separation of variables and exact solution to the dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry in the present article a complete separation of variables in the dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates the resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solution is discussed

breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps to identify and to explain coupling induced phase transitions in coupled map lattices cml has been a lingering enigma for about two decades in numerical simulations this phenomenon has always been observed preceded by a lowering of the lyapunov dimension suggesting that the transition might require changes of linear stability yet recent proofs of co existence of several phases in specially designed models work in the expanding regime where all lyapunov exponents remain positive in this paper we consider a family of cml composed by piecewise expanding individual map global interaction and finite number n of sites in the weak coupling regime where the cml is uniformly expanding we show mathematically for n 3 and numerically for n ge 3 that a transition in the asymptotic dynamics occurs as the coupling strength increases the transition breaks the milnor attractor into several chaotic pieces of positive lebesgue measure with distinct empiric averages it goes along with various symmetry breaking quantified by means of magnetization type characteristics despite that it only addresses finite dimensional systems to some extend this result reconciles the previous ones as it shows that loss of ergodicity symmetry breaking can occur in basic cml independently of any decay in the lyapunov dimension

complex networks effect of subtle changes in nature of randomness abstract in two different classes of network models namely the watts strogatz type and the euclidean type subtle changes have been introduced in the randomness in the watts strogatz type network rewiring has been done in different ways and although the qualitative results remain the same finite differences in the exponents are observed in the euclidean type networks where at least one finite phase transition occurs two models differing in a similar way have been considered the results show a possible shift in one of the phase transition points but no change in the values of the exponents the ws and euclidean type models are equivalent for extreme values of the parameters we compare their behaviour for intermediate values

equilibrium phase transitions in coupled map lattices a pedestrian approach a class of piecewise linear coupled map lattices with simple symbolic dynamics is constructed it can be solved analytically in terms of the statistical mechanics of spin lattices the corresponding hamiltonian is written down explicitly in terms of the parameters of the map the approach follows the line of recent mathematical investigations but the presentation is kept elementary so that phase transitions in the dynamical model can be studied in detail although the method works only for map lattices with repelling invariant sets some of the conclusions i e the role of local curvature of the single site map and properties of the nearest neighbour coupling might play an important role for phase transitions in general dynamical systems

critical droplets in metastable states of probabilistic cellular automata we consider the problem of metastability in a probabilistic cellular automaton pca with a parallel updating rule which is reversible with respect to a gibbs measure the dynamical rules contain two parameters beta and h which resemble but are not identical to the inverse temperature and external magnetic field in a ferromagnetic ising model in particular the phase diagram of the system has two stable phases when beta is large enough and h is zero and a unique phase when h is nonzero when the system evolves at small positive values of h from an initial state with all spins down the pca dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored phase inside the metastable phase reaches a critical size we give heuristic arguments to estimate the critical size in the limit of zero temperature beta to infty as well as estimates of the time required for the formation of such a droplet in a finite system monte carlo simulations give results in good agreement with the theoretical predictions

finite size effects for the ising model on random graphs with varying dilution abstract we investigate the finite size corrections to the equilibrium magnetization of an ising model on a random graph with n nodes and n edges with 1 2 by conveniently rescaling the coupling constant the free energy is made extensive as expected the system displays a phase transition of the mean field type for all the considered values of at the transition temperature of the fully connected curie weiss model finite size corrections are investigated for different values of the parameter using two different approaches a replica based finite n expansion and a cavity method numerical simulations are compared with theoretical predictions the cavity based analysis is shown to agree better with numerics

survival analysis without survival data connecting length biased and case control data we show that relative mean survival parameters of a semiparametric log linear model can be estimated using covariate data from an incident sample and a prevalent sample even when there is no prospective follow up to collect any survival data estimation is based on an induced semiparametric density ratio model for covariates from the two samples and it shares the same structure as for a logistic regression model for case control data likelihood inference coincides with well established methods for case control data we show two further related results first estimation of interaction parameters in a survival model can be performed using covariate information only from a prevalent sample analogous to a case only analysis furthermore propensity score and conditional exposure effect parameters on survival can be estimated using only covariate data collected from incident and prevalent samples

dynamical influence processes on networks general theory and applications to social contagion we study binary state dynamics on a network where each node acts in response to the average state of its neighborhood by allowing varying amounts of stochasticity in both the network and node responses we find different outcomes in random and deterministic versions of the model in the limit of a large dense network however we show that these dynamics coincide we construct a general mean field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics thus the behavior of the system can range from steady state to chaotic depending on the response functions network connectivity and update synchronicity as a specific example we model the competing tendencies of imitation and nonconformity by incorporating an off threshold into standard threshold models of social contagion in this way we attempt to capture important aspects of fashions and societal trends we compare our theory to extensive simulations of this limited imitation contagion model on poisson random graphs finding agreement between the mean field theory and stochastic simulations

monte carlo simulation of classical spin models with chaotic billiards it has recently been shown that the computing abilities of boltzmann machines or ising spin glass models can be implemented by chaotic billiard dynamics without any use of random numbers in this paper we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random monte carlo methods by applying it to classical spin models in statistical physics first we verify that the billiard dynamics can yield samples that converge to the true distribution of the ising model on a small lattice and we show that it appears to have the same convergence rate as random monte carlo sampling second we apply the billiard dynamics to finite size scaling analysis of the critical behavior of the ising model and show that the phase transition point and the critical exponents are correctly obtained third we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the potts model we also discuss the possibility of extensions to continuous valued models such as the xy model

estimation from cross sectional samples under bias and dependence 5summary a population can be entered at a known sequence of discrete times it is sampled crosssectionally and the sojourn times of individuals in the sample are observed it is well known that cross sectioning leads to length bias but less well known and often ignored that it may result also in dependence among the observations we show that observed sojourn times are independent 10 only under a multinomial entrance process we study asymptotic properties of parametric and nonparametric estimators of the sojourn time distribution using the product of marginals in spite of dependence and provide conditions under which this approach results in proper or improper and wrong inference we apply the proposed methods to data on hospitalization time after bowel and hernia surgeries collected by a cross sectional design 15

magnetic order in the ising model with parallel dynamics it is discussed how the equilibrium properties of the ising model are described by an hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics with the characteristics of a probabilistic cellular automaton is assumed to determine the temporal evolution of the system

statistical mechanics of probabilistic cellular automata we investigate the behavior of discrete time probabilistic cellular automata pca which are markov processes on spin configurations on ad dimensional lattice from a rigorous statistical mechanics point of view in particular we exploit whenever possible the correspondence between stationary measures on the space time histories of pcas on d and translation invariant gibbs states for a related hamiltonian on d 1 this leads to a simple large deviation formula for the space time histories of the pca and a proof that in a high temperature regime the stationary states of the pca are gibbsian we also obtain results about entropy fluctuations and correlation inequalities and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high noise regime we discuss phase transitions in the low noise or low temperature regime and review toom s proof of nonergodicity of a certain class of pcas

phase transition in a coevolving network of conformist and contrarian voters in the coevolving voter model each voter has one of two diametrically opposite opinions and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing the same opinion as we smoothly change the relative frequency of rewiring compared to that of adoption there occurs a phase transition between an active phase and a frozen phase by performing extensive monte carlo calculations we show that the phase transition is characterized by critical exponents ensuremath beta 0 54 1 and overline ensuremath nu 1 5 1 which differ from the existing mean field type prediction we furthermore extend the model by introducing a contrarian type that tries to have neighbors with the opposite opinion and show that the critical behavior still belongs to the same universality class irrespective of such contrarians fraction

analyzing multiple cross sectional samples with application to hospitalization time after surgeries repeated cross sectional sampling results in multiple biased samples with possibly different weight functions the standard non parametric maximum likelihood estimator for the lifetime distribution of interest solves a set of nonlinear equations and its variance has a very complicated form we suggest a simple closed form estimator for the case where entrances to the population of interest follow a poisson model the variance of the estimator and confidence intervals are easily calculated our motivating example concerns a series of cross sectional surveys conducted in israeli hospitals we discuss the bias mechanism in our data and suggest a simple design plan that provides valid estimators even when the weight functions are unknown the new method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries copyright 2015 john wiley sons ltd

nonparametric incidence estimation from prevalent cohort survival data incidence is an important epidemiological concept most suitably studied using an incident cohort study however data are often collected from the more feasible prevalent cohort study whereby diseased individuals are recruited through a cross sectional survey and followed in time in the absence of temporal trends in survival we derive an efficient nonparametric estimator of the cumulative incidence based on such data and study its asymptotic properties arbitrary calendar time variations in disease incidence are allowed age specific incidence and adjustments for both stratified sampling and temporal variations in survival are also discussed simulation results are presented and data from the canadian study of health and aging are analysed to infer the incidence of dementia in the canadian elderly population

effect of the nature of randomness on quenching dynamics of the ising model on complex networks randomness is known to affect the dynamical behavior of many systems to a large extent in this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of the ising model on two types of random networks in both networks which are embedded in a one dimensional space the first neighbor connections exist and the average degree is 4 per node in random model a the second neighbor connections are rewired with a probability p while in random model b additional connections between neighbors at a euclidean distance l l 1 are introduced with a probability p l proportionally l we find that for both models the dynamics leads to freezing such that the system gets locked in a disordered state the point at which the disorder of the nonequilibrium steady state is maximum is located the behavior of dynamical quantities such as residual energy order parameter and persistence are discussed and compared overall the behavior of physical quantities are similar although subtle differences are observed due to the difference in the nature of randomness

the survival curve under monotone density constraints with applications to two dimensional line segment processes summary several situations involving survival data are examined in which the nonparametric maximum likelihood estimator is not the kaplan meier estimator cases covered are inclusion of initial observations in field studies estimation of the length distribution from convex window sampling of line segment processes in two dimensions and estimation of a survival curve with monotone density the first two cases are nonstandard because survival and censoring are not independent and thus form simple tractable variable sum models williams lagakos 1977

multiplicative censoring renewal processes deconvolution and decreasing density nonparametric estimation on donne un estimateur du maximum de vraisemblance non parametrique pour une distribution de durees de vie il est base sur un modele d observations censurees de facon multiplicative et il generalise des problemes statistiques courants tels que l estimation d une fonction de repartition sous une contrainte de densite decroissante la deconvolution non parametrique d une variable aleatoire exponentielle ou un probleme d estimation dans les processus de renouvellement

separation of variables and exact solution of the dirac equation in nonstatic minkowski spacetimes using a second order formalism a complete separation of variables in the dirac equation for a free particle in nonstatic orthogonal curvilinear coordinates of the form t f u v x g u v y z is presented it is shown that the dirac equation is separable in eight nonequivalent coordinate systems where the klein gordon equation separates exact solutions of the dirac equation in the systems of coordinates obtained are presented

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

a note on the product limit estimator under right censoring and left truncation summary in many applications involving follow up studies individuals lifetimes may be subject to left truncation in addition to the usual right censoring here we consider the product limit estimator of the survival curve s or an appropriate conditional version of s the asymptotic behaviour of the estimator is briefly described together with an example

stochastic bifurcations in the nonlinear parallel ising model we investigate the phase transitions of a nonlinear parallel version of the ising model characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one this model arises in problems of opinion formation the mean field approximation shows chaotic oscillations by changing the couplings or the connectivity the spatial model shows bifurcations in the average magnetization similar to that seen in the mean field approximation induced by the change of the topology after rewiring short range to long range connection as predicted by the small world effect these coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins induced by long range couplings similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution degree of asynchronism of the updating we also examined the effects of inhomogeneity mixing ferromagnetic and antiferromagnetic coupling which induces an unexpected bifurcation diagram with a bubbling behavior as also happens for dilution

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

disorder induced phase transition in kinetic models of opinion dynamics abstract we propose a model of continuous opinion dynamics where mutual interactions can be both positive and negative different types of distributions for the interactions all characterized by a single parameter p denoting the fraction of negative interactions are considered results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p p c below which a consensus is reached although the order disorder transition is analogous to a ferromagnetic paramagnetic phase transition with comparable critical exponents the model is characterized by some distinctive features relevant to a social system

metastability for reversible probabilistic cellular automata with self interaction the problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the freidlin wentzel regime namely finite volume small magnetic field and small temperature the model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics in which the system can be trapped in its way to the stable phase our strategy is based on recent powerful approaches not needing a complete description of the fixed points of the dynamics but relying on few model dependent results we compute the exit time in the sense of logarithmic equivalence and characterize the critical droplet that is necessarily visited by the system during its excursion from the metastable to the stable state we need to supply two model dependent inputs 1 the communication energy that is the minimal energy barrier that the system must overcome to reach the stable state starting from the metastable one 2 a recurrence property stating that for any configuration different from the metastable state there exists a path starting from such a configuration and reaching a lower energy state such that its maximal energy is lower than the communication energy

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

from equilibrium spin models to probabilistic cellular automata the general equivalence betweend dimensional probabilistic cellular automata pca and d 1 dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams the critical behavior and the universality classes of some automata diagrammatic representations of time dependent correlation functions of pca are introduced two important classes of pca are singled out for which these correlation functions simplify 1 quasi hamiltonian automata which have a current carrying steady state and for which some correlation functions are those of ad dimensional static model pca satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes 2 linear and more generally affine pca for which the diagrammatics reduces to a random walk problem closely related to d 1 dimensional directed saws both problems display a critical behavior with mean field exponents in any dimension the correlation length and effective velocity of propagation of excitations can be calculated for affine pca as is shown on an explicitd 1 example we conclude with some remarks on nonlinear pca for which the diagrammatics is related to reaction diffusion processes and which belong in some cases to the universality class of reggeon field theory

phase transitions in coupled map lattices and in associated probabilistic cellular automata analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata the so called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices the importance of this condition for the suppression of phase transitions is illustrated by spatially one dimensional systems invariant densities and temporal correlations are calculated explicitly ising type phase transitions are found for one dimensional coupled map lattices acting on repelling sets and for a spatially two dimensional miller huse like system with stable long time dynamics critical exponents are calculated within a finite size scaling approach the relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

bifurcations in models of a society of reasonable contrarians and conformists we study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree but revert to a conformist behavior in the presence of an overwhelming majority in line with psychological experiments the model is studied in the mean field approximation and on small world and scale free networks in the mean field approximation a large fraction of conformists triggers a polarization of the opinions a pitchfork bifurcation while a majority of reasonable contrarians leads to coherent oscillations with an alternation of period doubling and pitchfork bifurcations up to chaos similar scenarios are obtained by changing the fraction of long range rewiring and the parameter of scale free networks related to the average connectivity

large sample theory of empirical distributions in biased sampling models vardi 1985a introduced an s sample model for biased sampling gave conditions which guarantee the existence and uniqueness of the nonparametric maximum likelihood estimator mathbb g n of the common underlying distribution g and discussed numerical methods for calculating the estimator here we examine the large sample behavior of the npmle mathbb g n including results on uniform consistency of mathbb g n convergence of sqrt n mathbb g n g to a gaussian process and asymptotic efficiency of mathbb g n as an estimator of g the proofs are based upon recent results for empirical processes indexed by sets and functions and convexity arguments we also give a careful proof of identifiability of the underlying distribution g under connectedness of a certain graph mathbf g examples and applications include length biased sampling stratified sampling enriched stratified sampling choice based sampling in econometrics and case control studies in biostatistics a final section discusses design issues and further problems

on separable solutions of dirac s equation for the electron the properties of coordinate systems that admit separation of the laplacian and hamilton jacobi operators have been thoroughly explored so that the nature of solutions in separable form of laplace s equation the wave equation schrodinger s equation and the hamilton jacobi equation are well understood the corresponding problems for the dirac operator in flat space time have been less completely examined and this paper contains studies intended to produce a more systematic account of possible solutions of dirac s equation because the dirac operator differs from the laplacian in being a first degree differential operator and in having matrix coefficients it is not possible to discuss possible solutions in as general a way and the separable solutions are far less rich than for equations with the laplacian in particular the forms of the potentials for which separable solutions are possible are not for the most part of physical interest although the discussion is confined to coordinates in flat space time some of the procedures are derived from those developed to solve dirac s equation in coordinates with a kerr metric

stationary states of toom cellular automata in simulations stationary states of toom probabilistic cellular automata are tested in computer experiments the aim of the tests is to identify the features characterizing the equilibrium states understood as in statistical mechanics namely we investigate the following scaling laws that involve critical parameters beta gamma and nu locality of the interactions and density of the relative entropy between stationary states the arguments showing that stationary toom states are not the equilibrium ones are provided

toom s model with glauber rates an exact solution using elementary methods a simple spatially two dimensional stochastic cellular automaton with asymmetric coupling and synchronous updating according to glauber rates is considered while detailed balance is violated it is still possible to compute analytically the stationary probability distribution by elementary means the stationary distribution can be written as a canonical equilibrium distribution of a spin system on a triangular lattice with nearest neighbour coupling thus the cellular automaton shows a nonequilibrium phase transition with ising critical behaviour

phase transitions of extended range probabilistic cellular automata with two absorbing states we study phase transitions in a long range one dimensional cellular automaton with two symmetric absorbing states it includes and extends several other models like the ising and domany kinzel ones it is characterized by competing ferromagnetic linear and antiferromagnetic nonlinear couplings despite its simplicity this model exhibits an extremely rich phase diagram we present numerical results and mean field approximations

topological bifurcations in a model society of reasonable contrarians people are often divided into conformists and contrarians the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority in practice however the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion which denotes a social norm such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets we present the opinion dynamics of a society of reasonable contrarian agents the model is a cellular automaton of ising type with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms we introduce the entropy of the collective variable as a way of comparing deterministic mean field and probabilistic simulations bifurcation diagrams in the mean field approximation the model exhibits bifurcations and a chaotic phase interpreted as coherent oscillations of the whole society however in a one dimensional spatial arrangement one observes incoherent oscillations and a constant average in simulations on watts strogatz networks with a small world effect the mean field behavior is recovered with a bifurcation diagram that resembles the mean field one but where the rewiring probability is used as the control parameter similar bifurcation diagrams are found for scale free networks and we are able to compute an effective connectivity for such networks