remarks on the multiplier operators associated with a cylindrical distance function abstract in this note we consider l p and maximal l p estimates for the generalized riesz means which are associated with the cylindrical distance function max d 1 d 1 r d r we prove these estimates up to the currently known range of the spherical bochner riesz and its maximal operators this is done by establishing implications between the corresponding estimates for the spherical bochner riesz and the cylindrical multiplier operators

additive one dimensional cellular automata are chaotic according to devaney s definition of chaos abstract we study the chaotic behavior of a particular class of dynamical systems cellular automata we specialize the definition of chaos given by devaney for general dynamical systems to the case of cellular automata a dynamical system x f is chaotic according to devaney s definition of chaos if its transition map f is sensitive to the initial conditions topologically transitive and has dense periodic orbits on x our main result is the proof that all the additive one dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of devaney

autonomous indefiniteness versus external indefiniteness theory of weak topped structure and its application to elementary local cellular automaton abstract we propose a theory to formalize the indefinite features of living systems in the framework of weak topped structure this theory contains two notions of indefiniteness one is called external indefiniteness and the other is called autonomous indefiniteness the former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure this theory is then applied to elementary local cellular automaton elca in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step followed by taking the closure or the weak closure in the appropriate space the behavior of elca is characterized by its algebraic and statistical properties in particular we show that self organized criticality soc like behavior appears in elca driven by the weakened closure operator

from stochastic partial difference equations to stochastic cellular automata through the ultra discretization we derive stochastic cellular automata with finite range interactions from stochastic partial difference equations through the ultra discrete limit a typical example for stochastic cellular automata is the domany kinzel model which is equivalent to mixed site bond oriented percolation as a special case

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

self organized criticality resulting from minimization of perpetual disequilibration abstract a bootstrapping system is proposed in order to describe nonlogical properties of living systems in which the velocity of observation propagation is finite a cellular automaton ca model of the system combines two logics which are the a priori non boolean logic and the a posteriori boolean logic because of inconsistency between the two logics the system evolves perpetually generating disequilibrium and perpetually equilibrating the generated disequilibrium the system tends to self organize to the border between order and disorder and shows critical behaviours as class iv ca although the critical behaviors of the two systems are similar the bootstrapping ssstem has twice stronger undecidability than class iv ca or edge of chaos dynamics it is stressed that real living systems are not computable and should be described by strongly undecidable systems

singular quasilinear equations with quadratic growth in the gradient without sign condition given a bounded domain in r n a nd af unctiona l q with q n 2 we study the existence of a positive solution for the quasilinear problem

lane emden systems with negative exponents we study the elliptic system u u pv qin v u rv sin u v 0on in a bounded domain rn n 1 with a smooth boundary p s 0 and q r 0 we investigate the existence non existence and uniqueness of c2 c solutions in terms of p q r and s a necessary and sufficient condition for the c1 regularity of solutions up to the boundary is also obtained

evolving cellular automata to perform computations mechanisms and impediments abstract we present results from experiments in which a genetic algorithm ga was used to evolve cellular automata cas to perform a particular computational task one dimensional density classification we look in detail at the evolutionary mechanisms producing the ga s behavior on this task and the impediments faced by the ga in particular we identify four epochs of innovation in which new ca strategies for solving the problem are discovered by the ga describe how these strategies are implemented in ca rule tables and identify the ga mechanisms underlying their discovery the epochs are characterized by a breaking of the task s symmetries on the part of the ga the symmetry breaking results in a short term fitness gain but ultimately prevents the discovery of the most highly fit strategies we discuss the extent to which symmetry breaking and other impediments are general phenomena in any ga search

on the existence of multiple positive entire solutions for a quasilinear elliptic systems abstract in this paper our main purpose is to establish the existence of infinitely positive bounded entire solutions of second order quasilinear elliptic systems these extend a work of zuodong yang zuodong yang existence of positive bounded entire solutions of quasilinear elliptic equations appl math comput 156 2004 743 754 which considered the single quasilinear elliptic equation these extend also a work of kawano and kusano n kawano t kusano on positive entire solutions of a class of second order semilinear elliptic systems math zeitschrift 186 3 1984 287 297 which studied the semilinear elliptic equation

propagation of singularities and maximal functions in the plane in this work we mainly generalize bourgain s circular maximal function to include variable coefficient averages our techniques involve a combination of bourgain s basic ideas plus microlocal analysis in particular to see the role of curvature we rely heavily on methods used in studying propogation of singularities for hyperbolic differential equations we also show that forp 2 there is local smoothing inl p for solutions to the wave equation

turbulent pattern bases for cellular automata abstract unpredictable patterns generated by cellular automata ca can be decomposed with respect to a turbulent positive entropy rate pattern basis the resulting filtered patterns uncover significant structural organization in a ca s dynamics and information processing capabilities we illustrate the decompostion technique by analyzing a binary range 2 cellular automaton having two invariant chaotic domains of different complexities and entropies once identified the domains are seen to organize the ca s state space and to dominate its evolution starting from the domains structures we show how to construct a finite state transducer that performs nonlinear spatial filtering such that the resulting space time patterns reveal the domains and the intervening walls and dislocations to show the statistical consequences of domain detection we compare the entropy and complexity densities of each domain with the globally averaged quantities a more graphical comparison uses difference patterns and difference plumes which trace the space time influence of a single site perturbation we also investigate the diversity of walls and particles emanating from the interface between two adjacent domains

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

criticality in cellular automata abstract using recent results obtained for the transition to turbulence via spatiotemporal intermittency in extended dynamical systems critical cellular automata rules are built thanks to a systematic procedure the continuous phase transition observed in a coupled map lattice is translated into a sequence of cellular automata rules for which the critical properties of the original system are reproduced as precisely as desired it is shown that criticality as understood from the point of view of statistical mechanics is intimately related to the various characteristics of wolfram s class iv rules this suggests in turn the picture of a critical surface in the space of rules and provides the basis for a discussion of the problem of classification schemes we review recent cellular automata studies where questions linked to criticality arise and argue that they are unified in light of our results leaving the relationship between computational and statistical characterizations of critical rules as the central problem for future studies on this subject

positive solutions of a class of second order semilinear elliptic equations in the plane on considere l equation elliptique a 2 dimensions u f x u u x r 2 ou x x 1 x 2 et f x u p est une fonction continue non negative sur r 2 r xr 2 on considere l existence de solutions positives definies dans tout r 2

exploiting regularities in large cellular spaces abstract we informally describe a computer algorithm for simulating deterministic cellular automata it grows smarter by selectively recording intermediate computations while operating on a compressed representation of the cellular space time no information is lost because configurations do not actually evolve instead the simulator accomodates random exploration of place times in the future of initial configurations embedded in an effectively unbounded void we use conway s life automaton as a model but the idea extends easily to other geometries dimensions and number of states

the existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term abstract we show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term u u p x f u v v v q x g u v on r n n 3 provided that nonlinearities f and g are positive and continuous the potentials p and q are continuous c positive and satisfy appropriate growth conditions at infinity we find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity while if f and g satisfy some growth conditions at infinity and p q are of slow decay or fast decay at infinity then the system has infinitely many entire solutions which are large or bounded

on the cone multiplier in r3 abstract we prove the sharp l 3 bounds for the cone multiplier in r 3 and the associated square function which is known as mockenhaupt s square function

weighted estimates for conic fourier multipliers we prove a weighted inequality which controls conic fourier multiplier operators in terms of lacunary directional maximal operators by bounding the maximal operators this enables us to conclude that the multiplier operators are bounded on l p mathbb r 3 with 1 p infty

radial fourier multipliers in high dimensions given a fixed p 2 we prove a simple and effective characterization of all radial multipliers of mathcal f l p left mathbb r d right provided that the dimension d is sufficiently large the method also yields new l q space time regularity results for solutions of the wave equation in high dimensions

combined effects of singular and superlinear nonlinearities in some singular boundary value problems abstract this paper deals with a class of singular semilinear elliptic dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results

predecessors and garden of eden configurations in parallel dynamical systems on maxterm and minterm boolean functions abstract in this work we solve the classical predecessor problems for parallel dynamical systems on maxterm and minterm boolean functions actually we solve analytically the predecessor existence problem by giving a characterization to have a predecessor for any given configuration as a consequence we also get a characterization of the garden of eden configurations of these systems moreover the structure of the predecessors found out allows us to give a solution to the unique predecessor problem the coexistence of predecessors problem and the number of predecessors problem

critical points for multiple integrals of the calculus of variations in this paper we deal with the existence of critical points of functional defined on the sobolev space w01 p p 1 by j u int limits omega vartheta x u du dx text where is a bounded open subset of n even for very simple examples in n the differentiability of j u can fail to overcome this difficulty we prove a suitable version of the ambrosetti rabinowitz mountain pass theorem applicable to functionals which are not differentiable in all directions existence and multiplicity of nonnegative critical points are also studied through the use of this theorem

scaling of overhangs in 1 1 dimensional directed processes in a gradient when a gradient is imposed in the control parameter of a directed process in a 1 1 dimensional directed process a front may occur the position of this front evolves in steps of size one in the direction opposite to the gradient and in steps of size equal to or larger than one in the other direction the larger steps are due to overhangs there is a critical value for the control parameter only if the first moment of the step size distribution in the direction of the gradient is not singular i e it takes on a finite value in the thermodynamic limit if there is a critical point this step size distribution is a power law at this point with an exponent larger than two and which the authors conjecture to be equal to 3 beta nu perpendicular to beta is the order parameter exponent and nu perpendicular to is the spatial correlation length exponent in a finite gradient there is a second exponent governing the upper cut off in the step size distribution this exponent is equal to nu perpendicular to 1 nu perpendicular to these two exponents govern the convergence of the position of the front towards the critical value of the control parameter the authors exemplify their discussion with directed site percolation and with two versions of a model originally designed to study catalytic reactions

characterization of random fluctuation based computation in cellular automata a brownian cellular automaton bca is an asynchronous cellular automaton aca in which the timing of the local cell state transitions approaches a poisson point process and the global transitions between cell configurations can be formulated as an irreducible and reversible markov chain bcas exploit fluctuations to find solutions of a computation via a stochastic search process this characteristic has been shown to contribute to a decreased complexity of bcas lee and peper 2008 as compared to non brownian acas with equivalent functionality this paper proposes a computationally universal bca that is based on a conventional aca rather than the previously employed block cellular automata which have transition rules that update each cell simultaneously with its neighboring cells the proposed allows for a more natural update model in which no need arises to locally synchronize the cells in a neighborhood the resulting bca is significantly less complex than equivalent non block non brownian acas which demonstrates that random fluctuations can serve as a powerful resource for efficient computation on cellular automata

on the multilinear restriction and kakeya conjectures we prove d linear analogues of the classical restriction and kakeya conjectures in rd our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians closely related to heat flow we conclude by giving some applications to the corresponding variable coefficient problems and the so called joints problem as well as presenting some n linear analogues for n d

wave front sets local smoothing and bourgain s circular maximal theorem the purpose of this paper is to improve certain known regularity results for the wave equation and to give a simple proof of bourgain s circular maximal theorem 1 we use easy wave front analysis along with techniques previously used in proofs of the carleson sj6lin theorem see 3 5 7 and in the proof of sharp regularity properties of fourier integral operators 13 the circular means operators are defined by

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

origin of complexity and conditional predictability in cellular automata a simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described this leads to introduce the concept of conditional predictability for systems whose trajectory can only be piecewise known the mechanism is used to construct a cellular automaton model for discrete chimeralike states where synchrony and incoherence in an ensemble of identical oscillators coexist the incoherent region is shown to have a periodicity that is three orders of magnitude longer than the period of the synchronous oscillation

1 f fluctuation in the game of life abstract the fourier power spectra are examined for the game of life and its variants the results show that only the game of life exhibits fluctuation by means of observing patterns and measuring entropy and difference pattern spreading rate we conclude that the game of life only belongs to wolfram s class iv cellular automata which are thought to be capable of supporting universal computation this predicts a connection between fluctuation and computational universality

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

the algebraic properties of finite cellular automata abstract the basic patterns by cellular automata have been phenomenologically classified into four types by wolfram i propose a new algebraic method to predict the types of patterns by the elementary cellular automata this method is one example of the application of brownian algebra which is very important in the area of cognitive science the classification carried out by this method is in good agreement with wolfram s classification a significant difference in the present classification is that class 3 by wolfram is divided into two types this difference is apparent in the property of the filter automata which are constructed by the same rule

analysis of one dimensional linear hybrid cellular automata over gf q the paper studies theoretical aspects of one dimensional linear hybrid cellular automata over a finite galois field general results concerning the characteristic polynomials of such automata are presented a probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given along with empirical results and a theoretical analysis cyclic boundary cellular automata are defined and related to the more common null boundary cellular automate an explicit similarity transform between a cellular automaton and its corresponding linear feedback shift register is derived

spontaneous emergence of spatio temporal order in class 4 automata abstract we report surprisingly regular behaviors observed for a class 4 cellular automaton the totalistic rule 20 starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space this is the first evidence that different types of spatio temporal order can emerge under specific conditions out of disorder in the same discrete rule based algorithm

bounded positive entire solutions of singular quasilinear elliptic equations abstract suppose that 0 is a constant and that f r n r r n r is a continuous function with r 0 this paper investigates n dimensional singular quasilinear elliptic equations of the form u f x u u u 0 x r n n 3 and gives some sufficient conditions for the equations to have i a decaying positive entire solution or ii infinitely many positive entire solutions each of which is bounded with a positive lower bound

ground state solutions for the singular lane emden fowler equation with sublinear convection term abstract we are concerned with singular elliptic equations of the form u p x g u f u u a in r n n 3 where p is a positive weight and 0 a 1 under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin we establish the existence of a ground state solution vanishing at infinity our arguments rely essentially on the maximum principle

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

existence of entire large positive solutions of a semilinear elliptic system we show that large positive radial solutions exist for the semilinear elliptic system du p x f v dv q x g u on r n n 3 for nonnegative nondecreasing continuous functions f and g provided the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0tp t dt and 0tq t dt and f g satisfy 1 s 0f t dt 1 2 ds 1 s 0g t dt 1 2 ds

a bilinear approach to the restriction and kakeya conjectures the purpose of this paper is to investigate bilinear variants of the restriction and kakeya conjectures to relate them to the standard formulations of these conjectures and to give applications of this bilinear approach to existing conjectures the methods used are based on several observations and results of bourgain see 2 6 together with some refinements by moyua vargas and vega 17 18 this paper is organized as follows in the first section we discuss bilinear restriction estimates and show how one can pass back and forth between these estimates and the standard restriction estimates we also generalize the 12 7 bilinear restriction estimate of 18 to higher dimensions in the second section we give analogues of the above results for the kakeya operator in particular we give a bilinear improvement to wolff s kakeya theorem in arbitrary dimension in the third section we give applications of these bilinear estimates in three dimensions for example we are able to improve the 42 11 exponent in wolff s restriction theorem to 34 9 we are also able to prove a sharp lp lq restriction theorem which improves on the classical l2 l4 tomas stein theorem and also give some concrete progress on a bilinear restriction conjecture of klainerman and machedon we also give a non bilinear approach to these estimates which gives weaker results but is more direct and probably has a wider range of application

decay symmetry and existence of solutions of semilinear elliptic systems our utmost aim was originally to establish the existence of solutions of system however in this effort we got sidetracked to consider other questions in this way we come to interesting results on asymptotic behavior of solutions on symmetry properties of such solutions and the existence of ground states

existence of entire large positive solutions of semilinear elliptic systems abstract we show that entire large positive radial solutions exist for the semilinear elliptic system u p x v v q x u on r n n 3 for positive and provided that the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0 tp t dt 0 tq t dt and greater than unity and 0 tp t dt and 0 tq t dt if neither nor is greater than one

positive solutions to a singular neumann problem abstract we show the existence of positive solution for the following class of singular neumann problem u a x u h x u p in b r with u 0 on b r where r 0 0 is a positive parameter 0 p 0 1 b r b r 0 r n a b r r and h b r r are radially symmetric nonnegative c 1 functions using variational methods and sub and supersolutions we obtain a solution for an approximated problem involving mixed boundary conditions the limit of the approximated solutions is a positive solution

existence and nonexistence of solutions for singular quadratic quasilinear equations we study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient whose model is 8

critical state between local and global interaction abstract if it is supposed that all phenomena in nature are programmable it must be admitted that the velocity of observation propagation is infinite in natural phenomena however especially in the biological process there are many situations in which the finite velocity of observation propagation cannot be ignored the finiteness of velocity of observation propagation also means that the difference between the speed of each process has to be taken into account there is certain problem of infinity in the form of interaction between macroscopic and microscopic measurements and a time lag between them the formal system proposed here is under the circumstance which the time lag between macroscopic and microscopic measurements leads to inconsistent computation as a result a system s behavior which contains unpredictable fluctuations can be decided by neither macroscopic nor the microscopic measurement the fluctuations due to the inconsistent computation makes the system proceed to decrease the contradiction and it entails self organized critical structures in addition the issue of what is difference and similarity between this system and the self organized criticality proposed by bak et al is discussed although the result of calculation here is similar with the self organized critical structures there is subtle different point of view on the fluctuation the fluctuation in the system of this paper is generated as the contradiction between macroscopic and microscopic measurements it is not given from the outside but from the inside of the system itself

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and jacobi fields abstract we characterize the complexity of geodesic paths on a curved statistical manifold m s through the asymptotic computation of the information geometric complexity v m s and the jacobi vector field intensity j m s the manifold m s is a 2 l dimensional gaussian model reproduced by an appropriate embedding in a larger 4 l dimensional gaussian manifold and endowed with a fisher rao information metric g with non trivial off diagonal terms these terms emerge due to the presence of a correlational structure embedding constraints among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r k first we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r k and conclude that the non trivial off diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates on m s finally we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the jacobi vector field intensity

towards the classification of all boolean cellular automata abstract a classification scheme for all boolean cellular automata models involving an arbitrary number of inputs is proposed the scheme is based upon counting the number of stable points for a given rule i e points whose time development is stable with respect to small perturbations when applied to all cellular automata with 2 3 4 or 5 boolean inputs the latter involving more than 4000 million cases it yields in each case a nontrivial classification i e there is no single class in which nearly all the rules lie in addition it is shown how rules satisfying a given boolean differential equation can easily be obtained

computational mechanics of cellular automata an example abstract we illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space time behavior of elementary one dimensional cellular automaton rule 54 the dominant regular domain of the cellular automation is identified and a domain filter is constructed to locate and classify defects in the domain the primary particles are identified and a range of interparticle interactions is studied the deterministic equation of motion of the filtered space time behavior is derived filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher level defects particle interactions and secondary domains we define the emergence time at which the space time behavior condenses into configurations consisting only of domains particles and particle interactions taken together these techniques serve as the basis for the investigation of pattern evolution and self organization in this representative system

connectivity dynamics and memory in reservoir computing with binary and analog neurons reservoir computing rc systems are powerful models for online computations on input sequences they consist of a memoryless readout neuron that is trained on top of a randomly connected recurrent neural network rc systems are commonly used in two flavors with analog or binary spiking neurons in the recurrent circuits previous work indicated a fundamental difference in the behavior of these two implementations of the rc idea the performance of an rc system built from binary neurons seems to depend strongly on the network connectivity structure in networks of analog neurons such clear dependency has not been observed in this letter we address this apparent dichotomy by investigating the influence of the network connectivity parameterized by the neuron in degree on a family of network models that interpolates between analog and binary networks our analyses are based on a novel estimation of the lyapunov exponent of the network dynamics with the help of branching process theory rank measures that estimate the kernel quality and generalization capabilities of recurrent networks and a novel mean field predictor for computational performance these analyses reveal that the phase transition between ordered and chaotic network behavior of binary circuits qualitatively differs from the one in analog circuits leading to differences in the integration of information over short and long timescales this explains the decreased computational performance observed in binary circuits that are densely connected the mean field predictor is also used to bound the memory function of recurrent circuits of binary neurons

symmetry results for semilinear elliptic systems in the whole space in this paper we obtain symmetry results of gidas ni nirenberg type for cooperative nonlinear elliptic systems in the whole space

existence results for quasilinear elliptic exterior problems involving convection term and nonlinear robin boundary conditions abstract in this paper the authors establish the existence of solutions for a class of elliptic exterior problems involving convection terms and nonlinear robin boundary conditions the proof of the result is made by combining galerkin method with a priori estimates for this kind of problem

multiplicity for strongly indefinite semilinear elliptic system abstract in this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system 2 u u g x v q 1 v in r n 2 v v f x u p 1 u in r n our interest is the relation between the number of solutions and the topology of the global minima set of a suitable ground energy function

phase transition in nk kauffman networks and its correction for boolean irreducibility abstract in a series of articles published in 1986 derrida and his colleagues studied two mean field treatments the quenched and the annealed for nk kauffman networks their main results lead to a phase transition curve k c 2 p c 1 p c 1 0 p c 1 for the critical average connectivity k c in terms of the bias p c of extracting a 1 for the output of the automata values of k bigger than k c correspond to the so called chaotic phase while k k c to an ordered phase in zertuche 2009 a new classification for the boolean functions called boolean irreducibility permitted the study of new phenomena of nk kauffman networks in the present work we study once again the mean field treatment for nk kauffman networks correcting it for boolean irreducibility a shifted phase transition curve is found in particular for p c 1 2 the predicted value k c 2 by derrida et al changes to k c 2 62140224613 we support our results with numerical simulations

primitive cellular automata threshold decomposition and ranked order operations a connection between ranked filters and primitive cellular automata is discussed primitive cellular automata are those whose nodes comprise a single bit of state information it is shown that these structures can perform ranked order operations on one dimensional k level signals by virtue of threshold decomposition extensions to the case of multidimensional signals are also possible

embedding computation in one dimensional automata by phase coding solitons it is shown that some kind of meaningful computation can be embedded in very simple microscopically homogeneous one dimensional automata and in particular filter automata with a parity next state rule a systematic procedure is given for generating moving periodic structures particles these particles exhibit soliton like properties that is they often pass through one another with phase shifts ways to encode information in the phase of these particles are discussed the search for useful logical operations is reduced to a search for paths in certain graphs as a demonstration of principle the details of implementing a carry ripple adder are given

parallel dynamical systems over directed dependency graphs abstract in this work we analyze the orbit structure of parallel discrete dynamical systems over directed dependency graphs with boolean functions as global functions in this sense for the cases corresponding to the simplest boolean functions and and or it is proved that only fixed or eventually fixed points appear as occurs over undirected dependency graphs however for general boolean functions it is shown that any period can appear so breaking the pattern found for the undirected case where only eventually fixed points or 2 periodic orbits can exist

substitution systems and nonextensive statistics abstract substitution systems evolve in time by generating sequences of symbols from a finite alphabet at a certain iteration step the existing symbols are systematically replaced by blocks of n k symbols also within the alphabet with n k a natural number being the length of the k th block of the substitution the dynamics of these systems leads naturally to fractals and self similarity by using b calculus garcia morales 2012 universal maps for deterministic substitution systems both of constant and non constant length are formulated in 1d it is then shown how these systems can be put in direct correspondence with tsallis entropy a second law of thermodynamics is also proved for these systems in the asymptotic limit of large words