SEARCH · Searcharxiv

Results for “nlin.CG”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3Linked to original sources

arXiv2008

Characterization Of any Non-linear Boolean function Using A Set of Linear Operators

Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize non-linear CA evolutions in the light of Boolean derivatives and Jacobian Matrices. In this paper two different efforts have been made: first we try to systematize non-linear CA evolution in the light of deviant states and non-deviant states. For all the non-deviant states the nearest linear rule matrix is applicable where as for the deviant states we have a set of other matrices. Second using algebraic manipulation, an efficient algorithm is proposed by which every Non-linear Boolean function can be characterized by a sequence of binary matrices.

cs.CC↗

arXiv2008

A housing-demographic multi-layered nonlinear model to test regulation strategies

We propose a novel multi-layered nonlinear model that is able to capture and predict the housing-demographic dynamics of the real-state market by simulating the transitions of owners among price-based house layers. This model allows us to determine which parameters are most effective to smoothen the severity of a potential market crisis. The International Monetary Fund (IMF) has issued severe warnings about the current real-state bubble in the United States, the United Kingdom, Ireland, the Netherlands, Australia and Spain in the last years. Madrid (Spain), in particular, is an extreme case of this bubble. It is, therefore, an excellent test case to analyze housing dynamics in the context of the empirical data provided by the Spanish National Institute of Statistics and other sources of data. The model is able to predict the mean house occupancy, and shows that i) the house market conditions in Madrid are unstable but not critical; and ii) the regulation of the construction rate is more effective than interest rate changes. Our results indicate that to accommodate the construction rate to the total population of first-time buyers is the most effective way to maintain the system near equilibrium conditions. In addition, we show that to raise interest rates will heavily affect the poorest housing bands of the population while the middle class layers remain nearly unaffected.

nlin.CG↗

arXiv2008

Simulation of traffic flow at a signalised intersection

We have developed a Nagel-Schreckenberg cellular automata model for describing of vehicular traffic flow at a single intersection. A set of traffic lights operating either in fixed-time or traffic adaptive scheme controls the traffic flow. Closed boundary condition is applied to the streets each of which conduct a uni-directional flow. Extensive Monte Carlo simulations are carried out to find the model characteristics. In particular, we investigate the dependence of the flows on the signalisation parameters.

nlin.CG↗

arXiv2008

Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation

The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.

physics.flu-dyn↗

arXiv2008

Periodic forcing in a three level cellular automata model for a vector transmitted disease

The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time-series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of absence of external periodic drive, the model predicts completely distinct long time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided the forcing term takes into account the local rainfall modulation. Finally, the dependence between epidemics threshold and vector control undergoes a transition from power law to stretched exponential behavior due to human mobility effect.

nlin.CG↗

arXiv2008

Exact Hydrodynamics of the Lattice BGK Equation

We apply the projection operator formalism to the problem of determining the asymptotic behavior of the lattice BGK equation in the hydrodynamic limit. As an alternative to the more usual Chapman-Enskog expansion, this approach offers many benefits. Most remarkably, it produces absolutely exact, though non-Markovian, hydrodynamic difference equations as an intermediate step. These are accurate to all orders in Knudsen number and hence contain all of the physics of the Burnett equations and beyond. If appropriate, these equations may then be Taylor expanded to second order in Knudsen number to obtain the usual hydrodynamic equations that result from the Chapman-Enskog analysis. The method offers the potential to derive hydrodynamic difference equations for complex fluids with sharp gradients, such as immiscible and amphiphilic flow, for which the assumptions underlying the Chapman-Enskog approach are generally invalid.

nlin.CG↗

arXiv2008

The Enlightened Game of Life

We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field energy. Light-induced self-structuring and self-healing abilities and various dynamic phases are displayed by the CA. Photo-driven genetic selection and the nonlinear feedback of the CA on the electromagnetic field are included in the model, and there are evidences of self-organized light-localization processes. The evolution of the electromagnetic field is based on the Finite Difference Time Domain (FDTD) approach. Applications are envisaged in evolutionary biology, artificial life, DNA replication, swarming, optical tweezing and field-driven soft-matter.

physics.optics↗

arXiv2008

Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation

Consider the macroscale modelling of microscale spatiotemporal dynamics. Here we develop a new approach to ensure coarse scale discrete models preserve important self-adjoint properties of the fine scale dynamics. The first part explores the discretisation of microscale continuum dynamics. The second addresses how dynamics on a fine lattice are mapped to lattice a factor of two coarser (as in multigrids). Such mapping of discrete lattice dynamics may be iterated to empower us in future research to explore scale dependent emergent phenomena. The support of dynamical systems, centre manifold, theory ensures that the coarse scale modelling applies with a finite spectral gap, in a finite domain, and for all time. The accuracy of the models is limited by the asymptotic resolution of subgrid coarse scale processes, and is controlled by the level of truncation. As given examples demonstrate, the novel feature of the approach developed here is that it ensures the preservation of important conservation properties of the microscale dynamics.

nlin.CG↗

arXiv2008

Issues on drawing the State Transition Diagram for arbitrary Cellular Automata

This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and length of the CA n. It also discusses the novelty, hardware cost and the complexities of these algorithms.

nlin.CG↗

arXiv2008

Isomorphisms of Additive Cellular Automata on Finite Groups

We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the index-group, monoid of automata rules, and its subgroup of reversible elements). However for some groups there exist not regular automata isomorphisms. A complete description of linear automorphisms of the monoid is obtained. These automorphisms cover the most part of all automata isomorphisms for small groups and are represented by reversible matrices M such that for any index-group circulant C the matrix M^{-1}CM is an index-group circulant.

nlin.CG↗

arXiv2008

Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems

We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a class G of graphs, an (F,G)-system is a boolean dynamical system with local transitions functions lying in F and graphs in G. We show that, if local transition functions are given by lookup tables, then the following complexity classification holds: Let F be a class of boolean functions closed under superposition and let G be a graph class closed under taking minors. If F contains all min-functions, all max-functions, or all self-dual and monotone functions, and G contains all planar graphs, then it is #P-complete to compute the number of fixed points in an (F,G)-system; otherwise it is computable in polynomial time. We also prove a dichotomy theorem for the case that local transition functions are given by formulas (over logical bases). This theorem has a significantly more complicated structure than the theorem for lookup tables. A corresponding theorem for boolean circuits coincides with the theorem for formulas.

cs.CC↗

arXiv2008

Flexible Time and the Evolution of One-Dimensional Cellular Automata

Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at different places differently. This allows to "jump" over the evolution of known structures in a single step.

nlin.CG↗

arXiv2009

Generative Network Automata: A Generalized Framework for Modeling Adaptive Network Dynamics Using Graph Rewritings

A variety of modeling frameworks have been proposed and utilized in complex systems studies, including dynamical systems models that describe state transitions on a system of fixed topology, and self-organizing network models that describe topological transformations of a network with little attention paid to dynamical state changes. Earlier network models typically assumed that topological transformations are caused by exogenous factors, such as preferential attachment of new nodes and stochastic or targeted removal of existing nodes. However, many real-world complex systems exhibit both of these two dynamics simultaneously, and they evolve largely autonomously based on the system's own states and topologies. Here we show that, by using the concept of graph rewriting, both state transitions and autonomous topology transformations of complex systems can be seamlessly integrated and represented in a unified computational framework.We call this novel modeling framework "Generative Network Automata (GNA)". In this chapter, we introduce basic concepts of GNA, its working definition, its generality to represent other dynamical systems models, and some of our latest results of extensive computational experiments that exhaustively swept over possible rewriting rules of simple binary-state GNA. The results revealed several distinct types of the GNA dynamics.

nlin.AO↗

arXiv2009

Flow Patterns of Cellular Automata and Optimal-velocity Traffic Models at Highway Bottlenecks

A bottleneck simulation of road traffic on a loop, using the deterministic cellular automata (CA) Nagel-Schreckenberg model with zero dawdling probability, reveals three types of stationary wave solutions. They consist of i) two shock waves, one at each bottleneck boundary, ii) one shock wave at the boundary and one on the "open" road, and iii) the trivial solution, i.e. homogeneous, uniform flow. These solutions are selected dynamically from a range of kinematicly permissible stationary shocks. This is similar in fashion to the wave selection in a bottleneck simulation of the optimal-velocity (OV) model, which is explained by a travelling wave phase-plane analysis of the corresponding continuum model. It is yet another strong indication that CA and OV models share certain underlying dynamics, although the former are discrete in space and time while the latter are continuous.

nlin.CG↗

arXiv2009

Synchronization and control of cellular automata

The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the control may be concentrated on the most expanding directions. This scheme is hard to follow for high-dimensional (extended) systems. This is particularly true for extended systems that exhibit stable chaos, that is, systems which are not chaotic in the usual sense, but are unpredictable for finite perturbations. Prototypical of this class are cellular automata, aka completely discrete dynamical systems. Although usual indicators of chaoticity such as the maximum Lyapunov exponent may be defined for such systems, we show that the usual approach may lead to counter intuitive results, and that it is possible to exploit the characteristics of the system in order to reduce the distance between two replicas with less control.

nlin.CG↗

arXiv2009

Complex dynamics emerging in Rule 30 with majority memory

In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particles, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.

nlin.CG↗

arXiv2009

Solutions on 1D and 2D Density Classification Problem Using Programmable Cellular Automata

This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA rules in 1D and 2D, and the advantage of PCA are embedded together to obtain the DCT solution. The advantage of PCA over standard CA is reported. A general 2D DCT of arbitrary shapes and sizes, its applicability and its solution using PCA is newly introduced.

nlin.CG↗

arXiv2009

Vehicular traffic flow at a intersection controlled by signal light with a new probability

We introduced a probability of traffic light, PL, at an intersection when approaching cars in two roads are in same conditions. As a application, we proposed a modified Nagel-Schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection. The results show that the plateau region in the fundamental diagrams, caused by the effect of interaction, is dependent not only on the probability PL, but also on the adaptive schemes.

physics.soc-ph↗