first passage times in renewal and nonrenewal systems fluctuations in stochastic systems are usually characterized by full counting statistics which analyzes the distribution of the number of events taking place in the fixed time interval in an alternative approach the distribution of the first passage times i e the time delays after which the counting variable reaches a certain threshold value is studied this paper presents the approach to calculate the first passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the markovian network using this approach it is shown that when the subsequent first passage times are uncorrelated there exist strict relations between the cumulants of the full counting statistics and the first passage time distribution on the other hand when the correlations of the first passage times are present their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics for example it may reveal the switching between different dynamical states of the system additionally i show that breaking of the fluctuation theorem for first passage times may reveal the multicyclic nature of the markovian network

skewness and kurtosis in statistical kinetics we obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes analogous to a well known lower bound on the randomness parameter the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter

linear transformations preserving symmetric rank one matrices let 1 be the space of n x n symmetric matrices over a commutative ring r with unit and let y y r be the subset of rank 1 that is the matrices where all 2 x 2 minors are zero our purpose is to study the invertible linear transformations z on v preserving y the study of such maps falls into two parts the first of which has already been carried out we know explicitly all the invertible t that formally preserve the vanishing of 2 x 2 minors the basic maps of that kind are in fact just the ones that first come to mind t x 1uxu for invertible u and a however as i explained in s descent theory shows that these mappings for even n automatically produce certain others as well and we call that larger set the natural transformations preserving rank d 1 an explicit description of them is given in section 1 below more precisely the theorem already known is this

firing statistics of a neuron model driven by long range correlated noise we study the statistics of the firing patterns of a perfect integrate and fire neuron model driven by additive long range correlated ornstein uhlenbeck noise using a quasistatic weak noise approximation we obtain expressions for the interspike interval isi probability density the power spectral density and the spike count fano factor we find unimodal long tailed isi densities lorenzian power spectra at low frequencies and a minimum in the fano factor as a function of counting time the implications of these results for signal detection are discussed

finite time generalization of the thermodynamic uncertainty relation for fluctuating currents in nonequilibrium steady states the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving we show that this relation holds not only for the long time limit of fluctuations as described by large deviation theory but also for fluctuations on arbitrary finite time scales this generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments for which infinite time scales are not accessible importantly often this finite time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long time limit we illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle

a general account of argumentation with preferences this paper builds on the recent aspic formalism to develop a general framework for argumentation with preferences we motivate a revised definition of conflict free sets of arguments adapt aspic to accommodate a broader range of instantiating logics and show that under some assumptions the resulting framework satisfies key properties and rationality postulates we then show that the generalised framework accommodates tarskian logic instantiations extended with preferences and then study instantiations of the framework by classical logic approaches to argumentation we conclude by arguing that aspic s modelling of defeasible inference rules further testifies to the generality of the framework and then examine and counter recent critiques of dung s framework and its extensions to accommodate preferences

algorithms for decision problems in argument systems under preferred semantics for dung s model of abstract argumentation under preferred semantics argumentation frameworks may have several distinct preferred extensions i e in informal terms sets of acceptable arguments thus the acceptance problem for a specific argument can consider deciding whether an argument is in at least one such extensions credulously accepted or in all such extensions skeptically accepted we start by presenting a new algorithm that enumerates all preferred extensions following this we build algorithms that decide the acceptance problem without requiring explicit enumeration of all extensions we analyze the performance of our algorithms by comparing these to existing ones and present experimental evidence that the new algorithms are more efficient with respect to the expected running time moreover we extend our techniques to solve decision problems in a widely studied development of dung s model namely value based argumentation frameworks vafs in this regard we examine analogous notions to the problem of enumerating preferred extensions and present algorithms that decide subjective respectively objective acceptance

reasoning about preferences in argumentation frameworks the abstract nature of dung s seminal theory of argumentation accounts for its widespread application as a general framework for various species of non monotonic reasoning and more generally reasoning in the presence of conflict a dung argumentation framework is instantiated by arguments and a binary conflict based attack relation defined by some underlying logical theory the justified arguments under different extensional semantics are then evaluated and the claims of these arguments define the inferences of the underlying theory to determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments however preference information is often itself defeasible conflicting and so subject to argumentation hence in this paper we extend dung s theory to accommodate arguments that claim preferences between other arguments thus incorporating meta level argumentation based reasoning about preferences in the object level we then define and study application of the full range of dung s extensional semantics to the extended framework and study special classes of the extended framework the extended theory preserves the abstract nature of dung s approach thus aiming at a general framework for non monotonic formalisms that accommodate defeasible reasoning about as well as with preference information we illustrate by formalising argument based logic programming with defeasible priorities in the extended theory

on the bilinearity rank of a proper cone and lyapunov like transformations a real square matrix q q is a bilinear complementarity relation on a proper cone k k in mathbb r n r n if begin aligned x in k s in k text and langle x s rangle 0 rightarrow x t qs 0 end aligned x k s k and x s 0 x t q s 0 where k k is the dual of k k the bilinearity rank of k k is the dimension of the linear space of all bilinear complementarity relations on k k in this article we continue the study initiated by rudolf et al math prog ser b 129 5 31 2011 we show that bilinear complementarity relations are related to lyapunov like transformations that appear in dynamical systems and in complementarity theory and further show that the bilinearity rank of k k is the dimension of the lie algebra of the automorphism group of k k in addition we correct a result of rudolf et al compute the bilinearity ranks of symmetric and completely positive cones and state some schur type results for lyapunov like transformations

a general framework for explaining the results of a multi attribute preference model the automatic generation of an explanation of the prescription made by a multi attribute decision model is crucial in many applications such as recommender systems this task is complex since the quantitative models are not designed to be easily explainable the major limitation of the previous research is that there is no formal justification of the arguments that are selected in the explanation the goal of this paper is to define a general framework to justify which arguments shall be selected in the case where the decision model is based on weights assigned to the attributes due to the complexity of explaining a preference model based on utility theory several explanation reasonings are necessary to cover all cases ranging from situations where the prescription is trivial to situations where the prescription is much more tight the set of selected arguments is in this framework a non dominated element of a combinatorial structure in the sense of an order relation our general approach is instantiated precisely on three models the probabilistic expected utility model the qualitative pessimistic minmax model and the concordance rule which are all constructed from a weight vector

long and short time asymptotics of the first passage time of the ornstein uhlenbeck and other mean reverting processes the first passage problem of the ornstein uhlenbeck ou process to a boundary is a long standing problem with no known closed form solution except in specifc cases taking this as a starting point and extending to a general mean reverting process we investigate the long and short time asymptotics using a combination of hopf cole and laplace transform techniques as a result we are able to give a single formula that is correct in both limits as well as being exact in certain special cases we demonstrate the results using a variety of other models

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

tightening the uncertainty principle for stochastic currents we connect two recent advances in the stochastic analysis of nonequilibrium systems the loose uncertainty principle for the currents which states that statistical errors are bounded by thermodynamic dissipation and the analysis of thermodynamic consistency of the currents in the light of symmetries employing the large deviation techniques presented by gingrich et al phys rev lett 116 120601 2016 prltao0031 900710 1103 physrevlett 116 120601 and pietzonka barato and seifert phys rev e 93 052145 2016 2470 004510 1103 physreve 93 052145 we provide a short proof of the loose uncertainty principle and prove a tighter uncertainty relation for a class of thermodynamically consistent currents j our bound involves a measure of partial entropy production that we interpret as the least amount of entropy that a system sustaining current j can possibly produce at a given steady state we provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal and finally we argue that the relationship for the fano factor of the entropy production rate var mean 2 is the most significant realization of the loose bound we base our analysis both on the formalism of diffusions and of markov jump processes in the light of schnakenberg s cycle analysis

z transformations on proper and symmetric cones z transformations motivated by the similarities between the properties of z matrices on r n and lyapunov and stein transformations on the semidefinite cone mathcal s n we introduce and study z transformations on proper cones we show that many properties of z matrices extend to z transformations we describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations finally we study the equivalence of q and p properties of z transformations on symmetric cones in particular we prove such an equivalence on the lorentz cone

universal bounds on current fluctuations for current fluctuations in nonequilibrium steady states of markovian processes we derive four different universal bounds valid beyond the gaussian regime different variants of these bounds apply to either the entropy change or any individual current e g the rate of substrate consumption in a chemical reaction or the electron current in an electronic device the bounds vary with respect to their degree of universality and tightness a universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production a second stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states these two bounds are conjectures based on extensive numerics an exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved this bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium an asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived this bound allows for the prediction of the asymptotic growth of the generating function even though our results are restricted to networks with a finite number of states we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle our bounds provide a general class of constraints for nonequilibrium systems

on the p property of z and lyapunov like transformations on euclidean jordan algebras abstract the p z and s properties of a linear transformation on a euclidean jordan algebra are generalizations of the corresponding properties of a square matrix on rn motivated by the equivalence of p and s properties for a z matrix 2 and a similar result for lyapunov and stein transformations on the space of real symmetric matrices 6 5 in this paper we present two results supporting the conjecture that p and s properties are equivalent for a z transformation on a euclidean jordan algebra we show that the conjecture holds for lyapunov like transformations and z transformations satisfying an additional condition

optimal stochastic restart renders fluctuations in first passage times universal stochastic restart may drastically reduce the expected run time of a computer algorithm expedite the completion of a complex search process or increase the turnover rate of an enzymatic reaction these diverse first passage time fpt processes seem to have very little in common but it is actually quite the other way around here we show that the relative standard deviation associated with the fpt of an optimally restarted process i e one that is restarted at a constant nonzero rate which brings the mean fpt to a minimum is always unity we interpret further generalize and discuss this finding and the implications arising from it

proof of the finite time thermodynamic uncertainty relation for steady state currents this paper presents the finite time version of the thermodynamic uncertainty relation for nonequilibrium steady states which sets a bound on the magnitude of current fluctuations the authors use a methodology that is similar to the proof for the long time limit but with large deviation theory applied to an ensemble of many copies

positive groups on hn are completely positive we prove that an operator generates a positive group on the real space of real or complex hermitian matrices if and only if it is a lyapunov operator in particular it follows that every group of positive operators in fact is a group of completely positive operators

an abstract argumentation theoretic approach to default reasoning abstract we present an abstract framework for default reasoning which includes theorist default logic logic programming autoepistemic logic non monotonic modal logics and certain instances of circumscription as special cases the framework can be understood as a generalisation of theorist the generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions an assumption can be defeated or attacked if its contrary can be proved possibly with the aid of other conflicting assumptions we show that given such a framework the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions as an extension of a given theory if and only if the set of assumptions is conflict free in the sense that it does not attack itself and it attacks every assumption not in the set we propose a more liberal argumentation theoretic semantics based upon the notion of admissible extension in logic programming we regard a set of assumptions in general as admissible if and only if it is conflict free and defends itself by attacking every set of assumptions which attacks it we identify conditions for the existence of extensions and for the equivalence of different semantics

approximating operators and semantics for abstract dialectical frameworks we provide a systematic in depth study of the semantics of abstract dialectical frameworks adfs a recent generalisation of dung s abstract argumentation frameworks this is done by associating with an adf its characteristic one step consequence operator and defining various semantics for adfs as different fixpoints of this operator we first show that several existing semantical notions are faithfully captured by our definition then proceed to define new adf semantics and show that they are proper generalisations of existing argumentation semantics from the literature most remarkably this operator based approach allows us to compare adfs to related nonmonotonic formalisms like dung argumentation frameworks and propositional logic programs we use polynomial faithful and modular translations to relate the formalisms and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs

monotonically positive matrices abstract a matrix a is monotonically positive mp if there exists a matrix u such that a u u t and each column of u is monotonically nonincreasing or nondecreasing following the approach in j nie 2014 15 we propose a semidefinite algorithm for checking whether or not a matrix is mp if it is not mp a certificate for it can be obtained if it is mp an mp decomposition can be obtained some computational experiments are presented to show how to do this

fluctuating currents in stochastic thermodynamics i gauge invariance of asymptotic statistics stochastic thermodynamics uses markovian jump processes to model random transitions between observable mesoscopic states physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states the asymptotic statistics of such currents are characterized by scaled cumulants in the present work we use the algebraic and topological structure of markovian models to prove a gauge invariance of the scaled cumulant generating function exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals we discuss how our approach generalizes the schnakenberg decomposition of the average entropy production rate and how it unifies previous work the application of our results to concrete models is presented in an accompanying publication

instantiating abstract argumentation with classical logic arguments postulates and properties in this paper we investigate the use of classical logic as a basis for instantiating abstract argumentation frameworks in the first part we propose desirable properties of attack relations in the form of postulates and classify several well known attack relations from the literature with regards to the satisfaction of these postulates furthermore we provide additional postulates that help us prove characterisation results for these attack relations in the second part of the paper we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic we then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics

the automorphism group of a completely positive cone and its lie algebra abstract given a closed cone c in r n we consider the corresponding completely positive convex cone k generated by uu t u c in s n under certain conditions on c we describe the automorphism group of k and its corresponding lie algebra in terms of those of c c and or c in particular we show that when c is a closed convex proper cone the automorphism groups of c and k are isomorphic and their corresponding lie algebras are isomorphic

simple bounds on fluctuations and uncertainty relations for first passage times of counting observables recent large deviation results have provided general lower bounds for the fluctuations of time integrated currents in the steady state of stochastic systems a corollary are so called thermodynamic uncertainty relations connecting precision of estimation to average dissipation here we consider this problem but for counting observables i e trajectory observables which in contrast to currents are non negative and nondecreasing in time and possibly symmetric under time reversal in the steady state their fluctuations to all orders are bound from below by a conway maxwell poisson distribution dependent only on the averages of the observable and of the dynamical activity we show how to obtain the corresponding bounds for first passage times times when a certain value of the counting variable is first reached and their uncertainty relations just like entropy production does for currents dynamical activity controls the bounds on fluctuations of counting observables

affinity and fluctuations in a mesoscopic noria we exhibit the invariance of cycle affinities in finite state markov processes under various natural probabilistic constructions for instance under conditioning and under a new combinatorial construction that we call drag and drop we show that cycle affinities have a natural probabilistic meaning related to first passage non equilibrium fluctuation relations that we establish

decision making in the arrow of time we show that the steady state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time here we apply wald s sequential probability ratio test to optimally decide on the direction of time s arrow in stationary markov processes furthermore the steady state entropy production rate can be estimated using mean first passage times of suitable physical variables we derive a first passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes

large deviations of ergodic counting processes a statistical mechanics approach the large deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations here we study this formalism through a statistical mechanics approach that is with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential we show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones providing is this way an alternative measurement interpretation of the thermodynamic approach general results are obtained for renewal counting processes that is those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution the underlying statistical mechanics is controlled by the same waiting time distribution rescaled by an exponential decay measured by the free energy function a scale invariance shift closure and intermittence phenomena are obtained and interpreted in this context similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution