approximate abstractions of stochastic hybrid systems we present a constructive procedure for obtaining a finite approximate abstraction of a discrete time stochastic hybrid system the procedure consists of a partition of the state space of the system and depends on a controllable parameter given proper continuity assumptions on the model the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition the abstraction is interpreted as a markov set chain we show that the enforcement of certain ergodic properties on the stochastic hybrid model implies the existence of a finite abstraction with finite error in time over the concrete model and allows introducing a finite time algorithm that computes the abstraction

stability criteria for matrices in this paper we study the stability of matrices using technologies of special matrices analysis several simple criteria for the stability for the matrix a aij cn n which is not diagonally dominant are obtained by aid of simple algebraic conditions of aij only

testing preorders for probabilistic processes can be characterized by simulations the domestic dog may be exceptionally well suited for behavioral genetic studies owing to its population history and the striking behavior differences among breeds to explore to what extent and ho

bisimulation indexes and their applications bisimulation expresses the equivalence of processes whose external actions are identical sometimes we may meet two processes which are not exactly bisimilar but more or less bisimilar in the sense that whenever a process makes an action the other can make an action different from but very similar to the action performed by the first one to describe this kind of looser bisimulations we propose the concept of bisimulation index in a labelled transition system and give its various properties especially those properties related to the operations of transition systems furthermore we establish a modal logical characterization of bisimulation indexes this characterization is a generalization of hennessy milner logic we study strong and weak bisimulation indexes in the basic asynchronous process calculus and some of their fundamental properties are derived bisimulation indexes are not substitutive under composition to overcome this defect we introduce an approximate communication rule to replace the original rule in process calculus this enables us to recover some useful properties of composition with respect to bisimulation indexes finally we present three examples in timed ccs and real time acp to demonstrate the usage of bisimulation indexes in the analysis of real time systems these examples show that bisimulation indexes are suitable formal tools for describing approximate implementations of real time systems

nonlinear parametric model for granger causality of time series the notion of granger causality between two time series examines if the prediction of one series could be improved by incorporating information of the other in particular if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one we propose a radial basis function approach to nonlinear granger causality the proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables still being suitable to evaluate causality usefulness of this measure of causality is shown in two applications in the first application a physiological one we consider time series of heart rate and blood pressure in congestive heart failure patients and patients affected by sepsis we find that sepsis patients unlike congestive heart failure patients show symmetric causal relationships between the two time series in the second application we consider the feedback loop in a model of excitatory and inhibitory neurons we find that in this system causality measures the combined influence of couplings and membrane time constants

stability analysis of diagonally equipotent matrices diagonally equipotent matrices are diagonally dominant matrices for which dominance is never strict in any coordinate they appear e g as laplacian matrices of signed graphs we show in this paper that for this class of matrices it is possible to provide a complete characterization of the stability properties based only on the signs of the entries of the matrices

a numerically efficient implementation of the expectation maximization algorithm for state space models empirical time series are subject to observational noise naive approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error in variables challenge state space models ssm explicitly include observational noise applying the expectation maximization em algorithm together with the kalman filter constitute a robust iterative procedure to estimate model parameters in the ssm as well as an approach to denoise the signal the em algorithm provides maximum likelihood parameter estimates at convergence the drawback of this approach is its high computational demand here we present an optimized implementation and demonstrate its superior performance to naive algorithms or implementations

spurious detection of phase synchronization in coupled nonlinear oscillators coupled nonlinear systems under certain conditions exhibit phase synchronization which may change for different frequency bands or with the presence of additive system noise in both cases fourier filtering is traditionally used to preprocess data we investigate to what extent the phase synchronization of two coupled r ossler oscillators depends on 1 the broadness of their power spectrum 2 the width of the bandpass filter and 3 the level of added noise we find that for identical coupling strengths oscillators with broader power spectra exhibit weaker synchronization further we find that within a broad bandwidth range bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth even when the coupling between the two oscillators remains the same

horizontal visibility graph transfer entropy hvg te a novel metric to characterize directed connectivity in large scale brain networks we propose a new measure horizontal visibility graph transfer entropy hvg te to estimate the direction of information flow between pairs of time series hvg te quantifies the transfer entropy between the degree sequences of horizontal visibility graphs derived from original time series twenty one rossler attractors unidirectionally coupled in the posterior to anterior direction were used to simulate 21 channel electroencephalography eeg brain networks and validate the performance of the hvg te we showed that the hvg te is robust to different levels of coupling strengths between the coupled rossler attractors a wide range of time delays different sample sizes the effects of noise and linear mixing and the choice of reference for eeg data we also applied hvg te to eeg data in 20 healthy controls and compared its performance to a recently introduces phase based te measure pte we found that compared with pte hvg te consistently detected stronger posterior to anterior information flow patterns in the alpha band 8 13hz eeg brain networks for three different references moreover in contrast to pte hvg te does not require an assumption on the periodicity of input signals therefore it can be more widely applicable even for non periodic signals this study shows that the hvg te is a directed connectivity measure to characterise the direction of information flow in large scale brain networks

approximation metrics for discrete and continuous systems established system relationships for discrete systems such as language inclusion simulation and bisimulation require system observations to be identical when interacting with the physical world modeled by continuous or hybrid systems exact relationships are restrictive and not robust in this paper we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion approximate simulation and approximate bisimulation relations we define a hierarchy of approximation pseudo metrics between two systems that quantify the quality of the approximation and capture the established exact relationships as zero sections our approximation framework is compositional for a synchronous composition operator algorithms are developed for computing the proposed pseudo metrics both exactly and approximately the exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations or dually the solution of a static game whose cost is the so called branching distance between the systems approximations for the pseudo metrics can be obtained by considering lyapunov like functions called simulation and bisimulation functions we illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems

framework to study dynamic dependencies in networks of interacting processes the analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions here we propose an information theoretic framework to analyze the dynamic dependencies in multivariate time evolving systems this framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and granger causality or transfer entropy we define multi information measures that allow us to study the global statistical structure of the system as a whole the total dependence between subsystems and the temporal statistical structure of each subsystem we develop a stationary and a nonstationary formulation of the framework we then examine different decompositions of these multi information measures the transfer entropy naturally appears as a term in some of these decompositions this allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework more generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems we illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions furthermore causal and noncausal statistical dependencies are not separable in particular the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems so it should not be interpreted as a measure of connectivity strength altogether in comparison to an analysis based on single isolated measures of interdependence this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics

maximal aggregation of polynomial dynamical systems ordinary differential equations odes with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models here we propose an aggregation technique that rests on two notions of equivalence relating ode variables whenever they have the same solution backward criterion or if a self consistent system can be written for describing the evolution of sums of variables in the same equivalence class forward criterion a key feature of our proposal is to encode a polynomial ode system into a finitary structure akin to a formal chemical reaction network this enables the development of a discrete algorithm to efficiently compute the largest equivalence building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements the physical interpretability of the aggregation is shown on polynomial ode systems for biochemical reaction networks gene regulatory networks and evolutionary game theory

information distance in multiples information distance is a parameter free similarity measure based on compression used in pattern recognition data mining phylogeny clustering and classification the notion of information distance is extended from pairs to multiples finite lists we study maximal overlap metricity universality minimal overlap additivity and normalized information distance in multiples we use the theoretical notion of kolmogorov complexity which for practical purposes is approximated by the length of the compressed version of the file involved using a real world compression program

axiomatizations for probabilistic finite state behaviors we study a process calculus which combines both nondeterministic and probabilistic behavior in the style of segala and lynch s probabilistic automata we consider various strong and weak behavioral equivalences and we provide complete axiomatizations for finite state processes restricted to guarded recursion in case of the weak equivalences we conjecture that in the general case of unguarded recursion the natural weak equivalences are undecidable this is the first work to our knowledge that provides a complete axiomatization for weak equivalences in the presence of recursion and both nondeterministic and probabilistic choice

metrics for labelled markov processes the notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions thus a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent this instability is due to the quantitative nature of probabilistic processes in a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence this paper studies a metric between labelled markov processes this metric has the property that processes are at zero distance if and only if they are bisimilar the metric is inspired by earlier work on logics for characterizing bisimulation and is related in spirit to the hutchinson metric

bisimulation for probabilistic transition systems a coalgebraic approach the notion of bisimulation as proposed by larsen and skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of aczel and mendier in terms of a set functor this coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving borel probability measures under reasonable conditions generalized probabilistic bisimilarity can be characterized categorically application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation

differential privacy in probabilistic systems abstract ever since proposed by dwork differential privacy has been a hot topic in academia however few attempts have been made on reasoning about differential privacy at a system level in this paper we propose a formal framework to verify differential privacy in probabilistic systems with a metric on the states of a system we formalize differential privacy by the ratio of the probabilities in the distributions after the same labeled transitions of relevant states we explain how traditional differential privacy can be embedded in our framework and raise an infimum metric the least distance between two states while not violating differential privacy it is proven that the infimum metric is also a metric instance of differential privacy itself furthermore we propose a two level logic a privacy variant of the familiar hennessy milner logic to characterize differential privacy in our framework our results have close relations to probabilistic bisimilarity as well

additive models of probabilistic processes we propose a new model of probabilistic processes in this model a probability is assigned to the action of a prefix and a probability distribution is assigned to the components of a parallel composition in addition the probability of a transition of a probabilistic summation is evaluated as the sum of the probabilities of the same transition of summands multiplied by the probabilities associated to them in the summation the concepts of strong bisimulation degree and weak bisimulation degree are introduced these notions provide us with continuous spectra of strong bisimilarities weak bisimilarities and observation congruences which equate probabilistic processes with different degrees of belief various equational laws of probabilistic processes with respect to these equivalence relations are presented and substitutivities of these equivalence relations under various combinators are established

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

a refined complexity analysis of degree anonymization in graphs motivated by a strongly growing interest in graph anonymization we study the np hard degree anonymity problem asking whether a graph can be made k anonymous by adding at most a given number of edges herein a graph is k anonymous if for every vertex in the graph there are at least k 1 other vertices of the same degree our algorithmic results shed light on the performance quality of a popular heuristic due to liu and terzi acm sigmod 2008 in particular we show that the heuristic provides optimal solutions if many edges need to be added based on this we develop a polynomial time data reduction yielding a polynomial size problem kernel for degree anonymity parameterized by the maximum vertex degree in terms of parameterized complexity analysis this result is in a sense tight since we also show that the problem is already np hard for h index three implying np hardness for smaller parameters such as average degree and degeneracy

robust measure for characterizing generalized synchronization generalized synchronization between two coupled systems can be characterized by recently proposed interdependency measures calculated from two simultaneously observed time series from them however numerical tests have shown that these measures cannot consistently indicate the direction of the coupling for strongly coupled systems or in situations with a large phase space neighbor size an interdependency measure is proposed here quantifying how close a conditional neighbor is to a true neighbor in terms of the degree of alignment of their principal axes numerical tests are carried out on time series generated from a coupled henon map and a lorenz model driven by a rossler model given that a driving system is more dependent on a response system the results show that the direction of the coupling is consistently detected by using the proposed measure even in those unfavorable cases for the measures mentioned above

mitigating the effects of measurement noise on granger causality computing granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years such causal relations if correctly estimated can yield significant insights into the dynamical organization of the system being investigated since experimental measurements are inevitably contaminated by noise it is thus important to understand the effects of such noise on granger causality estimation the first goal of this paper is to provide an analytical and numerical analysis of this problem specifically we show that due to noise contamination 1 spurious causality between two measured variables can arise and 2 true causality can be suppressed the second goal of the paper is to provide a denoising strategy to mitigate this problem specifically we propose a denoising algorithm based on the combined use of the kalman filter theory and the expectation maximization algorithm numerical examples are used to demonstrate the effectiveness of the denoising approach

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

assessing causality from multivariate time series in this work we propose a general nonparametric test of causality for weakly dependent time series more precisely we study the problem of attribution i e the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest we illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science

bisimulation and cocongruence for probabilistic systems we introduce a new notion of bisimulation called event bisimulation on labelled markov processes and compare it with the now standard notion of probabilistic bisimulation originally due to larsen and skou event bisimulation uses a sub algebra as the basic carrier of information rather than an equivalence relation the resulting notion is thus based on measurable subsets rather than on points hence the name event bisimulation applies smoothly for general measure spaces bisimulation on the other hand is known only to work satisfactorily for analytic spaces we prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary bisimulation these complexities only arise when we show that on analytic spaces the two concepts coincide we show that the concept of event bisimulation arises naturally from taking the cocongruence point of view for probabilistic systems we show that the theory can be given a pleasing categorical treatment in line with general coalgebraic principles as an easy application of these ideas we develop a notion of almost sure bisimulation the theory comes almost for free once we modify giry s monad appropriately

how to detect the granger causal flow direction in the presence of additive noise granger causality metrics have become increasingly popular tools to identify directed interactions between brain areas however it is known that additive noise can strongly affect granger causality metrics which can lead to spurious conclusions about neuronal interactions to solve this problem previous studies have proposed the detection of granger causal directionality i e the dominant granger causal flow using either the slope of the coherency phase slope index psi or by comparing granger causality values between original and time reversed signals reversed granger testing we show that for ensembles of vector autoregressive var models encompassing bidirectionally coupled sources these alternative methods do not correctly measure granger causal directionality for a substantial fraction of var models even in the absence of noise we then demonstrate that uncorrelated noise has fundamentally different effects on directed connectivity metrics than linearly mixed noise where the latter may result as a consequence of electric volume conduction uncorrelated noise only weakly affects the detection of granger causal directionality whereas linearly mixed noise causes a large fraction of false positives for standard granger causality metrics and psi but not for reversed granger testing we further show that we can reliably identify cases where linearly mixed noise causes a large fraction of false positives by examining the magnitude of the instantaneous influence coefficient in a structural var model by rejecting cases with strong instantaneous influence we obtain an improved detection of granger causal flow between neuronal sources in the presence of additive noise these techniques are applicable to real data which we demonstrate using actual area v1 and area v4 lfp data recorded from the awake monkey performing a visual attention task

measurable stochastics for brane calculus the main aim of this work is to give a stochastic extension of the brane calculus along the lines of recent work by cardelli and mardare 2010 12 in this approach the semantics of a process is a measure of the stochastic distribution of possible derivations to this end we first introduce a compositional finitely branching labelled transition system for brane calculus interestingly the associated strong bisimulation is a congruence then we give a stochastic semantics to brane systems by defining them as markov processes over the measurable space generated by terms up to syntactic congruence and where the measures are indexed by the actions of this new lts finally we provide an sos presentation of this stochastic semantics which is compositional and syntax driven and moreover the induced rate bisimilarity is a congruence

encompassing univariate models in multivariate time series a case study abstract through the encompassing principle univariate arima analysis could provide an important tool for diagnosis of var models the univariate arima models implied by the var should explain the results from univariate analysis this comparison is seldom performed possibly due to the paradox that while the implied arima models typically contain a very large number of parameters univariate analysis yields highly parsimonious models using a var application to six french macro economic variables it is seen how the encompassing check is straight forward to perform and surprisingly accurate

observation equivalence as a testing equivalence a notion of testing is developed for transition systems with divergence the forms of testing include traces refusals copying and global testing both denotational and operational formulations of testing are given the equivalence based on this notion of testing is shown to coincide with observation equivalence

a hierarchy of probabilistic system types we arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy our expressiveness criterion is the existence of a system translation from the less expressive type into the more expressive type that preserves and reflects probabilistic bisimilarity we model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature the theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy all these translations arise in a standard way from natural transformations between the two behaviour functors involved such a translation generally preserves coalgebraic bisimilarity we exploit a new result that under mild assumptions on the behaviour functors a system translation induced by a natural transformation with injective components also reflects bisimilarity

characterize branching distance in terms of η α bisimilarity in order to describe approximate equivalence between processes the notion of branching distance has been introduced in the framework of quantitative transition systems this paper introduces the notion of h a bisimilarity and explores the relationship between it and the branching distance

process algebra for performance evaluation this paper surveys the theoretical developments in the field of stochastic process algebras process algebras where action occurrences may be subject to a delay that is determined by a random variable a huge class of resource sharing systems like large scale computers client server architectures networks can accurately be described using such stochastic specification formalisms the main emphasis of this paper is the treatment of operational semantics notions of equivalence and sound and complete axiomatisations of these equivalences for different types of markovian process algebras where delays are governed by exponential distributions starting from a simple actionless algebra for describing time homogeneous continuous time markov chains we consider the integration of actions and random delays both as a single entity like in known markovian process algebras like tipp pepa and empa and as separate entities like in the timed process algebras timed csp and tccs in total we consider four related calculi and investigate their relationship to existing markovian process algebras we also briefly indicate how one can profit from the separation of time and actions when incorporating more general non markovian distributions

recursively defined metric spaces without contraction in this paper we use the theory of accessible categories to find fixed points of endofunctors on the category of 1 bounded complete metric spaces and nonexpansive functions in contrast to previous approaches we do not assume that the endofunctors are locally contractive and our results do not depend on banach s fixed point theorem our approach is particularly suitable for constructing models of systems that feature quantitative data for instance using the kantorovich metric on probability measures we construct a quantitative model for probabilistic transition systems the metric in our model can reasonably be seen as measuring the behavioural distance between states of the system it depends exclusively on the transition probabilities and not on an arbitrary discount factor

the effect of filtering on granger causality based multivariate causality measures in the past causality measures based on granger causality have been suggested for assessing directionality in neural signals in frequency domain analyses power or coherence of neural data it is common to preprocess the time series by filtering or decimating however in other fields it has been shown theoretically that filtering in combination with granger causality may lead to spurious or missed causalities we investigated whether this result translates to multivariate causality methods derived from granger causality with a a simulation study and b an application to magnetoencephalographic data to this end we performed extensive simulations of the effect of applying different filtering techniques and evaluated the performance of five different multivariate causality measures in combination with two numerical significance measures random permutation and leave one out method the analysis included three of the most widely used filters high pass low pass notch filter four different filter types butterworth chebyshev i and ii elliptic filter variation of filter order decimating and interpolation the simulation results suggest that preprocessing without a strong prior about the artifact to be removed disturbs the information content and time ordering of the data and leads to spurious and missed causalities only if apparent artifacts like a current or movement artifact are present filtering out the respective disturbance seems advisable while oversampling poses no problem decimation by a factor greater than the minimum time shift between the time series may lead to wrong inferences in general the multivariate causality measures are very sensitive to data preprocessing

kernel granger causality and the analysis of dynamical networks we propose a method of analysis of dynamical networks based on a recent measure of granger causality between time series based on kernel methods the generalization of kernel granger causality to the multivariate case here presented shares the following features with the bivariate measures i the nonlinearity of the regression model can be controlled by choosing the kernel function and ii the problem of false causalities arising as the complexity of the model increases is addressed by a selection strategy of the eigenvectors of a reduced gram matrix whose range represents the additional features due to the second time series moreover there is no a priori assumption that the network must be a directed acyclic graph we apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network it is shown that the underlying topology of the network can be reconstructed from time series of node s dynamics provided that a sufficient number of samples is available considering a linear dynamical network built by preferential attachment scheme we show that for limited data use of the bivariate granger causality is a better choice than methods using l1 minimization finally we consider real expression data from hela cells 94 genes and 48 time points the analysis of static correlations between genes reveals two modules corresponding to well known transcription factors granger analysis puts in evidence 19 causal relationships all involving genes related to tumor development

generalised filtering and stochastic dcm for fmri this paper is about the fitting or inversion of dynamic causal models dcms of fmri time series it tries to establish the validity of stochastic dcms that accommodate random fluctuations in hidden neuronal and physiological states we compare and contrast deterministic and stochastic dcms which do and do not ignore random fluctuations or noise on hidden states we then compare stochastic dcms which do and do not ignore conditional dependence between hidden states and model parameters generalised filtering and dynamic expectation maximisation respectively we first characterise state noise by comparing the log evidence of models with different a priori assumptions about its amplitude form and smoothness face validity of the inversion scheme is then established using data simulated with and without state noise to ensure that dcm can identify the parameters and model that generated the data finally we address construct validity using real data from an fmri study of internet addiction our analyses suggest the following i the inversion of stochastic causal models is feasible given typical fmri data ii state noise has nontrivial amplitude and smoothness iii stochastic dcm has face validity in the sense that bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity iv relaxing conditional independence assumptions can have greater construct validity in terms of revealing group differences not disclosed by variational schemes finally we note that the ability to model endogenous or random fluctuations on hidden neuronal and physiological states provides a new and possibly more plausible perspective on how regionally specific signals in fmri are generated

granger causality and information flow in multivariate processes the multivariate versus bivariate measures of granger causality were considered granger causality in the application to multivariate physiological time series has the meaning of the information flow between channels it was shown by means of simulations and by the example of experimental electroencephalogram signals that bivariate estimates of directionality in case of mutually interdependent channels give erroneous results therefore multivariate measures such as directed transfer function should be used for determination of the information flow

reliability of mobile processes with noisy channels to model the behavior of channels in real world mobile systems ying introduced an extension of the calculus by taking channel noise into account unfortunately this extension is not faithful in the sense that its semantics does not coincide with the standard one for the calculus in the noise free case in this paper we consider a simple variant of the calculus the asynchronous calculus a which has been used for modeling some concurrent systems with asynchronous communication to model these systems with noisy channels we propose a faithful extension of a called the a n calculus after giving a probabilistic transitional semantics of a n we introduce bisimilarity in a n and show that it is a partial input congruence if a specification of a system is described as a process p in a and we view the behavior of p in a n as an implementation of the specification then it is interesting to measure how far the behavior in a n is from that in a we thus introduce the notion of reliability degree which is based upon a new approximate bisimulation we find that bisimilar agents may have different reliability degrees and even the agent with the greatest reliability degree may not be satisfactory we thus appeal to shannon s noisy channel coding theorem and show that reliability degrees can be improved by employing coding techniques

probabilistic bisimulations for quantum processes modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification as a consequence a general framework formally describing communication and concurrency in complex quantum systems is necessary for this purpose we propose a model named qccs it is a natural quantum extension of classical value passing ccs which can deal with input and output of quantum states and unitary transformations and measurements on quantum systems the operational semantics of qccs is given in terms of probabilistic labeled transition system this semantics has many different features compared with the proposals in the available literature in order to describe the input and output of quantum systems which are possibly correlated with other components based on this operational semantics the notions of strong probabilistic bisimulation and weak probabilistic bisimulation between quantum processes are introduced furthermore some properties of these two probabilistic bisimulations such as congruence under various combinators are examined

non expansive e bisimulations for probabilistic processes e bisimulation equivalence has been proposed in the literature as a technique to study the concept of behavioral distance between probabilistic processes in this paper we first consider the generative model of probabilistic processes and introduce two stronger equivalence notions action e bisimulation and global e bisimulation for each of these three equivalence notions we propose an sos transition rule format ensuring the property of non expansiveness non expansiveness means that if the behavioral distance between s i and t i is e i then the behavioral distance between f s 1 s n and f t 1 t n is no more that e 1 e n as expected the stronger the e bisimulation considered the weaker the constraints of the transition rule format then we switch to the reactive model of probabilistic processes and we propose a rule format for e bisimulation and action e bisimulation arguing that global e bisimulation is not needed in such a context

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

validity of time reversal for testing granger causality inferring causal interactions from observed data is a challenging problem especially in the presence of measurement noise to alleviate the problem of spurious causality haufe 2013 proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time reversed data they show that this procedure time reversed granger causality trgc robustly rejects causal interpretations on mixtures of independent signals while promising results have been achieved in simulations it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction here we prove that for linear finite order autoregressive processes with unidirectional information flow between two variables the application of time reversal for testing granger causality indeed leads to correct estimates of information flow and its directionality using simulations we further show that trgc is able to infer correct directionality with similar statistical power as the net granger causality between two variables while being much more robust to the presence of measurement noise

iterative and sequential algorithms for multisensor signal enhancement in problems of enhancing a desired signal in the presence of noise multiple sensor measurements will typically have components from both the signal and the noise sources when the systems that couple the signal and the noise to the sensors are unknown the problem becomes one of joint signal estimation and system identification the authors specifically consider the two sensor signal enhancement problem in which the desired signal is modeled as a gaussian autoregressive ar process the noise is modeled as a white gaussian process and the coupling systems are modeled as linear time invariant finite impulse response fir filters the main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system and the authors apply the estimate maximize em algorithm for jointly estimating the desired signal the coupling systems and the unknown signal and noise spectral parameters the resulting algorithm can be viewed as the time domain version of the frequency domain approach of feder et al 1989 where instead of the noncausal frequency domain wiener filter the kalman smoother is used this approach leads naturally to a sequential adaptive algorithm by replacing the kalman smoother with the kalman filter and in place of successive iterations on each data block the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data a computationally efficient implementation of the algorithm is developed an expression for the log likelihood gradient based on the kalman smoother filter output is also developed and used to incorporate efficient gradient based algorithms in the estimation process

quantifying information leakage in process calculi building on simple information theoretic concepts we study two quantitative models of information leakage in the pi calculus the first model presupposes an attacker with an essentially unlimited computational power the resulting notion of absolute leakage measured in bits is in agreement with secrecy as defined by abadi and gordon a process has an absolute leakage of zero precisely when it satisfies secrecy the second model assumes a restricted observation scenario inspired by the testing equivalence framework where the attacker can only conduct repeated success or failure experiments on processes moreover each experiment has a cost in terms of communication effort the resulting notion of leakage rate measured in bits per action is in agreement with the first model the maximum amount of information that can be extracted by repeated experiments coincides with the absolute leakage a of the process moreover the overall extraction cost is at least a r where r is the rate of the process the compositionality properties of the two models are also investigated

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed

the max plus algebra of the natural numbers has no finite equational basis this paper shows that the collection of identities which hold in the algebra n of the natural numbers with constant zero and binary operations of sum and maximum is not finitely based moreover it is proven that for every n the equations in at most n variables that hold in n do not form an equational basis as a stepping stone in the proof of these facts several results of independent interest are obtained in particular explicit descriptions of the free algebras in the variety generated by n are offered such descriptions are based upon a geometric characterization of the equations that hold in n which also yields that the equational theory of n is decidable in exponential time

network discovery with dcm this paper is about inferring or discovering the functional architecture of distributed systems using dynamic causal modelling dcm we describe a scheme that recovers the dynamic bayesian dependency graph connections in a network using observed network activity this network discovery uses bayesian model selection to identify the sparsity structure absence of edges or connections in a graph that best explains observed time series the implicit adjacency matrix specifies the form of the network e g cyclic or acyclic and its graph theoretical attributes e g degree distribution the scheme is illustrated using functional magnetic resonance imaging fmri time series to discover functional brain networks crucially it can be applied to experimentally evoked responses activation studies or endogenous activity in task free resting state fmri studies unlike conventional approaches to network discovery dcm permits the analysis of directed and cyclic graphs furthermore it eschews implausible markovian assumptions about the serial independence of random fluctuations the scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability relative to other networks the networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed and reciprocal effective connectivity between connected nodes or regions we envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting state studies

granger causality and cross recurrence plots in rheochaos our stress relaxation measurements on wormlike micelles using a rheo sals rheology small angle light scattering apparatus allow simultaneous measurements of the stress and the scattered depolarized intensity the latter is sensitive to orientational ordering of the micelles to determine the presence of causal influences between the stress and the depolarized intensity time series we have used the technique of linear and nonlinear granger causality we find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa we have also studied the phase space dynamics of the stress and the depolarized intensity time series using the recently developed technique of cross recurrence plots crps the presence of diagonal line structures in the crps unambiguously proves that the two time series share similar phase space dynamics

undecidable verification problems for programs with unreliable channels we consider the class of finite state systems communicating through unbounded butlossyfifo channels calledlossy channel systems these systems have infinite state spaces due to the unboundedness of the channels in an earlier paper we showed that the problems of checking reachability safety properties and eventuality properties are decidable for lossy channel systems in this paper we show that the following problems are undecidable the model checking problem in propositional temporal logics such as propositional linear time temporal logic ptl and computation tree logic ctl the problem of deciding eventuality properties with fair channels do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions the results are obtained through reduction from a variant of the post correspondence problem

the decomposition and measurement of the interdependency between second order stationary processes for a given pair of multivariate stationary processes the process of one way effect is extracted from each of the processes each process is decomposed into two orthogonal processes namely into the process generated by the one way effect of the other process and the process orthogonal to it based on the decomposition three measures characterizing the interdependency of the pair of processes are introduced they are the measure of association the measure of one way effect and the measure of reciprocity each of the measures is defined as overall as well as frequencywise measure the paper shows that the measure of association is equal to the sum of the others it discusses the relationships of those measures to the ones proposed by gel fand yaglom and by geweke