holonomic functions of several complex variables and singularities of anisotropic ising n fold integrals focusing on examples associated with holonomic functions we try to bring new ideas on how to look at phase transitions for which the critical manifolds are not points but curves depending on a spectral variable or even fill higher dimensional submanifolds lattice statistical mechanics often provides a natural holonomic framework to perform singularity analysis with several complex variables that would in the most general mathematical framework be too complex or simply could not be defined in a learn by example approach considering several picard fuchs systems of two variables above calabi yau odes associated with double hypergeometric series we show that d finite holonomic functions are actually a good framework for finding properly the singular manifolds the singular manifolds are found to be genus zero curves we then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics the n fold integrals n corresponding to the n particle decomposition of the magnetic susceptibility of the anisotropic square ising model in this anisotropic case we revisit a set of so called nickelian singularities that turns out to be a two parameter family of elliptic curves we then find the first set of non nickelian singularities for 3 and 4 that also turns out to be rational or elliptic curves we underline the fact that these singular curves depend on the anisotropy of the ising model or equivalently that they depend on the spectral parameter of the model this has important consequences on the physical nature of the anisotropic n s which appear to be highly composite objects we address from a birational viewpoint the emergence of families of elliptic curves and that of calabi yau manifolds on such problems we also address the question of singularities of non holonomic functions with a discussion on the accumulation of these singular curves for the non holonomic anisotropic full susceptibility this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

the z invariant ising model via dimers the z invariant ising model baxter in philos trans r soc lond a math phys eng sci 289 1359 315 346 1978 is defined on an isoradial graph and has coupling constants depending on an elliptic parameter k when k 0 the model is critical and as k varies the whole range of temperatures is covered in this paper we study the corresponding dimer model on the fisher graph thus extending our papers boutillier and de tiliere in probab theory relat fields 147 379 413 2010 commun math phys 301 2 473 516 2011 to the fullz invariant case one of our main results is an explicit local formula for the inverse of the kasteleyn operator its most remarkable feature is that it is an elliptic generalization of boutillier and de tiliere 2011 it involves a local function and the massive discrete exponential function introduced in boutillier et al invent math 208 1 109 189 2017 this shows in particular that z invariance and not criticality is at the heart of obtaining local expressions we then compute asymptotics and deduce an explicit local expression for a natural gibbs measure we prove a local formula for the ising model free energy we also prove that this free energy is equal up to constants to that of the z invariant spanning forests of boutillier et al 2017 and deduce that the two models have the same second order phase transition in k next we prove a self duality relation for this model extending a result of baxter to all isoradial graphs in the last part we prove explicit local expressions for the dimer model on a bipartite graph corresponding to the xor version of this z invariant ising model

contains and inside relationships within combinatorial pyramids irregular pyramids are made of a stack of successively reduced graphs embedded in the plane such pyramids are used within the segmentation framework to encode a hierarchy of partitions the different graph models used within the irregular pyramid framework encode different types of relationships between regions this paper compares different graph models used within the irregular pyramid framework according to a set of relationships between regions we also define a new algorithm based on a pyramid of combinatorial maps which allows to determine if one region contains the other using only local calculus

synchronization of stochastic bistable systems by biperiodic signals we study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit schmitt trigger the signal we use is a biharmonic one i e a superposition of low and high frequency harmonic components it is shown that the mean switching frequency msf of the system can be locked at both low and high frequencies moreover the phenomenon of msf locking at the lower frequency can be induced and enhanced by the higher frequency excitation thus high frequency bias can control synchronization at the low frequency

deterministic stochastic resonance in a rossler oscillator we discuss the characteristics of stochastic resonancelike behavior observed in a deterministic system if a periodically forced rossler oscillator strays from the phase locking state it exhibits the intermittent behavior known as phase slips when the periodic force is modulated by a weak signal the phase slips synchronize with the weak signal statistically we numerically demonstrate in terms of interslip intervals and signal to noise ratio that the maximum synchronization can be achieved with the optimum intensity of chaotic fluctuations it is shown that the stochastic resonancelike behavior can be observed regardless of the choice of parameters the frequency dependence of the signal indicates that there is an optimum frequency for the maximum resonance the phase slip rate is derived based on the fact that the phase slips are caused by a boundary crisis caused by an unstable unstable pair bifurcation the interslip distributions obtained from the derived slip rate and the approximation theory of the time dependent poisson process agree with those obtained by numerical simulations in addition the maximum enhancement of a weak signal is shown to be achieved by adjusting the chaotic fluctuations even if a signal becomes mixed with noise

on the singularity structure of the 2d ising model susceptibility some simplifications of the integrals 2n 1 derived by wu et al 1976 13 316 that contribute to the zero field susceptibility of the 2d square lattice ising model are reported in particular several alternate expressions for the integrands in 2n 1 are determined which greatly facilitate both the generation of high temperature series and analytical analysis one can show that as series 2n 1 22n s 2 4n n 1 1 o s where s is the high temperature variable sin 2k with k the conventional normalized inverse temperature analysis of the integrals near symmetry points of the integrands shows that 2n 1 s is singular on the unit circle at sk exp ik where 2cos k cos 2 k 2n 1 cos 2 2n 1 n k n the singularities k 0 excepted are logarithmic branch points of order 2n n 1 1ln with 1 s sk there is numerical evidence from series that these van hove points in addition to the known points at s 1 and i exhaust the singularities on the unit circle barring cancellation from extra unobserved singularities one can conclude that s 1 is a natural boundary for the susceptibility

statistics of entrance times abstract the statistical properties of the transitions of a discrete markov process are investigated in terms of entrance times a simple formula for their density is given and used to measure the synchronization of a process with a periodic driving force for the mcnamara wiesenfeld model of stochastic resonance we find parameter regions in which the transition frequency of the process is locked with the frequency of the external driving

a new proposal for graph based image classification using frequent approximate subgraphs graph based data representations are an important research topic due to the suitability of this kind of data structure to model entities and the complex relations among them in computer vision graphs have been used to model images in order to add some high level information relations to the low level representation of individual parts how to deal with these representations for specific tasks is not easy due to the complexity of the data structure itself in this paper we propose to use a graph mining technique for image classification introducing approximate patterns discovery in the mining process in order to allow certain distortions in the data being modeled we are proposing to combine a powerful graph based image representation adapted to this specific task and frequent approximate subgraph fas mining algorithms in order to classify images in the case of image representation we are proposing to use more robust descriptors than our previous approach in this topic and we also suggest a criterion to select the isomorphism threshold for the graph mining step this proposal is tested in two well known collections to show the improvement with respect to the previous related works highlightswe propose a new framework for image classification which uses frequent approximate subgraph patterns as features we propose to compute automatically the substitution matrices needed in the process instead of using expert knowledge we propose to use a new graph based image representation we propose a criterion for selecting isomorphism threshold for the graph mining process

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

irrelevant operators in the two dimensional ising model by using conformal field theory we classify the possible irrelevant operators for the ising model with nearest neighbour interactions on the square and triangular lattices we analyse the existing results for the free energy and its derivatives and for the correlation length showing that they are in agreement with the conformal field theory predictions moreover these results imply that the nonlinear scaling field of the t operator where t is the energy momentum tensor vanishes at the critical point several other peculiar cancellations are explained in terms of a number of general conjectures we show that all existing results on the square and triangular lattices are consistent with the assumption that only nonzero spin operators are present

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

the susceptibility of the square lattice ising model new developments we have made substantial advances in elucidating the properties of the susceptibility of the square lattice ising model we discuss its analyticity properties certain closed form expressions for subsets of the coefficients and give an algorithm of complexity o n6 to determine its first n coefficients as a result we have generated and analyzed series with more than 300 terms in both the high and low temperature regime we quantify the effect of irrelevant variables to the scaling amplitude functions in particular we find and quantify the breakdown of simple scaling in the absence of irrelevant scaling fields arising first at order t tc 9 4 though high low temperature symmetry is still preserved at terms of order t tc 17 4 and beyond this symmetry is no longer present the short distance terms are shown to have the form t tc p log t tc q with p q2 conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments

factorization of the ising model form factors we present a general method for analytically factorizing the n fold form factor integrals f n n n t for the correlation functions of the ising model on the diagonal in terms of the hypergeometric functions 2f1 1 2 n 1 2 n 1 t which appear in the form factor f 1 n n t new quadratic recursion and quartic identities are obtained for the form factors for n 2 3 for n 2 3 4 explicit results are given for the form factors these factorizations are proved for all n for n 2 3 these results yield the emergence of palindromic polynomials canonically associated with elliptic curves as a consequence understanding the form factors amounts to describing and understanding an infinite set of palindromic polynomials canonically associated with elliptic curves from an analytical viewpoint the relation of these palindromic polynomials with hypergeometric functions associated with elliptic curves is made very explicitly and from a differential algebra viewpoint this corresponds to the emergence of direct sums of differential operators homomorphic to symmetric powers of a second order operator associated with elliptic curve

shot noise in the leaky integrate and fire neuron we study the influence of noise on the transmission of temporal information by a leaky integrate and fire neuron using the theory of shot noise the model includes a finite number of synapses and has a membrane potential variance de facto modulated by the input signal the phenomenon of stochastic resonance in spiking neurons is analytically exhibited using an inhomogeneous poisson process model of the spike trains and links with the traditional ornstein uhlenbeck process obtained by a diffusion approximation are given it is shown that the modulated membrane potential variance inherent to the model gives better signal processing capabilities than the diffusion approximation

scaling and universality in the two dimensional ising model with a magnetic field the scaling function of the two dimensional ising model on the square and triangular lattices is obtained numerically via baxter s variational corner transfer matrix approach the use of aharony fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses our results are in excellent agreement with quantum field theory calculations of fonseca and zamolodchikov as well as with many previously known exact and numerical calculations including susceptibility results by barouch mccoy tracy and wu

on the singularities in the susceptibility expansion for the two dimensional ising model for temperatures below the critical temperature the magnetic susceptibility for the two dimensional isotropic ising model can be expressed in terms of an infinite series of multiple integrals with respect to a parameter related to temperature and the interaction constant the integrals may be extended to functions analytic outside the unit circle in a groundbreaking paper nickel j phys a 32 3889 3906 1999 identified a class of singularities of these integrals on the unit circle in this note we show that there are no other singularities on the unit circle

complex temperature singularities in the d 2 ising model triangular and honeycomb lattices we study complex temperature singularities of the ising model on the triangular and honeycomb lattices we first discuss the complex t phases and their boundaries from exact results we determine the complex t singularities in the specific heat and magnetization for the triangular lattice we discuss the implications of the divergence of the magnetization at the point u d 1 where u d z 2 d e 4k and extend a previous study by guttmann of the susceptibility at this point with the use of differential approximants for the honeycomb lattice from an analysis of low temperature series expansions we have found evidence that the uniform and staggered susceptibilities n and n a both have divergent singularities at z d 1 z and our numerical values for the exponents are consistent with the hypothesis that the exact values are 0 d 0 a d 5 2 the critical amplitudes at this singularity were calculated using our exact results for 0 and together with numerical values for 0 from series analyses we find that the exponent relation 0 c 2 c 0 d 2 is violated at z d 1 on the honeycomb lattice the right hand side is consistent with being equal to 4 rather than 2 the connections of the critical exponents at these two singularities on the triangular and honeycomb lattice are discussed

addendum to on the singularity structure of the 2d ising model susceptibility a remarkable product formula first derived by palmer and tracy 1981 adv appl math 2 329 for the integrand of the two dimensional ising model susceptibility expansion coefficients 2n for temperatures t less than the critical t c is shown to apply equally for 2n 1 for t t c and agrees with formulae derived by yamada 1984 prog theor phys 71 1416 this new representation simplifies the derivation of the results in the original paper of this title 1999 j phys a math gen 32 3889 to the extent that the leading series behaviour and the singularity structure can be deduced almost by inspection the derivation of series is also simplified and i show using extended series and knowledge of the singularity structure that there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analysis

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

stochastic multiresonance and correlation time controlled stability for a harmonic oscillator with fluctuating frequency the long time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force and an additive thermal noise is considered analytically the colored fluctuations of the oscillator frequency are modeled as a three level markovian noise using the shapiro loginov formula the exact expressions of several stochastic resonance sr characteristics such as the spectral amplification the variance of the output signal the signal to noise ratio and the sr gain have been calculated the nonmonotonic dependence of the sr characteristics versus the noise parameters as well as versus the input signal frequency and also the conditions for the appearance of energetic instability are analyzed in particular the multiresonancelike behavior of the variance and the signal to noise ratio as functions of the noise correlation time are observed and the connection between the occurrence of energetic instability and the phenomenon of stochastic multiresonance is established some unexpected effects such as the hypersensitive response of the spectral amplification to small variations of the noise amplitude encountered in the case of a large flatness of the colored noise are also discussed

ising field theory quadratic difference equations for the n point green s functions on the lattice for the two dimensional ising model at arbitrary temperature a system of quadratic difference equations is presented involving the correlations of n order variables and that of n ensuremath 2 order and two disorder variables with suitable boundary conditions these equations specify the correlations

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

diagonal ising susceptibility elliptic integrals modular forms and calabi yau equations we give the exact expressions of the partial susceptibilities 3 d and 4 d for the diagonal susceptibility of the ising model in terms of modular forms and calabi yau odes and more specifically 3f2 1 3 2 3 3 2 1 1 z and 4f3 1 2 1 2 1 2 1 2 1 1 1 z hypergeometric functions by solving the connection problems we analytically compute the behavior at all finite singular points for 3 d and 4 d we also give new results for 5 d we see in particular the emergence of a remarkable order 6 operator which is such that its symmetric square has a rational solution these new exact results indicate that the linear differential operators occurring in the n fold integrals of the ising model are not only derived from geometry globally nilpotent but actually correspond to special geometry homomorphic to their formal adjoint this raises the question of seeing if these special geometry ising operators are special ones reducing in fact systematically to selected k balanced q 1fq hypergeometric functions or correspond to the more general solutions of calabi yau equations

finding the best not the most classification on structure data such as graphs has drawn wide interest in recent years due to the lack of explicit features to represent graphs for training classification models extensive studies have been focused on extracting the most discriminative subgraphs features from the training graph dataset to transfer graphs into vector data however such filter based methods suffer from two major disadvantages 1 the subgraph feature selection is separated from the model learning process so the selected most discriminative subgraphs may not best fit the subsequent learning model resulting in deteriorated classification results 2 all these methods rely on users to specify the number of subgraph features k and suboptimally specified k values often result in significantly reduced classification accuracy in this paper we propose a new graph classification paradigm which overcomes the above disadvantages by formulating subgraph feature selection as learning a k dimensional feature space from an implicit and large subgraph space with the optimal k value being automatically determined to achieve the goal we propose a regularized loss minimization driven rlmd feature selection method for graph classification rlmd integrates subgraph selection and model learning into a unified framework to find discriminative subgraphs with guaranteed minimum loss w r t the objective function to automatically determine the optimal number of subgraphs k from the exponentially large subgraph space an effective elastic net and a subgradient method are proposed to derive the stopping criterion so that k can be automatically obtained once rlmd converges the proposed rlmd method enjoys gratifying property including proved convergence and applicability to various loss functions experimental results on real life graph datasets demonstrate significant performance gain highlightsour algorithm selects the optimal subgaphs for graph classification we generalize the column generation technique of gboost for graph classification we use the elastic net to produce sparse and robust solutions for subgraph selection we derive an effective pruning rule for search space reduction we demonstrate the effectiveness of our algorithm

synchronization under periodic modulation of symmetric double square wells in a bistable stochastic system the features of the first passage time density function are analyzed theoretically in terms of synchronization between noise and periodic signal in a symmetric double square well system resonance is demonstrated as a maximum synchronization between them to have the maximum cooperation between signal and noise it is shown that the noise strength at resonance should increase linearly with the frequency of the signal the time scale of the process at resonance is also shown to increase linearly with the period of the signal

limit cycles and stochastic resonance in a periodically driven langevin equation subject to white noise we investigate stochastic resonance sr in a periodically driven langevin system on a circle the bifurcation parameter of the system and the amplitude of the periodic signal are controlled the response amplitude that characterizes the degree of the amplification of the input periodic signal and the quality factor that is a coherence measure of the spontaneous periodic motion sustained by noise are computed and plotted as functions of the noise intensity according to different parameter values four types of behaviour are observed as the results of interplay between two types of stochastic resonances the spontaneous sr and conventional sr respectively

limit cycles for extended bistable stochastic resonance system abstract bistable system is a typical model in stochastic resonance sr researching and it has been known that the deterministic dynamics of a noised system plays an important role in making sr phenomena occur by embedding a non autonomous system onto a cylinder or extending the one dimensional non autonomous system as a three dimensional autonomous system restricted on a cylinder this paper theoretically analyzes the dynamics of the well known periodically driven bistable system after three limit cycles equivalent to the periodic states of the un extended system are proved existent for subthreshold case they are shown to be preserved even in the suprathreshold case with large driving frequency moreover it is also proved in suprathreshold case that the three ones keep touching each other and combine into one larger globally stable limit cycle as the driving frequency decreases to some certain degree

integrability versus non integrability hard hexagons and hard squares compared in this paper we compare the integrable hard hexagon model with the nonintegrable hard squares model by means of partition function roots and transfer matrix eigenvalues we consider partition functions for toroidal cylindrical and free free boundary conditions up to sizes 40 40 and transfer matrices up to 30 sites for all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis the density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest and equal moduli and exhibits much greater structure than the corresponding density of hard hexagons we also study the special point z 1 of hard squares where all eigenvalues have unit modulus and we give several conjectures for the value at z 1 of the partition functions

system size stochastic resonance in a model for opinion formation we study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual imitation influence of fashion and randomness we show that in the absence of fashion the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following kramer s law we also demonstrate the existence of system size stochastic resonance by which there is an optimal value for the number of individuals n for which the average opinion follows better the fashion

numerical analysis of noise induced regular oscillations abstract constructive sufficient conditions for regular oscillations in systems with stochastic resonance are given using these conditions a numerical procedure for indicating domains of parameters corresponding to the regular oscillations are proposed the regular oscillations in systems with additive and multiplicative noise are considered results of numerical experiments are presented

susceptibility calculations in periodic and quasiperiodic planar ising models new results are presented for the wavevector dependent susceptibility of z invariant periodic and quasiperiodic ising models in the scaling limit generalizing old results of tracy and mccoy for the square lattice explicit results are worked out for the two leading singular terms of the susceptibility on four regular isotropic lattices the methods used provide a proof of the extended lattice lattice scaling hypothesis for the class of models under consideration

experimental mathematics on the magnetic susceptibility of the square lattice ising model we calculate very long low and high temperature series for the susceptibility of the square lattice ising model as well as very long series for the five particle contribution 5 and six particle contribution 6 these calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 cpu hours on computer clusters the series for low and high temperature regimes 5 and 6 are now extended to 2000 terms in addition for 5 10 000 terms of the series are calculated modulo a single prime and have been used to find the linear ode satisfied by 5 modulo a prime a diff pade analysis of the 2000 terms series for 5 and 6 confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n particle components of the susceptibility up to a small set of additional singularities the exponents at all the singularities of the fuchsian linear ode of 5 and the as yet unknown ode of 6 are given they are all rational numbers we find the presence of singularities at w 1 2 for the linear ode of 5 and w2 1 8 for the ode of 6 which are not singularities of the physical 5 and 6 that is to say the series solutions of the ode s which are analytic at w 0 furthermore analysis of the long series for 5 and 6 combined with the corresponding long series for the full susceptibility yields previously conjectured singularities in some n n 7 the exponents at all these singularities are also seen to be rational numbers we also present a mechanism of resummation of the logarithmic singularities of the n leading to the known power law critical behaviour occurring in the full and perform a power spectrum analysis giving strong arguments in favour of the existence of a natural boundary for the full susceptibility

the availability of logical operation induced by dichotomous noise for a nonlinear bistable system instead of a continuous system driven by gaussian white noise logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise which shows a phenomenon different from gaussian white noise we can realize two parallel logical operations by simply adjusting the values of these two thresholds besides to quantify the reliability of obtaining the correct logic output we numerically calculate the success probability and effects of dichotomous noise on the success probability are observed these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise

quantifying stochastic resonance in bistable systems response vs residence time distribution functions a wealth of research on stochastic resonance sr during the past decade has led to different ways of defining this phenomenon most prominent are measures based on the response function and on the residence time distribution function while the theory for the response functions is well developed a first fully systematic theory for the residence time distribution functions is developed in this paper subsequently we reconsider formerly introduced measures of sr based on the residence time distribution and compare with those based on the response function

scaling functions in the square ising model we show and give the linear differential operators of order for the integrals which appear in the two point correlation scaling function of ising model the integrals are given in expansion around in the basis of the formal solutions of with transcendental combination coefficients we find that the expression is a solution of the painleve vi equation in the scaling limit combinations of the analytic at solutions of sum to we show that the expression is the scaling limit of the correlation function and the differential galois groups of the factors occurring in the operators are given

isomonodromic deformation theory and the next to diagonal correlations of the anisotropic square lattice ising model in 1980 jimbo and miwa evaluated the diagonal two point correlation function of the square lattice ising model as a function of the sixth painleve system by constructing an associated isomonodromic system within their theory of holonomic quantum fields more recently an alternative isomonodromy theory was constructed based on bi orthogonal polynomials on the unit circle with regular semi classical weights for which the diagonal ising correlations arise as the leading coefficient of the polynomials specialized appropriately here we demonstrate that the next to diagonal correlations of the anisotropic ising model are evaluated as one of the elements of this isomonodromic system or essentially as the cauchy hilbert transform of one of the bi orthogonal polynomials

multipeaked probability distributions of recurrence times we determine probabilities of recurrence time into finite sized physically meaningful subsets of phase space we consider three different autonomous chaotic systems i scattering in a three peaked potential ii connected billiards and iii lorenz equations we find multipeaked probability distributions similar to the distributions found in driven stochastically resonant systems in nondriven systems such as ours only monotonic decaying distributions exponentials stretched exponentials power laws and slight variations or combinations of these have hitherto been reported discrete peaks in autonomous systems have as yet escaped attention in autonomous systems and correspond to specific trajectory subsets involving an integer number of loops

the ising susceptibility scaling function we have dramatically extended the zero field susceptibility series at both high and low temperature of the ising model on the triangular and honeycomb lattices and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and for the square and honeycomb lattices the antiferromagnetic critical point

phase velocity and phase diffusion in periodically driven discrete state systems we develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states this theory is applied to a dichotomically driven markovian two state system explicit expressions for the mean phase velocity the effective phase diffusion coefficient and the pe clet number are analytically calculated the latter indicates as a measure of phase coherence forced synchronization of the stochastic system with respect to the periodic driving and exhibits a bona fide resonance in a second step the theory is applied to a non markovian two state system modeling excitable systems the results prove again stochastic synchronization to the periodic driving and are in good agreement with simulations of a stochastic fitzhugh nagumo system

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

noise sensitivity of phase synchronization time in stochastic resonance theory and experiment recent numerical and heuristic arguments have revealed that the average phase synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation in particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value here we present an explicit formula for the average phase synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals we also provide experimental evidence for the cusplike behavior by using a bistable microelectronic circuit system

markov analysis of stochastic resonance in a periodically driven integrate and fire neuron we model the dynamics of the leaky integrate and fire neuron under periodic stimulation as a markov process with respect to the stimulus phase this avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long standing reset problem the neuron exhibits stochastic resonance both with respect to input noise intensity and stimulus frequency the latter resonance arises by matching the stimulus frequency to the refractory time of the neuron the markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism