Zoltán Toroczkai - Academia.edu (original) (raw)
Papers by Zoltán Toroczkai
Computing Research Repository, 1999
We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event s... more We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the Edwards-Wilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.
Springer Proceedings in Physics, 2001
The scalability of massively parallel algorithms is a fundamental question in computer science. W... more The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The parallel algorithm is applicable to a wide range of problems, including dynamic Monte Carlo simulations for large asynchronous systems with short-range interactions. The evolution of the simulated time horizon is analogous to a growing and fluctuating surface, and the efficiency of the algorithm corresponds to the density of local minima of this surface. In one dimension we find that the steady state of the macroscopic landscape is governed by the Edwards-Wilkinson Hamiltonian, which implies that the algorithm is scalable. Preliminary results for higher-dimensional logical topologies are discussed.
MRS Proceedings, 2001
Efficient and faithful parallel simulation of large asynchronous systems is a challenging computa... more Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.
Physical Review E, 1998
We present a new method for extracting the persistence exponent θ for the diffusion equation, bas... more We present a new method for extracting the persistence exponent θ for the diffusion equation, based on the distribution P of 'sign-times'. With the aid of a numerically verified Ansatz for P we derive an exact formula for θ in arbitrary spatial dimension d. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d ≃ 36, signalling the existence of a sharp change in the ergodic properties of the diffusion field.
Physical Review B, 2001
We study, through large scale stochastic simulations using the noise reduction technique, surface... more We study, through large scale stochastic simulations using the noise reduction technique, surface growth via vapor deposition e.g. molecular beam epitaxy (MBE), for simple nonequilibrium limited mobility solid-on-solid growth models, such as the Family (F) model, the Das Sarma-Tamborenea (DT) model, the Wolf-Villain (WV) model, the Larger Curvature (LC) model, and other related models. We find that d=2+1 dimensional surface growth in several noise reduced models (most notably the WV and the LC model) exhibits spectacular quasi-regular mound formation with slope selection in their dynamical surface morphology in contrast to the standard statistically scale invariant kinetically rough surface growth expected (and earlier reported in the literature) for such growth models. The mounding instability in these epitaxial growth models does not involve the Ehrlich-Schwoebel step edge diffusion barrier. The mounded morphology in these growth models arises from the interplay between the line tension along step edges in the plane parallel to the average surface and the suppression of noise and island nucleation. The line tension tends to stabilize some of the step orientations that coincide with in-plane high symmetry crystalline directions, and thus the mounds that are formed assume quasi-regular structures. The noise reduction technique developed originally for Eden type models can be used to control the stochastic noise and enhance diffusion along the step edge, which ultimately leads to the formation of quasi-regular mounds during growth. We show that by increasing the diffusion surface length together with supression of nucleation and deposition noise, one can obtain a self-organization of the pyramids in quasi-regular patterns. The mounding instability in these simple epitaxial growth models is closely related to the cluster-edge diffusion (as opposed to step edge barrier) driven mounding in MBE growth, which has been recently discussed in the literature. The epitaxial mound formation studied here is a kinetic-topological instability (which can happen only in d=2+1 dimensional, or higher dimensional, growth, but not in d=1+1 dimensional growth because no cluster diffusion around a closed surface loop is possible in "one dimensional" surfaces), which is likely to be quite generic in real MBE-type surface growth. Our extensive numerical simulations produce mounded (and slope-selected) surface growth morphologies which are strikingly visually similar to many recently reported experimental MBE growth morphologies.
Physics Letters A, 1994
Based on a simple geometrical construction, an algorithm is given for stabilizing hyperbolic peri... more Based on a simple geometrical construction, an algorithm is given for stabilizing hyperbolic periodic orbits of two-dimensional maps. The method does not require analytical knowledge of the system's dynamics, only a rough location of the linearized region around the periodic orbit to be stabilized (the target region). This construction can thus be used as a chaos controlling method of feedback type, accessible to experiments. A novel method to find the target regions is also given. 0375-9601/94/$07.00 ~) 1994 Elsevier Science B.V. All fights reserved SSDI0375-9601 (94)00365-V
Physical review letters, Jan 17, 2015
Based on Jaynes's maximum entropy principle, exponential random graphs provide a family of pr... more Based on Jaynes's maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry breaking, where predictions fail. Here we show that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. Exploiting these nonlinear relationships here we propose a solution to the degeneracy problem for a large class of systems via transformations that render the density of states function log-concave. The effectiveness of the method is demonstrated on examples.
Proceedings of The National Academy of Sciences, 2000
SIAM Journal on Discrete Mathematics, 2015
A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in... more A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two degree groups are placed as uniformly as possible. We prove that a swap Markov Chain Monte Carlo (MCMC) algorithm in the space of all balanced realizations of an arbitrary graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the number of nodes n. To prove fast mixing, we first prove a general factorization theorem similar to the Martin-Randall method for disjoint decompositions (partitions). This theorem can be used to bound from below the spectral gap with the help of fast mixing subchains within every partition and a bound on an auxiliary Markov chain between the partitions. Our proof of the general factorization theorem is direct and uses conductance based methods (Cheeger inequality).
Chaos (Woodbury, N.Y.), 2002
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
We apply the recently introduced distribution of sign-times (DST) to nonequilibrium interface gro... more We apply the recently introduced distribution of sign-times (DST) to nonequilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a nontrivial scaling relation. A critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and nonlinear growth mechanisms.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We investigate, using the noise reduction technique, the asymptotic universality class of the wel... more We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
The Horton-Strahler (HS) index r=max(i,j)+delta(i,j) has been shown to be relevant to a number of... more The Horton-Strahler (HS) index r=max(i,j)+delta(i,j) has been shown to be relevant to a number of physical (such as diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees), and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of n leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of nonlinear functional equations, we are able to give a double exponentially converging approximant to t...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
Lam and Tan [Phys. Rev. E 62, 6246 (2000)] recently studied the extremal-point densities of inter... more Lam and Tan [Phys. Rev. E 62, 6246 (2000)] recently studied the extremal-point densities of interface fluctuations in a quenched random medium. In this Comment we show that their results for systems on a lattice contain algebraic errors leading to invalid conclusions. Further, while most of their calculations for the continuum case are correct, they misinterpret the result to come to an agreement with the (erroneous) lattice calculations. We derive the correct expressions for the lattice, which agree with the correct interpretation of the continuum case.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1995
We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken... more We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two
PLoS ONE, 2010
Uniform sampling from graphical realizations of a given degree sequence is a fundamental componen... more Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stubmatching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without backtracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.
Disease spread in most biological populations requires the proximity of agents. In populations wh... more Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the "collision dynamics" of the agents, and thus the evolution of epidemics couples directly to the spatial dynamics of the population. We first briefly review the properties and the methodology of an agent-based simulation (EPISIMS) to model disease spread in realistic urban dynamic contact networks. Using the data generated by this simulation, we introduce the notion of dynamic proximity networks which takes into account the relevant time scales for disease spread: contact duration, infectivity period and rate of contact creation. This approach promises to be a good candidate for a unified treatment of epidemic types that are driven by agent collision dynamics. In particular, using a simple model, we show that it can can account for the observed qualitative differences between the degree distributions of contact graphs of diseases with short infectivity period (such as air-transmitted diseases) or long infectivity periods ( such as HIV).
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
We introduce and investigate the stochastic dynamics of the density of local extrema (minima and ... more We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of nonequilibrium surface fluctuations. We give a number of analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface-growth models. We show that, in spite of the nonuniversal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic of the macroscopic observables of the system. The quantities investigated here provide us with tools that give an unorthodox approach to the dynamics of surface morphologies: a statistical analysis from the short-wavelength end of the Fourier decomposition spectrum. In addition to surface-growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete-event simulations, which are extensively used in Monte Carlo simulatio...
Physical Review E, 1999
We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active p... more We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A + B → 2B and A + B → 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.
Computing Research Repository, 1999
We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event s... more We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the Edwards-Wilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.
Springer Proceedings in Physics, 2001
The scalability of massively parallel algorithms is a fundamental question in computer science. W... more The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The parallel algorithm is applicable to a wide range of problems, including dynamic Monte Carlo simulations for large asynchronous systems with short-range interactions. The evolution of the simulated time horizon is analogous to a growing and fluctuating surface, and the efficiency of the algorithm corresponds to the density of local minima of this surface. In one dimension we find that the steady state of the macroscopic landscape is governed by the Edwards-Wilkinson Hamiltonian, which implies that the algorithm is scalable. Preliminary results for higher-dimensional logical topologies are discussed.
MRS Proceedings, 2001
Efficient and faithful parallel simulation of large asynchronous systems is a challenging computa... more Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.
Physical Review E, 1998
We present a new method for extracting the persistence exponent θ for the diffusion equation, bas... more We present a new method for extracting the persistence exponent θ for the diffusion equation, based on the distribution P of 'sign-times'. With the aid of a numerically verified Ansatz for P we derive an exact formula for θ in arbitrary spatial dimension d. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d ≃ 36, signalling the existence of a sharp change in the ergodic properties of the diffusion field.
Physical Review B, 2001
We study, through large scale stochastic simulations using the noise reduction technique, surface... more We study, through large scale stochastic simulations using the noise reduction technique, surface growth via vapor deposition e.g. molecular beam epitaxy (MBE), for simple nonequilibrium limited mobility solid-on-solid growth models, such as the Family (F) model, the Das Sarma-Tamborenea (DT) model, the Wolf-Villain (WV) model, the Larger Curvature (LC) model, and other related models. We find that d=2+1 dimensional surface growth in several noise reduced models (most notably the WV and the LC model) exhibits spectacular quasi-regular mound formation with slope selection in their dynamical surface morphology in contrast to the standard statistically scale invariant kinetically rough surface growth expected (and earlier reported in the literature) for such growth models. The mounding instability in these epitaxial growth models does not involve the Ehrlich-Schwoebel step edge diffusion barrier. The mounded morphology in these growth models arises from the interplay between the line tension along step edges in the plane parallel to the average surface and the suppression of noise and island nucleation. The line tension tends to stabilize some of the step orientations that coincide with in-plane high symmetry crystalline directions, and thus the mounds that are formed assume quasi-regular structures. The noise reduction technique developed originally for Eden type models can be used to control the stochastic noise and enhance diffusion along the step edge, which ultimately leads to the formation of quasi-regular mounds during growth. We show that by increasing the diffusion surface length together with supression of nucleation and deposition noise, one can obtain a self-organization of the pyramids in quasi-regular patterns. The mounding instability in these simple epitaxial growth models is closely related to the cluster-edge diffusion (as opposed to step edge barrier) driven mounding in MBE growth, which has been recently discussed in the literature. The epitaxial mound formation studied here is a kinetic-topological instability (which can happen only in d=2+1 dimensional, or higher dimensional, growth, but not in d=1+1 dimensional growth because no cluster diffusion around a closed surface loop is possible in "one dimensional" surfaces), which is likely to be quite generic in real MBE-type surface growth. Our extensive numerical simulations produce mounded (and slope-selected) surface growth morphologies which are strikingly visually similar to many recently reported experimental MBE growth morphologies.
Physics Letters A, 1994
Based on a simple geometrical construction, an algorithm is given for stabilizing hyperbolic peri... more Based on a simple geometrical construction, an algorithm is given for stabilizing hyperbolic periodic orbits of two-dimensional maps. The method does not require analytical knowledge of the system's dynamics, only a rough location of the linearized region around the periodic orbit to be stabilized (the target region). This construction can thus be used as a chaos controlling method of feedback type, accessible to experiments. A novel method to find the target regions is also given. 0375-9601/94/$07.00 ~) 1994 Elsevier Science B.V. All fights reserved SSDI0375-9601 (94)00365-V
Physical review letters, Jan 17, 2015
Based on Jaynes's maximum entropy principle, exponential random graphs provide a family of pr... more Based on Jaynes's maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry breaking, where predictions fail. Here we show that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. Exploiting these nonlinear relationships here we propose a solution to the degeneracy problem for a large class of systems via transformations that render the density of states function log-concave. The effectiveness of the method is demonstrated on examples.
Proceedings of The National Academy of Sciences, 2000
SIAM Journal on Discrete Mathematics, 2015
A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in... more A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two degree groups are placed as uniformly as possible. We prove that a swap Markov Chain Monte Carlo (MCMC) algorithm in the space of all balanced realizations of an arbitrary graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the number of nodes n. To prove fast mixing, we first prove a general factorization theorem similar to the Martin-Randall method for disjoint decompositions (partitions). This theorem can be used to bound from below the spectral gap with the help of fast mixing subchains within every partition and a bound on an auxiliary Markov chain between the partitions. Our proof of the general factorization theorem is direct and uses conductance based methods (Cheeger inequality).
Chaos (Woodbury, N.Y.), 2002
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
We apply the recently introduced distribution of sign-times (DST) to nonequilibrium interface gro... more We apply the recently introduced distribution of sign-times (DST) to nonequilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a nontrivial scaling relation. A critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and nonlinear growth mechanisms.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We investigate, using the noise reduction technique, the asymptotic universality class of the wel... more We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
The Horton-Strahler (HS) index r=max(i,j)+delta(i,j) has been shown to be relevant to a number of... more The Horton-Strahler (HS) index r=max(i,j)+delta(i,j) has been shown to be relevant to a number of physical (such as diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees), and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of n leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of nonlinear functional equations, we are able to give a double exponentially converging approximant to t...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
Lam and Tan [Phys. Rev. E 62, 6246 (2000)] recently studied the extremal-point densities of inter... more Lam and Tan [Phys. Rev. E 62, 6246 (2000)] recently studied the extremal-point densities of interface fluctuations in a quenched random medium. In this Comment we show that their results for systems on a lattice contain algebraic errors leading to invalid conclusions. Further, while most of their calculations for the continuum case are correct, they misinterpret the result to come to an agreement with the (erroneous) lattice calculations. We derive the correct expressions for the lattice, which agree with the correct interpretation of the continuum case.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1995
We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken... more We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two
PLoS ONE, 2010
Uniform sampling from graphical realizations of a given degree sequence is a fundamental componen... more Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stubmatching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without backtracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.
Disease spread in most biological populations requires the proximity of agents. In populations wh... more Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the "collision dynamics" of the agents, and thus the evolution of epidemics couples directly to the spatial dynamics of the population. We first briefly review the properties and the methodology of an agent-based simulation (EPISIMS) to model disease spread in realistic urban dynamic contact networks. Using the data generated by this simulation, we introduce the notion of dynamic proximity networks which takes into account the relevant time scales for disease spread: contact duration, infectivity period and rate of contact creation. This approach promises to be a good candidate for a unified treatment of epidemic types that are driven by agent collision dynamics. In particular, using a simple model, we show that it can can account for the observed qualitative differences between the degree distributions of contact graphs of diseases with short infectivity period (such as air-transmitted diseases) or long infectivity periods ( such as HIV).
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
We introduce and investigate the stochastic dynamics of the density of local extrema (minima and ... more We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of nonequilibrium surface fluctuations. We give a number of analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface-growth models. We show that, in spite of the nonuniversal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic of the macroscopic observables of the system. The quantities investigated here provide us with tools that give an unorthodox approach to the dynamics of surface morphologies: a statistical analysis from the short-wavelength end of the Fourier decomposition spectrum. In addition to surface-growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete-event simulations, which are extensively used in Monte Carlo simulatio...
Physical Review E, 1999
We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active p... more We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A + B → 2B and A + B → 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.