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

  3. DNA topology and transcription

    Science.gov (United States)

    Kouzine, Fedor; Levens, David; Baranello, Laura

    2014-01-01

    Chromatin is a complex assembly that compacts DNA inside the nucleus while providing the necessary level of accessibility to regulatory factors conscripted by cellular signaling systems. In this superstructure, DNA is the subject of mechanical forces applied by variety of molecular motors. Rather than being a rigid stick, DNA possesses dynamic structural variability that could be harnessed during critical steps of genome functioning. The strong relationship between DNA structure and key genomic processes necessitates the study of physical constrains acting on the double helix. Here we provide insight into the source, dynamics, and biology of DNA topological domains in the eukaryotic cells and summarize their possible involvement in gene transcription. We emphasize recent studies that might inspire and impact future experiments on the involvement of DNA topology in cellular functions. PMID:24755522

  4. Molecular regionalization of the developing amphioxus neural tube challenges major partitions of the vertebrate brain.

    Science.gov (United States)

    Albuixech-Crespo, Beatriz; López-Blanch, Laura; Burguera, Demian; Maeso, Ignacio; Sánchez-Arrones, Luisa; Moreno-Bravo, Juan Antonio; Somorjai, Ildiko; Pascual-Anaya, Juan; Puelles, Eduardo; Bovolenta, Paola; Garcia-Fernàndez, Jordi; Puelles, Luis; Irimia, Manuel; Ferran, José Luis

    2017-04-01

    All vertebrate brains develop following a common Bauplan defined by anteroposterior (AP) and dorsoventral (DV) subdivisions, characterized by largely conserved differential expression of gene markers. However, it is still unclear how this Bauplan originated during evolution. We studied the relative expression of 48 genes with key roles in vertebrate neural patterning in a representative amphioxus embryonic stage. Unlike nonchordates, amphioxus develops its central nervous system (CNS) from a neural plate that is homologous to that of vertebrates, allowing direct topological comparisons. The resulting genoarchitectonic model revealed that the amphioxus incipient neural tube is unexpectedly complex, consisting of several AP and DV molecular partitions. Strikingly, comparison with vertebrates indicates that the vertebrate thalamus, pretectum, and midbrain domains jointly correspond to a single amphioxus region, which we termed Di-Mesencephalic primordium (DiMes). This suggests that these domains have a common developmental and evolutionary origin, as supported by functional experiments manipulating secondary organizers in zebrafish and mice.

  5. Topology optimum design of compliant mechanisms using modified ant colony optimization

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Kwang Seon; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)

    2015-08-15

    A Modified ant colony optimization (MACO) algorithm was suggested for topology optimal design of compliant mechanisms since standard ACO cannot provide an appropriate optimal topology. In order to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for compliant mechanisms, a continuous variable, called the 'Element contribution significance (ECS),'is employed, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. MACO algorithm was applied to topology optimizations of both linear and geometrically nonlinear compliant mechanisms using three kinds of objective functions, and optimized topologies were compared each other. From the comparisons, it was concluded that MACO algorithm can effectively be applied to topology optimizations of linear and geometrically nonlinear compliant mechanisms, and the ratio of Mutual potential energy (MPE) to Strain energy (SE) type of objective function is the best for topology optimal design of compliant mechanisms.

  6. Comparing topological charge definitions using topology fixing actions

    International Nuclear Information System (INIS)

    Bruckmann, Falk; Gruber, Florian; Jansen, Karl; Marinkovic, Marina; Urbach, Carsten; Wagner, Marc

    2009-05-01

    We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing. (orig.)

  7. Inducing magneto-electric response in topological insulator

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Lunwu, E-mail: 163.sin@163.com [Jiangsu Key Laboratory for Intelligent Agricultural Equipment, College of Engineering, Nanjing Agricultural University, Nanjing 210031 (China); Song, Runxia [Jiangsu Key Laboratory for Intelligent Agricultural Equipment, College of Engineering, Nanjing Agricultural University, Nanjing 210031 (China); Zeng, Jing [Faculty of Business and Economics, Macquarie University, NSW 2122 (Australia)

    2013-02-15

    Utilizing electric potential and magnetic scalar potential formulas, which contain zero-order Bessel functions of the first kind and the constitutive relations of topological insulators, we obtained the induced magnetic scalar potentials and induced magnetic monopole charges which are induced by a point charge in topological insulators. The results show that infinite image magnetic monopole charges are generated by a point electric charge. The magnitude of the induced magnetic monopole charges are determined not only by the point electric charge, but also by the material parameters. - Highlights: Black-Right-Pointing-Pointer Electric potential and magnetic scalar potential which contain zero-order Bessel function of the first kind were derived. Black-Right-Pointing-Pointer Boundary conditions of topological insulator were built. Black-Right-Pointing-Pointer Induced monopole charges were worked out.

  8. Nω –CLOSED SETS IN NEUTROSOPHIC TOPOLOGICAL SPACES

    Directory of Open Access Journals (Sweden)

    Santhi R.

    2016-08-01

    Full Text Available Neutrosophic set and Neutrosophic Topological spaces has been introduced by Salama. Neutrosophic Closed set and Neutrosophic Continuous Functions were introduced by Salama et. al.. In this paper, we introduce the concept of Nω- closed sets and their properties in Neutrosophic topological spaces.

  9. Min-max Extrapolation Scheme for Fast Estimation of 3D Potts Field Partition Functions. Application to the Joint Detection-Estimation of Brain Activity in fMRI

    International Nuclear Information System (INIS)

    Risser, L.; Vincent, T.; Ciuciu, P.; Risser, L.; Idier, J.; Risser, L.; Forbes, F.

    2011-01-01

    In this paper, we propose a fast numerical scheme to estimate Partition Functions (PF) of symmetric Potts fields. Our strategy is first validated on 2D two-color Potts fields and then on 3D two- and three-color Potts fields. It is then applied to the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated, deactivated and inactivated brain regions and to estimate region dependent hemodynamic filters. For any brain region, a specific 3D Potts field indeed embodies the spatial correlation over the hidden states of the voxels by modeling whether they are activated, deactivated or inactive. To make spatial regularization adaptive, the PFs of the Potts fields over all brain regions are computed prior to the brain activity estimation. Our approach is first based upon a classical path-sampling method to approximate a small subset of reference PFs corresponding to pre-specified regions. Then, we propose an extrapolation method that allows us to approximate the PFs associated to the Potts fields defined over the remaining brain regions. In comparison with preexisting methods either based on a path sampling strategy or mean-field approximations, our contribution strongly alleviates the computational cost and makes spatially adaptive regularization of whole brain fMRI datasets feasible. It is also robust against grid inhomogeneities and efficient irrespective of the topological configurations of the brain regions. (authors)

  10. The topological filtration of gamma-structures

    DEFF Research Database (Denmark)

    Li, Thomas; Reidys, Christian

    2013-01-01

    In this paper we study gamma-structures filtered by topological genus. gamma-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A gamma-structure is composed by specific building blocks, that have...... topological genus less than or equal to gamma, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for gamma-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem...... for the distribution of topological genus in gamma-structures of given length. In our derivation specific bivariate polynomials play a central role. Their coefficients count particular motifs of fixed topological genus and they are of relevance in the context of genus recursion and novel folding algorithms....

  11. Evolution of topological features in finite antiferromagnetic Heisenberg chains

    International Nuclear Information System (INIS)

    Chen Changfeng

    2003-01-01

    We examine the behavior of nonlocal topological order in finite antiferromagnetic Heisenberg chains using the density matrix renormalization group techniques. We find that chains with even and odd site parity show very different behavior in the topological string order parameter, reflecting interesting interplay of the intrinsic magnetic correlation and the topological term in the chains. Analysis of the calculated string order parameter as a function of the chain length and the topological angle indicates that S=1/2 and S=1 chains show special behavior while all S>1 chains have similar topological structure. This result supports an earlier conjecture on the classification of quantum spin chains based on an analysis of their phase diagrams. Implications of the topological behavior in finite quantum spin chains are discussed

  12. Complete theory of symmetry-based indicators of band topology.

    Science.gov (United States)

    Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

    2017-06-30

    The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

  13. Disrupted topological organization in whole-brain functional networks of heroin-dependent individuals: a resting-state FMRI study.

    Directory of Open Access Journals (Sweden)

    Guihua Jiang

    Full Text Available Neuroimaging studies have shown that heroin addiction is related to abnormalities in widespread local regions and in the functional connectivity of the brain. However, little is known about whether heroin addiction changes the topological organization of whole-brain functional networks. Seventeen heroin-dependent individuals (HDIs and 15 age-, gender-matched normal controls (NCs were enrolled, and the resting-state functional magnetic resonance images (RS-fMRI were acquired from these subjects. We constructed the brain functional networks of HDIs and NCs, and compared the between-group differences in network topological properties using graph theory method. We found that the HDIs showed decreases in the normalized clustering coefficient and in small-worldness compared to the NCs. Furthermore, the HDIs exhibited significantly decreased nodal centralities primarily in regions of cognitive control network, including the bilateral middle cingulate gyrus, left middle frontal gyrus, and right precuneus, but significantly increased nodal centralities primarily in the left hippocampus. The between-group differences in nodal centralities were not corrected by multiple comparisons suggesting these should be considered as an exploratory analysis. Moreover, nodal centralities in the left hippocampus were positively correlated with the duration of heroin addiction. Overall, our results indicated that disruptions occur in the whole-brain functional networks of HDIs, findings which may be helpful in further understanding the mechanisms underlying heroin addiction.

  14. Disrupted topological organization in whole-brain functional networks of heroin-dependent individuals: a resting-state FMRI study.

    Science.gov (United States)

    Jiang, Guihua; Wen, Xue; Qiu, Yingwei; Zhang, Ruibin; Wang, Junjing; Li, Meng; Ma, Xiaofen; Tian, Junzhang; Huang, Ruiwang

    2013-01-01

    Neuroimaging studies have shown that heroin addiction is related to abnormalities in widespread local regions and in the functional connectivity of the brain. However, little is known about whether heroin addiction changes the topological organization of whole-brain functional networks. Seventeen heroin-dependent individuals (HDIs) and 15 age-, gender-matched normal controls (NCs) were enrolled, and the resting-state functional magnetic resonance images (RS-fMRI) were acquired from these subjects. We constructed the brain functional networks of HDIs and NCs, and compared the between-group differences in network topological properties using graph theory method. We found that the HDIs showed decreases in the normalized clustering coefficient and in small-worldness compared to the NCs. Furthermore, the HDIs exhibited significantly decreased nodal centralities primarily in regions of cognitive control network, including the bilateral middle cingulate gyrus, left middle frontal gyrus, and right precuneus, but significantly increased nodal centralities primarily in the left hippocampus. The between-group differences in nodal centralities were not corrected by multiple comparisons suggesting these should be considered as an exploratory analysis. Moreover, nodal centralities in the left hippocampus were positively correlated with the duration of heroin addiction. Overall, our results indicated that disruptions occur in the whole-brain functional networks of HDIs, findings which may be helpful in further understanding the mechanisms underlying heroin addiction.

  15. Supersymmetric localization for BPS black hole entropy: 1-loop partition function from vector multiplets

    International Nuclear Information System (INIS)

    Gupta, Rajesh Kumar; Ito, Yuto; Jeon, Imtak

    2015-01-01

    We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2× S"2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one-loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one-loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one-loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.

  16. Real-space mapping of topological invariants using artificial neural networks

    Science.gov (United States)

    Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

    2018-03-01

    Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

  17. Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks

    Science.gov (United States)

    Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix

    2017-07-01

    We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.

  18. Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks

    Directory of Open Access Journals (Sweden)

    Daniel Litinski

    2017-09-01

    Full Text Available We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall–superconductor hybrids.

  19. On a characterization of path connected topological fields

    OpenAIRE

    Caicedo, Xavier; Mantilla-Soler, Guillermo

    2017-01-01

    The aim of this paper is to give a characterization of path connected topological fields, inspired by the classic Gelfand's correspondence between a compact Hausdorff topological space $X$ and the space of maximal ideals on the ring of real valued continuous functions $C(X,\\mathbb{R})$. More explicitly, our motivation is the following question: What is the essential property of the topological field $F=\\mathbb{R}$ that makes such correspondence valid for all compact Hausdorff spaces? It turns...

  20. RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory.

    Science.gov (United States)

    Garcia-Martin, Juan Antonio; Bayegan, Amir H; Dotu, Ivan; Clote, Peter

    2016-10-19

    RNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure s 0 , i.e. whose minimum free energy secondary structure is identical to the target s 0 . Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target s 0 . We introduce the program RNAdualPF, which computes the dual partition function Z ∗ , defined as the sum of Boltzmann factors exp(-E(a,s 0 )/RT) of all RNA nucleotide sequences a compatible with target structure s 0 . Using RNAdualPF, we efficiently sample RNA sequences that approximately fold into s 0 , where additionally the user can specify IUPAC sequence constraints at certain positions, and whether to include dangles (energy terms for stacked, single-stranded nucleotides). Moreover, since we also compute the dual partition function Z ∗ (k) over all sequences having GC-content k, the user can require that all sampled sequences have a precise, specified GC-content. Using Z ∗ , we compute the dual expected energy 〈E ∗ 〉, and use it to show that natural RNAs from the Rfam 12.0 database have higher minimum free energy than expected, thus suggesting that functional RNAs are under evolutionary pressure to be only marginally thermodynamically stable. We show that C. elegans precursor microRNA (pre-miRNA) is significantly non-robust with respect to mutations, by comparing the robustness of each wild type pre-miRNA sequence with 2000 [resp. 500] sequences of the same GC-content generated by RNAdualPF, which approximately [resp. exactly] fold into the wild type target structure. We confirm and strengthen earlier findings that precursor microRNAs and bacterial small noncoding RNAs display plasticity, a measure of structural diversity. We describe RNAdualPF, which rapidly computes the dual partition function Z ∗ and samples sequences having low energy with respect to a target structure, allowing sequence constraints and specified GC

  1. Topological Nodal Cooper Pairing in Doped Weyl Metals

    Science.gov (United States)

    Li, Yi; Haldane, F. D. M.

    2018-02-01

    We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.

  2. Topology optimization based on the harmony search method

    International Nuclear Information System (INIS)

    Lee, Seung-Min; Han, Seog-Young

    2017-01-01

    A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclu- sions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

  3. Topology optimization based on the harmony search method

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seung-Min; Han, Seog-Young [Hanyang University, Seoul (Korea, Republic of)

    2017-06-15

    A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclu- sions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

  4. Local-scale Partitioning of Functional and Phylogenetic Beta Diversity in a Tropical Tree Assemblage.

    Science.gov (United States)

    Yang, Jie; Swenson, Nathan G; Zhang, Guocheng; Ci, Xiuqin; Cao, Min; Sha, Liqing; Li, Jie; Ferry Slik, J W; Lin, Luxiang

    2015-08-03

    The relative degree to which stochastic and deterministic processes underpin community assembly is a central problem in ecology. Quantifying local-scale phylogenetic and functional beta diversity may shed new light on this problem. We used species distribution, soil, trait and phylogenetic data to quantify whether environmental distance, geographic distance or their combination are the strongest predictors of phylogenetic and functional beta diversity on local scales in a 20-ha tropical seasonal rainforest dynamics plot in southwest China. The patterns of phylogenetic and functional beta diversity were generally consistent. The phylogenetic and functional dissimilarity between subplots (10 × 10 m, 20 × 20 m, 50 × 50 m and 100 × 100 m) was often higher than that expected by chance. The turnover of lineages and species function within habitats was generally slower than that across habitats. Partitioning the variation in phylogenetic and functional beta diversity showed that environmental distance was generally a better predictor of beta diversity than geographic distance thereby lending relatively more support for deterministic environmental filtering over stochastic processes. Overall, our results highlight that deterministic processes play a stronger role than stochastic processes in structuring community composition in this diverse assemblage of tropical trees.

  5. A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

    International Nuclear Information System (INIS)

    Bedini, Andrea; Jacobsen, Jesper Lykke

    2010-01-01

    Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N = 100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ∼ exp(1.516√N), a substantial improvement over the exponential running time ∼exp (0.245N) provided by the hitherto best-known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.

  6. Pairing States of Spin-3/2 Fermions: Symmetry-Enforced Topological Gap Functions

    Science.gov (United States)

    Venderbos, Jörn W. F.; Savary, Lucile; Ruhman, Jonathan; Lee, Patrick A.; Fu, Liang

    2018-01-01

    We study the topological properties of superconductors with paired j =3/2 quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors, and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double- and triple-Dirac superconductors, with quadratic and cubic dispersion, respectively. Our approach, applied here to the case of j =3/2 Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.

  7. Wavelet approach to accelerator problems. 3: Melnikov functions and symplectic topology

    International Nuclear Information System (INIS)

    Fedorova, A.; Zeitlin, M.; Parsa, Z.

    1997-05-01

    This is the third part of a series of talks in which the authors present applications of methods of wavelet analysis to polynomial approximations for a number of accelerator physics problems. They consider the generalization of the variational wavelet approach to nonlinear polynomial problems to the case of Hamiltonian systems for which they need to preserve underlying symplectic or Poissonian or quasicomplex structures in any type of calculations. They use the approach for the problem of explicit calculations of Arnold-Weinstein curves via Floer variational approach from symplectic topology. The loop solutions are parameterized by the solutions of reduced algebraical problem--matrix Quadratic Mirror Filters equations. Also they consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems

  8. Topological Field Theory of Time-Reversal Invariant Insulators

    Energy Technology Data Exchange (ETDEWEB)

    Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

    2010-03-19

    We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

  9. A partitioned conjugate gradient algorithm for lattice Green functions

    International Nuclear Information System (INIS)

    Bowler, K.C.; Kenway, R.D.; Pawley, G.S.; Wallace, D.J.

    1984-01-01

    Partitioning reduces by one the dimensionality of the lattice on which a propagator need be calculated using, for example, the conjugate gradient algorithm. Thus the quark propagator in lattice QCD may be determined by a computation on a single spatial hyperplane. For free fermions on a 16 3 x N lattice 2N-bit accuracy in the propagator is required to avoid rounding errors. (orig.)

  10. Exact Path Integral for 3D Quantum Gravity.

    Science.gov (United States)

    Iizuka, Norihiro; Tanaka, Akinori; Terashima, Seiji

    2015-10-16

    Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.

  11. M-strings, Elliptic Genera and N=4 String Amplitudes

    CERN Document Server

    Hohenegger, Stefan

    2014-01-01

    We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of R^4 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T^2, which we calculate explicitly.

  12. Hierarchical partitioning of metazoan protein conservation profiles provides new functional insights.

    Directory of Open Access Journals (Sweden)

    Jonathan Witztum

    Full Text Available The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles. We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent, as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life.

  13. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole

    2005-01-01

    in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix $\\mathbf K$ and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression $ c = \\mathbf u^\\T \\tilde{\\mathbf K} \\mathbf u...... the arithmetic and harmonic average with the latter being the well known Reuss lower bound. [1] Bendsøe, MP and Sigmund, O 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, HK and Malalasekera, W 1995: An introduction to Computational Fluid Dynamics...

  14. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman...

  15. Correction: Conceptual design of tetraazaporphyrin- and subtetraazaporphyrin-based functional nanocarbon materials: electronic structures, topologies, optical properties, and methane storage capacities.

    Science.gov (United States)

    Belosludov, Rodion V; Rhoda, Hannah M; Zhdanov, Ravil K; Belosludov, Vladimir R; Kawazoe, Yoshiyuki; Nemykin, Victor N

    2017-08-02

    Correction for 'Conceptual design of tetraazaporphyrin- and subtetraazaporphyrin-based functional nanocarbon materials: electronic structures, topologies, optical properties, and methane storage capacities' by Rodion V. Belosludov et al., Phys. Chem. Chem. Phys., 2016, 18, 13503-13518.

  16. Topological Methods for Visualization

    Energy Technology Data Exchange (ETDEWEB)

    Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat

    2016-04-07

    This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

  17. Topological Taxonomy of Water Distribution Networks

    Directory of Open Access Journals (Sweden)

    Carlo Giudicianni

    2018-04-01

    Full Text Available Water Distribution Networks (WDNs can be regarded as complex networks and modeled as graphs. In this paper, Complex Network Theory is applied to characterize the behavior of WDNs from a topological point of view, reviewing some basic metrics, exploring their fundamental properties and the relationship between them. The crucial aim is to understand and describe the topology of WDNs and their structural organization to provide a novel tool of analysis which could help to find new solutions to several arduous problems of WDNs. The aim is to understand the role of the topological structure in the WDNs functioning. The methodology is applied to 21 existing networks and 13 literature networks. The comparison highlights some topological peculiarities and the possibility to define a set of best design parameters for ex-novo WDNs that could also be used to build hypothetical benchmark networks retaining the typical structure of real WDNs. Two well-known types of network ((a square grid; and (b random graph are used for comparison, aiming at defining a possible mathematical model for WDNs. Finally, the interplay between topology and some performance requirements of WDNs is discussed.

  18. A dynamic re-partitioning strategy based on the distribution of key in Spark

    Science.gov (United States)

    Zhang, Tianyu; Lian, Xin

    2018-05-01

    Spark is a memory-based distributed data processing framework, has the ability of processing massive data and becomes a focus in Big Data. But the performance of Spark Shuffle depends on the distribution of data. The naive Hash partition function of Spark can not guarantee load balancing when data is skewed. The time of job is affected by the node which has more data to process. In order to handle this problem, dynamic sampling is used. In the process of task execution, histogram is used to count the key frequency distribution of each node, and then generate the global key frequency distribution. After analyzing the distribution of key, load balance of data partition is achieved. Results show that the Dynamic Re-Partitioning function is better than the default Hash partition, Fine Partition and the Balanced-Schedule strategy, it can reduce the execution time of the task and improve the efficiency of the whole cluster.

  19. Introduction to topology

    CERN Document Server

    Gamelin, Theodore W

    1999-01-01

    A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.

  20. Ocean surface partitioning strategies using ocean colour remote Sensing: A review

    Science.gov (United States)

    Krug, Lilian Anne; Platt, Trevor; Sathyendranath, Shubha; Barbosa, Ana B.

    2017-06-01

    The ocean surface is organized into regions with distinct properties reflecting the complexity of interactions between environmental forcing and biological responses. The delineation of these functional units, each with unique, homogeneous properties and underlying ecosystem structure and dynamics, can be defined as ocean surface partitioning. The main purposes and applications of ocean partitioning include the evaluation of particular marine environments; generation of more accurate satellite ocean colour products; assimilation of data into biogeochemical and climate models; and establishment of ecosystem-based management practices. This paper reviews the diverse approaches implemented for ocean surface partition into functional units, using ocean colour remote sensing (OCRS) data, including their purposes, criteria, methods and scales. OCRS offers a synoptic, high spatial-temporal resolution, multi-decadal coverage of bio-optical properties, relevant to the applications and value of ocean surface partitioning. In combination with other biotic and/or abiotic data, OCRS-derived data (e.g., chlorophyll-a, optical properties) provide a broad and varied source of information that can be analysed using different delineation methods derived from subjective, expert-based to unsupervised learning approaches (e.g., cluster, fuzzy and empirical orthogonal function analyses). Partition schemes are applied at global to mesoscale spatial coverage, with static (time-invariant) or dynamic (time-varying) representations. A case study, the highly heterogeneous area off SW Iberian Peninsula (NE Atlantic), illustrates how the selection of spatial coverage and temporal representation affects the discrimination of distinct environmental drivers of phytoplankton variability. Advances in operational oceanography and in the subject area of satellite ocean colour, including development of new sensors, algorithms and products, are among the potential benefits from extended use, scope and

  1. Topological analysis of the electron density and of the electron localization function of pyrene and its radicals

    International Nuclear Information System (INIS)

    Hernandez-Trujillo, Jesus; Garcia-Cruz, Isidoro; Martinez-Magadan, Jose Manuel

    2005-01-01

    The topological properties of the charge distribution of pyrene and the three derived monoradicals in their ground state and of didehydrogenated pyrenes in the lowest singlet and triplet electronic states are discussed in detail by means of the quantum theory of atoms in molecules (TAIM) and by the electron localization function (ELF). The non-equivalence of the fused aromatic rings of pyrene prevents one from anticipating the stability and reactivity of these species from the chemistry of didehydrogenated species derived from benzene only. Whereas some of these didehydrogenated molecules were found to display a diradical character in the singlet ground state, the topological analysis reveals that others correspond to normal closed shells. Using these theoretical tools, the energetic and geometric details of o-, m- and p-benzyne-like pyrene derivatives are explained

  2. An extensive analysis of the parity of broken 3-diamond partitions

    OpenAIRE

    Radu, Silviu; Sellers, James A.

    2013-01-01

    In 2007, Andrews and Paule introduced the family of functions ? k ( n ) which enumerate the number of broken k-diamond partitions for a fixed positive integer k. Since then, numerous mathematicians have considered partitions congruences satisfied by ? k ( n ) for small values of k. In this work, we provide an extensive analysis of the parity of the function ? 3 ( n ) , including a number of Ramanujan-like congruences modulo 2. This will be accomplished by completely characterizing the values ...

  3. Fuzzy 2-partition entropy threshold selection based on Big Bang–Big Crunch Optimization algorithm

    Directory of Open Access Journals (Sweden)

    Baljit Singh Khehra

    2015-03-01

    Full Text Available The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA-based, Biogeography-based Optimization (BBO-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches.

  4. Tight Network Topology Dependent Bounds on Rounds of Communication

    OpenAIRE

    Chattopadhyay, Arkadev; Langberg, Michael; Li, Shi; Rudra, Atri

    2016-01-01

    We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems. Our main contri...

  5. Partitioning of Nanoparticles into Organic Phases and Model Cells

    Energy Technology Data Exchange (ETDEWEB)

    Posner, J.D.; Westerhoff, P.; Hou, W-C.

    2011-08-25

    dissolved substances" or "more like colloids" as the division between behaviors of macromolecules versus colloids remains ill-defined. Below we detail our work on two broadly defined objectives: (i) Partitioning of ENP into octanol, lipid bilayer, and water, and (ii) disruption of lipid bilayers by ENPs. We have found that the partitioning of NP reaches pseudo-equilibrium distributions between water and organic phases. The equilibrium partitioning most strongly depends on the particle surface charge, which leads us to the conclusion that electrostatic interactions are critical to understanding the fate of NP in the environment. We also show that the kinetic rate at which particle partition is a function of their size (small particles partition faster by number) as can be predicted from simple DLVO models. We have found that particle number density is the most effective dosimetry to present our results and provide quantitative comparison across experiments and experimental platforms. Cumulatively, our work shows that lipid bilayers are a more effective organic phase than octanol because of the definable surface area and ease of interpretation of the results. Our early comparison of NP partitioning between water and lipids suggest that this measurement can be predictive of bioaccumulation in aquatic organisms. We have shown that nanoparticle disrupt lipid bilayer membranes and detail how NP-bilayer interaction leads to the malfunction of lipid bilayers in regulating the fluxes of ionic charges and molecules. Our results show that the disruption of the lipid membranes is similar to that of toxin melittin, except single particles can disrupt a bilayer. We show that only a single particle is required to disrupt a 150 nm DOPC liposome. The equilibrium leakage of membranes is a function of the particle number density and particle surface charge, consistent with results from our partitioning experiments. Our disruption experiments with varying surface functionality show that

  6. p-topological Cauchy completions

    Directory of Open Access Journals (Sweden)

    J. Wig

    1999-01-01

    Full Text Available The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular, p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and only if it is “cushioned,” meaning that each equivalence class of nonconvergent Cauchy filters contains a smallest filter. For a Cauchy space allowing a p-topological completion, it is shown that a certain class of Reed completions preserve the p-topological property, including the Wyler and Kowalsky completions, which are, respectively, the finest and the coarsest p-topological completions. However, not all p-topological completions are Reed completions. Several extension theorems for p-topological completions are obtained. The most interesting of these states that any Cauchy-continuous map between Cauchy spaces allowing p-topological and p′-topological completions, respectively, can always be extended to a θ-continuous map between any p-topological completion of the first space and any p′-topological completion of the second.

  7. Emerging Trends in Topological Insulators and Topological ...

    Indian Academy of Sciences (India)

    /fulltext/reso/022/08/0787-0800. Keywords. Superconductor, quantum Hall effect, topological insulator, Majorana fermions. Abstract. Topological insulators are new class of materials which arecharacterized by a bulk band gap like ordinary ...

  8. Topologically-protected one-way leaky waves in nonreciprocal plasmonic structures

    Science.gov (United States)

    Hassani Gangaraj, S. Ali; Monticone, Francesco

    2018-03-01

    We investigate topologically-protected unidirectional leaky waves on magnetized plasmonic structures acting as homogeneous photonic topological insulators. Our theoretical analyses and numerical experiments aim at unveiling the general properties of these exotic surface waves, and their nonreciprocal and topological nature. In particular, we study the behavior of topological leaky modes in stratified structures composed of a magnetized plasma at the interface with isotropic conventional media, and we show how to engineer their propagation and radiation properties, leading to topologically-protected backscattering-immune wave propagation, and highly directive and tunable radiation. Taking advantage of the non-trivial topological properties of these leaky modes, we also theoretically demonstrate advanced functionalities, including arbitrary re-routing of leaky waves on the surface of bodies with complex shapes, as well as the realization of topological leaky-wave (nano)antennas with isolated channels of radiation that are completely independent and separately tunable. Our findings help shedding light on the behavior of topologically-protected modes in open wave-guiding structures, and may open intriguing directions for future antenna generations based on topological structures, at microwaves and optical frequencies.

  9. Beginning topology

    CERN Document Server

    Goodman, Sue E

    2009-01-01

    Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while i

  10. Topological Derivatives in Shape Optimization

    CERN Document Server

    Novotny, Antonio André

    2013-01-01

    The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intende...

  11. Grassmannian topological Kazama-Suzuki models and cohomology

    International Nuclear Information System (INIS)

    Blau, M.; Hussain, F.; Thompson, G.

    1995-10-01

    We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmanian for all values of the level k. We also analyze the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP(2) model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,K + 2), thus realizing the level-rank duality between this model and the G(2, k + 2) model at level one. (author). 28 refs

  12. Topological Gyroscopic Metamaterials

    Science.gov (United States)

    Nash, Lisa Michelle

    Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.

  13. Topology of Large-Scale Structure by Galaxy Type: Hydrodynamic Simulations

    Science.gov (United States)

    Gott, J. Richard, III; Cen, Renyue; Ostriker, Jeremiah P.

    1996-07-01

    The topology of large-scale structure is studied as a function of galaxy type using the genus statistic. In hydrodynamical cosmological cold dark matter simulations, galaxies form on caustic surfaces (Zeldovich pancakes) and then slowly drain onto filaments and clusters. The earliest forming galaxies in the simulations (defined as "ellipticals") are thus seen at the present epoch preferentially in clusters (tending toward a meatball topology), while the latest forming galaxies (defined as "spirals") are seen currently in a spongelike topology. The topology is measured by the genus (number of "doughnut" holes minus number of isolated regions) of the smoothed density-contour surfaces. The measured genus curve for all galaxies as a function of density obeys approximately the theoretical curve expected for random- phase initial conditions, but the early-forming elliptical galaxies show a shift toward a meatball topology relative to the late-forming spirals. Simulations using standard biasing schemes fail to show such an effect. Large observational samples separated by galaxy type could be used to test for this effect.

  14. Partition of some key regulating services in terrestrial ecosystems: Meta-analysis and review

    Energy Technology Data Exchange (ETDEWEB)

    Viglizzo, E.F., E-mail: evigliz@cpenet.com.ar [INTA, EEA Anguil, Grupo de Investigaciones en Gestión Ambiental (GIGA), Av. Spinetto 785, 6300 Santa Rosa, La Pampa (Argentina); INCITAP-CONICET, Ruta 35, km 335, 6300 Santa Rosa, La Pampa (Argentina); UNLPam, Facultad de Ciencias Exactas y Naturales, Av. Uruguay 151, 6300 Santa Rosa, La Pampa (Argentina); Jobbágy, E.G. [CONICET, Andes 950, 5700 San Luis, San Luis (Argentina); Grupo de Estudios Ambientales IMASL, Ejército de los, Andes 950, 5700 San Luis, San Luis (Argentina); Ricard, M.F. [INCITAP-CONICET, Ruta 35, km 335, 6300 Santa Rosa, La Pampa (Argentina); UNLPam, Facultad de Ciencias Exactas y Naturales, Av. Uruguay 151, 6300 Santa Rosa, La Pampa (Argentina); Paruelo, J.M. [Laboratorio de Análisis Regional y Teledetección, Departamento de Métodos Cuantitativos Sistemas de información, Facultad de Agronomía and IFEVA, Universidad de Buenos Aires and CONICET, Av. San Martín 4453, 1417 Buenos Aires (Argentina)

    2016-08-15

    Our knowledge about the functional foundations of ecosystem service (ES) provision is still limited and more research is needed to elucidate key functional mechanisms. Using a simplified eco-hydrological scheme, in this work we analyzed how land-use decisions modify the partition of some essential regulatory ES by altering basic relationships between biomass stocks and water flows. A comprehensive meta-analysis and review was conducted based on global, regional and local data from peer-reviewed publications. We analyzed five datasets comprising 1348 studies and 3948 records on precipitation (PPT), aboveground biomass (AGB), AGB change, evapotranspiration (ET), water yield (WY), WY change, runoff (R) and infiltration (I). The conceptual framework was focused on ES that are associated with the ecological functions (e.g., intermediate ES) of ET, WY, R and I. ES included soil protection, carbon sequestration, local climate regulation, water-flow regulation and water recharge. To address the problem of data normality, the analysis included both parametric and non-parametric regression analysis. Results demonstrate that PPT is a first-order biophysical factor that controls ES release at the broader scales. At decreasing scales, ES are partitioned as result of PPT interactions with other biophysical and anthropogenic factors. At intermediate scales, land-use change interacts with PPT modifying ES partition as it the case of afforestation in dry regions, where ET and climate regulation may be enhanced at the expense of R and water-flow regulation. At smaller scales, site-specific conditions such as topography interact with PPT and AGB displaying different ES partition formats. The probable implications of future land-use and climate change on some key ES production and partition are discussed. - Highlights: • The partition of regulatory services in ecosystems poses a major policy challenge. • We examined how partitions occur at the hydrosphere

  15. Partition of some key regulating services in terrestrial ecosystems: Meta-analysis and review

    International Nuclear Information System (INIS)

    Viglizzo, E.F.; Jobbágy, E.G.; Ricard, M.F.; Paruelo, J.M.

    2016-01-01

    Our knowledge about the functional foundations of ecosystem service (ES) provision is still limited and more research is needed to elucidate key functional mechanisms. Using a simplified eco-hydrological scheme, in this work we analyzed how land-use decisions modify the partition of some essential regulatory ES by altering basic relationships between biomass stocks and water flows. A comprehensive meta-analysis and review was conducted based on global, regional and local data from peer-reviewed publications. We analyzed five datasets comprising 1348 studies and 3948 records on precipitation (PPT), aboveground biomass (AGB), AGB change, evapotranspiration (ET), water yield (WY), WY change, runoff (R) and infiltration (I). The conceptual framework was focused on ES that are associated with the ecological functions (e.g., intermediate ES) of ET, WY, R and I. ES included soil protection, carbon sequestration, local climate regulation, water-flow regulation and water recharge. To address the problem of data normality, the analysis included both parametric and non-parametric regression analysis. Results demonstrate that PPT is a first-order biophysical factor that controls ES release at the broader scales. At decreasing scales, ES are partitioned as result of PPT interactions with other biophysical and anthropogenic factors. At intermediate scales, land-use change interacts with PPT modifying ES partition as it the case of afforestation in dry regions, where ET and climate regulation may be enhanced at the expense of R and water-flow regulation. At smaller scales, site-specific conditions such as topography interact with PPT and AGB displaying different ES partition formats. The probable implications of future land-use and climate change on some key ES production and partition are discussed. - Highlights: • The partition of regulatory services in ecosystems poses a major policy challenge. • We examined how partitions occur at the hydrosphere

  16. Network topology analysis.

    Energy Technology Data Exchange (ETDEWEB)

    Kalb, Jeffrey L.; Lee, David S.

    2008-01-01

    Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.

  17. Safety-Critical Partitioned Software Architecture: A Partitioned Software Architecture for Robotic

    Science.gov (United States)

    Horvath, Greg; Chung, Seung H.; Cilloniz-Bicchi, Ferner

    2011-01-01

    The flight software on virtually every mission currently managed by JPL has several major flaws that make it vulnerable to potentially fatal software defects. Many of these problems can be addressed by recently developed partitioned operating systems (OS). JPL has avoided adopting a partitioned operating system on its flight missions, primarily because doing so would require significant changes in flight software design, and the risks associated with changes of that magnitude cannot be accepted by an active flight project. The choice of a partitioned OS can have a dramatic effect on the overall system and software architecture, allowing for realization of benefits far beyond the concerns typically associated with the choice of OS. Specifically, we believe that a partitioned operating system, when coupled with an appropriate architecture, can provide a strong infrastructure for developing systems for which reusability, modifiability, testability, and reliability are essential qualities. By adopting a partitioned OS, projects can gain benefits throughout the entire development lifecycle, from requirements and design, all the way to implementation, testing, and operations.

  18. Tunable topological phases in photonic and phononic crystals

    KAUST Repository

    Chen, Zeguo

    2018-02-18

    Topological photonics/phononics, inspired by the discovery of topological insulators, is a prosperous field of research, in which remarkable one-way propagation edge states are robust against impurities or defect without backscattering. This dissertation discusses the implementation of multiple topological phases in specific designed photonic and phononic crystals. First, it reports a tunable quantum Hall phase in acoustic ring-waveguide system. A new three-band model focused on the topological transitions at the Γ point is studied, which gives the functionality that nontrivial topology can be tuned by changing the strengths of the couplings and/or the broken time-reversal symmetry. The resulted tunable topological edge states are also numerically verified. Second, based on our previous studied acoustic ring-waveguide system, we introduce anisotropy by tuning the couplings along different directions. We find that the bandgap topology is related to the frequency and directions. We report our proposal on a frequency filter designed from such an anisotropic topological phononic crystal. Third, motivated by the recent progress on quantum spin Hall phases, we propose a design of time-reversal symmetry broken quantum spin Hall insulators in photonics, in which a new quantum anomalous Hall phase emerges. It supports a chiral edge state with certain spin orientations, which is robust against the magnetic impurities. We also report the realization of the quantum anomalous Hall phase in phononics.

  19. Improved models for the prediction of activity coefficients in nearly athermal mixtures .2. A theoretically-based G(E)-model based on the van der Waals partition function

    DEFF Research Database (Denmark)

    Kontogeorgis, Georgios; Georgios, Nikolopoulos; Fredenslund, Aage

    1997-01-01

    of the generalized van der Waals partition function and attempts to account for all non-energetic effects of solutions of both short- and long-chain alkanes, including alkane polymers. Both the free-volume effects and the density-dependent rotational degrees of freedom are considered. The resulting G(E)-model which......, despite its derivation from a partition function resembles the Flory-Huggins formula, is suitable for vapor-liquid and solid-liquid equilibrium calculations for nearly athermal polymer solutions as well as for alkane systems. We show that using plausible assumptions for the free-volume and the external...

  20. Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theoryCohomological gauge theory, quiver matrix models and Donaldson-Thomas theory

    NARCIS (Netherlands)

    Cirafici, M.; Sinkovics, A.; Szabo, R.J.

    2009-01-01

    We study the relation between Donaldson–Thomas theory of Calabi–Yau threefolds and a six-dimensional topological Yang–Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques

  1. Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

    Directory of Open Access Journals (Sweden)

    Hongling Ye

    2015-01-01

    Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

  2. Topological organization of functional brain networks in healthy children: differences in relation to age, sex, and intelligence.

    Science.gov (United States)

    Wu, Kai; Taki, Yasuyuki; Sato, Kazunori; Hashizume, Hiroshi; Sassa, Yuko; Takeuchi, Hikaru; Thyreau, Benjamin; He, Yong; Evans, Alan C; Li, Xiaobo; Kawashima, Ryuta; Fukuda, Hiroshi

    2013-01-01

    Recent studies have demonstrated developmental changes of functional brain networks derived from functional connectivity using graph theoretical analysis, which has been rapidly translated to studies of brain network organization. However, little is known about sex- and IQ-related differences in the topological organization of functional brain networks during development. In this study, resting-state fMRI (rs-fMRI) was used to map the functional brain networks in 51 healthy children. We then investigated the effects of age, sex, and IQ on economic small-world properties and regional nodal properties of the functional brain networks. At a global level of whole networks, we found significant age-related increases in the small-worldness and local efficiency, significant higher values of the global efficiency in boys compared with girls, and no significant IQ-related difference. Age-related increases in the regional nodal properties were found predominately in the frontal brain regions, whereas the parietal, temporal, and occipital brain regions showed age-related decreases. Significant sex-related differences in the regional nodal properties were found in various brain regions, primarily related to the default mode, language, and vision systems. Positive correlations between IQ and the regional nodal properties were found in several brain regions related to the attention system, whereas negative correlations were found in various brain regions primarily involved in the default mode, emotion, and language systems. Together, our findings of the network topology of the functional brain networks in healthy children and its relationship with age, sex, and IQ bring new insights into the understanding of brain maturation and cognitive development during childhood and adolescence.

  3. Topological organization of functional brain networks in healthy children: differences in relation to age, sex, and intelligence.

    Directory of Open Access Journals (Sweden)

    Kai Wu

    Full Text Available Recent studies have demonstrated developmental changes of functional brain networks derived from functional connectivity using graph theoretical analysis, which has been rapidly translated to studies of brain network organization. However, little is known about sex- and IQ-related differences in the topological organization of functional brain networks during development. In this study, resting-state fMRI (rs-fMRI was used to map the functional brain networks in 51 healthy children. We then investigated the effects of age, sex, and IQ on economic small-world properties and regional nodal properties of the functional brain networks. At a global level of whole networks, we found significant age-related increases in the small-worldness and local efficiency, significant higher values of the global efficiency in boys compared with girls, and no significant IQ-related difference. Age-related increases in the regional nodal properties were found predominately in the frontal brain regions, whereas the parietal, temporal, and occipital brain regions showed age-related decreases. Significant sex-related differences in the regional nodal properties were found in various brain regions, primarily related to the default mode, language, and vision systems. Positive correlations between IQ and the regional nodal properties were found in several brain regions related to the attention system, whereas negative correlations were found in various brain regions primarily involved in the default mode, emotion, and language systems. Together, our findings of the network topology of the functional brain networks in healthy children and its relationship with age, sex, and IQ bring new insights into the understanding of brain maturation and cognitive development during childhood and adolescence.

  4. Functional determinants in gauge theory and string theory

    International Nuclear Information System (INIS)

    Della Pietra, V.J.

    1988-01-01

    Determinants arise whenever Gaussian functional integrals are evaluated. As a result, they are pervasive in physics. In this thesis the author studied, in a mathematically precise fashion, some questions concerning functional determinants in Quantum Field Theory and String Theory. The emphasis is on deriving explicit general identities which can be applied to physical problems. In Chapters 1-3, he studies determinants of families of Weyl operators on compact manifolds. The motivation for this work comes from Chiral Gauge Theory. In a theory containing chiral Fermions coupled to Bosons y, a partial integration in the functional integral over the Fermi fields yields terms involving determinants of Weyl operators ∂y. In Chapter 4 he turns his attention to a problem in String Theory. In the Polyakov formulation of string perturbation theory, the partition function and scattering amplitudes are calculated as sums of contributions from different world sheet topologies. The contribution from surfaces of a particular topology is given by a functional integral, which, after gauge-fixing, can be expressed as an integral of a certain measure over an appropriate moduli space. For an arbitrary finite group acting on a compact manifold, he defines an analytic torsion for the invariant subcomplex of the de Rham complex, generalizing the definition given by Ray and Singer in the absence of a group action. Motivated by the work of Quillen, he uses this torsion to define a natural norm on the determinant line of the invariant cohomology

  5. Novel Topology of Three-Phase Electric Spring and Its Control

    DEFF Research Database (Denmark)

    Wang, Qingsong; Cheng, Ming; Jiang, Yunlei

    2017-01-01

    A novel topology is proposed for three-phase electric spring (TPES) to achieve specific functionalities. With respect to the existing one, the novel topology contains an additional three-phase transformer with the primaries located at the position of the non-critical three-phase load (NCL......) of the existing topology and its secondaries connected to the new three-phase NCL, thus forming a new three-phase smart load (SL). To control the novel topology, the so-called modified δ control utilized for the single-phase electric springs is extended to the three-phase case. Thanks to these solutions, TPES...

  6. Length scale and manufacturability in density-based topology optimization

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Wang, Fengwen; Sigmund, Ole

    2016-01-01

    Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can...... provide competitive designs in terms of cost, materials and functionality under a wide set of constraints. However, the optimized topologies are often considered as conceptual due to loosely defined topologies and the need of postprocessing. Subsequent amendments can affect the optimized design...

  7. Calculation of site affinity constants and cooperativity coefficients for binding of ligands and/or protons to macromolecules. II. Relationships between chemical model and partition function algorithm.

    Science.gov (United States)

    Fisicaro, E; Braibanti, A; Lamb, J D; Oscarson, J L

    1990-05-01

    The relationships between the chemical properties of a system and the partition function algorithm as applied to the description of multiple equilibria in solution are explained. The partition functions ZM, ZA, and ZH are obtained from powers of the binary generating functions Jj = (1 + kappa j gamma j,i[Y])i tau j, where i tau j = p tau j, q tau j, or r tau j represent the maximum number of sites in sites in class j, for Y = M, A, or H, respectively. Each term of the generating function can be considered an element (ij) of a vector Jj and each power of the cooperativity factor gamma ij,i can be considered an element of a diagonal cooperativity matrix gamma j. The vectors Jj are combined in tensor product matrices L tau = (J1) [J2]...[Jj]..., thus representing different receptor-ligand combinations. The partition functions are obtained by summing elements of the tensor matrices. The relationship of the partition functions with the total chemical amounts TM, TA, and TH has been found. The aim is to describe the total chemical amounts TM, TA, and TH as functions of the site affinity constants kappa j and cooperativity coefficients bj. The total amounts are calculated from the sum of elements of tensor matrices Ll. Each set of indices (pj..., qj..., rj...) represents one element of a tensor matrix L tau and defines each term of the summation. Each term corresponds to the concentration of a chemical microspecies. The distinction between microspecies MpjAqjHrj with ligands bound on specific sites and macrospecies MpAqHR corresponding to a chemical stoichiometric composition is shown. The translation of the properties of chemical model schemes into the algorithms for the generation of partition functions is illustrated with reference to a series of examples of gradually increasing complexity. The equilibria examined concern: (1) a unique class of sites; (2) the protonation of a base with two classes of sites; (3) the simultaneous binding of ligand A and proton H to a

  8. Additive subgroups of topological vector spaces

    CERN Document Server

    Banaszczyk, Wojciech

    1991-01-01

    The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

  9. Gene Duplication of the zebrafish kit ligand and partitioning of melanocyte development functions to kit ligand a.

    Directory of Open Access Journals (Sweden)

    Keith A Hultman

    2007-01-01

    Full Text Available The retention of particular genes after the whole genome duplication in zebrafish has given insights into how genes may evolve through partitioning of ancestral functions. We examine the partitioning of expression patterns and functions of two zebrafish kit ligands, kit ligand a (kitla and kit ligand b (kitlb, and discuss their possible coevolution with the duplicated zebrafish kit receptors (kita and kitb. In situ hybridizations show that kitla mRNA is expressed in the trunk adjacent to the notochord in the middle of each somite during stages of melanocyte migration and later expressed in the skin, when the receptor is required for melanocyte survival. kitla is also expressed in other regions complementary to kita receptor expression, including the pineal gland, tail bud, and ear. In contrast, kitlb mRNA is expressed in brain ventricles, ear, and cardinal vein plexus, in regions generally not complementary to either zebrafish kit receptor ortholog. However, like kitla, kitlb is expressed in the skin during stages consistent with melanocyte survival. Thus, it appears that kita and kitla have maintained congruent expression patterns, while kitb and kitlb have evolved divergent expression patterns. We demonstrate the interaction of kita and kitla by morpholino knockdown analysis. kitla morphants, but not kitlb morphants, phenocopy the null allele of kita, with defects for both melanocyte migration and survival. Furthermore, kitla morpholino, but not kitlb morpholino, interacts genetically with a sensitized allele of kita, confirming that kitla is the functional ligand to kita. Last, we examine kitla overexpression in embryos, which results in hyperpigmentation caused by an increase in the number and size of melanocytes. This hyperpigmentation is dependent on kita function. We conclude that following genome duplication, kita and kitla have maintained their receptor-ligand relationship, coevolved complementary expression patterns, and that

  10. Polymers as reference partitioning phase: polymer calibration for an analytically operational approach to quantify multimedia phase partitioning

    DEFF Research Database (Denmark)

    Gilbert, Dorothea; Witt, Gesine; Smedes, Foppe

    2016-01-01

    Polymers are increasingly applied for the enrichment of hydrophobic organic chemicals (HOCs) from various types of samples and media in many analytical partitioning-based measuring techniques. We propose using polymers as a reference partitioning phase and introduce polymer-polymer partitioning......-air) and multimedia partition coefficients (lipid-water, air-water) were calculated by applying the new concept of a polymer as reference partitioning phase and by using polymer-polymer partition coefficients as conversion factors. The present study encourages the use of polymer-polymer partition coefficients...

  11. On topological RNA interaction structures.

    Science.gov (United States)

    Qin, Jing; Reidys, Christian M

    2013-07-01

    Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded γ-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues of γ structures: the RNA γ-interaction structures. These are RNA-RNA interaction structures that are constructed by a finite number of building blocks over two backbones having genus at most γ. Combinatorial properties of γ-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of γ-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures.

  12. Discovering the Network Topology: An Efficient Approach for SDN

    Directory of Open Access Journals (Sweden)

    Leonardo OCHOA-ADAY

    2016-11-01

    Full Text Available Network topology is a physical description of the overall resources in the network. Collecting this information using efficient mechanisms becomes a critical task for important network functions such as routing, network management, quality of service (QoS, among many others. Recent technologies like Software-Defined Networks (SDN have emerged as promising approaches for managing the next generation networks. In order to ensure a proficient topology discovery service in SDN, we propose a simple agents-based mechanism. This mechanism improves the overall efficiency of the topology discovery process. In this paper, an algorithm for a novel Topology Discovery Protocol (SD-TDP is described. This protocol will be implemented in each switch through a software agent. Thus, this approach will provide a distributed solution to solve the problem of network topology discovery in a more simple and efficient way.

  13. Sound intensity as a function of sound insulation partition

    OpenAIRE

    Cvetkovic , S.; Prascevic , R.

    1994-01-01

    In the modern engineering practice, the sound insulation of the partitions is the synthesis of the theory and of the experience acquired in the procedure of the field and of the laboratory measurement. The science and research public treat the sound insulation in the context of the emission and propagation of the acoustic energy in the media with the different acoustics impedance. In this paper, starting from the essence of physical concept of the intensity as the energy vector, the authors g...

  14. High-Harmonic Generation in Solids with and without Topological Edge States

    Science.gov (United States)

    Bauer, Dieter; Hansen, Kenneth K.

    2018-04-01

    High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present. The combination of strong-field laser physics with topological condensed matter opens up new possibilities to electronically control strong-field-based light or particle sources or—conversely—to steer by all optical means topological electronics.

  15. Stiffness design of geometrically nonlinear structures using topology optimization

    DEFF Research Database (Denmark)

    Buhl, Thomas; Pedersen, Claus B. Wittendorf; Sigmund, Ole

    2000-01-01

    of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective......The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities...... functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear...

  16. Strain-induced topological quantum phase transition in phosphorene oxide

    Science.gov (United States)

    Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun

    Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.

  17. Topological sensitivity based far-field detection of elastic inclusions

    Directory of Open Access Journals (Sweden)

    Tasawar Abbas

    2018-03-01

    Full Text Available The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion. 2000 MSC: 35R30, 35L05, 74B05, 47A52, 65J20, Keywords: Inverse elastic scattering, Elasticity imaging, Topological derivative, Resolution analysis, Stability analysis

  18. Polyacrylate–water partitioning of biocidal compounds: Enhancing the understanding of biocide partitioning between render and water

    DEFF Research Database (Denmark)

    Bollmann, Ulla E.; Ou, Yi; Mayer, Philipp

    2014-01-01

    -N-octylisothiazolinone). The correlation of the polyacrylate-water partition constants with the octanol-water partition constants is significant, but the polyacrylate-water partition constants were predominantly below octanol-water partition constants (Kow). The comparison with render-water distribution constants showed that estimating...

  19. Quantum computation with topological codes from qubit to topological fault-tolerance

    CERN Document Server

    Fujii, Keisuke

    2015-01-01

    This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.

  20. Topological domain walls in helimagnets

    Science.gov (United States)

    Schoenherr, P.; Müller, J.; Köhler, L.; Rosch, A.; Kanazawa, N.; Tokura, Y.; Garst, M.; Meier, D.

    2018-05-01

    Domain walls naturally arise whenever a symmetry is spontaneously broken. They interconnect regions with different realizations of the broken symmetry, promoting structure formation from cosmological length scales to the atomic level1,2. In ferroelectric and ferromagnetic materials, domain walls with unique functionalities emerge, holding great promise for nanoelectronics and spintronics applications3-5. These walls are usually of Ising, Bloch or Néel type and separate homogeneously ordered domains. Here we demonstrate that a wide variety of new domain walls occurs in the presence of spatially modulated domain states. Using magnetic force microscopy and micromagnetic simulations, we show three fundamental classes of domain walls to arise in the near-room-temperature helimagnet iron germanium. In contrast to conventional ferroics, the domain walls exhibit a well-defined inner structure, which—analogous to cholesteric liquid crystals—consists of topological disclination and dislocation defects. Similar to the magnetic skyrmions that form in the same material6,7, the domain walls can carry a finite topological charge, permitting an efficient coupling to spin currents and contributions to a topological Hall effect. Our study establishes a new family of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.

  1. Analyzing topological characteristics of neuronal functional networks in the rat brain

    International Nuclear Information System (INIS)

    Lu, Hu; Yang, Shengtao; Song, Yuqing; Wei, Hui

    2014-01-01

    In this study, we recorded spike trains from brain cortical neurons of several behavioral rats in vivo by using multi-electrode recordings. An NFN was constructed in each trial, obtaining a total of 150 NFNs in this study. The topological characteristics of NFNs were analyzed by using the two most important characteristics of complex networks, namely, small-world structure and community structure. We found that the small-world properties exist in different NFNs constructed in this study. Modular function Q was used to determine the existence of community structure in NFNs, through which we found that community-structure characteristics, which are related to recorded spike train data sets, are more evident in the Y-maze task than in the DM-GM task. Our results can also be used to analyze further the relationship between small-world characteristics and the cognitive behavioral responses of rats. - Highlights: • We constructed the neuronal function networks based on the recorded neurons. • We analyzed the two main complex network characteristics, namely, small-world structure and community structure. • NFNs which were constructed based on the recorded neurons in this study exhibit small-world properties. • Some NFNs have community structure characteristics

  2. Analyzing topological characteristics of neuronal functional networks in the rat brain

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Hu [School of Computer Science and Communication Engineering, Jiangsu University, Jiangsu 212003 (China); School of Computer Science, Fudan University, Shanghai 200433 (China); Yang, Shengtao [Institutes of Brain Science, Fudan University, Shanghai 200433 (China); Song, Yuqing [School of Computer Science and Communication Engineering, Jiangsu University, Jiangsu 212003 (China); Wei, Hui [School of Computer Science, Fudan University, Shanghai 200433 (China)

    2014-08-28

    In this study, we recorded spike trains from brain cortical neurons of several behavioral rats in vivo by using multi-electrode recordings. An NFN was constructed in each trial, obtaining a total of 150 NFNs in this study. The topological characteristics of NFNs were analyzed by using the two most important characteristics of complex networks, namely, small-world structure and community structure. We found that the small-world properties exist in different NFNs constructed in this study. Modular function Q was used to determine the existence of community structure in NFNs, through which we found that community-structure characteristics, which are related to recorded spike train data sets, are more evident in the Y-maze task than in the DM-GM task. Our results can also be used to analyze further the relationship between small-world characteristics and the cognitive behavioral responses of rats. - Highlights: • We constructed the neuronal function networks based on the recorded neurons. • We analyzed the two main complex network characteristics, namely, small-world structure and community structure. • NFNs which were constructed based on the recorded neurons in this study exhibit small-world properties. • Some NFNs have community structure characteristics.

  3. Topological BF field theory description of topological insulators

    International Nuclear Information System (INIS)

    Cho, Gil Young; Moore, Joel E.

    2011-01-01

    Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

  4. Inverse participation ratio and localization in topological insulator phase transitions

    International Nuclear Information System (INIS)

    Calixto, M; Romera, E

    2015-01-01

    Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with graphene but with a strong spin–orbit interaction. Using monotonic properties of the IPR, as a function of a perpendicular electric field (which provides a tunable band gap), we define topological-like quantum numbers that take different values in the topological-insulator and band-insulator phases. (paper)

  5. Topological estimation of aerodynamic controlled airplane system functionality of quality

    Directory of Open Access Journals (Sweden)

    С.В. Павлова

    2005-01-01

    Full Text Available  It is suggested to use topological methods for stage estimation of aerodynamic airplane control in widespread range of its conditions The estimation is based on normalized stage virtual non-isotropy of configurational airplane systems calculation.

  6. High-Harmonic Generation in Solids with and without Topological Edge States

    DEFF Research Database (Denmark)

    Bauer, Dieter; Hansen, Kenneth Christian Klochmann

    2018-01-01

    High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up...... to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present...

  7. Topologically protected bound states in one-dimensional Floquet acoustic waveguide systems

    Science.gov (United States)

    Peng, Yu-Gui; Geng, Zhi-Guo; Zhu, Xue-Feng

    2018-03-01

    Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

  8. Composition and partition functions of partially ionized hydrogen plasma in Non-Local Thermal Equilibrium (Non-LThE) and Non-Local Chemical Equilibrium (Non-LChE)

    International Nuclear Information System (INIS)

    Chen Kuan; Eddy, T.L.

    1993-01-01

    A GTME (Generalized MultiThermodynamic Equilibrium) plasma model is developed for plasmas in both Non-LThE (Non-Local Thermal Equilibrium) and Non-LChE (Non-Local Chemical Equilibrium). The model uses multitemperatures for thermal nonequilibrium and non-zero chemical affinities as a measure of the deviation from chemical equilibrium. The plasma is treated as an ideal gas with the Debye-Hueckel approximation employed for pressure correction. The proration method is used when the cutoff energy level is between two discrete levels. The composition and internal partition functions of a hydrogen plasma are presented for electron temperatures ranging from 5000 to 35000 K and pressures from 0.1 to 1000 kPa. Number densities of 7 different species of hydrogen plasma and internal partition functions of different energy modes (rotational, vibrational, and electronic excitation) are computed for three affinity values. The results differ from other plasma properties in that they 1) are not based on equilibrium properties; and 2) are expressed as a function of different energy distribution parameters (temperatures) within each energy mode of each species as appropriate. The computed number densities and partition functions are applicable to calculating the thermodynamic, transport, and radiation properties of a hydrogen plasma not in thermal and chemical equilibria. The nonequilibrium plasma model and plasma compositions presented in this paper are very useful to the diagnosis of high-speed and/or low-pressure plasma flows in which the assumptions of local thermal and chemical equilibrium are invalid. (orig.)

  9. Topological Aspects of Information Retrieval.

    Science.gov (United States)

    Egghe, Leo; Rousseau, Ronald

    1998-01-01

    Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)

  10. Topological entropy for finite invariant sets of Y

    International Nuclear Information System (INIS)

    Li Shihai; Ye Xiangdong.

    1992-12-01

    Let Y be the space {z is an element of C:z 3 is an element of [0,1]} with a metric defined by the arc length. Suppose that f is an element of C(Y,Y) and P is a finite f-invariant set. The topological entropy of (P,f), h(P), is the infimum of the topological entropies of maps from C(Y,Y) which agree with f on P. In this paper we construct a function C P is an element of C(Y,Y) satisfying C P | P =f| P which achieves the topological entropy of (P,f). (author). 14 refs

  11. Topological mass mechanism and exact fields mapping

    International Nuclear Information System (INIS)

    Amaral, R L P G; Ventura, O S; Buffon, L O; Costa, J V

    2006-01-01

    We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of (Ventura O S, Amaral R L P G, Costa J V, Buffon L O and Lemes V E R 2004 J. Phys. A: Math. Gen. 37 11711-23) for arbitrary dimensions

  12. Chimera states: Effects of different coupling topologies

    Science.gov (United States)

    Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar; Perc, Matjaž

    2017-04-01

    Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies as well as different types of coupling functions. Chimera states have recently received ample attention as a fascinating manifestation of collective behavior, in particular describing a symmetry breaking spatiotemporal pattern where synchronized and desynchronized states coexist in a network of coupled oscillators. In this perspective, we review the emergence of different chimera states, focusing on the effects of different coupling topologies that describe the interaction network connecting the oscillators. We cover chimera states that emerge in local, nonlocal and global coupling topologies, as well as in modular, temporal and multilayer networks. We also provide an outline of challenges and directions for future research.

  13. Developing Key Parameters for Green Performance of Partition Wall Blocks

    Directory of Open Access Journals (Sweden)

    Goh Cheng Siew

    2016-01-01

    Full Text Available To promote sustainable construction, it is important to consider green performance of construction materials throughout the life cycle. Selecting inappropriate materials could not only affect the functional performance but also preclude the achievement of green building performance as a whole. Green performance of construction materials has therefore been one of the primary considerations of green building assessment systems. Using partition wall blocks as an example, this paper examines green performance of building materials primarily from the cradle to gate boundaries. Nine key parameters are proposed for the green performance of partition wall blocks. Apart from environmental features, technical performance of partition wall blocks is also taken into consideration since it is the determinant of the lifecycle performance. This paper offers a roadmap to decision makers to make environmentally responsible choices for their materials of internal walls and partitions, and hence provides a potential sustainable solution for green buildings.

  14. The coupling of Poisson sigma models to topological backgrounds

    Energy Technology Data Exchange (ETDEWEB)

    Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)

    2016-12-13

    We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

  15. Improved creep strength of nickel-base superalloys by optimized γ/γ′ partitioning behavior of solid solution strengthening elements

    International Nuclear Information System (INIS)

    Pröbstle, M.; Neumeier, S.; Feldner, P.; Rettig, R.; Helmer, H.E.; Singer, R.F.; Göken, M.

    2016-01-01

    Solid solution strengthening of the γ matrix is one key factor for improving the creep strength of single crystal nickel-base superalloys at high temperatures. Therefore a strong partitioning of solid solution hardening elements to the matrix is beneficial for high temperature creep strength. Different Rhenium-free alloys which are derived from CMSX-4 are investigated. The alloys have been characterized regarding microstructure, phase compositions as well as creep strength. It is found that increasing the Titanium (Ti) as well as the Tungsten (W) content causes a stronger partitioning of the solid solution strengtheners, in particular W, to the γ phase. As a result the creep resistance is significantly improved. Based on these ideas, a Rhenium-free alloy with an optimized chemistry regarding the partitioning behavior of W is developed and validated in the present study. It shows comparable creep strength to the Rhenium containing second generation alloy CMSX-4 in the high temperature / low stress creep regime and is less prone to the formation of deleterious topologically close packed (TCP) phases. This more effective usage of solid solution strengtheners can enhance the creep properties of nickel-base superalloys while reducing the content of strategic elements like Rhenium.

  16. Self-consistent adjoint analysis for topology optimization of electromagnetic waves

    Science.gov (United States)

    Deng, Yongbo; Korvink, Jan G.

    2018-05-01

    In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

  17. Impact of topology in foliated quantum Einstein gravity.

    Science.gov (United States)

    Houthoff, W B; Kurov, A; Saueressig, F

    2017-01-01

    We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

  18. The complex formation-partition and partition-association models of solvent extraction of ions

    International Nuclear Information System (INIS)

    Siekierski, S.

    1976-01-01

    Two models of the extraction process have been proposed. In the first model it is assumed that the partitioning neutral species is at first formed in the aqueous phase and then transferred into the organic phase. The second model is based on the assumption that equivalent amounts of cations are at first transferred from the aqueous into the organic phase and then associated to form a neutral molecule. The role of the solubility parameter in extraction and the relation between the solubility of liquid organic substances in water and the partition of complexes have been discussed. The extraction of simple complexes and complexes with organic ligands has been discussed using the first model. Partition coefficients have been calculated theoretically and compared with experimental values in some very simple cases. The extraction of ion pairs has been discussed using the partition-association model and the concept of single-ion partition coefficients. (author)

  19. Combined shape and topology optimization of 3D structures

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman; Bærentzen, Jakob Andreas; Nobel-Jørgensen, Morten

    2015-01-01

    We present a method for automatic generation of 3D models based on shape and topology optimization. The optimization procedure, or model generation process, is initialized by a set of boundary conditions, an objective function, constraints and an initial structure. Using this input, the method...... will automatically deform and change the topology of the initial structure such that the objective function is optimized subject to the specified constraints and boundary conditions. For example, this tool can be used to improve the stiffness of a structure before printing, reduce the amount of material needed...

  20. A semi-supervised learning approach to predict synthetic genetic interactions by combining functional and topological properties of functional gene network

    Directory of Open Access Journals (Sweden)

    Han Kyungsook

    2010-06-01

    Full Text Available Abstract Background Genetic interaction profiles are highly informative and helpful for understanding the functional linkages between genes, and therefore have been extensively exploited for annotating gene functions and dissecting specific pathway structures. However, our understanding is rather limited to the relationship between double concurrent perturbation and various higher level phenotypic changes, e.g. those in cells, tissues or organs. Modifier screens, such as synthetic genetic arrays (SGA can help us to understand the phenotype caused by combined gene mutations. Unfortunately, exhaustive tests on all possible combined mutations in any genome are vulnerable to combinatorial explosion and are infeasible either technically or financially. Therefore, an accurate computational approach to predict genetic interaction is highly desirable, and such methods have the potential of alleviating the bottleneck on experiment design. Results In this work, we introduce a computational systems biology approach for the accurate prediction of pairwise synthetic genetic interactions (SGI. First, a high-coverage and high-precision functional gene network (FGN is constructed by integrating protein-protein interaction (PPI, protein complex and gene expression data; then, a graph-based semi-supervised learning (SSL classifier is utilized to identify SGI, where the topological properties of protein pairs in weighted FGN is used as input features of the classifier. We compare the proposed SSL method with the state-of-the-art supervised classifier, the support vector machines (SVM, on a benchmark dataset in S. cerevisiae to validate our method's ability to distinguish synthetic genetic interactions from non-interaction gene pairs. Experimental results show that the proposed method can accurately predict genetic interactions in S. cerevisiae (with a sensitivity of 92% and specificity of 91%. Noticeably, the SSL method is more efficient than SVM, especially for

  1. Topological mirror superconductivity.

    Science.gov (United States)

    Zhang, Fan; Kane, C L; Mele, E J

    2013-08-02

    We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

  2. Interactive Topology Optimization

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten

    Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... on theory of from human-computer interaction which is described in Chapter 2. Followed by a description of the foundations of topology optimization in Chapter 3. Our applications for topology optimization in 2D and 3D are described in Chapter 4 and a game which trains the human intuition of topology...... optimization is presented in Chapter 5. Topology optimization can also be used as an interactive modeling tool with local control which is presented in Chapter 6. Finally, Chapter 7 contains a summary of the findings and concludes the dissertation. Most of the presented applications of the thesis are available...

  3. COMPUTING VERTICES OF INTEGER PARTITION POLYTOPES

    Directory of Open Access Journals (Sweden)

    A. S. Vroublevski

    2015-01-01

    Full Text Available The paper describes a method of generating vertices of the polytopes of integer partitions that was used by the authors to calculate all vertices and support vertices of the partition polytopes for all n ≤ 105 and all knapsack partitions of n ≤ 165. The method avoids generating all partitions of n. The vertices are determined with the help of sufficient and necessary conditions; in the hard cases, the well-known program Polymake is used. Some computational aspects are exposed in more detail. These are the algorithm for checking the criterion that characterizes partitions that are convex combinations of two other partitions; the way of using two combinatorial operations that transform the known vertices to the new ones; and employing the Polymake to recognize a limited number (for small n of partitions that need three or more other partitions for being convexly expressed. We discuss the computational results on the numbers of vertices and support vertices of the partition polytopes and some appealing problems these results give rise to.

  4. The topology of architecture

    DEFF Research Database (Denmark)

    Marcussen, Lars

    2003-01-01

    Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum.......Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum....

  5. Cosmic Topology

    Science.gov (United States)

    Luminet, Jean-Pierre

    2015-08-01

    Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

  6. Elements of topology

    CERN Document Server

    Singh, Tej Bahadur

    2013-01-01

    Topological SpacesMetric Spaces Topologies Derived Concepts Bases Subspaces Continuity and ProductsContinuityProduct TopologyConnectednessConnected Spaces Components Path-Connected Spaces Local ConnectivityConvergence Sequences Nets Filters Hausdorff SpacesCountability Axioms 1st and 2nd Countable Spaces Separable and Lindelöf SpacesCompactnessCompact Spaces Countably Compact Spaces Compact Metric Spaces Locally Compact Spaces Proper Maps Topological Constructions Quotient Spaces Identification Maps Cones, Suspensions and Joins Wedge Sums and Smash Products Adjunction Spaces Coherent Topologie

  7. Graph topology and gap topology for unstable systems

    NARCIS (Netherlands)

    Zhu, S.Q.

    1989-01-01

    A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the

  8. Systematic design of microstructures by topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2003-01-01

    The topology optimization method can be used to determine the material distribution in a design domain such that an objective function is maximized and constraints are fulfilled. The method which is based on Finite Element Analysis may be applied to all kinds of material distribution problems like...... extremal material design, sensor and actuator design and MEMS synthesis. The state-of-the-art in topology optimization will be reviewed and older as well as new applications in phononic and photonic crystals design will be presented....

  9. The impact of aerosol composition on the particle to gas partitioning of reactive mercury.

    Science.gov (United States)

    Rutter, Andrew P; Schauer, James J

    2007-06-01

    A laboratory system was developed to study the gas-particle partitioning of reactive mercury (RM) as a function of aerosol composition in synthetic atmospheric particulate matter. The collection of RM was achieved by filter- and sorbent-based methods. Analyses of the RM collected on the filters and sorbents were performed using thermal extraction combined with cold vapor atomic fluorescence spectroscopy (CVAFS), allowing direct measurement of the RM load on the substrates. Laboratory measurements of the gas-particle partitioning coefficients of RM to atmospheric aerosol particles revealed a strong dependence on aerosol composition, with partitioning coefficients that varied by orders of magnitude depending on the composition of the particles. Particles of sodium nitrate and the chlorides of potassium and sodium had high partitioning coefficients, shifting the RM partitioning toward the particle phase, while ammonium sulfate, levoglucosan, and adipic acid caused the RM to partition toward the gas phase and, therefore, had partitioning coefficients that were lower by orders of magnitude.

  10. The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

    Czech Academy of Sciences Publication Activity Database

    Gabriyelyan, S.; Kąkol, Jerzy; Plebanek, G.

    2016-01-01

    Roč. 233, č. 2 (2016), s. 119-139 ISSN 0039-3223 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : locally convex-space Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/233/2/91577/the-ascoli-property-for-function-spaces- and -the-weak-topology-of-banach- and -frechet-spaces

  11. Newton-type method for the variational discretization of topology optimization problems

    DEFF Research Database (Denmark)

    Evgrafov, Anton

    2013-01-01

    We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...

  12. Accessing the topological susceptibility via the Gribov horizon

    Science.gov (United States)

    Dudal, D.; Felix, C. P.; Guimaraes, M. S.; Sorella, S. P.

    2017-10-01

    The topological susceptibility, χ4 , following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the η' mass, the so-called U (1 )A problem. A nonzero χ4 is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current Kμ. In this paper, we investigate the topological susceptibility, χ4, in S U (3 ) and S U (2 ) Euclidean Yang-Mills theory using an appropriate Padé approximation tool and a nonperturbative gluon propagator, within a Becchi-Rouet-Stora-Tyutin invariant framework and by taking into account Gribov copies in a general linear covariant gauge.

  13. 3D topology of orientation columns in visual cortex revealed by functional optical coherence tomography.

    Science.gov (United States)

    Nakamichi, Yu; Kalatsky, Valery A; Watanabe, Hideyuki; Sato, Takayuki; Rajagopalan, Uma Maheswari; Tanifuji, Manabu

    2018-04-01

    Orientation tuning is a canonical neuronal response property of six-layer visual cortex that is encoded in pinwheel structures with center orientation singularities. Optical imaging of intrinsic signals enables us to map these surface two-dimensional (2D) structures, whereas lack of appropriate techniques has not allowed us to visualize depth structures of orientation coding. In the present study, we performed functional optical coherence tomography (fOCT), a technique capable of acquiring a 3D map of the intrinsic signals, to study the topology of orientation coding inside the cat visual cortex. With this technique, for the first time, we visualized columnar assemblies in orientation coding that had been predicted from electrophysiological recordings. In addition, we found that the columnar structures were largely distorted around pinwheel centers: center singularities were not rigid straight lines running perpendicularly to the cortical surface but formed twisted string-like structures inside the cortex that turned and extended horizontally through the cortex. Looping singularities were observed with their respective termini accessing the same cortical surface via clockwise and counterclockwise orientation pinwheels. These results suggest that a 3D topology of orientation coding cannot be fully anticipated from 2D surface measurements. Moreover, the findings demonstrate the utility of fOCT as an in vivo mesoscale imaging method for mapping functional response properties of cortex in the depth axis. NEW & NOTEWORTHY We used functional optical coherence tomography (fOCT) to visualize three-dimensional structure of the orientation columns with millimeter range and micrometer spatial resolution. We validated vertically elongated columnar structure in iso-orientation domains. The columnar structure was distorted around pinwheel centers. An orientation singularity formed a string with tortuous trajectories inside the cortex and connected clockwise and counterclockwise

  14. Topological and non-topological soliton solutions to some time

    Indian Academy of Sciences (India)

    Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...

  15. Island Partition of Distribution System with Distributed Generators Considering Protection of Vulnerable Nodes

    Directory of Open Access Journals (Sweden)

    Gang Xu

    2017-10-01

    Full Text Available To improve the reliability of power supply in the case of the fault of distribution system with multiple distributed generators (DGs and reduce the influence of node voltage fluctuation on the stability of distribution system operation in power restoration, this paper proposes an island partition strategy of the distribution system considering the protection of vulnerable nodes. First of all, the electrical coupling coefficient of neighboring nodes is put forward according to distribution system topology and equivalent electrical impedance, and the power-dependence relationship between neighboring nodes is calculated based on the direction and level of the power flow between nodes. Then, the bidirectional transmission of the coupling features of neighboring nodes is realized through the modified PageRank algorithm, thus identifying the vulnerable nodes that have a large influence on the stability of distribution system operation. Next, combining the index of node vulnerability, an island partition model is constructed with the restoration of important loads as the primary goal. In addition, the mutually exclusive firefly algorithm (MEFA is also proposed to realize the interaction of learning and competition among fireflies, thus enhancing the globally optimal solution search ability of the algorithm proposed. The proposed island partition method is verified with a Pacific Gas and Electric Company (PG and E 60-node test system. Comparison with other methods demonstrates that the new method is feasible for the distribution system with multiple types of distributed generations and valid to enhance the stability and safety of the grid with a relatively power restoration ratio.

  16. Abe homotopy classification of topological excitations under the topological influence of vortices

    International Nuclear Information System (INIS)

    Kobayashi, Shingo; Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito

    2012-01-01

    Topological excitations are usually classified by the nth homotopy group π n . However, for topological excitations that coexist with vortices, there are cases in which an element of π n cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of π n corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π 1 on π n . In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κ n . The nth Abe homotopy group κ n is defined as a semi-direct product of π 1 and π n . In this framework, the action of π 1 on π n is understood as originating from noncommutativity between π 1 and π n . We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is S n /K, where S n is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).

  17. $L$-Topological Spaces

    Directory of Open Access Journals (Sweden)

    Ali Bajravani

    2018-04-01

    Full Text Available ‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.

  18. Topological effects in QCD and the problem of short-distance singularities

    International Nuclear Information System (INIS)

    Luescher, Martin

    2004-01-01

    The topological susceptibility and the higher moments of the topological charge distribution in QCD are expressed through certain n-point functions of the scalar and pseudo-scalar quark densities at vanishing momenta, which are free of short-distance singularities. Since the normalization of the correlation functions is determined by the non-singlet chiral Ward identities, these formulae provide an unambiguous regularization-independent definition of the moments and thus of the charge distribution

  19. A New Cost-Effective Multi-Drive Solution based on a Two-Stage Direct Power Electronic Conversion Topology

    DEFF Research Database (Denmark)

    Klumpner, Christian; Blaabjerg, Frede

    2002-01-01

    of a protection circuit involving twelve diodes with full voltage/current ratings used only during faulty situations, makes this topology not so attractive. Lately, two stage Direct Power Electronic Conversion (DPEC) topologies have been proposed, providing similar functionality as a matrix converter but allowing...... shared by many loads, making this topology more cost effective. The functionality of the proposed two-stage multi-drive direct power electronic conversion topology is validated by experiments on a realistic laboratory prototype....

  20. Topological superconductors: a review.

    Science.gov (United States)

    Sato, Masatoshi; Ando, Yoichi

    2017-07-01

    This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

  1. Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study

    International Nuclear Information System (INIS)

    Zhai, Qingqing; Yang, Jun; Zhao, Yu

    2014-01-01

    Variance-based sensitivity analysis has been widely studied and asserted itself among practitioners. Monte Carlo simulation methods are well developed in the calculation of variance-based sensitivity indices but they do not make full use of each model run. Recently, several works mentioned a scatter-plot partitioning method to estimate the variance-based sensitivity indices from given data, where a single bunch of samples is sufficient to estimate all the sensitivity indices. This paper focuses on the space-partition method in the estimation of variance-based sensitivity indices, and its convergence and other performances are investigated. Since the method heavily depends on the partition scheme, the influence of the partition scheme is discussed and the optimal partition scheme is proposed based on the minimized estimator's variance. A decomposition and integration procedure is proposed to improve the estimation quality for higher order sensitivity indices. The proposed space-partition method is compared with the more traditional method and test cases show that it outperforms the traditional one

  2. Topology optimization of vibration and wave propagation problems

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2007-01-01

    The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....

  3. A topological introduction to nonlinear analysis

    CERN Document Server

    Brown, Robert F

    2014-01-01

    This third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. For this third edition, several new chapters present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply...

  4. The partitioning of uranium and neptunium onto hydrothermally altered concrete

    International Nuclear Information System (INIS)

    Zhao, P.; Allen, P.G.; Sylwester, E.R.; Viani, B.E.

    2000-01-01

    Partition coefficients (K d ) of U(VI) and Np(V) on untreated and hydrothermally altered concrete were measured in 0.01 M NaCl and 0.01 M NaHCO 3 solutions as functions of concentration of the radionuclides, pH, and time. The partition coefficients for both U(VI) and Np(V) on hydrothermally altered concrete are significantly lower than those on untreated concrete. The partition of both U(VI) and Np(V) are pH dependent, although the pH dependence does not appear to reflect precipitation of U and Np-bearing phases. Both sorption and precipitation are likely processes controlling partitioning of U to concrete; sorption is the most likely process controlling the partitioning of Np to concrete. The presence of 0.01 M carbonate species in solution decreases K d of U(VI) for both hydrothermally altered and untreated concrete from ≥ 10 4 mL/g to ∝ 400 to 1000 mL/g indicating a significant impact on U(VI) sorption. In contrast, the presence of carbonate only reduced the K d of Np(V) by one order of magnitude or less. X-ray absorption spectroscopy analysis of U/concrete mixtures at different pHs and times indicate that uranyl ions are partitioned as monomeric species on untreated concrete, but oligomeric species on hydrothermally altered concrete. Similar analysis of Np/concrete mixtures shows that about half of the partitioned Np(V) is reduced to Np(IV) over a period of 6 months. (orig.)

  5. The partition coefficients of 133Xe between blood and bone

    International Nuclear Information System (INIS)

    Lahtinen, T.; Karjalainen, P.; Vaeaenaenen, A.; Lahtinen, R.; Alhava, E.M.

    1981-01-01

    The partition coefficients of 133 Xe between blood and haematopoietic bone marrow and homogenised bone have been determined in vitro. The partition coefficient lambda 1 corresponding to haematopoietic marrow was 0.95 ml g -1 while that corresponding to homogenised bone was a function of age, lambda 2 = 3.11 + 0.049(age)(ml g -1 ). These data can be used for calculating regional blood flow in healthy human femur by means of a simple 133 Xe radionuclide method. (author)

  6. Toric topology

    CERN Document Server

    Buchstaber, Victor M

    2015-01-01

    This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v

  7. Topological insulators

    CERN Document Server

    Franz, Marcel

    2013-01-01

    Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was

  8. The one-loop partition function of N=4 super-Yang-Mills theory on RxS3

    International Nuclear Information System (INIS)

    Spradlin, Marcus; Volovich, Anastasia

    2005-01-01

    We study weakly coupled SU(N)N=4 super-Yang-Mills theory on RxS 3 at infinite N, which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighboring sites and a generalization of Polya's counting of necklaces (gauge-invariant operators) to include necklaces with a 'pendant' (an operator which acts on neighboring beads). We find that the one-loop correction to the Hagedorn temperature is δlnT H =+λ/8π 2

  9. The prediction of blood-tissue partitions, water-skin partitions and skin permeation for agrochemicals.

    Science.gov (United States)

    Abraham, Michael H; Gola, Joelle M R; Ibrahim, Adam; Acree, William E; Liu, Xiangli

    2014-07-01

    There is considerable interest in the blood-tissue distribution of agrochemicals, and a number of researchers have developed experimental methods for in vitro distribution. These methods involve the determination of saline-blood and saline-tissue partitions; not only are they indirect, but they do not yield the required in vivo distribution. The authors set out equations for gas-tissue and blood-tissue distribution, for partition from water into skin and for permeation from water through human skin. Together with Abraham descriptors for the agrochemicals, these equations can be used to predict values for all of these processes. The present predictions compare favourably with experimental in vivo blood-tissue distribution where available. The predictions require no more than simple arithmetic. The present method represents a much easier and much more economic way of estimating blood-tissue partitions than the method that uses saline-blood and saline-tissue partitions. It has the added advantages of yielding the required in vivo partitions and being easily extended to the prediction of partition of agrochemicals from water into skin and permeation from water through skin. © 2013 Society of Chemical Industry.

  10. A general action for topological quantum field theories

    International Nuclear Information System (INIS)

    Dayi, O.F.

    1989-03-01

    Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs

  11. Topology and Edge Modes in Quantum Critical Chains

    Science.gov (United States)

    Verresen, Ruben; Jones, Nick G.; Pollmann, Frank

    2018-02-01

    We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk—in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c ∈1/2 N , and the topological invariant, ω ∈Z . Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.

  12. Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks

    International Nuclear Information System (INIS)

    Hasan, M Zahid; Xu, Su-Yang; Bian, Guang

    2015-01-01

    Unlike string theory, topological physics in lower dimensional condensed matter systems is an experimental reality since the bulk-boundary correspondence can be probed experimentally in lower dimensions. In addition, recent experimental discoveries of non-quantum-Hall-like topological insulators, topological superconductors, Weyl semimetals and other topological states of matter also signal a clear departure from the quantum-Hall-effect-like transport paradigm that has dominated the field since the 1980s. It is these new forms of matter that enabled realizations of topological-Dirac, Weyl cones, helical-Cooper-pairs, Fermi-arc-quasiparticles and other emergent phenomena in fine-tuned photoemission (ARPES) experiments since ARPES experiments directly allow the study of bulk-boundary (topological) correspondence. In this proceeding we provide a brief overview of the key experiments and discuss our perspectives regarding the new research frontiers enabled by these experiments. Taken collectively, we argue in favor of the emergence of ‘topological-condensed-matter-physics’ in laboratory experiments for which a variety of theoretical concepts over the last 80 years paved the way. (review)

  13. Bistable Topological Insulator with Exciton-Polaritons

    Science.gov (United States)

    Kartashov, Yaroslav V.; Skryabin, Dmitry V.

    2017-12-01

    The functionality of many nonlinear and quantum optical devices relies on the effect of optical bistability. Using microcavity exciton-polaritons in a honeycomb arrangement of microcavity pillars, we report the resonance response and bistability of topological edge states. A balance between the pump, loss, and nonlinearity ensures a broad range of dynamical stability and controls the distribution of power between counterpropagating states on the opposite edges of the honeycomb lattice stripe. Tuning energy and polarization of the pump photons, while keeping their momentum constant, we demonstrate control of the propagation direction of the dominant edge state. Our results facilitate the development of practical applications of topological photonics.

  14. Operator bases, S-matrices, and their partition functions

    Science.gov (United States)

    Henning, Brian; Lu, Xiaochuan; Melia, Tom; Murayama, Hitoshi

    2017-10-01

    Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where S-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. In this paper we use the S-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation). We introduce a partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the S-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries. In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to n = 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of n-point amplitudes. We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the S- matrix in the form of soft limits. The most na¨ıve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations. Although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.

  15. Topological classification of trigonometric polynomials related to affine Coxeter group A-tilde2

    International Nuclear Information System (INIS)

    Arnold, V.I.

    2006-06-01

    The family of trigonometric polynomials, is defined by the six?Cparametrical expression f(x, y) = a cos x + b sin x + c cos y + d sin y + p cos(x + y) + q sin(x + y). The trigonometric polynomials of this family, having the most complicated topological structure, have 6 critical points. These functions are classified up to the actions of the following groups: two functions are called to be topologically equivalent, if one is transformed to the other by two smooth diffeomorphisms of the manifolds T 2 and R (of the preimages and of the images of mapping f : T 2 → R). We suppose, that the images diffeomorphisms (dependent variable changes) preserve the orientation of the real line, and that the preimages spaces diffeomorphism is homotopic to the identity mapping of the torus. We shall see, that the trigonometric polynomials which have 6 nondegenerated critical points and six different critical values (that might be fixed at points {1, 2, 3, 4, 5, 6 }) form 6 equivalence classes of topologically different functions, while the general Morse functions on the torus, having six critical points and six fixed critical values, form an infinite set of the equivalence classes of functions. With respect to the Diff-equivalence all these functions form only 16 classes. All these unexpected results suggest, that in the 16 Cth Hilbert's problem (on the topological classification of real algebraic manifolds) one would ask to classify topologically rather the defining polynomials, than the real hypersurfaces of their zeros

  16. Beyond Group: Multiple Person Tracking via Minimal Topology-Energy-Variation.

    Science.gov (United States)

    Gao, Shan; Ye, Qixiang; Xing, Junliang; Kuijper, Arjan; Han, Zhenjun; Jiao, Jianbin; Ji, Xiangyang

    2017-12-01

    Tracking multiple persons is a challenging task when persons move in groups and occlude each other. Existing group-based methods have extensively investigated how to make group division more accurately in a tracking-by-detection framework; however, few of them quantify the group dynamics from the perspective of targets' spatial topology or consider the group in a dynamic view. Inspired by the sociological properties of pedestrians, we propose a novel socio-topology model with a topology-energy function to factor the group dynamics of moving persons and groups. In this model, minimizing the topology-energy-variance in a two-level energy form is expected to produce smooth topology transitions, stable group tracking, and accurate target association. To search for the strong minimum in energy variation, we design the discrete group-tracklet jump moves embedded in the gradient descent method, which ensures that the moves reduce the energy variation of group and trajectory alternately in the varying topology dimension. Experimental results on both RGB and RGB-D data sets show the superiority of our proposed model for multiple person tracking in crowd scenes.

  17. Impact of topology in foliated quantum Einstein gravity

    Energy Technology Data Exchange (ETDEWEB)

    Houthoff, W.B.; Saueressig, F. [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Nijmegen (Netherlands); Kurov, A. [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Nijmegen (Netherlands); Moscow State University, Department of Theoretical Physics, Moscow (Russian Federation)

    2017-07-15

    We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S{sup 1} x S{sup d}. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of ''gravitational instability'', modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S{sup 1} x T{sup d} (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology. (orig.)

  18. From topology to geometry

    International Nuclear Information System (INIS)

    Eberhart, M.

    1996-01-01

    A systematic study of the charge density topologies corresponding to a number of transition metal aluminides with the B2 structure indicates that unstable crystal structures are sometimes associated with uncharacteristic topologies. This observation invites the speculation that the distance to a topological instability might relate to a metals phase behavior. Following this speculation, a metric is imposed on the topological theory of Bader, producing a geometrical theory, where it is now possible to assign a distance from a calculated charge density topology to a topological instability. For the cubic transition metals, these distances are shown to correlate with single crystal elastic constants, where the metals that are furthest from an instability are observed to be the stiffest. (author). 16 refs., 1 tab., 9 figs

  19. Random fields, topology, and the Imry-Ma argument.

    Science.gov (United States)

    Proctor, Thomas C; Garanin, Dmitry A; Chudnovsky, Eugene M

    2014-03-07

    We consider an n-component fixed-length order parameter interacting with a weak random field in d=1, 2, 3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions are studied on lattices containing hundreds of millions of sites. At n ≤ d the presence of topological defects leads to strong metastability and glassy behavior, with the final state depending on the initial condition. At n=d+1, when topological structures are nonsingular, the system possesses a weak metastability. At n>d+1, when topological objects are absent, the final, lowest-energy state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument.

  20. Partitioning in P-T concept

    International Nuclear Information System (INIS)

    Zhang Peilu; Qi Zhanshun; Zhu Zhixuan

    2000-01-01

    Comparison of dry- and water-method for partitioning fission products and minor actinides from the spent fuels, and description of advance of dry-method were done. Partitioning process, some typical concept and some results of dry-method were described. The problems fond in dry-method up to now were pointed out. The partitioning study program was suggested

  1. Topological Acoustics

    Science.gov (United States)

    Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile

    2015-03-01

    The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.

  2. An efficient second-order SQP method for structural topology optimization

    DEFF Research Database (Denmark)

    Rojas Labanda, Susana; Stolpe, Mathias

    2016-01-01

    This article presents a Sequential Quadratic Programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in Morales et al. J Numer Anal 32(2):553–579 (2010) called SQP+. The topology optimization problem...... nonlinear solvers IPOPT and SNOPT. Numerical experiments on a large set of benchmark problems show good performance of TopSQP in terms of number of function evaluations. In addition, the use of second-order information helps to decrease the objective function value....

  3. General Topology of the Universe

    OpenAIRE

    Pandya, Aalok

    2002-01-01

    General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded.

  4. The Topological Analysis of Urban Transit System as a Small-World Network

    OpenAIRE

    Zhaosheng Yang; Huxing Zhou; Peng Gao; Hong Chen; Nan Zhang

    2011-01-01

    This paper proposes a topological analysis of urban transit system based on a functional representation network constructed from the urban transit system in Beijing. The representation gives a functional view on nodes named a transit line. Statistical measures are computed and introduced in complex network analysis. It shows that the urban transit system forms small-world networks and exhibits properties different from random networks and regular networks. Furthermore, the topological propert...

  5. Machine learning topological states

    Science.gov (United States)

    Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.

    2017-11-01

    Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.

  6. Topological methods in Euclidean spaces

    CERN Document Server

    Naber, Gregory L

    2000-01-01

    Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.

  7. Network module detection: Affinity search technique with the multi-node topological overlap measure.

    Science.gov (United States)

    Li, Ai; Horvath, Steve

    2009-07-20

    Many clustering procedures only allow the user to input a pairwise dissimilarity or distance measure between objects. We propose a clustering method that can input a multi-point dissimilarity measure d(i1, i2, ..., iP) where the number of points P can be larger than 2. The work is motivated by gene network analysis where clusters correspond to modules of highly interconnected nodes. Here, we define modules as clusters of network nodes with high multi-node topological overlap. The topological overlap measure is a robust measure of interconnectedness which is based on shared network neighbors. In previous work, we have shown that the multi-node topological overlap measure yields biologically meaningful results when used as input of network neighborhood analysis. We adapt network neighborhood analysis for the use of module detection. We propose the Module Affinity Search Technique (MAST), which is a generalized version of the Cluster Affinity Search Technique (CAST). MAST can accommodate a multi-node dissimilarity measure. Clusters grow around user-defined or automatically chosen seeds (e.g. hub nodes). We propose both local and global cluster growth stopping rules. We use several simulations and a gene co-expression network application to argue that the MAST approach leads to biologically meaningful results. We compare MAST with hierarchical clustering and partitioning around medoid clustering. Our flexible module detection method is implemented in the MTOM software which can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/MTOM/

  8. Ordered groups and topology

    CERN Document Server

    Clay, Adam

    2016-01-01

    This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

  9. Topology Identification of General Dynamical Network with Distributed Time Delays

    International Nuclear Information System (INIS)

    Zhao-Yan, Wu; Xin-Chu, Fu

    2009-01-01

    General dynamical networks with distributed time delays are studied. The topology of the networks are viewed as unknown parameters, which need to be identified. Some auxiliary systems (also called the network estimators) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied in designing these network estimators. Based on linear matrix inequalities and the Lyapunov function method, the sufficient condition for the achievement of topology identification is obtained. This method can also better monitor the switching topology of dynamical networks. Illustrative examples are provided to show the effectiveness of this method. (general)

  10. Minimum nonuniform graph partitioning with unrelated weights

    Science.gov (United States)

    Makarychev, K. S.; Makarychev, Yu S.

    2017-12-01

    We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G=(V,E) and k numbers ρ_1,\\dots, ρ_k. The goal is to partition V into k disjoint sets (bins) P_1,\\dots, P_k satisfying \\vert P_i\\vert≤ ρi \\vert V\\vert for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(\\sqrt{log \\vert V\\vert log k}) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints \\vert P_i\\vert ≤ (5+ \\varepsilon)ρi \\vert V\\vert. This algorithm is an improvement upon the O(log \\vert V\\vert)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and Programming (ICALP 2014). Bibliography: 7 titles.

  11. Partitioning planning studies: Preliminary evaluation of metal and radionuclide partitioning the high-temperature thermal treatment systems

    International Nuclear Information System (INIS)

    Liekhus, K.; Grandy, J.; Chambers, A.

    1997-03-01

    A preliminary study of toxic metals and radionuclide partitioning during high-temperature processing of mixed waste has been conducted during Fiscal Year 1996 within the Environmental Management Technology Evaluation Project. The study included: (a) identification of relevant partitioning mechanisms that cause feed material to be distributed between the solid, molten, and gas phases within a thermal treatment system; (b) evaluations of existing test data from applicable demonstration test programs as a means to identify and understand elemental and species partitioning; and, (c) evaluation of theoretical or empirical partitioning models for use in predicting elemental or species partitioning in a thermal treatment system. This preliminary study was conducted to identify the need for and the viability of developing the tools capable of describing and predicting toxic metals and radionuclide partitioning in the most applicable mixed waste thermal treatment processes. This document presents the results and recommendations resulting from this study that may serve as an impetus for developing and implementing these predictive tools

  12. Partitioning planning studies: Preliminary evaluation of metal and radionuclide partitioning the high-temperature thermal treatment systems

    Energy Technology Data Exchange (ETDEWEB)

    Liekhus, K.; Grandy, J.; Chambers, A. [and others

    1997-03-01

    A preliminary study of toxic metals and radionuclide partitioning during high-temperature processing of mixed waste has been conducted during Fiscal Year 1996 within the Environmental Management Technology Evaluation Project. The study included: (a) identification of relevant partitioning mechanisms that cause feed material to be distributed between the solid, molten, and gas phases within a thermal treatment system; (b) evaluations of existing test data from applicable demonstration test programs as a means to identify and understand elemental and species partitioning; and, (c) evaluation of theoretical or empirical partitioning models for use in predicting elemental or species partitioning in a thermal treatment system. This preliminary study was conducted to identify the need for and the viability of developing the tools capable of describing and predicting toxic metals and radionuclide partitioning in the most applicable mixed waste thermal treatment processes. This document presents the results and recommendations resulting from this study that may serve as an impetus for developing and implementing these predictive tools.

  13. Fine topology and locally Minkowskian manifolds

    Science.gov (United States)

    Agrawal, Gunjan; Sinha, Soami Pyari

    2018-05-01

    Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.

  14. Current-induced switching of magnetic molecules on topological insulator surfaces

    Science.gov (United States)

    Locane, Elina; Brouwer, Piet W.

    2017-03-01

    Electrical currents at the surface or edge of a topological insulator are intrinsically spin polarized. We show that such surface or edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface or edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.

  15. TEMPERATURE DEPENDENT PHASE BEHAVIOR AND PROTEIN PARTITIONING IN GIANT PLASMA MEMBRANE VESICLES

    OpenAIRE

    Johnson, SA; Stinson, BM; Go, M; Carmona, LM; Reminick, JI; Fang, X; Baumgart, T

    2010-01-01

    Liquid-ordered (Lo) and liquid-disordered (Ld) phase coexistence has been suggested to partition the plasma membrane of biological cells into lateral compartments, allowing for enrichment or depletion of functionally relevant molecules. This dynamic partitioning might be involved in fine-tuning cellular signaling fidelity through coupling to the plasma membrane protein and lipid composition. In earlier work, giant plasma membrane vesicles, obtained by chemically induced blebbing from cultured...

  16. Gapless Symmetry-Protected Topological Order

    Directory of Open Access Journals (Sweden)

    Thomas Scaffidi

    2017-11-01

    Full Text Available We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension (d-1 SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.

  17. Hawk: A Runtime System for Partitioned Objects

    NARCIS (Netherlands)

    Ben Hassen, S.; Bal, H.E.; Tanenbaum, A.S.

    1997-01-01

    Hawk is a language-independent runtime system for writing data-parallel programs using partitioned objects. A partitioned object is a multidimensional array of elements that can be partitioned and distributed by the programmer. The Hawk runtime system uses the user-defined partitioning of objects

  18. Geometrical interpretation of the topological recursion, and integrable string theories

    CERN Document Server

    Eynard, Bertrand

    2009-01-01

    Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative geometry like maps, partitions, Hurwitz numbers, intersection numbers, Gromov-Witten invariants... The problem is thus to understand what they count, or in other words, given a spectral curve, construct an enumerative geometry problem. This is what we do in a semi-heuristic approach in this article. Starting from a spectral curve, i.e. an integrable system, we use its flat connection and flat coordinates, to define a family of worldsheets, whose enumeration is indeed solved by the topological recursion and symplectic invariants. In other words, for any spectral curve, we construct a corresponding string theory, whose target space is a submanifold of the Jacobian.

  19. Truss topology optimization with simultaneous analysis and design

    Science.gov (United States)

    Sankaranarayanan, S.; Haftka, Raphael T.; Kapania, Rakesh K.

    1992-01-01

    Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.

  20. Chiral topological excitons in a Chern band insulator

    Science.gov (United States)

    Chen, Ke; Shindou, Ryuichi

    2017-10-01

    A family of semiconductors called Chern band insulators are shown to host exciton bands with nonzero topological Chern integers and chiral exciton edge modes. Using a prototypical two-band Chern insulator model, we calculate a cross-correlation function to obtain the exciton bands and their Chern integers. The lowest exciton band acquires Chern integers such as ±1 and ±2 in the electronic Chern insulator phase. The nontrivial topology can be experimentally observed both by a nonlocal optoelectronic response of exciton edge modes and by a phase shift in the cross-correlation response due to the bulk mode. Our result suggests that magnetically doped HgTe, InAs/GaSb quantum wells, and (Bi,Sb)2Te3 thin films are promising candidates for a platform of topological excitonics.

  1. Dynamical topology and statistical properties of spatiotemporal chaos.

    Science.gov (United States)

    Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

    2012-12-01

    For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

  2. Topology control

    NARCIS (Netherlands)

    Buchin, K.; Buchin, M.; Wagner, D.; Wattenhofer, R.

    2007-01-01

    Information between two nodes in a network is sent based on the network topology, the structure of links connecting pairs of nodes of a network. The task of topology control is to choose a connecting subset from all possible links such that the overall network performance is good. For instance, a

  3. Topology of membrane proteins-predictions, limitations and variations.

    Science.gov (United States)

    Tsirigos, Konstantinos D; Govindarajan, Sudha; Bassot, Claudio; Västermark, Åke; Lamb, John; Shu, Nanjiang; Elofsson, Arne

    2017-10-26

    Transmembrane proteins perform a variety of important biological functions necessary for the survival and growth of the cells. Membrane proteins are built up by transmembrane segments that span the lipid bilayer. The segments can either be in the form of hydrophobic alpha-helices or beta-sheets which create a barrel. A fundamental aspect of the structure of transmembrane proteins is the membrane topology, that is, the number of transmembrane segments, their position in the protein sequence and their orientation in the membrane. Along these lines, many predictive algorithms for the prediction of the topology of alpha-helical and beta-barrel transmembrane proteins exist. The newest algorithms obtain an accuracy close to 80% both for alpha-helical and beta-barrel transmembrane proteins. However, lately it has been shown that the simplified picture presented when describing a protein family by its topology is limited. To demonstrate this, we highlight examples where the topology is either not conserved in a protein superfamily or where the structure cannot be described solely by the topology of a protein. The prediction of these non-standard features from sequence alone was not successful until the recent revolutionary progress in 3D-structure prediction of proteins. Copyright © 2017 Elsevier Ltd. All rights reserved.

  4. Phase transition and field effect topological quantum transistor made of monolayer MoS2

    Science.gov (United States)

    Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

    2018-06-01

    We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

  5. Self-ordering of nontrivial topological polarization structures in nanoporous ferroelectrics.

    Science.gov (United States)

    Van Lich, Le; Shimada, Takahiro; Wang, Jie; Kitamura, Takayuki

    2017-10-19

    Topological field structures, such as skyrmions, merons, and vortices, are important features found in ordered systems with spontaneously broken symmetry. A plethora of topological field structures have been discovered in magnetic and ordered soft matter systems due to the presence of inherent chiral interactions, and this has provided a fruitful platform for unearthing additional groundbreaking functionalities. However, despite being one of the most important classes of ordered systems, ferroelectrics scarcely form topological polarization structures due to their lack of intrinsic chiral interactions. In the present study, we demonstrate using multiphysics phase-field modelling based on the Ginzburg-Landau theory that a rich assortment of nontrivial topological polarization structures, including hedgehogs, antivortices, multidirectional vortices, and vortex arrays, can be spontaneously formed in three-dimensional nanoporous ferroelectric structures. We realize that confining ferroelectrics to trivial geometries that are incompatible with the orientation symmetry may impose extrinsic frustration to the polarization field through the enhancement of depolarization fields at free porous surfaces. This frustration gives rise to symmetry breaking, resulting in the formation of nontrivial topological polarization structures as the ground state. We further topologically characterize the local accommodation of polarization structures by viewing them in a new perspective, in which polarization ordering can be mapped on the order parameter space, according to the topological theory of defects and homotopy theory. The results indicate that the nanoporous structures contain composite topological objects composed of two or more elementary topological polarization structures. The present study therefore offers a playground for exploring novel physical phenomena in ferroelectric systems as well as a novel nanoelectronics characterization platform for future topology

  6. [On the partition of acupuncture academic schools].

    Science.gov (United States)

    Yang, Pengyan; Luo, Xi; Xia, Youbing

    2016-05-01

    Nowadays extensive attention has been paid on the research of acupuncture academic schools, however, a widely accepted method of partition of acupuncture academic schools is still in need. In this paper, the methods of partition of acupuncture academic schools in the history have been arranged, and three typical methods of"partition of five schools" "partition of eighteen schools" and "two-stage based partition" are summarized. After adeep analysis on the disadvantages and advantages of these three methods, a new method of partition of acupuncture academic schools that is called "three-stage based partition" is proposed. In this method, after the overall acupuncture academic schools are divided into an ancient stage, a modern stage and a contemporary stage, each schoolis divided into its sub-school category. It is believed that this method of partition can remedy the weaknesses ofcurrent methods, but also explore a new model of inheritance and development under a different aspect through thedifferentiation and interaction of acupuncture academic schools at three stages.

  7. Strain effects in topological insulators: Topological order and the emergence of switchable topological interface states in Sb2Te3/Bi2Te3 heterojunctions

    Science.gov (United States)

    Aramberri, H.; Muñoz, M. C.

    2017-05-01

    We investigate the effects of strain on the topological order of the Bi2Se3 family of topological insulators by ab initio first-principles methods. Strain can induce a topological phase transition and we present the phase diagram for the 3D topological insulators, Bi2Te3 , Sb2Te3 , Bi2Se3 , and Sb2Se3 , under combined uniaxial and biaxial strain. Their phase diagram is universal and shows metallic and insulating phases, both topologically trivial and nontrivial. In particular, uniaxial tension can drive the four compounds into a topologically trivial insulating phase. We propose a Sb2Te3/Bi2Te3 heterojunction in which a strain-induced topological interface state arises in the common gap of this normal insulator-topological insulator heterojunction. Unexpectedly, the interface state is confined in the topologically trivial subsystem and is physically protected from ambient impurities. It can be switched on or off by means of uniaxial strain and therefore Sb2Te3 /Bi2Te3 heterojunctions provide a topological system which hosts tunable robust helical interface states with promising spintronic applications.

  8. Representation of magnetic fields with toroidal topology in terms of field-line invariants

    International Nuclear Information System (INIS)

    Lewis, H.R.

    1990-01-01

    Beginning with Boozer's representation of magnetic fields with toroidal topology [Phys. Fluids 26, 1288 (1983)], a general formalism is presented for the representation of any magnetic field with toroidal topology in terms of field-line invariants. The formalism is an application to the magnetic field case of results developed recently by Lewis et al. (submitted for publication to J. Phys. A) for arbitrary time-dependent Hamiltonian systems with one degree of freedom. Every magnetic field with toroidal topology can be associated with time-dependent Hamiltonian systems with one degree of freedom and every time-dependent Hamiltonian system with one degree of freedom can be associated with magnetic fields with toroidal topology. In the Hamiltonian context, given any particular function I(q,p,t), Lewis et al. derived those Hamiltonians for which I(q,p,t) is an invariant. In addition, for each of those Hamiltonians, they derived a function canonically conjugate to I(q,p,t) that is also an invariant. They applied this result to the case where I(q,p,t) is expressed as a function of two canonically conjugate functions. This general Hamiltonian formalism provides a basis for representing magnetic fields with toroidal topology in terms of field-line invariants. The magnetic fields usually contain plasma with flow and anisotropic pressure. A class of fields with or without rotational symmetry is identified for which there are magnetic surfaces. The formalism is developed for application to the case of vacuum magnetic fields

  9. Analysis of load balance in hybrid partitioning | Talib | Botswana ...

    African Journals Online (AJOL)

    In information retrieval systems, there are three types of index partitioning schemes - term partitioning, document partitioning, and hybrid partitioning. The hybrid-partitioning scheme combines both term and document partitioning schemes. Term partitioning provides high concurrency, which means that queries can be ...

  10. Topological massive sigma models

    International Nuclear Information System (INIS)

    Lambert, N.D.

    1995-01-01

    In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models. ((orig.))

  11. Topics in general topology

    CERN Document Server

    Morita, K

    1989-01-01

    Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.

  12. Mean value theorem in topological vector spaces

    International Nuclear Information System (INIS)

    Khan, L.A.

    1994-08-01

    The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs

  13. The Algebraic versus the Topological Approach to Additive Representations

    NARCIS (Netherlands)

    P.P. Wakker (Peter)

    1988-01-01

    textabstractIt is proved that, under a nontriviality assumption, an additive function on a Cartesian product of connected topological spaces is continuous, whenever the preference relation, represented by this function, is continuous. The result is used to generalize a theorem of Debreu ((1960).

  14. Topological geons with self-gravitating phantom scalar field

    Science.gov (United States)

    Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

    2017-12-01

    A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

  15. The total position-spread tensor: Spin partition

    International Nuclear Information System (INIS)

    El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry; Brea, Oriana; Fertitta, Edoardo; Bendazzoli, Gian Luigi

    2015-01-01

    The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H n (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system

  16. Generalized Enhanced Multivariance Product Representation for Data Partitioning: Constancy Level

    International Nuclear Information System (INIS)

    Tunga, M. Alper; Demiralp, Metin

    2011-01-01

    Enhanced Multivariance Product Representation (EMPR) method is used to represent multivariate functions in terms of less-variate structures. The EMPR method extends the HDMR expansion by inserting some additional support functions to increase the quality of the approximants obtained for dominantly or purely multiplicative analytical structures. This work aims to develop the generalized form of the EMPR method to be used in multivariate data partitioning approaches. For this purpose, the Generalized HDMR philosophy is taken into consideration to construct the details of the Generalized EMPR at constancy level as the introductory steps and encouraging results are obtained in data partitioning problems by using our new method. In addition, to examine this performance, a number of numerical implementations with concluding remarks are given at the end of this paper.

  17. Instanton effects in ABJM theory from Fermi gas approach

    Energy Technology Data Exchange (ETDEWEB)

    Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

    2012-11-19

    We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1, 2, 3, 4, 6 up to N=44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.

  18. Relational topology

    CERN Document Server

    Schmidt, Gunther

    2018-01-01

    This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.

  19. Simulation of a pulsatile total artificial heart: Development of a partitioned Fluid Structure Interaction model

    Science.gov (United States)

    Sonntag, Simon J.; Kaufmann, Tim A. S.; Büsen, Martin R.; Laumen, Marco; Linde, Torsten; Schmitz-Rode, Thomas; Steinseifer, Ulrich

    2013-04-01

    Heart disease is one of the leading causes of death in the world. Due to a shortage in donor organs artificial hearts can be a bridge to transplantation or even serve as a destination therapy for patients with terminal heart insufficiency. A pusher plate driven pulsatile membrane pump, the Total Artificial Heart (TAH) ReinHeart, is currently under development at the Institute of Applied Medical Engineering of RWTH Aachen University.This paper presents the methodology of a fully coupled three-dimensional time-dependent Fluid Structure Interaction (FSI) simulation of the TAH using a commercial partitioned block-Gauss-Seidel coupling package. Partitioned coupling of the incompressible fluid with the slender flexible membrane as well as a high fluid/structure density ratio of about unity led inherently to a deterioration of the stability (‘artificial added mass instability’). The objective was to conduct a stable simulation with high accuracy of the pumping process. In order to achieve stability, a combined resistance and pressure outlet boundary condition as well as the interface artificial compressibility method was applied. An analysis of the contact algorithm and turbulence condition is presented. Independence tests are performed for the structural and the fluid mesh, the time step size and the number of pulse cycles. Because of the large deformation of the fluid domain, a variable mesh stiffness depending on certain mesh properties was specified for the fluid elements. Adaptive remeshing was avoided. Different approaches for the mesh stiffness function are compared with respect to convergence, preservation of mesh topology and mesh quality. The resulting mesh aspect ratios, mesh expansion factors and mesh orthogonalities are evaluated in detail. The membrane motion and flow distribution of the coupled simulations are compared with a top-view recording and stereo Particle Image Velocimetry (PIV) measurements, respectively, of the actual pump.

  20. Analysis of Membrane Protein Topology in the Plant Secretory Pathway.

    Science.gov (United States)

    Guo, Jinya; Miao, Yansong; Cai, Yi

    2017-01-01

    Topology of membrane proteins provides important information for the understanding of protein function and intermolecular associations. Integrate membrane proteins are generally transported from endoplasmic reticulum (ER) to Golgi and downstream compartments in the plant secretory pathway. Here, we describe a simple method to study membrane protein topology along the plant secretory pathway by transiently coexpressing a fluorescent protein (XFP)-tagged membrane protein and an ER export inhibitor protein, ARF1 (T31N), in tobacco BY-2 protoplast. By fractionation, microsome isolation, and trypsin digestion, membrane protein topology could be easily detected by either direct confocal microscopy imaging or western-blot analysis using specific XFP antibodies. A similar strategy in determining membrane protein topology could be widely adopted and applied to protein analysis in a broad range of eukaryotic systems, including yeast cells and mammalian cells.