point process principal components analysis via geometric optimization there has been a fast growing demand for analysis tools for multivariate point process data driven by work in neural coding and more recently high frequency finance here we develop a true or exact as opposed to one based on time binning principal components analysis for preliminary processing of multivariate point processes we provide a maximum likelihood estimator an algorithm for maximization involving steepest ascent on two stiefel manifolds and novel constrained asymptotic analysis the method is illustrated with a simulation and compared with a binning approach

a branch and cut decomposition algorithm for solving chance constrained mathematical programs with finite support we present a new approach for exactly solving chance constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints such problems have been notoriously difficult to solve due to nonconvexity of the feasible region and most available methods are only able to find provably good solutions in certain very special cases our approach uses both decomposition to enable processing subproblems corresponding to one possible outcome at a time and integer programming techniques to combine the results of these subproblems to yield strong valid inequalities computational results on a chance constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed integer programming formulation and a simple decomposition approach that does not use strong valid inequalities we also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels as would be done when solving for the efficient frontier of risk and cost

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

rate limitations of unitary event analysis unitary event analysis is a new method for detecting episodes of synchronized neural activity riehle gruun diesmann aertsen 1997 it detects time intervals that contain coincident firing at higher rates than would be expected if the neurons fired as independent inhomogeneous poisson processes all coincidences in such intervals are called unitary events ues changes in the frequency of ues that are correlated with behavioral states may indicate synchronization of neural firing that mediates or represents the behavioral state we show that ue analysis is subject to severe limitations due to the underlying discrete statistics of the number of coincident events these limitations are particularly stringent for low 0 10 spikes s firing rates under these conditions the frequency of ues is a random variable with a large variation relative to its mean the relative variation decreases with increasing firing rate and we compute the lowest firing rate at which the 95 confidence interval around the mean frequency of ues excludes zero this random variation in ue frequency makes interpretation of changes in ues problematic for neurons with low firing rates as a typical example when analyzing 150 trials of an experiment using an averaging window 100 ms wide and a 5ms coincidence window firing rates should be greater than 7 spikes per second

a binless correlation measure reduces the variability of memory reactivation estimates summary the standard procedure for measuring correlations between pairs of spike trains is to count the numbers of spikes occurring within a specified set of time intervals partitioning the continuous time line into discrete bins of width w seconds one then computes the pearson correlation between pairs of the bin occupancy vectors this method introduces a form of quantization noise similar to that in analog to digital signal processing devices due to the arbitrary positioning of bin boundaries relative to pairs of spikes small changes in bin width and small uniform shifts in bin boundaries typically produce large variations in the apparent correlation an alternative method of determining a correlation between pairs of spike trains was recently introduced rather than discretize the data in time the original spike trains are convolved with a gaussian kernel with parameter chosen to give an effective width matching the bin width w 12 calculating the pearson correlation of the resulting smooth functions gives an estimate of the correlation between the spike trains matching that given by the bin based procedure without introducing the significant variability of the bin based estimate measures of memory reactivation based on the partial correlations between ensembles of pairwise spike train correlations are biased downwards by the quantization noise present in the pairwise correlation estimates using a binless method to measure pairwise correlation we find that the partial correlation or explained variance of rat hippocampal maze activity and post maze sleep taking into account pre maze sleep correlations increases significantly over estimates made with the standard bin based procedure copyright 2007 john wiley sons ltd

neural coding higher order temporal patterns in the neurostatistics of cell assemblies recent advances in the technology of multiunit recordings make it possible to test hebb s hypothesis that neurons do not function in isolation but are organized in assemblies this has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data we mention three possible measures for the presence of higher order patterns of neural activation coef ficients of log linear models connected cumulants and redundancies and present arguments in favor of the coefficients of loglinear models we present test statistics for detecting the presence of higher order interactions in spike train data by parameterizing these interactions in terms of coefficients of log linear models we also present a bayesian approach for inferring the existence or absence of interactions and estimating their strength the two methods the frequentist and the bayesian one are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other a heuristic for the analysis of temporal patterns is also proposed finally a bayesian test is presented that establishes stochastic differences between recorded segments of data the methods are applied to experimental data and synthetic data drawn from our statistical models our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys the somatosensory cortex of anesthetized rats and multiunit recordings in the visual cortex of behaving monkeys

unitary events in multiple single neuron spiking activity ii nonstationary data in order to detect members of a functional group cell assembly in simultaneously recorded neuronal spiking activity we adopted the widely used operational definition that membership in a common assembly is expressed in near simultaneous spike activity unitary event analysis a statistical method to detect the significant occurrence of coincident spiking activity in stationary data was recently developed see the companion article in this issue the technique for the detection of unitary events is based on the assumption that the underlying processes are stationary in time this requirement however is usually not fulfilled in neuronal data here we describe a method that properly normalizes for changes of rate the unitary events by moving window analysis uemwa analysis for unitary events is performed separately in overlapping time segments by sliding a window of constant width along the data in each window stationarity is assumed performance and sensitivity are demonstrated by use of simulated spike trains of independently firing neurons into which coincident events are inserted if cortical neurons organize dynamically into functional groups the occurrence of near simultaneous spike activity should be time varying and related to behavior and stimuli uemwa also accounts for these potentially interesting nonstationarities and allows locating them in time the potential of the new method is illustrated by results from multiple single unit recordings from frontal and motor cortical areas in awake behaving monkey

a comparison of descriptive models of a single spike train by information geometric measure in examining spike trains different models are used to describe their structure the different models often seem quite similar but because they are cast in different formalisms it is often difficult to compare their predictions here we use the information geometric measure an orthogonal coordinate representation of point processes to express different models of stochastic point processes in a common coordinate system within such a framework it becomes straightforward to visualize higher order correlations of different models and thereby assess the differences between models we apply the information geometric measure to compare two similar but not identical models of neuronal spike trains the inhomogeneous markov and the mixture of poisson models it is shown that they differ in the second and higher order interaction terms in the mixture of poisson model the second and higher order interactions are of comparable magnitude within each order whereas in the inhomogeneous markov model they have alternating signs over different orders this provides guidance about what measurements would effectively separate the two models as newer models are proposed they also can be compared to these models using information geometry

decomposition algorithms for two stage chance constrained programs we study a class of chance constrained two stage stochastic optimization problems where second stage feasible recourse decisions incur additional cost in addition we propose a new model where recovery decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second stage problem we develop decomposition algorithms with specialized optimality and feasibility cuts to solve this class of problems computational results on a chance constrained resource planing problem indicate that our algorithms are highly effective in solving these problems compared to a mixed integer programming reformulation and a naive decomposition method

new reformulations for probabilistically constrained quadratic programs abstract the mixed integer quadratic programming miqp reformulation by zheng sun li and cui 2012 for probabilistically constrained quadratic programs pcqp recently published in ejor significantly dominates the standard miqp formulation ruszczynski 2002 benati and rizzi 2007 which has been widely adopted in the literature stimulated by the dimensionality problem which zheng et al 2012 acknowledge themselves for their reformulations we study further the characteristics of pcqp and develop new miqp reformulations for pcqp with fewer variables and constraints the results from numerical tests demonstrate that our reformulations clearly outperform the state of the art miqp in zheng et al 2012

lifting valid inequalities for the precedence constrained knapsack problem this paper considers the precedence constrained knapsack problem more specifically we are interested in classes of valid inequalities which are facet defining for the precedence constrained knapsack polytope we study the complexity of obtaining these facets using the standard sequential lifting procedure applying this procedure requires solving a combinatorial problem for valid inequalities arising from minimal induced covers we identify a class of lifting coefficients for which this problem can be solved in polynomial time by using a supermodular function and for which the values of the lifting coefficients have a combinatorial interpretation for the remaining lifting coefficients it is shown that this optimization problem is strongly np hard the same lifting procedure can be applied to 1 k configurations although in this case the same combinatorial interpretation no longer applies we also consider k covers to which the same procedure need not apply in general we show that facets of the polytope can still be generated using a similar lifting technique for tree knapsack problems we observe that all lifting coefficients can be obtained in polynomial time computational experiments indicate that these facets significantly strengthen the lp relaxation

random payoff two person zero sum game with joint chance constraints abstract we study a two person zero sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability we prove that for the general random payoff zero sum game there exists a weak duality between the two formulations i e the optimal value of the minimizing player is an upper bound of the one of the maximizing player under certain assumptions we show that there also exists a strong duality where their optimal values are equal moreover we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed finally numerical examples are given to illustrate the performances of the proposed approaches

lagrangian decomposition and mixed integer quadratic programming reformulations for probabilistically constrained quadratic programs abstract probabilistically constrained quadratic programming pcqp problems arise naturally from many real world applications and have posed a great challenge in front of the optimization society for years due to the nonconvex and discrete nature of its feasible set we consider in this paper a special case of pcqp where the random vector has a finite discrete distribution we first derive second order cone programming socp relaxation and semidefinite programming sdp relaxation for the problem via a new lagrangian decomposition scheme we then give a mixed integer quadratic programming miqp reformulation of the pcqp and show that the continuous relaxation of the miqp is exactly the socp relaxation this new miqp reformulation is more efficient than the standard miqp reformulation in the sense that its continuous relaxation is tighter than or at least as tight as that of the standard miqp we report preliminary computational results to demonstrate the tightness of the new convex relaxations and the effectiveness of the new miqp reformulation

cortical activity flips among quasi stationary states parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden markov process the parallel spike trains were considered as a multivariate poisson process whose vector firing rates change with time as a consequence of this approach the complete recording can be segmented into a sequence of a few statistically discriminated hidden states whose dynamics are modeled as a first order markov chain the biological validity and benefits of this approach were examined in several independent ways i the statistical consistency of the segmentation and its correspondence to the behavior of the animals ii direct measurement of the collective flips of activity obtained by the model and iii the relation between the segmentation and the pair wise short term cross correlations between the recorded spike trains comparison with surrogate data was also carried out for each of the above examinations to assure their significance our results indicated the existence of well separated states of activity within which the firing rates were approximately stationary with our present data we could reliably discriminate six to eight such states the transitions between states were fast and were associated with concomitant changes of firing rates of several neurons different behavioral modes and stimuli were consistently reflected by different states of neural activity moreover the pair wise correlations between neurons varied considerably between the different states supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons

a linear programming approach for linear programs with probabilistic constraints we study a class of mixed integer programs for solving linear programs with joint probabilistic constraints from random right hand side vectors with finite distributions we present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs we provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed integer formulation of luedtke et al 2010 13 as well as via lower bounds produced by their cutting plane method while we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics we also prove that the theoretical worst case solution quality for these algorithms is arbitrarily far from optimal our computational study compares our heuristics against both the extended mixed integer programming formulation and the cutting plane method of luedtke et al 2010 13 our heuristics efficiently and consistently produce solutions with small optimality gaps while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5

cortical potential distributions and information processing the use of sets of spatiotemporal cortical potential distributions cpds as the basis for cognitive information processing results in a very large space of cognitive elements with natural metrics results obtained from current source density csd analysis suggest that in the cpd picture action potentials may make only a relatively minor contribution to the brain s code in order to establish if two cpds are close we consider standard metrics in spaces of continuous functions and these may be employed to ascertain if two stimuli will be identified as the same the correspondence between the electrical activity within brain regions including not only action potentials but all postsynaptic potentials psps and cpds is considered we examine the possibility of using the csd approach to find potential distributions using the descriptive approach in which precise sets of times are ascribed to the occurrence of action potentials and psps using metrics in the multidimensional space of paths of collections of point processes we show that closeness of cpds is implied by closeness of sets of spike times and psp times if a certain metric is used but not others we also set forth a dynamical model consisting of a system of reaction dif fusion equations for ionic concentrations coupled with nerve membrane potential equations and active transport systems making the approximation of a descriptive approach the correspondence between sets of spike times and psp times and cpds is obtained as with the csd method however since it is not possible to ascribe precise times to the occurrence of psps and action potentials the descriptive approach cannot be used to describe the configuration of electrical activity in cortical regions accurately we also discuss how the cpd framework relates to the binding problem and submillisecond timing

discrete and continuous time probabilistic models and algorithms for inferring neuronal up and down states up and down states the periodic fluctuations between increased and decreased spiking activity of a neuronal population are a fundamental feature of cortical circuits understanding up down state dynamics is important for understanding how these circuits represent and transmit information in the brain to date limited work has been done on characterizing the stochastic properties of up down state dynamics we present a set of markov and semi markov discrete and continuous time probability models for estimating up and down states from multiunit neural spiking activity we model multiunit neural spiking activity as a stochastic point process modulated by the hidden up and down states and the ensemble spiking history we estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation maximization em algorithm and a monte carlo em algorithm that uses reversible jump markov chain monte carlo sampling in the e step we apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow wave sleep our approach provides a statistical characterization of up down state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process

a flexible method to measure synchrony in neuronal firing neurons can transmit information about the characteristics of a stimulus through the spike rate of neurons and synchronization of the neurons various association measure can be used to describe how synchronous two spike trains are we propose a new measure of synchrony the conditional synchrony measure which is the probability of firing together given that at least one of the two neurons is active focus is on the specification of a flexible marginal model for multivariate correlated binary data together with a pseudolikelihood estimation approach to adequately and directly describe the measures of interest a joint model must allow different time and covariate dependent firing rates for each neuron and also must account for the association between them the association between neurons might depend on covariates as well

genetic algorithm based technique for solving chance constrained problems management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information chance constrained programming ccp have been used for modelling and analysis of risks in a number of application domains however the resulting mathematical problems are non trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non linear non convex and the stochastic nature we develop and implement c classes to represent such ccp problems we propose a framework consisting of genetic algorithm and monte carlo simulation in order to process the problems the non linear and non convex nature of the ccp problems are processed using genetic algorithm whereas the stochastic nature is addressed through simulation the computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems

pattern based modeling and solution of probabilistically constrained optimization problems we propose a new modeling and solution method for probabilistically constrained optimization problems the methodology is based on the integration of the stochastic programming and combinatorial pattern recognition fields it permits the fast solution of stochastic optimization problems in which the random variables are represented by an extremely large number of scenarios the method involves the binarization of the probability distribution and the generation of a consistent partially defined boolean function pdbf representing the combination f p of the binarized probability distribution f and the enforced probability level p we show that the pdbf representing f p can be compactly extended as a disjunctive normal form dnf the dnf is a collection of combinatorial p patterns each defining sufficient conditions for a probabilistic constraint to hold we propose two linear programming formulations for the generation of p patterns that can be subsequently used to derive a linear programming inner approximation of the original stochastic problem a formulation allowing for the concurrent generation of a p pattern and the solution of the deterministic equivalent of the stochastic problem is also proposed the number of binary variables included in the deterministic equivalent formulation is not an increasing function of the number of scenarios used to represent uncertainty results show that large scale stochastic problems in which up to 50 000 scenarios are used to describe the stochastic variables can be consistently solved to optimality within a few seconds

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

multi objective probabilistically constrained programs with variable risk models for multi portfolio financial optimization abstract we consider a class of multi objective probabilistically constrained programs mopcp with a joint probabilistic constraint and a variable risk level we consider two cases with only a random right hand side vector or a multi row random technology matrix and propose a boolean modeling framework to derive new mixed integer linear programs milp that are either equivalent reformulations or inner approximations of mopcp respectively via testing randomly generated mopcp instances we demonstrate modeling insights pertaining to the most suitable milp to the trade offs between conflicting objectives of cost revenue and reliability and to the parameter scalarization determining relative importance of each objective we then focus on several mopcp variants of a multi portfolio financial optimization problem to implement a downside risk measure which can be used in a centralized or decentralized investment context we study the impact of modeling parameters on the portfolios show via a cross validation study robustness of mopcp and perform a comparative analysis of the optimal investment decisions

data driven chance constrained stochastic program in this paper we study data driven chance constrained stochastic programs or more specifically stochastic programs with distributionally robust chance constraints dccs in a data driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters we consider a family of density based confidence sets based on a general phi divergence measure and formulate dcc from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set we derive an equivalent reformulation for dcc and show that it is equivalent to a classical chance constraint with a perturbed risk level we also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general phi divergence measures in several special cases our results can be strengthened such that we can derive closed form expressions for the perturbed risk levels in addition we show that the conservatism of dcc vanishes as the size of historical data goes to infinity furthermore we analyze the relationship between the conservatism of dcc and the size of historical data which can help indicate the value of data finally we conduct extensive computational experiments to test the performance of the proposed dcc model and compare various phi divergence measures based on a capacitated lot sizing problem with a quality of service requirement

a branch reduce cut algorithm for the global optimization of probabilistically constrained linear programs we consider probabilistically constrained linear programs with general distributions for the uncertain parameters these problems involve non convex feasible sets we develop a branch and bound algorithm that searches for a global optimal solution to this problem by successively partitioning the non convex feasible region and by using bounds on the objective function to fathom inferior partition elements this basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partition elements and hence tighten bounds the proposed branch reduce cut algorithm exploits the monotonicity properties inherent in the problem and requires solving linear programming subproblems we provide convergence proofs for the algorithm some illustrative numerical results involving problems with discrete distributions are presented

analysis of spike statistics in neuronal systems with continuous attractors or multiple discrete attractor states attractor networks are likely to underlie working memory and integrator circuits in the brain it is unknown whether continuous quantities are stored in an analog manner or discretized and stored in a set of discrete attractors in order to investigate the important issue of how to differentiate the two systems here we compare the neuronal spiking activity that arises from a continuous line attractor with that from a series of discrete attractors stochastic fluctuations cause the position of the system along its continuous attractor to vary as a random walk whereas in a discrete attractor noise causes spontaneous transitions to occur between discrete states at random intervals we calculate the statistics of spike trains of neurons firing as a poisson process with rates that vary according to the underlying attractor network since individual neurons fire spikes probabilistically and since the state of the network as a whole drifts randomly the spike trains of individual neurons follow a doubly stochastic poisson point process we compare the series of spike trains from the two systems using the autocorrelation function fano factor and interspike interval isi distribution although the variation in rate can be dramatically different especially for short time intervals surprisingly both the autocorrelation functions and fano factors are identical given appropriate scaling of the noise terms since the range of firing rates is limited in neurons we also investigate systems for which the variation in rate is bounded by either rigid limits or because of leak to a single attractor state such as the ornstein uhlenbeck process in these cases the time dependence of the variance in rate can be different between discrete and continuous systems so that in principle these processes can be distinguished using second order spike statistics

spotting neural spike patterns using an adversary background model the detection of a specific stochastic pattern embedded in an unknown background noise is a difficult pattern recognition problem encountered in many applications such as word spotting in speech a similar problem emerges when trying to detect a multineural spike pattern in a single electrical recording embedded in the complex cortical activity of a behaving animal solving this problem is crucial for the identification of neuronal code words with specific meaning the technical difficulty of this detection is due to the lack of a good statistical model for the background activity which rapidly changes with the recording conditions and activity of the animal this work introduces the use of an adversary background model this model assumes that the background knows the pattern sought up to a first order statistics and this knowledge creates a background composed of all the permutations of our pattern we show that this background model is tightly connected to the type based information theoretic approach furthermore we show that computing the likelihood ratio is actually decomposing the log likelihood distribution according to types of the empirical counts we demonstrate the application of this method for detection of the reward patterns in the basal ganglia of behaving monkeys yielding some unexpected biological results

robustness of optimal portfolios under risk and stochastic dominance constraints abstract solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation estimation and incomplete information the obtained results recommendations for the risk and portfolio manager should be then carefully analyzed we shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity based global contamination bounds results obtained in our paper dupacova j kopa m 2012 robustness in stochastic programs with risk constraints annals of operations research 200 55 74 were derived for the risk and second order stochastic dominance constraints under suitable smoothness and or convexity assumptions that are fulfilled e g for the markowitz mean variance model in this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints local bounds for problems of a special structure are obtained under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test

cell and bound algorithm for chance constrained programs with discrete distributions abstract chance constrained programing ccp is often encountered in real world applications when there is uncertainty in the data and parameters we consider in this paper a special case of ccp with finite discrete distributions we propose a novel approach for solving ccp the methodology is based on the connection between ccp and arrangement of hyperplanes by involving cell enumeration methods for an arrangement of hyperplanes in discrete geometry we develop a cell and bound algorithm to identify an exact solution to ccp which is much more efficient than branch and bound algorithms especially in the worst case furthermore based on the cell and bound algorithm a new polynomial solvable subclass of ccp is discovered we also find that the probabilistic version of the classical transportation problem is polynomially solvable when the number of customers is fixed we report preliminary computational results to demonstrate the effectiveness of our algorithm

extracting state transition dynamics from multiple spike trains using hidden markov models with correlated poisson distribution neural activity is nonstationary and varies across time hidden markov models hmms have been used to track the state transition among quasi stationary discrete neural states within this context an independent poisson model has been used for the output distribution of hmms hence the model is incapable of tracking the change in correlation without modulating the firing rate to achieve this we applied a multivariate poisson distribution with correlation terms for the output distribution of hmms we formulated a variational bayes vb inference for the model the vb could automatically determine the appropriate number of hidden states and correlation types while avoiding the overlearning problem we developed an efficient algorithm for computing posteriors using the recursive relationship of a multivariate poisson distribution we demonstrated the performance of our method on synthetic data and real spike trains recorded from a songbird

messages of oscillatory correlograms a spike train model oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm in most cases the statistical analysis of cross correlation histograms cch features is based on the null model of independent processes and the resulting conclusions about the underlying processes remain qualitative therefore we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the cch to parameters of the underlying processes the model focuses particularly on asymmetric central peaks which differ in slope and width on the two sides asymmetric peaks can be associated with phase offsets in the sub millisecond range these spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes the proposed model includes a single temporal parameter that accounts for this peak asymmetry the model provides approaches for the analysis of oscillatory correlograms taking into account dependencies and nonstationarities in the underlying processes in particular the auto and the cross correlogram can be investigated in a joint analysis because they depend on the same spike train parameters particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated the analysis is demonstrated by application to a simulated data set

information geometry of boltzmann machines a boltzmann machine is a network of stochastic neurons the set of all the boltzmann machines with a fixed topology forms a geometric manifold of high dimension where modifiable synaptic weights of connections play the role of a coordinate system to specify networks a learning trajectory for example is a curve in this manifold it is important to study the geometry of the neural manifold rather than the behavior of a single network in order to know the capabilities and limitations of neural networks of a fixed topology using the new theory of information geometry a natural invariant riemannian metric and a dual pair of affine connections on the boltzmann neural network manifold are established the meaning of geometrical structures is elucidated from the stochastic and the statistical point of view this leads to a natural modification of the boltzmann machine learning rule

synchronous firing and higher order interactions in neuron pool the stochastic mechanism of synchronous firing in a population of neurons is studied from the point of view of information geometry higher order interactions of neurons which cannot be reduced to pairwise correlations are proved to exist in synchronous firing in a neuron pool where each neuron fires stochastically the probability distribution q r of the activity r which is the fraction of firing neurons in the pool is studied when q r has a widespread distribution in particular when q r has two peaks the neurons fire synchronously at one time and are quiescent at other times the mechanism of generating such a probability distribution is interesting because the activity r is concentrated on its mean value when each neuron fires independently because of the law of large numbers even when pairwise interactions or third order interactions exist the concentration is not resolved this shows that higher order interactions are necessary to generate widespread activity distributions we analyze a simple model in which neurons receive common overlapping inputs and prove that such a model can have a widespread distribution of activity generating higher order stochastic interactions

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals usually this is done for pairs of neurons at a time using correlation based techniques chornoboy schramm and karr 1988 proposed maximum likelihood methods for the simultaneous analysis of multiple pair wise interactions among an ensemble of neurons one of these methods is an iterative continuous time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions we devised a discrete time version of this algorithm that includes a new efficient computational strategy a principled method to compute starting values and a principled stopping criterion in an analysis of simulated neural spike trains from ensembles of interacting neurons the algorithm recovered the correct connectivity matrices and interaction parameters in the analysis of spike trains from an ensemble of rat hippocampal place cells the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons spatial receptive fields these results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

iis branch and cut for joint chance constrained stochastic programs and application to optimal vaccine allocation we present a new method for solving stochastic programs with joint chance constraints with random technology matrices and discretely distributed random data the problem can be reformulated as a large scale mixed 0 1 integer program we derive a new class of optimality cuts called iis cuts and apply them to our problem the cuts are based on irreducibly infeasible subsystems iis of an lp defined by requiring that all scenarios be satisfied we propose a method for improving the upper bound of the problem when no cut can be found we derive and implement a branch and cut algorithm based on iis cuts and refer to this algorithm as the iis branch and cut algorithm we report on computational results with several test instances from optimal vaccine allocation the computational results are promising as the iis branch and cut algorithm gives better results than a state of the art commercial solver on one class of problems

from cvar to uncertainty set implications in joint chance constrained optimization we review and develop different tractable approximations to individual chance constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional value at risk cvar measure we extend the idea to joint chance constrained problems and provide a new formulation that improves upon the standard approach our approach builds on a classical worst case bound for order statistics problems and is applicable even if the constraints are correlated we provide an application of the model on a network resource allocation problem with uncertain demand

closed form two sided bounds for probabilities that at least r and exactly r out of n events occur in two previous papers prekopa prekopa a 1986a boole bonferroni inequalities and linear programming oper res 36 145 162 prekopa a 1986b sharp bounds on probabilities using linear programming to appear in oper res gave algorithms to approximate probabilities that at least r and exactly r out of n events occur 1 r n primal and dual linear programming problems were formulated and solved by dual type algorithms the purpose of the present paper is to give closed forms for the basis inverse and the corresponding dual vector in case of an arbitrary basis furthermore to give closed forms for the lower and upper bounds approximating the probability in question in case of a dual feasible basis in the case when the probability that at least one out of n events occurs is approximated it is shown that the absolute values of the components of any dual vector form a monotonically decreasing sequence the paper improves the method of inclusion exclusion proves new probability inequalities and

scenario min max optimization and the risk of empirical costs we consider convex optimization problems in the presence of stochastic uncertainty the min max sample based solution is the solution obtained by minimizing the max of the cost functions corresponding to a finite sample of the uncertainty parameter the empirical costs are instead the cost values that the solution incurs for the various parameter realizations that have been sampled our goal is to evaluate the risks associated with the empirical costs where the risk associated with a cost is the probability that the cost is exceeded when a new realization of the uncertainty parameter is seen this task is accomplished without resorting to uncertainty realizations other than those used in optimization the theoretical result proved in this paper is that these risks form a random vector whose probability distribution is an ordered dirichlet distribution irrespective of the probability measure of the stochastic uncertainty parameter this result provides a distribution free characterization of the risks as

the effects of pair wise and higher order correlations on the firing rate of a postsynaptic neuron coincident firing of neurons projecting to a common target cell is likely to raise the probability of firing of this postsynaptic cell therefore synchronized firing constitutes a significant event for postsynaptic neurons and is likely to play a role in neuronal information processing physiological data on synchronized firing in cortical networks are based primarily on paired recordings and cross correlation analysis however pair wise correlations among all inputs onto a postsynaptic neuron do not uniquely determine the distribution of simultaneous postsynaptic events we develop a framework in order to calculate the amount of synchronous firing that based on maximum entropy should exist in a homogeneous neural network in which the neurons have known pair wise correlations and higher order structure is absent according to the distribution of maximal entropy synchronous events in which a large proportion of the neurons participates should exist even in the case of weak pair wise correlations network simulations also exhibit these highly synchronous events in the case of weak pair wise correlations if such a group of neurons provides input to a common postsynaptic target these network bursts may enhance the impact of this input especially in the case of a high postsynaptic threshold the proportion of neurons participating in synchronous bursts can be approximated by our method under restricted conditions when these conditions are not fulfilled the spike trains have less than maximal entropy which is indicative of the presence of higher order structure in this situation the degree of synchronicity cannot be derived from the pair wise correlations

an integer programming approach for linear programs with probabilistic constraints linear programs with joint probabilistic constraints pclp are difficult to solve because the feasible region is not convex we consider a special case of pclp in which only the right hand side is random and this random vector has a finite distribution we give a mixed integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint we obtain two strengthened formulations as a byproduct of this analysis we obtain new results for the previously studied mixing set subject to an additional knapsack inequality we present computational results which indicate that by using our strengthened formulations instances that are considerably larger than have been considered before can be solved to optimality

a polyhedral study on chance constrained program with random right hand side the essential structure of the mixed integer programming formulation for chance constrained program ccp is the intersection of multiple mixing sets with a 0 1 knapsack to improve our computational capacity on ccp an underlying substructure the single mixing set with a 0 1 knapsack has received substantial attentions recently in this study we consider a ccp problem with stochastic right hand side under a finite discrete distribution we first present a family of strong inequalities that subsumes known facet defining ones for that single mixing set due to the flexibility of our generalized inequalities we develop a new separation heuristic that has a complexity much less than existing one and guarantees generated cutting planes are facet defining for the polyhedron of ccp then we study lifting and superadditive lifting on knapsack cover inequalities and provide an implementable procedure on deriving another family of strong inequalities for the single mixing set finally different from the traditional approach that aggregates original constraints to investigate polyhedral implications due to their interactions we propose a novel blending procedure that produces strong valid inequalities for ccp by integrating those derived from individual mixing sets we show that under certain conditions they are the first type of facet defining inequalities describing intersection of multiple mixing sets and design an efficient separation heuristic for implementation in the computational experiments we perform a systematic study and illustrate the efficiency of the proposed inequalities on solving chance constrained static probabilistic lot sizing problems

correlations without synchrony peaks in spike train correlograms are usually taken as indicative of spike timing synchronization between neurons strictly speaking however a peak merely indicates that the two spike trains were not independent two biologically plausible ways of departing from independence that are capable of generating peaks very similar to spike timing peaks are described here covariations over trials in response latency and covariations over trials in neuronal excitability since peaks due to these interactions can be similar to spike timing peaks interpreting a correlogram may be a problem with ambiguous solutions what peak shapes do latency or excitability interactions generate when are they similar to spike timing peaks when can they be ruled out from having caused an observed correlogram peak these are the questions addressed here the previous article in this issue proposes quantitative methods to tell cases apart when latency or excitability covariations cannot be ruled out

cluster variation method pade approximants and critical behavior in the present paper we show how nonclassical quite accurate critical exponents can be extracted in a very simple way from the pad e analysis of the results obtained by mean field like approximation schemes and in particular by the cluster variation method we study the critical behavior of the ising model on several lattices quadratic triangular simple cubic and face centered cubic and two problems of surface critical behavior both unbiased and biased approximants are used and results are in very good agreement with the exact or numerical ones

on the mixing set with a knapsack constraint we study a substructure appearing in mixed integer programming reformulations of chance constrained programs with stochastic right hand sides over a finite discrete distribution which we call the mixing set with a knapsack constraint recently luedtke et al math program 122 2 247 272 2010 and kucukyavuz math program 132 1 31 56 2012 studied valid inequalities for such sets however most of their results were focused on the equal probabilities case when the knapsack constraint reduces to a cardinality constraint in this paper we focus on the general probabilities case general knapsack constraint we characterize the valid inequalities that do not come from the knapsack polytope and use this characterization to generalize the results previously derived for the equal probabilities case our results allow for a deep understanding of the relationship that the set under consideration has with the knapsack polytope moreover they allow us to establish benchmarks that can be used to identify when a relaxation will be useful for the considered types of reformulations of chance constrained programs

solving chance constrained optimization problems with stochastic quadratic inequalities we propose a new and systematic reformulation and algorithmic approach to solve a complex class of stochastic programming problems involving a joint chance constraint with random technology matrix and stochastic quadratic inequalities the method is general enough to apply to nonconvex as well as nonseparable quadratic terms we derive two new reformulations and give sufficient conditions under which the reformulated problem is equivalent the second reformulation provides a much sparser representation of the feasible set of the chance constraint and offers tremendous computational advantages this new reformulation method can be used for linear stochastic inequalities and will also significantly improve the solution of such joint chance constrained problems we provide general and easily identifiable conditions under which the base reformulations can be linearized we show that the size of the reformulated problems in particular their number of binary variables and quadratic mixed integer terms does n

on mixing sets arising in chance constrained programming the mixing set with a knapsack constraint arises in deterministic equivalent of chance constrained programming problems with finite discrete distributions we first consider the case that the chance constrained program has equal probabilities for each scenario we study the resulting mixing set with a cardinality constraint and propose facet defining inequalities that subsume known explicit inequalities for this set we extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint in addition we propose a compact extended reformulation with polynomial number of variables and constraints that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities we introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets we propose a polynomial size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation we also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case we illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot sizing problems

functional structure of cortical neuronal networks grown in vitro we apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro we infer connectivity between two neurons via the measurement of the mutual information between their spike trains in addition we measure higher point multi information between any two spike trains conditional on the activity of a third cell as a means to identify and distinguish classes of functional connectivity among three neurons the use of a conditional three cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells we analyze the resultant connectivity graphs in light of other complex networks and demonstrate that despite their ex vivo development the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient network diameter and assortative mixing specifically we show that these networks are weakly disassortative small world graphs which differ significantly in their structure from randomized graphs with the same degree we expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks derived from time series data

surrogate data methods based on a shuffling of the trials for synchrony detection the centering issue we investigate several distribution free dependence detection procedures all based on a shuffling of the trials from a statistical point of view the mathematical justification of such procedures lies in the bootstrap principle and its approximation properties in particular we show that such a shuffling has mainly to be done on centered quantities that is quantities with zero mean under independence to construct correct p values meaning that the corresponding tests control their false positive fp rate thanks to this study we introduce a method named permutation ue which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count each involved single test of this procedure achieves the prescribed level so that the corresponding multiple testing procedure controls the false discovery rate fdr and this with as few assumptions as possible on the underneath distribution except independence and identical distribution across trials the mathematical meaning of this assumption is discussed and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross trials stationarity some simulations show moreover that permutation ue outperforms the trial shuffling of pipa and grun 2003 and the mtgaue method of tuleau malot eti al 2014 in terms of single levels and fdr for a comparable amount of false negatives application to real data is also provided

detection of hidden structures in nonstationary spike trains we propose an algorithm for simultaneously estimating state transitions among neural states and nonstationary firing rates using a switching state space model sssm this algorithm enables us to detect state transitions on the basis of not only discontinuous changes in mean firing rates but also discontinuous changes in the temporal profiles of firing rates e g temporal correlation we construct estimation and learning algorithms for a nongaussian sssm whose nongaussian property is caused by binary spike events local variational methods can transform the binary observation process into a quadratic form the transformed observation process enables us to construct a variational bayes algorithm that can determine the number of neural states based on automatic relevance determination additionally our algorithm can estimate model parameters from single trial data using a priori knowledge about state transitions and firing rates synthetic data analysis reveals that our algorithm has higher performance for estimating nonstationary firing rates than previous methods the analysis also confirms that our algorithm can detect state transitions on the basis of discontinuous changes in temporal correlation which are transitions that previous hidden markov models could not detect we also analyze neural data recorded from the medial temporal area the statistically detected neural states probably coincide with transient and sustained states that have been detected heuristically estimated parameters suggest that our algorithm detects the state transitions on the basis of discontinuous changes in the temporal correlation of firing rates these results suggest that our algorithm is advantageous in real data analysis

model dependence in quantification of spike interdependence by joint peri stimulus time histogram multineuronal recordings have enabled us to examine context dependent changes in the relationship between the activities of multiple cells the joint peri stimulus time histogram jpsth is a much used method for investigating the dynamics of the interdependence of spike events between pairs of cells its results are often taken as an estimate of interaction strength between cells independent of modulations in the cells firing rates we evaluate the adequacy of this estimate by examining the mathematical structure of how the jpsth quantifies an interaction strength after excluding the contribution of firing rates we introduce a simple probabilistic model of interacting point processes to generate simulated spike data and show that the normalized jpsth incorrectly infers the temporal structure of variations in the interaction parameter strength this occurs because in our model the correct normalization of firing rate contributions is different than that used in aertsen gerstein habib and palm s 1989 effective connectivity model this demonstrates that firing rate modulations cannot be corrected for in a model independent manner and therefore the effective connectivity does not represent a universal characteristic that is independent of modulation of the firing rates aertsen et al s 1989 effective connectivity may still be used in the analysis of experimental data provided we are aware that this is simply one of many ways of describing the structure of interdependence we also discuss some measure independent characteristics of the structure of interdependence

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

dependence of neuronal correlations on filter characteristics and marginal spike train statistics correlated neural activity has been observed at various signal levels e g spike count membrane potential local field potential eeg fmri bold most of these signals can be considered as superpositions of spike trains filtered by components of the neural system synapses membranes and the measurement process it is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are in this study we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations we demonstrate that correlation functions and statistical second order measures like the variance the covariance and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains we point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations in many applications the coherence allows a filter independent quantification of correlated activity in different network models we discuss the estimation of network connectivity from the high frequency coherence of simultaneous intracellular recordings of pairs of neurons

generation of synthetic spike trains with defined pairwise correlations recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross correlation this report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation pairs of spike trains with any pairwise correlation can be generated and higher order correlations are compatible with common synaptic input relations between allowable mean rates and correlations within a population are discussed the algorithm is highly efficient its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross correlated pairs

mathematical programming approaches for generating p efficient points abstract probabilistically constrained problems in which the random variables are finitely distributed are non convex in general and hard to solve the p efficiency concept has been widely used to develop efficient methods to solve such problems those methods require the generation of p efficient points pleps and use an enumeration scheme to identify pleps in this paper we consider a random vector characterized by a finite set of scenarios and generate pleps by solving a mixed integer programming mip problem we solve this computationally challenging mip problem with a new mathematical programming framework it involves solving a series of increasingly tighter outer approximations and employs as algorithmic techniques a bundle preprocessing method strengthening valid inequalities and a fixing strategy the method is exact resp heuristic and ensures the generation of pleps resp quasi pleps if the fixing strategy is not resp is employed and it can be used to generate multiple pleps to the best of our knowledge generating a set of pleps using an optimization based approach and developing effective methods for the application of the p efficiency concept to the random variables described by a finite set of scenarios are novel we present extensive numerical results that highlight the computational efficiency and effectiveness of the overall framework and of each of the specific algorithmic techniques

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

can spike coordination be differentiated from rate covariation there has been a long and lively debate on whether rate covariance and temporal coordination of spikes regarded as potential origins for correlations in cortical spike signals fulfill different roles in the cortical code in this context studies that report spike coordination have often been criticized for ignoring fast nonstationarities which would result in wrongly assigned spike coordination the underlying hypothesis of this critique is that spike coordination is essentially identical to rate covariation only on a shorter timescale this study investigates the validity of this critique we provide a decomposition for the cross correlation function of doubly stochastic point processes where each of the components corresponds precisely to the concepts of dependence under investigation this allows us to correct the correlation function for rate effects which implies that spike coordination and rate covariation are statistically separable concepts of dependence furthermore we present direct and intuitive model implementations of the discussed concepts and illustrate that their difference is not a matter of timescale analysis of data generated by our models and analytical description of the relevant estimators reveals however that spike coordination dramatically influences the accuracy of rate covariance estimation as a consequence extreme parameter combinations can lead to situations where the concept of dependence cannot be identified empirically however for a wide range of parameters the concept of dependence underlying a given data set can be identified regardless of its timescale

improvements to the sensitivity of gravitational clustering for multiple neuron recordings we outline two improvements to the technique of gravitational clustering for detection of neuronal synchrony which are capable of improving the method s detection of weak synchrony with limited data the advantages of the enhancements are illustrated using data with known levels of synchrony and different interspike interval distributions the novel simulation method described can easily generate such test data an important dependence of the sensitivity of gravitational clustering to the interspike interval distribution of the analysed spike trains is described

boole bonferroni inequalities and linear programming we present a method to obtain sharp lower and upper bounds for the probability that at least one out of a number of events in an arbitrary probability space will occur the input data are some of the binomial moments of the occurrences such as the sum of the probabilities of the individual events or the sum of the joint probabilities of all pairs of events we develop a special very simple linear programming algorithm to obtain these bounds the method allows us to compute good bounds in an optimal way utilizing only the first few terms in the inclusion exclusion formula possible applications include obtaining bounds for the reliability of a stochastic system solving algorithmically some stochastic programming problems and approximating multivariate probabilities in statistics in a numerical example we approximate the probability that a gaussian process runs below a given level in a number of consecutive epochs

the upward bias in measures of information derived from limited data samples extracting information measures from limited experimental samples such as those normally available when using data recorded in vivo from mammalian cortical neurons is known to be plagued by a systematic error which tends to bias the estimate upward we calculate here the average of the bias under certain conditions as an asymptotic expansion in the inverse of the size of the data sample the result agrees with numerical simulations and is applicable as an additive correction term to measurements obtained under such conditions moreover we discuss the implications for measurements obtained through other usual procedures

finite state automata resulting from temporal information maximization and a temporal learning rule we extend linkser s infomax principle for feedforward neural networks to a measure for stochastic interdependence that captures spatial and temporal signal properties in recurrent systems this measure stochastic interaction quantifies the kullback leibler divergence of a markov chain from a product of split chains for the single unit processes for unconstrained markov chains the maximization of stochastic interaction also called temporal infomax has been previously shown to result in almost deterministic dynamics this letter considers temporal infomax on constrained markov chains where some of the units are clamped to prescribed stochastic processes providing input to the system temporal infomax in that case leads to finite state automata either completely deterministic or weakly nondeterministic transitions between internal states of these systems are almost perfectly predictable given the complete current state and the input but the activity of each single unit alone is virtually random the results are demonstrated by means of computer simulations and confirmed analytically it is furthermore shown numerically that temporal infomax leads to a high information flow from the input to internal units and that a simple temporal learning rule can approximately achieve the optimization of temporal interaction we relate these results to experimental data concerning the correlation dynamics and functional connectivities observed in multiple electrode recordings

on three new cluster variation approximations abstract we discuss in some detail three new cluster variation approximations we used in a previous paper in connection with pade approximants to investigate critical behaviour of classical spin models on various lattices the approximations are applied to the ising model on the simple cubic face centered cubic and semi infinite simple cubic lattices the natural iteration equations and estimates for the critical temperatures and for the range of validity of the approximations are given

unitary events in multiple single neuron spiking activity i detection and significance it has been proposed that cortical neurons organize dynamically into functional groups cell assemblies by the temporal structure of their joint spiking activity here we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons the statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint surprise the method is tested and calibrated on the basis of simulated stationary spike trains of independently firing neurons into which coincident joint spike events were inserted under controlled conditions the sensitivity and specificity of the method are investigated for their dependence on physiological parameters firing rate coincidence precision coincidence pattern complexity and temporal resolution of the analysis in the companion article in this issue we describe an extension of the method designed to deal with nonstationary firing rates

probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra we consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions they can be reformulated as large scale mixed integer programming problems with knapsack constraints using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems we also develop methods for lifting these inequalities these procedures are used in a general iterative algorithm for solving probabilistically constrained problems the results are illustrated with a numerical example

investigation of possible neural architectures underlying information geometric measures a novel analytical method based on information geometry was recently proposed and this method may provide useful insights into the statistical interactions within neural groups the link between informationgeometric measures and the structure of neural interactions has not yet been elucidated however because of the ill posed nature of the problem here possible neural architectures underlying information geometric measures are investigated using an isolated pair and an isolated triplet of model neurons by assuming the existence of equilibrium states we derive analytically the relationship between the information geometric parameters and these simple neural architectures for symmetric networks the first and second order information geometric parameters represent respectively the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log linear model and the number of neurons in the network are the same for asymmetric networks however these parameters are dependent on both the intrinsic connections and the external inputs to each neuron in addition we derive the relation between the information geometric parameter corresponding to the two neuron interaction and a conventional cross correlation measure we also show that the information geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log linear model this finding suggests a need to examine the information geometric method carefully a possible criterion for choosing an appropriate orthogonal coordinate is also discussed this article points out the importance of a model based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis

information geometric measures for estimation of connection weight under correlated inputs the brain processes information in a highly parallel manner determination of the relationship between neural spikes and synaptic connections plays a key role in the analysis of electrophysiological data information geometry ig has been proposed as a powerful analysis tool for multiple spike data providing useful insights into the statistical interactions within a population of neurons previous work has demonstrated that ig measures can be used to infer the connection weight between two neurons in a neural network this property is useful in neuroscience because it provides a way to estimate learning induced changes in synaptic strengths from extracellular neuronal recordings a previous study has shown however that this property would hold only when inputs to neurons are not correlated since neurons in the brain often receive common inputs this would hinder the application of the ig method to real data we investigated the two neuron ig measures in higher order log linear models to overcome this limitation first we mathematically showed that the estimation of uniformly connected synaptic weight can be improved by taking into account higher order log linear models second we numerically showed that the estimation can be improved for more general asymmetrically connected networks considering the estimated number of the synaptic connections in the brain we showed that the two neuron ig measure calculated by the fourth or fifth order log linear model would provide an accurate estimation of connection strength within approximately a 10 error these studies suggest that the two neuron ig measure with higher order log linear expansion is a robust estimator of connection weight even under correlated inputs providing a useful analytical tool for real multineuronal spike data

revealing pairwise coupling in linear nonlinear networks through an asymptotic analysis of a simple network we derive an estimate of the coupling between a pair of units when all other units are unobservable the analysis is based on a model where the response of each unit is a linear nonlinear function of a white noise stimulus the results accurately determine the coupling when all unmeasured units respond to the stimulus differently than the measured pair to account for the possibility of unmeasured units similar to the measured pair we cast our results in the framework of subpopulations which are defined as a group of units who respond to the stimulus similarly we demonstrate that we can determine when correlations between two units are caused by a connection between their subpopulations although the precise identity of the units involved in the connection may remain ambiguous the result is rigorously valid only when the coupling is sufficiently weak to justify a second order approximation in the coupling strength we demonstrate through simulations that the results are still valid even with stronger coupling and in the presence of some deviations from the linear nonlinear model the analysis is presented in terms of neuronal networks although the general framework is more widely applicable

information geometric measure for neural spikes this study introduces information geometric measures to analyze neural firing patterns by taking not only the second order but also higher order interactions among neurons into account information geometry provides useful tools and concepts for this purpose including the orthogonality of coordinate parameters and the pythagoras relation in the kullback leibler divergence based on this orthogonality we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders as a result purely pairwise triple wise and higher order interactions are singled out we also demonstrate the benefits of our proposal by using several examples

stochastic control with uncertain parameters via chance constrained control chance constrained methods handle problem uncertainty by formulating the constraints probabilistically and only guaranteeing their satisfaction up to a given violation level this paper extends existing chance constrained methods to handle both uncertainty in the system state as well as in the constraint parameters due to the imperfect knowledge of the system state caused by motion sensor and environment uncertainty the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically prior work has primarily only dealt with uncertainty in the system state or constraint parameters but not both simultaneously however in many motivating applications both frequently occur to handle this case previous approaches either approximate the distribution leading to a nonconvex optimization program or use sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution to address these limitations a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty it is shown that under certain conditions the resulting optimization program using this hybrid representation is convex to check the convexity an efficient a priori sufficient condition is developed furthermore by using this hybrid representation this method drastically reduces the computational complexity over previous methods which is demonstrated through two examples consequently this method has the ability to enable real time stochastic control for the motivating applications

on the convergence of kikuchi s natural iteration method in this article we investigate on the convergence of the natural iteration method a numerical procedure widely employed in the statistical mechanics of lattice systems to minimize kikuchi s cluster variational free energies we discuss a sufficient condition for the convergence based on the coefficients of the cluster entropy expansion depending on the lattice geometry we also show that such a condition is satisfied for many lattices usually studied in applications finally we consider a recently proposed class of methods for the minimization of kikuchi functionals showing that the natural iteration method turns out as a particular instance of that class

influence of external inputs and asymmetry of connections on information geometric measures involving up to ten neuronal interactions the investigation of neural interactions is crucial for understanding information processing in the brain recently an analysis method based on information geometry ig has gained increased attention and the property of the pairwise ig measure has been studied extensively in relation to the two neuron interaction however little is known about the property of ig measures involving more neuronal interactions in this study we systematically investigated the influence of external inputs and the asymmetry of connections on the ig measures in cases ranging from 1 neuron to 10 neuron interactions first the analytical relationship between the ig measures and external inputs was derived for a network of 10 neurons with uniform connections our results confirmed that the single and pairwise ig measures were good estimators of the mean background input and of the sum of the connection weights respectively for the ig measures involving 3 to 10 neuronal interactions we found that the influence of external inputs was highly nonlinear second by computer simulation we extended our analytical results to asymmetric connections for a network of 10 neurons the simulation showed that the behavior of the ig measures in relation to external inputs was similar to the analytical solution obtained for a uniformly connected network when the network size was increased to 1000 neurons the influence of external inputs almost disappeared this result suggests that all ig measures from 1 neuron to 10 neuron interactions are robust against the influence of external inputs in addition we investigated how the strength of asymmetry influenced the ig measures computer simulation of a 1000 neuron network showed that all the ig measures were robust against the modulation of the asymmetry of connections our results provide further support for an information geometric approach and will provide useful insights when these ig measures are applied to real experimental spike data

threshold boolean form for joint probabilistic constraints with random technology matrix we develop a new modeling and solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed we binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined boolean function pdbf representing the probabilistic constraint we then construct a tight threshold boolean minorant for the pdbf any separating structure of the tight threshold boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints we use the separating structure to derive three new deterministic formulations for the studied stochastic problem and we derive a set of strengthening valid inequalities a crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty the computational study based on instances of the stochastic capital rationing problem shows that the mixed integer linear programming formulations are orders of magnitude faster to solve than the mixed integer nonlinear programming formulation the method integrating the valid inequalities in a branch and bound algorithm has the best performance

problem based optimal scenario generation and reduction in stochastic programming scenarios are indispensable ingredients for the numerical solution of stochastic programs earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures in this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data for linear two stage stochastic programs we show that the problem based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi infinite program we show that the latter is convex if either right hand sides or costs are random and can be transformed into a semi infinite program in a number of cases we also consider problem based optimal scenario reduction for two stage models and optimal scenario generation for chance constrained programs finally we discuss problem based scenario generation for the classical newsvendor problem