Propagator of stochastic electrodynamics
International Nuclear Information System (INIS)
Cavalleri, G.
1981-01-01
The ''elementary propagator'' for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density proportionalω 3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to psipsi* where psi is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics
The propagator of stochastic electrodynamics
Cavalleri, G.
1981-01-01
The "elementary propagator" for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density ~ω3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to ψψ* where ψ is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics.
On the power propagation time of a graph
Bozeman, Chassidy
2016-01-01
In this paper, we give Nordhaus-Gaddum upper and lower bounds on the sum of the power propagation time of a graph and its complement, and we consider the effects of edge subdivisions and edge contractions on the power propagation time of a graph. We also study a generalization of power propagation time, known as $k-$power propagation time, by characterizing all simple graphs on $n$ vertices whose $k-$power propagation time is $n-1$ or $n-2$ (for $k\\geq 1$) and $n-3$ (for $k\\geq 2$). We determ...
Generalized belief propagation on tree robust structured region graphs
Gelfand, A.E.; Welling, M.; Murphy, K.; de Freitas, N.
2012-01-01
This paper provides some new guidance in the construction of region graphs for Generalized Belief Propagation (GBP). We connect the problem of choosing the outer regions of a LoopStructured Region Graph (SRG) to that of finding a fundamental cycle basis of the corresponding Markov network. We also
Equivalence of massive propagator distance and mathematical distance on graphs
International Nuclear Information System (INIS)
Filk, T.
1992-01-01
It is shown in this paper that the assignment of distance according to the massive propagator method and according to the mathematical definition (length of minimal path) on arbitrary graphs with a bound on the degree leads to equivalent large scale properties of the graph. Especially, the internal scaling dimension is the same for both definitions. This result holds for any fixed, non-vanishing mass, so that a really inequivalent definition of distance requires the limit m → 0
Front Propagation in Stochastic Neural Fields
Bressloff, Paul C.
2012-01-01
We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.
Stochastic and epistemic uncertainty propagation in LCA
DEFF Research Database (Denmark)
Clavreul, Julie; Guyonnet, Dominique; Tonini, Davide
2013-01-01
of epistemic uncertainty representation using fuzzy intervals. The propagation methods used are the Monte Carlo analysis for probability distribution and an optimisation on alpha-cuts for fuzzy intervals. The proposed method (noted as Independent Random Set, IRS) generalizes the process of random sampling...... to probability distributions as well as fuzzy intervals, thus making the simultaneous use of both representations possible.The results highlight the fundamental difference between the probabilistic and possibilistic representations: while the Monte Carlo analysis generates a single probability distribution...... or expert judgement (epistemic uncertainty). The possibility theory has been developed over the last decades to address this problem. The objective of this study is to present a methodology that combines probability and possibility theories to represent stochastic and epistemic uncertainties in a consistent...
A scalable community detection algorithm for large graphs using stochastic block models
Peng, Chengbin
2017-11-24
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of
A scalable community detection algorithm for large graphs using stochastic block models
Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.
2017-01-01
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of
Belief propagation and loop series on planar graphs
International Nuclear Information System (INIS)
Chertkov, Michael; Teodorescu, Razvan; Chernyak, Vladimir Y
2008-01-01
We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R) [cond-mat/0601487]; 2006 J. Stat. Mech. P06009 [cond-mat/0603189]) is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation (Fisher 1961 Phys. Rev. 124 1664), to evaluating the partition function of the dimer-matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn (1961 Physics 27 1209). This allows us to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed
Stochastic Systems Uncertainty Quantification and Propagation
Grigoriu, Mircea
2012-01-01
Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: · A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis · Probabilistic models for random variables an...
Image interpolation via graph-based Bayesian label propagation.
Xianming Liu; Debin Zhao; Jiantao Zhou; Wen Gao; Huifang Sun
2014-03-01
In this paper, we propose a novel image interpolation algorithm via graph-based Bayesian label propagation. The basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices, then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones. This process can be posed as a Bayesian inference, in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation. Specially, our algorithm first constructs a set of local interpolation models, which predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of the available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Moreover, a graph-Laplacian-based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the global loss of the locally linear regression, square error of prediction bias on the available LR samples, and the manifold regularization term. It can be solved with a closed-form solution as a convex optimization problem. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art image interpolation algorithms.
Front Propagation in Stochastic Neural Fields
Bressloff, Paul C.; Webber, Matthew A.
2012-01-01
We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement
Ion stochastic heating by obliquely propagating magnetosonic waves
International Nuclear Information System (INIS)
Gao Xinliang; Lu Quanming; Wu Mingyu; Wang Shui
2012-01-01
The ion motions in obliquely propagating Alfven waves with sufficiently large amplitudes have already been studied by Chen et al.[Phys. Plasmas 8, 4713 (2001)], and it was found that the ion motions are stochastic when the wave frequency is at a fraction of the ion gyro-frequency. In this paper, with test particle simulations, we investigate the ion motions in obliquely propagating magnetosonic waves and find that the ion motions also become stochastic when the amplitude of the magnetosonic waves is sufficiently large due to the resonance at sub-cyclotron frequencies. Similar to the Alfven wave, the increase of the propagating angle, wave frequency, and the number of the wave modes can lower the stochastic threshold of the ion motions. However, because the magnetosonic waves become more and more compressive with the increase of the propagating angle, the decrease of the stochastic threshold with the increase of the propagating angle is more obvious in the magnetosonic waves than that in the Alfven waves.
Dynamic analysis of a stochastic delayed rumor propagation model
Jia, Fangju; Lv, Guangying; Wang, Shuangfeng; Zou, Guang-an
2018-02-01
The rapid development of the Internet, especially the emergence of the social networks, has led rumor propagation into a new media era. In this paper, we are concerned with a stochastic delayed rumor propagation model. Firstly, we obtain the existence of the global solution. Secondly, sufficient conditions for extinction of the rumor are established. Lastly, the boundedness of solution is proved and some simulations are given to verify our results.
Front propagation and clustering in the stochastic nonlocal Fisher equation
Ganan, Yehuda A.; Kessler, David A.
2018-04-01
In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.
Expectation propagation for continuous time stochastic processes
International Nuclear Information System (INIS)
Cseke, Botond; Schnoerr, David; Sanguinetti, Guido; Opper, Manfred
2016-01-01
We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems. (paper)
Dynamic analysis of a stochastic rumor propagation model
Jia, Fangju; Lv, Guangying
2018-01-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
PROPAGATOR: a synchronous stochastic wildfire propagation model with distributed computation engine
D´Andrea, M.; Fiorucci, P.; Biondi, G.; Negro, D.
2012-04-01
PROPAGATOR is a stochastic model of forest fire spread, useful as a rapid method for fire risk assessment. The model is based on a 2D stochastic cellular automaton. The domain of simulation is discretized using a square regular grid with cell size of 20x20 meters. The model uses high-resolution information such as elevation and type of vegetation on the ground. Input parameters are wind direction, speed and the ignition point of fire. The simulation of fire propagation is done via a stochastic mechanism of propagation between a burning cell and a non-burning cell belonging to its neighbourhood, i.e. the 8 adjacent cells in the rectangular grid. The fire spreads from one cell to its neighbours with a certain base probability, defined using vegetation types of two adjacent cells, and modified by taking into account the slope between them, wind direction and speed. The simulation is synchronous, and takes into account the time needed by the burning fire to cross each cell. Vegetation cover, slope, wind speed and direction affect the fire-propagation speed from cell to cell. The model simulates several mutually independent realizations of the same stochastic fire propagation process. Each of them provides a map of the area burned at each simulation time step. Propagator simulates self-extinction of the fire, and the propagation process continues until at least one cell of the domain is burning in each realization. The output of the model is a series of maps representing the probability of each cell of the domain to be affected by the fire at each time-step: these probabilities are obtained by evaluating the relative frequency of ignition of each cell with respect to the complete set of simulations. Propagator is available as a module in the OWIS (Opera Web Interfaces) system. The model simulation runs on a dedicated server and it is remote controlled from the client program, NAZCA. Ignition points of the simulation can be selected directly in a high-resolution, three
Simulating activation propagation in social networks using the graph theory
Directory of Open Access Journals (Sweden)
František Dařena
2010-01-01
Full Text Available The social-network formation and analysis is nowadays one of objects that are in a focus of intensive research. The objective of the paper is to suggest the perspective of representing social networks as graphs, with the application of the graph theory to problems connected with studying the network-like structures and to study spreading activation algorithm for reasons of analyzing these structures. The paper presents the process of modeling multidimensional networks by means of directed graphs with several characteristics. The paper also demonstrates using Spreading Activation algorithm as a good method for analyzing multidimensional network with the main focus on recommender systems. The experiments showed that the choice of parameters of the algorithm is crucial, that some kind of constraint should be included and that the algorithm is able to provide a stable environment for simulations with networks.
iBGP: A Bipartite Graph Propagation Approach for Mobile Advertising Fraud Detection
Directory of Open Access Journals (Sweden)
Jinlong Hu
2017-01-01
Full Text Available Online mobile advertising plays a vital financial role in supporting free mobile apps, but detecting malicious apps publishers who generate fraudulent actions on the advertisements hosted on their apps is difficult, since fraudulent traffic often mimics behaviors of legitimate users and evolves rapidly. In this paper, we propose a novel bipartite graph-based propagation approach, iBGP, for mobile apps advertising fraud detection in large advertising system. We exploit the characteristics of mobile advertising user’s behavior and identify two persistent patterns: power law distribution and pertinence and propose an automatic initial score learning algorithm to formulate both concepts to learn the initial scores of non-seed nodes. We propose a weighted graph propagation algorithm to propagate the scores of all nodes in the user-app bipartite graphs until convergence. To extend our approach for large-scale settings, we decompose the objective function of the initial score learning model into separate one-dimensional problems and parallelize the whole approach on an Apache Spark cluster. iBGP was applied on a large synthetic dataset and a large real-world mobile advertising dataset; experiment results demonstrate that iBGP significantly outperforms other popular graph-based propagation methods.
Inferior vena cava segmentation with parameter propagation and graph cut.
Yan, Zixu; Chen, Feng; Wu, Fa; Kong, Dexing
2017-09-01
The inferior vena cava (IVC) is one of the vital veins inside the human body. Accurate segmentation of the IVC from contrast-enhanced CT images is of great importance. This extraction not only helps the physician understand its quantitative features such as blood flow and volume, but also it is helpful during the hepatic preoperative planning. However, manual delineation of the IVC is time-consuming and poorly reproducible. In this paper, we propose a novel method to segment the IVC with minimal user interaction. The proposed method performs the segmentation block by block between user-specified beginning and end masks. At each stage, the proposed method builds the segmentation model based on information from image regional appearances, image boundaries, and a prior shape. The intensity range and the prior shape for this segmentation model are estimated based on the segmentation result from the last block, or from user- specified beginning mask if at first stage. Then, the proposed method minimizes the energy function and generates the segmentation result for current block using graph cut. Finally, a backward tracking step from the end of the IVC is performed if necessary. We have tested our method on 20 clinical datasets and compared our method to three other vessel extraction approaches. The evaluation was performed using three quantitative metrics: the Dice coefficient (Dice), the mean symmetric distance (MSD), and the Hausdorff distance (MaxD). The proposed method has achieved a Dice of [Formula: see text], an MSD of [Formula: see text] mm, and a MaxD of [Formula: see text] mm, respectively, in our experiments. The proposed approach can achieve a sound performance with a relatively low computational cost and a minimal user interaction. The proposed algorithm has high potential to be applied for the clinical applications in the future.
Stochastic Models for Laser Propagation in Atmospheric Turbulence.
Leland, Robert Patton
In this dissertation, stochastic models for laser propagation in atmospheric turbulence are considered. A review of the existing literature on laser propagation in the atmosphere and white noise theory is presented, with a view toward relating the white noise integral and Ito integral approaches. The laser beam intensity is considered as the solution to a random Schroedinger equation, or forward scattering equation. This model is formulated in a Hilbert space context as an abstract bilinear system with a multiplicative white noise input, as in the literature. The model is also modeled in the Banach space of Fresnel class functions to allow the plane wave case and the application of path integrals. Approximate solutions to the Schroedinger equation of the Trotter-Kato product form are shown to converge for each white noise sample path. The product forms are shown to be physical random variables, allowing an Ito integral representation. The corresponding Ito integrals are shown to converge in mean square, providing a white noise basis for the Stratonovich correction term associated with this equation. Product form solutions for Ornstein -Uhlenbeck process inputs were shown to converge in mean square as the input bandwidth was expanded. A digital simulation of laser propagation in strong turbulence was used to study properties of the beam. Empirical distributions for the irradiance function were estimated from simulated data, and the log-normal and Rice-Nakagami distributions predicted by the classical perturbation methods were seen to be inadequate. A gamma distribution fit the simulated irradiance distribution well in the vicinity of the boresight. Statistics of the beam were seen to converge rapidly as the bandwidth of an Ornstein-Uhlenbeck process was expanded to its white noise limit. Individual trajectories of the beam were presented to illustrate the distortion and bending of the beam due to turbulence. Feynman path integrals were used to calculate an
Agha-mohammadi, Ali-akbar
2013-06-01
This paper is concerned with the problem of stochastic optimal control (possibly with imperfect measurements) in the presence of constraints. We propose a computationally tractable framework to address this problem. The method lends itself to sampling-based methods where we construct a graph in the state space of the problem, on which a Dynamic Programming (DP) is solved and a closed-loop feedback policy is computed. The constraints are seamlessly incorporated to the control policy selection by including their effect on the transition probabilities of the graph edges. We present a unified framework that is applicable both in the state space (with perfect measurements) and in the information space (with imperfect measurements).
iBGP: A Bipartite Graph Propagation Approach for Mobile Advertising Fraud Detection
Hu, Jinlong; Liang, Junjie; Dong, Shoubin
2017-01-01
Online mobile advertising plays a vital financial role in supporting free mobile apps, but detecting malicious apps publishers who generate fraudulent actions on the advertisements hosted on their apps is difficult, since fraudulent traffic often mimics behaviors of legitimate users and evolves rapidly. In this paper, we propose a novel bipartite graph-based propagation approach, iBGP, for mobile apps advertising fraud detection in large advertising system. We exploit the characteristics of m...
Acoustic wave propagation and stochastic effects in metamaterial absorbers
DEFF Research Database (Denmark)
Christensen, Johan; Willatzen, Morten
2014-01-01
We show how stochastic variations of the effective parameters of anisotropic structured metamaterials can lead to increased absorption of sound. For this, we derive an analytical model based on the Bourret approximation and illustrate the immediate connection between material disorder and attenua...
The propagation of travelling waves for stochastic generalized KPP equations
International Nuclear Information System (INIS)
Elworthy, K.D.; Zhao, H.Z.
1993-09-01
We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs
Spectral changes in stochastic anisotropic electromagnetic beams propagating through turbulent ocean
Tang, Miaomiao; Zhao, Daomu
2014-02-01
Based on the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light, the spectral changes of stochastic anisotropic electromagnetic beams propagating through oceanic turbulence are revealed. As an example, some numerical calculations are illustrated for an anisotropic electromagnetic Gaussian Schell-model beam propagating in a homogeneous and isotropic turbulent ocean. It is shown that, under the influence of oceanic turbulence, the on-axis spectrum is always blue-shifted along with the propagation distance, however, for the off-axis positions, red-blue spectral switch can be found.
On the relationship between Gaussian stochastic blockmodels and label propagation algorithms
International Nuclear Information System (INIS)
Zhang, Junhao; Hu, Junfeng; Chen, Tongfei
2015-01-01
The problem of community detection has received great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to fit weight of edges in networks for non-overlapping community detection. The maximum likelihood estimation of this model has the same objective function as general label propagation with node preference. The node preference of a specific vertex turns out to be a value proportional to the intra-community eigenvector centrality (the corresponding entry in principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community) under maximum likelihood estimation. Additionally, the maximum likelihood estimation of a constrained version of our model is highly related to another extension of the label propagation algorithm, namely, the label propagation algorithm under constraint. Experiments show that the proposed Gaussian stochastic blockmodel performs well on various benchmark networks. (paper)
Mariano-Goulart, D; Fourcade, M; Bernon, J L; Rossi, M; Zanca, M
2003-01-01
Thanks to an experimental study based on simulated and physical phantoms, the propagation of the stochastic noise in slices reconstructed using the conjugate gradient algorithm has been analysed versus iterations. After a first increase corresponding to the reconstruction of the signal, the noise stabilises before increasing linearly with iterations. The level of the plateau as well as the slope of the subsequent linear increase depends on the noise in the projection data.
Directory of Open Access Journals (Sweden)
Deborah A Striegel
2015-08-01
Full Text Available Pancreatic islets of Langerhans consist of endocrine cells, primarily α, β and δ cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. β cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Due to the central functional significance of this local connectivity in the placement of β cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of β cells in an islet requires mathematical methods that can capture topological connectivity in the entire β-cell population in an islet. Graph theory provides such a framework. Using large-scale imaging data for thousands of islets containing hundreds of thousands of cells in human organ donor pancreata, we show that quantitative graph characteristics differ between control and type 2 diabetic islets. Further insight into the processes that shape and maintain this architecture is obtained by formulating a stochastic theory of β-cell rearrangement in whole islets, just as the normal equilibrium distribution of the Ornstein-Uhlenbeck process can be viewed as the result of the interplay between a random walk and a linear restoring force. Requiring that rearrangements maintain the observed quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that β-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets.
Striegel, Deborah A; Hara, Manami; Periwal, Vipul
2015-08-01
Pancreatic islets of Langerhans consist of endocrine cells, primarily α, β and δ cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. β cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Due to the central functional significance of this local connectivity in the placement of β cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of β cells in an islet requires mathematical methods that can capture topological connectivity in the entire β-cell population in an islet. Graph theory provides such a framework. Using large-scale imaging data for thousands of islets containing hundreds of thousands of cells in human organ donor pancreata, we show that quantitative graph characteristics differ between control and type 2 diabetic islets. Further insight into the processes that shape and maintain this architecture is obtained by formulating a stochastic theory of β-cell rearrangement in whole islets, just as the normal equilibrium distribution of the Ornstein-Uhlenbeck process can be viewed as the result of the interplay between a random walk and a linear restoring force. Requiring that rearrangements maintain the observed quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that β-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets.
Front propagation and effect of memory in stochastic desertification models with an absorbing state
Herman, Dor; Shnerb, Nadav M.
2017-08-01
Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.
Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues
Energy Technology Data Exchange (ETDEWEB)
Luo, Meilan; Chen, Qi; Hua, Limin; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com
2014-01-10
The general analytical expression of the stochastic electromagnetic vortex beams through turbulent biological tissues is derived based on the fractal model. The statistical properties, including the spectral density, the spectral degree of coherence and the spectral degree of polarization are investigated in detail. It can be found that the normalized spectral density of the stochastic electromagnetic vortex beams with higher topological charge is less influenced by turbulence than that with lower topological charge. In addition, the change of the degree of polarization versus propagation distance of the anisotropic vortex beams in biological tissues differs from that of the isotropic vortex beams. The findings might be useful in the investigation of the structures of biological tissues and operation of communication and sensing systems involving biological tissues turbulence channels.
Suppression of propagating TE modes in the FNAL antiproton source stochastic beam cooling system
International Nuclear Information System (INIS)
Barry, W.C.
1985-05-01
A method of attenuating the propagation of waveguide modes in the stochastic cooling array beam pipes to be utilized in the accumulator and debuncher rings of the Fermilab antiproton source is described. The attenuation method treated involves lining the vertical walls of the beam pipes with a ferrimagnetic material. The general solution for propagation in a nonhomogeneously loaded waveguide is presented along with numerical results specific to the antiproton source beam cooling system. Also described is a broadband, automated technique for the simultaneous measurement of complex μ and epsilon developed to aid in the characterization of different ferrite materials. Permittivity and permeability data for a typical ferrite are presented along with a discussion of the effects of these parameters on waveguide mode attenuation in the ferrite lined beam pipes
International Nuclear Information System (INIS)
De Santis, Emilio; Marinelli, Carlo
2007-01-01
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume
Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fraction of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.
Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
International Nuclear Information System (INIS)
Morningstar, C.; Lenkner, D.; Wong, C.H.; Bulava, J.; Foley, J.; Juge, K.J.; Peardon, M.
2011-08-01
A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. Z N noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I=0,1,2 on large anisotropic 24 3 x 128 lattices with spatial spacing a s ∝0.12 fm and temporal spacing a t ∝0.034 fm for pion masses m π ∼ 390 and 240 MeV. (orig.)
Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Morningstar, C.; Lenkner, D.; Wong, C.H. [Pittsburgh Univ., PA (United States). Dept. of Physics; Bulava, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Foley, J. [Utah Univ., Salt Lake City, UT (United States). Dept. of Physics and Astronomy; Juge, K.J. [University of the Pacific, Stockton, CA (United States). Dept. of Physics; Peardon, M. [Trinity College, Dublin (Ireland). School of Mathematics
2011-08-15
A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. Z{sub N} noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I=0,1,2 on large anisotropic 24{sup 3} x 128 lattices with spatial spacing a{sub s} {proportional_to}0.12 fm and temporal spacing a{sub t} {proportional_to}0.034 fm for pion masses m{sub {pi}} {approx} 390 and 240 MeV. (orig.)
Stochastic self-propagating star formation in three-dimensional disk galaxy simulations
International Nuclear Information System (INIS)
Statler, T.; Comins, N.; Smith, B.F.
1983-01-01
Stochastic self-propagating star formation (SSPSF) is a process of forming new stars through the compression of the interstellar medium by supernova shock waves. Coupling this activity with galactic differential rotation produces spiral structure in two-dimensional disk galaxy simulations. In this paper the first results of a three-dimensional SSPSF simulation of disk galaxies are reported. Our model generates less impressive spirals than do the two-dimensional simulations. Although some spirals do appear in equilibrium, more frequently we observe spirals as non-equilibrium states of the models: as the spiral arms evolve, they widen until the spiral structure is no longer discernible. The two free parameters that we vary in this study are the probability of star formation due to a recent, nearby explosion, and the relaxation time for the interstellar medium to return to a condition of maximum star formation after it has been cleared out by an explosion and subsequent star formation. We find that equilibrium spiral structure is formed over a much smaller range of these parameters in our three-dimensional SSPSF models than in similar two-dimensional models. We discuss possible reasons for these results as well as improvements on the model which are being explored
Preston, L. A.
2017-12-01
Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories
A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
Malenova, G.; Motamed, M.; Runborg, O.; Tempone, Raul
2016-01-01
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.
A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
Malenova, G.
2016-09-08
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.
International Nuclear Information System (INIS)
Holden, J.E.; Halama, J.R.; Hasegawa, B.H.
1986-01-01
The use of Fourier analysis in nuclear medicine gated blood ventriculography provides a useful example of the application of Fourier methods to digital medical imaging. In particular, the nuclear medicine experience demonstrates that there is diagnostic significance not only in the pixel averages of temporal Fourier magnitude and phase computed in various image regions, but also in the distributions of the individual pixel values about those averages. However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values. The authors have studied this noise component of both the magnitude and phase distributions using phantom studies and computer simulation. In both approaches, several thousand one-pixel 'ventriculograms' were generated, all identical to each other except for stochastic noise. Fourier magnitudes and phases at several frequencies were calculated and histograms generated. A theoretical prediction of the distributions was developed and shown to fit the experimental results well. The authors' formalism can be used to estimate study count requirements or, for fixed study counts, to assess the stochastic noise contribution in the interpretation of measured phase and magnitude distributions. (author)
A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks
Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed
2015-01-01
We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056
Méndez, Vicenç; Bartumeus, Frederic
2014-01-01
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies. Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems. Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mat...
Propagation of mechanical waves through a stochastic medium with spherical symmetry
Avendaño, Carlos G.; Reyes, J. Adrián
2018-01-01
We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.
International Nuclear Information System (INIS)
Davis, A. B.
2007-01-01
A simple and effective framework is presented for modeling transport processes unfolding at computationally and/or observationally unresolved scales in scattering, absorbing and emitting media. The new approach acts directly on the spatial (i.e., propagation) part of the kernel in the integral formulation of the generic linear transport equation framed for stochastic media with a wide variety of spatial correlations, going far beyond the Markov-Poisson class used in the classic Pomraning-Levermore model. This statistical look at the extinction of un-collided particle beams takes us away from the standard exponential law of transmission. New transmission laws arise that are generally not exponential, often not even for asymptotically large jumps. This means that, from this perspective on random spatial variability, there is no 'effective medium' per se nor homogenization technique that can be used to describe the effects of unresolved fluctuations of the collision coefficient. However, one can still rewrite the transport equation, at least in its integral form, in a manner that looks like its counterpart for uniform media, but with a modified propagation kernel. Implementation in a Monte Carlo scheme is trivially simple and numerical results are presented that illustrate the bulk effect of the new parameterization for plane-parallel geometry. We survey time-domain diagnostics of solar radiative transfer in the Earth's cloudy atmosphere obtained recently from high-resolution ground-based spectroscopy, and it is shown that they are explained comprehensively by the new model. Finally, we discuss possible applications of this modeling framework in nuclear engineering. (authors)
Groupies in multitype random graphs
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.
Groupies in multitype random graphs.
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.
Introduction to quantum graphs
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...
A cluster algorithm for graphs
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)
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
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.
Scalable inference for stochastic block models
Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.
2017-01-01
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference
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.
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...
Coloring geographical threshold graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
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...
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
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...
Stochastic quantization and gravity
International Nuclear Information System (INIS)
Rumpf, H.
1984-01-01
We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
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...
Disease management research using event graphs.
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.
Performance criteria for graph clustering and Markov cluster experiments
S. van Dongen
2000-01-01
textabstractIn~[1] a cluster algorithm for graphs was introduced called the Markov cluster algorithm or MCL~algorithm. The algorithm is based on simulation of (stochastic) flow in graphs by means of alternation of two operators, expansion and inflation. The results in~[2] establish an intrinsic
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...
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.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Graph visualization (Invited talk)
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.
Efficient dynamic graph construction for inductive semi-supervised learning.
Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y
2017-10-01
Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.
Pragmatic Graph Rewriting Modifications
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...
Kuramoto model for infinite graphs with kernels
Canale, Eduardo
2015-01-07
In this paper we study the Kuramoto model of weakly coupled oscillators for the case of non trivial network with large number of nodes. We approximate of such configurations by a McKean-Vlasov stochastic differential equation based on infinite graph. We focus on circulant graphs which have enough symmetries to make the computations easier. We then focus on the asymptotic regime where an integro-partial differential equation is derived. Numerical analysis and convergence proofs of the Fokker-Planck-Kolmogorov equation are conducted. Finally, we provide numerical examples that illustrate the convergence of our method.
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...
Interacting particle systems on graphs
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
International Nuclear Information System (INIS)
Rumpf, H.
1987-01-01
We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)
Adaptive Graph Convolutional Neural Networks
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...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Stochastic TDHF and the Boltzman-Langevin equation
International Nuclear Information System (INIS)
Suraud, E.; Reinhard, P.G.
1991-01-01
Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations
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.
SBOAT: A Stochastic BPMN Analysis and Optimisation Tool
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Hansen, Zaza Nadja Lee; Jacobsen, Peter
2014-01-01
In this paper we present a description of a tool development framework, called SBOAT, for the quantitative analysis of graph based process modelling languages based upon the Business Process Modelling and Notation (BPMN) language, extended with intention preserving stochastic branching and parame......In this paper we present a description of a tool development framework, called SBOAT, for the quantitative analysis of graph based process modelling languages based upon the Business Process Modelling and Notation (BPMN) language, extended with intention preserving stochastic branching...
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
Graphing Inequalities, Connecting Meaning
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…
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.
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,
Fuzzy Graph Language Recognizability
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.
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
Sequential neural models with stochastic layers
DEFF Research Database (Denmark)
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
Stochastic quantization for the axial model
International Nuclear Information System (INIS)
Farina, C.; Montani, H.; Albuquerque, L.C.
1991-01-01
We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process
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
Simplicial complexes of graphs
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.
Graphing trillions of triangles.
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.
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
Content Propagation in Online Social Networks
Blenn, N.
2014-01-01
This thesis presents methods and techniques to analyze content propagation within online social networks (OSNs) using a graph theoretical approach. Important factors and different techniques to analyze and describe content propagation, starting from the smallest entity in a network, representing a
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...
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...
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.
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
Creating more effective graphs
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
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.
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...
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.
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Stochastic quantization of gravity and string fields
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
The stochastic quantization method of Parisi and Wu is generalized so as to make it applicable to Einstein's theory of gravitation. The generalization is based on the existence of a preferred metric in field configuration space, involves Ito's calculus, and introduces a complex stochastic process adapted to Lorentzian spacetime. It implies formally the path integral measure of DeWitt, a causual Feynman propagator, and a consistent stochastic perturbation theory. The lineraized version of the theory is also obtained from the stochastic quantization of the free string field theory of Siegel and Zwiebach. (Author)
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.
International Nuclear Information System (INIS)
Klauder, J.R.
1983-01-01
The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)
A graph rewriting programming language for graph drawing
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...
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
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
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...
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
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...
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
Generalized connectivity of graphs
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.
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...
African Journals Online (AJOL)
eobe
STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.
Learning a Nonnegative Sparse Graph for Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung
2015-09-01
Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.
Autoregressive Moving Average Graph Filtering
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...
Subgraph detection using graph signals
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.
Subgraph detection using graph signals
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.
Bounded-Degree Approximations of Stochastic Networks
Energy Technology Data Exchange (ETDEWEB)
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.
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
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Manifold Adaptive Label Propagation for Face Clustering.
Pei, Xiaobing; Lyu, Zehua; Chen, Changqing; Chen, Chuanbo
2015-08-01
In this paper, a novel label propagation (LP) method is presented, called the manifold adaptive label propagation (MALP) method, which is to extend original LP by integrating sparse representation constraint into regularization framework of LP method. Similar to most LP, first of all, MALP also finds graph edges from given data and gives weights to the graph edges. Our goal is to find graph weights matrix adaptively. The key advantage of our approach is that MALP simultaneously finds graph weights matrix and predicts the label of unlabeled data. This paper also derives efficient algorithm to solve the proposed problem. Extensions of our MALP in kernel space and robust version are presented. The proposed method has been applied to the problem of semi-supervised face clustering using the well-known ORL, Yale, extended YaleB, and PIE datasets. Our experimental evaluations show the effectiveness of our method.
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
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.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
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.
Collective Rationality in Graph Aggregation
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
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
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 ...
Limits for Stochastic Reaction Networks
DEFF Research Database (Denmark)
Cappelletti, Daniele
Reaction systems have been introduced in the 70s to model biochemical systems. Nowadays their range of applications has increased and they are fruitfully used in dierent elds. The concept is simple: some chemical species react, the set of chemical reactions form a graph and a rate function...... is associated with each reaction. Such functions describe the speed of the dierent reactions, or their propensities. Two modelling regimes are then available: the evolution of the dierent species concentrations can be deterministically modelled through a system of ODE, while the counts of the dierent species...... at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...
International Nuclear Information System (INIS)
Bisognano, J.; Leemann, C.
1982-03-01
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron
Stochastic synchronization in finite size spiking networks
Doiron, Brent; Rinzel, John; Reyes, Alex
2006-09-01
We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.
Stochastic background of atmospheric cascades
International Nuclear Information System (INIS)
Wilk, G.; Wlodarczyk, Z.
1993-01-01
Fluctuations in the atmospheric cascades developing during the propagation of very high energy cosmic rays through the atmosphere are investigated using stochastic branching model of pure birth process with immigration. In particular, we show that the multiplicity distributions of secondaries emerging from gamma families are much narrower than those resulting from hadronic families. We argue that the strong intermittent like behaviour found recently in atmospheric families results from the fluctuations in the cascades themselves and are insensitive to the details of elementary interactions
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
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.
Jointly-check iterative decoding algorithm for quantum sparse graph codes
International Nuclear Information System (INIS)
Jun-Hu, Shao; Bao-Ming, Bai; Wei, Lin; Lin, Zhou
2010-01-01
For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement. (general)
On some covering graphs of a graph
Directory of Open Access Journals (Sweden)
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Space-time-modulated stochastic processes
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Fundamentals of algebraic graph transformation
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...
The STAPL Parallel Graph Library
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.
Graph theoretical model of a sensorimotor connectome in zebrafish.
Stobb, Michael; Peterson, Joshua M; Mazzag, Borbala; Gahtan, Ethan
2012-01-01
Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.
Graph theoretical model of a sensorimotor connectome in zebrafish.
Directory of Open Access Journals (Sweden)
Michael Stobb
Full Text Available Mapping the detailed connectivity patterns (connectomes of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.
Stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''
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''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
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.
ALBERTO CARLOS DE QUEIROZ PINTO; VICTOR GALÁN SAÚCO; SISIR KUMAR MITRA; FRANCISCO RICARDO FERREIRA
2018-01-01
ABSTRACT This Chapter has the objectives to search, through the review of the available literature, important informations on the evolution of mango propagation regarding theoretical and practical aspects from cellular base of sexual propagation, nursery structures and organizations, substrate compositions and uses, importance of rootstock and scion selections, also it will be described the preparation and transport of the grafts (stem and bud) as well as the main asexual propagation methods...
Quantitative graph theory mathematical foundations and applications
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
Content-Agnostic Malware Detection in Heterogeneous Malicious Distribution Graph
Alabdulmohsin, Ibrahim; Han, Yufei; Shen, Yun; Zhang, Xiangliang
2016-01-01
graph has more than 4 million edges and 2.7 million nodes that differ in type, such as IPs, URLs, and files. We propose a novel Bayesian label propagation model to unify the multi-source information, including content-agnostic features of different node
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
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...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Graph embedding with rich information through heterogeneous graph
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
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.
Handbook of graph grammars and computing by graph transformation
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
Topics in graph theory graphs and their Cartesian product
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.
Label Information Guided Graph Construction for Semi-Supervised Learning.
Zhuang, Liansheng; Zhou, Zihan; Gao, Shenghua; Yin, Jingwen; Lin, Zhouchen; Ma, Yi
2017-09-01
In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
DEFF Research Database (Denmark)
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
Scalable inference for stochastic block models
Peng, Chengbin
2017-12-08
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.
The STAPL Parallel Graph Library
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
International Nuclear Information System (INIS)
Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.
1975-01-01
A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)
Directory of Open Access Journals (Sweden)
Romanu Ekaterini
2006-01-01
Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.
On the mixing time of geographical threshold graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory
2009-01-01
In this paper, we study the mixing time of random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
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.
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
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.
Graph transformation tool contest 2008
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
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) =.
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.
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...
Directory of Open Access Journals (Sweden)
ALBERTO CARLOS DE QUEIROZ PINTO
2018-03-01
Full Text Available ABSTRACT This Chapter has the objectives to search, through the review of the available literature, important informations on the evolution of mango propagation regarding theoretical and practical aspects from cellular base of sexual propagation, nursery structures and organizations, substrate compositions and uses, importance of rootstock and scion selections, also it will be described the preparation and transport of the grafts (stem and bud as well as the main asexual propagation methods their uses and practices. Finally, pattern and quality of graft mangos and their commercialization aspects will be discussed in this Chapter.
Stochastic analysis for finance with simulations
Choe, Geon Ho
2016-01-01
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoret...
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
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
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....
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.
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.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
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
Graph Sampling for Covariance Estimation
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.
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...
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.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
Markov Stochastic Technique to Determine Galactic Cosmic Ray ...
Indian Academy of Sciences (India)
A new numerical model of particle propagation in the Galaxy has been developed, which allows the study of cosmic-ray production and propagation in 2D. The model has been used to solve cosmic ray diffusive transport equation with a complete network of nuclear interactions using the time backward Markov stochastic ...
Growing hierarchical probabilistic self-organizing graphs.
López-Rubio, Ezequiel; Palomo, Esteban José
2011-07-01
Since the introduction of the growing hierarchical self-organizing map, much work has been done on self-organizing neural models with a dynamic structure. These models allow adjusting the layers of the model to the features of the input dataset. Here we propose a new self-organizing model which is based on a probabilistic mixture of multivariate Gaussian components. The learning rule is derived from the stochastic approximation framework, and a probabilistic criterion is used to control the growth of the model. Moreover, the model is able to adapt to the topology of each layer, so that a hierarchy of dynamic graphs is built. This overcomes the limitations of the self-organizing maps with a fixed topology, and gives rise to a faithful visualization method for high-dimensional data.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Regular graph construction for semi-supervised learning
International Nuclear Information System (INIS)
Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang
2014-01-01
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN
Energy losses (gains) of massive coloured particles in stochastic colour medium
International Nuclear Information System (INIS)
Leonidov, A.; Rossijskaya Akademiya Nauk, Moscow
1995-01-01
The propagation of massive coloured particles in stochastic background chromoelectric field is studied using the semiclassical equations of motion. Depending on the nature of the stochastic background we obtain the formulae for the energy losses of heavy coloured projectile in nonperturbative hadronic medium and for the energy gains in the stochastic field present, e.g., in the turbulent plasma. The result appears to be significantly dependent on the form of the correlation function of stochastic external field. (orig.)
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 $Hcong overline{F_n}$.
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...
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
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
Discrete geometric analysis of message passing algorithm on graphs
Watanabe, Yusuke
2010-04-01
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graph Algorithm Animation with Grrr
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...
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.
Eulerian Graphs and Related Topics
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
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
International Nuclear Information System (INIS)
Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas
2004-01-01
We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise
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.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
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.
Propagation of dynamic measurement uncertainty
International Nuclear Information System (INIS)
Hessling, J P
2011-01-01
The time-dependent measurement uncertainty has been evaluated in a number of recent publications, starting from a known uncertain dynamic model. This could be defined as the 'downward' propagation of uncertainty from the model to the targeted measurement. The propagation of uncertainty 'upward' from the calibration experiment to a dynamic model traditionally belongs to system identification. The use of different representations (time, frequency, etc) is ubiquitous in dynamic measurement analyses. An expression of uncertainty in dynamic measurements is formulated for the first time in this paper independent of representation, joining upward as well as downward propagation. For applications in metrology, the high quality of the characterization may be prohibitive for any reasonably large and robust model to pass the whiteness test. This test is therefore relaxed by not directly requiring small systematic model errors in comparison to the randomness of the characterization. Instead, the systematic error of the dynamic model is propagated to the uncertainty of the measurand, analogously but differently to how stochastic contributions are propagated. The pass criterion of the model is thereby transferred from the identification to acceptance of the total accumulated uncertainty of the measurand. This increases the relevance of the test of the model as it relates to its final use rather than the quality of the calibration. The propagation of uncertainty hence includes the propagation of systematic model errors. For illustration, the 'upward' propagation of uncertainty is applied to determine if an appliance box is damaged in an earthquake experiment. In this case, relaxation of the whiteness test was required to reach a conclusive result
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.
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.
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
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...
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)
Graph Sampling for Covariance Estimation
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
Network reconstruction via graph blending
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.
Partition function expansion on region graphs and message-passing equations
International Nuclear Information System (INIS)
Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong
2011-01-01
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)
Planar graphs theory and algorithms
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.
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)
RJSplot: Interactive Graphs with R.
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.
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.
Graph embedding with rich information through heterogeneous graph
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.
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
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...
Noise propagation in two-step series MAPK cascade.
Directory of Open Access Journals (Sweden)
Venkata Dhananjaneyulu
Full Text Available Series MAPK enzymatic cascades, ubiquitously found in signaling networks, act as signal amplifiers and play a key role in processing information during signal transduction in cells. In activated cascades, cell-to-cell variability or noise is bound to occur and thereby strongly affects the cellular response. Commonly used linearization method (LM applied to Langevin type stochastic model of the MAPK cascade fails to accurately predict intrinsic noise propagation in the cascade. We prove this by using extensive stochastic simulations for various ranges of biochemical parameters. This failure is due to the fact that the LM ignores the nonlinear effects on the noise. However, LM provides a good estimate of the extrinsic noise propagation. We show that the correct estimate of intrinsic noise propagation in signaling networks that contain at least one enzymatic step can be obtained only through stochastic simulations. Noise propagation in the cascade depends on the underlying biochemical parameters which are often unavailable. Based on a combination of global sensitivity analysis (GSA and stochastic simulations, we developed a systematic methodology to characterize noise propagation in the cascade. GSA predicts that noise propagation in MAPK cascade is sensitive to the total number of upstream enzyme molecules and the total number of molecules of the two substrates involved in the cascade. We argue that the general systematic approach proposed and demonstrated on MAPK cascade must accompany noise propagation studies in biological networks.
Stochasticity in the yeast mating pathway
International Nuclear Information System (INIS)
Hong-Li, Wang; Zheng-Ping, Fu; Xin-Hang, Xu; Qi, Ouyang
2009-01-01
We report stochastic simulations of the yeast mating signal transduction pathway. The effects of intrinsic and external noise, the influence of cell-to-cell difference in the pathway capacity, and noise propagation in the pathway have been examined. The stochastic temporal behaviour of the pathway is found to be robust to the influence of inherent fluctuations, and intrinsic noise propagates in the pathway in a uniform pattern when the yeasts are treated with pheromones of different stimulus strengths and of varied fluctuations. In agreement with recent experimental findings, extrinsic noise is found to play a more prominent role than intrinsic noise in the variability of proteins. The occurrence frequency for the reactions in the pathway are also examined and a more compact network is obtained by dropping most of the reactions of least occurrence
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.
Semantic graphs and associative memories
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.
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.
On the abelianity of the stochastic sandpile model
Nunzi, François
2016-01-01
We consider a stochastic variant of the Abelian Sandpile Model (ASM) on a finite graph, introduced by Chan, Marckert and Selig. Even though it is a more general model, some nice properties still hold. We show that on a certain probability space, even if we lose the group structure due to topplings not being deterministic, some operators still commute. As a corollary, we show that the stationary distribution still does not depend on how sand grains are added onto the graph in our model, answer...
On the theory of stochastic dynamics of magnetically confined plasma
Energy Technology Data Exchange (ETDEWEB)
El-Sharif, R.N.; El-Atoy, N.S. [Plasma and Nuclear Fusion Dept., N.R.C, Atomic Energy Authority, Cairo (Egypt)]|[Physics Dept., Girls Colleges, KSA (Saudi Arabia)
2004-07-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
On the theory of stochastic dynamics of magnetically confined plasma
International Nuclear Information System (INIS)
El-Sharif, R.N.; El-Atoy, N.S.
2004-01-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
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...
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...
Graphs with Eulerian unit spheres
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...
International Nuclear Information System (INIS)
Hermansson, B.R.
1989-01-01
The main part of this thesis consists of 15 published papers, in which the numerical Beam Propagating Method (BPM) is investigated, verified and used in a number of applications. In the introduction a derivation of the nonlinear Schroedinger equation is presented to connect the beginning of the soliton papers with Maxwell's equations including a nonlinear polarization. This thesis focuses on the wide use of the BPM for numerical simulations of propagating light and particle beams through different types of structures such as waveguides, fibers, tapers, Y-junctions, laser arrays and crystalline solids. We verify the BPM in the above listed problems against other numerical methods for example the Finite-element Method, perturbation methods and Runge-Kutta integration. Further, the BPM is shown to be a simple and effective way to numerically set up the Green's function in matrix form for periodic structures. The Green's function matrix can then be diagonalized with matrix methods yielding the eigensolutions of the structure. The BPM inherent transverse periodicity can be untied, if desired, by for example including an absorptive refractive index at the computational window edges. The interaction of two first-order soliton pulses is strongly dependent on the phase relationship between the individual solitons. When optical phase shift keying is used in coherent one-carrier wavelength communication, the fiber attenuation will suppress or delay the nonlinear instability. (orig.)
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
International Nuclear Information System (INIS)
Ding Chaoliang; Lue Baida; Pan Liuzhan
2009-01-01
The unified theory of coherence and polarization proposed by Wolf is extended from stochastic stationary electromagnetic beams to stochastic spatially and spectrally partially coherent electromagnetic pulsed beams. Taking the stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the expressions for the spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic GSMP beams propagating in free space are derived. Some special cases are analyzed. The illustrative examples are given and the results are interpreted physically.
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
Modeling Passive Propagation of Malwares on the WWW
Chunbo, Liu; Chunfu, Jia
Web-based malwares host in websites fixedly and download onto user's computers automatically while users browse. This passive propagation pattern is different from that of traditional viruses and worms. A propagation model based on reverse web graph is proposed. In this model, propagation of malwares is analyzed by means of random jump matrix which combines orderness and randomness of user browsing behaviors. Explanatory experiments, which has single or multiple propagation sources respectively, prove the validity of the model. Using this model, people can evaluate the hazardness of specified websites and take corresponding countermeasures.
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Equilibrium statistical mechanics on correlated random graphs
Barra, Adriano; Agliari, Elena
2011-02-01
Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]\\to [0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved.
Equilibrium statistical mechanics on correlated random graphs
International Nuclear Information System (INIS)
Barra, Adriano; Agliari, Elena
2011-01-01
Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]→[0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved
Quantum Graphical Models and Belief Propagation
International Nuclear Information System (INIS)
Leifer, M.S.; Poulin, D.
2008-01-01
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described
Properly colored connectivity of graphs
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.
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.
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.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Generating random networks and graphs
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...
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
A faithful functor among algebras and graphs
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.
Graphs with branchwidth at most three
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
A Modal-Logic Based Graph Abstraction
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
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...
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...
Building Scalable Knowledge Graphs for Earth Science
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.
Port-Hamiltonian Systems on Open Graphs
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
Constructing Dense Graphs with Unique Hamiltonian Cycles
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…
Skew-adjacency matrices of graphs
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
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.
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)
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.
Stochastic quantization of the Kink solution of phi4 field theory
International Nuclear Information System (INIS)
Kates, R.; Rosenblum, A.
1989-01-01
The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator for Phi 4 field theory by perturbing the Kink solution
Interactive Graph Layout of a Million Nodes
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...
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.
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.
Content-Agnostic Malware Detection in Heterogeneous Malicious Distribution Graph
Alabdulmohsin, Ibrahim
2016-10-26
Malware detection has been widely studied by analysing either file dropping relationships or characteristics of the file distribution network. This paper, for the first time, studies a global heterogeneous malware delivery graph fusing file dropping relationship and the topology of the file distribution network. The integration offers a unique ability of structuring the end-to-end distribution relationship. However, it brings large heterogeneous graphs to analysis. In our study, an average daily generated graph has more than 4 million edges and 2.7 million nodes that differ in type, such as IPs, URLs, and files. We propose a novel Bayesian label propagation model to unify the multi-source information, including content-agnostic features of different node types and topological information of the heterogeneous network. Our approach does not need to examine the source codes nor inspect the dynamic behaviours of a binary. Instead, it estimates the maliciousness of a given file through a semi-supervised label propagation procedure, which has a linear time complexity w.r.t. the number of nodes and edges. The evaluation on 567 million real-world download events validates that our proposed approach efficiently detects malware with a high accuracy. © 2016 Copyright held by the owner/author(s).
Artistic image analysis using graph-based learning approaches.
Carneiro, Gustavo
2013-08-01
We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.
Elitism and Stochastic Dominance
Bazen, Stephen; Moyes, Patrick
2011-01-01
Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Locating sources within a dense sensor array using graph clustering
Gerstoft, P.; Riahi, N.
2017-12-01
We develop a model-free technique to identify weak sources within dense sensor arrays using graph clustering. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial coherence matrix of a wave field as a matrix whose support is a connectivity matrix of a graph with sensors as vertices. In a dense network, well-separated sources induce clusters in this graph. The geographic spread of these clusters can serve to localize the sources. The support of the covariance matrix is estimated from limited-time data using a hypothesis test with a robust phase-only coherence test statistic combined with a physical distance criterion. The latter criterion ensures graph sparsity and thus prevents clusters from forming by chance. We verify the approach and quantify its reliability on a simulated dataset. The method is then applied to data from a dense 5200 element geophone array that blanketed of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array and oil production facilities.
Stochastic beam dynamics in storage rings
International Nuclear Information System (INIS)
Pauluhn, A.
1993-12-01
In this thesis several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Markov processes. The mathematical theory of Markov processes is well known. Nevertheless, analytical solutions can be found only in special cases and numerical algorithms are required. Several numerical integration schemes for stochastic differential equations will therefore be tested in analytical solvable examples and then applied to examples from accelerator physics. In particular the stochastically perturbed synchrotron motion is treated. For the special case of a double rf system several perturbation theoretical methods for deriving the Fokker-Planck equation in the action variable are used and compared with numerical results. The second part is concerned with the dynamics of electron storage rings. Due to the synchrotron radiation the electron motion is influenced by damping and exciting forces. An algorithm for the computation of the density function in the phase space of such a dissipative stochastically excited system is introduced. The density function contains all information of a process, e.g. it determines the beam dimensions and the lifetime of a stored electron beam. The new algorithm consists in calculating a time propagator for the density function. By means of this propagator the time evolution of the density is modelled very computing time efficient. The method is applied to simple models of the beam-beam interaction (one-dimensional, round beams) and the results of the density calculations are compared with results obtained from multiparticle tracking. Furthermore some modifications of the algorithm are introduced to improve its efficiency concerning computing time and storage requirements. Finally, extensions to two-dimensional beam-beam models are described. (orig.)
Eigenfunction statistics on quantum graphs
International Nuclear Information System (INIS)
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
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.
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)
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
Integer Flows and Circuit Covers of Graphs and Signed Graphs
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
Graph theory and binary alloys passivated by nickel
International Nuclear Information System (INIS)
McCafferty, E.
2005-01-01
The passivity of a nickel binary alloy is considered in terms of a network of -Ni-O-Ni- bridges in the oxide film, where Ni is the component of the binary alloy which produces passivity. The structure of the oxide is represented by a mathematical graph, and graph theory is used to calculate the connectivity of the oxide, given by the product of the number of edges in the graph and the Randic index. A stochastic calculation is employed to insert ions of the second metal into the oxide film so as to disrupt the connectivity of the -Ni-O-Ni- network. This disruption occurs at a critical ionic concentration of the oxide film. Mathematical relationships are developed for the introduction of a general ion B +n into the oxide film, and critical ionic compositions are calculated for oxide films on the nickel binary alloys. The notation B refers to any metal B which produces B +n ions in the oxide film, where +n is the oxidation number of the ion. The results of this analysis for Fe-Ni and Cu-Ni binary alloys are in good agreement with experimental results
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
International Nuclear Information System (INIS)
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
Stochastic analytic regularization
International Nuclear Information System (INIS)
Alfaro, J.
1984-07-01
Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)
Instantaneous stochastic perturbation theory
International Nuclear Information System (INIS)
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.
2017-01-01
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of
Meyer, Joerg M.
2018-01-01
The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.
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...
The fascinating world of graph theory
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
Graph-based modelling in engineering
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. .
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
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...... 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 four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic bounded consensus of second-order multi-agent systems in noisy environment
International Nuclear Information System (INIS)
Ren Hong-Wei; Deng Fei-Qi
2017-01-01
This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally, a numerical simulation is illustrated to check the effectiveness of the proposed algorithms. (paper)
Stochastic sensitivity analysis and Langevin simulation for neural network learning
International Nuclear Information System (INIS)
Koda, Masato
1997-01-01
A comprehensive theoretical framework is proposed for the learning of a class of gradient-type neural networks with an additive Gaussian white noise process. The study is based on stochastic sensitivity analysis techniques, and formal expressions are obtained for stochastic learning laws in terms of functional derivative sensitivity coefficients. The present method, based on Langevin simulation techniques, uses only the internal states of the network and ubiquitous noise to compute the learning information inherent in the stochastic correlation between noise signals and the performance functional. In particular, the method does not require the solution of adjoint equations of the back-propagation type. Thus, the present algorithm has the potential for efficiently learning network weights with significantly fewer computations. Application to an unfolded multi-layered network is described, and the results are compared with those obtained by using a back-propagation method
Multiple graph regularized protein domain ranking
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.
Multiple graph regularized protein domain ranking
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.
Multiple graph regularized protein domain ranking.
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.
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.
The R{sup ∗}-operation for Feynman graphs with generic numerators
Energy Technology Data Exchange (ETDEWEB)
Herzog, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Ruijl, Ben [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University,Niels Bohrweg 1, 2333 CA Leiden (Netherlands)
2017-05-08
The R{sup ∗}-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R{sup ∗}-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ{sup 3} theory.
Time-translation noninvariance of temporal gauge propagator
International Nuclear Information System (INIS)
Lim, S.C.
1992-07-01
We show that within the framework of stochastic mechanics, the quantization of a free electromagnetic or Yang-Mills field in the temporal gauge can be consistently carried out. The resulting longitudinal component of the photon or gluon propagator is time-translation noninvariant. The exact form of the propagator depends on the additional boundary condition which fully fixes the temporal gauge. (author). 11 refs
Assessing and accounting for time heterogeneity in stochastic actor oriented models
Lospinoso, Joshua A.; Schweinberger, Michael; Snijders, Tom A. B.; Ripley, Ruth M.
This paper explores time heterogeneity in stochastic actor oriented models (SAOM) proposed by Snijders (Sociological methodology. Blackwell, Boston, pp 361-395, 2001) which are meant to study the evolution of networks. SAOMs model social networks as directed graphs with nodes representing people,
Stochastic quantization of fermionic theories: renormalization of the massive Thirring model
Energy Technology Data Exchange (ETDEWEB)
Brunelli, J C
1992-10-01
Using the Langevin approach for stochastic processes we study the renormalizability of the massive Thirring model. At finite fictitious time, we prove the absence of induced quadrilinear counterterms by verifying the cancellation of the divergencies of graphs with four external lines. This implies that the vanishing of the renormalization group beta function already occurs at finite times. (author). 12 refs., 3 figs.
Diagram of collisional regimes for particle diffusion in a stochastic magnetic field
International Nuclear Information System (INIS)
Misguich, J.H.; Balescu, R.
1995-01-01
This document deals with static stochastic fields, where magnetic lines experience exponential separation and magnetic diffusion. It more particularly focuses on the diffusivity of collisional particles in such a fields and presents a general graph which describes most regimes of collisional and weakly collisional diffusion for guiding centers in a time-independent magnetic field. (TEC). 9 refs., 1 fig., 2 tabs
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Isoperimetric inequalities for minimal graphs
International Nuclear Information System (INIS)
Pacelli Bessa, G.; Montenegro, J.F.
2007-09-01
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Contracting a planar graph efficiently
DEFF Research Database (Denmark)
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Multilayer Network Modeling of Change Propagation for Engineering Change Management
2010-06-01
generalization, rather than statistical generalization. As such, a single case can be used to advance a theory, similarly to how scientific experiments are...ation 411 PNC C ac 2 C PC Not Predicted & Propagated wI Comunication ENot Predicted & Not Propagated w ConPnCcation 04 PPC 5CPredicted & Propagated w...Engineering Management 48(3): 292-306. 5. Clark, J. and Holton, D.A. (2005). A First Look at Graph Theory. World Scientific . 6. Clarkson P.J., Simons, C
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.
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Towards a theory of geometric graphs
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...
Bounds on Gromov hyperbolicity constant in graphs
Indian Academy of Sciences (India)
Infinite graphs; Cartesian product graphs; independence number; domin- ation number; geodesics ... the secure transmission of information through the internet (see [15, 16]). In particular, ..... In particular, δ(G) is an integer multiple of 1/4.
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
Torsional rigidity, isospectrality and quantum graphs
International Nuclear Information System (INIS)
Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)
Tsunamis: stochastic models of occurrence and generation mechanisms
Geist, Eric L.; Oglesby, David D.
2014-01-01
The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.
Bond graph modeling of centrifugal compression systems
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...
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.
Sphere and dot product representations of graphs
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
Deep Learning with Dynamic Computation Graphs
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...
Constructs for Programming with Graph Rewrites
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...
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Remarks on stochastic acceleration
International Nuclear Information System (INIS)
Graeff, P.
1982-12-01
Stochastic acceleration and turbulent diffusion are strong turbulence problems since no expansion parameter exists. Hence the problem of finding rigorous results is of major interest both for checking approximations and for reference models. Since we have found a way of constructing such models in the turbulent diffusion case the question of the extension to stochastic acceleration now arises. The paper offers some possibilities illustrated by the case of 'stochastic free fall' which may be particularly interesting in the context of linear response theory. (orig.)
Stochastic quantization and gauge-fixing of the linearized gravitational field
International Nuclear Information System (INIS)
Hueffel, H.; Rumpf, H.
1984-01-01
Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)
Propagating Characteristics of Pulsed Laser in Rain
Directory of Open Access Journals (Sweden)
Jing Guo
2015-01-01
Full Text Available To understand the performance of laser ranging system under the rain weather condition, we need to know the propagating characteristics of laser pulse in rain. In this paper, the absorption and attenuation coefficients were calculated based on the scattering theories in discrete stochastic media, and the propagating characteristics of laser pulse in rain were simulated and analyzed using Monte-Carlo method. Some simulation results were verified by experiments, and the simulation results are well matched with the experimental data, with the maximal deviation not less than 7.5%. The results indicated that the propagating laser beam would be attenuated and distorted due to the scattering and absorption of raindrops, and the energy attenuation and pulse shape distortion strongly depended on the laser pulse widths.
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....
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…
The groupies of random multipartite graphs
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.
Modeling Software Evolution using Algebraic Graph Rewriting
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
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
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....
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...
Cycles in weighted graphs and related topics
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
Graph Transformation Semantics for a QVT Language
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
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Improper colouring of (random) unit disk graphs
Kang, R.J.; Müller, T.; Sereni, J.S.
2008-01-01
For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed
Alliances and Bisection Width for Planar Graphs
DEFF Research Database (Denmark)
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
RATGRAPH: Computer Graphing of Rational Functions.
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)
A new cluster algorithm for graphs
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
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...
A new characterization of trivially perfect graphs
Directory of Open Access Journals (Sweden)
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
47 CFR 80.761 - Conversion graphs.
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...
International Nuclear Information System (INIS)
Picard, R.R.
1989-01-01
Topics covered in this chapter include a discussion of exact results as related to nuclear materials management and accounting in nuclear facilities; propagation of error for a single measured value; propagation of error for several measured values; error propagation for materials balances; and an application of error propagation to an example of uranium hexafluoride conversion process
Multi-label literature classification based on the Gene Ontology graph
Directory of Open Access Journals (Sweden)
Lu Xinghua
2008-12-01
Full Text Available Abstract Background The Gene Ontology is a controlled vocabulary for representing knowledge related to genes and proteins in a computable form. The current effort of manually annotating proteins with the Gene Ontology is outpaced by the rate of accumulation of biomedical knowledge in literature, which urges the development of text mining approaches to facilitate the process by automatically extracting the Gene Ontology annotation from literature. The task is usually cast as a text classification problem, and contemporary methods are confronted with unbalanced training data and the difficulties associated with multi-label classification. Results In this research, we investigated the methods of enhancing automatic multi-label classification of biomedical literature by utilizing the structure of the Gene Ontology graph. We have studied three graph-based multi-label classification algorithms, including a novel stochastic algorithm and two top-down hierarchical classification methods for multi-label literature classification. We systematically evaluated and compared these graph-based classification algorithms to a conventional flat multi-label algorithm. The results indicate that, through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods can significantly improve predictions of the Gene Ontology terms implied by the analyzed text. Furthermore, the graph-based multi-label classifiers are capable of suggesting Gene Ontology annotations (to curators that are closely related to the true annotations even if they fail to predict the true ones directly. A software package implementing the studied algorithms is available for the research community. Conclusion Through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods have better potential than the conventional flat multi-label classification approach to facilitate
Front propagation in flipping processes
International Nuclear Information System (INIS)
Antal, T; Ben-Avraham, D; Ben-Naim, E; Krapivsky, P L
2008-01-01
We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random process exhibits rich phenomenology. First, there is a front, defined by the position of the leftmost occupied site, that propagates at a nontrivial velocity. Second, the front involves a depletion zone with an excess of vacant sites. The total excess Δ k increases logarithmically, Δ k ≅ ln k, with the distance k from the front. Third, the front exhibits ageing-young fronts are vigorous but old fronts are sluggish. We investigate these phenomena using a quasi-static approximation, direct solutions of small systems and numerical simulations
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Introduction to stochastic calculus
Karandikar, Rajeeva L
2018-01-01
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
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.
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.
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
The stochastic goodwill problem
Marinelli, Carlo
2003-01-01
Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...
International Nuclear Information System (INIS)
Hueffel, H.
1990-01-01
After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)
Subsampling for graph power spectrum estimation
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.
On 4-critical t-perfect graphs
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...
Subsampling for graph power spectrum estimation
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.
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)
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.
Born's reciprocity principle in stochastic phase space
International Nuclear Information System (INIS)
Prugovecki, E.
1981-01-01
It is shown that the application of Born's reciprocity principle to relativistic quantum mechanics in stochastic phase space (by the requirement that the proper wave functions of extended particles satisfy the Born-Lande as well as the Klein-Gordon equation) leads to the unique determination of these functions for any given value of their rms radius. The resulting particle propagators display not only Lorentz but also reciprocal invariance. This feature remains true even in the case of mass-zero particles, such as photons, when their localization is achieved by means of extended test particles whose proper wave functions obey the reciprocity principle. (author)
Significance evaluation in factor graphs
DEFF Research Database (Denmark)
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Flux networks in metabolic graphs
International Nuclear Information System (INIS)
Warren, P B; Queiros, S M Duarte; Jones, J L
2009-01-01
A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms
3-biplacement of bipartite graphs
Directory of Open Access Journals (Sweden)
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
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.
Quantum walk on a chimera graph
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.
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.
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.
Parallel External Memory Graph Algorithms
DEFF Research Database (Denmark)
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
A CARRIAZO, L M FERN ´ANDEZ and A RODRÍGUEZ-HIDALGO. Department of Geometry and Topology, ..... by means of trees (connected graphs without cycles) and forests (disjoint unions of trees, see [6]) given in [3], by extending it to weak ... CR-submanifold. In this case, every tree is a K2. Finally, Theorem 3.8 of [3] can ...
Topological structure of dictionary graphs
International Nuclear Information System (INIS)
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Quantum spacetime operationally based on propagators for extended test particles
International Nuclear Information System (INIS)
Prugovecki, E.
1981-01-01
By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws of motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle
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.)
An Application of Graph Theory in Markov Chains Reliability Analysis
Directory of Open Access Journals (Sweden)
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
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.
The cavity approach to parallel dynamics of Ising spins on a graph
International Nuclear Information System (INIS)
Neri, I; Bollé, D
2009-01-01
We use the cavity method to study the parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single-site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for the stationary distribution. We present the phase diagrams for an Ising model on an asymmetric Bethe lattice and for a neural network with Hebbian interactions on an asymmetric scale-free graph. For graphs with a nonzero fraction of symmetric edges the equations can be solved for a finite number of time steps. Theoretical predictions are confirmed by simulations. Using a heuristic method the cavity equations are extended to a set of equations that determine the marginals of the stationary distribution of Ising models on graphs with a nonzero fraction of symmetric edges. The results from this method are discussed and compared with simulations
International Nuclear Information System (INIS)
Haran, O.; Shvarts, D.; Thieberger, R.
1998-01-01
Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption
Community Detection for Large Graphs
Peng, Chengbin
2014-05-04
Many real world networks have inherent community structures, including social networks, transportation networks, biological networks, etc. For large scale networks with millions or billions of nodes in real-world applications, accelerating current community detection algorithms is in demand, and we present two approaches to tackle this issue -A K-core based framework that can accelerate existing community detection algorithms significantly; -A parallel inference algorithm via stochastic block models that can distribute the workload.
Stochastic dynamic modeling of regular and slow earthquakes
Aso, N.; Ando, R.; Ide, S.
2017-12-01
Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
XI Symposium on Probability and Stochastic Processes
Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo
2015-01-01
This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...
Stochastic approach to microphysics
Energy Technology Data Exchange (ETDEWEB)
Aron, J.C.
1987-01-01
The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
Stochastic cooling at Fermilab
International Nuclear Information System (INIS)
Marriner, J.
1986-08-01
The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system
Forecasting financial asset processes: stochastic dynamics via learning neural networks.
Giebel, S; Rainer, M
2010-01-01
Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.
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)
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...
Stochastic multiresonance in coupled excitable FHN neurons
Li, Huiyan; Sun, Xiaojuan; Xiao, Jinghua
2018-04-01
In this paper, effects of noise on Watts-Strogatz small-world neuronal networks, which are stimulated by a subthreshold signal, have been investigated. With the numerical simulations, it is surprisingly found that there exist several optimal noise intensities at which the subthreshold signal can be detected efficiently. This indicates the occurrence of stochastic multiresonance in the studied neuronal networks. Moreover, it is revealed that the occurrence of stochastic multiresonance has close relationship with the period of subthreshold signal Te and the noise-induced mean period of the neuronal networks T0. In detail, we find that noise could induce the neuronal networks to generate stochastic resonance for M times if Te is not very large and falls into the interval ( M × T 0 , ( M + 1 ) × T 0 ) with M being a positive integer. In real neuronal system, subthreshold signal detection is very meaningful. Thus, the obtained results in this paper could give some important implications on detecting subthreshold signal and propagating neuronal information in neuronal systems.
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
Decomposing a graph into bistars
DEFF Research Database (Denmark)
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...... is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1)....
Stochastic Feedforward Control Technique
Halyo, Nesim
1990-01-01
Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.
Markov stochasticity coordinates
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
DEFF Research Database (Denmark)
Simonsen, Maria
This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
On path hypercompositions in graphs and automata
Directory of Open Access Journals (Sweden)
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Attack Graph Construction for Security Events Analysis
Directory of Open Access Journals (Sweden)
Andrey Alexeevich Chechulin
2014-09-01
Full Text Available The paper is devoted to investigation of the attack graphs construction and analysis task for a network security evaluation and real-time security event processing. Main object of this research is the attack modeling process. The paper contains the description of attack graphs building, modifying and analysis technique as well as overview of implemented prototype for network security analysis based on attack graph approach.
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Density conditions for triangles in multipartite graphs
DEFF Research Database (Denmark)
Bondy, Adrian; Shen, Jin; Thomassé, Stephan
2006-01-01
subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has...... a triangle, provided that the edge density between any two parts is greater than 1/2....
Efficient Algorithmic Frameworks via Structural Graph Theory
2016-10-28
constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein
Bayesian Estimation and Inference using Stochastic Hardware
Directory of Open Access Journals (Sweden)
Chetan Singh Thakur
2016-03-01
Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
Bayesian Estimation and Inference Using Stochastic Electronics.
Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André
2016-01-01
In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
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....
Stochastic quantisation: theme and variation
International Nuclear Information System (INIS)
Klauder, J.R.; Kyoto Univ.
1987-01-01
The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)
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.
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...
Mechatronic modeling and simulation using bond graphs
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 ...
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...
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....
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.
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....
Reconstructing Nearly Simple Polytopes from their Graph
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...
A Reduction of the Graph Reconstruction Conjecture
Directory of Open Access Journals (Sweden)
Monikandan S.
2014-08-01
Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible
Total dominator chromatic number of a graph
Directory of Open Access Journals (Sweden)
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
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].
VT Digital Line Graph Miscellaneous Transmission Lines
Vermont Center for Geographic Information — (Link to Metadata) This datalayer is comprised of Miscellaineous Transmission Lines. Digital line graph (DLG) data are digital representations of cartographic...
Adaptive two-regime method: Application to front propagation
Energy Technology Data Exchange (ETDEWEB)
Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG (United Kingdom); Flegg, Mark, E-mail: mark.flegg@monash.edu [School of Mathematical Sciences, Faculty of Science, Monash University Wellington Road, Clayton, Victoria 3800 (Australia)
2014-03-28
The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in terms of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.
Stochastic quantization of Proca field
International Nuclear Information System (INIS)
Lim, S.C.
1981-03-01
We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)
Stochastic Estimation via Polynomial Chaos
2015-10-01
AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic
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
Energy Technology Data Exchange (ETDEWEB)
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Schrager, D.F.
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing
Composite stochastic processes
Kampen, N.G. van
Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This
Entropy Production in Stochastics
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2017-10-01
Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Research in Stochastic Processes.
1982-10-31
Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Predicting population extinction or disease outbreaks with stochastic models
Directory of Open Access Journals (Sweden)
Linda J. S. Allen
2017-01-01
Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.
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.
The complexity of the matching-cut problem for planar graphs and other graph classes
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
Robustness of networks against propagating attacks under vaccination strategies
International Nuclear Information System (INIS)
Hasegawa, Takehisa; Masuda, Naoki
2011-01-01
We study the effect of vaccination on the robustness of networks against propagating attacks that obey the susceptible–infected–removed model. By extending the generating function formalism developed by Newman (2005 Phys. Rev. Lett. 95 108701), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degree-based defense where hubs are preferentially vaccinated. We show that, when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are relatively efficient, the scale-free network with the degree-based defense is more robust than the random graph with the random defense and the scale-free network with the random defense
Project Integration Architecture: A Practical Demonstration of Information Propagation
Jones, William Henry
2005-01-01
One of the goals of the Project Integration Architecture (PIA) effort is to provide the ability to propagate information between disparate applications. With this ability, applications may then be formed into an application graph constituting a super-application. Such a super-application would then provide all of the analysis appropriate to a given technical system. This paper reports on a small demonstration of this concept in which a Computer Aided Design (CAD) application was connected to an inlet analysis code and geometry information automatically propagated from one to the other. The majority of the work reported involved not the technology of information propagation, but rather the conversion of propagated information into a form usable by the receiving application.
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
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.
Stochastic motion due to a single wave in a magnetoplasma
International Nuclear Information System (INIS)
Smith, G.R.
1979-01-01
A single electrostatic wave in a magnetoplasma causes stochastic ion motion in several physically different situations. Various magnetic fields (uniform, tokamak, and mirror) and various propagation angles with respect to the field have been studied. A brief review of this work shows that all situations can be understood using the concept of overlapping resonances. Analytical calculations of the wave amplitude necessary for stochasticity have been carried out in some cases and compared with computer and laboratory experiments. In the case of an axisymmetric mirror field the calculations predict stochastic motion of ions with energy below a threshold that depends weakly on the wave amplitude and on the scale lengths of the magnetic field. Studies with an azimuthally asymmetric field show that the asymmetry causes substantial changes in the motion of some ions
Alfven-wave current drive and magnetic field stochasticity
International Nuclear Information System (INIS)
Litwin, C.; Hegna, C.C.
1993-01-01
Propagating Alfven waves can generate parallel current through an alpha effect. In resistive MHD however, the dynamo field is proportional to resistivity and as such cannot drive significant currents for realistic parameters. In the search for an enhancement of this effect the authors investigate the role of magnetic field stochasticity. They show that the presence of a stochastic magnetic field, either spontaneously generated by instabilities or induced externally, can enhance the alpha effect of the wave. This enhancement is caused by an increased wave dissipation due to both current diffusion and filamentation. For the range of parameters of current drive experiments at Phaedrus-T tokamak, a moderate field stochasticity leads to significant modifications in the loop voltage
Peccati, Giovanni
2016-01-01
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolvi...
Linear response in stochastic mean-field theories and the onset of instabilities
International Nuclear Information System (INIS)
Colonna, M.; Chomaz, Ph.
1993-01-01
The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs
Memory and other properties of multiple test procedures generated by entangled graphs.
Maurer, Willi; Bretz, Frank
2013-05-10
Methods for addressing multiplicity in clinical trials have attracted much attention during the past 20 years. They include the investigation of new classes of multiple test procedures, such as fixed sequence, fallback and gatekeeping procedures. More recently, sequentially rejective graphical test procedures have been introduced to construct and visualize complex multiple test strategies. These methods propagate the local significance level of a rejected null hypothesis to not-yet rejected hypotheses. In the graph defining the test procedure, hypotheses together with their local significance levels are represented by weighted vertices and the propagation rule by weighted directed edges. An algorithm provides the rules for updating the local significance levels and the transition weights after rejecting an individual hypothesis. These graphical procedures have no memory in the sense that the origin of the propagated significance level is ignored in subsequent iterations. However, in some clinical trial applications, memory is desirable to reflect the underlying dependence structure of the study objectives. In such cases, it would allow the further propagation of significance levels to be dependent on their origin and thus reflect the grouped parent-descendant structures of the hypotheses. We will give examples of such situations and show how to induce memory and other properties by convex combination of several individual graphs. The resulting entangled graphs provide an intuitive way to represent the underlying relative importance relationships between the hypotheses, are as easy to perform as the original individual graphs, remain sequentially rejective and control the familywise error rate in the strong sense. Copyright © 2012 John Wiley & Sons, Ltd.
Hybrid Model For Reverberant Indoor Radio Channels Using Rays and Graphs
DEFF Research Database (Denmark)
Steinböck, Gerhard; Gan, Mingming; Meissner, Paul
2016-01-01
efficient calculation of the channel transfer function considering infinitely many components. We use ray-tracing and the theory of room electromagnetics to obtain the parameter settings for the propagation graph. Thus the proposed hybrid model does not require new or additional parameters in comparison...... to ray-tracing. Simulation results show good agreement with measurements with respect to the inclusion of the diffuse tail in both the delay power spectrum and the azimuth delay power spectrum....
Isospectral graphs with identical nodal counts
International Nuclear Information System (INIS)
Oren, Idan; Band, Ram
2012-01-01
According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 8921–33). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs. (paper)
Compression-based inference on graph data
Bloem, P.; van den Bosch, A.; Heskes, T.; van Leeuwen, D.
2013-01-01
We investigate the use of compression-based learning on graph data. General purpose compressors operate on bitstrings or other sequential representations. A single graph can be represented sequentially in many ways, which may in uence the performance of sequential compressors. Using Normalized
On minimum degree conditions for supereulerian graphs
Broersma, Haitze J.; Xiong, L.
1999-01-01
A graph is called supereulerian if it has a spanning closed trail. Let $G$ be a 2-edge-connected graph of order $n$ such that each minimal edge cut $E \\subseteq E (G)$ with $|E| \\le 3$ satisfies the property that each component of $G-E$ has order at least $(n-2)/5$. We prove that either $G$ is
On the exterior structure of graphs
International Nuclear Information System (INIS)
Kastler, Daniel
2004-01-01
After a detailed ab initio description of the exterior structure of graphs as handled by Connes and Kreimer in their work on renormalization (illustrated by the example of the φ 3 model in six dimensions) we spell out in detail their study of the Lie algebra of infinitesimal characters and of the group of characters of the Hopf algebra of Feynman graphs
The Minimum Distance of Graph Codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2011-01-01
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other...... geometries. We give results on the minimum distances of the codes....
Domination versus disjunctive domination in graphs | Henning ...
African Journals Online (AJOL)
Domination versus disjunctive domination in graphs. Michael A Henning, Sinclair A Marcon. Abstract. A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number of G is the minimum cardinality of a dominating set of G. For a positive integer b, ...
Eigenvalues and expansion of bipartite graphs
DEFF Research Database (Denmark)
Høholdt, Tom; Janwa, Heeralal
2012-01-01
We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...
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,.
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.
Graphs, Ideal Flow, and the Transportation Network
Teknomo, Kardi
2016-01-01
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.
Supplantation of Mental Operations on Graphs
Vogel, Markus; Girwidz, Raimund; Engel, Joachim
2007-01-01
Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…
Some remarks on definability of process graphs
Grabmayer, C.A.; Klop, J.W.; Luttik, B.; Baier, C.; Hermanns, H.
2006-01-01
We propose the notions of "density" and "connectivity" of infinite process graphs and investigate them in the context of the wellknown process algebras BPA and BPP. For a process graph G, the density function in a state s maps a natural number n to the number of states of G with distance less or
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)
Declarative Process Mining for DCR Graphs
DEFF Research Database (Denmark)
Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard
2017-01-01
We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...
A Graph Library Extension of SVG
DEFF Research Database (Denmark)
Nørmark, Kurt
2007-01-01
be aggregated as a single node, and an entire graph can be embedded in a single node. In addition, a number of different graph animations are described. The starting point of the SVG extension is a library that provides an exact of mirror of SVG 1.1 in the functional programming language Scheme. Each element...
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...
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
Pixels to Graphs by Associative Embedding
Newell, Alejandro; Deng, Jia
2017-01-01
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
Isomorphisms and traversability of directed path graphs
Broersma, Haitze J.; Li, Xueliang; Li, X.
1998-01-01
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph $\\forw P_k(D)$ of a digraph $D$ is obtained by representing the directed paths on $k$ vertices of $D$ by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in $D$
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Perfect secure domination in graphs
Directory of Open Access Journals (Sweden)
S.V. Divya Rashmi
2017-07-01
Full Text Available Let $G=(V,E$ be a graph. A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $Vsetminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $vin Vsetminus S$ there exists $uin S$ such that $v$ is adjacent to $u$ and $S_1=(Ssetminus{u}cup {v}$ is a dominating set. If further the vertex $uin S$ is unique, then $S$ is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of $G$ is called the perfect secure domination number of $G$ and is denoted by $gamma_{ps}(G.$ In this paper we initiate a study of this parameter and present several basic results.
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.
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.
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
in a third syntactic theory. The structure of the store-based abstract machine corresponding to this third syntactic theory oincides with that of Turner's original reduction machine. The three syntactic theories presented here The three syntactic heories presented here therefore have the following......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
, as a store-based reduction semantics of combinatory term graphs. We then refocus this store-based reduction semantics into a store-based abstract machine. The architecture of this store-based abstract machine coincides with that of Turner's original reduction machine. The three syntactic theories presented......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...
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...
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).
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].
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
A model of language inflection graphs
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.
Pixels to Graphs by Associative Embedding
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.
Approximate Computing Techniques for Iterative Graph Algorithms
Energy Technology Data Exchange (ETDEWEB)
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram
2017-12-18
Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.
Inferring ontology graph structures using OWL reasoning
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.
Inferring ontology graph structures using OWL reasoning.
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.
Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher; Karshenas, Cyrus; Rabani, Eran; Baer, Roi
2014-08-15
We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.
Susceptibility of optimal train schedules to stochastic disturbances of process times
DEFF Research Database (Denmark)
Larsen, Rune; Pranzo, Marco; D’Ariano, Andrea
2013-01-01
study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact...... and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced...
Evidence of stochastic region near a rational surface in core plasmas of LHD
International Nuclear Information System (INIS)
Ida, K.; Tamura, N.; Tuchiya, H.
2010-11-01
Clear evidence of stochastization of the magnetic surfaces near a rational surface is observed in the core plasma with weak magnetic shear in the Large Helical Device (LHD) by applying heat pulses driven by modulated electron cyclotron heating (MECH). The stochastization of the magnetic surfaces is confirmed by the observation of flattening of electron temperature (T e ) profiles and very fast propagation of the heat pulse, which is in contrast to the slow heat pulse propagation observed in the T e flat region of the nested magnetic island. (author)
Co-clustering directed graphs to discover asymmetries and directional communities.
Rohe, Karl; Qin, Tai; Yu, Bin
2016-10-21
In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.