critical exponents from power spectra we have simulated the two and three dimensional ising models at their respective critical points with a conventional monte carlo algorithm from the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz 2 16 2 19 andz 2 05 in agreement with the results quoted in the literature we have also studied the power spectrum for the kardar parisi zhang and sun guo grant equations describing interface dynamics arguments similar to what was recently used to conclude thatz 4 for model b in critical dynamics were applied to the sun guo grant growth model and the known exact values for the roughening and dynamic exponents were obtained from an analysis of the corresponding power spectrum in self organized critical sand models one obtains a recently proposed hyperscaling relation

contraction analysis of monotone systems via separable functions in this paper we study incremental stability of monotone nonlinear systems through contraction analysis we provide sufficient conditions for incremental asymptotic stability in terms of the lie derivatives of differential one forms or lie brackets of vector fields these conditions can be viewed as sum or max separable conditions respectively for incremental exponential stability we show that the existence of such separable functions is both necessary and sufficient under standard assumptions for the converse lyapunov theorem of exponential stability as a by product we also provide necessary and sufficient conditions for exponential stability of positive linear time varying systems the results are illustrated through examples

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

antichaos in a class of random boolean cellular automata abstract a variant of kauffman s model of cellular metabolism is presented it is a randomly generated network of boolean gates identical to kauffman s except for a small bias in favor of boolean gates that depend on at most one input the bias is asymptotic to 0 as the number of gates increases upper bounds on the time until the network reaches a state cycle and the size of the state cycle as functions of the number of gates n are derived for any c 0 if the bias approaches 0 slowly enough the state cycles will be smaller than nc

universality along the critical line of the ising cellular automata the author checks the hypothesis of universality along the critical line of the ising cellular automata ica by measuring critical exponents of damage propagation at the transition temperature tk in zero field and at higher temperatures in nonzero field and at the kauffman limit t infinity numerical results support the claim of universality

immersion and invariance stabilization of nonlinear systems via virtual and horizontal contraction the main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design namely the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step i to replace attractivity of the manifold by virtual contraction of the off the manifold coordinate and ii to ensure the attractivity of the manifold rendering it horizontally contractive this makes more systematic the design with more explicit degrees of freedom to accomplish the task several examples including the classical case of systems in feedback form are used to illustrate the proposed design

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

control of the immune response by a threshold automata model on a lattice abstract the kut mean field model for the immune response is generalized on a lattice using boolcan and threshold automata it is shown that the lattice model can exhibit properties that the mean field model cannot even if the biological meaning of the lattice geometry is dubious the attractors of the mean field model become unstable under mixing of populations and the system may reach the paralysis state instead of the memory vaccinated the probability of vaccination is calculated analytically and checked numerically a threshold automata model which includes interactions with the antigen and uses random neighbours and random time delays is proposed allowing control of the immune response by the concentration of antigen finally quantitative results of the dynamics are given using the model itself unlike previous works that used differential equations the numerical results show low and high dose paralysis versus medium dose vaccination

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

reduction theorems for stability of closed sets with application to backstepping control design we present a solution to the following reduction problem for asymptotic stability of closed sets in nonlinear systems given two closed positively invariant subsets of the state space of a nonlinear system c 1 c 2 assuming that c 1 is asymptotically stable relative to c 2 find conditions under which c 1 is asymptotically stable we also investigate analogous reduction problems for stability and attractivity we illustrate the implications of our results on the stability of sets for cascade connected systems and on a hierarchical control design problem for upper triangular control systems we present a reduction based backstepping technique that does not require the knowledge of a lyapunov function and mitigates the problem of controller complexity arising in classical backstepping design

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

on the dynamic exponent of the two dimensional ising model the authors use the method of damage spreading to measure the time taken for the equilibrium damage the magnetization to disappear in finite systems 10 or 2 27

immersion and invariance a new tool for stabilization and adaptive control of nonlinear systems a new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented the method relies upon the notions of system immersion and manifold invariance and in principle does not require the knowledge of a control lyapunov function the construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the invariant output zeroing manifold and its friend the method is well suited in situations where we know a stabilizing controller of a nominal reduced order model which we would like to robustify with respect to higher order dynamics this is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one we also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective our construction does not invoke certainty equivalence nor requires a linear parameterization furthermore viewed from a lyapunov perspective it provides a procedure to add cross terms between the parameter estimates and the plant states finally it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form yielding new stabilizing control laws we illustrate the method with several academic and practical examples including a mechanical system with flexibility modes an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application

damage spreading in the kawasaki ising model abstract we observe no phase transition in the damage spreading probability at the curie point of the 2d ising model with nearest neighbor spin exchange dynamics furthermore we report values of the growth exponent z close to unity implying speed of light transmission of information and values of the exponents describing the scaling behavior of the damage mass with time and distance close to two finally we discuss the spreading of damage in a one dimensional system

effective analysis of damage spreading in ising models using large lattices and different methods of simulation and analysis the kinetic critical exponent z for damage spreading is shown to be consistent with z 2 in two to five dimensions without the logarithmic problems seen in some earlier work

the role of droplet fluctuations in kinetic ising models the authors examine by monte carlo simulation and the damage algorithm the late time behaviour of fluctuations in the low temperature ordered phase of the two dimensional kinetic ising model it has been suggested that at late times correlations could be dominated by long lived droplet fluctuations of the other ordered phase giving rise to stretched exponential decays of the spin auto correlation function over the time regimes they have studied they see no evidence for anomalous long lived droplets and find that the probability distribution for droplet lifetimes decays by an ordinary exponential

critical dynamics of the three dimensional ising model a monte carlo study extensive monte carlo simulations have been performed to analyze the dynamical behavior of the three dimensional ising model with local dynamics we have studied the equilibrium correlation functions and the power spectral densities of odd and even observables the exponential relaxation times have been calculated in the asymptotic one exponential time region we find that the critical exponentz 2 09 0 02 characterizes the algebraic divergence with lattice size for all observables the influence of scaling corrections has been analyzed we have determined integrated relaxation times as well their dynamical exponentzint agrees withz for correlations of the magnetization and its absolute value but it is different for energy correlations we have applied a scaling method to analyze the behavior of the correlation functions this method verifies excellent scaling behavior and yields a dynamical exponentzscal which perfectly agrees withz

renormalization in the complete mellin representation of feynman amplitudes the feynman amplitudes are renormalized in the formalism of the cm representation this mellin barnes type integral representation previously introduced for the study of asymptotic behaviours is shown to have the following interesting property in contrast with the usual subtraction procedures the renormalization leaves the cm integrand unchanged and only results into translations of the integration path the explicit cm representation of the renormalized amplitudes is given in addition the dimensional regularization and the extension to spinor amplitudes are sketched

domain growth kinetics and symmetry breaking in a thermally quenched system the authors simulate thermal quenches on a two dimensional hard core model with symmetry breaking phase transition by dividing large configurations into many small sub squares lack of self averaging is avoided and statistics are improved dynamic scaling is observed during more than two decades

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

deducing local rules for solving global tasks with random boolean networks abstract it has been shown that uniform as well as non uniform cellular automata ca can be evolved to perform certain computational tasks random boolean networks are a generalization of two state cellular automata where the interconnection topology and the cell s rules are specified at random here we present a novel analytical approach to find the local rules of random boolean networks rbns to solve the global density classification and the synchronization task from any initial configuration we quantitatively and qualitatively compare our results with previously published work on cellular automata and show that randomly interconnected automata are computationally more efficient in solving these two global tasks our approach also provides convergence and quality estimates and allows the networks to be randomly rewired during operation without affecting the global performance finally we show that rbns outperform small world topologies on the density classification task and that they perform equally well on the synchronization task our novel approach and the results may have applications in designing robust complex networks and locally interacting distributed computing systems for solving global tasks

a percolation approach to the kauffman model a study is made of the spreading of damage in the random but deterministic kauffman model on the square lattice with the spreading from one edge of the lattice the critical value of the parameterp c above which the system becomes chaotic is found to bep c 0 298 the possibility of suppression of the chaotic phase by noise is also studied it is found that forp p c an extremely large noise levelg 0 99 is required if possible at all

dynamic exponent for 2d ising model by power spectra method we consider power spectra for fluctuating quantities at a critical point p omega varies as omega phi where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered from the magnetization spectra obtained with simulations z is found to be 2 13 or 0 03 for the two dimensional glauber kinetic ising model hence in accord with recent monte carlo relaxational studies but at odds with those obtained by series expansion and damage spreading methods excellent dynamic finite size scaling for system sizes l 10 to 128 supports our estimate

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

multivalley structure in kauffman s model analogy with spin glasses kauffman s model describes a random network of automata the authors calculations indicate that the multivalley structure of the basins of attraction in kauffman s model is very similar to that of infinite range spin glasses the similarity with spin glasses is tested quantitatively by computing the probability that two initial configurations fall into the same valley

reversible boolean networks ii phase transitions oscillations and local structures we continue our consideration of a class of models describing the reversible dynamics of n boolean variables each with k inputs we investigate in detail the behavior of the hamming distance as well as of the distribution of orbit lengths as n and k are varied we present numerical evidence for a phase transition in the behavior of the hamming distance at a critical value kc 1 62 and also an analytic theory that yields the exact bounds 1 5 k c 2 we also discuss the large oscillations that we observe in the hamming distance for k k c as a function of time as well as in the distribution of cycle lengths as a function of cycle length for moderate k both greater than and less than kc we propose that local structures or subsets of spins whose dynamics are not fully coupled to the other spins in the system play a crucial role in generating these oscillations the simplest of these structures are linear chains called linkages and rings called circuits we discuss the properties of the linkages in some detail and sketch the properties of circuits we argue that the observed oscillation phenomena can be largely understood in terms of these local structures 2001 published by elsevier science b v

a differential lyapunov framework for contraction analysis lyapunov s second theorem is an essential tool for stability analysis of differential equations the paper provides an analog theorem for incremental stability analysis by lifting the lyapunov function to the tangent bundle the lyapunov function endows the state space with a finsler structure incremental stability is inferred from infinitesimal contraction of the finsler metrics through integration along solutions curves

the dynamic critical exponent of the three dimensional ising model we measure the dynamic exponent of the three dimensional ising model using a damage spreading monte carlo approach as described by macisaac and jan we simulate systems froml 5 tol 60 at the critical temperature tc 4 5115 we report a dynamic exponent z 2 35 0 05 a value much larger than the consensus value of 2 02 whereas if we assume logarithmic corrections we find thatz 2 05 0 05

fractal dimensions in three dimensional kauffman cellular automata the kauffman random networks of automata are studied on a simple cubic lattice by computer simulations each automaton follows random rules depending on its six neighbours and fixed in time a transition between the frozen and the chaotic phase is observed and the fractal dimension of the asymptotic actual damage at the phase transition is measured

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics