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preprint2016arXiv

Master Equation approach to Reversible and Conservative Discrete Systems

A master equation approach is applied to a reversible and conservative cellular automata model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configurational space is composed by a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [Phys. Rev. A 38, 427-433 (1988)], a coarse-graining approach is applied to the time series of the total magnetization leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, it is shown that the master equation leads to a tractable probability transfer matrix of moderate size which provides a master equation for a coarse-grained probability distribution. The method is validated and some explicit examples are discussed.

preprint2016arXiv

The Braess Paradox in a network of totally asymmetric exclusion processes

We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-len

preprint2016arXiv

Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems

Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an equivalent isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) in which the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, widely regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new fram

preprint2008arXiv

Assessing Random Dynamical Network Architectures for Nanoelectronics

Independent of the technology, it is generally expected that future nanoscale devices will be built from vast numbers of densely arranged devices that exhibit high failure rates. Other than that, there is little consensus on what type of technology and computing architecture holds most promises to go far beyond today's top-down engineered silicon devices. Cellular automata (CA) have been proposed in the past as a possible class of architectures to the von Neumann computing architecture, which is not generally well suited for future parallel and fine-grained nanoscale electronics. While the top-down engineered semi-conducting technology favors regular and locally interconnected structures, future bottom-up self-assembled devices tend to have irregular structures because of the current lack precise control over these processes. In this paper, we will assess random dynamical networks, namely Random Boolean Networks (RBNs) and Random Threshold Networks (RTNs), as alternative computing architectures and models for future information processing devices. We will illustrate that--from a theoretical perspective--they offer superior properties over classical CA-based architectures, such

preprint1997arXiv

Artificial Neural Networks for Solving Ordinary and Partial Differential Equations

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions and contains no adjustable parameters. The second part is constructed so as not to affect the boundary conditions. This part involves a feedforward neural network, containing adjustable parameters (the weights). Hence by construction the boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ODE's, to systems of coupled ODE's and also to PDE's. In this article we illustrate the method by solving a variety of model problems and present comparisons with finite elements for several cases of partial differential equations.

preprint2016arXiv

Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the

preprint2015arXiv

Model of the Belousov-Zhabotinsky reaction Part 2: Central role of the internal excitationgrowth rate

The model of the Belousov-Zhabotinsky reaction, so-called hodgepodge machine, is discussed in detail and compared with the experimentally determined system trajectory. We show that many of the features observed in the experiment may be found at different internal excitation growth rates, the g/maxState ratios. The g/maxState ratio determines the structure of the limit set and defines also details of the system state-space trajectory. While the limit set identical to the experiment and the model may be found, there is not a single g/maxState level which defines the trajectory identical to the experiment. We also propose that there is an inherent experimental time unit defined by the time extent of the bottleneck chemical reaction process which defines the g/maxState ratio and the spatial element of the process.

preprint2016arXiv

Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks

A major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing, disease-free state at sufficiently long times due to the finite size of the networks where epidemics evolves. In the present work, we compare different quasistationary (QS) simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved. We analyze the standard QS (SQS) method, where the sampling is constrained to active configurations, the reflecting boundary condition (RBC), where the dynamics returns to the pre-absorbing configuration, and hub reactivation (HR), where the most connected vertex of the network is reactivated after a visit to an absorbing state. We apply the methods to the contact process (CP) and susceptible-infected-susceptible (SIS) models on regular and scale free networks. The investigated methods yield the same epidemic threshold for both models. For CP, that undergoes a standard collective phase transition, the methods are equivalent. For SIS, whose phase transition is ruled by the hub mutual reactivation, the SQS and HR methods are able to capture localize

preprint2016arXiv

A lattice model of reduced jamming by barrier

We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). Particularly, we discover an interesting non--monotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and mean-field model well-known aspects like faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional model with variable barrier permeability to capture qualitatively the behavior of the residence time with respect to the parameters. We report our first steps towards the understanding to which extent the presence of obstacles can fluidize pedestrian and biological transport in crowded heterogeneous environments.

preprint2016arXiv

Three phase classification of an uninterrupted traffic flow: a $k$-means clustering study

We investigate the speed time series of the vehicles recorded by a camera at a section of a highway in the city of Isfahan, Iran. Using $k$-means clustering algorithm, we find that the natural number of clustering for this set of data is $3$. This is in agreement with the three-phase theory of uninterrupted traffic flows. According to this theory, the three traffic phases are categorized as {\em free flow} (F), {\em synchronized} (S) and {\em wide moving jam} (J). We obtain the transition speeds and densities at F-S and also S-J transitions. We also apply the Shannon entropy analysis on the speed time series over finite windows, which equips us to monitor in areal time the instant state of a traffic flow.

preprint2016arXiv

The effects of overtaking strategy in the Nagel-Schreckenberg model

Based on the Nagel-Schreckenberg (NS) model with periodic boundary conditions, we proposed the NSOS model by adding the overtaking strategy (OS). In our model, overtaking vehicles are randomly selected with probability $q$ at each time step, and the successful overtaking is determined by their velocities. We observed that (i) traffic jams still occur in the NSOS model; (ii) OS increases the traffic flow in the regime where the densities exceed the maximum flow density. We also studied the phase transition (from free flow phase to jammed phase) of the NSOS model by analyzing the overtaking success rate, order parameter, relaxation time and correlation function, respectively. It was shown that the NSOS model differs from the NS model mainly in the jammed regime, and the influence of OS on the transition density is dominated by the braking probability $p$

preprint2016arXiv

Equivalence of Deterministic walks on regular lattices on the plane

We consider deterministic walks on square, triangular and hexagonal two dimensional lattices. In each case, there is a scatterer at every site that can be in one of two states that force the walker to turn either to his/her immediate right or left. After the walker is scattered, the scatterer changes state. A lattice with an arrangement of scatterers is an environment. We show that there are only two environments for which the scattering rules are injective, mirrors or rotators, on the three lattices. On hexagonal lattices, B. Z. Webb and E. G. D. Cohen, proved that given an initial position and velocity of the walker and an environment of one type of scatterers, mirrrors or rotators, there is an environment of the other type such that the walks on both environments are equivalent, meaning they visit the same sites at the same time steps. We prove the equivalence of walks on square and triangular lattices and include a proof of the equivalence of walks on hexagonal lattices. The proofs are based both on the geometry of the lattice and the structure of the scattering rule.

preprint2016arXiv

Measuring directed interactions using cellular neural networks with complex connection topologies

We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by complex topologies that include both short- and long-ranged connections. With an exemplary time-resolved analysis of asymmetric nonlinear interdependences between the seizure generating area and its immediate surrounding we provide first evidence for complex CNN connection topologies to allow for a faster network optimization together with an improved approximation accuracy of directed interactions.

preprint2016arXiv

A Linear Acceleration Theorem for 2D Cellular Automata on all Complete Neighborhoods

Linear acceleration theorems are known for most computational models. Although such results have been proved for two-dimensional cellular automata working on specific neighborhoods, no general construction was known. We present here a technique of linear acceleration for all two-dimensional languages recognized by cellular automata working on complete neighborhoods.

preprint2016arXiv

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA.

preprint2016arXiv

Constructing Orthogonal Latin Squares from Linear Cellular Automata

We undertake an investigation of combinatorial designs engendered by cellular automata (CA), focusing in particular on orthogonal Latin squares and orthogonal arrays. The motivation is of cryptographic nature. Indeed, we consider the problem of employing CA to define threshold secret sharing schemes via orthogonal Latin squares. We first show how to generate Latin squares through bipermutive CA. Then, using a characterization based on Sylvester matrices, we prove that two linear CA induce a pair of orthogonal Latin squares if and only if the polynomials associated to their local rules are relatively prime.

preprint2016arXiv

Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects

We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while, in the absence of the TDB, the same lattice admits bi-directional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.

preprint2016arXiv

Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their calibration and test against empirical data are generally restricted to global, averaged quantities, the statistics compiled from the time series of individual escapes (" microscopic " statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the " microscopic " statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with novel features that afford a semi-quantitative reproduction of the experimental " microscopic " statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may

preprint2016arXiv

A Computation in a Cellular Automaton Collider Rule 110

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.

preprint2016arXiv

Effects of individual attitudes and motion decisions in room evacuation models

In this work we present a model for the evacuation of pedestrians from an enclosure considering a continuous space substrate and discrete time. We analyze the influence of behavioral features that affect the use of the empty space, that can be linked to the attitudes or characters of the pedestrians. We study how the interaction of different behavioral profiles affects the needed time to evacuate completely a room and the occurrence of clogging. We find that neither fully egotistic nor fully cooperative attitudes are optimal from the point of view of the crowd. In contrast, intermediate behaviors provide lower evacuation times. This lead us to identify some phenomena closely analogous to the {\em faster-is-slower} effect. The proposed model enables for the introduction of Game Theory elements to solve conflicts between pedestrians which try to occupy the same space. Moreover, it allows for distinguishing between the role of the attitudes in the search for empty space and the attitudes in the conflicts. In the present version we only focus on the first of these instances.

preprint1997arXiv

Quantum lattice gases and their invariants

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger equations, in different continuum limits. By analyzing the discrete analogues of plane waves in this sector we find conserved quantities corresponding to energy and momentum. We show that the Klein paradox obtains so that in some regimes the model must be considered to be relativistic and the negative energy modes interpreted as positive energy modes of antiparticles. With a formally similar approach--the Bethe ansatz--we find the evolution eigenfunctions in the two particle sector of the quantum lattice gas automaton and conclude by discussing consequences of these calculations and their extension to more particles, additional velocities, and higher dimensions.

preprint1995arXiv

Approximate Lie Group Analysis of a Model Advection Equation on an Unstructured Grid

A technique of ``approximate group analysis'' recently developed by Baikov, Gazizov and Ibragimov is applied to a differential approximation (otherwise referred to as an equivalent differential equation) corresponding to the finite difference approximation of a nonlinear advection equation on unstructured grid. We determine which groups from the infinite variety of groups admitted by a nonlinear advection equation ``survive'' the discretization. The situations arising for different choices of an arbitrary function (local speed of propagation) are also studied.

preprint2005arXiv

Mesoscopic two-phase model for describing apparent slip in micro-channel flows

The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactins. The weakly-inhomogeneous limit of this model is solved analytically. The present mesoscopic approach permits to access much larger scales than molecular dynamics, and comparable with those attained by continuum methods. However, at variance with the continuum approach, the existence of a gas layer near the wall does not need to be postulated a priori, but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is therefore argued that a mesoscopic Lattice Boltzmann approach with non-ideal fluid-fluid and fluid-wall interactions might achieve an optimal compromise between physical realism and computational efficiency for the study of channel micro-flows.

preprint2004arXiv

Intensity Coding in Two-Dimensional Excitable Neural Networks

In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.

356 works