WorldWideScience

Sample records for topological formal treatment

  1. Topology in quantum states. PEPS formalism and beyond

    Energy Technology Data Exchange (ETDEWEB)

    Aguado, M [Max-Planck-Institut fuer Quantenoptik. Hans-Kopfermann-Str. 1. D-85748 Garching (Germany); Cirac, J I [Max-Planck-Institut fuer Quantenoptik. Hans-Kopfermann-Str. 1. D-85748 Garching (Germany); Vidal, G [School of Physical Sciences. University of Queensland, Brisbane, QLD, 4072 (Australia)

    2007-11-15

    Topology has been proposed as a tool to protect quantum information encoding and processes. Work concerning the meaning of topology in quantum states as well as its characterisation in the projected entangled pair state (PEPS) formalism and related schemes is reviewed.

  2. The Mathai-Quillen formalism and topological field theory

    International Nuclear Information System (INIS)

    Blau, Matthias.

    1992-01-01

    These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over space of connections. (author). 44 refs

  3. 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

  4. The topology of the possible: formal spaces underlying patterns of evolutionary change.

    Science.gov (United States)

    Stadler, B M; Stadler, P F; Wagner, G P; Fontana, W

    2001-11-21

    The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotype-phenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pre-topology. Patterns of phenotypic evolution-such as punctuation, irreversibility, modularity--result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. We introduce the mathematical concepts and tools necessary to formalize the notion of accessibility pre-topology relative to which we can speak of continuity in the genotype-phenotype map and in evolutionary trajectories. We connect the factorization of a pre-topology into a product space with the notion of phenotypic character and derive a condition for factorization. Based on anecdotal evidence from the RNA model, we conjecture that this condition is not globally fulfilled, but rather confined to regions where the genotype-phenotype map is continuous. Equivalently, local regions of genotype space on which the map is discontinuous are associated with the loss of character autonomy. This is consistent with the importance of these regions for phenotypic innovation. The intention of the present paper is to offer a perspective, a framework to implement this perspective, and a few results illustrating how this framework can

  5. 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.)

  6. Topology

    CERN Document Server

    Kuratowski, Kazimierz

    1968-01-01

    Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte

  7. Formal groups and applications

    CERN Document Server

    Hazewinkel, Michiel

    2012-01-01

    This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.

  8. The Jasper Framework: Towards a Platform Independent, Formal Treatment of Web Programming

    Directory of Open Access Journals (Sweden)

    James Smith

    2012-10-01

    Full Text Available This paper introduces Jasper, a web programming framework which allows web applications to be developed in an essentially platform indepedent manner and which is also suited to a formal treatment. It outlines Jasper conceptually and shows how Jasper is implemented on several commonplace platforms. It also introduces the Jasper Music Store, a web application powered by Jasper and implemented on each of these platforms. And it briefly describes a formal treatment and outlines the tools and languages planned that will allow this treatment to be automated.

  9. 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.

  10. Thermodynamic treatment of nonphysical systems: formalism and an example (single-lane traffic)

    International Nuclear Information System (INIS)

    Reiss, H.; Hammerich, A.D.; Montroll, E.W.

    1986-01-01

    An effort is made to introduce thermodynamic and statistical thermodynamic methods into the treatment of nonphysical (e.g., social, economic, etc.) systems. Emphasis is placed on the use of the entire thermodynamic framework, not merely entropy. Entropy arises naturally, related in a simple manner to other measurables, but does not occupy a primary position in the theory. However, the maximum entropy formalism is a convenient procedure for deriving the thermodynamic analog framework in which undetermined multipliers are thermodynamic-like variables which summarize the collective behavior of the system. The authors discuss the analysis of Levine and his coworkers showing that the maximum entropy formalism is the unique algorithm for achieving consistent inference of probabilities. The thermodynamic-like formalism for treating a single lane of vehicular traffic is developed and applied to traffic in which the interaction between cars is chosen to be a particular form of the ''follow-the-leader'' type. The equation of state of the traffic, the distributions of velocity and headway, and the various thermodynamic-like parameters, e.g., temperature (collective sensitivity), pressure, etc. are determined for the example of the Holland Tunnel. Nearest-neighbor and pair correlation functions for the vehicles are also determined. Interesting and suggestive results are obtained

  11. Formalization of treatment guidelines using Fuzzy Cognitive Maps and semantic web tools.

    Science.gov (United States)

    Papageorgiou, Elpiniki I; Roo, Jos De; Huszka, Csaba; Colaert, Dirk

    2012-02-01

    Therapy decision making and support in medicine deals with uncertainty and needs to take into account the patient's clinical parameters, the context of illness and the medical knowledge of the physician and guidelines to recommend a treatment therapy. This research study is focused on the formalization of medical knowledge using a cognitive process, called Fuzzy Cognitive Maps (FCMs) and semantic web approach. The FCM technique is capable of dealing with situations including uncertain descriptions using similar procedure such as human reasoning does. Thus, it was selected for the case of modeling and knowledge integration of clinical practice guidelines. The semantic web tools were established to implement the FCM approach. The knowledge base was constructed from the clinical guidelines as the form of if-then fuzzy rules. These fuzzy rules were transferred to FCM modeling technique and, through the semantic web tools, the whole formalization was accomplished. The problem of urinary tract infection (UTI) in adult community was examined for the proposed approach. Forty-seven clinical concepts and eight therapy concepts were identified for the antibiotic treatment therapy problem of UTIs. A preliminary pilot-evaluation study with 55 patient cases showed interesting findings; 91% of the antibiotic treatments proposed by the implemented approach were in fully agreement with the guidelines and physicians' opinions. The results have shown that the suggested approach formalizes medical knowledge efficiently and gives a front-end decision on antibiotics' suggestion for cystitis. Concluding, modeling medical knowledge/therapeutic guidelines using cognitive methods and web semantic tools is both reliable and useful. Copyright © 2011 Elsevier Inc. All rights reserved.

  12. Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

    Directory of Open Access Journals (Sweden)

    Zhanpeng Fang

    2015-01-01

    Full Text Available A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.

  13. From geometry to topology

    CERN Document Server

    Flegg, H Graham

    2001-01-01

    This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.

  14. Differential topology an introduction

    CERN Document Server

    Gauld, David B

    2006-01-01

    Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curv

  15. Homotopical topology

    CERN Document Server

    Fomenko, Anatoly

    2016-01-01

    This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role ...

  16. A formal treatment of uncertainty sources in a level 2 PSA

    International Nuclear Information System (INIS)

    Ahn, Kwang Il; Yang, Joon Eon

    2003-01-01

    The methodological framework of the level 2 PSA appears to be currently standardized in a formalized fashion, but there have been different opinions on the way the sources of uncertainty are characterized and treated. This is primarily because the level 2 PSA deals with complex phenomenological processes that are deterministic in nature rather than random processes, and there are no probabilistic models characterizing them clearly. As a result, the probabilistic quantification of the level 2 PSA is often subjected to two sources of uncertainty: (a) incomplete modeling of accident pathways or different predictions for the behavior of phenomenological events and (b) expert-to-expert variation in estimating the occurrence probability of phenomenological events. While a clear definition of the two sources of uncertainty involved in the level 2 PSA makes it possible to treat an uncertainty in a consistent manner, careless application of these different sources of uncertainty may produce different conclusions in the decision-making process. The primary purpose of this paper is to characterize typical sources of uncertainty that would often be addressed in the level 2 PSA and their impacts on the PSA level 2 risk results. An additional purpose of this paper is to give a formal approach on how to combine random uncertainties addressed in the level 1 PSA with subjectivistic uncertainties addressed in the level 2 PSA

  17. Enzymatic treatment of duck hepatitis B virus: Topology of the surface proteins for virions and noninfectious subviral particles

    International Nuclear Information System (INIS)

    Franke, Claudia; Matschl, Urte; Bruns, Michael

    2007-01-01

    The large surface antigen L of duck hepatitis B virus exhibits a mixed topology with the preS domains of the protein alternatively exposed to the particles' interior or exterior. After separating virions from subviral particles (SVPs), we compared their L topologies and showed that both particle types exhibit the same amount of L with the following differences: 1-preS of intact virions was enzymatically digested with chymotrypsin, whereas in SVPs only half of preS was accessible, 2-phosphorylation of L at S118 was completely removed by phosphatase treatment only in virions, 3-iodine-125 labeling disclosed a higher ratio of exposed preS to S domains in virions compared to SVPs. These data point towards different surface architectures of virions and SVPs. Because the preS domain acts in binding to a cellular receptor of hepatocytes, our findings implicate the exclusion of SVPs as competitors for the receptor binding and entry of virions

  18. Formal Design and Analysis of a Wastewater Treatment Control System based on Petrinet

    Directory of Open Access Journals (Sweden)

    Seno D. Panjaitan

    2012-04-01

    Full Text Available This paper proposes a new control design approach for industrial wastewater treatment where its logic control is verifiable. In this research, a treatment control design in a lab-scale was controlled by a microcontroller circuit. The developed system combined anaerobic digestion, aeration and filtration process. Its logic control algorithm was designed by using Signal Interpreted Petri Net. In the logic verification, six analysis properties were satisfied: conflict free (logical process had no conflict behavior, termination (the process could be terminated from any state, non-contradictory outputs, live (any process state could always be reached from other state, deadlock-free, and reversible (the process could always back to initial condition. In the design evaluation, the average value of transparency metrics was 0.984 close to 1 as the best value. The system performance was evaluated by pollutant removal efficiency. The highest removal efficiencies were obtained when each anaerobic and aeration treatment were performed for three days respectively and followed by filtration. Within this condition, the system obtained average removal efficiency 91.7% of Chemical Oxygen Demand and 95.4% of Total Suspended Solids. In terms of electricity consumption, the system needed only 1,857.6 Watt-hour for a batch treatment process.

  19. Coefficient rings of formal group laws

    International Nuclear Information System (INIS)

    Buchstaber, V M; Ustinov, A V

    2015-01-01

    We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. Bibliography: 37 titles

  20. Topological Excitations in Quantum Spin Systems

    Directory of Open Access Journals (Sweden)

    Ranjan Chaudhury

    2013-01-01

    Full Text Available The origin and significance of topological excitations in quantum spin models in low dimensions are presented in detail. Besides a general review, our own work in this area is described in great depth. Apart from theoretical analysis of the existence and properties of spin vortices and antivortices, the possible experimental consequences and signatures are also highlighted. In particular, the distinguishing features between the even and odd charged topological excitations are brought out through a detailed analysis of the topological term in the quantum action. Moreover, an interesting symmetry property is predicted between the excitations from a ferromagnetic model and an antiferromagnetic model. Through a novel approach of ours, a bridge is established between field theoretical formalism and the well-known statistical mechanical treatment of Berezinskii-Kosterlitz-Thouless (BKT transition involving these topological excitations. Furthermore, a detailed phenomenological analysis of the experimentally observed static and dynamic magnetic properties of the layered magnetic materials, possessing XY anisotropy in the in-plane spin-spin couplings, is undertaken to test the theoretical predictions regarding the behaviour of these excitations. The importance and the crucial role of quantum spin fluctuations in these studies are also brought out very clearly by our analysis.

  1. Differential topology

    CERN Document Server

    Margalef-Roig, J

    1992-01-01

    ...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

  2. 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...

  3. 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.

  4. Topological susceptibility from the overlap

    DEFF Research Database (Denmark)

    Del Debbio, Luigi; Pica, Claudio

    2003-01-01

    The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge....... Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study...... the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high...

  5. Superfield formalism

    Indian Academy of Sciences (India)

    dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original. 4D theory. Keywords. Non-Abelian 1-form gauge theory; Dirac fields; (anti-)Becchi–Roucet–Stora–. Tyutin invariance; superfield formalism; ...

  6. 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

  7. Superfield formalism

    Indian Academy of Sciences (India)

    framework of the usual superfield approach to BRST formalism [1–9]. This ap- proach, however, has not been able ... within the framework of the superfield formulation. The central theme of a couple of very ... define [23a] the curvature tensor Fµν = ∂µAν −∂νAµ +iAµ ×Aν. Here B and ¯B are the auxiliary fields that satisfy the ...

  8. Beyond formalism

    Science.gov (United States)

    Denning, Peter J.

    1991-01-01

    The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.

  9. Intuitive Topology

    Indian Academy of Sciences (India)

    Topology is usually taught in India in the second year of a master's degree programme. Much of the time is spent on developing such basic notions as connectedness, compactness, product topology, and the course ends with. Tychonov's theorem or Urysohn's lemma. At best, the student learns a bit about the fundamental ...

  10. Topological field patterns in the Yang–Mills theory

    Indian Academy of Sciences (India)

    Abstract. We present a formalism where the topological configurations of pure Yang–Mills the- ory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topological SO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the 't ...

  11. 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

  12. 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

  13. Neutrosophic Topology

    Directory of Open Access Journals (Sweden)

    Serkan Karatas

    2016-12-01

    Full Text Available In this paper, we redefine the neutrosophic set operations and, by using them, we introduce neutrosophic topology and investigate some related properties such as neutrosophic closure, neutrosophic closure, neutrosophic interior, neutrosophic exterior, neutrosophic boundary and neutrosophic subspace.

  14. Effects of pre-deformation in topological characterization of inconel 600 submitted to isothermal treatments

    International Nuclear Information System (INIS)

    Mourao, D.R.; Monteiro, E.

    1980-01-01

    INCONEL 600 samples were performed at thermal treatment between 550 0 C and 790 0 C during 3 hours after uniaxial tension testing. At each pair hardening-temperature were determined the microhardness and microstrostructure. With the objetive of to determine the influence of the hardening up to INCONEL's mechanical behavior, were plotted microhardness X temperature. (Author) [pt

  15. Topology essentials

    CERN Document Server

    Milewski, Emil G

    2013-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co

  16. Pseudoperiodic topology

    CERN Document Server

    Arnold, Vladimir; Zorich, Anton

    1999-01-01

    This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors … have done much to s

  17. 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.

  18. Algebraic Topology

    CERN Document Server

    Oliver, Bob; Pawałowski, Krzystof

    1991-01-01

    As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.

  19. Topology optimization

    DEFF Research Database (Denmark)

    Bendsøe, Martin P.; Sigmund, Ole

    2007-01-01

    Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...

  20. ALGEBRAIC TOPOLOGY

    Indian Academy of Sciences (India)

    TOPOLOGY. Allen Hatcher. October 2004 Volume 9 Number 10. GENERAL ARTICLES. 10 Taylor the Sailor. V Radhakrishnan. 19 Twisted Winged Endoparasitoids. An Enigma for Entomologists. Alpana Mazumdar. 25 Xanthan - A Versatile Gum. Anil Lachke. 34 From Natural Numbers to Numbers and. Curves in Nature - II.

  1. RNA topology

    OpenAIRE

    Frank-Kamenetskii, Maxim D.

    2013-01-01

    A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases.

  2. ALGEBRAIC TOPOLOGY

    Indian Academy of Sciences (India)

    tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

  3. A global wave-driven magnetohydrodynamic solar model with a unified treatment of open and closed magnetic field topologies

    Energy Technology Data Exchange (ETDEWEB)

    Oran, R.; Van der Holst, B.; Landi, E.; Jin, M.; Sokolov, I. V.; Gombosi, T. I., E-mail: oran@umich.edu [Atmospheric, Oceanic and Atmospheric Sciences, University of Michigan, 2455 Hayward, Ann Arbor, MI, 48105 (United States)

    2013-12-01

    We describe, analyze, and validate the recently developed Alfvén Wave Solar Model, a three-dimensional global model starting from the top of the chromosphere and extending into interplanetary space (out to 1-2 AU). This model solves the extended, two-temperature magnetohydrodynamics equations coupled to a wave kinetic equation for low-frequency Alfvén waves. In this picture, heating and acceleration of the plasma are due to wave dissipation and to wave pressure gradients, respectively. The dissipation process is described by a fully developed turbulent cascade of counterpropagating waves. We adopt a unified approach for calculating the wave dissipation in both open and closed magnetic field lines, allowing for a self-consistent treatment in any magnetic topology. Wave dissipation is the only heating mechanism assumed in the model; no geometric heating functions are invoked. Electron heat conduction and radiative cooling are also included. We demonstrate that the large-scale, steady state (in the corotating frame) properties of the solar environment are reproduced, using three adjustable parameters: the Poynting flux of chromospheric Alfvén waves, the perpendicular correlation length of the turbulence, and a pseudoreflection coefficient. We compare model results for Carrington rotation 2063 (2007 November-December) with remote observations in the extreme-ultraviolet and X-ray ranges from the Solar Terrestrial Relations Observatory, Solar and Heliospheric Observatory, and Hinode spacecraft and with in situ measurements by Ulysses. The results are in good agreement with observations. This is the first global simulation that is simultaneously consistent with observations of both the thermal structure of the lower corona and the wind structure beyond Earth's orbit.

  4. Comparisons of π-Electron Ring-Current and Bond-Current Patterns Calculated by Topological (‘HLPM’ and Ab Initio (‘Ipso-Centric’ Formalisms for Two Isomeric Conjugated Hydrocarbons, Corazulene and Cornaphthalene

    Directory of Open Access Journals (Sweden)

    T. K. Dickens

    2015-12-01

    Full Text Available The π-electron ring-currents and bond-currents associated with the isomeric structures corazulene (1 and cornaphthalene (2 are calculated by means of the rudimentary topological Hückel–London–Pople–McWeeny (HLPM method (which is entirely equivalent to the recently named ‘graph-theoretical CD–HL’ approach.These currents are compared with analogous quantities computed by Lillington et al. by use of the more-sophisticated ipso–centric ab initio approach. The simple HLPM method is seen to exhibit a remarkable ability to reproduce complex patterns of current in large polycyclic hydrocarbons — the successful prediction of which, ostensibly, might naïvely be expected to be the preserve only of more sophisticated, and much less intuitive, ab initio calculations. This conclusion is entirely consistent with findings from contemporary work on other structures by the present, and other, authors.

  5. A treatment of the Zeeman effect using Stokes formalism and its implementation in the Atmospheric Radiative Transfer Simulator (ARTS)

    International Nuclear Information System (INIS)

    Larsson, Richard; Buehler, Stefan A.; Eriksson, Patrick; Mendrok, Jana

    2014-01-01

    This paper presents the practical theory that was used to implement the Zeeman effect using Stokes formalism in the Atmospheric Radiative Transfer Simulator (ARTS). ARTS now treats the Zeeman effect in a general manner for several gas species for all polarizations and takes into account variations in both magnetic and atmospheric fields along a full 3D geometry. We present how Zeeman splitting affects polarization in radiative transfer simulations and find that the effect may be large in Earth settings for polarized receivers in limb observing geometry. We find that not taking a spatially varying magnetic field into account can result in absolute errors in the measurement vector of at least 10 K in Earth magnetic field settings. The paper also presents qualitative tests for O 2 lines against previous models (61.15 GHz line) and satellite data from Odin-SMR (487.25 GHz line), and the overall consistency between previous models, satellite data, and the new ARTS Zeeman module seems encouraging. -- Highlights: • We implement the Zeeman effect with Stokes formalism in ARTS. • We give a practical theory for the implementation. • Examples of how the Zeeman effect change RT are presented. • Qualitative Odin-SMR O 2 limb sounding model indicates the Zeeman effect is necessary

  6. The formal de Rham complex

    Science.gov (United States)

    Zharinov, V. V.

    2013-02-01

    We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.

  7. As abordagens teóricas e os formalismos para o tratamento computacional do significado lexical Theoretical approaches and formalisms for the computational treatment of lexical meaning

    Directory of Open Access Journals (Sweden)

    Ariani Di Felippo

    2010-01-01

    Full Text Available No âmbito do Processamento Automático de Línguas Naturais (PLN, o desenvolvimento de recursos léxico-semânticos é premente. Ao conceber os sistemas de PLN como um exercício de "engenharia da linguagem humana", acredita-se que o desenvolvimento de tais recursos pode ser beneficiado pelos modelos de "representação do conhecimento", desenvolvidos pela Engenharia do Conhecimento. Esses modelos, em particular, fornecem simultaneamente o arcabouço teórico-metodológico e a metalinguagem formal para o tratamento computacional do significado das unidades lexicais. Neste artigo, após a apresentação da concepção linguístico-computacional de léxico, elucidam-se os principais paradigmas de representação do conhecimento, enfatizando a abordagem do significado e a metalinguagem formal vinculadas a cada um deles.The development of lexical-semantic resources for natural language processing is urgent. Conceiving the computational systems which process natural languages as an exercise of "human language engineering", the development of such resources can benefit from the "knowledge representation models" provided by Knowledge Engineering. These models provide both the theoretical-methodological premises and the formal metalanguage for the computational treatment of word meaning. In this paper, we first present the linguistic-computational conception of "lexicon". Then, we describe the main knowledge representation paradigms emphasizing the theoretical approach to word meaning and the formalism related to each of them.

  8. Refined topological strings on local ℙ2

    International Nuclear Information System (INIS)

    Iqbal, Amer; Kozçaz, Can

    2017-01-01

    We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on ℙ 2 (the local ℙ 2 ). The refined topological vertex formalism can not be directly applied to local ℙ 2 therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local ℙ 2 .

  9. 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.

  10. Differential topology

    CERN Document Server

    Guillemin, Victor

    2010-01-01

    Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main

  11. Mechanized Extraction of Topology Anti-patterns in Wireless Networks

    NARCIS (Netherlands)

    Woehrle, M.; Bakhshi, R.R.; Mousavi, M.R.

    2012-01-01

    Exhaustive and mechanized formal verification of wireless networks is hampered by the huge number of possible topologies and the large size of the actual networks. However, the generic communication structure in such networks allows for reducing the root causes of faults to faulty (sub-)topologies,

  12. Comparison of the ESTRO formalism for monitor unit calculation with a Clarkson based algorithm of a treatment planning system and a traditional ''full-scatter'' methodology

    International Nuclear Information System (INIS)

    Pirotta, M.; Aquilina, D.; Bhikha, T.; Georg, D.

    2005-01-01

    The ESTRO formalism for monitor unit (MU) calculations was evaluated and implemented to replace a previous methodology based on dosimetric data measured in a full-scatter phantom. This traditional method relies on data normalised at the depth of dose maximum (z m ), as well as on the utilisation of the BJR 25 table for the conversion of rectangular fields into equivalent square fields. The treatment planning system (TPS) was subsequently updated to reflect the new beam data normalised at a depth z R of 10 cm. Comparisons were then carried out between the ESTRO formalism, the Clarkson-based dose calculation algorithm on the TPS (with beam data normalised at z m and z R ), and the traditional ''full-scatter'' methodology. All methodologies, except for the ''full-scatter'' methodology, separated head-scatter from phantom-scatter effects and none of the methodologies; except for the ESTRO formalism, utilised wedge depth dose information for calculations. The accuracy of MU calculations was verified against measurements in a homogeneous phantom for square and rectangular open and wedged fields, as well as blocked open and wedged fields, at 5, 10, and 20 cm depths, under fixed SSD and isocentric geometries for 6 and 10 MV. Overall, the ESTRO Formalism showed the most accurate performance, with the root mean square (RMS) error with respect to measurements remaining below 1% even for the most complex beam set-ups investigated. The RMS error for the TPS deteriorated with the introduction of a wedge, with a worse RMS error for the beam data normalised at z m (4% at 6 MV and 1.6% at 10 MV) than at z R (1.9% at 6 MV and 1.1% at 10 MV). The further addition of blocking had only a marginal impact on the accuracy of this methodology. The ''full-scatter'' methodology showed a loss in accuracy for calculations involving either wedges or blocking, and performed worst for blocked wedged fields (RMS errors of 7.1% at 6 MV and 5% at 10 MV). The origins of these discrepancies were

  13. Masses of Formal Philosophy

    DEFF Research Database (Denmark)

    Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions....

  14. Emerging Trends in Topological Insulators and Topological ...

    Indian Academy of Sciences (India)

    Moreover, proximity induced superconductivity in these systemscan lead to a state that supports zero energy Majoranafermions, and the phase is known as topological superconductors.In this article, the basic idea of topological insulatorsand topological superconductors are presented alongwith their experimental ...

  15. 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

  16. Constrained analysis of topologically massive gravity

    Energy Technology Data Exchange (ETDEWEB)

    Barcelos-Neto, J. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica; Dargam, T.G. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica

    1995-08-01

    We quantize the Einstein gravity in the formalism of weak gravitational fields by using the constrained Hamiltonian method. Special emphasis is given to the 2+1 spacetime dimensional case where a (topological) Chern-Simons term is added to the Lagrangian. (orig.)

  17. Geometric quantization of topological gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Barcelos-Neto, J. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica; De Souza, S.M. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica

    1995-03-01

    We show that Abelian gauge theories in 2 + 1 space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case. (orig.)

  18. Axion topological field theory of topological superconductors

    Science.gov (United States)

    Qi, Xiao-Liang; Witten, Edward; Zhang, Shou-Cheng

    2013-04-01

    Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of “axions” with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special “chiral” vortex lines, which can be realized by considering s-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.

  19. 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....

  20. Optical image encryption topology.

    Science.gov (United States)

    Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen

    2009-10-15

    Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.

  1. Anyonic entanglement and topological entanglement entropy

    Science.gov (United States)

    Bonderson, Parsa; Knapp, Christina; Patel, Kaushal

    2017-10-01

    We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.

  2. Pragmatics for formal semantics

    DEFF Research Database (Denmark)

    Danvy, Olivier

    2011-01-01

    This tech talk describes how to write and how to inter-derive formal semantics for sequential programming languages. The progress reported here is (1) concrete guidelines to write each formal semantics to alleviate their proof obligations, and (2) simple calculational tools to obtain a formal sem...

  3. Strongly Correlated Topological Insulators

    Science.gov (United States)

    2016-02-03

    Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials...in which a topologically nontrivial quasi-flat band is fractionally filled and then subject to strong interactions. The views, opinions and/or

  4. Explorations in topology map coloring, surfaces and knots

    CERN Document Server

    Gay, David

    2013-01-01

    Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigation

  5. The Quantum Formalism and the GRW Formalism

    Science.gov (United States)

    Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino

    2012-10-01

    The Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world.

  6. Industrial use of formal methods formal verification

    CERN Document Server

    Boulanger, Jean-Louis

    2012-01-01

    At present the literature gives students and researchers of the very general books on the formal technics. The purpose of this book is to present in a single book, a return of experience on the used of the "formal technics" (such proof and model-checking) on industrial examples for the transportation domain. This book is based on the experience of people which are completely involved in the realization and the evaluation of safety critical system software based.  The implication of the industrialists allows to raise the problems of confidentiality which could appear and so allow

  7. Informal work and formal plans

    DEFF Research Database (Denmark)

    Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm

    2012-01-01

    INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer...... trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...

  8. [French Society for Biological Psychiatry and Neuropsychopharmacology and Fondation FondaMental task force: Formal Consensus for the management of treatment-resistant depression].

    Science.gov (United States)

    Charpeaud, T; Genty, J-B; Destouches, S; Yrondi, A; Lancrenon, S; Alaïli, N; Bellivier, F; Bennabi, D; Bougerol, T; Camus, V; D'amato, T; Doumy, O; Haesebaert, F; Holtzmann, J; Lançon, C; Lefebvre, M; Moliere, F; Nieto, I; Richieri, R; Schmitt, L; Stephan, F; Vaiva, G; Walter, M; Leboyer, M; El-Hage, W; Haffen, E; Llorca, P-M; Courtet, P; Aouizerate, B

    2017-09-01

    Major depression represents among the most frequent psychiatric disorders in the general population with an estimated lifetime prevalence of 16-17%. It is characterized by high levels of comorbidities with other psychiatric conditions or somatic diseases as well as a recurrent or chronic course in 50 to 80% of the cases leading to negative repercussions on the daily functioning, with an impaired quality of life, and to severe direct/indirect costs. Large cohort studies have supported that failure of a first-line antidepressant treatment is observed in more than 60% of patients. In this case, several treatment strategies have been proposed by classical evidence-based guidelines from internationally recognized scientific societies, referring primarily on: I) the switch to another antidepressant of the same or different class; II) the combination with another antidepressant of complementary pharmacological profile; III) the addition of a wide range of pharmacological agents intending to potentiate the therapeutic effects of the ongoing antidepressant medication; IV) the association with appropriate psychological therapies; and, V) the use of non-invasive brain stimulation techniques. However, although based on the most recently available data and rigorous methodology, standard guidelines have the significant disadvantage of not covering a large variety of clinical conditions, while currently observed in everyday clinical practice. From these considerations, formalized recommendations by a large panel of French experts in the management of depressed patients have been developed under the shared sponsorship of the French Association of Biological Psychiatry and Neuropsychopharmacology (AFPBN) and the Fondation FondaMental. These French recommendations are presented in this special issue in order to provide relevant information about the treatment choices to make, depending particularly on the clinical response to previous treatment lines or the complexity of clinical

  9. Emerging Trends in Topological Insulators and Topological ...

    Indian Academy of Sciences (India)

    Emerging Trends in Topological Insulators and. Topological Superconductors. Arijit Saha and Arun M Jayannavar. Arijit Saha is a Reader-F at the Institute of Physics,. Bhubaneswar. His research interest lies broadly in the areas of mesoscopic physics and strongly correlated electrons. Arun M Jayannavar is a.

  10. A topological derivative method for topology optimization

    DEFF Research Database (Denmark)

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

    2007-01-01

    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...

  11. Artabilitation ICMC Panel paper Denmark 2007:Non-Formal Rehabilitation via Immersiveinteractive Music Environments

    DEFF Research Database (Denmark)

    Brooks, Tony; Petersson, Eva; Eaglestone, Barry

    2007-01-01

    This paper brings together perspectives of the ICMC 2007 ArtAbilitation Panel on non-formal rehabilitation via immersive interactive music environments. Issues covered are sound therapy, musical topologies, brainwave control and research methodology....

  12. Integrating semi-formal and formal requirements

    NARCIS (Netherlands)

    Wieringa, Roelf J.; Olivé, Antoni; Dubois, Eric; Pastor, Joan Antoni; Huyts, Sander

    1997-01-01

    In this paper, we report on the integration of informal, semiformal and formal requirements specification techniques. We present a framework for requirements specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of

  13. Topological vector spaces and distributions

    CERN Document Server

    Horvath, John

    2012-01-01

    ""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o

  14. Book Review: Computational Topology

    DEFF Research Database (Denmark)

    Raussen, Martin

    2011-01-01

    Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5......Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5...

  15. Elementary concepts of topology

    CERN Document Server

    Alexandroff, Paul

    1961-01-01

    Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.

  16. Free Boolean Topological Groups

    Directory of Open Access Journals (Sweden)

    Ol’ga Sipacheva

    2015-11-01

    Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.

  17. Fear of the Formal

    DEFF Research Database (Denmark)

    du Gay, Paul; Lopdrup-Hjorth, Thomas

    Over recent decades, institutions exhibiting high degrees of formality have come in for severe criticism. From the private to the public sector, and across a whole spectrum of actors spanning from practitioners to academics, formal organization is viewed with increasing doubt and skepticism. In a...

  18. Geometry and Formal Linguistics.

    Science.gov (United States)

    Huff, George A.

    This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

  19. Topological antiferromagnetic spintronics

    Science.gov (United States)

    Šmejkal, Libor; Mokrousov, Yuriy; Yan, Binghai; MacDonald, Allan H.

    2018-03-01

    The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.

  20. 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.

  1. Real Topological Cyclic Homology

    DEFF Research Database (Denmark)

    Høgenhaven, Amalie

    The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum......, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call...... real topological cyclic homology. The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G...

  2. Triple Point Topological Metals

    Directory of Open Access Journals (Sweden)

    Ziming Zhu

    2016-07-01

    Full Text Available Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.

  3. Photonic Floquet topological insulators

    Science.gov (United States)

    Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander

    2013-09-01

    Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on the surface. In two dimensions, surface electrons in topological insulators do not scatter despite defects and disorder, providing robustness akin to superconductors. Topological insulators are predicted to have wideranging applications in fault-tolerant quantum computing and spintronics. Recently, large theoretical efforts were directed towards achieving topological insulation for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional, and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. However, since magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatterfree edge states requires a fundamentally different mechanism - one that is free of magnetic fields. Recently, a number of proposals for photonic topological transport have been put forward. Specifically, one suggested temporally modulating a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, where temporal variations in solidstate systems induce topological edge states. Here, we propose and experimentally demonstrate the first external field-free photonic topological insulator with scatter-free edge transport: a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate acts as `time'. Thus the waveguides

  4. Necessity of Integral Formalism

    International Nuclear Information System (INIS)

    Tao Yong

    2011-01-01

    To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrödinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrödinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description. (general)

  5. Fear of the Formal

    DEFF Research Database (Denmark)

    du Gay, Paul; Lopdrup-Hjorth, Thomas

    2016-01-01

    Over recent decades, ‘formal’ organisations have come in for severe criticism. Not only is formal organisation represented as ill suited to the realities of the contemporary organisational world, but as a key source from which organisational dysfunctions themselves emerge. For that reason informal...... and spontaneous modes of organising have emerged, or better re-emerged, as preferable substitutes, because they, in contrast to the formal, allegedly allow for creativity, inventiveness, flexibility, speed, and freedom. Thus, the province of the formal is significantly devalued. In this paper, we explore what we...

  6. Formalizing Arrow's theorem

    Indian Academy of Sciences (India)

    Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...

  7. Formalizing typical crosscutting concerns

    NARCIS (Netherlands)

    Marin, A.M.

    2006-01-01

    We present a consistent system for referring crosscutting functionality, relating crosscutting concerns to specific implementation idioms, and formalizing their underlying relations through queries. The system is based on generic crosscutting concerns that we organize and describe in a catalog. We

  8. Topological Hall and spin Hall effects in disordered skyrmionic textures

    KAUST Repository

    Ndiaye, Papa Birame

    2017-02-24

    We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering.

  9. Topological evolution of virtual social networks by modeling social activities

    Science.gov (United States)

    Sun, Xin; Dong, Junyu; Tang, Ruichun; Xu, Mantao; Qi, Lin; Cai, Yang

    2015-09-01

    With the development of Internet and wireless communication, virtual social networks are becoming increasingly important in the formation of nowadays' social communities. Topological evolution model is foundational and critical for social network related researches. Up to present most of the related research experiments are carried out on artificial networks, however, a study of incorporating the actual social activities into the network topology model is ignored. This paper first formalizes two mathematical abstract concepts of hobbies search and friend recommendation to model the social actions people exhibit. Then a social activities based topology evolution simulation model is developed to satisfy some well-known properties that have been discovered in real-world social networks. Empirical results show that the proposed topology evolution model has embraced several key network topological properties of concern, which can be envisioned as signatures of real social networks.

  10. 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.

  11. Fuzzy Soft Topological Groups

    Directory of Open Access Journals (Sweden)

    S. Nazmul

    2014-03-01

    Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.

  12. Topological Foundations of Electromagnetism

    CERN Document Server

    Barrett, Terrence W

    2008-01-01

    Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic field

  13. Informal work and formal plans

    DEFF Research Database (Denmark)

    Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm

    2012-01-01

    trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...

  14. 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.

  15. 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.

  16. 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.

  17. Formality in Brackets

    DEFF Research Database (Denmark)

    Garsten, Christina; Nyqvist, Anette

    suits’ (Nyqvist 2013), and of doing ‘ethnography by failure’ (Garsten 2013). In this paper, we explore the layers of informality and formality in our fieldwork experiences among financial investors and policy experts, and discuss how to ethnographically represent embodied fieldwork practices. How do we...... stage and informal for others. Walking the talk, donning the appropriate attire, wearing the proper suit, may be part of what is takes to figure out the code of formal organizational settings – an entrance ticket to the backstage, as it were. Oftentimes, it involves a degree of mimicry, of ‘following...... conceptualize and articulate the informal and the formal? How do we represent the multidimensional character of organizations while maintaining a degree of integrity of informants? And how do we decide on relevance as we transpose our fieldwork experiences into text? We suggest that ethnographic organization...

  18. Formalizing Probabilistic Safety Claims

    Science.gov (United States)

    Herencia-Zapana, Heber; Hagen, George E.; Narkawicz, Anthony J.

    2011-01-01

    A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.

  19. Ontology or formal ontology

    Science.gov (United States)

    Žáček, Martin

    2017-07-01

    Ontology or formal ontology? Which word is correct? The aim of this article is to introduce correct terms and explain their basis. Ontology describes a particular area of interest (domain) in a formal way - defines the classes of objects that are in that area, and relationships that may exist between them. Meaning of ontology consists mainly in facilitating communication between people, improve collaboration of software systems and in the improvement of systems engineering. Ontology in all these areas offer the possibility of unification of view, maintaining consistency and unambiguity.

  20. Modeling Internet Topology Dynamics

    NARCIS (Netherlands)

    Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.

    Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements,

  1. Topology optimization approaches

    DEFF Research Database (Denmark)

    Sigmund, Ole; Maute, Kurt

    2013-01-01

    Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...

  2. Manufacturing tolerant topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2009-01-01

    (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization...

  3. Reconfigurable topological photonic crystal

    Science.gov (United States)

    Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.

    2018-02-01

    Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.

  4. Introduction to topology

    CERN Document Server

    Mendelson, Bert

    1990-01-01

    Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

  5. Amorphous Gyroscopic Topological Metamaterials

    Science.gov (United States)

    Mitchell, Noah P.; Nash, Lisa M.; Hexner, Daniel; Turner, Ari M.; Irvine, William T. M.

    Mechanical topological metamaterials display striking mechanical responses, such as unidirectional surface modes that are impervious to disorder. This behavior arises from the topology of their vibrational spectra. All examples of topological metamaterials to date are finely-tuned structures such as crystalline lattices or jammed packings. Here, we present robust recipes for building amorphous topological metamaterials with arbitrary underlying structure and no long-range order. Using interacting gyroscopes as a model system, we demonstrate through experiment, simulation, and theoretical methods that the local geometry and interactions are sufficient to generate topological mobility gaps, allowing for spatially-resolved, real-space calculations of the Chern number. The robustness of our approach enables the design and self-assembly of non-crystalline materials with protected, unidirectional waveguides on the micro and macro scale.

  6. 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...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...... software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based...

  7. 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.

  8. Criteria for logical formalization

    Czech Academy of Sciences Publication Activity Database

    Peregrin, Jaroslav; Svoboda, Vladimír

    2013-01-01

    Roč. 190, č. 14 (2013), s. 2897-2924 ISSN 0039-7857 R&D Projects: GA ČR(CZ) GAP401/10/1279 Institutional support: RVO:67985955 Keywords : logic * logical form * formalization * reflective equilibrium Subject RIV: AA - Philosophy ; Religion Impact factor: 0.637, year: 2013

  9. Formal Verification -26 ...

    Indian Academy of Sciences (India)

    This is a short tutorial on formal methods which are techniques for specifying and verifying com- plex software and hardware systems. A few ex- amples of successful industrial use of these are also presented. Computers are ubiquitous these days and are used to control various safety critical systems like aircrafts, satel-.

  10. Formalization of Medical Guidelines

    Czech Academy of Sciences Publication Activity Database

    Peleška, Jan; Anger, Z.; Buchtela, David; Šebesta, K.; Tomečková, Marie; Veselý, Arnošt; Zvára, K.; Zvárová, Jana

    2005-01-01

    Roč. 1, - (2005), s. 133-141 ISSN 1801-5603 R&D Projects: GA AV ČR 1ET200300413 Institutional research plan: CEZ:AV0Z10300504 Keywords : GLIF model * formalization of guidelines * prevention of cardiovascular diseases Subject RIV: IN - Informatics, Computer Science

  11. The Benefits of Formalization

    DEFF Research Database (Denmark)

    Rand, John; Torm, Nina Elisabeth

    2012-01-01

    Based on unique panel data consisting of both formal and informal firms, this paper uses a matched double difference approach to examine the relationship between legal status and firm level outcomes in micro, small and medium manufacturing enterprises (SMEs) in Vietnam. Controlling for determining...

  12. Formalizing Arrow's theorem

    Indian Academy of Sciences (India)

    a formalization is done using a computer program called a proof checker or proof assistant. Such a proof assistant .... means 'Prototype Verification System', but the system is far more than a prototype. It actually is one of the ... related to the Lisp programming language (ACL2 means 'A Computational Logic for. Applicative ...

  13. Formalizing physical security procedures

    NARCIS (Netherlands)

    Meadows, C.; Pavlovic, Dusko

    Although the problems of physical security emerged more than 10,000 years before the problems of computer security, no formal methods have been developed for them, and the solutions have been evolving slowly, mostly through social procedures. But as the traffic on physical and social networks is now

  14. Fermionic topological quantum states as tensor networks

    Science.gov (United States)

    Wille, C.; Buerschaper, O.; Eisert, J.

    2017-06-01

    Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

  15. Elements of differential topology

    CERN Document Server

    Shastri, Anant R

    2011-01-01

    Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups.The first two chapters review differential and integral calculus of several variables and present fundamental results that are used throughout the text. The next few chapters focus on smooth manifo

  16. Signatures of topological superconductivity

    Energy Technology Data Exchange (ETDEWEB)

    Peng, Yang

    2017-07-19

    The prediction and experimental discovery of topological insulators brought the importance of topology in condensed matter physics into the limelight. Topology hence acts as a new dimension along which more and more new states of matter start to emerge. One of these topological states of matter, namely topological superconductors, comes into the focus because of their gapless excitations. These gapless excitations, especially in one dimensional topological superconductors, are Majorana zero modes localized at the ends of the superconductor and exhibit exotic nonabelian statistics, which can be potentially applied to fault-tolerant quantum computation. Given their highly interesting physical properties and potential applications to quantum computation, both theorists and experimentalists spend great efforts to realize topological supercondoctors and to detect Majoranas. In two projects within this thesis, we investigate the properties of Majorana zero modes in realistic materials which are absent in simple theoretical models. We find that the superconducting proximity effect, an essential ingredient in all existing platforms for topological superconductors, plays a significant role in determining the localization property of the Majoranas. Strong proximity coupling between the normal system and the superconducting substrate can lead to strongly localized Majoranas, which can explain the observation in a recent experiment. Motivated by experiments in Molenkamp's group, we also look at realistic quantum spin Hall Josephson junctions, in which charge puddles acting as magnetic impurities are coupled to the helical edge states. We find that with this setup, the junction generically realizes an exotic 8π periodic Josephson effect, which is absent in a pristine Josephson junction. In another two projects, we propose more pronounced signatures of Majoranas that are accessible with current experimental techniques. The first one is a transport measurement, which uses

  17. Topology general & algebraic

    CERN Document Server

    Chatterjee, D

    2007-01-01

    About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

  18. Global Topology Optimisation

    Science.gov (United States)

    2016-10-31

    AFRL-AFOSR-UK-TR-2017-0002 Global Topology Optimisation Robert Jack UNIVERSITY OF BATH Final Report 10/31/2016 DISTRIBUTION A: Distribution approved...01 Aug 2015 to 31 Jul 2016 4.  TITLE AND SUBTITLE Global Topology Optimisation 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-15-1-0317 5c...future work. 15.  SUBJECT TERMS EOARD, Topology Optimization, Non Convex 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION OF       ABSTRACT SAR 18

  19. Algebraic topology and concurrency

    DEFF Research Database (Denmark)

    Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric

    2006-01-01

    We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...

  20. Plasmonics in Topological Insulators

    Directory of Open Access Journals (Sweden)

    Yi-Ping Lai

    2014-04-01

    Full Text Available With strong spin-orbit coupling, topological insulators have an insulating bulk state, characterized by a band gap, and a conducting surface state, characterized by a Dirac cone. Plasmons in topological insulators show high frequency-tunability in the mid-infrared and terahertz spectral regions with transverse spin oscillations, also called “spin-plasmons”. This paper presents a discussion and review of the developments in this field from the fundamental theory of plasmons in bulk, thin-film, and surface-magnetized topological insulators to the techniques of plasmon excitation and future applications.

  1. Duality and topology

    Science.gov (United States)

    Sacramento, P. D.; Vieira, V. R.

    2018-04-01

    Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.

  2. Experiments in topology

    CERN Document Server

    Barr, Stephen

    1989-01-01

    ""A mathematician named KleinThought the Moebius band was divine.Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.' "" - Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)The Shortest Moebius StripThe

  3. Elementary topology problem textbook

    CERN Document Server

    Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M

    2008-01-01

    This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr

  4. Topologically massive supergravity

    Directory of Open Access Journals (Sweden)

    S. Deser

    1983-01-01

    Full Text Available The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.

  5. Topological pregauge-pregeometry

    International Nuclear Information System (INIS)

    Akama, Keiichi; Oda, Ichiro.

    1990-12-01

    The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions is investigated from the viewpoint of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale. (author)

  6. Topological systems versus attachment relations | Guido ...

    African Journals Online (AJOL)

    ... localification procedure introduced by S. Vickers for topological systems. Keywords: Adjoint functor, algebra, attachment relation, embedding functor, localification of topological systems, spatialization of topological systems, topological system, topological theory, variety of algebras. Quaestiones Mathematicae 37(2014), ...

  7. Formalized Informal Learning

    DEFF Research Database (Denmark)

    Levinsen, Karin Tweddell; Sørensen, Birgitte Holm

    2013-01-01

    are examined and the relation between network society competences, learners’ informal learning strategies and ICT in formalized school settings over time is studied. The authors find that aspects of ICT like multimodality, intuitive interaction design and instant feedback invites an informal bricoleur approach......Longitudinal research projects into social practices are both subject to and capture changes in society, meaning that research is conducted in a fluid context and that new research questions appear during the project’s life cycle. In the present study emerging new performances and uses of ICT....... When integrated into certain designs for teaching and learning, this allows for Formalized Informal Learning and support is found for network society competences building....

  8. Readings in Formal Epistemology

    DEFF Research Database (Denmark)

    Formal epistemology’ is a term coined in the late 1990s for a new constellation of interests in philosophy,the roots of which are found in earlier works of epistemologists, philosophers of science, and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty......, rationality, deliberation, decision, strategy, action and agent interaction – and it does so using methods from logic, probability, computability, decision, and game theory. This volume presents 42 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy...... and its neighbouring intellectual disciplines. The editors provide introductions to five basic subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Logics of Knowledge and Belief. The volume also includes a thorough index and suggestions for further reading...

  9. Many body topological invariants in topological phases with point group symmetry

    Science.gov (United States)

    Shiozaki, Ken; Shapourian, Hassan; Ryu, Shinsei

    A way to detect topological phases from a given short-range entangled state is discussed. Many body topological invariants are defined as partition functions of topological quantum field theory (TQFT) on space-time manifolds, for example, real projective spaces. It is expected that by translating TQFT partition functions to the operator formalism one can get a definition of many body topological invariants made from ground state wave functions and symmetry operations. We propose that a kind of non-local operator, the ''partial point group transformation'', on a short-range entangled state is a unified measure to detect topologically nontrivial phases with point group symmetry. In this talk, I introduce (i) the partial rotations on (2 +1)d chiral superconductors, and (ii) the Z16 invariant from the partial inversion on (3 +1)d superconductors. These partial point group transformations can be analytically calculated from the boundary theory. We confirmed that analytical results from the boundary theory match with direct numerical calculations on bulk.

  10. The operator formalism and contact terms in string theory

    International Nuclear Information System (INIS)

    Doyle, M.D.

    1992-01-01

    The operator formalism has proven to be a powerful tool in string theory. In particular, by making explicit the role of a choice of local coordinates (or, equivalently, a normal-ordering prescription) at vertex operator insertions, it provides a framework for understanding the insertion of very general states in both on-shell string theory and string field theory, for formulating a semirigid N = 2 geometry-based approach to topological gravity, for resolving ambiguities in fermionic string theory, and for analyzing contact interactions. The main focus of this thesis on this last application of the operator formalism, although it touches on each of the others. The first goal is the analysis of the dilaton contact terms required for the dilaton equation in the bosonic and heterotic strings. In the bosonic case, a coordinate family appropriate for a punctured sphere is given and is used to calculate dilaton two-point functions. This coordinate family is later generalized to a 'good' coordinate family appropriate for dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton contact terms are improperly normalized resulting in the failure of the dilaton equation, suggesting that the zero-momentum dilaton is not the string coupling constant. This seems to be the result of a tachyon divergence. A similar calculation in the heterotic case, where there is no tachyon, shows that the dilaton contact terms are properly normalized, and that the dilaton equation and the interpretation of the dilaton as the string coupling constant goes through. The other major goal is re-examination of Green and Seiberg's work which showed that, in simple treatments of fermionic string theory, it is necessary to introduce contact interactions when vertex operators collide to avoid the failure of certain superconformal Ward identities

  11. A novel VU-MRCC formalism for the simultaneous treatment of strong relaxation and correlation effects with applications to electron affinity of neutral radicals

    International Nuclear Information System (INIS)

    Jana, Debasis; Datta, Dipayan; Mukherjee, Debashis

    2006-01-01

    We present and implement in this paper a novel spin-free valence-universal multi-reference coupled cluster (VU-MRCC) formalism for energy differences which can capture orbital relaxation and correlation relaxation to all orders. Unlike in the traditional normal ordered cluster Ansatz for computing energy differences, this cluster expansion formalism allows contractions between various valence excitation operators with valence spectator lines. These contractions simulate the orbital relaxation and correlation relaxation effects for the ionized/excited states via Thouless-like exponential type of operators. Generally such operators are non-commuting. To ensure that each distinct excitation generated by contracted composites formed by these operators appear only once in the wave-operators, the factors accompanying these composites have to be judiciously chosen. Hence, the combinatoric factors accompanying such contracted composites are not taken to be 1/n! for nth-power, but rather the inverse of the automorphic factor (the number of ways the n operators can be connected in various permutations generating the same composite). It is shown that this Ansatz leads to a set of VU-MRCC equations for the valence cluster amplitudes, in which all the cluster operators are attached to the hamiltonian by at least one non-spectator line (a strongly connected series). The series is thus terminating at the quartic power. Illustrative applications are presented by computing electron affinity of neutral doublet radicals (viz., NH 2 , OH, F, BO and CN), where the orbital relaxation effect attendant on the anion formation is considerable. Several basis-sets capable of describing the anions have been studied. It has been found that aug-cc-pVTZ basis gives the best overall results, while aug-cc-pVQZ overestimates the electron affinity, presumably because of an imbalance in describing the neutral radicals. The method performs consistently much better then the one with the traditional

  12. Foundations of relational realism a topological approach to quantum mechanics and the philosophy of nature

    CERN Document Server

    Epperson, Michael

    2013-01-01

    This book presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. More broadly, as a philosophical enterprise, the authors propose this conceptual framework as a speculative ontological program that includes a rigorous mathematical formalism, providing a coherent and intuitive ontological scheme that is both novel and applicable practically to the physical sciences.

  13. Topological Solitons in Physics.

    Science.gov (United States)

    Parsa, Zohreh

    1979-01-01

    A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)

  14. Topological susceptibility from slabs

    Energy Technology Data Exchange (ETDEWEB)

    Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)

    2015-12-14

    In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.

  15. Topology for analysis

    CERN Document Server

    Wilansky, Albert

    2008-01-01

    Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.

  16. Topological Susceptibility from Slabs

    CERN Document Server

    Bietenholz, Wolfgang; Gerber, Urs

    2015-01-01

    In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.

  17. Games for topological fixpoint logic

    NARCIS (Netherlands)

    Bezhanishvili, N.; Kupke, C.

    2016-01-01

    Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators

  18. Modelling Dynamic Topologies via Extensions of VDM-RT

    DEFF Research Database (Denmark)

    Nielsen, Claus Ballegård

    Only a few formal methods include descriptions of the network topology that the modelled system is deployed onto. In VDM Real-Time (VDM-RT) this has been enabled for distributed systems that have a static structure. However, when modelling dynamic systems this fixed topology becomes an issue....... Systems with highly distributed and alternating relationships cannot be expressed correctly in a static model. This document describes how VDM-RT can be extended with new language constructs to enable the description of dynamic reconfiguration of the network topology during the runtime execution...... of a model. The extension is developed on the basis of a case study involving a dynamic system that has a constant changing system topology. With a basis in the case study a model is developed that uses the static version of VDM-RT in order to reveal the limitations of the language. The case study...

  19. Topological properties of instantons

    International Nuclear Information System (INIS)

    Mello, E.R.B. de.

    1978-07-01

    The pure Yang-Mills theory defined in R 4 space is considered and some relevant properties of gauge field like Instanton are shown. The vacuum structure of the theory is discussed, as well as the problem of topological numbers associated with the Instantons and anti-Instantons solutions. A procedure is presented showing how we can alter this topological number by of any variation in the field parameters. (Author) [pt

  20. The refined topological vertex

    International Nuclear Information System (INIS)

    Iqbal, Amer; Kozcaz, Can; Vafa, Cumrun

    2009-01-01

    We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.

  1. Manufacturing tolerant topology optimization

    OpenAIRE

    Sigmund, Ole

    2009-01-01

    In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining an...

  2. Noncommutative topological dynamics

    International Nuclear Information System (INIS)

    Ramos, C. Correia; Martins, Nuno; Severino, Ricardo; Ramos, J. Sousa

    2006-01-01

    We study noncommutative dynamical systems associated to unimodal and bimodal maps of the interval. To these maps we associate subshifts and the correspondent AF-algebras and Cuntz-Krieger algebras. As an example we consider systems having equal topological entropy log(1 + φ), where φ is the golden number, but distinct chaotic behavior and we show how a new numerical invariant allows to distinguish that complexity. Finally, we give a statistical interpretation to the topological numerical invariants associated to bimodal maps

  3. Tunable Topological Phononic Crystals

    KAUST Repository

    Chen, Zeguo

    2016-05-27

    Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

  4. Essentials of topology with applications

    CERN Document Server

    Krantz, Steven G

    2009-01-01

    Fundamentals What Is Topology? First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory

  5. 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.

  6. Formal Methods in Industry

    Directory of Open Access Journals (Sweden)

    Alexei Serna A.

    2012-12-01

    Full Text Available The application of formal methods in industry has progressed extensively over the past decade and the results are promising. But despite these achievements and it have been documented in numerous studies, it is still very common the skepticism about its usefulness and applicability. The goal of this paper is to show that its evolution over the past decade exceeds all previous processes and each time they do a better job to satisfy industrial needs. This is achieved by the description of some experiments and the result of various applications in industry and through an analyzing of the needs of companies that must be satisfy the research community in this field.

  7. Formalizing the concept of sound.

    Energy Technology Data Exchange (ETDEWEB)

    Kaper, H. G.; Tipei, S.

    1999-08-03

    The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.

  8. Formalization of Database Systems -- and a Formal Definition of {IMS}

    DEFF Research Database (Denmark)

    Bjørner, Dines; Løvengreen, Hans Henrik

    1982-01-01

    Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....

  9. Formalization of Database Systems -- and a Formal Definition of {IMS}

    DEFF Research Database (Denmark)

    Bjørner, Dines; Løvengreen, Hans Henrik

    1982-01-01

    come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics......Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....

  10. 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.

  11. Formal Methods in Knowledge Engineering

    NARCIS (Netherlands)

    Harmelen, van F.A.H.; Fensel, D.

    1995-01-01

    This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this by

  12. 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.

  13. A Formal Calculus for Categories

    DEFF Research Database (Denmark)

    Cáccamo, Mario José

    This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...

  14. Algebraic topology a primer

    CERN Document Server

    Deo, Satya

    2018-01-01

    This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...

  15. Topology optimized microbioreactors

    DEFF Research Database (Denmark)

    Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna

    2011-01-01

    This article presents the fusion of two hitherto unrelated fields—microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein....... Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement...... in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced....

  16. Architecture, Drawing, Topology

    DEFF Research Database (Denmark)

    This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...... the intricate issues of the imagination and the moving ratio in the topological culture, over urban topology, diagrammatisation, mediality and dynamics of transduction in the contemporary artificial environment....

  17. Riemann, topology, and physics

    CERN Document Server

    Monastyrsky, Michael I

    2008-01-01

    This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...

  18. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  19. The Topological Vertex

    CERN Document Server

    Aganagic, M; Marino, M; Vafa, C; Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

    2005-01-01

    We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of Calabi-Yau. We interpret this result as an operator computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

  20. In/formalization

    Directory of Open Access Journals (Sweden)

    Alan Smart

    2017-12-01

    Full Text Available Addressing a variety of locations and subjects across several social contexts and countries, this forum intends to stimulate novel ways of conceptualizing the inevitable interpenetration and entanglement of formalization and informalization as two interlinked social processes. Rather than proposing a new coherent definition of “informality”, we propose to consider “in/formalization” as a space of practice and reflection which is crucial for engaging with contemporary economy, law and politics and their current local and global articulations and scenarios. The forum features contributions by Stamatis Amarianakis, Lenka Brunclíková, Dolores Koenig, B. Lynne Milgram, Sarah Muir, Antonio Maria Pusceddu, Alan Smart, Mechthild von Vacano, Filippo M. Zerilli & Julie Trappe.

  1. Formal aspects of resilience

    Directory of Open Access Journals (Sweden)

    Diana-Maria Drigă

    2015-12-01

    Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.

  2. Formalized informal learning

    DEFF Research Database (Denmark)

    Levinsen, Karin; Sørensen, Birgitte Holm

    2011-01-01

    This paper presents findings from a large-scale longitudinal, qualitative study - Project ICT and Learning (PIL) - that engaged the participation of eight primary schools in Denmark, and was conducted between 2006 and 2008. The research design was based on action research, involving teachers...... and other relevant stakeholders, as well as participant observations in the classroom documented by thick descriptions, formal and informal interviews and focus group interviews. The aim of the study was to explore and identify relations between designs for teaching and learning and the students' learning...... of school subjects within defined learning goals and curricula, along with various implementations of ICT in the pedagogical everyday practice (Levinsen & Sørensen 2008). However, another research strand - the topic of this paper - emerged during the project's life cycle as a consequence of ongoing changes...

  3. Filters in topology optimization

    DEFF Research Database (Denmark)

    Bourdin, Blaise

    1999-01-01

    In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...

  4. Differential topology first steps

    CERN Document Server

    Wallace, Andrew H

    1968-01-01

    Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of d

  5. Topological approximations of multisets

    Directory of Open Access Journals (Sweden)

    El-Sayed A. Abo-Tabl

    2013-07-01

    Full Text Available Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset base of multiset topology induced by a multiset relation. Moreover, the relationships between generalized rough msets and mset topologies are given. In addition, an illustrative example is given to illustrate the relationships between different types of generalized definitions of rough multiset approximations.

  6. Topology in Condensed Matter

    CERN Document Server

    Monastyrsky, M I

    2006-01-01

    This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

  7. Topological Schemas of Memory Spaces

    Directory of Open Access Journals (Sweden)

    Andrey Babichev

    2018-04-01

    Full Text Available Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

  8. Topological Masses From Broken Supersymmetry

    CERN Document Server

    Antoniadis, Ignatios; Antoniadis, Ignatios; Taylor, Tomasz R.

    2004-01-01

    We develop a formalism for computing one-loop gravitational corrections to the effective action of D-branes. In particular, we study bulk to brane mediation of supersymmetry breaking in models where supersymmetry is broken at the tree-level in the closed string sector (bulk) by Scherk-Schwarz boundary conditions, while it is realized on a collection of D-branes in a linear or non-linear way. We compute the gravitational corrections to the fermion masses $m_{1/2}$ (gauginos or goldstino) induced from the exchange of closed strings, which are non-vanishing for world-sheets with Euler characteristic -1 (``genus 3/2'') due to a string diagram with one handle and one hole. We show that the corrections have a topological origin and that in general, for a small gravitino mass, the induced mass behaves as $m_{1/2}\\propto g^4 m_{3/2}$, with $g$ the gauge coupling. In generic orbifold compactifications however, this leading term vanishes as a consequence of cancellations caused by discrete symmetries, and the remainder...

  9. Linear topologies and sequential compactness in topological modules

    African Journals Online (AJOL)

    We prove that an absolute semi-valued ring is rst-countable if the set of invertibles is separable and its closure contains 0. We also show that every linearly topologized topological module over an absolute semi-valued ring whose invertibles approach 0 has the trivial topology. We also show that every sequentially compact ...

  10. Formal verification of an oral messages algorithm for interactive consistency

    Science.gov (United States)

    Rushby, John

    1992-01-01

    The formal specification and verification of an algorithm for Interactive Consistency based on the Oral Messages algorithm for Byzantine Agreement is described. We compare our treatment with that of Bevier and Young, who presented a formal specification and verification for a very similar algorithm. Unlike Bevier and Young, who observed that 'the invariant maintained in the recursive subcases of the algorithm is significantly more complicated than is suggested by the published proof' and who found its formal verification 'a fairly difficult exercise in mechanical theorem proving,' our treatment is very close to the previously published analysis of the algorithm, and our formal specification and verification are straightforward. This example illustrates how delicate choices in the formulation of the problem can have significant impact on the readability of its formal specification and on the tractability of its formal verification.

  11. Electromagnetic topology: Characterization of internal electromagnetic coupling

    Science.gov (United States)

    Parmantier, J. P.; Aparicio, J. P.; Faure, F.

    1991-01-01

    The main principles are presented of a method dealing with the resolution of electromagnetic internal problems: Electromagnetic Topology. A very interesting way is to generalize the multiconductor transmission line network theory to the basic equation of the Electromagnetic Topology: the BLT equation. This generalization is illustrated by the treatment of an aperture as a four port junction. Analytical and experimental derivations of the scattering parameters are presented. These concepts are used to study the electromagnetic coupling in a scale model of an aircraft, and can be seen as a convenient means to test internal electromagnetic interference.

  12. Topological field theories and duality

    International Nuclear Information System (INIS)

    Stephany, J.; Universidad Simon Bolivar, Caracas

    1996-05-01

    Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs

  13. Topology optimization of viscoelastic rectifiers

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin

    2012-01-01

    An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...

  14. Spinor formalism and complex-vector formalism of general relativity

    International Nuclear Information System (INIS)

    Han-ying, G.; Yong-shi, W.; Gendao, L.

    1974-01-01

    In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra

  15. Coherence Multiplex System Topologies

    NARCIS (Netherlands)

    Meijerink, Arjan; Taniman, R.O.; Heideman, G.H.L.M.; van Etten, Wim

    2007-01-01

    Coherence multiplexing is a potentially inexpensive form of optical code-division multiple access, which is particularly suitable for short-range applications with moderate bandwidth requirements, such as access networks, LANs, or interconnects. Various topologies are known for constructing an

  16. Architecture, Drawing, Topology

    DEFF Research Database (Denmark)

    This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...

  17. Towards topological quantum computer

    Science.gov (United States)

    Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

    2018-01-01

    Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

  18. Slope constrained Topology Optimization

    DEFF Research Database (Denmark)

    Petersson, J.; Sigmund, Ole

    1998-01-01

    The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing...

  19. Counterexamples in topology

    CERN Document Server

    Steen, Lynn Arthur

    1978-01-01

    Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.

  20. LHCb Topological Trigger Reoptimization

    CERN Document Server

    INSPIRE-00400931; Ilten, Philip; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael

    2015-12-23

    The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. ...

  1. Towards topological quantum computer

    Directory of Open Access Journals (Sweden)

    D. Melnikov

    2018-01-01

    Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

  2. Topological Trigger Developments

    CERN Multimedia

    Likhomanenko, Tatiana

    2015-01-01

    The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger utilized a custom boosted decision tree algorithm, selected an almost 100% pure sample of b-hadrons with a typical efficiency of 60-70%, and its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and uBoost. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. These inclu...

  3. Rendering the Topological Spines

    Energy Technology Data Exchange (ETDEWEB)

    Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-05-05

    Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.

  4. Adjoint entropy vs topological entropy

    OpenAIRE

    Giordano Bruno, Anna

    2012-01-01

    Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

  5. Topology of Document Retrieval Systems.

    Science.gov (United States)

    Everett, Daniel M.; Cater, Steven C.

    1992-01-01

    Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…

  6. Noncommuting Momenta of Topological Solitons

    Science.gov (United States)

    Watanabe, Haruki; Murayama, Hitoshi

    2014-05-01

    We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

  7. Topological Properties of Superconducting Junctions

    NARCIS (Netherlands)

    Pikulin, D.I.; Nazarov, Y.V.

    Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically

  8. Multifractal formalisms of human behavior.

    Science.gov (United States)

    Ihlen, Espen A F; Vereijken, Beatrix

    2013-08-01

    With the mounting realization that variability is an inevitable part of human behavior comes the need to integrate this phenomenon in concomitant models and theories of motor control. Among other things, this has resulted in a debate throughout the last decades about the origin of variability in behavior, the outcome of which has important implications for motor control theories. To date, a monofractal formalism of variability has been used as the basis for arguing for component- versus interaction-oriented theories of motor control. However, monofractal formalism alone cannot decide between the opposing sides of the debate. The present theoretical overview introduces multifractal formalisms as a necessary extension of the conventional monofractal formalism. In multifractal formalisms, the scale invariance of behavior is numerically defined as a spectrum of scaling exponents, rather than a single average exponent as in the monofractal formalism. Several methods to estimate the multifractal spectrum of scaling exponents - all within two multifractal formalisms called large deviation and Legendre formalism - are introduced and briefly discussed. Furthermore, the multifractal analyses within these two formalisms are applied to several performance tasks to illustrate how explanations of motor control vary with the methods used. The main section of the theoretical overview discusses the implications of multifractal extensions of the component- and interaction-oriented models for existing theories of motor control. Copyright © 2013 Elsevier B.V. All rights reserved.

  9. Gauge symmetries, topology, and quantisation

    International Nuclear Information System (INIS)

    Balachandran, A.P.

    1994-01-01

    The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem

  10. Topology optimized permanent magnet systems

    DEFF Research Database (Denmark)

    Bjørk, Rasmus; Bahl, Christian; Insinga, Andrea Roberto

    2017-01-01

    Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron...... and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a ΛcoolΛcool figure of merit of 0...

  11. 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.

  12. Undergraduate topology a working textbook

    CERN Document Server

    McCluskey, Aisling

    2014-01-01

    This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i

  13. Formalizing Implementation Strategies for First-Class Continuations

    DEFF Research Database (Denmark)

    Danvy, Olivier

    2000-01-01

    We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstract machines for continuation-passing style (CPS) programs with a special treatment for the current continuation, accounting for the essence of first-class continuations...

  14. Games for Topological Fixpoint Logic

    Directory of Open Access Journals (Sweden)

    Nick Bezhanishvili

    2016-09-01

    Full Text Available Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we introduce games characterising clopen fixpoints of monotone operators on Stone spaces. These fixpoint games allow us to characterise the semantics for our topological fixpoint logic using a two-player graph game. Adequacy of this game is the main result of our paper. Finally, we define bisimulations for the topological structures under consideration and use our game semantics to prove that the truth of a formula of our topological fixpoint logic is bisimulation-invariant.

  15. Floquet topological insulators for sound

    Science.gov (United States)

    Fleury, Romain; Khanikaev, Alexander B.; Alù, Andrea

    2016-06-01

    The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.

  16. Generalized topological spaces in evolutionary theory and combinatorial chemistry.

    Science.gov (United States)

    Stadler, Bärbel M R; Stadler, Peter F

    2002-01-01

    The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a nongraphical structure of the combinatorial search spaces. These structures, and their implications for search process itself, are heretofore not well understood in general. In this contribution we review a very general formalism from point set topology and discuss its application to combinatorial search spaces, fitness landscapes, evolutionary trajectories, and artificial chemistries.

  17. Leibniz' First Formalization of Syllogistics

    DEFF Research Database (Denmark)

    Robering, Klaus

    2014-01-01

    of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity...

  18. Outline of Neutron Scattering Formalism

    OpenAIRE

    Berk, N. F.

    1993-01-01

    Neutron scattering formalism is briefly surveyed. Topics touched upon include coherent and incoherent scattering, bound and free cross-sections, the Van Hove formalism, magnetic scattering, elastic scattering, the static approximation, sum rules, small angle scattering, inelastic scattering, thermal diffuse scattering, quasielastic scattering, and neutron optics.

  19. A Formalization of Linkage Analysis

    DEFF Research Database (Denmark)

    Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.

    In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been ...

  20. Formal Methods: Practice and Experience

    DEFF Research Database (Denmark)

    Woodcock, Jim; Larsen, Peter Gorm; Bicarregui, Juan

    2009-01-01

    Formal methods use mathematical models for analysis and verification at any part of the program life-cycle. We describe the state of the art in the industrial use of formal methods, concentrating on their increasing use at the earlier stages of specification and design. We do this by reporting on...

  1. Computational differential topology

    Directory of Open Access Journals (Sweden)

    Denis Blackmore

    2007-04-01

    Full Text Available Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational differential categories are proven, and evaluated from the perspective of effective computability (algorithmic solvability. In addition, the elements of innovative, effectively computable approaches for analyzing and obtaining computer generated representations of geometric objects based upon singularity/stratification theory and obstruction theory are formulated. New methods for characterizing complicated intersection sets are proven using differential analysis and homology theory. Also included are brief descriptions of several implementation aspects of some of the approaches described, as well as applications of the results in such areas as virtual sculpting, virtual surgery, modeling of heterogeneous biomaterials, and high speed visualizations.

  2. Design as Topology

    DEFF Research Database (Denmark)

    Ekman, Ulrik

    2015-01-01

    This article discusses the issue of approaching the design of the ubiquitous city as a matter of topology. The general context here is the design of contemporary global urbanity in the form of u-cities, smart cities, or intelligent cities emerging with the second phase of network societies...... that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...

  3. Network topology mapper

    Science.gov (United States)

    Quist, Daniel A [Los Alamos, NM; Gavrilov, Eugene M [Los Alamos, NM; Fisk, Michael E [Jemez, NM

    2008-01-15

    A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.

  4. Topology in Molecular Biology

    CERN Document Server

    Monastyrsky, Michail Ilych

    2007-01-01

    The book presents a class of new results in molecular biology for which topological methods and ideas are important. These include: the large-scale conformation properties of DNA; computational methods (Monte Carlo) allowing the simulation of large-scale properties of DNA; the tangle model of DNA recombination and other applications of Knot theory; dynamics of supercoiled DNA and biocatalitic properties of DNA; the structure of proteins; and other very recent problems in molecular biology. The text also provides a short course of modern topology intended for the broad audience of biologists and physicists. The authors are renowned specialists in their fields and some of the new results presented here are documented for the first time in monographic form.

  5. Topological signal processing

    CERN Document Server

    Robinson, Michael

    2014-01-01

    Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information.  Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known.  This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations.  Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.

  6. Topologies of climate change

    DEFF Research Database (Denmark)

    Blok, Anders

    2010-01-01

    Climate change is quickly becoming a ubiquitous socionatural reality, mediating extremes of sociospatial scale from the bodily to the planetary. Although environmentalism invites us to ‘think globally and act locally', the meaning of these scalar designations remains ambiguous. This paper explores...... the topological presuppositions of social theory in the context of global climate change, asking how carbon emissions ‘translate' into various sociomaterial forms. Staging a meeting between Tim Ingold's phenomenology of globes and spheres and the social topologies of actor-network theory (ANT), the paper advances...... a ‘relational-scalar' analytics of spatial practices, technoscience, and power. As technoscience gradually constructs a networked global climate, this ‘grey box' comes to circulate within fluid social spaces, taking on new shades as it hybridizes knowledges, symbols, and practices. Global climates thus come...

  7. Operator algebras and topology

    International Nuclear Information System (INIS)

    Schick, T.

    2002-01-01

    These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)

  8. Topological confinement and superconductivity

    Energy Technology Data Exchange (ETDEWEB)

    Al-hassanieh, Dhaled A [Los Alamos National Laboratory; Batista, Cristian D [Los Alamos National Laboratory

    2008-01-01

    We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.

  9. The topology of fullerenes

    DEFF Research Database (Denmark)

    Schwerdtfeger, Peter; Wirz, Lukas; Avery, James Emil

    2014-01-01

    Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar g....... In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems....

  10. Technologies for converter topologies

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Yan; Zhang, Haiyu

    2017-02-28

    In some embodiments of the disclosed inverter topologies, an inverter may include a full bridge LLC resonant converter, a first boost converter, and a second boost converter. In such embodiments, the first and second boost converters operate in an interleaved manner. In other disclosed embodiments, the inverter may include a half-bridge inverter circuit, a resonant circuit, a capacitor divider circuit, and a transformer.

  11. New procedure for departure formalities

    CERN Multimedia

    HR & GS Departments

    2011-01-01

    As part of the process of simplifying procedures and rationalising administrative processes, the HR and GS Departments have introduced new personalised departure formalities on EDH. These new formalities have applied to students leaving CERN since last year and from 17 October 2011 this procedure will be extended to the following categories of CERN personnel: Staff members, Fellows and Associates. It is planned to extend this electronic procedure to the users in due course. What purpose do departure formalities serve? The departure formalities are designed to ensure that members of the personnel contact all the relevant services in order to return any necessary items (equipment, cards, keys, dosimeter, electronic equipment, books, etc.) and are aware of all the benefits to which they are entitled on termination of their contract. The new departure formalities on EDH have the advantage of tailoring the list of services that each member of the personnel must visit to suit his individual contractual and p...

  12. Topological Substituent Descriptors

    Directory of Open Access Journals (Sweden)

    Mircea V. DIUDEA

    2002-12-01

    Full Text Available Motivation. Substituted 1,3,5-triazines are known as useful herbicidal substances. In view of reducing the cost of biological screening, computational methods are carried out for evaluating the biological activity of organic compounds. Often a class of bioactives differs only in the substituent attached to a basic skeleton. In such cases substituent descriptors will give the same prospecting results as in case of using the whole molecule description, but with significantly reduced computational time. Such descriptors are useful in describing steric effects involved in chemical reactions. Method. Molecular topology is the method used for substituent description and multi linear regression analysis as a statistical tool. Results. Novel topological descriptors, XLDS and Ws, based on the layer matrix of distance sums and walks in molecular graphs, respectively, are proposed for describing the topology of substituents linked on a chemical skeleton. They are tested for modeling the esterification reaction in the class of benzoic acids and herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino-1,3,5-triazines. Conclusions. Ws substituent descriptor, based on walks in graph, satisfactorily describes the steric effect of alkyl substituents behaving in esterification reaction, with good correlations to the Taft and Charton steric parameters, respectively. Modeling the herbicidal activity of the seo of 1,3,5-triazines exceeded the models reported in literature, so far.

  13. Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals

    OpenAIRE

    Cortese, Dario; Eggers, Jens; Liverpool, Tanniemola

    2018-01-01

    We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parame...

  14. Pair creation, motion, and annihilation of topological defects in 2D nematics

    OpenAIRE

    Cortese, Dario; Eggers, Jens; Liverpool, Tanniemola B.

    2017-01-01

    We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parame...

  15. Transportation Network Topologies

    Science.gov (United States)

    Holmes, Bruce J.; Scott, John

    2004-01-01

    A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which

  16. 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

  17. Formal verification - Robust and efficient code: Introduction to Formal Verification

    CERN Multimedia

    CERN. Geneva

    2016-01-01

    In general, FV means "proving that certain properties hold for a given system using formal mathematics". This definition can certainly feel daunting, however, as we will learn, we can reap benefits from the paradigm without digging too deep into ...

  18. 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.

  19. Scalable Techniques for Formal Verification

    CERN Document Server

    Ray, Sandip

    2010-01-01

    This book presents state-of-the-art approaches to formal verification techniques to seamlessly integrate different formal verification methods within a single logical foundation. It should benefit researchers and practitioners looking to get a broad overview of the spectrum of formal verification techniques, as well as approaches to combining such techniques within a single framework. Coverage includes a range of case studies showing how such combination is fruitful in developing a scalable verification methodology for industrial designs. This book outlines both theoretical and practical issue

  20. Leibniz' First Formalization of Syllogistics

    DEFF Research Database (Denmark)

    Robering, Klaus

    2014-01-01

    of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity......In his Dissertatio de Arte Combinatoria from 1666 Leibniz provides a formal presentation of syllogistics within the framework of his general-combinatoric program. He does not set up an axiomatic system for the derivation of all valid syllogistic mode, rather he formulates a set of rules which...

  1. Layer Construction of 3D Topological States and String Braiding Statistics

    Directory of Open Access Journals (Sweden)

    Chao-Ming Jian

    2014-12-01

    Full Text Available While the topological order in two dimensions has been studied extensively since the discovery of the integer and fractional quantum Hall systems, topological states in three spatial dimensions are much less understood. In this paper, we propose a general formalism for constructing a large class of three-dimensional topological states by stacking layers of 2D topological states and introducing coupling between them. Using this construction, different types of topological states can be obtained, including those with only surface topological order and no bulk topological quasiparticles, and those with topological order both in the bulk and at the surface. For both classes of states, we study its generic properties and present several explicit examples. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between string excitations. In addition to studying the string-string braiding in the example system, we propose a topological field-theory description for the layer-constructed systems, which captures not only the string-particle braiding statistics but also the string-string braiding statistics when the coupling is twisted. Last, we provide a proof of a general identity for Abelian string statistics and discuss an example system with non-Abelian strings.

  2. Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions.

    Directory of Open Access Journals (Sweden)

    Bo Liu

    Full Text Available In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS and Artificial Intelligence (AI. Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1 23 different topological relations between a simple crisp region and a simple fuzzy region; (2 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.

  3. Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

    Science.gov (United States)

    Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi

    2015-01-01

    In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452

  4. Einstein's lifts and topologies topological investigations on the Principle of Equivalence

    CERN Document Server

    Segrè, G

    2002-01-01

    The gedanken-experiment of Einstein's lift is analyzed in order of determining whether the free-falling observer inside the lift can detect the eventual topological non-triviality of space-time, as it would seem considering a non-globally-hamiltonian action of the symmetry group of the observer's action (that, unfortunately, can be obtained only submitting the lift also to a suitable electromagnetic field) and considering that the observer can locally detect the topological alteration of the constants-of-motion's algebra. It follows that a problem exists in formalizing the Principle of Equivalence, owing to its indetermination as to the topology of the reference's flat space-time defining the special relativistic laws to which, up to first order terms in the normal coordinates of the lift's Lorentz moving inertial frame, all the non-gravitational Laws of Physics have to collapse. It is then shown how the problem may be avoided getting rid of the Principle of Equivalence following the Hawking-Ellis' axiomatiza...

  5. Formalizing Real-Time Embedded System into Promela

    Directory of Open Access Journals (Sweden)

    Sukvanich Punwess

    2015-01-01

    Full Text Available We propose an alternative of formalization of the real-time embedded system into Promela model. The proposed formal model supports the essential features of the real-time embedded system, including system resource-constrained handling, task prioritization, task synchronization, real-time preemption, the parallelism of resources via DMA. Meanwhile, the model is also fully compatible with the partial order reduction algorithm for model checking. The timed automata of the real-time embedded system are considered and transformed into Promela, in our approach, by replacing time ticking into the repeated cycle of the timed values to do the conditional guard to enable the synchronization among the whole system operations. Our modeling approach could satisfactorily verify a small real-time system with parameterized dependent tasks and different scheduling topologies.

  6. Topological imprint for periodic orbits

    International Nuclear Information System (INIS)

    Martín, Jesús San; Moscoso, Ma José; Gómez, A González

    2012-01-01

    The more self-crossing points an orbit has the more complex it is. We introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade. The period-doubling cascade topological imprint determines the topological imprint for orbits in chaotic bands. In addition, there is a closer link between this concept and the braids studied by Lettelier et al (2000 J. Phys. A: Math. Gen. 33 1809–25). (paper)

  7. Intuitionistic supra fuzzy topological spaces

    International Nuclear Information System (INIS)

    Abbas, S.E.

    2004-01-01

    In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space

  8. Topological X-Rays Revisited

    Science.gov (United States)

    Lynch, Mark

    2012-01-01

    We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…

  9. Topological Order in Silicon Photonics

    Science.gov (United States)

    2017-02-07

    AFRL-AFOSR-VA-TR-2017-0037 Topological orders in Silicon photonics Mohammad Hafezi MARYLAND UNIV COLLEGE PARK 3112 LEE BLDG COLLEGE PARK, MD 20742...15 SEP 2016 4. TITLE AND SUBTITLE Topological Order in Silicon Photonics 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA-9550-14-1-0267 5c. PROGRAM...matter to ultra cold gases. Recently, photonic systems have been under investigation to explore various types of topological orders and to potentially

  10. OPTIMAL NETWORK TOPOLOGY DESIGN

    Science.gov (United States)

    Yuen, J. H.

    1994-01-01

    This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.

  11. Topologically clean distance fields.

    Science.gov (United States)

    Gyulassy, Attila; Duchaineau, Mark; Natarajan, Vijay; Pascucci, Valerio; Bringa, Eduardo; Higginbotham, Andrew; Hamann, Bernd

    2007-01-01

    Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.

  12. El Salvador - Formal Technical Education

    Data.gov (United States)

    Millennium Challenge Corporation — With a budget of nearly $20 million, the Formal Technical Education Sub-Activity was designed to strengthen technical and vocational educational institutions in the...

  13. Concepts of formal concept analysis

    Science.gov (United States)

    Žáček, Martin; Homola, Dan; Miarka, Rostislav

    2017-07-01

    The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.

  14. Readings in Formal Epistemology : Sourcebook

    NARCIS (Netherlands)

    Arló-Costa, H.; Hendricks, V.F.; van Benthem, J.

    2016-01-01

    This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory,

  15. Lieb polariton topological insulators

    Science.gov (United States)

    Li, Chunyan; Ye, Fangwei; Chen, Xianfeng; Kartashov, Yaroslav V.; Ferrando, Albert; Torner, Lluis; Skryabin, Dmitry V.

    2018-02-01

    We predict that the interplay between the spin-orbit coupling, stemming from the transverse electric-transverse magnetic energy splitting, and the Zeeman effect in semiconductor microcavities supporting exciton-polariton quasiparticles, results in the appearance of unidirectional linear topological edge states when the top microcavity mirror is patterned to form a truncated dislocated Lieb lattice of cylindrical pillars. Periodic nonlinear edge states are found to emerge from the linear ones. They are strongly localized across the interface and they are remarkably robust in comparison to their counterparts in honeycomb lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move steadily along the lattice edge.

  16. Architecture, Drawing, Topology

    DEFF Research Database (Denmark)

    Meldgaard, Morten

    This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...

  17. Introduction to generalized topological spaces

    Directory of Open Access Journals (Sweden)

    Irina Zvina

    2011-04-01

    Full Text Available We introduce the notion of generalized topological space (gt-space. Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants in terms of generalized spaces.

  18. FLIC-overlap fermions and topology

    International Nuclear Information System (INIS)

    Kamleh, W.; Kusterer, D.J.; Leinweber, D.B.; Williams, A.G.

    2003-01-01

    APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F μν in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(α 4 )-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice

  19. Topological social choice

    CERN Document Server

    1997-01-01

    The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi­ ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets": additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel­ fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ­ omists and mathematicians, yet there is no authoritative collection of papers in the a...

  20. 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...

  1. Algebraic topology of finite topological spaces and applications

    CERN Document Server

    Barmak, Jonathan A

    2011-01-01

    This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

  2. Chains of topological oscillators with instantons and calculable topological observables in topological quantum mechanics

    Directory of Open Access Journals (Sweden)

    L. Baulieu

    2016-11-01

    Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.

  3. Formalization of an environmental model using formal concept analysis - FCA

    Science.gov (United States)

    Bourdon-García, Rubén D.; Burgos-Salcedo, Javier D.

    2016-08-01

    Nowadays, there is a huge necessity to generate novel strategies for social-ecological systems analyses for resolving global sustainability problems. This paper has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Ángel Maya, who without a doubt, was one of the most important environmental philosophers in South America; Ángel Maya proposed and established that Ecosystem-Culture relations, instead Human-Nature ones, are determinants in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept-superconcept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne-Guigues base), were determined for the ecosystem-culture relations.

  4. Topological arguments for Kolmogorov complexity

    Directory of Open Access Journals (Sweden)

    Alexander Shen

    2012-08-01

    Full Text Available We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.

  5. Coverings, Networks and Weak Topologies

    Czech Academy of Sciences Publication Activity Database

    Dow, A.; Junnila, H.; Pelant, Jan

    2006-01-01

    Roč. 53, č. 2 (2006), s. 287-320 ISSN 0025-5793 R&D Projects: GA ČR GA201/97/0216 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak topologies * networks topologies Subject RIV: BA - General Mathematics

  6. A Course on Topological Groups

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 8. A Course on Topological Groups - A Pellucid Little Book on Topological Groups. K Parthasarathy. Book Review Volume 2 Issue 8 August 1997 pp 82-83. Fulltext. Click here to view fulltext PDF. Permanent link:

  7. Topology optimization of turbulent flows

    DEFF Research Database (Denmark)

    Dilgen, Cetin B.; Dilgen, Sumer B.; Fuhrman, David R.

    2018-01-01

    The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient...

  8. Redundancy of multiset topological spaces

    OpenAIRE

    Ghareeb, A.

    2016-01-01

    In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\\star(U),\\sqsubseteq)$ and $(\\mathcal{P}(X\\times\\mathbb{N}),\\subseteq)$. It therefore follows that multiset topologies are superfluous and unnecessary in the theoretical view point.

  9. Topological phases of quantum matter

    Indian Academy of Sciences (India)

    Although first to mention topological phases, not really the first Nobel prize for topological phases. First - 1982 Nobel to Klaus von Klitzing for `discovery of quantised. Hall effect '. Second - 1998 Nobel to RobertLaughlin, Horst Stormer and. Daniel Tsui for `discovery of a new form of quantum fluid with fractionally charged ...

  10. Cartography – morphology – topology

    DEFF Research Database (Denmark)

    Dinesen, Cort Ross; Peder Pedersen, Claus

    I 2004 a Summer School was established on the Greek island of Hydra. The was to be the basis of research-based morphological and topological studies, which have since taken place for 4 weeks of every year. Starting with Hydra’s topography different ways of considering topology were developed...

  11. On Neutrosophic Soft Topological Space

    Directory of Open Access Journals (Sweden)

    Tuhin Bera

    2018-03-01

    Full Text Available In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also. Then, the notion of neutrosophic soft continuous mapping on a neutrosophic soft topological space and it’s properties are developed here.

  12. Topology optimized RF MEMS switches

    DEFF Research Database (Denmark)

    Philippine, M. A.; Zareie, H.; Sigmund, Ole

    2013-01-01

    Topology optimization is a rigorous and powerful method that should become a standard MEMS design tool - it can produce unique and non-intuitive designs that meet complex objectives and can dramatically improve the performance and reliability of MEMS devices. We present successful uses of topolog...

  13. Observational modeling of topological spaces

    International Nuclear Information System (INIS)

    Molaei, M.R.

    2009-01-01

    In this paper a model for a multi-dimensional observer by using of the fuzzy theory is presented. Relative form of Tychonoff theorem is proved. The notion of topological entropy is extended. The persistence of relative topological entropy under relative conjugate relation is proved.

  14. Topological Electride Y2C.

    Science.gov (United States)

    Huang, Huaqing; Jin, Kyung-Hwan; Zhang, Shunhong; Liu, Feng

    2018-02-22

    Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y 2 C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y 2 C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y 2 C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.

  15. Solving equations by topological methods

    Directory of Open Access Journals (Sweden)

    Lech Górniewicz

    2005-01-01

    Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

  16. Concept Model on Topological Learning

    Science.gov (United States)

    Ae, Tadashi; Kioi, Kazumasa

    2010-11-01

    We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.

  17. Combined Shape and Topology Optimization

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman

    Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead...

  18. Streamline topology of axisymmetric flows

    DEFF Research Database (Denmark)

    Brøns, Morten

    Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....

  19. Transportation Network Topologies

    Science.gov (United States)

    Alexandrov, Natalia (Editor)

    2004-01-01

    The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.

  20. Mooses, topology and Higgs

    International Nuclear Information System (INIS)

    Gregoire, Thomas; Wacker, Jay G.

    2002-01-01

    New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking. (author)

  1. Formal connections in deformation quantization

    DEFF Research Database (Denmark)

    Masulli, Paolo

    product on a Poisson manifold that is in general non-commutative and corresponds to the composition of the quantized observables. While in general it is difficult to express a star product globally on a curved manifold in an explicit way, we consider a case where this is possible, namely that of a Kähler...... terms. This allows us to express the equations determining a trivialization of the formal connection completely in graph terms, and solving them amounts to finding a linear combination of graphs whose derivative is equal to a given expression. We shall also look at another approach to the problem...... that is more calculative. Moreover we use the graph formalism to give a set of recursive equations determining the formal connection for a given family of star products....

  2. Cultural Topology of Creativity

    Directory of Open Access Journals (Sweden)

    L. M. Andryukhina

    2012-01-01

    Full Text Available The man in the modern culture faces the challenge of either being creative or forced to leave the stage, which reflects the essential basics of life. The price of lost opportunities, caused by mental stereotypes and encapsulation, is gradually rising. The paper reveals the socio-cultural conditions and the necessary cultural topology of creativity development, as well as the man’s creative potential in the 21st century. The content of the creativity concept is specified along with the phenomenon of its fast expansion in the modern discourse. That results from the global spreading of numerous creative practices in various spheres of life, affecting the progress directions in economics, business, industrial technologies, labor, employment and social stratification. The author emphasizes the social features of creativity, the rising number of, so called, creative class, and outlines the two opposing strategies influencing the topology modification of the social and cultural environment. The first one, applied by the developed countries, facilitates the development of the creative human potential, whereas the other one, inherent in our country, holds that a creative person is able to make progress by himself. However, for solving the urgent problem of innovative development, the creative potential of modern Russia is not sufficient, and following the second strategy will result in unrealized social opportunities and ever lasting social and cultural situation demanding further investment. According to the author, to avoid such a perspective, it is necessary to overcome the three deeply rooted archetypes: the educational disciplinary centrism, organizational absolutism and cultural ostracism. 

  3. Circuit topology of self-interacting chains: implications for folding and unfolding dynamics.

    Science.gov (United States)

    Mugler, Andrew; Tans, Sander J; Mashaghi, Alireza

    2014-11-07

    Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, the topology is preserved when continuously stretching the chain while maintaining the contact arrangement. Here we investigate how the folding and unfolding of linear chains with binary contacts is guided by the topology of contact arrangements. We formalize the topology by describing the relations between any two contacts in the structure, which for a linear chain can either be in parallel, in series, or crossing each other. We show that even when other determinants of folding rate such as contact order and size are kept constant, this 'circuit' topology determines folding kinetics. In particular, we find that the folding rate increases with the fractions of parallel and crossed relations. Moreover, we show how circuit topology constrains the conformational phase space explored during folding and unfolding: the number of forbidden unfolding transitions is found to increase with the fraction of parallel relations and to decrease with the fraction of series relations. Finally, we find that circuit topology influences whether distinct intermediate states are present, with crossed contacts being the key factor. The approach presented here can be more generally applied to questions on molecular dynamics, evolutionary biology, molecular engineering, and single-molecule biophysics.

  4. COMPACTNESS IN INTUITIONISTIC FUZZY MULTISET TOPOLOGY

    OpenAIRE

    Kunnambath, Shinoj Thekke; John, Sunil Jacob

    2017-01-01

    – In this paper, we discussVarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spacesarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spaces

  5. Logical formalization and the formalization of logic(s)

    Czech Academy of Sciences Publication Activity Database

    Peregrin, Jaroslav; Svoboda, Vladimír

    2016-01-01

    Roč. 59, č. 233 (2016), s. 55-80 ISSN 0024-5836 R&D Projects: GA ČR(CZ) GA13-21076S Institutional support: RVO:67985955 Keywords : logical formalization * logical analysis * reflective equilibrium Subject RIV: AA - Philosophy ; Religion

  6. Integrating Semi-formal and Formal Software Specification Techniques

    NARCIS (Netherlands)

    Wieringa, Roelf J.; Dubois, Eric

    1998-01-01

    In this paper, we report on the integration of informal, semiformal and formal system specification techniques. We present a framework for system specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of structured

  7. DNA elasticity: topology of self-avoidance

    International Nuclear Information System (INIS)

    Samuel, Joseph; Sinha, Supurna; Ghosh, Abhijit

    2006-01-01

    We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self-avoiding ribbons and provide an underlying justification for the worm-like rod chain (WLRC) model proposed by Bouchiat and Mezard. Some theoretical points regarding the WLRC model are clarified: the 'local writhe formula' and the use of an adjustable cut-off parameter to 'regularize' the model. Our treatment brings out the precise relation between the worm-like chain (WLC), the paraxial worm-like chain (PWLC) and the WLRC models. We describe the phenomenon of 'topological untwisting' and the resulting collapse of link sectors in the WLC model and note that this leads to a free energy profile periodic in the applied link. This periodicity disappears when one takes into account the topology of self-avoidance or at large stretch forces (paraxial limit). We note that the difficult non-local notion of self-avoidance can be replaced (in an approximation) by the simpler local notion of 'south avoidance'. This gives an explanation for the efficacy of the approach of Bouchiat and Mezard in explaining the 'hat curves' using the WLRC model, which is a south avoiding model. We propose a new class of experiments to probe the continuous transition between the periodic and aperiodic behaviour of the free energy

  8. 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.

  9. Formal Institutions and Subjective Wellbeing

    DEFF Research Database (Denmark)

    Bjørnskov, Christian; Dreher, Axel; Fischer, Justina A.V.

    2010-01-01

    A long tradition in economics explores the association between the quality of formal institutions and economic performance. The literature on the relationship between such institutions and happiness is, however, rather limited, and inconclusive. In this paper, we revisit the findings from recent...... cross-country studies on the institution-happiness association. Our findings suggest that their conclusions are qualitatively rather insensitive to the specific measure of 'happiness' used, while the associations between formal institutions and subjective well-being differ among poor and rich countries...

  10. Equivariant topological quantum field theory and symmetry protected topological phases

    Energy Technology Data Exchange (ETDEWEB)

    Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)

    2017-03-01

    Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.

  11. Aspects of NT ≥ 2 topological gauge theories and D-branes

    International Nuclear Information System (INIS)

    Blau, M.; Thompson, G.

    1996-12-01

    Recently, topological field theories with extended N T > 1 topological symmetries have appeared in various contexts, e.g. in the discussion of S-duality in supersymmetry gauge theories, as world volume theories of Dirichlet p-branes in string theory, and in a general discussion of 'balanced' or critical topological theories. Here we will comment on, explain, or expand on various aspects of these theories, thus complementing the already existing discussions of such models in the literature. We comment on various aspects of topological gauge theories possessing N T ≥ 2 topological symmetry: 1. We show that the construction of Vafa-Witten and Dijkgraaf-Moore of 'balanced' topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. 2. We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. 3. We show that the topological twist of N = 4 d = 4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. 4. We construct a novel N T = 2 topological twist of N = 4 d = 3 Yang-Mills theory, a 'mirror' of the Casson invariant model, with certain unusual features (e.g. no bosonic scalar field and hence no underlying equivariant cohomology). 5. We give a complete classification of the topological twists of N = 8 d = 3 Yang-Mills theory and show that they are realized as world-volume theories of Dirichlet two-brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G 2 -holonomy Joyce manifolds. 6. We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3s and Calabi-Yau 3-folds. 48 refs

  12. Qualitative simulation in formal process modelling

    International Nuclear Information System (INIS)

    Sivertsen, Elin R.

    1999-01-01

    In relation to several different research activities at the OECD Halden Reactor Project, the usefulness of formal process models has been identified. Being represented in some appropriate representation language, the purpose of these models is to model process plants and plant automatics in a unified way to allow verification and computer aided design of control strategies. The present report discusses qualitative simulation and the tool QSIM as one approach to formal process models. In particular, the report aims at investigating how recent improvements of the tool facilitate the use of the approach in areas like process system analysis, procedure verification, and control software safety analysis. An important long term goal is to provide a basis for using qualitative reasoning in combination with other techniques to facilitate the treatment of embedded programmable systems in Probabilistic Safety Analysis (PSA). This is motivated from the potential of such a combination in safety analysis based on models comprising both software, hardware, and operator. It is anticipated that the research results from this activity will benefit V and V in a wide variety of applications where formal process models can be utilized. Examples are operator procedures, intelligent decision support systems, and common model repositories (author) (ml)

  13. Charging transient in polyvinyl formal

    Indian Academy of Sciences (India)

    Unknown

    401–406. © Indian Academy of Sciences. 401. Charging transient in polyvinyl formal. P K KHARE*, P L JAIN† and R K PANDEY‡. Department of Postgraduate Studies & Research in Physics & Electronics, Rani Durgavati University,. Jabalpur 482 001, India. †Department of Physics, Government PG College, Damoh 470 ...

  14. Formal monkey linguistics : The debate

    NARCIS (Netherlands)

    Schlenker, Philippe; Chemla, Emmanuel; Schel, Anne M.; Fuller, James; Gautier, Jean Pierre; Kuhn, Jeremy; Veselinović, Dunja; Arnold, Kate; Cäsar, Cristiane; Keenan, Sumir; Lemasson, Alban; Ouattara, Karim; Ryder, Robin; Zuberbühler, Klaus

    2016-01-01

    We explain why general techniques from formal linguistics can and should be applied to the analysis of monkey communication - in the areas of syntax and especially semantics. An informed look at our recent proposals shows that such techniques needn't rely excessively on categories of human language:

  15. Rotor and wind turbine formalism

    DEFF Research Database (Denmark)

    Branlard, Emmanuel Simon Pierre

    2017-01-01

    The main conventions used in this book for the study of rotors are introduced in this chapter. The main assumptions and notations are provided. The formalism specific to wind turbines is presented. The forces, moments, velocities and dimensionless coefficients used in the study of rotors...

  16. Formalization in Component Based Development

    DEFF Research Database (Denmark)

    Holmegaard, Jens Peter; Knudsen, John; Makowski, Piotr

    2006-01-01

    may be specified in a formal language convenient for its purpose and, in principle, unrelated to languages for other aspects. Each aspect forms its own semantic domain, although a semantic domain may be parameterized by values derived from other aspects. The proposed conceptual framework is introduced...

  17. Formal tautologies in Czech language

    OpenAIRE

    Bílková, Jana

    2006-01-01

    The main purpose ofthis work was to describe and classify FT used in the contemporary Czech language and to demonstrate formal and semantic variety and high functional potential of this specific class of sentences. Powered by TCPDF (www.tcpdf.org)

  18. Formal systems for persuasion dialogue

    NARCIS (Netherlands)

    Prakken, Henry

    This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various

  19. Automatic Testing with Formal Methods

    NARCIS (Netherlands)

    Tretmans, G.J.; Belinfante, Axel

    1999-01-01

    The use of formal system specifications makes it possible to automate the derivation of test cases from specifications. This allows to automate the whole testing process, not only the test execution part of it. This paper presents the state of the art and future perspectives in testing based on

  20. UML-ising formal techniques

    DEFF Research Database (Denmark)

    Bjørner, Dines; George, Chris W.; Haxthausen, Anne Elisabeth

    2004-01-01

    these different UML views are unified, integrated, correlated or merely co-located is for others to dispute. We also seek to support multiple views, but are also in no doubt that there must be sound, well defined relations between such views. We thus report on ways and means of integrating formal techniques...

  1. Topological and non-topological soliton solutions to some time ...

    Indian Academy of Sciences (India)

    topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.

  2. Spherical Orbifolds for Cosmic Topology

    International Nuclear Information System (INIS)

    Kramer, Peter

    2012-01-01

    Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.

  3. Topology optimised wavelength dependent splitters

    DEFF Research Database (Denmark)

    Hede, K. K.; Burgos Leon, J.; Frandsen, Lars Hagedorn

    A photonic crystal wavelength dependent splitter has been constructed by utilising topology optimisation1. The splitter has been fabricated in a silicon-on-insulator material (Fig. 1). The topology optimised wavelength dependent splitter demonstrates promising 3D FDTD simulation results....... This complex photonic crystal structure is very sensitive against small fabrication variations from the expected topology optimised design. A wavelength dependent splitter is an important basic building block for high-performance nanophotonic circuits. 1J. S. Jensen and O. Sigmund, App. Phys. Lett. 84, 2022...

  4. Topology optimization for coated structures

    DEFF Research Database (Denmark)

    Clausen, Anders; Andreassen, Erik; Sigmund, Ole

    2015-01-01

    This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....

  5. Topological Rankings in Communication Networks

    DEFF Research Database (Denmark)

    Aabrandt, Andreas; Hansen, Vagn Lundsgaard; Træholt, Chresten

    2015-01-01

    In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only...... if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components...

  6. Formalizing ICD coding rules using Formal Concept Analysis.

    Science.gov (United States)

    Jiang, Guoqian; Pathak, Jyotishman; Chute, Christopher G

    2009-06-01

    With the 11th revision of the International Classification of Disease (ICD) being officially launched by the World Health Organization (WHO), the significance of a formal representation for ICD coding rules has emerged as a pragmatic concern. To explore the role of Formal Concept Analysis (FCA) on examining ICD10 coding rules and to develop FCA-based auditing approaches for the formalization process. We propose a model for formalizing ICD coding rules underlying the ICD Index using FCA. The coding rules are generated from FCA models and represented in the Semantic Web Rule Language (SWRL). Two auditing approaches were developed focusing upon non-disjoint nodes and anonymous nodes manifest in the FCA model. The candidate domains (i.e. any three character code with their sub-codes) of all 22 chapters of the ICD10 2006 version were analyzed using the two auditing approaches. Case studies and a preliminary evaluation were performed for validation. A total of 2044 formal contexts from the candidate domains of 22 ICD chapters were generated and audited. We identified 692 ICD codes having non-disjoint nodes in all chapters; chapters 19 and 21 contained the highest proportion of candidate domains with non-disjoint nodes (61.9% and 45.6%). We also identified 6996 anonymous nodes from 1382 candidate domains. Chapters 7, 11, 13, and 17, have the highest proportion of candidate domains having anonymous nodes (97.5%, 95.4%, 93.6% and 93.0%) while chapters 15 and 17 have the highest proportion of anonymous nodes among all chapters (45.5% and 44.0%). Case studies and a limited evaluation demonstrate that non-disjoint nodes and anonymous nodes arising from FCA are effective mechanisms for auditing ICD10. FCA-based models demonstrate a practical solution for formalizing ICD coding rules. FCA techniques could not only audit ICD domain knowledge completeness for a specific domain, but also provide a high level auditing profile for all ICD chapters.

  7. PS-Regular Sets in Topology and Generalized Topology

    Directory of Open Access Journals (Sweden)

    Ankit Gupta

    2014-01-01

    Full Text Available We define and study a new class of regular sets called PS-regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using PS-regular sets. Semiconnectedness is characterized by using PS-regular sets. PS-continuity and almost PS-continuity are introduced and investigated.

  8. Quantum magnetotransport properties of topological insulators under strain

    KAUST Repository

    Tahir, M.

    2012-08-15

    We present a detailed theoretical investigation of the quantum magnetotransport properties of topological insulators under strain. We consider an external magnetic field perpendicular to the surface of the topological insulator in the presence of strain induced by the substrate. The strain effects mix the lower and upper surface states of neighboring Landau levels into two unequally spaced energy branches. Analytical expressions are derived for the collisional conductivity for elastic impurity scattering in the first Born approximation. We also calculate the Hall conductivity using the Kubo formalism. Evidence for the beating of Shubnikov–de Haas oscillations is found from the temperature and magnetic field dependence of the collisional and Hall conductivities. In the regime of a strong magnetic field, the beating pattern is replaced by a splitting of the magnetoresistance peaks due to finite strain energy. These results are in excellent agreement with recent HgTe transport experiments.

  9. Topology of tokamak orbits

    International Nuclear Information System (INIS)

    Rome, J.A.; Peng, Y.K.M.

    1978-09-01

    Guiding center orbits in noncircular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, zeta, psi/sub m/). Here, v is the particle speed, zeta is the pitch angle with respect to the parallel equilibrium current, J/sub parallels/, and psi/sub m/ is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding center orbit. Two D-shaped equilibria in a flux-conserving tokamak having β's of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point and different types of orbits (e.g., circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher β (7.7%) equilibrium results in a dramatically different orbit topology from that of the lower β case. The differences indicate the confinement of additional high energy (v → c, within the guiding center approximation) trapped, co- and countercirculating particles whose orbit psi/sub m/ falls within the absolute B well

  10. Topological characteristics of model gels

    International Nuclear Information System (INIS)

    Miller, Mark A; Hansen, Jean-Pierre; Blaak, Ronald

    2010-01-01

    The Euler characteristic of an object is a topological invariant determined by the number of handles and holes that it contains. Here, we use the Euler characteristic to profile the topology of model three-dimensional gel-forming fluids as a function of increasing length scale. These profiles act as a 'topological fingerprint' of the structure, and can be interpreted in terms of three types of topological events. As model fluids we have considered a system of dipolar dumbbells, and suspensions of adhesive hard spheres with isotropic and patchy interactions in turn. The correlation between the percolation threshold and the length scale on which the Euler characteristic passes through zero is examined and found to be system-dependent. A scheme for the efficient calculation of the Euler characteristic with and without periodic boundary conditions is described.

  11. Intuitive concepts in elementary topology

    CERN Document Server

    Arnold, BH

    2011-01-01

    Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

  12. Topology Based Domain Search (TBDS)

    National Research Council Canada - National Science Library

    Manning, William

    2002-01-01

    This effort will explore radical changes in the way Domain Name System (DNS) is used by endpoints in a network to improve the resilience of the endpoint and its applications in the face of dynamically changing infrastructure topology...

  13. A topological quantum optics interface.

    Science.gov (United States)

    Barik, Sabyasachi; Karasahin, Aziz; Flower, Christopher; Cai, Tao; Miyake, Hirokazu; DeGottardi, Wade; Hafezi, Mohammad; Waks, Edo

    2018-02-09

    The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

  14. Topology optimized electrothermal polysilicon microgrippers

    DEFF Research Database (Denmark)

    Sardan Sukas, Özlem; Petersen, Dirch Hjorth; Mølhave, Kristian

    2008-01-01

    This paper presents the topology optimized design procedure and fabrication of electrothermal polysilicon microgrippers for nanomanipulation purposes. Performance of the optimized microactuators is compared with a conventional three-beam microactuator design through finite element analysis...

  15. Two-dimensional topological photonics

    Science.gov (United States)

    Khanikaev, Alexander B.; Shvets, Gennady

    2017-12-01

    Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.

  16. 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.)

  17. 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

  18. The coarsest Hausdorff Lebesgue topology | Conradie ...

    African Journals Online (AJOL)

    If a Riesz space E contains an order dense Riesz subspace which admits a Hausdorff Lebesgue (i.e. order continuous) topology, then there is a coarsest Hausdorff Lebesgue topology on E. This topology extends uniquely to a Hausdorff Lebesgue topology on the universal completion of E, and is always minimal amongst ...

  19. Scalar-tensor approach to the construction of theory of topological transformations

    International Nuclear Information System (INIS)

    Konstantinov, M.Yu.

    1985-01-01

    Problem of construction of the classical gravitational theory, which solutions in the explicit form contain description of topological transformations, is under study. With this object in view, the scalar-tensor formalism is considered based on a representation of some subclass of space-like hypersurfaces as surfaces of a smooth function level in four-dimensional manifolds. Solutions of the theory along with the Lorentz space-time structure and space-like surface topology define some reference system, but the type of topological transformations is not dependent on the reference system option. All these facts prove the above approach correctness. Two variants of the scalar-tensor theory of topological transformations are considered as an example; one of them is reduced to the Einstein gravitational theory in the regular space region and another represents a nontrivial modification of the Brans-Dikker theory

  20. Elements of mathematics general topology

    CERN Document Server

    Bourbaki, Nicolas

    1995-01-01

    This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.

  1. Topology Optimized Photonic Wire Splitters

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Borel, Peter Ingo; Jensen, Jakob Søndergaard

    2006-01-01

    Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm.......Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm....

  2. Topology Optimization of Nanophotonic Devices

    DEFF Research Database (Denmark)

    Yang, Lirong

    This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....

  3. Symmetry and topology in evolution

    International Nuclear Information System (INIS)

    Lukacs, B.; Berczi, S.; Molnar, I.; Paal, G.

    1991-10-01

    This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)

  4. Topological Fidelity in Sensor Networks

    OpenAIRE

    Chintakunta, Harish; Krim, Hamid

    2011-01-01

    Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection ...

  5. Topological excitations in semiconductor heterostructures

    International Nuclear Information System (INIS)

    Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.

    2013-01-01

    Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements

  6. Topological Photonics for Continuous Media

    Science.gov (United States)

    Silveirinha, Mario

    Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.

  7. Relativity of topology and dynamics

    International Nuclear Information System (INIS)

    Finkelstein, D.; Rodriguez, E.

    1984-01-01

    Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute time-space dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group (O(m,n). Because quantum theory cannot take the universe as physical system, a ''third relativity'' is proposed. The division between observer and observed is arbitrary. Then it is wrong to ask for ''the'' topology and dynamics of a system, in the same sense that it is wrong to ask for the ''the'' psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer. (author)

  8. Topology change and quantum physics

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Marmo, G.; Simoni, A.

    1995-03-01

    The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-statistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized. (author). 22 refs, 3 figs

  9. Topological orders in rigid states

    International Nuclear Information System (INIS)

    Wen, X.G.

    1990-01-01

    The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation

  10. Continuous-variable topological codes

    Science.gov (United States)

    Morimae, Tomoyuki

    2013-10-01

    Topological code is a stabilizer quantum error correcting code whose generators are local but logical operators are topologically nontrivial and nonlocal. It offers interesting features such as the homological deformations of string operators and anyonic excitations on it. Topological codes are also closely related to the “topological order,” which has been an important concept in condensed-matter physics. In this paper, we consider continuous-variable versions of topological codes, including the toric code by Kitaev [A. Y. Kitaev, Ann. Phys.APNYA60003-491610.1016/S0003-4916(02)00018-0 303, 2 (2003)] with a single type of stabilizer on the checkerboard lattice, and the color code by Bombin and Martin-Delgado [H. Bombin and M. A. Martin-Delgado, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.97.180501 97, 180501 (2006)]. We show that it is possible to consider continuous-variable analog of these topological codes.

  11. Galois conjugates of topological phases

    Science.gov (United States)

    Freedman, M. H.; Gukelberger, J.; Hastings, M. B.; Trebst, S.; Troyer, M.; Wang, Z.

    2012-01-01

    Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the “Gaffnian” wave function can not be the ground state of a gapped fractional quantum Hall state.

  12. Radiation-Induced Topological Disorder in Irradiated Network Structures

    Energy Technology Data Exchange (ETDEWEB)

    Hobbs, Linn W.

    2002-12-21

    This report summarizes results of a research program investigating the fundamental principles underlying the phenomenon of topological disordering in a radiation environment. This phenomenon is known popularly as amorphization, but is more formally described as a process of radiation-induced structural arrangement that leads in crystals to loss of long-range translational and orientational correlations and in glasses to analogous alteration of connectivity topologies. The program focus has been on a set compound ceramic solids with directed bonding exhibiting structures that can be described as networks. Such solids include SiO2, Si3N4, SiC, which are of interest to applications in fusion energy production, nuclear waste storage, and device manufacture involving ion implantation or use in radiation fields. The principal investigative tools comprise a combination of experimental diffraction-based techniques, topological modeling, and molecular-dynamics simulations that have proven a rich source of information in the preceding support period. The results from the present support period fall into three task areas. The first comprises enumeration of the rigidity constraints applying to (1) more complex ceramic structures (such as rutile, corundum, spinel and olivine structures) that exhibit multiply polytopic coordination units or multiple modes of connecting such units, (2) elemental solids (such as graphite, silicon and diamond) for which a correct choice of polytope is necessary to achieve correct representation of the constraints, and (3) compounds (such as spinel and silicon carbide) that exhibit chemical disorder on one or several sublattices. With correct identification of the topological constraints, a unique correlation is shown to exist between constraint and amorphizability which demonstrates that amorphization occurs at a critical constraint loss. The second task involves the application of molecular dynamics (MD) methods to topologically-generated models

  13. Radiation-Induced Topological Disorder in Irradiated Network Structures

    International Nuclear Information System (INIS)

    Hobbs, Linn W.

    2002-12-01

    This report summarizes results of a research program investigating the fundamental principles underlying the phenomenon of topological disordering in a radiation environment. This phenomenon is known popularly as amorphization, but is more formally described as a process of radiation-induced structural arrangement that leads in crystals to loss of long-range translational and orientational correlations and in glasses to analogous alteration of connectivity topologies. The program focus has been on a set compound ceramic solids with directed bonding exhibiting structures that can be described as networks. Such solids include SiO2, Si3N4, SiC, which are of interest to applications in fusion energy production, nuclear waste storage, and device manufacture involving ion implantation or use in radiation fields. The principal investigative tools comprise a combination of experimental diffraction-based techniques, topological modeling, and molecular-dynamics simulations that have proven a rich source of information in the preceding support period. The results from the present support period fall into three task areas. The first comprises enumeration of the rigidity constraints applying to (1) more complex ceramic structures (such as rutile, corundum, spinel and olivine structures) that exhibit multiply polytopic coordination units or multiple modes of connecting such units, (2) elemental solids (such as graphite, silicon and diamond) for which a correct choice of polytope is necessary to achieve correct representation of the constraints, and (3) compounds (such as spinel and silicon carbide) that exhibit chemical disorder on one or several sublattices. With correct identification of the topological constraints, a unique correlation is shown to exist between constraint and amorphizability which demonstrates that amorphization occurs at a critical constraint loss. The second task involves the application of molecular dynamics (MD) methods to topologically-generated models

  14. The application of molecular topology for ulcerative colitis drug discovery.

    Science.gov (United States)

    Bellera, Carolina L; Di Ianni, Mauricio E; Talevi, Alan

    2018-01-01

    Although the therapeutic arsenal against ulcerative colitis has greatly expanded (including the revolutionary advent of biologics), there remain patients who are refractory to current medications while the safety of the available therapeutics could also be improved. Molecular topology provides a theoretic framework for the discovery of new therapeutic agents in a very efficient manner, and its applications in the field of ulcerative colitis have slowly begun to flourish. Areas covered: After discussing the basics of molecular topology, the authors review QSAR models focusing on validated targets for the treatment of ulcerative colitis, entirely or partially based on topological descriptors. Expert opinion: The application of molecular topology to ulcerative colitis drug discovery is still very limited, and many of the existing reports seem to be strictly theoretic, with no experimental validation or practical applications. Interestingly, mechanism-independent models based on phenotypic responses have recently been reported. Such models are in agreement with the recent interest raised by network pharmacology as a potential solution for complex disorders. These and other similar studies applying molecular topology suggest that some therapeutic categories may present a 'topological pattern' that goes beyond a specific mechanism of action.

  15. Polynomials formalism of quantum numbers

    International Nuclear Information System (INIS)

    Kazakov, K.V.

    2005-01-01

    Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

  16. Contextual approach to quantum formalism

    CERN Document Server

    Khrennikov, Andrei

    2009-01-01

    The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems...

  17. Musical Formalism and Political Performances

    Directory of Open Access Journals (Sweden)

    Jonathan A. Neufeld

    2009-01-01

    Full Text Available Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing any description of the music can tell us, is inconsistent with Kivy's quite compelling account of performance. This shows the difficulty that actual performances pose to overly rigid conceptions of music. Daniel Barenboim's unannounced performance of Wagner in Israel in 2001 shows that the problem of the boundaries of musical relevance is no mere philosophical puzzle. It is a pressing problem in the musical public sphere.

  18. Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory

    Science.gov (United States)

    Ospina, Juan

    2015-05-01

    The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called "open-closed stringy topological quantum computer" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided.

  19. Stroh formalism and Rayleigh waves

    CERN Document Server

    Tanuma, Kazumi

    2008-01-01

    Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations

  20. Formal Women-only Networks

    DEFF Research Database (Denmark)

    Villesèche, Florence; Josserand, Emmanuel

    2017-01-01

    /organisations and the wider social group of women in business. Research limitations/implications: The authors focus on the distinction between external and internal formal women-only networks while also acknowledging the broader diversity that can characterise such networks. Their review provides the reader with an insight...... member level, the authors suggest that such networks can be of value for organisations and the wider social group of women in management and leadership positions....

  1. Review of the helicity formalism

    International Nuclear Information System (INIS)

    Barreiro, F.; Cerrada, M.; Fernandez, E.

    1972-01-01

    Our purpose in these notes has been to present a brief and general review of the helicity formalism. We begin by discussing Lorentz invariance, spin and helicity ideas, in section 1 . In section 2 we deal with the construction of relativistic states and scattering amplitudes in the helicity basis and we study their transformation properties under discrete symmetries. Finally we present some more sophisticated topics like kinematical singularities of helicity amplitudes, kinematical constraints and crossing relations 3, 4, 5 respectively. (Author) 8 refs

  2. Variational formalism for spin particles

    International Nuclear Information System (INIS)

    Horvathy, P.

    1977-11-01

    The geometrical formulation of Hamilton's principle presented in a previous paper has been related to the usual one in terms of Lagrangian functions. The exact conditions for their equivalence are obtained and a method is given for the construction of a Lagrangian function. The formalism is extended to spin particles and a local Lagrangian is constructed in this case, too. However, this function cannot be extended to a global one. (D.P.)

  3. Ashtekar formalism with real variables

    International Nuclear Information System (INIS)

    Kalau, W.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1990-12-01

    A new approach to canonical gravity is presented which is based on the Ashtekar formalism. But, in contrast to Ashtekar's variables, this formulation does not need complex quantities nor does it lead to second class constraints. This is achieved using SO(3,1) as a gauge group instead of complexified SO(3). Because of the larger group additional first class constraints are needed which turn out to be cubic and quartic in the momenta. (author). 13 refs

  4. The Countabilities of Soft Topological Spaces

    OpenAIRE

    Weijian Rong

    2012-01-01

    Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft first-countable spaces, soft second-countable spaces and soft separable spaces, and some basic properties of these concepts are explored.

  5. Magnetoresistance of Mn-decorated topological line defects in graphene

    KAUST Repository

    Obodo, Tobechukwu Joshua

    2015-01-13

    We study the spin polarized transport through Mn-decorated 8-5-5-8 topological line defects in graphene using the nonequilibrium Green\\'s function formalism. Strong preferential bonding overcomes the high mobility of transition metal atoms on graphene and results in stable structures. Despite a large distance between the magnetic centers, we find a high magnetoresistance and attribute this unexpected property to very strong induced π magnetism, in particular for full coverage of all octagonal hollow sites by Mn atoms. In contrast to the magnetoresistance of graphene nanoribbon edges, the proposed system is well controlled and therefore suitable for applications.

  6. Extending topological surgery to natural processes and dynamical systems.

    Directory of Open Access Journals (Sweden)

    Stathis Antoniou

    Full Text Available Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

  7. Peirce's semiotic version of the semantic tradition in formal logic

    OpenAIRE

    Tiercelin, Claudine

    1991-01-01

    The aim of the text is not so much to stress the importance of Peirce's formal contributions to the semantic view (Boole, Schröder, Lôwenheim) in formal logic (his treatment of the quantifiers, a correct definition of validity for the sentential calculus, his work in the logic of relations, etc.) as to argue that Peirce's semantic trend is part and parcel of his semiotic treatment of a general theory of meaning, understanding, and interpretation, a theory of how signs function which enables h...

  8. Topological strings from quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group

    2014-12-15

    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{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 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.

  9. Magnonic topological insulators in antiferromagnets

    Science.gov (United States)

    Nakata, Kouki; Kim, Se Kwon; Klinovaja, Jelena; Loss, Daniel

    2017-12-01

    Extending the notion of symmetry protected topological phases to insulating antiferromagnets (AFs) described in terms of opposite magnetic dipole moments associated with the magnetic N e ´el order, we establish a bosonic counterpart of topological insulators in semiconductors. Making use of the Aharonov-Casher effect, induced by electric field gradients, we propose a magnonic analog of the quantum spin Hall effect (magnonic QSHE) for edge states that carry helical magnons. We show that such up and down magnons form the same Landau levels and perform cyclotron motion with the same frequency but propagate in opposite direction. The insulating AF becomes characterized by a topological Z2 number consisting of the Chern integer associated with each helical magnon edge state. Focusing on the topological Hall phase for magnons, we study bulk magnon effects such as magnonic spin, thermal, Nernst, and Ettinghausen effects, as well as the thermomagnetic properties of helical magnon transport both in topologically trivial and nontrivial bulk AFs and establish the magnonic Wiedemann-Franz law. We show that our predictions are within experimental reach with current device and measurement techniques.

  10. Braiding knots with topological strings

    International Nuclear Information System (INIS)

    Gu, Jie

    2015-08-01

    For an arbitrary knot in a three-sphere, the Ooguri-Vafa conjecture associates to it a unique stack of branes in type A topological string on the resolved conifold, and relates the colored HOMFLY invariants of the knot to the free energies on the branes. For torus knots, we use a modified version of the topological recursion developed by Eynard and Orantin to compute the free energies on the branes from the Aganagic-Vafa spectral curves of the branes, and find they are consistent with the known colored HOMFLY knot invariants a la the Ooguri-Vafa conjecture. In addition our modified topological recursion can reproduce the correct closed string free energies, which encode the information of the background geometry. We conjecture the modified topological recursion is applicable for branes associated to hyperbolic knots as well, encouraged by the observation that the modified topological recursion yields the correct planar closed string free energy from the Aganagic-Vafa spectral curves of hyperbolic knots. This has implications for the knot theory concerning distinguishing mutant knots with colored HOMFLY invariants. Furthermore, for hyperbolic knots, we present methods to compute colored HOMFLY invariants in nonsymmetric representations of U(N). The key step in this computation is computing quantum 6j-symbols in the quantum group U q (sl N ).

  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. Effective Topological Charge Cancelation Mechanism.

    Science.gov (United States)

    Mesarec, Luka; Góźdź, Wojciech; Iglič, Aleš; Kralj, Samo

    2016-06-01

    Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.

  13. Topological Strings and Integrable Hierarchies

    CERN Document Server

    Aganagic, M; Klemm, A D; Marino, M; Vafa, C; Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

    2006-01-01

    We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.

  14. Measuring the effect of formalization

    International Nuclear Information System (INIS)

    Stoelen, K.; Mohn, P.

    1998-01-01

    We present an ongoing research activity concerned with measuring the effect of an increased level of formalization in software development. We summarize the experiences from a first experimental development. Based on these experiences, we discuss a number of technical issues; in particular, problems connected to metrics based on fault reports. First of all, what is a fault? Secondly, how should the fault counting be integrated in the development process? Thirdly, any reasonable definition of fault depends on a notion of satisfaction. Hence, we must address the question: What does it mean for a specification or an implementation to satisfy a requirement imposed by a more high-level specification? (author)

  15. Introduction to topological groups

    CERN Document Server

    Husain, Taqdir

    2018-01-01

    Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

  16. Lattice QCD without topology barriers

    CERN Document Server

    Lüscher, Martin

    2011-01-01

    As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.

  17. Aeroelastic Wingbox Stiffener Topology Optimization

    Science.gov (United States)

    Stanford, Bret K.

    2017-01-01

    This work considers an aeroelastic wingbox model seeded with run-out blade stiffeners along the skins. Topology optimization is conducted within the shell webs of the stiffeners, in order to add cutouts and holes for mass reduction. This optimization is done with a global-local approach in order to moderate the computational cost: aeroelastic loads are computed at the wing-level, but the topology and sizing optimization is conducted at the panel-level. Each panel is optimized separately under stress, buckling, and adjacency constraints, and periodically reassembled to update the trimmed aeroelastic loads. The resulting topology is baselined against a design with standard full-depth solid stiffener blades, and found to weigh 7.43% less.

  18. Topology of helical fluid flow

    DEFF Research Database (Denmark)

    Andersen, Morten; Brøns, Morten

    2014-01-01

    Phys. Fluids 25, 1949–1952) contains an infinite sum of modified Bessel functions. Using the approach by Okulov (Okulov, V. L. 1995 Russ. J. Eng. Thermophys. 5, 63–75) we obtain a closed-form approximation which is considerably easier to analyse. Critical points of the stream function can be found from...... 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...

  19. Topology optimization of flexoelectric structures

    Science.gov (United States)

    Nanthakumar, S. S.; Zhuang, Xiaoying; Park, Harold S.; Rabczuk, Timon

    2017-08-01

    We present a mixed finite element formulation for flexoelectric nanostructures that is coupled with topology optimization to maximize their intrinsic material performance with regards to their energy conversion potential. Using Barium Titanate (BTO) as the model flexoelectric material, we demonstrate the significant enhancement in energy conversion that can be obtained using topology optimization. We also demonstrate that non-smooth surfaces can play a key role in the energy conversion enhancements obtained through topology optimization. Finally, we examine the relative benefits of flexoelectricity, and surface piezoelectricity on the energy conversion efficiency of nanobeams. We find that the energy conversion efficiency of flexoelectric nanobeams is comparable to the energy conversion efficiency obtained from nanobeams whose electromechanical coupling occurs through surface piezoelectricity, but are ten times thinner. Overall, our results not only demonstrate the utility and efficiency of flexoelectricity as a nanoscale energy conversion mechanism, but also its relative superiority as compared to piezoelectric or surface piezoelectric effects.

  20. A survey of formal languages for contracts

    DEFF Research Database (Denmark)

    Hvitved, Tom

    2010-01-01

    In this short paper we present the current status on formal languages and models for contracts. By a formal model is meant an unambiguous and rigorous representation of contracts, in order to enable their automatic validation, execution, and analysis — activates that are collectively referred...... to as contract lifecycle management (CLM). We present a set of formalism requirements, which represent features that any ideal contract model should support, based on which we present a comparative survey of existing contract formalisms....

  1. 19 CFR 4.9 - Formal entry.

    Science.gov (United States)

    2010-04-01

    ... 19 Customs Duties 1 2010-04-01 2010-04-01 false Formal entry. 4.9 Section 4.9 Customs Duties U.S... FOREIGN AND DOMESTIC TRADES Arrival and Entry of Vessels § 4.9 Formal entry. (a) General. Section 4.3 provides which vessels are subject to formal entry and where and when entry must be made. The formal entry...

  2. Topological Characterization of Fractured Coal

    Science.gov (United States)

    Jing, Yu; Armstrong, Ryan T.; Ramandi, Hamed L.; Mostaghimi, Peyman

    2017-12-01

    Coal transport properties are highly dependent on the underlying fractured network, known as cleats, which are characterized by geometrical and topological properties. X-ray microcomputed tomography (micro-CT) has been widely applied to obtain 3-D digital representations of the cleat network. However, segmentation of 3-D data is often problematic due to image noise, which will result in inaccurate estimation of coal properties (e.g., porosity and specific surface area). To circumvent this issue, a discrete fracture network (DFN) model is proposed. We develop a characterization framework to determine if the developed DFN models can preserve the topological properties of the coal cleat network found in micro-CT data. We compute the Euler characteristic, fractal dimension, and percolation quantities to analyze the topology locally and globally and compare the results between micro-CT data (before denoising), filtered micro-CT data (after denoising), and the DFN model. We find that micro-CT data with noise have extensive connectivity while filtered micro-CT data and DFN models have similar topology both globally and locally. It is concluded that the topology of the DFN models are closer to that of the realistic cleat network that do not have segmentation-induced pores. In addition, micro-CT imaging always struggles with the trade-off between sample size and resolution, while the presented DFN models are not restricted by imaging resolution and thus can be constructed with extended domain size. Overall, the presented DFN model is a reliable alternative with realistic cleat topology, extended domain size and favorable data format for direct numerical simulations.

  3. The Topology ToolKit.

    Science.gov (United States)

    Tierny, Julien; Favelier, Guillaume; Levine, Joshua A; Gueunet, Charles; Michaux, Michael

    2017-08-29

    This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependency-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions

  4. Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology

    Science.gov (United States)

    Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund

    2017-06-01

    Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities. These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our compan-ion paper [1]. In the present paper we provide a mathematical discussion of this topological algebra. In particular, we argue that the structures can be understood in the language of extended equivariant cohomology. To keep the discussion self-contained, we provide a ba-sic review of the algebraic construction of equivariant cohomology and explain how it can be understood in familiar terms as a superspace gauge algebra. We demonstrate how the Schwinger-Keldysh construction can be succinctly encoded in terms a thermal equivariant cohomology algebra which naturally acts on the operator (super)-algebra of the quantum system. The main rationale behind this exploration is to extract symmetry statements which are robust under renormalization group flow and can hence be used to understand low-energy effective field theory of near-thermal physics. To illustrate the general prin-ciples, we focus on Langevin dynamics of a Brownian particle, rephrasing some known results in terms of thermal equivariant cohomology. As described elsewhere, the general framework enables construction of effective actions for dissipative hydrodynamics and could potentially illumine our understanding of black holes.

  5. Formalizing the concept phase of product development

    NARCIS (Netherlands)

    Schuts, M.; Hooman, J.

    2015-01-01

    We discuss the use of formal techniques to improve the concept phase of product realisation. As an industrial application, a new concept of interventional X-ray systems has been formalized, using model checking techniques and the simulation of formal models. cop. Springer International Publishing

  6. Formal Testing of Correspondence Carrying Software

    NARCIS (Netherlands)

    Bujorianu, M.C.; Bujorianu, L.M.; Maharaj, S.

    2008-01-01

    Nowadays formal software development is characterised by use of multitude formal specification languages. Test case generation from formal specifications depends in general on a specific language, and, moreover, there are competing methods for each language. There is a need for a generic approach to

  7. Topological insulators fundamentals and perspectives

    CERN Document Server

    Ortmann, Frank; Valenzuela, Sergio O

    2015-01-01

    There are only few discoveries and new technologies in physical sciences that have the potential to dramatically alter and revolutionize our electronic world. Topological insulators are one of them. The present book for the first time provides a full overview and in-depth knowledge about this hot topic in materials science and condensed matter physics. Techniques such as angle-resolved photoemission spectrometry (ARPES), advanced solid-state Nuclear Magnetic Resonance (NMR) or scanning-tunnel microscopy (STM) together with key principles of topological insulators such as spin-locked electronic

  8. Improving Topology Optimization using Games

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas

    structures. Consequently, we have created a game, the TopOptGame, which improves the player's topology optimization intuition in a fun and engaging way while collecting data about the users performance. Technically, the TopOptGame builds on the TopOptApp [1] - an interactive topology optimization application...... designed for hand-held devices. The TopOptApp solves the 2D minimum compliance problem with interactive control of loads, supports and volume fraction, and thus the TopOptApp allows the user to change the problem on the y and watch the design evolve to a new optimum in real time. TopOptApp is available...

  9. International Conference on Algebraic Topology

    CERN Document Server

    Cohen, Ralph; Miller, Haynes; Ravenel, Douglas

    1989-01-01

    These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and was conceived as a successor to the Aarhus conferences of 1978 and 1982. Some thirty papers are included in this volume, mostly at a research level. Subjects include cyclic homology, H-spaces, transformation groups, real and rational homotopy theory, acyclic manifolds, the homotopy theory of classifying spaces, instantons and loop spaces, and complex bordism.

  10. Topology optimization of flow problems

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund

    2007-01-01

    transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... of the computed topology design using standard, credible analysis tools with a body-fitted mesh. Also, the thesis encompasses work on how to utilize the finite volume method (FVM) in the topology optimization context. This is motivated by the momentous position the FVM has in the fluid dynamics community...

  11. Optimal Network-Topology Design

    Science.gov (United States)

    Li, Victor O. K.; Yuen, Joseph H.; Hou, Ting-Chao; Lam, Yuen Fung

    1987-01-01

    Candidate network designs tested for acceptability and cost. Optimal Network Topology Design computer program developed as part of study on topology design and analysis of performance of Space Station Information System (SSIS) network. Uses efficient algorithm to generate candidate network designs consisting of subsets of set of all network components, in increasing order of total costs and checks each design to see whether it forms acceptable network. Technique gives true cost-optimal network and particularly useful when network has many constraints and not too many components. Program written in PASCAL.

  12. 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.

  13. 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

  14. Topological magnetoelectric effects in microwave far-field radiation

    Energy Technology Data Exchange (ETDEWEB)

    Berezin, M.; Kamenetskii, E. O.; Shavit, R. [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel)

    2016-07-21

    Similar to electromagnetism, described by the Maxwell equations, the physics of magnetoelectric (ME) phenomena deals with the fundamental problem of the relationship between electric and magnetic fields. Despite a formal resemblance between the two notions, they concern effects of different natures. In general, ME-coupling effects manifest in numerous macroscopic phenomena in solids with space and time symmetry breakings. Recently, it was shown that the near fields in the proximity of a small ferrite particle with magnetic-dipolar-mode (MDM) oscillations have the space and time symmetry breakings and the topological properties of these fields are different from the topological properties of the free-space electromagnetic fields. Such MDM-originated fields—called magnetoelectric (ME) fields—carry both spin and orbital angular momenta. They are characterized by power-flow vortices and non-zero helicity. In this paper, we report on observation of the topological ME effects in far-field microwave radiation based on a small microwave antenna with a MDM ferrite resonator. We show that the microwave far-field radiation can be manifested with a torsion structure where an angle between the electric and magnetic field vectors varies. We discuss the question on observation of the regions of localized ME energy in far-field microwave radiation.

  15. A first course in topology an introduction to mathematical thinking

    CERN Document Server

    Conover, Robert A

    1975-01-01

    Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects.Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces a

  16. Star Products and Topological Quantum Groups

    International Nuclear Information System (INIS)

    Akhoumach, K.; Belbaraka, N.; Guedira, F.; Mansour, M.

    2001-01-01

    A well-behaved topological quantum algebra structure on a quantized enveloping topological algebra is given by a star product on the corresponding exact compact connected Poisson-Lie group of its triangular Lie bi-algebra. (author)

  17. Topological phases: Wormholes in quantum matter

    NARCIS (Netherlands)

    Schoutens, K.

    2009-01-01

    Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.

  18. Formal modeling of virtual machines

    Science.gov (United States)

    Cremers, A. B.; Hibbard, T. N.

    1978-01-01

    Systematic software design can be based on the development of a 'hierarchy of virtual machines', each representing a 'level of abstraction' of the design process. The reported investigation presents the concept of 'data space' as a formal model for virtual machines. The presented model of a data space combines the notions of data type and mathematical machine to express the close interaction between data and control structures which takes place in a virtual machine. One of the main objectives of the investigation is to show that control-independent data type implementation is only of limited usefulness as an isolated tool of program development, and that the representation of data is generally dictated by the control context of a virtual machine. As a second objective, a better understanding is to be developed of virtual machine state structures than was heretofore provided by the view of the state space as a Cartesian product.

  19. Formal analysis of electromagnetic optics

    Science.gov (United States)

    Khan-Afshar, Sanaz; Hasan, Osman; Tahar, Sofiène

    2014-09-01

    Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.

  20. Formal algorithmic elimination for PDEs

    CERN Document Server

    Robertz, Daniel

    2014-01-01

    Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.

  1. Topological freeness for Hilbert bimodules

    DEFF Research Database (Denmark)

    Kwasniewski, Bartosz

    2014-01-01

    It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description and a s...

  2. Topological Insulator Nanowires and Nanoribbons

    KAUST Repository

    Kong, Desheng

    2010-01-13

    Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se5 nanomaterials with a variety of morphologies. The synthesis of Bi 2Se5 nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [1120] direction with a rectangular cross-section and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with ∼ 1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitais to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states. © 2010 American Chemical Society.

  3. Topological Aspects of Quantum Chromodynamics

    NARCIS (Netherlands)

    Hooft, G. 't

    2000-01-01

    Absolute confinement of its color charges is a natural property of gauge theories such as quantum chromodynamics. On the one hand, it can be attributed to the existence of color-magnetic monopoles, a topological feature of the theory, but one can also maintain that all non-Abelian gauge theories

  4. Structural Topology Optimization with Eigenvalues

    Czech Academy of Sciences Publication Activity Database

    Achtziger, W.; Kočvara, Michal

    2007-01-01

    Roč. 18, č. 4 (2007), s. 1129-1164 ISSN 1052-6234 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : Topology optimization * Vibration of structures * Optimization of Eigenvalues Subject RIV: BA - General Mathematics Impact factor: 1.554, year: 2007

  5. Deformations of topological open strings

    NARCIS (Netherlands)

    Hofman, C.; Ma, Whee Ky

    Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra - the complex of multilinear maps on the boundary Hilbert space.

  6. Algebraic topology of spin glasses

    International Nuclear Information System (INIS)

    Koma, Tohru

    2011-01-01

    We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.

  7. Independent Study Project, Topic: Topology.

    Science.gov (United States)

    Notre Dame High School, Easton, PA.

    Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…

  8. Topology of molecular interaction networks

    NARCIS (Netherlands)

    Winterbach, W.; Van Mieghem, P.; Reinders, M.; Wang, H.; De Ridder, D.

    2013-01-01

    Molecular interactions are often represented as network models which have become the common language of many areas of biology. Graphs serve as convenient mathematical representations of network models and have themselves become objects of study. Their topology has been intensively researched over

  9. Magnetic Field Topology in Jets

    Science.gov (United States)

    Gardiner, T. A.; Frank, A.

    2000-01-01

    We present results on the magnetic field topology in a pulsed radiative. jet. For initially helical magnetic fields and periodic velocity variations, we find that the magnetic field alternates along the, length of the jet from toroidally dominated in the knots to possibly poloidally dominated in the intervening regions.

  10. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  11. Time-Space Topology Optimization

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2008-01-01

    A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young...

  12. Classical topology and quantum states

    Indian Academy of Sciences (India)

    We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its - and ∞ - structures) can be reconstructed using Gel'fand–Naimark theory and ...

  13. Topology optimization of microfluidic mixers

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe; Gersborg, Allan Roulund; Sigmund, Ole

    2009-01-01

    This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering...

  14. Topology optimization for acoustic problems

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard

    2006-01-01

    In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...

  15. Phantom stars and topology change

    International Nuclear Information System (INIS)

    DeBenedictis, Andrew; Garattini, Remo; Lobo, Francisco S. N.

    2008-01-01

    In this work, we consider time-dependent dark-energy star models, with an evolving parameter ω crossing the phantom divide ω=-1. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark-energy star into a wormhole. The criteria for this topology change are discussed and, in particular, we consider a Casimir energy approach involving quasilocal energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark-energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.

  16. Crystallographic topology and its applications

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, C.K.; Burnett, M.N. [Oak Ridge National Lab., TN (United States); Dunbar, W.D. [Simon`s Rock Coll., Great Barrington, MA (United States). Div. of Natural Sciences and Mathematics

    1996-10-01

    Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.

  17. Wave Manipulation by Topology Optimization

    DEFF Research Database (Denmark)

    Andkjær, Jacob Anders

    topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...

  18. 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.

  19. Topology Optimization for Convection Problems

    DEFF Research Database (Denmark)

    Alexandersen, Joe

    2011-01-01

    .This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...

  20. Topological excitations in magnetic materials

    Energy Technology Data Exchange (ETDEWEB)

    Bazeia, D., E-mail: bazeia@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Doria, M.M. [Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Rodrigues, E.I.B. [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil)

    2016-05-20

    In this work we propose a new route to describe topological excitations in magnetic systems through a single real scalar field. We show here that spherically symmetric structures in two spatial dimensions, which map helical excitations in magnetic materials, admit this formulation and can be used to model skyrmion-like structures in magnetic materials.

  1. Topological visual mapping in robotics.

    Science.gov (United States)

    Romero, Anna; Cazorla, Miguel

    2012-08-01

    A key problem in robotics is the construction of a map from its environment. This map could be used in different tasks, like localization, recognition, obstacle avoidance, etc. Besides, the simultaneous location and mapping (SLAM) problem has had a lot of interest in the robotics community. This paper presents a new method for visual mapping, using topological instead of metric information. For that purpose, we propose prior image segmentation into regions in order to group the extracted invariant features in a graph so that each graph defines a single region of the image. Although others methods have been proposed for visual SLAM, our method is complete, in the sense that it makes all the process: it presents a new method for image matching; it defines a way to build the topological map; and it also defines a matching criterion for loop-closing. The matching process will take into account visual features and their structure using the graph transformation matching (GTM) algorithm, which allows us to process the matching and to remove out the outliers. Then, using this image comparison method, we propose an algorithm for constructing topological maps. During the experimentation phase, we will test the robustness of the method and its ability constructing topological maps. We have also introduced new hysteresis behavior in order to solve some problems found building the graph.

  2. Topologies on the algebra of test functions

    International Nuclear Information System (INIS)

    Hofmann, G.

    1977-01-01

    The algebraical structure of deltasub(THETA) (tensor algebra over the Schwartz space) defines two topologies, tausub(P)tausub(THETA). Some properties are studied of the locally convex topologies situated between tausub(P) and tausub(THETA). A lot of topologies is constructed in which the cone of positive elements is a normal one and regards the continuity of the Wightman functionals of free fields and of the Wick squares in free fields and their derivatives in such topologies

  3. Topology Discovery Using Cisco Discovery Protocol

    OpenAIRE

    Rodriguez, Sergio R.

    2009-01-01

    In this paper we address the problem of discovering network topology in proprietary networks. Namely, we investigate topology discovery in Cisco-based networks. Cisco devices run Cisco Discovery Protocol (CDP) which holds information about these devices. We first compare properties of topologies that can be obtained from networks deploying CDP versus Spanning Tree Protocol (STP) and Management Information Base (MIB) Forwarding Database (FDB). Then we describe a method of discovering topology ...

  4. SATA II - Stochastic Algebraic Topology and Applications

    Science.gov (United States)

    2017-01-30

    AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications... Topology and Applications Continuation of, and associated with SATA: Stochastic Algebraic Topology and Applications FA8655-11-1-3039, 09/1/2011–08/31/2014

  5. 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.

  6. Jakob Nielsen and His Contributions to Topology

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1999-01-01

    The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology.......The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology....

  7. Formal Modelling and Analysis of Socio-Technical Systems

    NARCIS (Netherlands)

    Probst, Christian W.; Kammüller, Florian; Rydhof Hansen, René; Probst, Christian W.; Hankin, Chris; Rydhof Hansen, René

    2015-01-01

    Attacks on systems and organisations increasingly exploit human actors, for example through social engineering. This non-technical aspect of attacks complicates their formal treatment and automatic identification. Formalisation of human behaviour is difficult at best, and attacks on socio-technical

  8. Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications.

    Directory of Open Access Journals (Sweden)

    Bosiljka Tadić

    Full Text Available Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listener's concentration to the story, confirmed by self-rating, and closeness to the speaker's brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listener's group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listener's rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures (besides standard graph measures for characterising functional brain networks under different stimuli.

  9. Towards a Formal Framework for Mobile, Service-Oriented Sensor-Actuator Networks

    Directory of Open Access Journals (Sweden)

    Helena Gruhn

    2013-02-01

    Full Text Available Service-oriented sensor-actuator networks (SOSANETs are deployed in health-critical applications like patient monitoring and have to fulfill strong safety requirements. However, a framework for the rigorous formal modeling and analysis of SOSANETs does not exist. In particular, there is currently no support for the verification of correct network behavior after node failure or loss/addition of communication links. To overcome this problem, we propose a formal framework for SOSANETs. The main idea is to base our framework on the π-calculus, a formally defined, compositional and well-established formalism. We choose KLAIM, an existing formal language based on the π-calculus as the foundation for our framework. With that, we are able to formally model SOSANETs with possible topology changes and network failures. This provides the basis for our future work on prediction, analysis and verification of the network behavior of these systems. Furthermore, we illustrate the real-life applicability of this approach by modeling and extending a use case scenario from the medical domain.

  10. On topological spaces whose topology is induced by a binary relation

    African Journals Online (AJOL)

    We study the problem of characterizing which topologies on a nonemptybset are generated by a binary relation by means of its lower and upper contour sets. In this direction we consider different classical categories of topological spaces whose topology is defined by at least one binary relation. Given a topology defined by ...

  11. Origin of the pure spinor and Green-Schwarz formalisms

    Energy Technology Data Exchange (ETDEWEB)

    Berkovits, Nathan [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP - Universidade Estadual Paulista,Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil)

    2015-07-20

    The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂x{sup m}(γ{sub m}λ){sub α}=0 where λ{sup α} is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint ∂x{sup m}∂x{sub m}=0, and the Green-Schwarz fermionic spacetime spinor variables θ{sup α} arise as Faddeev-Popov ghosts for this constraint. In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor λ{sup α} with a d=10 projective pure spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and superstring are then obtained as different gauge-fixings of this purely bosonic classical action, and the Green-Schwarz kappa symmetry is directly related to the pure spinor BRST symmetry. Since a d=10 projective pure spinor parameterizes ((SO(10))/(U(5))), this action can be interpreted as a standard ĉ=5 topological action where one integrates over the ((SO(10))/(U(5))) choice of complex structure. Finally, a purely bosonic action for the d=11 supermembrane is proposed which reduces upon double-dimensional reduction to the purely bosonic action for the d=10 Type IIA superstring.

  12. Excitations in Topological Superfluids and Superconductors

    Science.gov (United States)

    Wu, Hao

    In this thesis I present the theoretical work on Fermionic surface states, and %the bulk Bosonic collective excitations in topological superfluids and superconductors. Broken symmetries %Bulk-edge correspondence in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. (Abstract shortened by ProQuest.).

  13. Invertibility in L-Topological Spaces

    Directory of Open Access Journals (Sweden)

    Anjaly Jose

    2014-03-01

    Full Text Available In this paper, we extend the concept of invertibility to L-topological spaces and delineate its properties. Then, we study further completely invertible L-topological spaces and introduce two types of invertible L-topologies based on the inverting maps, studying their sums, subspaces and simple extensions.

  14. Dual Feynman rules - topological asymptotic freedom

    International Nuclear Information System (INIS)

    Chew, G.F.; Levinson, M.; California Univ., Berkeley

    1983-01-01

    Feynman-graph rules are formulated for the strong - interaction components of the topological expansion - defined as those graphs all of whose vertices are zero - entropy connected parts. These rules imply a ''topological asymptotic freedom'' and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry. (orig.)

  15. A review of formal orthogonality in Lanczos-based methods

    Science.gov (United States)

    Brezinski, C.; Zaglia, M. Redivo; Sadok, H.

    2002-03-01

    Krylov subspace methods and their variants are presently the favorite iterative methods for solving a system of linear equations. Although it is a purely linear algebra problem, it can be tackled by the theory of formal orthogonal polynomials. This theory helps to understand the origin of the algorithms for the implementation of Krylov subspace methods and, moreover, the use of formal orthogonal polynomials brings a major simplification in the treatment of some numerical problems related to these algorithms. This paper reviews this approach in the case of Lanczos method and its variants, the novelty being the introduction of a preconditioner.

  16. Topological analysis of telecommunications networks

    Directory of Open Access Journals (Sweden)

    Milojko V. Jevtović

    2011-01-01

    Full Text Available A topological analysis of the structure of telecommunications networks is a very interesting topic in the network research, but also a key issue in their design and planning. Satisfying multiple criteria in terms of locations of switching nodes as well as their connectivity with respect to the requests for capacity, transmission speed, reliability, availability and cost are the main research objectives. There are three ways of presenting the topology of telecommunications networks: table, matrix or graph method. The table method is suitable for a network of a relatively small number of nodes in relation to the number of links. The matrix method involves the formation of a connection matrix in which its columns present source traffic nodes and its rows are the switching systems that belong to the destination. The method of the topology graph means that the network nodes are connected via directional or unidirectional links. We can thus easily analyze the structural parameters of telecommunications networks. This paper presents the mathematical analysis of the star-, ring-, fully connected loop- and grid (matrix-shaped topology as well as the topology based on the shortest path tree. For each of these topologies, the expressions for determining the number of branches, the middle level of reliability, the medium length and the average length of the link are given in tables. For the fully connected loop network with five nodes the values of all topological parameters are calculated. Based on the topological parameters, the relationships that represent integral and distributed indicators of reliability are given in this work as well as the values of the particular network. The main objectives of the topology optimization of telecommunications networks are: achieving the minimum complexity, maximum capacity, the shortest path message transfer, the maximum speed of communication and maximum economy. The performance of telecommunications networks is

  17. Constructing a logical, regular axis topology from an irregular topology

    Science.gov (United States)

    Faraj, Daniel A.

    2014-07-01

    Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.

  18. Formal modelling and analysis of socio-technical systems

    DEFF Research Database (Denmark)

    Probst, Christian W.; Kammüller, Florian; Hansen, Rene Rydhof

    2016-01-01

    -technical systems are still mostly identified through brainstorming of experts. In this work we discuss several approaches to formalising socio-technical systems and their analysis. Starting from a flow logic-based analysis of the insider threat, we discuss how to include the socio aspects explicitly, and show......Attacks on systems and organisations increasingly exploit human actors, for example through social engineering. This non-technical aspect of attacks complicates their formal treatment and automatic identification. Formalisation of human behaviour is difficult at best, and attacks on socio...... a formalisation that proves properties of this formalisation. On the formal side, our work closes the gap between formal and informal approaches to socio-technical systems. On the informal side, we show how to steal a birthday cake from a bakery by social engineering....

  19. On type-2 m-topological spaces

    Directory of Open Access Journals (Sweden)

    Sk. Nazmul

    2017-12-01

    Full Text Available In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.

  20. Topological data analysis for scientific visualization

    CERN Document Server

    Tierny, Julien

    2017-01-01

    Combining theoretical and practical aspects of topology, this book delivers a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a thorough but intuitive manner, with many high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in details, and their application is carefully illustrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis, for lecturers, students and researchers.

  1. Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals

    Science.gov (United States)

    Cortese, Dario; Eggers, Jens; Liverpool, Tanniemola B.

    2018-02-01

    We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q =1 /2 and q =-1 /2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

  2. Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect

    Directory of Open Access Journals (Sweden)

    Ashvin Vishwanath

    2013-02-01

    Full Text Available We discuss physical properties of “integer” topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free-fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response θ, which, somewhat surprisingly, is an odd multiple of 2π. Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. We identify a bulk-field theory consistent with these properties, which is a multicomponent background-field theory supplemented, crucially, with a topological term. We also provide bulk sigma-model field theories of these phases and discuss a possible topological phase characterized by the thermal analog of the magnetoelectric effect.

  3. Applications of the Decoherence Formalism

    Science.gov (United States)

    Brun, Todd Andrew

    In this work the decoherence formalism of quantum mechanics is explored and applied to a number of interesting problems in quantum physics. The boundary between quantum and classical physics is examined, and demonstration made that quantum histories corresponding to classical equations of motion become more probable for a broad class of models, including linear and nonlinear models of Brownian motion. The link between noise, dissipation, and decoherence is studied. This work is then applied to systems which classically exhibit dissipative chaotic dynamics. A theory is explicated for treating these systems, and the ideas are applied to a particular model of the forced, damped Duffing oscillator, which is chaotic for certain parameter values. Differences between classical and quantum chaos are examined, particularly differences arising in the structure of fractal strange attractors, and the conceptual difficulties in framing standard notions of chaos in a quantum system. A brief discussion of previous work on quantum chaos is included, and the differences between Hamiltonian and dissipative chaos pointed out; a somewhat different interpretation of quantum chaos from the standard one is suggested. A class of histories for quantum systems, in phase space rather than configuration space, is studied. Different ways of representing projections in phase space are discussed, and expressions for the probability of phase space histories are derived; conditions for such histories to decohere are also estimated in the semiclassical limit.

  4. A Formal Description of Problem Frames

    OpenAIRE

    Souleymane KOUSSOUBE; Roger NOUSSI; Balira O. KONFE

    2014-01-01

    Michael Jackson defines a Problem Frame as a mean to describe and classify software development problems. The initial description of problem Frames is essentially graphical. A weakness of this proposal is the lack of formal specification allowing efficient reasoning tools. This paper deals with Problem Frames’ formal specification with Description Logics. We first propose a formal terminology of Problem Frames leading to the specification of a Problem Frames’ TBOX and a specific problem’s ABO...

  5. Survey of Existing Tools for Formal Verification.

    Energy Technology Data Exchange (ETDEWEB)

    Punnoose, Ratish J.; Armstrong, Robert C.; Wong, Matthew H.; Jackson, Mayo

    2014-12-01

    Formal methods have come into wide use because of their effectiveness in verifying "safety and security" requirements of digital systems; a set of requirements for which testing is mostly ineffective. Formal methods are routinely used in the design and verification of high-consequence digital systems in industry. This report outlines our work in assessing the capabilities of commercial and open source formal tools and the ways in which they can be leveraged in digital design workflows.

  6. Formal Information Model for Representing Production Resources

    OpenAIRE

    Siltala, Niko; Järvenpää, Eeva; Lanz, Minna

    2017-01-01

    Part 2: Intelligent Manufacturing Systems; International audience; This paper introduces a concept and associated descriptions to formally describe physical production resources for modular and reconfigurable production systems. These descriptions are source of formal information for (automatic) production system design and (re-)configuration. They can be further utilized during the system deployment and execution. The proposed concept and the underlying formal resource description model is c...

  7. What Determines Firms’ Decisions to Formalize?

    OpenAIRE

    Neil McCulloch; Günther G. Schulze; Janina Voss

    2010-01-01

    In this paper we analyze the decision of small and micro firms to formalize, i.e. to obtain business and other licenses in rural Indonesia. We use the rural investment climate survey (RICS) that consists of non-farm rural enterprises, most of them microenterprises, and analyze the effect of formalization on tax payments, corruption, access to credit and revenue, taking into account the endogeneity of the formalization decision to such benefits and costs. We show, contrary to most of the liter...

  8. Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

    Directory of Open Access Journals (Sweden)

    P. A. Deymier

    2016-12-01

    Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.

  9. Symmetric Topological Phases and Tensor Network States

    Science.gov (United States)

    Jiang, Shenghan

    Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

  10. Cartography – morphology – topology

    DEFF Research Database (Denmark)

    Dinesen, Cort Ross; Peder Pedersen, Claus

    . The work was approached from a new angle every year through a series of associated questions, resulting in an extensive body of drawings describing the various discourses raised. The developed observational forms reflected in the collected body of drawings constitute a topological landscape with a great...... and developing topological emergence as a passage between cartographic appropriation and creative becoming while simultaneously lifting the material out of its mimetic reference, makes room for the of a movement towards a production of meaning as well as a basis for initiating architectonic practices. We seek...... to provoke a level of operation between the real and the virtual from this body holding the sensing body as its pivot along with the phenomenology of the object; omnipresently considering and shaping virtual constructions. This questioning of architectonic discourse is capable of instrumentalizing ambiguity...

  11. Magnetic topology, nonequilibrium, and dissipation

    International Nuclear Information System (INIS)

    Parker, E.N.

    1985-01-01

    Static equilibrium of a magnetic field throughout a large volume of highly conducting fluid requires a degree of topological symmetry that is generally lacking in nature. The dynamical nonequilibrium of the magnetic topologies in the real world forms current sheets across which there is active reconnection of the field, dissipating the energy of the magnetic strains and reducing the fields toward simpler forms. The magnetic fields in astronomical settings are generally subject to continual straining by the convection within their parent body. The work done on the field by the convection appears in the energy of the small-scale strains, and is soon dissipated by the reconnection. The intense heating of the tenuous outer atmosphere of stars by this mechanism appears to be responsible for most of the X-ray emission of ordinary stars

  12. Effective Topology from Spacetime Tomography

    International Nuclear Information System (INIS)

    Wallden, Petros

    2007-01-01

    We recover the effective topology of spacetime using the notion of record from the decoherent histories approach to Quantum Theory. From a series of (gedanken) experiments, we obtain the set of possible events, grouped into sub-sets that corresponds to histories, but with no other information such as (causal) order or any notion of proximity. This corresponds to tomography of the 'effective' spacetime, that is done in an operational way. Making certain assumptions about these records, and using the existence of upper bound in the speed of transfer of matter and information, we recover the full partial (causal) order up to certain ambiguities. The partially ordered set of events corresponds to an 'effective' causal set which is a discretized version of spacetime with the causal relation as defining feature. We conclude with a derivation of the topology of this effective discretized spacetime

  13. A Mathematical Formalization Proposal for Business Growth

    Directory of Open Access Journals (Sweden)

    Gheorghe BAILESTEANU

    2013-01-01

    Full Text Available Economic sciences have known a spectacular evolution in the last century; beginning to use axiomatic methods, applying mathematical instruments as a decision-making tool. The quest to formalization needs to be addressed from various different angles, reducing entry and operating formal costs, increasing the incentives for firms to operate formally, reducing obstacles to their growth, and searching for inexpensive approaches through which to enforce compliancy with government regulations. This paper proposes a formalized approach to business growth, based on mathematics and logics, taking into consideration the particularities of the economic sector.

  14. Soft set theory and topology

    Directory of Open Access Journals (Sweden)

    D. N. Georgiou

    2014-04-01

    Full Text Available In this paper we study and discuss the soft set theory giving new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets. Furthermore, we investigate the theory of soft topological spaces and we present new definitions, characterizations, and properties concerning the soft closure, the soft interior, the soft boundary, the soft continuity, the soft open and closed maps, and the soft homeomorphism.

  15. Topological 2-dimensional quantum mechanics

    International Nuclear Information System (INIS)

    Dasnieres de Veigy, A.; Ouvry, S.

    1992-12-01

    A Chern-Simons Lagrangian is defined for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. Exact N-body eigenstates are proposed and a perturbative algorithm is set up. The case where some particles are fixed on a lattice, is discussed, and curved manifolds are considered. (author) 14 refs

  16. Performance of Topological Insulator Interconnects

    OpenAIRE

    Philip, Timothy M.; Hirsbrunner, Mark R.; Park, Moon Jip; Gilbert, Matthew J.

    2016-01-01

    The poor performance of copper interconnects at the nanometer scale calls for new material solutions for continued scaling of integrated circuits. We propose the use of three dimensional time-reversal-invariant topological insulators (TIs), which host backscattering-protected surface states, for this purpose. Using semiclassical methods, we demonstrate that nanoscale TI interconnects have a resistance 1-3 orders of magnitude lower than copper interconnects and graphene nanoribbons at the nano...

  17. Time-Space Topology Optimization

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2008-01-01

    A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....

  18. Topological Insulator Nanowires and Nanoribbons

    Energy Technology Data Exchange (ETDEWEB)

    Kong, D.S.

    2010-06-02

    Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi{sub 2}Se{sub 3} material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi{sub 2}Se{sub 3} nanomaterials with a variety of morphologies. The synthesis of Bi{sub 2}Se{sub 3} nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [11-20] direction with a rectangular crosssection and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with {approx}1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitals to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states.

  19. Topological K-Kolmogorov groups

    International Nuclear Information System (INIS)

    Abd El-Sattar, A. Dabbour.

    1987-07-01

    The idea of the K-groups was used to define K-Kolmogorov homology and cohomology (over pairs of coefficient groups) which are descriptions of certain modifications of the Kolmogorov groups. The present work is devoted to the study of the topological properties of the K-Kolmogorov groups which lie at the root of the group duality based essentially upon Pontrjagin's concept of group multiplication. 14 refs

  20. Membrane topology of hedgehog acyltransferase.

    Science.gov (United States)

    Matevossian, Armine; Resh, Marilyn D

    2015-01-23

    Hedgehog acyltransferase (Hhat) is a multipass transmembrane enzyme that mediates the covalent attachment of the 16-carbon fatty acid palmitate to the N-terminal cysteine of Sonic Hedgehog (Shh). Palmitoylation of Shh by Hhat is critical for short and long range signaling. Knowledge of the topological organization of Hhat transmembrane helices would enhance our understanding of Hhat-mediated Shh palmitoylation. Bioinformatics analysis of transmembrane domains within human Hhat using 10 different algorithms resulted in highly consistent predictions in the C-terminal, but not in the N-terminal, region of Hhat. To empirically determine the topology of Hhat, we designed and exploited Hhat constructs containing either terminal or 12 different internal epitope tags. We used selective permeabilization coupled with immunofluorescence as well as a protease protection assay to demonstrate that Hhat contains 10 transmembrane domains and 2 re-entrant loops. The invariant His and highly conserved Asp residues within the membrane-bound O-acyltransferase (MBOAT) homology domain are segregated on opposite sides of the endoplasmic reticulum membrane. The localization of His-379 on the lumenal membrane surface is consistent with a role for this invariant residue in catalysis. Analysis of the activity and stability of the Hhat constructs revealed that the C-terminal MBOAT domain is especially sensitive to manipulation. Moreover, there was remarkable similarity in the overall topological organization of Hhat and ghrelin O-acyltransferase, another MBOAT family member. Knowledge of the topological organization of Hhat could serve as an important tool for further design of selective Hhat inhibitors. © 2015 by The American Society for Biochemistry and Molecular Biology, Inc.

  1. Topological defects in extended inflation

    International Nuclear Information System (INIS)

    Copeland, E.J.; Kolb, E.W.; Chicago Univ., IL; Liddle, A.R.

    1990-04-01

    We consider the production of topological defects, especially cosmic strings, in extended inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings. 18 refs

  2. Topological defects in extended inflation

    International Nuclear Information System (INIS)

    Copeland, E.J.; Kolb, E.W.; Liddle, A.R.

    1990-01-01

    We consider the production of topological defects, especially cosmic strings, in extended-inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of the bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings

  3. Lectures on the Topological Vertex

    CERN Document Server

    Mariño, M

    2008-01-01

    In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...

  4. Review of possible SICAM topologies

    Energy Technology Data Exchange (ETDEWEB)

    Ljusev, P.

    2002-12-15

    In this report some possible topologies and approaches towards construction of a SIngle Conversion stage AMpli er - SICAM are explored. Operation of such amplifier from a single phase voltage grid - AC mains, imposes some stringent limitations over the audio amplifier construction and possible topologies. It will be shown that these restrictions will necessitate the use of reactive energy storage elements at the SICAM input, still making some kind of a power supply needed. Therefore, SICAM should be conceived not as a single stage, but as a sophisticated interconnection of two dedicated stages, that are optimised and designed for the best performance in the audio range, leading to better efficiency, lower losses, reduced volume and cost of the integrated components. Several topologies will be presented, starting with the straightforward AC to AC conversion, continuing with DC-AC and ending with DC to DC conversion. Extensions, advantages, drawbacks and trade-offs will be thoroughly investigated, leading to conclusions for the direction of future research and development. (au)

  5. Algebraic topology a first course

    CERN Document Server

    Fulton, William

    1995-01-01

    To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ­ ential topology, etc.), we concentrate our attention on concrete prob­ lems in low dimensions, introducing only as much algebraic machin­ ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol­ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel­ opment of the subject. What would we like a student to know after a first course in to­ pology (assuming we reject the answer: ...

  6. Topological qubit design and leakage

    Energy Technology Data Exchange (ETDEWEB)

    Ainsworth, R; Slingerland, J K, E-mail: robert.ainsworth@nuim.ie, E-mail: joost@thphys.nuim.ie [Department of Mathematical Physics, National University of Ireland Maynooth, Co. Kildare (Ireland)

    2011-06-15

    We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Operations are performed on these by exchanging the anyons. One might argue that in order to have as many simple single-qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups, which implies that they are valid for all anyon models. We also make some remarks about generalizations to other exchange groups.

  7. TopoGen: A Network Topology Generation Architecture with application to automating simulations of Software Defined Networks

    CERN Document Server

    Laurito, Andres; The ATLAS collaboration

    2017-01-01

    Simulation is an important tool to validate the performance impact of control decisions in Software Defined Networks (SDN). Yet, the manual modeling of complex topologies that may change often during a design process can be a tedious error-prone task. We present TopoGen, a general purpose architecture and tool for systematic translation and generation of network topologies. TopoGen can be used to generate network simulation models automatically by querying information available at diverse sources, notably SDN controllers. The DEVS modeling and simulation framework facilitates a systematic translation of structured knowledge about a network topology into a formal modular and hierarchical coupling of preexisting or new models of network entities (physical or logical). TopoGen can be flexibly extended with new parsers and generators to grow its scope of applicability. This permits to design arbitrary workflows of topology transformations. We tested TopoGen in a network engineering project for the ATLAS detector ...

  8. TopoGen: A Network Topology Generation Architecture with application to automating simulations of Software Defined Networks

    CERN Document Server

    Laurito, Andres; The ATLAS collaboration

    2018-01-01

    Simulation is an important tool to validate the performance impact of control decisions in Software Defined Networks (SDN). Yet, the manual modeling of complex topologies that may change often during a design process can be a tedious error-prone task. We present TopoGen, a general purpose architecture and tool for systematic translation and generation of network topologies. TopoGen can be used to generate network simulation models automatically by querying information available at diverse sources, notably SDN controllers. The DEVS modeling and simulation framework facilitates a systematic translation of structured knowledge about a network topology into a formal modular and hierarchical coupling of preexisting or new models of network entities (physical or logical). TopoGen can be flexibly extended with new parsers and generators to grow its scope of applicability. This permits to design arbitrary workflows of topology transformations. We tested TopoGen in a network engineering project for the ATLAS detector ...

  9. Formal language constrained path problems

    Energy Technology Data Exchange (ETDEWEB)

    Barrett, C.; Jacob, R.; Marathe, M.

    1997-07-08

    In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.

  10. Towards an Advanced Modelling of Complex Economic Phenomena Pretopological and Topological Uncertainty Research Tools

    CERN Document Server

    Aluja, Jaime Gil

    2012-01-01

    Little by little we are being provided with an arsenal of operative instruments of a non-numerical nature, in the shape of models and algorithms, capable of providing answers to the “aggressions” which our economics and management systems must withstand, coming from an environment full of turmoil.   In the work which we are presenting, we dare to propose a set of elements from which we hope arise focuses capable of renewing those structures of economic thought which are upheld by the geometrical idea.   The concepts of pretopology and topology, habitually marginalized in economics and management studies, have centred our interest in recent times.  We consider that it is not possible to conceive formal structures capable of representing the Darwinism concept of economic behaviour today without recurring to this fundamental generalisation of metric spaces.   In our attempts to find a solid base to the structures proposed for the treatment of economic phenomena, we have frequently resorted to the theory ...

  11. A Conceptual Formalization of Crosscutting in AOSD

    NARCIS (Netherlands)

    van den Berg, Klaas; Conejero, J.M.

    2005-01-01

    We propose a formalization of crosscutting based on a conceptual framework for AOSD. Crosscutting is clearly distinguished from the related concepts scattering and tangling. The definitions of these concepts are formalized and visualized with matrices and matrix operations. This allows more precise

  12. Formalizing Evaluation in Music Information Retrieval

    DEFF Research Database (Denmark)

    Sturm, Bob L.

    2013-01-01

    We develop a formalism to disambiguate the evaluation of music information retrieval systems. We define a ``system,'' what it means to ``analyze'' one, and make clear the aims, parts, design, execution, interpretation, and assumptions of its ``evaluation.'' We apply this formalism to discuss...

  13. Applicability of four parameter formalisms in interpreting ...

    Indian Academy of Sciences (India)

    terms of applicability of the three well known four-parameter formalisms for the representation of the thermody- namic properties of binary systems. The study indicates that the derived values of the infinite dilution parameters based on the formalisms compare favourably with the computed data available in the literature.

  14. Hamiltonian path integral formalism with higher derivatives

    Energy Technology Data Exchange (ETDEWEB)

    Barcelos-Neto, J.; Natividade, C.P. (Rio de Janeiro Univ. (Brazil). Inst. de Fisica)

    1991-07-01

    We study the Hamiltonian path integral formalism for systems containing higher derivatives. First we show the consistency of the formalism in applications involving only scalar fields. Later we use the Maxwell electromagnetic theory with a higher order regularization term to show that the Batalin-Fradkin-Vilkovisky (BFV) theory can also be consistently described. (orig.).

  15. DNA expressions - A formal notation for DNA

    NARCIS (Netherlands)

    Vliet, Rudy van

    2015-01-01

    We describe a formal notation for DNA molecules that may contain nicks and gaps. The resulting DNA expressions denote formal DNA molecules. Different DNA expressions may denote the same molecule. Such DNA expressions are called equivalent. We examine which DNA expressions are minimal, which

  16. Formal balancing of chemical reaction networks

    NARCIS (Netherlands)

    van der Schaft, Abraham; Rao, S.; Jayawardhana, B.

    2016-01-01

    In this paper we recall and extend the main results of Van der Schaft, Rao, Jayawardhana (2015) concerning the use of Kirchhoff’s Matrix Tree theorem in the explicit characterization of complex-balanced reaction networks and the notion of formal balancing. The notion of formal balancing corresponds

  17. Restorative Practices as Formal and Informal Education

    Science.gov (United States)

    Carter, Candice C.

    2013-01-01

    This article reviews restorative practices (RP) as education in formal and informal contexts of learning that are fertile sites for cultivating peace. Formal practices involve instruction about response to conflict, while informal learning occurs beyond academic lessons. The research incorporated content analysis and a critical examination of the…

  18. Formal Engineering Hybrid Systems: Semantic Underpinnings

    NARCIS (Netherlands)

    Bujorianu, M.C.; Bujorianu, L.M.

    2008-01-01

    In this work we investigate some issues in applying formal methods to hybrid system development and develop a categorical framework. We study the themes of stochastic reasoning, heterogeneous formal specification and retrenchment. Hybrid systems raise a rich pallets of aspects that need to be

  19. Industrial Practice in Formal Methods : A Review

    DEFF Research Database (Denmark)

    Bicarregui, Juan C.; Fitzgerald, John; Larsen, Peter Gorm

    2009-01-01

    We examine the the industrial application of formal methods using data gathered in a review of 62 projects taking place over the last 25 years. The review suggests that formal methods are being applied in a wide range of application domains, with increasingly strong tool support. Significant chal...

  20. Formal Analysis of a Fair Payment Protocol

    NARCIS (Netherlands)

    Cederquist, J.G.; Dashti, Muhammad Torabi; Dimitrakos, Theo; Martinelli, Fabio

    We formally specify a payment protocol described by Vogt et al. This protocol is intended for fair exchange of time-sensitive data. Here the mCRL language is used to formalize the protocol. Fair exchange properties are expressed in the regular alternation-free mu-calculus. These properties are then

  1. The simplest formal argument for fitness optimization

    Indian Academy of Sciences (India)

    2008-12-23

    Dec 23, 2008 ... The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those ...

  2. The simplest formal argument for fitness optimization

    Indian Academy of Sciences (India)

    The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those biologists who believe ...

  3. Topological and quasi-topological field theories in two dimensions

    International Nuclear Information System (INIS)

    Cunha, Bruno G. Carneiro da; Teotonio-Sobrinho, Paulo

    1997-01-01

    We study a class of lattice field theories in two dimensions that include quantum Yang-Mills theory as a particular example. Given a two dimensional orientable surface of genus g, the partition function Ζ is defined for a triangulation with η is defined for a triangulation with η triangles of size ε only. We compute the portion function and show that the continuum limit is well defined if when ε -> 0 the model approaches a topological theory. we show that the universality classes of such models can be easily classified. (author)

  4. Enhancing System Realisation in Formal Model Development

    DEFF Research Database (Denmark)

    Tran-Jørgensen, Peter Würtz Vinther

    – a formal methods tool that supports the Vienna Development Method. The development of the code generation infrastructure has involved the re-design of the software architecture of Overture. The new architecture brings forth the reuse and extensibility features of Overture to take into account the needs......Software for mission-critical systems is sometimes analysed using formal specification to increase the chances of the system behaving as intended. When sufficient insights into the system have been obtained from the formal analysis, the formal specification is realised in the form of a software...... implementation. One way to realise the system’s software is by automatically generating it from the formal specification – a technique referred to as code generation. However, in general it is difficult to make guarantees about the correctness of the generated code – especially while requiring automation...

  5. Topological supersymmetric structure of hadron cross sections

    International Nuclear Information System (INIS)

    Gauron, P.; Nicolescu, B.; Ouvry, S.

    1980-12-01

    Recently a way of fully implementing unitarity in the framework of a Dual Topological Unitarization theory, including not only mesons but also baryons, was found. This theory consists in the topological description of hadron interactions involving confined quarks in terms of two 2-dimensional surfaces (a closed 'quantum' surface and a bounded 'classical' surface). We show that this description directly leads, at the zeroth order of the topological expansion, to certain relations between hadron cross-sections, in nice agreement with experimental data. A new topological suppression mechanism is shown to play an important dynamical role. We also point out a new topological supersymmetry property, which leads to realistic experimental consequences. A possible topological origin of the rho and ω universality relations emerges as a by-product of our study

  6. 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...

  7. 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)

  8. Multi-planed unified switching topologies

    Science.gov (United States)

    Chen, Dong; Heidelberger, Philip; Sugawara, Yutaka

    2017-07-04

    An apparatus and method for extending the scalability and improving the partitionability of networks that contain all-to-all links for transporting packet traffic from a source endpoint to a destination endpoint with low per-endpoint (per-server) cost and a small number of hops. An all-to-all wiring in the baseline topology is decomposed into smaller all-to-all components in which each smaller all-to-all connection is replaced with star topology by using global switches. Stacking multiple copies of the star topology baseline network creates a multi-planed switching topology for transporting packet traffic. Point-to-point unified stacking method using global switch wiring methods connects multiple planes of a baseline topology by using the global switches to create a large network size with a low number of hops, i.e., low network latency. Grouped unified stacking method increases the scalability (network size) of a stacked topology.

  9. Introduction to topological quantum matter & quantum computation

    CERN Document Server

    Stanescu, Tudor D

    2017-01-01

    What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...

  10. Topological theory of dynamical systems recent advances

    CERN Document Server

    Aoki, N

    1994-01-01

    This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

  11. Personalized anticancer therapy selection using molecular landscape topology and thermodynamics.

    Science.gov (United States)

    Rietman, Edward A; Scott, Jacob G; Tuszynski, Jack A; Klement, Giannoula Lakka

    2017-03-21

    Personalized anticancer therapy requires continuous consolidation of emerging bioinformatics data into meaningful and accurate information streams. The use of novel mathematical and physical approaches, namely topology and thermodynamics can enable merging differing data types for improved accuracy in selecting therapeutic targets. We describe a method that uses chemical thermodynamics and two topology measures to link RNA-seq data from individual patients with academically curated protein-protein interaction networks to select clinically relevant targets for treatment of low-grade glioma (LGG). We show that while these three histologically distinct tumor types (astrocytoma, oligoastrocytoma, and oligodendroglioma) may share potential therapeutic targets, the majority of patients would benefit from more individualized therapies. The method involves computing Gibbs free energy of the protein-protein interaction network and applying a topological filtration on the energy landscape to produce a subnetwork known as persistent homology. We then determine the most likely best target for therapeutic intervention using a topological measure of the network known as Betti number. We describe the algorithm and discuss its application to several patients.

  12. TQFT - a new direction in algebraic topology

    OpenAIRE

    Picken, R. F.; Semiao, P. A.

    1999-01-01

    We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few simple examples of TQFTs, and discuss some other approaches that have been taken to defining TQFT. We then propose a new formulation of TQFT, which is closer in spirit to the way conventional functors of algebraic topology, like homology, are presented. In...

  13. Signature of Topological Phases in Zitterbewegung

    KAUST Repository

    Ghosh, Sumit

    2016-09-02

    We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.

  14. Preimage entropy dimension of topological dynamical systems

    OpenAIRE

    Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao

    2014-01-01

    We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...

  15. Charges and Electromagnetic Radiation as Topological Excitations

    Directory of Open Access Journals (Sweden)

    Manfried Faber

    2017-01-01

    Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.

  16. An Intrinsic Topology for Orthomodular Lattices

    Science.gov (United States)

    Brunet, Olivier

    2007-11-01

    We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.

  17. An application of relative topology in biology

    Energy Technology Data Exchange (ETDEWEB)

    Nada, S.I. [Mathematics Department, Faculty of Science, Menoufia University (Egypt)], E-mail: shokrynada@yahoo.com; Zohny, H. [Mathematics Department, Faculty of Science, Al-Azher University (Egypt)], E-mail: ElZohny_7@yahoo.com

    2009-10-15

    The aim of the present article is to provide an important example for the application of relative topology in biology. The model presented allows one to trace development of an embryo from zygote until birth by using basic concepts in topology, namely relative subspaces, together with dynamical topology and folding. This leads to insight into the stage at which medication should be used to stop any abnormality during pregnancy.

  18. Topological color code and symmetry-protected topological phases

    Science.gov (United States)

    Yoshida, Beni

    2015-06-01

    We study (d -1 ) -dimensional excitations in the d -dimensional color code that are created by transversal application of the Rd phase operators on connected subregions of qubits. We find that such excitations are the superpositions of electric charges and can be characterized by the fixed-point wave functions of (d -1 ) -dimensional bosonic symmetry-protected topological (SPT) phases with (Z2) ⊗d symmetry. While these SPT excitations are localized on (d -1 ) -dimensional boundaries, their creation requires operations acting on all qubits inside the boundaries, reflecting the nontriviality of emerging SPT wave functions. Moreover, these SPT excitations can be physically realized as transparent gapped domain walls which exchange excitations in the color code. Namely, in the three-dimensional color code, the domain wall, associated with the transversal R3 operator, exchanges a magnetic flux and a composite of a magnetic flux and the looplike SPT excitation, revealing rich possibilities of boundaries in higher-dimensional TQFTs. We also find that magnetic fluxes and the looplike SPT excitations exhibit nontrivial three-loop braiding statistics in three dimensions as a result of the fact that the R3 phase operator belongs to the third level of the Clifford hierarchy. We believe that the connection between SPT excitations, fault-tolerant logical gates and gapped domain walls, established in this paper, can be generalized to a large class of topological quantum codes and TQFTs.

  19. Geometry, topology, and string theory

    Energy Technology Data Exchange (ETDEWEB)

    Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  20. Constructive topology of bishop spaces

    OpenAIRE

    Petrakis, Iosif

    2015-01-01

    The theory of Bishop spaces (TBS) is so far the least developed approach to constructive topology with points. Bishop introduced function spaces, here called Bishop spaces, in 1967, without really exploring them, and in 2012 Bridges revived the subject. In this Thesis we develop TBS. Instead of having a common space-structure on a set X and R, where R denotes the set of constructive reals, that determines a posteriori which functions of type X -> R are continuous with respect to it, wi...

  1. Topological entropy of autonomous flows

    Energy Technology Data Exchange (ETDEWEB)

    Badii, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1997-06-01

    When studying fluid dynamics, especially in a turbulent regime, it is crucial to estimate the number of active degrees of freedom or of localized structures in the system. The topological entropy quantifies the exponential growth of the number of `distinct` orbits in a dynamical system as a function of their length, in the infinite spatial resolution limit. Here, I illustrate a novel method for its evaluation, which extends beyond maps and is applicable to any system, including autonomous flows: these are characterized by lack of a definite absolute time scale for the orbit lengths. (author) 8 refs.

  2. The ABCD of topological recursion

    DEFF Research Database (Denmark)

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

    an interesting problem which we study here. We provide some elementary, Lie-algebraic tools to address this problem, and give some elements of classification for dim V = 2. We also describe four more interesting classes of quantum Airy structures, coming from respectively Frobenius algebras (here we retrieve...... 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....

  3. Geometry, topology, and string theory

    International Nuclear Information System (INIS)

    Varadarajan, Uday

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated

  4. Topological Structure of Vague Soft Sets

    Directory of Open Access Journals (Sweden)

    Chang Wang

    2014-01-01

    Full Text Available We introduce vague soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of vague soft open sets, vague soft closed sets, vague soft interior, vague soft closure, and vague soft boundary are introduced and their basic properties and relations are investigated. Furthermore, with the help of examples they established that some properties of topological spaces and soft topological spaces do not hold in vague soft topological spaces. Vague soft connectedness and vague soft compactness are also studied.

  5. Critical fluctuations in topologically massive superconductors

    International Nuclear Information System (INIS)

    Malbouisson, A.P.C.; Nogueira, F.S.; Svaiter, N.F.

    1996-09-01

    We consider a topologically massive Ginzburg-Landau model of superconductivity. In the context of a mean field calculation, we show that there is an increase in the critical temperature driven by the topological term. It is shown that this effect persists even if we take into account the critical fluctuations. The renormalization group analysis gives further insight on this behavior. The fixed point structure is such that the critical exponents tend to their mean field for very large values of the topological mass. In this sense, the topological term stabilizes the critical fluctuations of the order parameters. (author). 13 refs

  6. Compactification, topology change and surgery theory

    International Nuclear Information System (INIS)

    Hartnoll, Sean A

    2003-01-01

    We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any topology change in dimensions ≥5 may be achieved via a causally continuous cobordism. This extends the known result for four dimensions. Therefore, there is no selection rule for compactification at the level of causal continuity. Theorems from surgery theory and handle theory are seen to be very relevant for understanding topology change in higher dimensions. Compactification via parallelizable cobordisms is particularly amenable to study with these tools

  7. Topology and symmetries in gyroscopic lattices

    Science.gov (United States)

    Nash, Lisa M.; Mitchell, Noah P.; Turner, Ari M.; Irvine, William T. M.

    Mechanical metamaterials - including static frames, coupled pendula, and gyroscopic lattices - can support topologically protected vibrational behavior. In particular, fast-spinning gyroscopes pinned on a honeycomb lattice break time-reversal symmetry and exhibit topologically protected, one-way edge modes. As in electronic systems, symmetries play an important role in determining the topological properties of the material. Here we present the roles of inversion symmetry, local coordination number, and time reversal symmetry on the band topology of gyroscopic metamaterials with several lattice geometries.

  8. Topology of polymer chains under nanoscale confinement.

    Science.gov (United States)

    Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza

    2017-08-24

    Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l p under a spherical confinement of radius R c . At low values of l p /R c , the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l p /R c , the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l p /R c , at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross

  9. Topological Semimetals Studied by Ab Initio Calculations

    Science.gov (United States)

    Hirayama, Motoaki; Okugawa, Ryo; Murakami, Shuichi

    2018-04-01

    In topological semimetals such as Weyl, Dirac, and nodal-line semimetals, the band gap closes at points or along lines in k space which are not necessarily located at high-symmetry positions in the Brillouin zone. Therefore, it is not straightforward to find these topological semimetals by ab initio calculations because the band structure is usually calculated only along high-symmetry lines. In this paper, we review recent studies on topological semimetals by ab initio calculations. We explain theoretical frameworks which can be used for the search for topological semimetal materials, and some numerical methods used in the ab initio calculations.

  10. Topological fluid mechanics of Axisymmetric Flow

    DEFF Research Database (Denmark)

    Brøns, Morten

    1998-01-01

    Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...

  11. Quantum field theory in topology changing spacetimes

    International Nuclear Information System (INIS)

    Bauer, W.

    2007-03-01

    The goal of this diploma thesis is to present an overview of how to reduce the problem of topology change of general spacetimes to the investigation of elementary cobordisms. In the following we investigate the possibility to construct quantum fields on elementary cobordisms, in particular we discuss the trousers topology. Trying to avoid the problems occuring at spacetimes with instant topology change we use a model for simulating topology change. We construct the algebra of observables for a free scalar field with the algebraic approach to quantum field theory. Therefore we determine a fundamental solution of the eld equation. (orig.)

  12. Static analysis of topology-dependent broadcast networks

    DEFF Research Database (Denmark)

    Nanz, Sebastian; Nielson, Flemming; Nielson, Hanne Riis

    2010-01-01

    changing network topology is a crucial ingredient. In this paper, we develop a static analysis that automatically constructs an abstract transition system, labelled by actions and connectivity information, to yield a mobility-preserving finite abstraction of the behaviour of a network expressed......Broadcast semantics poses significant challenges over point-to-point communication when it comes to formal modelling and analysis. Current approaches to analysing broadcast networks have focused on fixed connectivities, but this is unsuitable in the case of wireless networks where the dynamically...... in a process calculus with asynchronous local broadcast. Furthermore, we use model checking based on a 3-valued temporal logic to distinguish network behaviour which differs under changing connectivity patterns. (C) 2009 Elsevier Inc. All rights reserved....

  13. Informal work and formal plans

    DEFF Research Database (Denmark)

    Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm

    2012-01-01

    trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... participation. When looking at integrated care from the perspective of patients, the development of a more holistic and personalized approach is needed....

  14. Intrinsic synergistic-topological mechanism versus synergistic-topological matrix in microtubule self-organization

    Directory of Open Access Journals (Sweden)

    Buljan Vlado A

    2014-12-01

    Overall our data indicate that under crowded conditions in vitro, the self-organization of a microtubule fiber is governed by an intrinsic synergistic-topological mechanism, which in conjunction with the topological changes, GTP-tubulin depletion, and cooperative motion of fiber constituting microtubules, may generate and maintain a ‘synergistic-topological matrix’. Failure of the mechanism to form biologically feasible microtubule synergistic-topological matrix may, per se, precondition tumorigenesis.

  15. Formal Semantics: Origins, Issues, Early Impact

    Directory of Open Access Journals (Sweden)

    Barbara H. Partee

    2010-12-01

    . Davidson and G.F. Harman, 253–355 and addendum 763–769. Dordrecht: Reidel.Lakoff, G. 1968. Pronouns and Reference. Parts I and II. Bloomington: Indiana University Linguistics Club.Lewis, D. 1970. ‘General semantics’. Synthese 22: 18–67. Reprinted in Davidson and Harman, eds. Semantics of Natural Language, 1972, Dordrecht: Reidel. 169–218. Also reprinted in Partee 1976, 1–50.Link, G. 1979. Montague-Grammatik. Die logische Grundlagen. Munich: Wilhelm Fink Verlag.May, R. 1977. The grammar of quantification. Ph.D. thesis, MIT.McCawley, J. 1968. ‘The Role of Semantics in a Grammar’. In E. Bach & R. Harms (eds.‘Universals in Linguistic Theory’, 124–169. New York: Holt, Rinehart, & Winston.McCawley, J. 1971. ‘Where do Noun Phrases come from?’ In D. Steinberg & L. Jakobovits (eds.‘Semantics. An Interdisciplinary Reader in Philosophy, Linguistics and Psychology’, 217–231. Cambridge: Cambridge University Press.Montague, R. 1960. ‘Logical necessity, physical necessity, ethics, and quantifiers’. Inquiry 4: 259–269. Reprinted in Montague (1974, 71–83.Montague, R. 1968. ‘Pragmatics’. In R. Klibanski (ed. ‘Contemporary Philosophy’, 102–121. Florence: La Nuova Italia Editrice. Reprinted in Montague (1974, 95–118.Montague, R. 1969. ‘On the Nature of Certain Philosophical Entities’. The Monist 53: 159–194. Reprinted in Montague (1974, 148–187.Montague, R. 1970a. ‘Pragmatics and intensional logic’. Synthese 22: 68–94. Reprinted in Davidson and Harman, eds., 1972, 142-168; Reprinted in Montague (1974, 119–147.Montague, R. 1970b. ‘Universal grammar’. Theoria 36: 373–398. Reprinted in Montague (1974,222–246.Montague, R. 1970c. ‘English as a Formal Language’. In B. Visentini (ed. ‘Linguaggi nella Societá e nella Tecnica’, 189–224. Milan: Edizioni di Comunità. Reprinted in Montague (1974, 188–221.Montague, R. 1973. ‘The proper treatment of quantification in ordinary English’. In J. M. E. Moravcsik K. J

  16. Formalized Medical Guidelines and a Structured Electronic Health Record.

    Czech Academy of Sciences Publication Activity Database

    Peleška, Jan; Anger, Z.; Buchtela, David; Šebesta, K.; Tomečková, Marie; Veselý, Arnošt; Zvára, K.; Zvárová, Jana

    2005-01-01

    Roč. 11, - (2005), s. 4652-4656 ISSN 1727-1983. [EMBEC'05. European Medical and Biomedical Conference /3./. Prague, 20.11.2005-25.11.2005] R&D Projects: GA AV ČR 1ET200300413 Institutional research plan: CEZ:AV0Z10300504 Keywords : formalization of guidelines in cardilogy * GLIF model * structure electronic health record * algorithm in cardiovascular diagnostics and treatment Subject RIV: BD - Theory of Information

  17. Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

    Science.gov (United States)

    Yao, Shunyu; Yan, Zhongbo; Wang, Zhong

    2017-11-01

    Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) a systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the symmetry classes are obtained and studied. (ii) A general theory of Floquet topological defects, based on the proposed topological invariants. (iii) Models and proposals of Floquet topological defects in low dimensions. Among other defect modes, we investigate Floquet Majorana zero modes and Majorana Pi modes in vortices of topologically trivial superconductors under a periodic drive. In addition, we clarified several notable issues about Floquet topological invariants. Among other issues, we prove the equivalence between the effective-Hamiltonian-based band topological invariants and the frequency-domain band topological invariants.

  18. Class of continuous timelike curves determines the topology of spacetime. [Causal, topological, differential, and conformal structure

    Energy Technology Data Exchange (ETDEWEB)

    Malament, D.B.

    1977-07-01

    The title assertion is proven, and two corollaries are established. First, the topology of every past and future distinguishing spacetime is determined by its causal structure. Second, in every spacetime the path topology of Hawking, King, and McCarthy codes topological, differential, and conformal structure.

  19. On Fitting a Formal Method into Practice

    DEFF Research Database (Denmark)

    Gmehlich, Rainer; Grau, Katrin; Hallerstede, Stefan

    2011-01-01

    of industrial use. We report on where Event-B and its tools have succeeded, where they have not. We also report on advances that were inspired by the case study. Interestingly, the case study was not a pure formal methods problem. In addition to Event-B, it used Problem Frames for capturing requirements....... The interaction between the two proved to be crucial for the success of the case study. The heart of the problem was tracing informal requirements from Problem Frames descriptions to formal Event-B models. To a large degree, this issue dictated the approach that had to be used for formal modelling. A dedicated...

  20. Towards Formal Implementation of PUS Standard

    Science.gov (United States)

    Ilić, D.

    2009-05-01

    As an effort to promote the reuse of on-board and ground systems ESA developed a standard for packet telemetry and telecommand - PUS. It defines a set of standard service models with the corresponding structures of the associated telemetry and telecommand packets. Various missions then can choose to implement those standard PUS services that best conform to their specific requirements. In this paper we propose a formal development (based on the Event-B method) of reusable service patterns, which can be instantiated for concrete application. Our formal models allow us to formally express and verify specific service properties including various telecommand and telemetry packet structure validation.

  1. From topological quantum field theories to supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Bossard, G.

    2007-10-01

    This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

  2. Vacuum Topology of the Two Higgs Doublet Model

    CERN Document Server

    Battye, Richard A; Pilaftsis, Apostolos

    2011-01-01

    We perform a systematic study of generic accidental Higgs-family and CP symmetries that could occur in the two-Higgs-doublet-model potential, based on a Majorana scalar-field formalism which realizes a subgroup of GL(8,C). We derive the general conditions of convexity and stability of the scalar potential and present analytical solutions for two non-zero neutral vacuum expectation values of the Higgs doublets for a typical set of six symmetries, in terms of the gauge-invariant parameters of the theory. By means of a homotopy-group analysis, we identify the topological defects associated with the spontaneous symmetry breaking of each symmetry, as well as the massless Goldstone bosons emerging from the breaking of the continuous symmetries. We find the existence of domain walls from the breaking of Z_2, CP1 and CP2 discrete symmetries, vortices in models with broken U(1)_PQ and CP3 symmetries and a global monopole in the SO(3)_HF-broken model. The spatial profile of the topological defect solutions is studied i...

  3. Lattice topology dictates photon statistics.

    Science.gov (United States)

    Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A

    2017-08-21

    Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.

  4. An introduction to algebraic topology

    CERN Document Server

    Rotman, Joseph J

    1988-01-01

    There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details. There are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques (e. g. , most students know very little homological algebra); the second obstacle is that the basic defini­ tions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed (e. g. , homology with coeffi­ cients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat-singular, sim­ ...

  5. Topological inflation with graceful exit

    Energy Technology Data Exchange (ETDEWEB)

    Marunović, Anja; Prokopec, Tomislav, E-mail: a.marunovic@uu.nl, E-mail: t.prokopec@uu.nl [Institute for Theoretical Physics, Spinoza Institute and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Postbus 80.195, 3508 TD Utrecht (Netherlands)

    2016-04-01

    We investigate a class of models of topological inflation in which a super-Hubble-sized global monopole seeds inflation. These models are attractive since inflation starts from rather generic initial conditions, but their not so attractive feature is that, unless symmetry is again restored, inflation never ends. In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation. While the monopole core grows during inflation, the growth stops after inflation, such that the monopole eventually enters the Hubble radius, and shrinks to its Minkowski space size, rendering it immaterial for the subsequent Universe's dynamics. Furthermore, we find that our model can produce cosmological perturbations that source CMB temperature fluctuations and seed large scale structure statistically consistent (within one standard deviation) with all available data. In particular, for small and (in our convention) negative nonminimal couplings, the scalar spectral index can be as large as n {sub s} ≅ 0.955, which is about one standard deviation lower than the central value quoted by the most recent Planck Collaboration.

  6. Topology and condensed matter physics

    CERN Document Server

    Mj, Mahan; Bandyopadhyay, Abhijit

    2017-01-01

    This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field.  The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a qui...

  7. Topological structure of dictionary graphs

    International Nuclear Information System (INIS)

    Fuks, Henryk; Krzeminski, Mark

    2009-01-01

    We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

  8. Curvature-Controlled Topological Defects

    Directory of Open Access Journals (Sweden)

    Luka Mesarec

    2017-05-01

    Full Text Available Effectively, two-dimensional (2D closed films exhibiting in-plane orientational ordering (ordered shells might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.

  9. Topological dynamics in supramolecular rotors.

    Science.gov (United States)

    Palma, Carlos-Andres; Björk, Jonas; Rao, Francesco; Kühne, Dirk; Klappenberger, Florian; Barth, Johannes V

    2014-08-13

    Artificial molecular switches, rotors, and machines are set to establish design rules and applications beyond their biological counterparts. Herein we exemplify the role of noncovalent interactions and transient rearrangements in the complex behavior of supramolecular rotors caged in a 2D metal-organic coordination network. Combined scanning tunneling microscopy experiments and molecular dynamics modeling of a supramolecular rotor with respective rotation rates matching with 0.2 kcal mol(-1) (9 meV) precision, identify key steps in collective rotation events and reconfigurations. We notably reveal that stereoisomerization of the chiral trimeric units entails topological isomerization whereas rotation occurs in a topology conserving, two-step asynchronous process. In supramolecular constructs, distinct displacements of subunits occur inducing a markedly lower rotation barrier as compared to synchronous mechanisms of rigid rotors. Moreover, the chemical environment can be instructed to control the system dynamics. Our observations allow for a definition of mechanical cooperativity based on a significant reduction of free energy barriers in supramolecules compared to rigid molecules.

  10. ATLAS Level-1 Topological Trigger

    CERN Document Server

    Zheng, Daniel; The ATLAS collaboration

    2018-01-01

    The ATLAS experiment has introduced and recently commissioned a completely new hardware sub-system of its first-level trigger: the topological processor (L1Topo). L1Topo consist of two AdvancedTCA blades mounting state-of-the-art FPGA processors, providing high input bandwidth (up to 4 Gb/s) and low latency data processing (200 ns). L1Topo is able to select collision events by applying kinematic and topological requirements on candidate objects (energy clusters, jets, and muons) measured by calorimeters and muon sub-detectors. Results from data recorded using the L1Topo trigger will be presented. These results demonstrate a significantly improved background event rejection, thus allowing for a rate reduction without efficiency loss. This improvement has been shown for several physics processes leading to low-pT leptons, including H->tau tau and J/Psi->mu mu. In addition to describing the L1Topo trigger system, we will discuss the use of an accurate L1Topo simulation as a powerful tool to validate and optimize...

  11. Topological inflation with graceful exit

    International Nuclear Information System (INIS)

    Marunović, Anja; Prokopec, Tomislav

    2016-01-01

    We investigate a class of models of topological inflation in which a super-Hubble-sized global monopole seeds inflation. These models are attractive since inflation starts from rather generic initial conditions, but their not so attractive feature is that, unless symmetry is again restored, inflation never ends. In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation. While the monopole core grows during inflation, the growth stops after inflation, such that the monopole eventually enters the Hubble radius, and shrinks to its Minkowski space size, rendering it immaterial for the subsequent Universe's dynamics. Furthermore, we find that our model can produce cosmological perturbations that source CMB temperature fluctuations and seed large scale structure statistically consistent (within one standard deviation) with all available data. In particular, for small and (in our convention) negative nonminimal couplings, the scalar spectral index can be as large as n s ≅ 0.955, which is about one standard deviation lower than the central value quoted by the most recent Planck Collaboration.

  12. Superfield formalism for the one loop effective action and CP(N) model in three dimensions

    International Nuclear Information System (INIS)

    Cho, Jin-Ho; Hahn, Sang-Ok; Oh, Phillial; Park, Cheonsoo; Park, Jeong-Hyuck

    2004-01-01

    To obtain the one loop effective action for a given superfield theory, one encounters the notion such as the 'super trace' of a differential operator on superspace. We develop, in a systematic way for the superspace of arbitrary dimension, a method to determine the super trace precisely. We present a formula to express the super trace explicitly as the superspace integral, which enables us to write the one loop effective action within the superfield formalism and still maintain the manifest supersymmetry. In the second part of the paper, we apply the result to a three dimensional N=1 supersymmetric CP(N) model in the auxiliary superfield formalism. The model contains a novel topological interaction term. We show in the large N limit the one loop effective action is given by the supersymmetric Maxwell-Chern-Simons theory. (author)

  13. Topological sectors and measures on moduli space in quantum Yang-Mills on a Riemann surface

    Science.gov (United States)

    Fine, Dana Stanley

    1996-03-01

    Previous path integral treatments of Yang-Mills on a Riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations. This paper extends the path integral formulation to treat separately each topological sector. The formulation is sufficiently explicit to calculate Wilson line expectations exactly. Further, it suggests two new measures on the moduli space of flat connections, one of which proves to agree with the small-volume limit of the Yang-Mills measure.

  14. The Intersituational Generality of Formal Thought

    Science.gov (United States)

    Stone, Mary Ann; Ausubel, David P.

    1969-01-01

    Shows that, contrary to Piagetian Theory, formal thought in a variety of subject matters is not possible until sufficient requisite concrete background experience in each content area involved has been attained. (MH)

  15. Graphical And Textual Notations In Formal Specification

    Energy Technology Data Exchange (ETDEWEB)

    Bove, Rocco; Dipoppa, Giovanni; Groven, Arne-Kristian; Sivertsen, Terje

    1996-07-01

    The present report describes the current status of the co-operative project between ENEA and the OECD Halden Reactor Project on graphical and formal methods for software specification. The aim of this project is to contribute to a clarification of the relationship between graphical descriptions and formal specifications, and to provide guidelines for how they can be combined in order to utilize the strengths of' each approach. The overall aim of such a combination is to improve the formal basis of graphical descriptions and make formal specifications more generally comprehensible. The research reported includes the application of the IPTES technology on the APRM case example, an approach to the translation of Petri nets into algebraic specification, and the specification of real-time distributed systems using time-extended LOTOS. (author)

  16. El Salvador - Non-Formal Skills Development

    Data.gov (United States)

    Millennium Challenge Corporation — The Non-Formal Skills Development Sub-Activity had a budget of $5 million (USD) to provide short-term training to vulnerable populations in El Salvador's Northern...

  17. Transitions from Formal Education to the Workplace

    Science.gov (United States)

    Olson, Joann S.

    2014-01-01

    This chapter frames the transition to adulthood in the context of the moving from formal educational settings to the often less-structured learning that occurs in workplace settings. Although schooling may end, learning continues.

  18. Regla formal de justicia, valores y principios

    OpenAIRE

    López Ruiz, Francisco

    1995-01-01

    SUMARIO: 1. Racionalidad y regla formal de justicia. 2. Las diferencias estructurales entre normas y principios. 3. Clases de principios. 4. Funciones de los principios. 5. Principios y racionalidad material del Derecho. Publicado

  19. Formal specification of human-computer interfaces

    Science.gov (United States)

    Auernheimer, Brent

    1990-01-01

    A high-level formal specification of a human computer interface is described. Previous work is reviewed and the ASLAN specification language is described. Top-level specifications written in ASLAN for a library and a multiwindow interface are discussed.

  20. Formalisms for reuse and systems integration

    CERN Document Server

    Rubin, Stuart

    2015-01-01

    Reuse and integration are defined as synergistic concepts, where reuse addresses how to minimize redundancy in the creation of components; while, integration focuses on component composition. Integration supports reuse and vice versa. These related concepts support the design of software and systems for maximizing performance while minimizing cost. Knowledge, like data, is subject to reuse; and, each can be interpreted as the other. This means that inherent complexity, a measure of the potential utility of a system, is directly proportional to the extent to which it maximizes reuse and integration. Formal methods can provide an appropriate context for the rigorous handling of these synergistic concepts. Furthermore, formal languages allow for non ambiguous model specification; and, formal verification techniques provide support for insuring the validity of reuse and integration mechanisms.   This edited book includes 12 high quality research papers written by experts in formal aspects of reuse and integratio...