cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

automated pattern detection an algorithm for constructing optimally synchronizing multi regular language filters in the computational mechanics structural analysis of one dimensional cellular automata the following automata theoretic analogue of the change point problem from time series analysis arises given a string and a collection di offinite automata identify the regions of that belong to each di and in particular the boundaries separating them we present two methods for solving this multi regular language filtering problem the first although providing the ideal solution requires a stack has a worst case compute time that grows quadratically in s length and conditions its output at any point on arbitrarily long windows of future input the second method is to algorithmically construct a finite transducer that approximates the first algorithm in contrast to the stack based algorithm however the transducer requires only a finite amount of memory runs in linear time and gives immediate output for each letter read it is moreover the best possible finite state approximation with these three features

reductions of hidden information sources in all but special circumstances measurements of time dependent processes reflect internal structures and correlations only indirectly building predictive models of such hidden information sources requires discovering in some way the internal states and mechanisms unfortunately there are often many possible models that are observationally equivalent here we show that the situation is not as arbitrary as one would think we show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics the e machine on the way to developing deeper measure theoretic foundations for the latter we introduce a new two step reduction process the first step internal event reduction produces the smallest observationally equivalent algebra and the second internal state reduction removes algebra components that are redundant for optimal prediction for several classes of stochastic dynamical systems these reductions produce representations that are equivalent to e machines

computation in finitary stochastic and quantum processes abstract we introduce stochastic and quantum finite state transducers as computation theoretic models of classical stochastic and quantum finitary processes formal process languages representing the distribution over a process behaviors are recognized and generated by suitable specializations we characterize and compare deterministic and nondeterministic versions summarizing their relative computational power in a hierarchy of finitary process languages quantum finite state transducers and generators are a first step toward a computation theoretic analysis of individual repeatedly measured quantum dynamical systems they are explored via several physical systems including an iterated beam splitter an atom in a magnetic field and atoms in an ion trap a special case of which implements the deutsch quantum algorithm we show that these systems behaviors and so their information processing capacity depends sensitively on the measurement protocol

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

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

application of computational mechanics to the analysis of natural data an example in geomagnetism we discuss how the ideal formalism of computational mechanics can be adapted to apply to a noninfinite series of corrupted and correlated data that is typical of most observed natural time series specifically a simple filter that removes the corruption that creates rare unphysical causal states is demonstrated and the concept of effective soficity is introduced we believe that computational mechanics cannot be applied to a noisy and finite data series without invoking an argument based upon effective soficity a related distinction between noise and unresolved structure is also defined noise can only be eliminated by increasing the length of the time series whereas the resolution of previously unresolved structure only requires the finite memory of the analysis to be increased the benefits of these concepts are demonstrated in a simulated times series by a the effective elimination of white noise corruption from a periodic signal using the expletive filter and b the appearance of an effectively sofic region in the statistical complexity of a biased poisson switch time series that is insensitive to changes in the word length memory used in the analysis the new algorithm is then applied to an analysis of a real geomagnetic time series measured at halley antarctica two principal components in the structure are detected that are interpreted as the diurnal variation due to the rotation of the earth based station under an electrical current pattern that is fixed with respect to the sun earth axis and the random occurrence of a signature likely to be that of the magnetic substorm in conclusion some useful terminology for the discussion of model construction in general is introduced

quantum automata and quantum grammars abstract to study quantum computation it might be helpful to generalize structures from language and automata theory to the quantum case to that end we propose quantum versions of finite state and push down automata and regular and context free grammars we find analogs of several classical theorems including pumping lemmas closure properties rational and algebraic generating functions and greibach normal form we also show that there are quantum context free languages that are not context free so qcfl cfl

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

computational complexity of symbolic dynamics at the onset of chaos in a variety of studies of dynamical systems the edge of order and chaos has been singled out as a region of complexity it was suggested by wolfram on the basis of qualitative behaviour of cellular automata that the computational basis for modelling this region is the universal turing machine in this paper following a suggestion of crutchfield we try to show that the turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos in particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval from the point of view of language theory we show that in relation to the extended chomsky hierarchy the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages while the bimodal case is modeled by the linear bounded automaton or the related context sensitive languages

computing with distributed chaos we describe and discuss in detail some recent results by sinha and ditto phys rev lett 81 2156 1998 demonstrating the capacity of a lattice of threshold coupled chaotic maps to perform computations such systems are shown to emulate logic gates encode numbers and perform specific arithmetic operations such as addition and multiplication as well as yield more specialized operations such as the calculation of the least common multiplier of a sequence of numbers furthermore we extend the scheme to multidimensional continuous time dynamics in particular to a system relevant to chaotic lasers

simultaneous stabilization of multiplicatively perturbed plants necessary and sufficient conditions are obtained for simultaneous stabilizability of a given linear time invariant multi input multi output nominal plant and a multiplicatively perturbed plant where the multiplicative perturbation is stable these conditions are derived from the general parity interlacing property applicable to any two arbitrary plants and are expressed explicitly in terms of the real axis poles and zeros of the nominal plant and the perturbation the class of perturbations for which simultaneous stabilization is achievable are characterized using these conditions a special class of unknown diagonal perturbations is also considered and simultaneously stabilizing controllers are designed for the nominal plant under any such unknown perturbation

strong and weak optimizations in classical and quantum models of stochastic processes among the predictive hidden markov models that describe a given stochastic process the epsilon text machine is strongly minimal in that it minimizes every renyi based memory measure quantum models can be smaller still in contrast with the epsilon text machine s unique role in the classical setting however among the class of processes described by pure state hidden quantum markov models there are those for which there does not exist any strongly minimal model quantum memory optimization then depends on which memory measure best matches a given problem s circumstance

detecting treatment covariate interactions using permutation methods the primary objective of a randomized clinical trial usually is to investigate whether one treatment is better than its alternatives on average however treatment effects may vary across different patient subpopulations in contrast to demonstrating one treatment is superior to another on the average sense one is often more concerned with the question that for a particular patient or a group of patients with similar characteristics which treatment strategy is most appropriate to achieve a desired outcome various interaction tests have been proposed to detect treatment effect heterogeneity however they typically examine covariates one at a time do not offer an integrated approach that incorporates all available information and can greatly increase the chance of a false positive finding when the number of covariates is large we propose a new permutation test for the null hypothesis of no interaction effects for any covariate the proposed test allows us to consider the interaction effects of many covariates simultaneously without having to group subjects into subsets based on pre specified criteria and applies generally to randomized clinical trials of multiple treatments the test provides an attractive alternative to the standard likelihood ratio test especially when the number of covariates is large we illustrate the proposed methods using a dataset from the treatment of adolescents with depression study

predictive rate distortion for infinite order markov processes predictive rate distortion analysis suffers from the curse of dimensionality clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length the challenge is compounded for infinite order markov processes since conditioning on finite sequences cannot capture all of their past dependencies spectral arguments confirm a popular intuition algorithms that cluster finite length sequences fail dramatically when the underlying process has long range temporal correlations and can fail even for processes generated by finite memory hidden markov models we circumvent the curse of dimensionality in rate distortion analysis of finite and infinite order processes by casting predictive rate distortion objective functions in terms of the forward and reverse time causal states of computational mechanics examples demonstrate that the resulting algorithms yield substantial improvements

validating effectiveness of subgroup identification for longitudinal data in clinical trials and biomedical studies treatments are compared to determine which one is effective against illness however individuals can react to the same treatment very differently we propose a complete process for longitudinal data that identifies subgroups of the population that would benefit from a specific treatment a random effects linear model is used to evaluate individual treatment effects longitudinally where the random effects identify a positive or negative reaction to the treatment over time with the individual treatment effects and characteristics of the patients various classification algorithms are applied to build prediction models for subgrouping while many subgrouping approaches have been developed recently most of them do not check its validity in this paper we further propose a simple validation approach which not only determines if the subgroups used are appropriate and beneficial but also compares methods to predict individual treatment effects this entire procedure is readily implemented by existing packages in statistical software the effectiveness of the proposed method is confirmed with simulation studies and analysis of data from the women entering care study on depression

self organized criticality abstract dissipative dynamical systems with many degrees of freedom naturally evolve to a critical state with fluctuations extending over all length and time scales it is suggested and supported by simulations on simple toy model systems that turbulence earthquakes 1 f noise and economics may operate at the self organized critical state

statistical dynamics of the royal road genetic algorithm abstract metastability is a common phenomenon many evolutionary processes both natural and artificial alternate between periods of stasis and brief periods of rapid change in their behavior in this paper an analytical model for the dynamics of a mutation only genetic algorithm ga is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics the ga s population dynamics is described in terms of flows in the space of fitness distributions the trajectories through fitness distribution space are derived in closed form in the limit of infinite populations we then show how finite populations induce metastability even in regions where fitness does not exhibit a local optimum in particular the model predicts the occurrence of fitness epochs periods of stasis in population fitness distributions at finite population size and identifies the locations of these fitness epochs with the flow s hyperbolic fixed points this enables exact predictions of the metastable fitness distributions during the fitness epochs as well as giving insight into the nature of the periods of stasis and the innovations between them all these results are obtained as closed form expressions in terms of the ga s parameters an analysis of the jacobian matrices in the neighborhood of an epoch s metastable fitness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state space s topological structure more general quantitative features of the dynamics fitness fluctuation amplitudes epoch stability and speed of the innovations are also determined from the jacobian eigenvalues the analysis shows how quantitative predictions for a range of dynamical behaviors that are specific to the finite population dynamics can be derived from the solution of the infinite population dynamics the theoretical predictions are shown to agree very well with statistics from ga simulations we also discuss the connections of our results with those from population genetics and molecular evolution theory

inference for subgroup analysis with a structured logistic normal mixture model in this article we propose a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership the need for such subgroup identification arises in clinical trials and in market segmentation analysis by using a structured logistic normal mixture model our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups and at the same time to construct predictive scores for the subgroup membership the inferential procedure proposed in the article is built on the recent literature on hypothesis testing for gaussian mixtures but the structured logistic normal mixture model enjoys some distinctive properties that are unavailable to the simpler gaussian mixture models with the bootstrap approximations the proposed tests are shown to be powerful and equally importantly insensitive to the choice of tuning parameters as an illustration we analyze a dataset fr

a fisher gradient complexity in systems with spatio temporal dynamics abstract we define a benchmark for definitions of complexity in systems with spatio temporal dynamics and employ it in the study of collective motion we show that lmc s complexity displays interesting properties in such systems while a statistical complexity model scm based on autocorrelation reasonably meets our perception of complexity however this scm is not as general as desirable as it does not merely depend on the system s probability distribution function inspired by the notion of fisher information we develop a scm candidate which we call the fisher gradient complexity which exhibits nice properties from the viewpoint of our benchmark

quasiperiodicity in dissipative systems a renormalization group analysis abstract dynamical systems with quasiperiodic behavior i e two incommensurate frequencies may be studied via discrete maps which show smooth continuous invariant curves with irrational winding number in this paper these curves are followed using renormalization group techniques which are applied to a one dimensional system circle and also to an area contracting map of an annulus two fixed points are found representing different types of universal behavior a trivial fixed point for smooth motion and a nontrivial fixed point the latter representsthe incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow fixed point functions are determined numerically and via an e expansion and eigenvalues are calculated

bayesian structural inference for hidden processes we introduce a bayesian approach to discovering patterns in structurally complex processes the proposed method of bayesian structural inference bsi relies on a set of candidate unifilar hidden markov model uhmm topologies for inference of process structure from a data series we employ a recently developed exact enumeration of topological e machines a sequel then removes the topological restriction this subset of the uhmm topologies has the added benefit that inferred models are guaranteed to be e machines irrespective of estimated transition probabilities properties of e machines and uhmms allow for the derivation of analytic expressions for estimating transition probabilities inferring start states and comparing the posterior probability of candidate model topologies despite process internal structure being only indirectly present in data we demonstrate bsi s effectiveness in estimating a process s randomness as reflected by the shannon entropy rate and its structure as quantified by the statistical complexity we also compare using the posterior distribution over candidate models and the single maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values we apply bsi to in class examples of finite and infinite order markov processes as well to an out of class infinite state hidden process

maximizing multivariate information with error correcting codes multivariate mutual information provides a conceptual framework for characterizing higher order interactions in complex systems two well known measures of multivariate information total correlation and dual total correlation admit a spectrum of measures with varying sensitivity to intermediate orders of dependence unfortunately these intermediate measures have not received much attention due to their opaque representation of information here we draw on results from matroid theory to show that these measures are closely related to error correcting codes this connection allows us to derive the class of global maximizers for each measure which coincide with maximum distance separable codes of order k in addition to deepening the understanding of these measures and multivariate information more generally we use these results to show that previously proposed bounds on information geometric quantities are met with equality for the global min and max

correlated biased random walk with latency in one and two dimensions asserting patterned and unpredictable movement the correlated biased random walk with latency in one and two dimensions is discussed with regard to the portion of irreducible random movement and structured movement it is shown how a quantitative analysis can be carried out by using computational mechanics the stochastic matrix for both dynamics are reported latency introduces new states in the finite state machine description of the system in both dimensions allowing for a full nearest neighbor coordination in the two dimensional case complexity analysis is used to characterize the movement independently of the set of control parameters making it suitable for the discussion of other random walk models the complexity map of the system dynamics is reported for the two dimensional case

the calculi of emergence computation dynamics and induction abstract defining structure and detecting the emergence of complexity in nature are inherently subjective though essential scientific activities despite the difficulties these problems can be analyzed in terms of how model building observers infer from measurements the computational capabilities embedded in nonlinear processes an observer s notion of what is ordered what is random and what is complex in its environment depends directly on its computational resources the amount of raw measurement data of memory and of time available for estimation and inference the discovery of structure in an environment depends more critically and subtlely though on how those resources are organized the descriptive power of the observer s chosen or implicit computational model class for example can be an overwhelming determinant in finding regularity in data this paper presents an overview of an inductive framework hierarchical machine reconstruction in which the emergence of complexity is associated with the innovation of new computational model classes complexity metrics for detecting structure and quantifying emergence along with an analysis of the constraints on the dynamics of innovation are outlined illustrative examples are drawn from the onset of unpredictability in nonlinear systems finitary nondeterministic processes and cellular automata pattern recognition they demonstrate how finite inference resources drive the innovation of new structures and so lead to the emergence of complexity

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

dynamically changing interface as a model of measurement in complex systems abstract we propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system we call this approach hyper dilation and cover it under the label of measurement oriented physics mop as compared with state oriented physics sop the essential difference between the two concerns the concepts of state to which they refer mop deals with two different concepts of state non measured states with infinite precision and measured states with finite precision the measurement process is expressed as a dynamically changing interface between them sop deals with one single concept of state and does not comprise a corresponding distinction we show fundamental differences between mop and sop with respect to the noise characteristics of complex systems around critical states mop can give rise to exact and universal 1 noise while sop shows 1 noise with 1 in general in mop a self similar return map can be degenerate with a cantor set rendering a solution for a basic measurement paradox the significance of this degeneracy as a model for emergent properties is discussed

minimum memory for generating rare events we classify the rare events of structured memoryful stochastic processes and use this to analyze sequential and parallel generators for these events given a stochastic process we introduce a method to construct a process whose typical realizations are a given process rare events this leads to an expression for the minimum memory required to generate rare events we then show that the recently discovered classical quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations

qrt fifo automata breadth first grammars and their relations abstract some classes of queue automata deterministic and nondeterministic i e machines equipped with one or more fifo tapes and corresponding languages are considered for quasi real time qrt deterministic machines recognition power closure properties and counting capabilities are studied for such machines by showing that the language l j j j 1 l j l j ba n 1 b a n j ca n j b can be recognized with j queues but not with fewer an infinite hierarchy theorem which contradicts the known results for nondeterministic machines is proved restricted palindromes can be recognized with two queues we introduce a generative system for some queue languages the breadth first context free grammars bcf which are the same as context free grammars but for the ordering of terminals which is breadth first i e the least recently produced nonterminal symbol must be rewritten first bcf languages are recognized essentially by stateless queue automata they are semilinear closed with respect to permutation and homomorphism but not with respect to intersection with regular sets a periodicity property pumping lemma is proved for bcf languages whence comparisons with other families are obtained finally a homomorphic characterization of any queue language is presented l h r b where h is a homomorphism nonerasing if l is qrt r a regular set and b a bcf language the result can be extended to multiqueue automata

extracting finite state representations from recurrent neural networks trained on chaotic symbolic sequences concerns neural based modeling of symbolic chaotic time series we investigate the knowledge induction process associated with training recurrent mural nets rnn on single long chaotic symbolic sequences even though training rnn to predict the next symbol leaves the standard performance measures such as the mean square error on the network output virtually unchanged the nets extract a lot of knowledge we monitor the knowledge extraction process by considering the nets stochastic sources and letting them generate sequences which are then confronted with the training sequence via information theoretic entropy and cross entropy measures we also study the possibility of reformulating the knowledge gained by rnn in a compact easy to analyze form of finite state stochastic machines the experiments are performed on two sequences with different complexities measured by the size and state transition structure of the induced crutchfield s spl epsiv machines 1991 1994 the extracted machines can achieve comparable or even better entropy and cross entropy performance they reflect the training sequence complexity in their dynamical state representations that can be reformulated using finite state means the findings are confirmed by a much more detailed analysis of model generated sequences we also introduce a visual representation of allowed block structure in the studied sequences that allows for an illustrative insight into both rnn training and finite state stochastic machine extraction processes

comment i on simple measure for complexity we critique the measure of complexity introduced by shiner davison and landsberg phys rev e 59 1459 1999 in particular we point out that it is over universal in the sense that it has the same dependence on disorder for structurally distinct systems we then give counterexamples to the claim that complexity is synonymous with being out of equilibrium equilibrium systems can be structurally complex and nonequilibrium systems can be structurally simple we also correct a misinterpretation of a result given by two of the present authors j p crutchfield and d p feldman phys rev e 55 r1239 1997

classification of temporal patterns in dynamic biological networks a general method is presented to classify temporal patterns generated by rhythmic biological networks when synaptic connections and cellular properties are known the method is discrete in nature and relies on algebraic properties of state transitions and graph theory elements of the set of rhythms generated by a network are compared using a metric that quantifies the functional differences among them the rhythms are then classified according to their location in a metric space examples are given and biological implications are discussed

structural information in two dimensional patterns entropy convergence and excess entropy we develop information theoretic measures of spatial structure and pattern in more than one dimension as is well known the entropy density of a two dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies we show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension we compare and contrast entropy convergence with mutual information and structure factor techniques for quantifying and detecting spatial structure

orthomodular lattice obtained from addressing a fixed point abstract one of us previously proposed a model of internal measurement that is not only an interaction between internal elements but also involves the notion of an indefinite observer measuring the interaction in this model all interactions encompass the notion of detection the latter can be expressed as a process generating a contradiction hereby a fixed point becomes invalid after inducing the contradiction instead of embedding this process as an instance along the time axis we here represent the logical jump via a contradiction fixed point specifically a new operation is defined which replaces the operation by which a fixed point is induced and we show that both a set as a fixed point and this particular operation on a set can give rise to an orthomodular lattice that is a model of quantum logic the new procedure is a mixture of inducing a fixed point and addressing a fixed point it can be compared to mixing up indicating an element with indicating a set consisting of elements that is to russel s paradox finally we point out that orthomodularity can ubiquitously be found in the evolutionary complex systems because it is generally relevant to resolving a paradox or a logical jump

the crystallizing substochastic sequential machine extractor cryssmex this letter presents an algorithm cryssmex for extracting minimal finite state machine descriptions of dynamic systems such as recurrent neural networks unlike previous algorithms cryssmex is parameter free and deterministic and it efficiently generates a series of increasingly refined models a novel finite stochastic model of dynamic systems and a novel vector quantization function have been developed to take into account the state space dynamics of the system the experiments show that 1 extraction from systems that can be described as regular grammars is trivial 2 extraction from high dimensional systems is feasible and 3 extraction of approximative models from chaotic systems is possible the results are promising and an analysis of shortcomings suggests some possible further improvements some largely overlooked connections of the field of rule extraction from recurrent neural networks to other fields are also identified

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

identifiability of hidden markov information sources and their minimum degrees of freedom if only a function of the state in a finite state markov chain is observed then the stochastic process is no longer markovian in general this type of information source is found widely and the basic problem of its identifiability remains open that is the problem of showing when two different markov chains generate the same stochastic process the identifiability problem is completely solved by linear algebra where a block structure of a markov transition matrix plays a fundamental role and from which the minimum degree of freedom for a source is revealed

subgroup detection and sample size calculation with proportional hazards regression for survival data in this paper we propose a testing procedure for detecting and estimating the subgroup with an enhanced treatment effect in survival data analysis here we consider a new proportional hazard model that includes a nonparametric component for the covariate effect in the control group and a subgroup treatment interaction effect defined by a change plane we develop a score type test for detecting the existence of the subgroup which is doubly robust against misspecification of the baseline effect model or the propensity score but not both under mild assumptions for censoring when the null hypothesis of no subgroup is rejected the change plane parameters that define the subgroup can be estimated on the basis of supremum of the normalized score statistic the asymptotic distributions of the proposed test statistic under the null and local alternative hypotheses are established on the basis of established asymptotic distributions we further propose a sample size calculation formula for detecting a given subgroup effect and derive a numerical algorithm for implementing the sample size calculation in clinical trial designs the performance of the proposed approach is evaluated by simulation studies an application to an aids clinical trial data is also given for illustration

evaluating markers for selecting a patient s treatment selecting the best treatment for a patient s disease may be facilitated by evaluating clinical characteristics or biomarker measurements at diagnosis we consider how to evaluate the potential impact of such measurements on treatment selection algorithms for example magnetic resonance neurographic imaging is potentially useful for deciding whether a patient should be treated surgically for carpal tunnel syndrome or should receive less invasive conservative therapy we propose a graphical display the selection impact si curve that shows the population response rate as a function of treatment selection criteria based on the marker the curve can be useful for choosing a treatment policy that incorporates information on the patient s marker value exceeding a threshold the si curve can be estimated using data from a comparative randomized trial conducted in the population as long as treatment assignment in the trial is independent of the predictive marker estimating the si curve is therefore part of a post hoc analysis to determine whether the marker identifies patients that are more likely to benefit from one treatment over another nonparametric and parametric estimates of the si curve are proposed in this article asymptotic distribution theory is used to evaluate the relative efficiencies of the estimators simulation studies show that inference is straightforward with realistic sample sizes we illustrate the si curve and statistical inference for it with data motivated by an ongoing trial of surgery versus conservative therapy for carpal tunnel syndrome

computational mechanics pattern and prediction structure and simplicity computational mechanics an approach to structural complexity defines a process s causal states and gives a procedure for finding them we show that the causal state representation an machine is the minimal one consistent with accurate prediction we establish several results on machine optimality and uniqueness and on how machines compare to alternative representations further results relate measures of randomness and structural complexity obtained from machines to those from ergodic and information theories

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

inferring markov chains bayesian estimation model comparison entropy rate and out of class modeling markov chains are a natural and well understood tool for describing one dimensional patterns in time or space we show how to infer kth order markov chains for arbitrary k from finite data by applying bayesian methods to both parameter estimation and model order selection extending existing results for multinomial models of discrete data we connect inference to statistical mechanics through information theoretic type theory techniques we establish a direct relationship between bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate finally we introduce a method that uses finite data size scaling with model order comparison to infer the structure of out of class processes

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

change plane analysis for subgroup detection and sample size calculation abstractwe propose a systematic method for testing and identifying a subgroup with an enhanced treatment effect we adopts a change plane technique to first test the existence of a subgroup and then identify the subgroup if the null hypothesis on nonexistence of such a subgroup is rejected a semiparametric model is considered for the response with an unspecified baseline function and an interaction between a subgroup indicator and treatment a doubly robust test statistic is constructed based on this model and asymptotic distributions of the test statistic under both null and local alternative hypotheses are derived moreover a sample size calculation method for subgroup detection is developed based on the proposed statistic the finite sample performance of the proposed test is evaluated via simulations finally the proposed methods for subgroup identification and sample size calculation are applied to a data from an aids study

statistical complexity measures as telltale of relevant scales in emergent dynamics of spatial systems abstract the definition of complexity through statistical complexity measures scm has recently seen major improvements mostly the effort is concentrated in measures on time series we propose a scm definition for spatial dynamical systems our definition is in line with the trend to combine entropy with measures of structure such as disequilibrium we study the behaviour of our definition against the vectorial noise model of collective motion from a global perspective we show how our scm is minimal at both the microscale and macroscale while it reaches a maximum at the ranges that define the mesoscale in this model from a local perspective the scm is minimum both in highly ordered and disordered areas while it reaches a maximum at the edges between such areas these characteristics suggest this is a good candidate for detecting the mesoscale of arbitrary dynamical systems as well as regions where the complexity is maximal in such systems