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Sample records for graphs feller brownian

  1. Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.

    Directory of Open Access Journals (Sweden)

    Björn Böttcher

    Full Text Available We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.

  2. Functionals of Brownian motion, localization and metric graphs

    International Nuclear Information System (INIS)

    Comtet, Alain; Desbois, Jean; Texier, Christophe

    2005-01-01

    We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)

  3. Occupation times distribution for Brownian motion on graphs

    CERN Document Server

    Desbois, J

    2002-01-01

    Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)

  4. Quasi-Feller Markov chains

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    Jean B. Lasserre

    2000-01-01

    Full Text Available We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.

  5. Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

    International Nuclear Information System (INIS)

    Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing

    2009-01-01

    The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

  6. Feller-buncher Operator Breaks Power Line

    Science.gov (United States)

    J. Thompson

    2014-01-01

    On a summer day in the South, a rubber-tired feller-buncher operator was performing a first thinning in a pine plantation. The feller-buncher was working in a new area of the stand, removing the take-down row and thinning the two rows on either side. The trees were approximately 15 years old, and there was a relatively thick layer of underbrush. The stand of timber...

  7. Population death sequences and Cox processes driven by interacting Feller diffusions

    CERN Document Server

    Wei Gang; Feng Jian Feng

    2002-01-01

    We carry out a complete study on the relationship between Cox processes driven by interacting Feller diffusions and death sequences of immigration-emigration linked population networks. It is first proved that the Cox process driven by a Feller diffusion is equivalent to the death sequence of a birth and death process. The conclusion is then generalized to the case of Cox processes driven by interacting Feller diffusions and death sequences of interacting populations.

  8. Population death sequences and Cox processes driven by interacting Feller diffusions

    International Nuclear Information System (INIS)

    Wei Gang; Clifford, Peter; Feng Jianfeng

    2002-01-01

    We carry out a complete study on the relationship between Cox processes driven by interacting Feller diffusions and death sequences of immigration-emigration linked population networks. It is first proved that the Cox process driven by a Feller diffusion is equivalent to the death sequence of a birth and death process. The conclusion is then generalized to the case of Cox processes driven by interacting Feller diffusions and death sequences of interacting populations

  9. Population death sequences and Cox processes driven by interacting Feller diffusions

    Energy Technology Data Exchange (ETDEWEB)

    Wei Gang [Department of Mathematics, Baptist University, Hong Kong (China); Clifford, Peter [Department of Statistics, 1 South Parks Road, Oxford (United Kingdom); Feng Jianfeng [COGS, Sussex University, Brighton (United Kingdom)

    2002-11-08

    We carry out a complete study on the relationship between Cox processes driven by interacting Feller diffusions and death sequences of immigration-emigration linked population networks. It is first proved that the Cox process driven by a Feller diffusion is equivalent to the death sequence of a birth and death process. The conclusion is then generalized to the case of Cox processes driven by interacting Feller diffusions and death sequences of interacting populations.

  10. Stochastic flows in the Brownian web and net

    Czech Academy of Sciences Publication Activity Database

    Schertzer, E.; Sun, R.; Swart, Jan M.

    2014-01-01

    Roč. 227, č. 1065 (2014), s. 1-160 ISSN 0065-9266 R&D Projects: GA ČR GA201/07/0237; GA ČR GA201/09/1931 Institutional support: RVO:67985556 Keywords : Brownian web * Brownian net * stochastic flow of kernels * measure-valued process * Howitt-Warren flow * linear system * random walk in random environment * finite graph representation Subject RIV: BA - General Mathematics Impact factor: 1.727, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf

  11. Avaliação operacional e econômica do "feller-buncher" em dois subsistemas de colheita de florestas de eucalipto Technical and economic analysis of a feller-buncher in two harvest subsystems of eucalyptus forests

    Directory of Open Access Journals (Sweden)

    Fábio Murilo Tieghi Moreira

    2004-04-01

    Full Text Available O objetivo deste trabalho foi avaliar técnica e economicamente o feller-buncher em dois subsistemas de colheita em florestas de eucalipto. A análise técnica englobou um estudo de tempos e movimentos e de produtividade. A análise econômica englobou os parâmetros custo operacional, custo de produção e rendimento energético. O elemento parcial que consumiu a maior parte do tempo do ciclo operacional foi o busca e corte, com aproximadamente 50% do tempo total do ciclo nos dois subsistemas. Os elementos deslocamento vazio e descarregamento consumiram cerca de 39% do tempo total do ciclo do feller-buncher. O custo operacional do feller-buncher foi de US$55,27/he; os custos de produção foram de 1,69 e 1,55 US$/m³cc, nos subsistemas 1 e 2, respectivamente; e o rendimento energético foi de 4,45 e 4,09 g/kW*m³cc, nos subsistemas 1 e 2, respectivamente.This work aimed to evaluate a feller-buncher operationally and economically, under two eucalyptus forest harvest subsystems. The operational analysis included a productivity and motion and time study. The economic analysis included the parameters operational cost, production cost and energy consumption. Searching and cutting consumed most of the operational time, approximately 50% of the total cycle time in both subsystems. Empty displacement and unloading consumed together about 39% of the total feller-buncher cycle time. The feller-buncher operational cost was US$55.27/he. The production costs were US$1.69 and 1.55/m³cc in subsystems 1 and 2, respectively. The energy consumption rates were 4.45 and 4.09 g/kW*m³cc in subsystems 1 and 2, respectively.

  12. Avaliação de alguns fatores ergonômicos nos tratores "Feller-buncher" e "Skidder" utilizados na colheita de madeira Evaluation of some ergonomic factors in Feller-buncher and Skidder tractors used in wood harvesting

    Directory of Open Access Journals (Sweden)

    Julião Soares de Souza Lima

    2005-04-01

    Full Text Available Este trabalho foi realizado com tratores florestais utilizados em um sistema mecanizado de colheita de madeira em povoamento de eucalipto, tendo como objetivo avaliar quantiqualitativamente as dimensões de acesso, assento, comandos, campo visual, condições térmicas e vibração no posto dos operadores. O acesso ao posto do operador no trator "Feller-buncher" apresentou um grau de dificuldade, sendo classificado, na avaliação qualitativa, como médio e, no "Skidder", como bom. A abertura das portas de acesso apresenta ângulo menor que 90º, dificultando, assim, a entrada e saída do operador. O posto do operador do trator "Feller-buncher" foi classificado como médio na avaliação qualitativa, em virtude de o espaço livre da plataforma de apoio ser de 30% da área total e, no "Skidder", de 55% da área total, sendo classificado como bom. O campo visual frontal do "Feller-buncher", mesmo tendo uma área do pára-brisa maior, é limitado pela presença do cabeçote, tanto em operações diurnas quanto noturnas, sendo, portanto, inferior ao do "Skidder".This work was carried out in forest tractors used in a mechanized system for wood harvesting in a stand of eucalyptus, to evaluate quanti-qualitatively the dimensions of access, seat, commands, field view, thermal conditions and vibration in the operators' station. The access to the operator's station in the Feller-Buncher tractor presented a degree of difficulty classified in the qualitative evaluation as average and the Skidder as good. The opening of the access doors presents an angle smaller than 90º, thus rendering the entrance and exit of the operator more difficult. The operators station of the Feller-Buncher tractor was classified as medium in the qualitative evaluation, due to the free space of the support platform being 30% of the total area, and in the Skidder 55%, therefore being classified as good. The front field view in Feller-Buncher, even having a wider windscreen area, is

  13. Statistical mixing and aggregation in Feller diffusion

    International Nuclear Information System (INIS)

    Anteneodo, C; Duarte Queirós, S M

    2009-01-01

    We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and population dynamics in the natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate—a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time-dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales

  14. On Feller's criterion for the law of the iterated logarithm

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    Deli Li

    1994-01-01

    Full Text Available Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985 and Egorov (1971. In addition, these results are compared with the corresponding results of Teicher (1974, Tomkins (1983 and Tomkins (1990

  15. Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process

    DEFF Research Database (Denmark)

    Ditlevsen, Susanne Dalager; Ditlevsen, Ove Dalager

    2008-01-01

    a subjective graphical test of the applicability of the OU process or the Feller process when applied to a reasonably large sample of observed first-passage data. These non-stationary processes have several applications in biomedical research, for example as idealized models of the neuron membrane potential...... random time break through to the material surface and become observable. However, the OU process has as a model of physical phenomena the defect of not being bounded to the negative side. This defect is not present for the Feller process, which therefore may provide a useful modeling alternative...

  16. Visibility graph approach to exchange rate series

    Science.gov (United States)

    Yang, Yue; Wang, Jianbo; Yang, Huijie; Mang, Jingshi

    2009-10-01

    By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.

  17. Brownian entanglement

    International Nuclear Information System (INIS)

    Allahverdyan, A.E.; Khrennikov, A.; Nieuwenhuizen, Th.M.

    2005-01-01

    For two classical Brownian particles an analog of continuous-variable quantum entanglement is presented: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot always be prepared via mixing of any factorized distributions referring to the two particles separately. This is possible for particles which have interacted in the past, but do not interact at present. Three factors are crucial for the effect: (1) separation of time scales of coordinate and momentum which motivates the definition of coarse-grained velocities; (2) the resulting uncertainty relations between the coordinate of the Brownian particle and the change of its coarse-grained velocity; (3) the fact that the coarse-grained velocity, though pertaining to a single Brownian particle, is defined on a common context of two particles. The Brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the Brownian motion. Analogies with the quantum situation are discussed, as well as possibilities of experimental realization of the effect in examples of macroscopic Brownian motion

  18. Constructive role of Brownian motion: Brownian motors and Stochastic Resonance

    Science.gov (United States)

    Hänggi, Peter

    2005-03-01

    Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.

  19. Production and cost analysis of a feller-buncher in central Appalachian hardwood forest

    Science.gov (United States)

    Charlie Long; Jingxin Wang; Joe McNeel; John Baumgras; John Baumgras

    2002-01-01

    A time study was conducted to evaluate the productivity and cost of a feller-buncher operating in a Central Appalachian hardwood forest. The sites harvested during observation consisted of primarily red maple and black cherry. Trees felled in the study had an average diameter at breast height (DBH) of 16.1 in. and a total merchantable height of 16 ft. A Timbco 445C...

  20. Conception of Brownian coil

    OpenAIRE

    Zhang, Jiayuan

    2018-01-01

    This article proposes a conception of Brownian coil. Brownian coil is a tiny coil with the same size of pollen. Once immersed into designed magnetic field and liquid, the coil will be moved and deformed macroscopically, due to the microscopic thermodynamic molecular collisions. Such deformation and movement will change the magnetic flux through the coil, by which an ElectroMotive Force (EMF) is produced. In this work, Brownian heat exchanger and Brownian generator are further designed to tran...

  1. Singular solution of the Feller diffusion equation via a spectral decomposition

    Science.gov (United States)

    Gan, Xinjun; Waxman, David

    2015-01-01

    Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

  2. Brownian modulated optical nanoprobes

    International Nuclear Information System (INIS)

    Behrend, C.J.; Anker, J.N.; Kopelman, R.

    2004-01-01

    Brownian modulated optical nanoprobes (Brownian MOONs) are fluorescent micro- and nanoparticles that resemble moons: one hemisphere emits a bright fluorescent signal, while an opaque metal darkens the other hemisphere. Brownian motion causes the particles to tumble and blink erratically as they rotate literally through the phases of the moon. The fluctuating probe signals are separated from optical and electronic backgrounds using principal components analysis or images analysis. Brownian MOONs enable microrheological measurements on size scales and timescales that are difficult to study with other methods. Local chemical concentrations can be measured simultaneously, using spectral characteristics of indicator dyes embedded within the MOONs

  3. PRODUTIVIDADE E CUSTOS DO FELLER-BUNCHER E PROCESSADOR FLORESTAL EM POVOAMENTO DE EUCALIPTO DE PRIMEIRO CORTE

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    Danilo Simões

    2014-09-01

    Full Text Available http://dx.doi.org/10.5902/1980509815742A racionalização da colheita florestal e a minimização dos custos é uma busca constante por parte dos gestores envolvidos nesse processo, competindo a esses deliberar práticas economicamente viáveis para otimizar essa operação. O objetivo deste estudo foi avaliar técnica e economicamente a produtividade do feller-buncher e do processador florestal em povoamento de eucalipto em primeiro corte. A análise técnica englobou um estudo de tempos e movimentos, produtividade, eficiência operacional e disponibilidade mecânica. A análise econômica englobou os parâmetros do custo operacional, custo de colheita florestal e rendimento energético. Visando à otimização do custo de colheita florestal, o sistema composto pelo feller-buncher e processador florestal apresenta-se como uma alternativa viável tecnicamente e economicamente para a colheita em povoamentos de eucalipto de primeiro corte ou para povoamentos que não possuam árvores bifurcadas.

  4. Radical Enformel in the Oeuvre of Ivo Gattin and Eugen Feller

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    Ješa Denegri

    2016-01-01

    Full Text Available The paper focuses on Ivo Gattin and Eugen Feller as prominent figures in the so-called “radical Enformel”, an artistic trend in Croatian painting during the late 1950s and early 1960s. Besides them, the representatives of radical Enformel include Vlado Kristl, Marijan Javšovar, and Đuro Seder, who likewise participated in the exhibition Informel 1956-1962 at Nova Gallery in 1977. The theoretical platform for this trend in painting was found in hypotheses presented in the influential text “Materia, tecnica e storia nell’informale” (1959 by the Italian artcritic Giulio Carlo Argan, which were adapted to the specific Croatian circumstances and examples.

  5. Compaction and soil fertility after eucalyptus harvesting using Feller Buncher and Skidder

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    Ana Lúcia Piedade Sodero Martins Pincelli

    2014-06-01

    Full Text Available This study analyzed, the impact of Feller Buncher and Skidder traffic in harvesting areas of eucalyptus in Mogi Guaçu, considering the compaction and fertilization effects in the range of soil next to the carrier during the cycle of forest growth. An increase in soil compaction, caused by machinery traffic in topsoil (0-10 cm, was observed in the area recently harvested. The soils of the study areas, with eucalyptus 1.4 and 6.0 years old, showed good fertility conditions, especially the older area, where decomposition of forest residues possibly contributed to such fertility.

  6. A multiscale guide to Brownian motion

    International Nuclear Information System (INIS)

    Grebenkov, Denis S; Belyaev, Dmitry; Jones, Peter W

    2016-01-01

    We revise the Lévy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ‘geometrical features’ at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains. (topical review)

  7. O'Connell's process as a vicious Brownian motion

    International Nuclear Information System (INIS)

    Katori, Makoto

    2011-01-01

    Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

  8. Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

    Science.gov (United States)

    Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

    2011-01-01

    A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

  9. The Brownian loop soup

    OpenAIRE

    Lawler, Gregory F.; Werner, Wendelin

    2003-01-01

    We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ``chronologically add Brownian loops'' to simple curves in the plane.

  10. q-deformed Brownian motion

    CERN Document Server

    Man'ko, V I

    1993-01-01

    Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.

  11. Langevin theory of anomalous Brownian motion made simple

    International Nuclear Information System (INIS)

    Tothova, Jana; Vasziova, Gabriela; Lisy, VladimIr; Glod, Lukas

    2011-01-01

    During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.

  12. Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement

    OpenAIRE

    Gyftopoulos, Elias P.

    2006-01-01

    Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.

  13. Properties of Brownian Image Models in Scale-Space

    DEFF Research Database (Denmark)

    Pedersen, Kim Steenstrup

    2003-01-01

    Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix......In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...

  14. Irreversible Brownian Heat Engine

    Science.gov (United States)

    Taye, Mesfin Asfaw

    2017-10-01

    We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

  15. Behavior of aerosols undergoing Brownian coagulation, Brownian diffusion and gravitational settling in a closed chamber

    International Nuclear Information System (INIS)

    Okuyama, Kikuo; Kousaka, Yasuo; Yoshida, Tetsuo

    1976-01-01

    The behavior of aerosols undergoing Brownian coagulation. Brownian diffusion and gravitational settling in a closed chamber was studied by solving the basic equation, the so-called population balance equation, numerically for a polydisperse aerosol system and analytically for a monodisperse system, and then the results were examined by experiment. In solving the basic equation, two dimensionless parameters, which are determined by the initial properties of an aerosol and the chamber dimension and also characterize the relative effects of Brownian coagulation and Brownian diffusion to gravitational settling, were introduced in order to generalize the behavior under arbitrary conditions. The calculated results, the time-dependent changes in particle number concentration and particle size distribution for a polydisperse system, were presented graphically by using the above two parameters. And further using these parameters, the domains of the three controlling factors were mapped to show the extent of each effect of these factors under various conditions for a monodisperse system. Some of the calculated results were compared with the experimental results obtained by the ultramicroscopic size analysis previously developed by the authors. (auth.)

  16. A hydrodynamic formalism for Brownian systems

    International Nuclear Information System (INIS)

    Pina, E.; Rosales, M.A.

    1981-01-01

    A formal hydrodynamic approach to Brownian motion is presented and the corresponding equations are derived. Hydrodynamic quantities are expressed in terms of the physical variables characterizing the Brownian systems. Contact is made with the hydrodynamic model of Quantum Mechanics. (author)

  17. Self-induced temperature gradients in Brownian dynamics

    Science.gov (United States)

    Devine, Jack; Jack, M. W.

    2017-12-01

    Brownian systems often surmount energy barriers by absorbing and emitting heat to and from their local environment. Usually, the temperature gradients created by this heat exchange are assumed to dissipate instantaneously. Here we relax this assumption to consider the case where Brownian dynamics on a time-independent potential can lead to self-induced temperature gradients. In the same way that externally imposed temperature gradients can cause directed motion, these self-induced gradients affect the dynamics of the Brownian system. The result is a coupling between the local environment and the Brownian subsystem. We explore the resulting dynamics and thermodynamics of these coupled systems and develop a robust method for numerical simulation. In particular, by focusing on one-dimensional situations, we show that self-induced temperature gradients reduce barrier-crossing rates. We also consider a heat engine and a heat pump based on temperature gradients induced by a Brownian system in a nonequilibrium potential.

  18. Brownian dynamics with hydrodynamic interactions

    International Nuclear Information System (INIS)

    Ermak, D.L.; McCammon, J.A.

    1978-01-01

    A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker--Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution

  19. Operator Fractional Brownian Motion and Martingale Differences

    Directory of Open Access Journals (Sweden)

    Hongshuai Dai

    2014-01-01

    Full Text Available It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.

  20. Brownian Optimal Stopping and Random Walks

    International Nuclear Information System (INIS)

    Lamberton, D.

    2002-01-01

    One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk

  1. Near-Field, On-Chip Optical Brownian Ratchets.

    Science.gov (United States)

    Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L

    2016-08-10

    Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.

  2. Conformal correlation functions in the Brownian loop soup

    Science.gov (United States)

    Camia, Federico; Gandolfi, Alberto; Kleban, Matthew

    2016-01-01

    We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

  3. Conformal correlation functions in the Brownian loop soup

    Energy Technology Data Exchange (ETDEWEB)

    Camia, Federico, E-mail: federico.camia@nyu.edu [New York University Abu Dhabi (United Arab Emirates); VU University, Amsterdam (Netherlands); Gandolfi, Alberto, E-mail: albertogandolfi@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Università di Firenze (Italy); Kleban, Matthew, E-mail: kleban@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Center for Cosmology and Particle Physics, Department of Physics, New York University (United States)

    2016-01-15

    We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

  4. Conformal correlation functions in the Brownian loop soup

    Directory of Open Access Journals (Sweden)

    Federico Camia

    2016-01-01

    Full Text Available We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

  5. Generalized Arcsine Laws for Fractional Brownian Motion.

    Science.gov (United States)

    Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

    2018-01-26

    The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

  6. Decay ratio for third order Brownian oscillators

    International Nuclear Information System (INIS)

    Konno, H.; Kanemoto, S.

    1998-01-01

    We have obtained the analytical expressions of the decay ratios for two types of third order Brownian oscillators which are generalizations of the second order Brownian oscillator driven by the Gaussian-white noise. The resulting expressions will provide us useful baseline information for more complicated practical problems and their applications

  7. Dissipation and decoherence in Brownian motion

    Energy Technology Data Exchange (ETDEWEB)

    Bellomo, Bruno [Dipartimento di Scienze Fisiche ed Astronomiche dell' Universita di Palermo, Via Archirafi, 36, 90123 Palermo (Italy); Barnett, Stephen M [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom)

    2007-05-15

    We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.

  8. Brownian movement and molecular reality

    CERN Document Server

    Perrin, Jean

    2005-01-01

    How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this ""Brownian motion"" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownia

  9. Brownian diode: Molecular motor based on a semi-permeable Brownian particle with internal potential drop

    International Nuclear Information System (INIS)

    Plyukhin, A.V.

    2013-01-01

    A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.

  10. Comment on 'Finding viscosity of liquids from Brownian motion at students' laboratory' and 'Brownian motion using video capture'

    International Nuclear Information System (INIS)

    Greczylo, Tomasz; Debowska, Ewa

    2007-01-01

    The authors make comments and remarks on the papers by Salmon et al (2002 Eur. J. Phys. 23 249-53) and their own (2005 Eur. J. Phys. 26 827-33) concerning Brownian motion in two-dimensional space. New, corrected results of calculations and measurements for students' experiments on finding the viscosity of liquids from Brownian motion are presented. (letters and comments)

  11. Brownian quasi-particles in statistical physics

    International Nuclear Information System (INIS)

    Tellez-Arenas, A.; Fronteau, J.; Combis, P.

    1979-01-01

    The idea of a Brownian quasi-particle and the associated differentiable flow (with nonselfadjoint forces) are used here in the context of a stochastic description of the approach towards statistical equilibrium. We show that this quasi-particle flow acquires, at equilibrium, the principal properties of a conservative Hamiltonian flow. Thus the model of Brownian quasi-particles permits us to establish a link between the stochastic description and the Gibbs description of statistical equilibrium

  12. Stock price prediction using geometric Brownian motion

    Science.gov (United States)

    Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM

    2018-03-01

    Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.

  13. Static structure of active Brownian hard disks

    Science.gov (United States)

    de Macedo Biniossek, N.; Löwen, H.; Voigtmann, Th; Smallenburg, F.

    2018-02-01

    We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.

  14. Reflection Negative Kernels and Fractional Brownian Motion

    Directory of Open Access Journals (Sweden)

    Palle E. T. Jorgensen

    2018-06-01

    Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .

  15. TECHNICAL AND ECONOMIC EVALUATION OF THE HARVEST OF EUCALYPTUS WITH FELLER-BUNCHER IN DIFFERENT OPERATING CONDITIONS

    Directory of Open Access Journals (Sweden)

    Danilo Simões

    2010-12-01

    Full Text Available This study aimed to technically and economically evaluate the Feller-buncher in different conditions of harvest in eucalyptus forests of second cut. The technical analysis included a study of time and movements by the method of continuous time, and operational performance was determined by volume in cubic meters of harvested wood. The economic analysis included the parameters of operational cost, harvest cost and energy consumption. The analysis of the data showed that the composition of main line harvesting and the arrangement of bundles of trees influenced operational performance. The average operational cost was US$ 86.26 per hour of actual work, which resulted in an average cost of forest harvesting of US$ 1.09 m-³.

  16. Spherical particle Brownian motion in viscous medium as non-Markovian random process

    International Nuclear Information System (INIS)

    Morozov, Andrey N.; Skripkin, Alexey V.

    2011-01-01

    The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.

  17. Brownian motion probe for water-ethanol inhomogeneous mixtures

    Science.gov (United States)

    Furukawa, Kazuki; Judai, Ken

    2017-12-01

    Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.

  18. On some generalization of fractional Brownian motions

    International Nuclear Information System (INIS)

    Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying

    2006-01-01

    The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given

  19. Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices

    International Nuclear Information System (INIS)

    Qian Mengcen; Jiang Zhiqiang; Zhou Weixing

    2010-01-01

    The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors. There are marked discrepancies in the allometric scaling behaviors between the stock indices and the Brownian motions. Using surrogate time series, we find that these discrepancies are caused by the fat-tailedness of the return distribution and the nonlinear long-term correlation.

  20. A multiscale approach to Brownian motors

    International Nuclear Information System (INIS)

    Pavliotis, G.A.

    2005-01-01

    The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this Letter. Multiscale techniques are used to derive general formulae for the steady state particle current and the effective diffusion tensor. These formulae are then applied to calculate the effective diffusion coefficient for a Brownian particle in a periodic potential driven simultaneously by additive Gaussian white and colored noise. Our theoretical findings are supported by numerical simulations

  1. Random motion and Brownian rotation

    International Nuclear Information System (INIS)

    Wyllie, G.

    1980-01-01

    The course is centred on the Brownian motion - the random movement of molecules arising from thermal fluctuations of the surrounding medium - and starts with the classical theory of A. Einstein, M.v. Smoluchowski and P. Langevin. The first part of this article is quite elementary, and several of the questions raised in it have been instructively treated in a much more sophisticated way in recent reviews by Pomeau and Resibois and by Fox. This simple material may nevertheless be helpful to some readers whose main interest lies in approaching the work on Brownian rotation reviewed in the latter part of the present article. The simplest, and most brutally idealised, problem in our field of interest is that of the random walk in one dimension of space. Its solution leads on, through the diffusivity-mobility relation of Einstein, to Langevin's treatment of the Brownian motion. The application of these ideas to the movement of a molecule in a medium of similar molecules is clearly unrealistic, and much energy has been devoted to finding a suitable generalisation. We shall discuss in particular ideas due to Green, Zwanzig and Mori. (orig./WL)

  2. Fractional Brownian motion and long term clinical trial recruitment.

    Science.gov (United States)

    Zhang, Qiang; Lai, Dejian

    2011-05-01

    Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.

  3. Manipulation and controlled amplification of Brownian motion of microcantilever sensors

    International Nuclear Information System (INIS)

    Mehta, Adosh; Cherian, Suman; Hedden, David; Thundat, Thomas

    2001-01-01

    Microcantilevers, such as those used in atomic force microscopy, undergo Brownian motion due to mechanical thermal noise. The root mean square amplitude of the Brownian motion of a cantilever typically ranges from 0.01--0.1 nm, which limits its use in practical applications. Here we describe a technique by which the Brownian amplitude and the Q factor in air and water can be amplified by three and two orders of magnitude, respectively. This technique is similar to a positive feedback oscillator, wherein the Brownian motion of the vibrating cantilever controls the frequency output of the oscillator. This technique can be exploited to improve sensitivity of microcantilever-based chemical and biological sensors, especially for sensors in liquid environments

  4. Biased Brownian dynamics for rate constant calculation.

    OpenAIRE

    Zou, G; Skeel, R D; Subramaniam, S

    2000-01-01

    An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampl...

  5. Slow kinetics of Brownian maxima.

    Science.gov (United States)

    Ben-Naim, E; Krapivsky, P L

    2014-07-18

    We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.

  6. Optimum analysis of a Brownian refrigerator.

    Science.gov (United States)

    Luo, X G; Liu, N; He, J Z

    2013-02-01

    A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

  7. Analyzing animal movements using Brownian bridges.

    Science.gov (United States)

    Horne, Jon S; Garton, Edward O; Krone, Stephen M; Lewis, Jesse S

    2007-09-01

    By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

  8. Time rescaling and Gaussian properties of the fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)

  9. How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

    Science.gov (United States)

    de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; van de Koppel, Johan

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern. PMID:24225464

  10. How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement.

    Science.gov (United States)

    de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J; Hengeveld, Geerten M; Nolet, Bart A; Herman, Peter M J; van de Koppel, Johan

    2014-01-07

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern.

  11. Conformal geometry and invariants of 3-strand Brownian braids

    International Nuclear Information System (INIS)

    Nechaev, Sergei; Voituriez, Raphael

    2005-01-01

    We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case

  12. Area distribution of an elastic Brownian motion

    International Nuclear Information System (INIS)

    Rajabpour, M A

    2009-01-01

    We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self-adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will focus on the power of self-adjoint extension to investigate different possible boundary conditions for the stochastic processes. We also discuss some possible physical applications.

  13. Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models

    Directory of Open Access Journals (Sweden)

    Tomasz Kajdanowicz

    2016-09-01

    Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

  14. Eigenfunction expansion for fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

  15. From a stochastic to a macroscopic approach to brownian motion

    International Nuclear Information System (INIS)

    Bocquet, L.

    1998-01-01

    In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)

  16. Deep inelastic collisions viewed as Brownian motion

    International Nuclear Information System (INIS)

    Gross, D.H.E.; Freie Univ. Berlin

    1980-01-01

    Non-equilibrium transport processes like Brownian motion, are studied since perhaps 100 years and one should ask why does one not use these theories to explain deep inelastic collision data. These theories have reached a high standard of sophistication, experience, and precision that I believe them to be very usefull for our problem. I will try to sketch a possible form of an advanced theory of Brownian motion that seems to be suitable for low energy heavy ion collisions. (orig./FKS)

  17. Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

    Directory of Open Access Journals (Sweden)

    Yuquan Cang

    2014-01-01

    Full Text Available We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1(Si+1H2-SiH2, as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.

  18. Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

    International Nuclear Information System (INIS)

    Han Yuecai; Hu Yaozhong; Song Jian

    2013-01-01

    We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.

  19. Brownian gas models for extreme-value laws

    International Nuclear Information System (INIS)

    Eliazar, Iddo

    2013-01-01

    In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Fréchet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Fréchet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented. (paper)

  20. Brownian dynamic simulations and experiments of MR fluids

    International Nuclear Information System (INIS)

    Segovia-Gutiérrez, J P; Vicente, J de; Hidalgo, R; Puertas, A M

    2013-01-01

    The use of computational techniques in magnetorheology is not new. I general, these approaches assume dipolar magnetic interactions, hard sphere repulsions, and no-slip conditions. In this contribution we focus on the dynamics of the equilibrium state in the presence of uniaxial DC fields. To achieve this goal we make use of Brownian Dynamic Simulations. We highlight the importance of the Brownian forces versus magnetic dipolar interaction in the range of low magnetic field strengths. We monitor the formation of columnar structures and their dynamics, in competition with the Brownian motion, until a hexatic crystal phase appears at high field strengths for monodisperse systems. The shear viscosity is computed from the Einstein relation and eventually compared with experimental data at very low-shear rates. A reasonably good agreement between both data sets is observed.

  1. On the motion of a Brownian particle with an asymmetric bias

    International Nuclear Information System (INIS)

    Kim, K.S.

    1981-01-01

    On the infinite three dimensional cubic lattice, the transport process of a Brownian particle biased on the direction (in the case of nearest-neighbor jumping) is discussed. The Brownian particle is considered as a walker of the random process. By introducing the theorem that the probability density P(l,t) becomes Gaussian for large t, P(l,t) is completely specified when the first and second moments of P(l,t) become known. The respective values for the transprot averaged velocity and dispersion of a biased Brownian particle are obtained. Finally as t becomes large we find Gaussian packets of a biased Brownian particle which propagate with a constant velocity and have a dispersion proportional to time t. (KAERI)

  2. Interacting Brownian Swarms: Some Analytical Results

    Directory of Open Access Journals (Sweden)

    Guillaume Sartoretti

    2016-01-01

    Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.

  3. Fast orthogonal transforms and generation of Brownian paths.

    Science.gov (United States)

    Leobacher, Gunther

    2012-04-01

    We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length [Formula: see text] can be generated in [Formula: see text] floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.

  4. A graph rewriting programming language for graph drawing

    OpenAIRE

    Rodgers, Peter

    1998-01-01

    This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...

  5. Directed motion of a Brownian motor in a temperature gradient

    Science.gov (United States)

    Liu, Yibing; Nie, Wenjie; Lan, Yueheng

    2017-05-01

    Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.

  6. Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

    Science.gov (United States)

    Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

    2018-03-01

    In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

  7. Intrinsic and extrinsic measurement for Brownian motion

    International Nuclear Information System (INIS)

    Castro-Villarreal, Pavel

    2014-01-01

    Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR ⊥ . The Weingarten–Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for 〈δR〉 and 〈δR 2 〉 on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes. (paper)

  8. Non-colliding Brownian Motions and the Extended Tacnode Process

    Science.gov (United States)

    Johansson, Kurt

    2013-04-01

    We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.

  9. Entropic Approach to Brownian Movement.

    Science.gov (United States)

    Neumann, Richard M.

    1980-01-01

    A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)

  10. Exponential functionals of Brownian motion, I: Probability laws at fixed time

    OpenAIRE

    Matsumoto, Hiroyuki; Yor, Marc

    2005-01-01

    This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.

  11. Breaking the symmetry of a Brownian motor with symmetric potentials

    International Nuclear Information System (INIS)

    Hagman, H; Zelan, M; Dion, C M

    2011-01-01

    The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.

  12. Diffusion in one dimensional random medium and hyperbolic Brownian motion

    International Nuclear Information System (INIS)

    Comtet, A.; Monthus, C.; Paris-6 Univ., 75

    1995-03-01

    Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. This relationship is analyzed in detail and various distributions are studied using stochastic calculus and functional integration. (author) 17 refs

  13. Simple Brownian diffusion an introduction to the standard theoretical models

    CERN Document Server

    Gillespie, Daniel T

    2013-01-01

    Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.

  14. Graph Aggregation

    NARCIS (Netherlands)

    Endriss, U.; Grandi, U.

    Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference

  15. Meandering Brownian Donkeys

    Science.gov (United States)

    Eichhorn, R.; Reimann, P.

    2004-04-01

    We consider a Brownian particle whose motion is confined to a ``meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ``donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results.

  16. Meandering Brownian Donkeys

    International Nuclear Information System (INIS)

    Eichhorn, R.; Reimann, P.

    2004-01-01

    We consider a Brownian particle whose motion is confined to a ''meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ''donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results. (author)

  17. The Intersection Probability of Brownian Motion and SLEκ

    Directory of Open Access Journals (Sweden)

    Shizhong Zhou

    2015-01-01

    Full Text Available By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.

  18. QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION

    Directory of Open Access Journals (Sweden)

    A.E.Kobryn

    2003-01-01

    Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

  19. Quantum description of the Brownian movement in an external field

    International Nuclear Information System (INIS)

    Svin'in, I.R.

    1976-01-01

    The Schroedinger equation for brownian motion in an external field is obtained on the basis of the classical Langevin equation. The specific features of the approach proposed are illustrated by the example of the brownian motion of the quantum oscillator. The influence of the fluctuations on the various physical quantities is considered

  20. Reflected Brownian motions in the KPZ universality class

    CERN Document Server

    Weiss, Thomas; Spohn, Herbert

    2017-01-01

    This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processe...

  1. Deterministic Brownian motion generated from differential delay equations.

    Science.gov (United States)

    Lei, Jinzhi; Mackey, Michael C

    2011-10-01

    This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.

  2. Quantum Brownian motion model for the stock market

    Science.gov (United States)

    Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

    2016-06-01

    It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

  3. Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids

    NARCIS (Netherlands)

    Ahuja, Vishal Raju

    2018-01-01

    This thesis deals with model development for particle-based flow simulations of non-Newtonian fluids such as polymer solutions. A novel computational technique called Hydrodynamically Coupled Brownian Dynamics (HCBD) is presented in this thesis. This technique essentially couples the Brownian motion

  4. Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

    Science.gov (United States)

    Wang, Na; Li, Dong; Wang, Qiwen

    2012-12-01

    The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government

  5. Survival probabilities for branching Brownian motion with absorption

    OpenAIRE

    Harris, John; Harris, Simon

    2007-01-01

    We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\\rho$, undergo dyadic branching at rate $\\beta>0$, and are killed on hitting the origin. In the case $\\rho>\\sqrt{2\\beta}$ the extinction time for this process, $\\zeta$, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $P^x(\\zeta>t)$ in the case $\\rho>\\sqrt{2\\beta}$, where $P^x$ is...

  6. Quantum dynamical framework for Brownian heat engines

    Science.gov (United States)

    Agarwal, G. S.; Chaturvedi, S.

    2013-07-01

    We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

  7. Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

    Science.gov (United States)

    Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra

    2017-06-01

    Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

  8. Phase transition for absorbed Brownian motion with drift

    International Nuclear Information System (INIS)

    Ferrari, P.A.; Martinez, S.; San Martin, J.

    1997-01-01

    We study one-dimensional Brownian motion with constant drift toward the origin and initial distribution concentrated in the strictly positive real line. We say that at the first time the process hits the origin, it is absorbed. We study the asymptotic behavior, as t → ∞, of m t , the conditional distribution at time zero of the process conditioned on survival up to time t and on the process having a fixed value at time t. We find that there is a phase transition in the decay rate of the initial condition. For fast decay rate (subcritical case) m t is localized, in the critical case m t is located around √t, and for slow rates (supercritical case) m, is located around t. The critical rate is given by the decay of the minimal quasistationary distribution of this process. We also study in each case the asymptotic distribution of the process, scaled by √t, conditioned as before. We prove that in the subcritical case this distribution is a Brownian excursion. In the critical case it is a Brownian bridge attaining 0 for the first time at time 1, with some initial distribution. In the supercritical case, after centering around the expected value-which is of the order of t we show that this process converges to a Brownian bridge arriving at 0 at time 1 and with a Gaussian initial distribution

  9. Algorithm for generating a Brownian motion on a sphere

    International Nuclear Information System (INIS)

    Carlsson, Tobias; Elvingson, Christer; Ekholm, Tobias

    2010-01-01

    We present a new algorithm for generation of a random walk on a two-dimensional sphere. The algorithm is obtained by viewing the 2-sphere as the equator in the 3-sphere surrounded by an infinitesimally thin band with boundary which reflects Brownian particles and then applying known effective methods for generating Brownian motion on the 3-sphere. To test the method, the diffusion coefficient was calculated in computer simulations using the new algorithm and, for comparison, also using a commonly used method in which the particle takes a Brownian step in the tangent plane to the 2-sphere and is then projected back to the spherical surface. The two methods are in good agreement for short time steps, while the method presented in this paper continues to give good results also for larger time steps, when the alternative method becomes unstable.

  10. Directed Transport of Brownian Particles in a Periodic Channel

    International Nuclear Information System (INIS)

    Jiang Jie; Ai Bao-Quan; Wu Jian-Chun

    2015-01-01

    The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears. (paper)

  11. Brownian motion and stochastic calculus

    CERN Document Server

    Karatzas, Ioannis

    1998-01-01

    This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

  12. Under which conditions is quantum Brownian motion observable in a microscope?

    International Nuclear Information System (INIS)

    Helseth, L.E.

    2010-01-01

    We investigate under which conditions we can expect to observe quantum Brownian motion in a microscope. Using the fluctuation-dissipation theorem, we investigate quantum Brownian motion in an ohmic bath, and estimate temporal and spatial accuracy required to observe a crossover from classical to quantum behavior.

  13. The single- and double-particle properties and the current reversal of coupled Brownian motors

    International Nuclear Information System (INIS)

    Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang; Fan, Hong; Shen, Wen-Mei

    2017-01-01

    In this paper, we investigate the directed transport of coupled Brownian motors composed of two identical particles which is individually subject to a time-symmetric rocking force in spatially-symmetric periodic potentials. We find that both the coupling free length and the coupling strength can induce the reversed motion of the coupled Brownian motors, the essence of which is the coupled Brownian motors can exhibit completely different single- or double-particle properties under certain conditions. Namely, the current reversal is the result of the mutual conversion between the single- and double-particle properties of the coupled Brownian motors. Moreover, the directed current of coupled Brownian motors can be optimized and manipulated by adjusting the strength, the period, the phase difference of the rocking forces, and the noise intensity. (paper)

  14. Microscopic derivation of open quantum Brownian motion: a particular example

    International Nuclear Information System (INIS)

    Sinayskiy, Ilya; Petruccione, Francesco

    2015-01-01

    The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions. (topical article)

  15. Presentation of quantum Brownian movement in the collective coordinate method

    International Nuclear Information System (INIS)

    Oksak, A.I.; Sukhanov, A.D.

    2003-01-01

    Two explicitly solved models of quantum randomized processes described by the Langevin equation, i. e. a free quantum Brownian particle and a quantum Brownian harmonic oscillator, are considered. The Hamiltonian (string) realization of the models reveals soliton-like structure of classical solutions. Accordingly, the method of zero mode collective coordinate is an adequate means for describing the models quantum dynamics [ru

  16. Chromatic graph theory

    CERN Document Server

    Chartrand, Gary; Rosen, Kenneth H

    2008-01-01

    Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...

  17. Adiabatic Processes Realized with a Trapped Brownian Particle

    Science.gov (United States)

    Martínez, Ignacio A.; Roldán, Édgar; Dinis, Luis; Petrov, Dmitri; Rica, Raúl A.

    2015-03-01

    The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.

  18. Stochastic calculus for fractional Brownian motion and related processes

    CERN Document Server

    Mishura, Yuliya S

    2008-01-01

    The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional mark...

  19. Entropy production of a Brownian ellipsoid in the overdamped limit.

    Science.gov (United States)

    Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik

    2016-01-01

    We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

  20. On the validity of Brownian assumptions in the spin van der Waals model

    International Nuclear Information System (INIS)

    Oh, Suhk Kun

    1985-01-01

    A simple Brownian motion theory of the spin van der Waals model, which can be stationary, Markoffian or Gaussian, is studied. By comparing the Brownian motion theory with an exact theory called the generalized Langevin equation theory, the validity of the Brownian assumptions is tested. Thereby, it is shown explicitly how the Markoffian and Gaussian properties are modified in the spin van der Waals model under the influence of quantum fluctuations and long range ordering. (Author)

  1. Coupling of lever arm swing and biased Brownian motion in actomyosin.

    Directory of Open Access Journals (Sweden)

    Qing-Miao Nie

    2014-04-01

    Full Text Available An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

  2. Coupling of lever arm swing and biased Brownian motion in actomyosin.

    Science.gov (United States)

    Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P

    2014-04-01

    An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

  3. On the definition of an admitted Lie group for stochastic differential equations with multi-Brownian motion

    International Nuclear Information System (INIS)

    Srihirun, B; Meleshko, S V; Schulz, E

    2006-01-01

    The definition of an admitted Lie group of transformations for stochastic differential equations has been already presented for equations with one-dimensional Brownian motion. The transformation of the dependent variables involves time as well, and it has been proven that Brownian motion is transformed to Brownian motion. In this paper, we will discuss this concept for stochastic differential equations involving multi-dimensional Brownian motion and present applications to a variety of stochastic differential equations

  4. How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

    OpenAIRE

    de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; van de Koppel, Johan

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein’s original theory ...

  5. Graph sampling

    OpenAIRE

    Zhang, L.-C.; Patone, M.

    2017-01-01

    We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.

  6. Volume of the domain visited by N spherical Brownian particles

    International Nuclear Information System (INIS)

    Berezhkovskii, A.M.

    1994-01-01

    The average value and variance of the volume of the domain visited in time t by N spherical Brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point Brownian particle in the presence of one and two spherical traps. As an illustration, explicit time dependences are obtained for the average volume in one and three dimensions

  7. Algorithms for Planar Graphs and Graphs in Metric Spaces

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...

  8. Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences

    International Nuclear Information System (INIS)

    McKane, Alan

    2003-01-01

    This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes

  9. Fractional Brownian motion with a reflecting wall

    Science.gov (United States)

    Wada, Alexander H. O.; Vojta, Thomas

    2018-02-01

    Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α implications of these findings, in particular, for applications that are dominated by rare events.

  10. Brownian motion of tethered nanowires.

    Science.gov (United States)

    Ota, Sadao; Li, Tongcang; Li, Yimin; Ye, Ziliang; Labno, Anna; Yin, Xiaobo; Alam, Mohammad-Reza; Zhang, Xiang

    2014-05-01

    Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.

  11. Brownian motion, martingales, and stochastic calculus

    CERN Document Server

    Le Gall, Jean-François

    2016-01-01

    This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

  12. On modeling animal movements using Brownian motion with measurement error.

    Science.gov (United States)

    Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun

    2014-02-01

    Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

  13. Achieving swift equilibration of a Brownian particle using flow-fields

    Science.gov (United States)

    Patra, Ayoti; Jarzynski, Christopher

    Can a system be driven to a targeted equilibrium state on a timescale that is much shorter than its natural equilibration time? In a recent experiment, the swift equilibration of an overdamped Brownian particle was achieved by use of an appropriately designed, time-dependent optical trap potential. Motivated by these results, we develop a general theoretical approach for guiding an ensemble of Brownian particles to track the instantaneous equilibrium distribution of a desired potential U (q , t) . In our approach, we use flow-fields associated with the parametric evolution of the targeted equilibrium state to construct an auxiliary potential U (q , t) , such that dynamics under the composite potential U (t) + U (t) achieves the desired evolution. Our results establish a close connection between the swift equilibration of Brownian particles, quantum shortcuts to adiabaticity, and the dissipationless driving of a classical, Hamiltonian system.

  14. Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion

    Directory of Open Access Journals (Sweden)

    Kaminsky A. V.

    2010-04-01

    Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.

  15. Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion

    Directory of Open Access Journals (Sweden)

    Kaminsky A. V.

    2010-07-01

    Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.

  16. Brownian coagulation at high particle concentrations

    NARCIS (Netherlands)

    Trzeciak, T.M.

    2012-01-01

    The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids,

  17. Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

    Directory of Open Access Journals (Sweden)

    P. Anusha Devi

    2015-10-01

    Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$  The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.

  18. How superdiffusion gets arrested: ecological encounters explain shift from Levy to Brownian movement

    NARCIS (Netherlands)

    de Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; de Koppel, J.

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

  19. How superdiffusion gets arrested : ecological encounters explain shift from Levy to Brownian movement

    NARCIS (Netherlands)

    de Jager, Monique; Bartumeus, Frederic; Kolzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; de Koppel, Johan van

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

  20. How superdiffusion gets arrested : Ecological encounters explain shift from Levy to Brownian movement

    NARCIS (Netherlands)

    de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M.J.; van de Koppel, Johan

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

  1. Introduction to graph theory

    CERN Document Server

    Trudeau, Richard J

    1994-01-01

    Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or

  2. Graph Theory. 2. Vertex Descriptors and Graph Coloring

    Directory of Open Access Journals (Sweden)

    Lorentz JÄNTSCHI

    2002-12-01

    Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.

  3. On an edge partition and root graphs of some classes of line graphs

    Directory of Open Access Journals (Sweden)

    K Pravas

    2017-04-01

    Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.

  4. Graphs and matrices

    CERN Document Server

    Bapat, Ravindra B

    2014-01-01

    This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

  5. Graphs cospectral with a friendship graph or its complement

    Directory of Open Access Journals (Sweden)

    Alireza Abdollahi

    2013-12-01

    Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.

  6. Estimation of the global regularity of a multifractional Brownian motion

    DEFF Research Database (Denmark)

    Lebovits, Joachim; Podolskij, Mark

    This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a ...... that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst functional parameter, which is, under weak assumptions, identical to the global regularity index of the path....

  7. Self-Intersection Local Times of Generalized Mixed Fractional Brownian Motion as White Noise Distributions

    International Nuclear Information System (INIS)

    Suryawan, Herry P.; Gunarso, Boby

    2017-01-01

    The generalized mixed fractional Brownian motion is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst parameters. It is a Gaussian process with stationary increments, posseses self-similarity property, and, in general, is neither a Markov process nor a martingale. In this paper we study the generalized mixed fractional Brownian motion within white noise analysis framework. As a main result, we prove that for any spatial dimension and for arbitrary Hurst parameter the self-intersection local times of the generalized mixed fractional Brownian motions, after a suitable renormalization, are well-defined as Hida white noise distributions. The chaos expansions of the self-intersection local times in the terms of Wick powers of white noises are also presented. (paper)

  8. Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion

    Directory of Open Access Journals (Sweden)

    Di Pan

    2013-01-01

    Full Text Available Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.

  9. Graph embedding with rich information through heterogeneous graph

    KAUST Repository

    Sun, Guolei

    2017-11-12

    Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.

  10. Topics in graph theory graphs and their Cartesian product

    CERN Document Server

    Imrich, Wilfried; Rall, Douglas F

    2008-01-01

    From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.

  11. Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph

    Science.gov (United States)

    Nagarathinam, R.; Parvathi, N.

    2018-04-01

    Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat

  12. Exact master equation for a noncommutative Brownian particle

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Nuno Prata, Joao

    2009-01-01

    We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale

  13. Nuclear resonant scattering of synchrotron radiation from nuclei in the Brownian motion

    International Nuclear Information System (INIS)

    Razdan, Ashok

    2003-01-01

    The time evolution of the coherent forward scattering of the synchrotron radiation for resonant nuclei in Brownian motion is studied. Apart from target thickness, the appearance of the dynamical beats also depends on 'α' which is the ratio of the harmonic force constant to the damping force constant of harmonic oscillator undergoing Brownian motion

  14. The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

    International Nuclear Information System (INIS)

    Tian-Fu, Gao; Jin-Can, Chen; Yue, Zhang

    2009-01-01

    Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper. (general)

  15. Handbook of graph grammars and computing by graph transformation

    CERN Document Server

    Engels, G; Kreowski, H J; Rozenberg, G

    1999-01-01

    Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran

  16. Brownian ratchets from statistical physics to bio and nano-motors

    CERN Document Server

    Cubero, David

    2016-01-01

    Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.

  17. Dual-frequency magnetic particle imaging of the Brownian particle contribution

    Energy Technology Data Exchange (ETDEWEB)

    Viereck, Thilo, E-mail: t.viereck@tu-bs.de; Kuhlmann, Christian; Draack, Sebastian; Schilling, Meinhard; Ludwig, Frank

    2017-04-01

    Magnetic particle imaging (MPI) is an emerging medical imaging modality based on the non-linear response of magnetic nanoparticles to an exciting magnetic field. MPI has been recognized as a fast imaging technique with high spatial resolution in the mm range. For some applications of MPI, especially in the field of functional imaging, the determination of the particle mobility (Brownian rotation) is of great interest, as it enables binding detection in MPI. It also enables quantitative imaging in the presence of Brownian-dominated particles, which is otherwise implausible. Discrimination of different particle responses in MPI is possible via the joint reconstruction approach. In this contribution, we propose a dual-frequency acquisition scheme to enhance sensitivity and contrast in the detection of different particle mobilities compared to a standard single-frequency MPI protocol. The method takes advantage of the fact, that the magnetization response of the tracer is strongly frequency-dependent, i.e. for low excitation frequencies a stronger Brownian contribution is observed.

  18. Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations

    International Nuclear Information System (INIS)

    Bessa, Carlos H. G.; Bezerra, V. B.; Ford, L. H.

    2009-01-01

    We consider the effects of the vacuum fluctuations of a quantized electromagnetic field on particles in an expanding universe. We find that these particles typically undergo Brownian motion and acquire a nonzero mean squared velocity that depends on the scale factor of the universe. This Brownian motion can be interpreted as due to noncancellation of anticorrelated vacuum fluctuations in the time-dependent background spacetime. Alternatively, one can interpret this effect as the particles acquiring energy from the background spacetime geometry, a phenomenon that cannot occur in a static spacetime. We treat several types of coupling between the electromagnetic field and the particles and several model universes. We also consider both free particles, which, on the average, move on geodesics, and particles in bound systems. There are significant differences between these two cases, which illustrates that nongeodesic motion alters the effects of the vacuum fluctuations. We discuss the possible applications of this Brownian motion effect to cosmological scenarios.

  19. Brownian motion in a flowing fluid revisited

    International Nuclear Information System (INIS)

    Ramshaw, J.D.

    1981-01-01

    It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations

  20. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  1. Non-Markovian quantum Brownian motion in one dimension in electric fields

    Science.gov (United States)

    Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.

    2018-04-01

    Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.

  2. Swarming behavior of gradient-responsive Brownian particles in a porous medium

    Science.gov (United States)

    Grančič, Peter; Štěpánek, František

    2012-07-01

    Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers.

  3. How superdiffusion gets arrested: Ecological encounters explain shift from Lévy to Brownian movement

    NARCIS (Netherlands)

    De Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Van de Koppel, J.

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

  4. How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

    NARCIS (Netherlands)

    Jager, de M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Koppel, van de J.

    2014-01-01

    Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

  5. Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

    Directory of Open Access Journals (Sweden)

    Katona Gyula Y.

    2014-11-01

    Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

  6. The Diffusion Process in Small Particles and Brownian Motion

    Science.gov (United States)

    Khoshnevisan, M.

    Albert Einstein in 1926 published his book entitled ''INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT''. He investigated the process of diffusion in an undissociated dilute solution. The diffusion process is subject to Brownian motion. Furthermore, he elucidated the fact that the heat content of a substance will change the position of the single molecules in an irregular fashion. In this paper, I have shown that in order for the displacement of the single molecules to be proportional to the square root of the time, and for v/2 - v 1 Δ =dv/dx , (where v1 and v2 are the concentrations in two cross sections that are separated by a very small distance), ∫ - ∞ ∞ Φ (Δ) dΔ = I and I/τ ∫ - ∞ ∞Δ2/2 Φ (Δ) dΔ = D conditions to hold, then equation (7a) D =√{ 2 D }√{ τ} must be changed to Δ =√{ 2 D }√{ τ} . I have concluded that D =√{ 2 D }√{ τ} is an unintended error, and it has not been amended for almost 90 years in INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT, 1926 publication.

  7. Biased and flow driven Brownian motion in periodic channels

    Science.gov (United States)

    Martens, S.; Straube, A.; Schmid, G.; Schimansky-Geier, L.; Hänggi, P.

    2012-02-01

    In this talk we will present an expansion of the common Fick-Jacobs approximation to hydrodynamically as well as by external forces driven Brownian transport in two-dimensional channels exhibiting smoothly varying periodic cross-section. We employ an asymptotic analysis to the components of the flow field and to stationary probability density for finding the particles within the channel in a geometric parameter. We demonstrate that the problem of biased Brownian dynamics in a confined 2D geometry can be replaced by Brownian motion in an effective periodic one-dimensional potential ψ(x) which takes the external bias, the change of the local channel width, and the flow velocity component in longitudinal direction into account. In addition, we study the influence of the external force magnitude, respectively, the pressure drop of the fluid on the particle transport quantities like the averaged velocity and the effective diffusion coefficient. The critical ratio between the external force and pressure drop where the average velocity equals zero is identified and the dependence of the latter on the channel geometry is derived. Analytic findings are confirmed by numerical simulations of the particle dynamics in a reflection symmetric sinusoidal channel.

  8. Dynamics of a Brownian particle in a plasma in the long-time limit

    International Nuclear Information System (INIS)

    Dickman, R.; Varley, R.L.

    1981-01-01

    The velocity autocorrelation function (VAF) of a Brownian particle in a plasma is calculated in the long-time limit. The Brownian particle VAF exhibits the same qualitative behavior as the electron VAF in a one-component plasma: oscillations at the plasma frequency and decay approx. t -3 sup(/) 2 . (orig.)

  9. Graphs and Homomorphisms

    CERN Document Server

    Hell, Pavol

    2004-01-01

    This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an

  10. On the Generalized Brownian Motion and its Applications in Finance

    DEFF Research Database (Denmark)

    Høg, Esben; Frederiksen, Per; Schiemert, Daniel

    This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force...... of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable...

  11. Brownian motion of solitons in a Bose-Einstein condensate.

    Science.gov (United States)

    Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B

    2017-03-07

    We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

  12. Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

    Science.gov (United States)

    Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

    2017-09-01

    Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

  13. The probability of an encounter of two Brownian particles before escape

    International Nuclear Information System (INIS)

    Holcman, D; Kupka, I

    2009-01-01

    We study the probability of meeting of two Brownian particles before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance between the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double-strand DNA break repairs in confined environments.

  14. The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment

    Directory of Open Access Journals (Sweden)

    Chao Wang

    2015-01-01

    Full Text Available Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.

  15. Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

    DEFF Research Database (Denmark)

    Bensmail, Julien; Renault, Gabriel

    2016-01-01

    An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...

  16. On correlations between certain random variables associated with first passage Brownian motion

    International Nuclear Information System (INIS)

    Kearney, Michael J; Pye, Andrew J; Martin, Richard J

    2014-01-01

    We analyse how the area swept out by a Brownian motion up to its first passage time correlates with the first passage time itself, obtaining several exact results in the process. Additionally, we analyse the relationship between the time average of a Brownian motion during a first passage and the maximum value attained. The results, which find various applications, are in excellent agreement with simulations. (paper)

  17. Non-heuristic reduction of the graph in graph-cut optimization

    International Nuclear Information System (INIS)

    Malgouyres, François; Lermé, Nicolas

    2012-01-01

    During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.

  18. Graph embedding with rich information through heterogeneous graph

    KAUST Repository

    Sun, Guolei

    2017-01-01

    Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most

  19. From Levy to Brownian: a computational model based on biological fluctuation.

    Directory of Open Access Journals (Sweden)

    Surya G Nurzaman

    Full Text Available BACKGROUND: Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. METHODOLOGY/PRINCIPAL FINDINGS: We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. CONCLUSIONS/SIGNIFICANCE: Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

  20. Non-intersecting Brownian walkers and Yang-Mills theory on the sphere

    International Nuclear Information System (INIS)

    Forrester, Peter J.; Majumdar, Satya N.; Schehr, Gregory

    2011-01-01

    We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L c (N)∼√(N) in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ('watermelons' with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.

  1. Graphing trillions of triangles.

    Science.gov (United States)

    Burkhardt, Paul

    2017-07-01

    The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

  2. Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations

    Science.gov (United States)

    Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako

    2014-03-01

    We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.

  3. Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

    KAUST Repository

    Franz, Benjamin

    2013-06-19

    Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.

  4. Adaptive Graph Convolutional Neural Networks

    OpenAIRE

    Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou

    2018-01-01

    Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...

  5. On the distribution of estimators of diffusion constants for Brownian motion

    International Nuclear Information System (INIS)

    Boyer, Denis; Dean, David S

    2011-01-01

    We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.

  6. Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

    Directory of Open Access Journals (Sweden)

    Mehmet Fatih Öçal

    2017-01-01

    Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.

  7. High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs

    Science.gov (United States)

    Kempton, Mark

    This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.

  8. 3-d brownian motion simulator for high-sensitivity nanobiotechnological applications.

    Science.gov (United States)

    Toth, Arpád; Banky, Dániel; Grolmusz, Vince

    2011-12-01

    A wide variety of nanobiotechnologic applications are being developed for nanoparticle based in vitro diagnostic and imaging systems. Some of these systems make possible highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes impossible the classical, partial differential equation-based mathematical simulation of the motion of the nanoparticles involved. We present a three-dimensional Brownian motion simulation tool for the prediction of the movement of nanoparticles in various thermal, viscosity, and geometric settings in a rectangular cuvette. For nonprofit users the server is freely available at the site http://brownian.pitgroup.org.

  9. X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

    Science.gov (United States)

    2017-09-01

    are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph

  10. On the sizes of expander graphs and minimum distances of graph codes

    DEFF Research Database (Denmark)

    Høholdt, Tom; Justesen, Jørn

    2014-01-01

    We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....

  11. Similarity Measure of Graphs

    Directory of Open Access Journals (Sweden)

    Amine Labriji

    2017-07-01

    Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and  offers a contribution to solving the problem mentioned above.

  12. Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2009-01-01

    Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

  13. Spectra of Graphs

    NARCIS (Netherlands)

    Brouwer, A.E.; Haemers, W.H.

    2012-01-01

    This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association

  14. From Lévy to Brownian: a computational model based on biological fluctuation.

    Science.gov (United States)

    Nurzaman, Surya G; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

    2011-02-03

    Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

  15. Feedback control of two-headed Brownian motors in flashing ratchet potential

    International Nuclear Information System (INIS)

    Zhao A-Ke; Zhang Hong-Wei; Li Yu-Xiao

    2010-01-01

    We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency

  16. Pattern graph rewrite systems

    Directory of Open Access Journals (Sweden)

    Aleks Kissinger

    2014-03-01

    Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.

  17. Brownian relaxation of an inelastic sphere in air

    Energy Technology Data Exchange (ETDEWEB)

    Bird, G. A., E-mail: gab@gab.com.au [University of Sydney, Sydney, NSW 2006 (Australia)

    2016-06-15

    The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.

  18. On middle cube graphs

    Directory of Open Access Journals (Sweden)

    C. Dalfo

    2015-10-01

    Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.

  19. Graph visualization (Invited talk)

    NARCIS (Netherlands)

    Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.

    2012-01-01

    Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.

  20. Adventures in graph theory

    CERN Document Server

    Joyner, W David

    2017-01-01

    This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...

  1. Non-intersecting Brownian motions leaving from and going to several points

    Science.gov (United States)

    Adler, Mark; van Moerbeke, Pierre; Vanderstichelen, Didier

    2012-03-01

    Consider n non-intersecting Brownian motions on R, depending on time t∈[0,1], with mi particles forced to leave from ai at time t=0, 1≤i≤q, and nj particles forced to end up at bj at time t=1, 1≤j≤p. For arbitrary p and q, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time 0miracle! Unfortunately we were unable to find its explicit expression. The case p=q=2 will be discussed in the last section.

  2. Brownian motion model with stochastic parameters for asset prices

    Science.gov (United States)

    Ching, Soo Huei; Hin, Pooi Ah

    2013-09-01

    The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.

  3. Distance-regular graphs

    NARCIS (Netherlands)

    van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

    2016-01-01

    This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

  4. Brownian motion, dynamical randomness and irreversibility

    International Nuclear Information System (INIS)

    Gaspard, Pierre

    2005-01-01

    A relationship giving the entropy production as the difference between a time-reversed entropy per unit time and the standard one is applied to stochastic processes of diffusion of Brownian particles between two reservoirs at different concentrations. The entropy production in the nonequilibrium steady state is interpreted in terms of a time asymmetry in the dynamical randomness between the forward and backward paths of the diffusion process

  5. Finding viscosity of liquids from Brownian motion at students' laboratory

    International Nuclear Information System (INIS)

    Greczylo, Tomasz; Debowska, Ewa

    2005-01-01

    Brownian motion appears to be a good subject for investigation at advanced students' laboratory [1]. The paper presents such an investigation carried out in Physics Laboratory II at the Institute of Experimental Physics of Wroclaw University. The experiment has been designed to find viscosity of liquids from Brownian motion phenomenon. Authors use modern technology that helps to proceed with measurements and makes the procedure less time and effort consuming. Discussion of the process of setting up the experiment and the results obtained for three different solutions of glycerin in water are presented. Advantages and disadvantages of the apparatus are pointed out along with descriptions of possible future uses

  6. On the strong metric dimension of generalized butterfly graph, starbarbell graph, and {C}_{m}\\odot {P}_{n} graph

    Science.gov (United States)

    Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri

    2018-04-01

    Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u,v\\in V(G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u ‑ v path. A vertex s\\in V(G) strongly resolves two vertices u and v if u belongs to a shortest v ‑ s path or v belongs to a shortest u ‑ s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a generalized butterfly graph, starbarbell graph, and {C}mȯ {P}n graph. We obtain the strong metric dimension of generalized butterfly graph is sdim(BFn ) = 2n ‑ 2. The strong metric dimension of starbarbell graph is sdim(S{B}{m1,{m}2,\\ldots,{m}n})={\\sum }i=1n({m}i-1)-1. The strong metric dimension of {C}mȯ {P}n graph are sdim({C}mȯ {P}n)=2m-1 for m > 3 and n = 2, and sdim({C}mȯ {P}n)=2m-2 for m > 3 and n > 2.

  7. Subgraph detection using graph signals

    KAUST Repository

    Chepuri, Sundeep Prabhakar

    2017-03-06

    In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

  8. Subgraph detection using graph signals

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2017-01-01

    In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

  9. Graph spectrum

    NARCIS (Netherlands)

    Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.

    2012-01-01

    This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.

  10. Pragmatic Graph Rewriting Modifications

    OpenAIRE

    Rodgers, Peter; Vidal, Natalia

    1999-01-01

    We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...

  11. Simplicial complexes of graphs

    CERN Document Server

    Jonsson, Jakob

    2008-01-01

    A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.

  12. The STAPL Parallel Graph Library

    KAUST Repository

    Harshvardhan,

    2013-01-01

    This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.

  13. Topic Model for Graph Mining.

    Science.gov (United States)

    Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

    2015-12-01

    Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.

  14. Modern graph theory

    CERN Document Server

    Bollobás, Béla

    1998-01-01

    The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...

  15. A graph edit dictionary for correcting errors in roof topology graphs reconstructed from point clouds

    Science.gov (United States)

    Xiong, B.; Oude Elberink, S.; Vosselman, G.

    2014-07-01

    In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.

  16. Brownian Movement and Avogadro's Number: A Laboratory Experiment.

    Science.gov (United States)

    Kruglak, Haym

    1988-01-01

    Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)

  17. Collective motion of active Brownian particles with polar alignment.

    Science.gov (United States)

    Martín-Gómez, Aitor; Levis, Demian; Díaz-Guilera, Albert; Pagonabarraga, Ignacio

    2018-04-04

    We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

  18. Introduction to quantum graphs

    CERN Document Server

    Berkolaiko, Gregory

    2012-01-01

    A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...

  19. Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

    International Nuclear Information System (INIS)

    Bocquet, L.; Hansen, J.P.; Piasecki, J.

    1997-01-01

    In this work, we show that in any finite system, the binary friction tenser for two Brownian particles cannot be directly estimated from an evaluation of the microscopic Green Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tenser from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a finite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles

  20. Relaxation property of the fractional Brownian particle

    International Nuclear Information System (INIS)

    Wang Litan; Lung, C.W.

    1988-08-01

    Dynamic susceptibility of a diffusion system associated with the fractional Brownian motion (fBm) was examined for the fractal property of the Non-Debye relaxation process. The comparisons between fBm and other approaches were made. Anomalous diffusion and the Non-Debye relaxation processes were discussed with this approach. (author). 8 refs, 1 fig

  1. Graph Generator Survey

    Energy Technology Data Exchange (ETDEWEB)

    Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2013-10-01

    The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.

  2. Functions and graphs

    CERN Document Server

    Gelfand, I M; Shnol, E E

    1969-01-01

    The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu

  3. Loose Graph Simulations

    DEFF Research Database (Denmark)

    Mansutti, Alessio; Miculan, Marino; Peressotti, Marco

    2017-01-01

    We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...

  4. Brownian Motion of 2D Vacancy Islands by Adatom Terrace Diffusion

    International Nuclear Information System (INIS)

    Morgenstern, Karina; Laegsgaard, Erik; Besenbacher, Flemming

    2001-01-01

    We have studied the Brownian motion of two-dimensional (2D) vacancy islands on Ag(110) at temperatures between 175 and 215K. While the detachment of adatoms from the island and their diffusion on the terrace are permitted in this temperature range, the periphery diffusion of single adatoms is prohibited. The present scanning tunneling microscopy results provide the first direct experimental proof that the Brownian motion of the islands follows a simple scaling law with terrace diffusion being the rate limiting process. The activation energy of the vacancy island motion is determined to 0.41eV

  5. Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

    International Nuclear Information System (INIS)

    Liu Ai-Jie; Zheng Lian-Cun; Zhang Xin-Xin; Ma Lian-Xi

    2015-01-01

    In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. (general)

  6. Autoregressive Moving Average Graph Filtering

    OpenAIRE

    Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert

    2016-01-01

    One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...

  7. On cyclic orthogonal double covers of circulant graphs by special infinite graphs

    Directory of Open Access Journals (Sweden)

    R. El-Shanawany

    2017-12-01

    Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.

  8. Quantum walks on quotient graphs

    International Nuclear Information System (INIS)

    Krovi, Hari; Brun, Todd A.

    2007-01-01

    A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup

  9. The escape of brownian particle over potential barriers

    International Nuclear Information System (INIS)

    Zhong Yunxiao

    1985-01-01

    A convenient method is introduced to calculate the rate of escape of Brownian particle over potential barriers by exact solution of Smoluchowskian equation. This method is applied to calculate the nuclear fission probabilities. The results for four different cases are compared with the results of other theories

  10. Fundamentals of algebraic graph transformation

    CERN Document Server

    Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele

    2006-01-01

    Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...

  11. Graph-based modelling in engineering

    CERN Document Server

    Rysiński, Jacek

    2017-01-01

    This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .

  12. Time-averaged MSD of Brownian motion

    OpenAIRE

    Andreanov, Alexei; Grebenkov, Denis

    2012-01-01

    We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we de...

  13. Rotational and translational Brownian motion

    International Nuclear Information System (INIS)

    Coffey, W.T.; Salford Univ.

    1980-01-01

    In this review it is proposed to summarise the work on the theory of the translational and rotational Brownian movement which has been carried on over roughly the past 30 years. The review is intended to take the form of a tutorial paper rather than a list of the results obtained by the various investigators over the period in question. In this vein then it seems appropriate to firstly give a brief account of those parts of the theory of probability which are relevant to the problems under discussion. (orig.)

  14. BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

    Science.gov (United States)

    Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

    2013-02-01

    Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

  15. Hydrodynamic interactions induce movement against an external load in a ratchet dimer Brownian motor.

    Science.gov (United States)

    Fornés, José A

    2010-01-15

    We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.

  16. Equipackable graphs

    DEFF Research Database (Denmark)

    Vestergaard, Preben Dahl; Hartnell, Bert L.

    2006-01-01

    There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...

  17. Khovanov homology of graph-links

    Energy Technology Data Exchange (ETDEWEB)

    Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2012-08-31

    Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.

  18. Generalized connectivity of graphs

    CERN Document Server

    Li, Xueliang

    2016-01-01

    Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

  19. On two energy-like invariants of line graphs and related graph operations

    Directory of Open Access Journals (Sweden)

    Xiaodan Chen

    2016-02-01

    Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.

  20. Price Competition on Graphs

    OpenAIRE

    Adriaan R. Soetevent

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...

  1. Price Competition on Graphs

    OpenAIRE

    Pim Heijnen; Adriaan Soetevent

    2014-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...

  2. Skew-adjacency matrices of graphs

    NARCIS (Netherlands)

    Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

    2012-01-01

    The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

  3. Graph theory

    CERN Document Server

    Diestel, Reinhard

    2017-01-01

    This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...

  4. Acyclicity in edge-colored graphs

    DEFF Research Database (Denmark)

    Gutin, Gregory; Jones, Mark; Sheng, Bin

    2017-01-01

    A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...

  5. Brownian motion in complex fluids: venerable field and frontier of modern physics

    International Nuclear Information System (INIS)

    Vizcarra-Rendon, A.; Medina-Noyola, M.; Ruiz-Estrada, H.; Arauz-Lara, J.L.

    1989-01-01

    This paper reviews the current status of our understanding of tracer-diffusion phenomena in colloidal suspensions. This is the most direct observation of the Brownian motion executed by labelled Brownian particles interacting with the rest of colloidal particles in a suspension. The fundamental description of this phenomenon constitutes today one of the most relevant problems in the process of understanding the dynamic properties of this important class of complex fluids, from the experimental and theoretical perspective of physical research. This paper describes the recent developments in the extension of the classical theory of Brownian motion and its application to the description of the effects of direct and hydrodynamic interactions among colloidal particles. As a result, a coherent pictured has emerged in which the agreement between theory and experiment from nature fields of physics. The moral of the paper is that the use of well established concepts as statistical physics, assisted by modern experimental techniques, are contributing to transform complex fluids into a more amialbe class of materials from the point of view of the physicist. (Author)

  6. Stochastic interactions of two Brownian hard spheres in the presence of depletants

    International Nuclear Information System (INIS)

    Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi

    2014-01-01

    A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions

  7. Graph Sampling for Covariance Estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar

    2017-04-25

    In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

  8. Price competition on graphs

    NARCIS (Netherlands)

    Soetevent, A.R.

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial

  9. Graphing the order of the sexes: constructing, recalling, interpreting, and putting the self in gender difference graphs.

    Science.gov (United States)

    Hegarty, Peter; Lemieux, Anthony F; McQueen, Grant

    2010-03-01

    Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N = 741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men's data first, and graphed powerful groups (Study 3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author "bias" inferred that the author graphed his or her own gender group first (Study 5). Women's, but not men's, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific thinking have yet acknowledged.

  10. Collective Rationality in Graph Aggregation

    NARCIS (Netherlands)

    Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.

    2014-01-01

    Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the

  11. GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

    Energy Technology Data Exchange (ETDEWEB)

    Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor

    2014-08-25

    Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.

  12. Graph Theory. 1. Fragmentation of Structural Graphs

    Directory of Open Access Journals (Sweden)

    Lorentz JÄNTSCHI

    2002-12-01

    Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.

  13. Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

    International Nuclear Information System (INIS)

    Diestler, D.J.; Riley, M.E.

    1985-01-01

    We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed

  14. On-chip measurements of Brownian relaxation vs. concentration of 40nm magnetic beads

    DEFF Research Database (Denmark)

    Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt

    2012-01-01

    We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields...... are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response...... is proportional to the bead concentration. For bead concentrations higher than or equal to 500 mu g/ml, we extract a hydrodynamic diameter of 47(1) nm for the beads, which is close to the nominal bead size of 40 nm. Furthermore, we study the signal vs. bead concentration at a fixed frequency close to the Brownian...

  15. Statistics of the first passage time of Brownian motion conditioned by maximum value or area

    International Nuclear Information System (INIS)

    Kearney, Michael J; Majumdar, Satya N

    2014-01-01

    We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated. (paper)

  16. Brownian motion in short range random potentials

    International Nuclear Information System (INIS)

    Romero, A.H.; Romero, A.H.; Sancho, J.M.

    1998-01-01

    A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on. copyright 1998 The American Physical Society

  17. Introductory graph theory

    CERN Document Server

    Chartrand, Gary

    1984-01-01

    Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap

  18. Natural convection in nano-fluids: Are the thermophoresis and Brownian motion effects significant in nano-fluid heat transfer enhancement?

    International Nuclear Information System (INIS)

    Haddad, Zoubida; Abu-Nada, Eiyad; Oztop, Hakan F.; Mataoui, Amina

    2012-01-01

    Natural convection heat transfer and fluid flow of CuO-Water nano-fluids is studied using the Rayleigh-Benard problem. A two component non-homogenous equilibrium model is used for the nano-fluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nano-particle distribution, local and mean Nusselt numbers and nano-particle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nano-particles. However, the enhancement is more pronounced at low volume fraction of nano-particles and the heat transfer decreases by increasing nano-particle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nano-particles. (authors)

  19. Creating more effective graphs

    CERN Document Server

    Robbins, Naomi B

    2012-01-01

    A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr

  20. Graph Compression by BFS

    Directory of Open Access Journals (Sweden)

    Alberto Apostolico

    2009-08-01

    Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.

  1. Graphing Inequalities, Connecting Meaning

    Science.gov (United States)

    Switzer, J. Matt

    2014-01-01

    Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

  2. Fuzzy Graph Language Recognizability

    OpenAIRE

    Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros

    2012-01-01

    Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

  3. Bell inequalities for graph states

    International Nuclear Information System (INIS)

    Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.

    2005-01-01

    Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)

  4. An explicit local uniform large deviation bound for Brownian bridges

    NARCIS (Netherlands)

    Wittich, O.

    2005-01-01

    By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.

  5. Brownian agents and active particles collective dynamics in the natural and social sciences

    CERN Document Server

    Schweitzer, Frank

    2007-01-01

    ""This book lays out a vision for a coherent framework for understanding complex systems"" (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from

  6. Quantitative graph theory mathematical foundations and applications

    CERN Document Server

    Dehmer, Matthias

    2014-01-01

    The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat

  7. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    Directory of Open Access Journals (Sweden)

    Xiao-Li Ding

    2018-01-01

    Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

  8. Dynamic Representations of Sparse Graphs

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Fagerberg, Rolf

    1999-01-01

    We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....

  9. Spectral fluctuations of quantum graphs

    International Nuclear Information System (INIS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-01-01

    We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry

  10. Multiple graph regularized protein domain ranking.

    Science.gov (United States)

    Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

    2012-11-19

    Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

  11. Quantum Darwinism in Quantum Brownian Motion

    Science.gov (United States)

    Blume-Kohout, Robin; Zurek, Wojciech H.

    2008-12-01

    Quantum Darwinism—the redundant encoding of information about a decohering system in its environment—was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state—a macroscopic superposition—the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.

  12. Acyclicity in edge-colored graphs

    DEFF Research Database (Denmark)

    Gutin, Gregory; Jones, Mark; Sheng, Bin

    2017-01-01

    A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...

  13. ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS

    OpenAIRE

    Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache

    2016-01-01

    In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

  14. Practical graph mining with R

    CERN Document Server

    Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan

    2014-01-01

    Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...

  15. Brownian motion, Minkowski space and principle of special relativity

    International Nuclear Information System (INIS)

    Caubet, J.-P.

    1977-01-01

    From the assumption that the brownian diffusion locally behaves like an ideal gas (pressure being inversely proportional to volume according to Boyle's law) one can deduce the signature +++- of the Minkowski space, the Lorentz addition of velocities, and the principle of special relativity [fr

  16. A seminar on graph theory

    CERN Document Server

    Harary, Frank

    2015-01-01

    Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc

  17. Uniform Single Valued Neutrosophic Graphs

    Directory of Open Access Journals (Sweden)

    S. Broumi

    2017-09-01

    Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

  18. Extremal graph theory

    CERN Document Server

    Bollobas, Bela

    2004-01-01

    The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A

  19. Frustrated Brownian Motion of Nonlocal Solitary Waves

    International Nuclear Information System (INIS)

    Folli, V.; Conti, C.

    2010-01-01

    We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.

  20. The quantum brownian particle and memory effects

    International Nuclear Information System (INIS)

    Britani, J.R.; Mizrahi, S.S.; Pimentel, B.M.

    1991-01-01

    The Quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a Generalized Master Equation (GME). The heat bath degrees of freedom are considered to be either white noise or coloured noise correlated,while the GME is considered under either the Markov or Non-Markov approaches. The comparison between these considerations are fully developed and their physical meaning is discussed. (author)

  1. Multiple graph regularized protein domain ranking

    KAUST Repository

    Wang, Jim Jing-Yan

    2012-11-19

    Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

  2. Multiple graph regularized protein domain ranking

    KAUST Repository

    Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

    2012-01-01

    Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

  3. Multiple graph regularized protein domain ranking

    Directory of Open Access Journals (Sweden)

    Wang Jim

    2012-11-01

    Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

  4. Asset pricing puzzles explained by incomplete Brownian equilibria

    DEFF Research Database (Denmark)

    Christensen, Peter Ove; Larsen, Kasper

    We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....

  5. Canonical Labelling of Site Graphs

    Directory of Open Access Journals (Sweden)

    Nicolas Oury

    2013-06-01

    Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.

  6. Synchronization and collective motion of globally coupled Brownian particles

    International Nuclear Information System (INIS)

    Sevilla, Francisco J; Heiblum-Robles, Alexandro; Dossetti, Victor

    2014-01-01

    In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group. Our results show a clear connection between collective motion and the Kuramoto model for synchronization, in our case, for the direction of motion of the particles. (paper)

  7. Laser light scattering in Brownian medium

    International Nuclear Information System (INIS)

    Suwono; Santoso, Budi; Baiquni, A.

    1983-01-01

    The principle of laser light scattering in Brownian medium and photon correlation spectroscopy are described in detail. Their application to the study of the behaviour of a polystyrene latex solution are discussed. The auto-correlation function of light scattered by the polystyrene latex solution in various angle, various temperature and in various sample times, have been measured. Information on the translation diffusion coefficient and size on the particle can be obtained from the auto-correlation function. Good agreement between the available data and experiment is shown. (author)

  8. Domination criticality in product graphs

    Directory of Open Access Journals (Sweden)

    M.R. Chithra

    2015-07-01

    Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.

  9. Graph Creation, Visualisation and Transformation

    Directory of Open Access Journals (Sweden)

    Maribel Fernández

    2010-03-01

    Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.

  10. Graph Colouring Algorithms

    DEFF Research Database (Denmark)

    Husfeldt, Thore

    2015-01-01

    This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...

  11. The fascinating world of graph theory

    CERN Document Server

    Benjamin, Arthur; Zhang, Ping

    2015-01-01

    Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin

  12. Classical dynamics on graphs

    International Nuclear Information System (INIS)

    Barra, F.; Gaspard, P.

    2001-01-01

    We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes

  13. Groupies in multitype random graphs

    OpenAIRE

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  14. CNT based thermal Brownian motor to pump water in nanodevices

    DEFF Research Database (Denmark)

    Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore

    2016-01-01

    asymmetry drive the water ow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed......Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through...... Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by flxing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial...

  15. Quantum information processing with graph states

    International Nuclear Information System (INIS)

    Schlingemann, Dirk-Michael

    2005-04-01

    Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)

  16. Fibonacci number of the tadpole graph

    Directory of Open Access Journals (Sweden)

    Joe DeMaio

    2014-10-01

    Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

  17. On the biased motion of a brownian particle for the pausing time behavior of the CTRW

    International Nuclear Information System (INIS)

    Kim, K.S.

    1982-01-01

    The purpose of this paper is to discuss the biased Brownian motion with the absorbing barrier for the pausing time behavior of the CTRW (continuous-time random walk method), regarding a Brownian particle as a walker. For two pausing time density functions, the respective values for the transport averaged velocity and the dispersion are calculated as the time t becomes large. (KAERI)

  18. On characterizing terrain visibility graphs

    Directory of Open Access Journals (Sweden)

    William Evans

    2015-06-01

    Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.

  19. Network reconstruction via graph blending

    Science.gov (United States)

    Estrada, Rolando

    2016-05-01

    Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.

  20. Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

    Science.gov (United States)

    Tyagi, Neha; Cherayil, Binny J.

    2018-03-01

    The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.

  1. Algorithms for Brownian first-passage-time estimation

    Science.gov (United States)

    Adib, Artur B.

    2009-09-01

    A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

  2. Current fluctuations of interacting active Brownian particles

    OpenAIRE

    Pre, Trevor Grand; Limmer, David T.

    2018-01-01

    We derive the distribution function for particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particle's orientation, and ...

  3. Interaction graphs

    DEFF Research Database (Denmark)

    Seiller, Thomas

    2016-01-01

    Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...

  4. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

    Science.gov (United States)

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

    Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

  5. Experimental Studies of the Brownian Diffusion of Boomerang Colloidal Particle in a Confined Geometry

    Science.gov (United States)

    Chakrabarty, Ayan; Wang, Feng; Joshi, Bhuwan; Wei, Qi-Huo

    2011-03-01

    Recent studies shows that the boomerang shaped molecules can form various kinds of liquid crystalline phases. One debated topic related to boomerang molecules is the existence of biaxial nematic liquid crystalline phase. Developing and optical microscopic studies of colloidal systems of boomerang particles would allow us to gain better understanding of orientation ordering and dynamics at ``single molecule'' level. Here we report the fabrication and experimental studies of the Brownian motion of individual boomerang colloidal particles confined between two glass plates. We used dark-field optical microscopy to directly visualize the Brownian motion of the single colloidal particles in a quasi two dimensional geometry. An EMCCD was used to capture the motion in real time. An indigenously developed imaging processing algorithm based on MatLab program was used to precisely track the position and orientation of the particles with sub-pixel accuracy. The experimental finding of the Brownian diffusion of a single boomerang colloidal particle will be discussed.

  6. Groupies in multitype random graphs.

    Science.gov (United States)

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  7. The Harary index of a graph

    CERN Document Server

    Xu, Kexiang; Trinajstić, Nenad

    2015-01-01

    This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...

  8. A Modal-Logic Based Graph Abstraction

    NARCIS (Netherlands)

    Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.

    2008-01-01

    Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract

  9. From Brownian Dynamics to Markov Chain: An Ion Channel Example

    KAUST Repository

    Chen, Wan; Erban, Radek; Chapman, S. Jonathan

    2014-01-01

    is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal

  10. Eigenfunction statistics of Wishart Brownian ensembles

    International Nuclear Information System (INIS)

    Shukla, Pragya

    2017-01-01

    We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)

  11. Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.

    Science.gov (United States)

    Warnke-Sommer, Julia; Ali, Hesham

    2016-05-06

    The assembly of Next Generation Sequencing (NGS) reads remains a challenging task. This is especially true for the assembly of metagenomics data that originate from environmental samples potentially containing hundreds to thousands of unique species. The principle objective of current assembly tools is to assemble NGS reads into contiguous stretches of sequence called contigs while maximizing for both accuracy and contig length. The end goal of this process is to produce longer contigs with the major focus being on assembly only. Sequence read assembly is an aggregative process, during which read overlap relationship information is lost as reads are merged into longer sequences or contigs. The assembly graph is information rich and capable of capturing the genomic architecture of an input read data set. We have developed a novel hybrid graph in which nodes represent sequence regions at different levels of granularity. This model, utilized in the assembly and analysis pipeline Focus, presents a concise yet feature rich view of a given input data set, allowing for the extraction of biologically relevant graph structures for graph mining purposes. Focus was used to create hybrid graphs to model metagenomics data sets obtained from the gut microbiomes of five individuals with Crohn's disease and eight healthy individuals. Repetitive and mobile genetic elements are found to be associated with hybrid graph structure. Using graph mining techniques, a comparative study of the Crohn's disease and healthy data sets was conducted with focus on antibiotics resistance genes associated with transposase genes. Results demonstrated significant differences in the phylogenetic distribution of categories of antibiotics resistance genes in the healthy and diseased patients. Focus was also evaluated as a pure assembly tool and produced excellent results when compared against the Meta-velvet, Omega, and UD-IDBA assemblers. Mining the hybrid graph can reveal biological phenomena captured

  12. Distance-transitive graphs

    NARCIS (Netherlands)

    Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.

    2004-01-01

    In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite

  13. TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

    Science.gov (United States)

    Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

    2016-01-01

    We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

  14. Temporal Representation in Semantic Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Levandoski, J J; Abdulla, G M

    2007-08-07

    A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.

  15. The complexity of the matching-cut problem for planar graphs and other graph classes

    NARCIS (Netherlands)

    Bonsma, P.S.

    2009-01-01

    The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it

  16. Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.

    Science.gov (United States)

    Kranstauber, Bart; Safi, Kamran; Bartumeus, Frederic

    2014-01-01

    In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion. Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk. We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the "move" package for R.

  17. PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION

    Directory of Open Access Journals (Sweden)

    W. Dorner

    2016-06-01

    Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.

  18. Integer Flows and Circuit Covers of Graphs and Signed Graphs

    Science.gov (United States)

    Cheng, Jian

    The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it

  19. Port-Hamiltonian Systems on Open Graphs

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    2010-01-01

    In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

  20. Towards a theory of geometric graphs

    CERN Document Server

    Pach, Janos

    2004-01-01

    The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

  1. Active Brownian motion models and applications to ratchets

    Science.gov (United States)

    Fiasconaro, A.; Ebeling, W.; Gudowska-Nowak, E.

    2008-10-01

    We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.

  2. Quantum walk on a chimera graph

    Science.gov (United States)

    Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

    2018-05-01

    We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

  3. Software for Graph Analysis and Visualization

    Directory of Open Access Journals (Sweden)

    M. I. Kolomeychenko

    2014-01-01

    Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.

  4. What Would a Graph Look Like in this Layout? A Machine Learning Approach to Large Graph Visualization.

    Science.gov (United States)

    Kwon, Oh-Hyun; Crnovrsanin, Tarik; Ma, Kwan-Liu

    2018-01-01

    Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to selecting a good layout is to use aesthetic criteria and visual inspection. However, fully calculating various layouts and their associated aesthetic metrics is computationally expensive. In this paper, we present a machine learning approach to large graph visualization based on computing the topological similarity of graphs using graph kernels. For a given graph, our approach can show what the graph would look like in different layouts and estimate their corresponding aesthetic metrics. An important contribution of our work is the development of a new framework to design graph kernels. Our experimental study shows that our estimation calculation is considerably faster than computing the actual layouts and their aesthetic metrics. Also, our graph kernels outperform the state-of-the-art ones in both time and accuracy. In addition, we conducted a user study to demonstrate that the topological similarity computed with our graph kernel matches perceptual similarity assessed by human users.

  5. Text-Filled Stacked Area Graphs

    DEFF Research Database (Denmark)

    Kraus, Martin

    2011-01-01

    -filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....

  6. Enhancement of transport properties of a Brownian particle due to quantum effects: Smoluchowski limit

    International Nuclear Information System (INIS)

    Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray

    2012-01-01

    Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: ► Transport of a quantum Brownian particle in a periodic potential has been addressed. ► Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. ► A coordinate transformation is used to recast QSE with constant diffusion. ► Transport properties increases in comparison to the corresponding classical result. ► This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.

  7. On Graph Rewriting, Reduction and Evaluation

    DEFF Research Database (Denmark)

    Zerny, Ian

    2010-01-01

    We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...

  8. Graph transformation tool contest 2008

    NARCIS (Netherlands)

    Rensink, Arend; van Gorp, Pieter

    This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case

  9. On dominator colorings in graphs

    Indian Academy of Sciences (India)

    colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.

  10. Graphs with branchwidth at most three

    NARCIS (Netherlands)

    Bodlaender, H.L.; Thilikos, D.M.

    1997-01-01

    In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph

  11. Planar graphs theory and algorithms

    CERN Document Server

    Nishizeki, T

    1988-01-01

    Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

  12. Graph Quasicontinuous Functions and Densely Continuous Forms

    Directory of Open Access Journals (Sweden)

    Lubica Hola

    2017-07-01

    Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.

  13. The open quantum Brownian motions

    International Nuclear Information System (INIS)

    Bauer, Michel; Bernard, Denis; Tilloy, Antoine

    2014-01-01

    Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H z : orbital (walker) Hilbert space, C Z in the discrete, L 2 (R) in the continuum H c : internal spin (or gyroscope) Hilbert space H sys =H z ⊗H c : system Hilbert space H p : probe (or quantum coin) Hilbert space, H p =C 2 ρ t tot : density matrix for the total system (walker + internal spin + quantum coins) ρ-bar t : reduced density matrix on H sys : ρ-bar t =∫dxdy ρ-bar t (x,y)⊗|x〉 z 〈y| ρ-hat t : system density matrix in a quantum trajectory: ρ-hat t =∫dxdy ρ-hat t (x,y)⊗|x〉 z 〈y|. If diagonal and localized in position: ρ-hat t =ρ t ⊗|X t 〉 z 〈X t | ρ t : internal density matrix in a simple quantum trajectory X t : walker position in a simple quantum trajectory B t : normalized Brownian motion ξ t , ξ t † : quantum noises (paper)

  14. CORECLUSTER: A Degeneracy Based Graph Clustering Framework

    OpenAIRE

    Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis

    2014-01-01

    International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...

  15. Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints

    Science.gov (United States)

    Fiore, Andrew M.; Swan, James W.

    2018-01-01

    Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle

  16. Brownian motion of a nano-colloidal particle: the role of the solvent.

    Science.gov (United States)

    Torres-Carbajal, Alexis; Herrera-Velarde, Salvador; Castañeda-Priego, Ramón

    2015-07-15

    Brownian motion is a feature of colloidal particles immersed in a liquid-like environment. Usually, it can be described by means of the generalised Langevin equation (GLE) within the framework of the Mori theory. In principle, all quantities that appear in the GLE can be calculated from the molecular information of the whole system, i.e., colloids and solvent molecules. In this work, by means of extensive Molecular Dynamics simulations, we study the effects of the microscopic details and the thermodynamic state of the solvent on the movement of a single nano-colloid. In particular, we consider a two-dimensional model system in which the mass and size of the colloid are two and one orders of magnitude, respectively, larger than the ones associated with the solvent molecules. The latter ones interact via a Lennard-Jones-type potential to tune the nature of the solvent, i.e., it can be either repulsive or attractive. We choose the linear momentum of the Brownian particle as the observable of interest in order to fully describe the Brownian motion within the Mori framework. We particularly focus on the colloid diffusion at different solvent densities and two temperature regimes: high and low (near the critical point) temperatures. To reach our goal, we have rewritten the GLE as a second kind Volterra integral in order to compute the memory kernel in real space. With this kernel, we evaluate the momentum-fluctuating force correlation function, which is of particular relevance since it allows us to establish when the stationarity condition has been reached. Our findings show that even at high temperatures, the details of the attractive interaction potential among solvent molecules induce important changes in the colloid dynamics. Additionally, near the critical point, the dynamical scenario becomes more complex; all the correlation functions decay slowly in an extended time window, however, the memory kernel seems to be only a function of the solvent density. Thus, the

  17. Dependence of Brownian and Néel relaxation times on magnetic field strength

    International Nuclear Information System (INIS)

    Deissler, Robert J.; Wu, Yong; Martens, Michael A.

    2014-01-01

    Purpose: In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. Methods: The Fokker–Planck equation with Brownian relaxation and the Fokker–Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. Results: The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present—if the particles are embedded in a solid for instance—the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the

  18. Coloring sums of extensions of certain graphs

    Directory of Open Access Journals (Sweden)

    Johan Kok

    2017-12-01

    Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

  19. One-Dimensional Brownian Motion of Charged Nanoparticles along Microtubules: A Model System for Weak Binding Interactions

    OpenAIRE

    Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

    2010-01-01

    Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs ...

  20. On a conjecture concerning helly circle graphs

    Directory of Open Access Journals (Sweden)

    Durán Guillermo

    2003-01-01

    Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.

  1. Optimization Problems on Threshold Graphs

    Directory of Open Access Journals (Sweden)

    Elena Nechita

    2010-06-01

    Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.

  2. Hierarchy of modular graph identities

    Energy Technology Data Exchange (ETDEWEB)

    D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)

    2016-11-09

    The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

  3. Hierarchy of modular graph identities

    International Nuclear Information System (INIS)

    D’Hoker, Eric; Kaidi, Justin

    2016-01-01

    The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

  4. Well-covered graphs and factors

    DEFF Research Database (Denmark)

    Randerath, Bert; Vestergaard, Preben D.

    2006-01-01

    A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...

  5. On the centrality of some graphs

    Directory of Open Access Journals (Sweden)

    Vecdi Aytac

    2017-10-01

    Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.

  6. Enabling Graph Appliance for Genome Assembly

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL

    2015-01-01

    In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.

  7. On 4-critical t-perfect graphs

    OpenAIRE

    Benchetrit, Yohann

    2016-01-01

    It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...

  8. Local adjacency metric dimension of sun graph and stacked book graph

    Science.gov (United States)

    Yulisda Badri, Alifiah; Darmaji

    2018-03-01

    A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

  9. Mechatronic modeling and simulation using bond graphs

    CERN Document Server

    Das, Shuvra

    2009-01-01

    Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...

  10. An Extreme-Value Analysis of the LIL for Brownian Motion

    OpenAIRE

    Khoshnevisan, Davar; Levin, David; Shi, Zhan

    2005-01-01

    We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also proves, in a paragraph, the classical theorem of Darling and Erdős (1956).

  11. Statistical properties of laser light scattering in Brownian medium

    International Nuclear Information System (INIS)

    Suwono; Santoso, Budi; Baiquni, A.

    1983-01-01

    Relationship between statistical properties of laser light scattering in Brownian medium and photon-counting distributions are described in detail. A coherence optical detection has been constructed and by using photon-counting technique the ensemble distribution of the scattered field within space and time coherence has been measured. Good agreement between theory and experiment is shown. (author)

  12. Non-cooperative Brownian donkeys: A solvable 1D model

    Science.gov (United States)

    Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.

    2003-12-01

    A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.

  13. Time-averaged MSD of Brownian motion

    International Nuclear Information System (INIS)

    Andreanov, Alexei; Grebenkov, Denis S

    2012-01-01

    We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution

  14. Time-averaged MSD of Brownian motion

    Science.gov (United States)

    Andreanov, Alexei; Grebenkov, Denis S.

    2012-07-01

    We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution.

  15. Expert interpretation of bar and line graphs: The role of graphicacy in reducing the effect of graph format.

    Directory of Open Access Journals (Sweden)

    David ePeebles

    2015-10-01

    Full Text Available The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987 has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 x 2 'interaction' bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices - and contrary to the assumptions of several graph comprehension models - experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.

  16. Proving termination of graph transformation systems using weighted type graphs over semirings

    NARCIS (Netherlands)

    Bruggink, H.J.S.; König, B.; Nolte, D.; Zantema, H.; Parisi-Presicce, F.; Westfechtel, B.

    2015-01-01

    We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a

  17. New methods for simulation of fractional Brownian motion

    International Nuclear Information System (INIS)

    Yin, Z.M.

    1996-01-01

    We present new algorithms for simulation of fractional Brownian motion (fBm) which comprises a set of important random functions widely used in geophysical and physical modeling, fractal image (landscape) simulating, and signal processing. The new algorithms, which are both accurate and efficient, allow us to generate not only a one-dimensional fBm process, but also two- and three-dimensional fBm fields. 23 refs., 3 figs

  18. Linear response approach to active Brownian particles in time-varying activity fields

    Science.gov (United States)

    Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe

    2018-05-01

    In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

  19. DIMENSI METRIK GRAPH LOBSTER Ln (q;r

    Directory of Open Access Journals (Sweden)

    PANDE GDE DONY GUMILAR

    2013-05-01

    Full Text Available The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r. Lobster graph Ln (q;r is a regular lobster graph with vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n, q, r element of N. We obtain the metric dimension of lobster graph L2 (1;1 is 1, the metric dimension of lobster graph L2 (1;1 for n > 2 is 2.

  20. Summary: beyond fault trees to fault graphs

    International Nuclear Information System (INIS)

    Alesso, H.P.; Prassinos, P.; Smith, C.F.

    1984-09-01

    Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability

  1. Characterization of turbulence stability through the identification of multifractional Brownian motions

    Science.gov (United States)

    Lee, K. C.

    2013-02-01

    Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

  2. Characterization of turbulence stability through the identification of multifractional Brownian motions

    Directory of Open Access Journals (Sweden)

    K. C. Lee

    2013-02-01

    Full Text Available Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

  3. Interactive Graph Layout of a Million Nodes

    Directory of Open Access Journals (Sweden)

    Peng Mi

    2016-12-01

    Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.

  4. Eulerian Graphs and Related Topics

    CERN Document Server

    Fleischner, Herbert

    1990-01-01

    The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a

  5. The One Universal Graph — a free and open graph database

    Science.gov (United States)

    Ng, Liang S.; Champion, Corbin

    2016-02-01

    Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks.

  6. Degree-based graph construction

    International Nuclear Information System (INIS)

    Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A

    2009-01-01

    Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)

  7. Downhill Domination in Graphs

    Directory of Open Access Journals (Sweden)

    Haynes Teresa W.

    2014-08-01

    Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

  8. Subsampling for graph power spectrum estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2016-01-01

    In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

  9. Proving relations between modular graph functions

    International Nuclear Information System (INIS)

    Basu, Anirban

    2016-01-01

    We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links. (paper)

  10. Subsampling for graph power spectrum estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar

    2016-10-06

    In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

  11. Semantic graphs and associative memories

    Science.gov (United States)

    Pomi, Andrés; Mizraji, Eduardo

    2004-12-01

    Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

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

    Directory of Open Access Journals (Sweden)

    Namhee Kim

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

  13. A generalization of total graphs

    Indian Academy of Sciences (India)

    M Afkhami

    2018-04-12

    Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.

  14. Large shear deformation of particle gels studied by Brownian Dynamics simulations

    NARCIS (Netherlands)

    Rzepiela, A.A.; Opheusden, van J.H.J.; Vliet, van T.

    2004-01-01

    Brownian Dynamics (BD) simulations have been performed to study structure and rheology of particle gels under large shear deformation. The model incorporates soft spherical particles, and reversible flexible bond formation. Two different methods of shear deformation are discussed, namely affine and

  15. Decomposing a planar graph into an independent set and a 3-degenerate graph

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2001-01-01

    We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....

  16. Commuting graphs of matrix algebras

    International Nuclear Information System (INIS)

    Akbari, S.; Bidkhori, H.; Mohammadian, A.

    2006-08-01

    The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)

  17. Graph-theoretical concepts and physicochemical data

    Directory of Open Access Journals (Sweden)

    Lionello Pogliani

    2003-02-01

    Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.

  18. Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

    Science.gov (United States)

    Koide, T; Kodama, T

    2011-06-01

    We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

  19. Second order limit laws for occupation times of the fractional Brownian motion

    OpenAIRE

    Xu, Fangjun

    2013-01-01

    We prove second order limit laws for (additive) functionals of the $d$-dimensional fractional Brownian motion with Hurst index $H=\\frac{1}{d}$, using the method of moments, extending the Kallianpur-Robbins law.

  20. Graphs whose complement and square are isomorphic

    DEFF Research Database (Denmark)

    Pedersen, Anders Sune

    2014-01-01

    We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...

  1. Graphs & digraphs

    CERN Document Server

    Chartrand, Gary; Zhang, Ping

    2010-01-01

    Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...

  2. Packing Degenerate Graphs Greedily

    Czech Academy of Sciences Publication Activity Database

    Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana

    2017-01-01

    Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

  3. Continuous-time quantum walks on star graphs

    International Nuclear Information System (INIS)

    Salimi, S.

    2009-01-01

    In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K 2 graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

  4. Tailored Random Graph Ensembles

    International Nuclear Information System (INIS)

    Roberts, E S; Annibale, A; Coolen, A C C

    2013-01-01

    Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.

  5. The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

    Directory of Open Access Journals (Sweden)

    Unil Yun

    2016-05-01

    Full Text Available Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

  6. Relating zeta functions of discrete and quantum graphs

    Science.gov (United States)

    Harrison, Jonathan; Weyand, Tracy

    2018-02-01

    We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

  7. Configurational entropy and effective temperature in systems of active Brownian particles

    NARCIS (Netherlands)

    Preisler, Zdeněk; Dijkstra, Marjolein

    2016-01-01

    We propose a method to determine the effective density of states and configurational entropy in systems of active Brownian particles by measuring the probability distribution function of potential energy at varying temperatures. Assuming that the entropy is a continuous and monotonically increasing

  8. The One Universal Graph — a free and open graph database

    International Nuclear Information System (INIS)

    Ng, Liang S.; Champion, Corbin

    2016-01-01

    Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks. (paper)

  9. Fundamental energy limits of SET-based Brownian NAND and half-adder circuits. Preliminary findings from a physical-information-theoretic methodology

    Science.gov (United States)

    Ercan, İlke; Suyabatmaz, Enes

    2018-06-01

    The saturation in the efficiency and performance scaling of conventional electronic technologies brings about the development of novel computational paradigms. Brownian circuits are among the promising alternatives that can exploit fluctuations to increase the efficiency of information processing in nanocomputing. A Brownian cellular automaton, where signals propagate randomly and are driven by local transition rules, can be made computationally universal by embedding arbitrary asynchronous circuits on it. One of the potential realizations of such circuits is via single electron tunneling (SET) devices since SET technology enable simulation of noise and fluctuations in a fashion similar to Brownian search. In this paper, we perform a physical-information-theoretic analysis on the efficiency limitations in a Brownian NAND and half-adder circuits implemented using SET technology. The method we employed here establishes a solid ground that enables studying computational and physical features of this emerging technology on an equal footing, and yield fundamental lower bounds that provide valuable insights into how far its efficiency can be improved in principle. In order to provide a basis for comparison, we also analyze a NAND gate and half-adder circuit implemented in complementary metal oxide semiconductor technology to show how the fundamental bound of the Brownian circuit compares against a conventional paradigm.

  10. Recognition of fractal graphs

    NARCIS (Netherlands)

    Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

    1999-01-01

    Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

  11. Interactive Graph Layout of a Million Nodes

    OpenAIRE

    Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North

    2016-01-01

    Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...

  12. RATGRAPH: Computer Graphing of Rational Functions.

    Science.gov (United States)

    Minch, Bradley A.

    1987-01-01

    Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

  13. Graph algorithms in the titan toolkit.

    Energy Technology Data Exchange (ETDEWEB)

    McLendon, William Clarence, III; Wylie, Brian Neil

    2009-10-01

    Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.

  14. A Graph Calculus for Predicate Logic

    Directory of Open Access Journals (Sweden)

    Paulo A. S. Veloso

    2013-03-01

    Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.

  15. Deep Learning with Dynamic Computation Graphs

    OpenAIRE

    Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter

    2017-01-01

    Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...

  16. Constructs for Programming with Graph Rewrites

    OpenAIRE

    Rodgers, Peter

    2000-01-01

    Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...

  17. Quantum chaos on discrete graphs

    International Nuclear Information System (INIS)

    Smilansky, Uzy

    2007-01-01

    Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)

  18. RJSplot: Interactive Graphs with R.

    Science.gov (United States)

    Barrios, David; Prieto, Carlos

    2018-03-01

    Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  19. Bipartite separability and nonlocal quantum operations on graphs

    Science.gov (United States)

    Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

    2016-07-01

    In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

  20. Intermittency and multifractional Brownian character of geomagnetic time series

    Directory of Open Access Journals (Sweden)

    G. Consolini

    2013-07-01

    Full Text Available The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008, which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.

  1. Brownian Motion of Boomerang Colloidal Particles

    Science.gov (United States)

    Wei, Qi-Huo; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Chakrabarty, Ayan

    2014-03-01

    We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

  2. Algorithms and Data Structures for Graphs

    DEFF Research Database (Denmark)

    Rotenberg, Eva

    are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...

  3. On the nullity number of graphs

    Directory of Open Access Journals (Sweden)

    Mustapha Aouchiche

    2017-10-01

    Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

  4. Graph Transforming Java Data

    NARCIS (Netherlands)

    de Mol, M.J.; Rensink, Arend; Hunt, James J.

    This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class

  5. Graph processing platforms at scale: practices and experiences

    Energy Technology Data Exchange (ETDEWEB)

    Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL

    2015-01-01

    Graph analysis unveils hidden associations of data in many phenomena and artifacts, such as road network, social networks, genomic information, and scientific collaboration. Unfortunately, a wide diversity in the characteristics of graphs and graph operations make it challenging to find a right combination of tools and implementation of algorithms to discover desired knowledge from the target data set. This study presents an extensive empirical study of three representative graph processing platforms: Pegasus, GraphX, and Urika. Each system represents a combination of options in data model, processing paradigm, and infrastructure. We benchmarked each platform using three popular graph operations, degree distribution, connected components, and PageRank over a variety of real-world graphs. Our experiments show that each graph processing platform shows different strength, depending the type of graph operations. While Urika performs the best in non-iterative operations like degree distribution, GraphX outputforms iterative operations like connected components and PageRank. In addition, we discuss challenges to optimize the performance of each platform over large scale real world graphs.

  6. Generalized hypercube graph $\\Q_n(S$, graph products and self-orthogonal codes

    Directory of Open Access Journals (Sweden)

    Pani Seneviratne

    2016-01-01

    Full Text Available A generalized hypercube graph $\\Q_n(S$ has $\\F_{2}^{n}=\\{0,1\\}^n$ as the vertex set and two vertices being adjacent whenever their mutual Hamming distance belongs to $S$, where $n \\ge 1$ and $S\\subseteq \\{1,2,\\ldots, n\\}$. The graph $\\Q_n(\\{1\\}$ is the $n$-cube, usually denoted by $\\Q_n$.We study graph boolean products $G_1 = \\Q_n(S\\times \\Q_1, G_2 = \\Q_{n}(S\\wedge \\Q_1$, $G_3 = \\Q_{n}(S[\\Q_1]$ and show that binary codes from neighborhood designs of $G_1, G_2$ and $G_3$ are self-orthogonal for all choices of $n$ and $S$. More over, we show that the class of codes $C_1$ are self-dual. Further we find subgroups of the automorphism group of these graphs and use these subgroups to obtain PD-sets for permutation decoding. As an example we find a full error-correcting PD set for the binary $[32, 16, 8]$ extremal self-dual code.

  7. Stochastic heating of a single Brownian particle by charge fluctuations in a radio-frequency produced plasma sheath

    Science.gov (United States)

    Schmidt, Christian; Piel, Alexander

    2015-10-01

    The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p-2. The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.

  8. Survey of Approaches to Generate Realistic Synthetic Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2016-10-01

    A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broad set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.

  9. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  10. Chromatic polynomials of random graphs

    International Nuclear Information System (INIS)

    Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian

    2010-01-01

    Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

  11. On some labelings of triangular snake and central graph of triangular snake graph

    Science.gov (United States)

    Agasthi, P.; Parvathi, N.

    2018-04-01

    A Triangular snake Tn is obtained from a path u 1 u 2 … u n by joining ui and u i+1 to a new vertex wi for 1≤i≤n‑1. A Central graph of Triangular snake C(T n ) is obtained by subdividing each edge of Tn exactly once and joining all the non adjacent vertices of Tn . In this paper the ways to construct square sum, square difference, Root Mean square, strongly Multiplicative, Even Mean and Odd Mean labeling for Triangular Snake and Central graph of Triangular Snake graphs are reported.

  12. Orientations of infinite graphs with prescribed edge-connectivity

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2016-01-01

    We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....

  13. Orbital diamagnetism of a charged Brownian particle undergoing birth-death process

    International Nuclear Information System (INIS)

    Jayannawar, A.M.; Kumar, N.

    1980-06-01

    We consider the magnetic response of a charged Brownian particle undergoing a stochastic birth-death process. The latter simulates the electron-hole pair production and recombination in semiconductors. We obtain non-zero, orbital diamagnetism which can be large without violating the Van Leeuwen theorem. (author)

  14. Genus Ranges of 4-Regular Rigid Vertex Graphs.

    Science.gov (United States)

    Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin

    2015-01-01

    A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 2 n vertices ( n > 1), we prove that all intervals [ a, b ] for all a genus ranges. For graphs with 2 n - 1 vertices ( n ≥ 1), we prove that all intervals [ a, b ] for all a genus ranges. We also provide constructions of graphs that realize these ranges.

  15. A new cluster algorithm for graphs

    NARCIS (Netherlands)

    S. van Dongen

    1998-01-01

    textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a

  16. Chemical Graph Transformation with Stereo-Information

    DEFF Research Database (Denmark)

    Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel

    2017-01-01

    Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...

  17. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif

    2017-01-07

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  18. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair

    2017-01-01

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  19. Graph Algorithm Animation with Grrr

    OpenAIRE

    Rodgers, Peter; Vidal, Natalia

    2000-01-01

    We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...

  20. Quantum work fluctuation theorem: Nonergodic Brownian motion case

    International Nuclear Information System (INIS)

    Bai, Zhan-Wu

    2014-01-01

    The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

  1. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    OpenAIRE

    Xiao-Li Ding; Juan J. Nieto

    2018-01-01

    In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

  2. My Bar Graph Tells a Story

    Science.gov (United States)

    McMillen, Sue; McMillen, Beth

    2010-01-01

    Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

  3. An intersection graph of straight lines

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2002-01-01

    G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....

  4. Trajectories entropy in dynamical graphs with memory

    Directory of Open Access Journals (Sweden)

    Francesco eCaravelli

    2016-04-01

    Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

  5. On revealing graph cycles via boundary measurements

    International Nuclear Information System (INIS)

    Belishev, M I; Wada, N

    2009-01-01

    This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)

  6. OPEX: Optimized Eccentricity Computation in Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2011-11-14

    Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).

  7. Pixels to Graphs by Associative Embedding

    KAUST Repository

    Newell, Alejandro

    2017-06-22

    Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.

  8. A faithful functor among algebras and graphs

    OpenAIRE

    Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)

    2016-01-01

    The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.

  9. Environmental context explains Lévy and Brownian movement patterns of marine predators.

    Science.gov (United States)

    Humphries, Nicolas E; Queiroz, Nuno; Dyer, Jennifer R M; Pade, Nicolas G; Musyl, Michael K; Schaefer, Kurt M; Fuller, Daniel W; Brunnschweiler, Juerg M; Doyle, Thomas K; Houghton, Jonathan D R; Hays, Graeme C; Jones, Catherine S; Noble, Leslie R; Wearmouth, Victoria J; Southall, Emily J; Sims, David W

    2010-06-24

    An optimal search theory, the so-called Lévy-flight foraging hypothesis, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned. Consequently, whether foragers exhibit Lévy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Lévy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Lévy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Lévy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis, supporting the contention that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.

  10. Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

    Directory of Open Access Journals (Sweden)

    Marc-Thorsten Hütt

    2012-06-01

    Full Text Available Cellular automata (CA are a remarkably  efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata,  where the update  rules depend  only on the density of neighboring states, are at the same time a versatile  tool for exploring  dynamical  processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation  towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.

  11. First passage Brownian functional properties of snowmelt dynamics

    Science.gov (United States)

    Dubey, Ashutosh; Bandyopadhyay, Malay

    2018-04-01

    In this paper, we model snow-melt dynamics in terms of a Brownian motion (BM) with purely time dependent drift and difusion and examine its first passage properties by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We introduce several probability distribution functions (PDFs) associated with such time dependent BMs. For instance, for a BM with initial starting point x0, we derive analytical expressions for : (i) the PDF P(tf|x0) of the first passage time tf which specify the lifetime of such stochastic process, (ii) the PDF P(A|x0) of the area A till the first passage time and it provides us numerous valuable information about the total fresh water availability during melting, (iii) the PDF P(M) associated with the maximum size M of the BM process before the first passage time, and (iv) the joint PDF P(M; tm) of the maximum size M and its occurrence time tm before the first passage time. These P(M) and P(M; tm) are useful in determining the time of maximum fresh water availability and in calculating the total maximum amount of available fresh water. These PDFs are examined for the power law time dependent drift and diffusion which matches quite well with the available data of snowmelt dynamics.

  12. The color space of a graph

    DEFF Research Database (Denmark)

    Jensen, T.R.; Thomassen, Carsten

    2000-01-01

    If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....

  13. Box graphs and resolutions I

    Directory of Open Access Journals (Sweden)

    Andreas P. Braun

    2016-04-01

    Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.

  14. Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations

    International Nuclear Information System (INIS)

    Yannouleas, C.

    1984-05-01

    From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)

  15. Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

    Directory of Open Access Journals (Sweden)

    Borowiecka-Olszewska Marta

    2017-05-01

    Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.

  16. 47 CFR 80.761 - Conversion graphs.

    Science.gov (United States)

    2010-10-01

    ... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...

  17. Building Scalable Knowledge Graphs for Earth Science

    Science.gov (United States)

    Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian

    2017-01-01

    Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.

  18. On the diameter of dot-critical graphs

    Directory of Open Access Journals (Sweden)

    Doost Ali Mojdeh

    2009-01-01

    Full Text Available A graph G is \\(k\\-dot-critical (totaly \\(k\\-dot-critical if \\(G\\ is dot-critical (totaly dot-critical and the domination number is \\(k\\. In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006, 11-18] the following question is posed: What are the best bounds for the diameter of a \\(k\\-dot-critical graph and a totally \\(k\\-dot-critical graph \\(G\\ with no critical vertices for \\(k \\geq 4\\? We find the best bound for the diameter of a \\(k\\-dot-critical graph, where \\(k \\in\\{4,5,6\\}\\ and we give a family of \\(k\\-dot-critical graphs (with no critical vertices with sharp diameter \\(2k-3\\ for even \\(k \\geq 4\\.

  19. graphkernels: R and Python packages for graph comparison.

    Science.gov (United States)

    Sugiyama, Mahito; Ghisu, M Elisabetta; Llinares-López, Felipe; Borgwardt, Karsten

    2018-02-01

    Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch. Supplementary data are available online at Bioinformatics. © The Author(s) 2017. Published by Oxford University Press.

  20. Brownian dynamics of aggregation kinetics of hard spheres with flexibele bounds

    NARCIS (Netherlands)

    Rzepiela, A.A.; Opheusden, van J.; Vliet, van T.

    2001-01-01

    Brownian dynamics (BD) simulations have been performed on the aggregation dynamics of colloidal particles within the context of a ball-and-string model. Particles are treated as hard spheres that can bind irreversibly through a string attached to their surface. The model is set up to mimic some

  1. Graph anomalies in cyber communications

    Energy Technology Data Exchange (ETDEWEB)

    Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory

    2011-01-11

    Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.

  2. Graphs, groups and surfaces

    CERN Document Server

    White, AT

    1985-01-01

    The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.

  3. Subdominant pseudoultrametric on graphs

    Energy Technology Data Exchange (ETDEWEB)

    Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

    2013-08-31

    Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

  4. Equitable Colorings Of Corona Multiproducts Of Graphs

    Directory of Open Access Journals (Sweden)

    Furmánczyk Hanna

    2017-11-01

    Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].

  5. Experimental measurement of efficiency and transport coherence of a cold-atom Brownian motor in optical lattices.

    Science.gov (United States)

    Zelan, M; Hagman, H; Labaigt, G; Jonsell, S; Dion, C M

    2011-02-01

    The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.

  6. Sphere and dot product representations of graphs

    NARCIS (Netherlands)

    R.J. Kang (Ross); T. Müller (Tobias)

    2012-01-01

    textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such

  7. The relativistic Brownian motion: Interdisciplinary applications

    International Nuclear Information System (INIS)

    Aragones-Munoz, A; Sandoval-Villalbazo, A

    2010-01-01

    Relativistic Brownian motion theory will be applied to the study of analogies between physical and economic systems, emphasizing limiting cases in which Gaussian distributions are no longer valid. The characteristic temperatures of the particles will be associated with the concept of variance, and this will allow us to choose whether the pertinent distribution is classical or relativistic, while working specific situations. The properties of particles can be interpreted as economic variables, in order to study the behavior of markets in terms of Levy financial processes, since markets behave as stochastic systems. As far as we know, the application of the Juettner distribution to the study of economic systems is a new idea.

  8. Graph Query Portal

    OpenAIRE

    Dayal, Amit; Brock, David

    2018-01-01

    Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...

  9. An Association-Oriented Partitioning Approach for Streaming Graph Query

    Directory of Open Access Journals (Sweden)

    Yun Hao

    2017-01-01

    Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.

  10. A comparative study of applying Mason’s Rule in the case of flow-graphs and bond-graphs

    Directory of Open Access Journals (Sweden)

    Adriana Grava

    2009-05-01

    Full Text Available The paper presents two methods to analyzethe electric circuits using the flow-graphs and thebond-graphs studying the differences between thesemethods.As it can be noticed, the two methods are totallydifferent; their common point being Mason’s rule thatis applied in both cases but it is applied differently foreach type of graphs.

  11. An algebraic approach to graph codes

    DEFF Research Database (Denmark)

    Pinero, Fernando

    This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...

  12. Replica methods for loopy sparse random graphs

    International Nuclear Information System (INIS)

    Coolen, ACC

    2016-01-01

    I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

  13. The STAPL Parallel Graph Library

    KAUST Repository

    Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence

    2013-01-01

    This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable

  14. Coloring and The Lonely Graph

    OpenAIRE

    Rabern, Landon

    2007-01-01

    We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...

  15. Graph Mining Meets the Semantic Web

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL

    2015-01-01

    The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.

  16. A model of language inflection graphs

    Science.gov (United States)

    Fukś, Henryk; Farzad, Babak; Cao, Yi

    2014-01-01

    Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

  17. Incremental Frequent Subgraph Mining on Large Evolving Graphs

    KAUST Repository

    Abdelhamid, Ehab

    2017-08-22

    Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.

  18. Smooth Bundling of Large Streaming and Sequence Graphs

    NARCIS (Netherlands)

    Hurter, C.; Ersoy, O.; Telea, A.

    2013-01-01

    Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling

  19. The groupies of random multipartite graphs

    OpenAIRE

    Portmann, Marius; Wang, Hongyun

    2012-01-01

    If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.

  20. Brownian motion after Einstein and Smoluchowski: Some new applications and new experiments

    DEFF Research Database (Denmark)

    Dávid, Selmeczi; Tolic-Nørrelykke, S.F.; Schäffer, E.

    2007-01-01

    The first half of this review describes the development in mathematical models of Brownian motion after Einstein's and Smoluchowski's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of such precision ...

  1. Velocity persistence of Brownian particles generated in a glow discharge

    International Nuclear Information System (INIS)

    Hurd, A.J.; Ho, P.

    1989-01-01

    Quasielastic light scattering from Brownian particles in the rarefied environment of a glow discharge exhibits Gaussianlike intensity correlation functions owing to the long mean free paths of the particles. The shape of the correlation function depends on the particles' average thermal velocity and friction coefficient, which can be related to aggregate mass and structure, and indicates a crossover from kinetic to hydrodynamic behavior

  2. Open Graphs and Computational Reasoning

    Directory of Open Access Journals (Sweden)

    Lucas Dixon

    2010-06-01

    Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

  3. Properly colored connectivity of graphs

    CERN Document Server

    Li, Xueliang; Qin, Zhongmei

    2018-01-01

    A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.

  4. On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

    Energy Technology Data Exchange (ETDEWEB)

    Hiotelis, Nicos [1st Lyceum of Athens, Ipitou 15, Plaka, 10557, Athens (Greece); Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr [Dipartimento di Fisica e Astronomia, University Of Catania, Viale Andrea Doria 6, 95125, Catania (Italy)

    2017-03-01

    We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.

  5. Inferring ontology graph structures using OWL reasoning

    KAUST Repository

    Rodriguez-Garcia, Miguel Angel

    2018-01-05

    Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

  6. Inferring ontology graph structures using OWL reasoning.

    Science.gov (United States)

    Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

    2018-01-05

    Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

  7. Optical generation of matter qubit graph states

    International Nuclear Information System (INIS)

    Benjamin, S C; Eisert, J; Stace, T M

    2005-01-01

    We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus

  8. XML Graphs in Program Analysis

    DEFF Research Database (Denmark)

    Møller, Anders; Schwartzbach, Michael I.

    2011-01-01

    of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...

  9. Graphs with Eulerian unit spheres

    OpenAIRE

    Knill, Oliver

    2015-01-01

    d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...

  10. An adjustable Brownian heat engine

    International Nuclear Information System (INIS)

    Asfaw, Mesfin; Bekele, Mulugeta

    2002-09-01

    A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found a closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs either with maximum power or with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines. (author)

  11. The Container Problem in Bubble-Sort Graphs

    Science.gov (United States)

    Suzuki, Yasuto; Kaneko, Keiichi

    Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

  12. The many faces of graph dynamics

    Science.gov (United States)

    Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

    2017-06-01

    The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

  13. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector

    2017-07-08

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure\\'s range of applications and demonstrating the weaknesses of computable measures of complexity.

  14. Multiple graph regularized nonnegative matrix factorization

    KAUST Repository

    Wang, Jim Jing-Yan

    2013-10-01

    Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.

  15. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

    2017-01-01

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

  16. Graph Sampling for Covariance Estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2017-01-01

    specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non

  17. Particle transport in breathing quantum graph

    International Nuclear Information System (INIS)

    Matrasulov, D.U.; Yusupov, J.R.; Sabirov, K.K.; Sobirov, Z.A.

    2012-01-01

    Full text: Particle transport in nanoscale networks and discrete structures is of fundamental and practical importance. Usually such systems are modeled by so-called quantum graphs, the systems attracting much attention in physics and mathematics during past two decades [1-5]. During last two decades quantum graphs found numerous applications in modeling different discrete structures and networks in nanoscale and mesoscopic physics (e.g., see reviews [1-3]). Despite considerable progress made in the study of particle dynamics most of the problems deal with unperturbed case and the case of time-dependent perturbation has not yet be explored. In this work we treat particle dynamics for quantum star graph with time-dependent bonds. In particular, we consider harmonically breathing quantum star graphs, the cases of monotonically contracting and expanding graphs. The latter can be solved exactly analytically. Edge boundaries are considered to be time-dependent, while branching point is assumed to be fixed. Quantum dynamics of a particle in such graphs is studied by solving Schrodinger equation with time-dependent boundary conditions given on a star graph. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph. It is found that for certain frequencies energy is a periodic function of time, while for others it can be non-monotonically growing function of time. Such a feature can be caused by possible synchronization of the particles motion and the motions of the moving edges of graph bonds. (authors) References: [1] Tsampikos Kottos and Uzy Smilansky, Ann. Phys., 76, 274 (1999). [2] Sven Gnutzmann and Uzy Smilansky, Adv. Phys. 55, 527 (2006). [3] S. GnutzmannJ.P. Keating, F. Piotet, Ann. Phys., 325, 2595 (2010). [4] P.Exner, P.Seba, P.Stovicek, J. Phys. A: Math. Gen. 21, 4009 (1988). [5] J. Boman, P. Kurasov, Adv. Appl. Math., 35, 58 (2005)

  18. One-dimensional Brownian motion of charged nanoparticles along microtubules: a model system for weak binding interactions.

    Science.gov (United States)

    Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

    2010-04-21

    Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  19. Interacting particle systems on graphs

    Science.gov (United States)

    Sood, Vishal

    In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations

  20. Transduction on Directed Graphs via Absorbing Random Walks.

    Science.gov (United States)

    De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li

    2017-08-11

    In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.

  1. High-performance analysis of filtered semantic graphs

    OpenAIRE

    Buluç, A; Fox, A; Gilbert, JR; Kamil, S; Lugowski, A; Oliker, L; Williams, S

    2012-01-01

    High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry \\attributes" of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must either view the graph through a filter that passes only those individual vertices and edges of interest, or else must first materialize a subgraph or subgraphs consisting of only the vertices ...

  2. Bond graph modeling of centrifugal compression systems

    OpenAIRE

    Uddin, Nur; Gravdahl, Jan Tommy

    2015-01-01

    A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...

  3. On the local edge antimagicness of m-splitting graphs

    Science.gov (United States)

    Albirri, E. R.; Dafik; Slamin; Agustin, I. H.; Alfarisi, R.

    2018-04-01

    Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v‧ in every vertex v‧ such that v‧ adjacent to v in graph G. An m-splitting graph is a graph which has m v‧-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V, E) graph is a bijection f:V (G)\\to \\{1,2,3,\\ldots,|V(G)|\\} in which for any two adjacent edges e 1 and e 2 satisfies w({e}1)\

  4. Augmented marked graphs

    CERN Document Server

    Cheung, King Sing

    2014-01-01

    Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume

  5. Co-Roman domination in graphs

    Indian Academy of Sciences (India)

    1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.

  6. Nested Dynamic Condition Response Graphs

    DEFF Research Database (Denmark)

    Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs

    2012-01-01

    We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...

  7. A cluster algorithm for graphs

    NARCIS (Netherlands)

    S. van Dongen

    2000-01-01

    textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)

  8. Generating random networks and graphs

    CERN Document Server

    Coolen, Ton; Roberts, Ekaterina

    2017-01-01

    This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...

  9. On the Recognition of Fuzzy Circular Interval Graphs

    OpenAIRE

    Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier

    2011-01-01

    Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

  10. The Thickness of Amalgamations and Cartesian Product of Graphs

    Directory of Open Access Journals (Sweden)

    Yang Yan

    2017-08-01

    Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.

  11. Generating Realistic Labelled, Weighted Random Graphs

    Directory of Open Access Journals (Sweden)

    Michael Charles Davis

    2015-12-01

    Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

  12. On The Roman Domination Stable Graphs

    Directory of Open Access Journals (Sweden)

    Hajian Majid

    2017-11-01

    Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].

  13. Disease management research using event graphs.

    Science.gov (United States)

    Allore, H G; Schruben, L W

    2000-08-01

    Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.

  14. Measuring Two-Event Structural Correlations on Graphs

    Science.gov (United States)

    2012-08-01

    2012 to 00-00-2012 4. TITLE AND SUBTITLE Measuring Two-Event Structural Correlations on Graphs 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ...by event simulation on the DBLP graph. Then we examine the efficiency and scala - bility of the framework with a Twitter network. The third part of...correlation pattern mining for large graphs. In Proc. of the 8th Workshop on Mining and Learning with Graphs, pages 119–126, 2010. [23] T. Smith. A

  15. Reconstructing Nearly Simple Polytopes from their Graph

    OpenAIRE

    Doolittle, Joseph

    2017-01-01

    We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...

  16. Hierarchical organisation of causal graphs

    International Nuclear Information System (INIS)

    Dziopa, P.

    1993-01-01

    This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs

  17. Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion

    Directory of Open Access Journals (Sweden)

    Didier Kumwimba Seya

    2015-11-01

    Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.

  18. Graph Transformation Semantics for a QVT Language

    NARCIS (Netherlands)

    Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel

    It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to

  19. Modeling Software Evolution using Algebraic Graph Rewriting

    NARCIS (Netherlands)

    Ciraci, Selim; van den Broek, Pim

    We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the

  20. Cycles in weighted graphs and related topics

    NARCIS (Netherlands)

    Zhang, Shenggui

    2002-01-01

    This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain