a generalizable formulation of conditional logit with diagnostics abstract the conditional logit model is a multinomial logit model that permits the inclusion of choice specific attributes this article shows that the conditional logit model will maximize entropy given a set of attribute value preserving constraints a correspondence between the maximum entropy me and maximum likelihood ml estimates for logit probabilities is established some easily computable and useful diagnostics for logit analysis are provided and it is shown that an evaluation of the relative importance of attributes can be made using the me formulation the me formulation is also generalized to accommodate initial choice probabilities into the logit model an example is given key words choice models entropy kullback leibler discrimination information function relative importance

partially ordered permutation complexity of coupled time series abstract a new information theoretic complexity measure of coupling among multiple time series is proposed based on ordinal patterns we regard ordinal patterns extracted from time series as total orders and exploit their algebraic properties to introduce a multiplication among them the result of the multiplication is in general a partial order a kullback leibler divergence for the partial orders gives rise to a complexity measure of coupling in the sense that it vanishes in two extreme cases when time series are uncoupled and when they are identical the performance of the proposed complexity measure is tested on two model multivariate dynamical systems and its advantage over the existing complexity measures is discussed

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

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

exact solution of a coagulation equation with a product kernel in the multicomponent case abstract in this paper we obtain the general solution for the continuous smoluchowski equation in the multicomponent case with a product kernel as a series expansion the solution of the problem involves the laplace transform in several dimensions we obtain a nonlinear partial differential equation pde of the advective kind generalizing the one previously given by other authors for the mono component case as in its relative mono component case gelation is produced at some point the conditions for its occurrence being the same as those for the mono component case though substituting a sum of derivatives by a derivative in the laplace transform field we demonstrate that for a multicomponent particle size distribution psd of multiplicative form it is sufficient for one of the marginal psds to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent psd the general solution is applied to several specific cases a discrete case that recovers a previously known solution and another two continuous cases which can be used to check numerical methods designed to directly solve the smoluchowski equation in more general cases we have compared the solutions for the multicomponent psd for constant additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono component and the multicomponent case finally we have analysed the shape of the solutions for multicomponent psd for constant additive and product kernels for very small masses of components obtaining a qualitatively different behaviour for the product kernel this has effects in the mixing state of the sol phase as time passes

maximum likelihood estimation of agreement in the constant predictive probability model and its relation to cohen s kappa the alpha agreement parameter is defined as the proportion of a population of items that are classified identically for cause by two classifiers the remaining items being classified at random the parameters of the corresponding constant predictive probability model are shown to be estimable by the method of maximum likelihood and a simulation study indicates applicability of the asymptotic results to finite samples the new estimator tends to be larger than cohen s kappa except in the case of uniform margins an application is made to the validity of cancer risk items included in a cancer registry

irreducible multiparty correlations in quantum states without maximal rank the correlations of an n partite quantum state are classified into a series of irreducible k party ones 2 ensuremath le k ensuremath le n with the irreducible k party correlation being the correlation in the states of k parties but nonexistent in the states of k ensuremath 1 parties a measure of the degree of irreducible k party correlation is defined based on the principle of maximal entropy adopting a continuity approach we overcome the difficulties in calculating the degrees of irreducible multiparty correlations for the multipartite states without maximal rank in particular we obtain the degrees of irreducible multiparty correlations in the n qubit stabilizer states and the n qubit generalized greenberger horne zeilinger states which reveals the distribution of multiparty correlations

general observer agreement measures on individual subjects and groups of subjects general chance corrected measures of agreement on individual subjects for several observers using nominal or ordinal categories are developed the subject specific measures can be used to identify subjects whom the observers find difficult to rate the relationship of the subject specific measures to a general chance corrected measure of agreement for a group of subjects is demonstrated by suitable choices of disagreement functions the measure of agreement for a group of subjects is shown to include as special cases many of the kappa like statistics also it is asymptotically equivalent to various intraclass correlation coefficients the measures do not require that the observers all use the classification scale in the same way the asymptotic null and non null variances obtained by taylorseries approximations for the statistics are presented the application of the measures is illustrated by data obtained when seven pathologists classified slides on a five point ordinal scale for the diagnosis of carcinoma in situ of the uterine cervix

an exact solution of the discrete smoluchowski equation and its correspondence to the solution of the continuous equation an exact general solution of the discrete smoluchowski equation for the kernel kk a b k j is derived rules are given for taking the continuous limit of the discrete solution the limit obtained is an exact general solution of the continuous smoluchowski equation examples of limits are given for specific initial distributions for the case of constant kernel

statistical mechanics of the us supreme court we build simple models for the distribution of voting patterns in a group using the supreme court of the united states as an example the maximum entropy model consistent with the observed pairwise correlations among justices votes an ising spin glass agrees quantitatively with the data while all correlations perhaps surprisingly are positive the effective pairwise interactions in the spin glass model have both signs recovering the intuition that ideologically opposite justices negatively influence each another despite the competing interactions a strong tendency toward unanimity emerges from the model organizing the voting patterns in a relatively simple energy landscape besides unanimity other energy minima in this landscape or maxima in probability correspond to prototypical voting states such as the ideological split or a tightly correlated conservative core the model correctly predicts the correlation of justices with the majority and gives us a measure of their influence on the majority decision these results suggest that simple models grounded in statistical physics can capture essential features of collective decision making quantitatively even in a complex political context

ghz extraction yield for multipartite stabilizer states let psi be an arbitrary stabilizer state distributed between three remote parties such that each party holds several qubits let s be a stabilizer group of psi we show that psi can be converted by local unitaries into a collection of singlets ghz states and local one qubit states the numbers of singlets and ghzs are determined by dimensions of certain subgroups of s for an arbitrary number of parties m we find a formula for the maximal number of m partite ghz states that can be extracted from psi by local unitaries a connection with earlier introduced measures of multipartite correlations is made an example of an undecomposable four party stabilizer state with more than one qubit per party is given these results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local clifford group operators as a simple application we study three party entanglement in two dimensional lattice models that can be exactly solved by the stabilizer formalism

cyclization in bipartite random graphs in this paper the time evolution of a finite bipartite graph initially comprising two sorts of isolated vertices is considered the graph is assumed to evolve by adding edges one at a time each new edge connects either two linked components and forms a new component of a larger order coalescence of graphs or increases by one the number of edges in a given linked component cycling any state of the graph is thus characterized by the set of occupation numbers the numbers of linked components comprising a given numbers of vertexes of the both sorts and a given number of edges once the rate of appearance of an extra edge in the graph being known the master equation governing the time evolution of the probability to find the random graph in a given state is reformulated in terms of the functional generating the probability to find the evolving graph in a given state the exact solution of the evolution equation for the generating functional applies for analyzing the average population numbers of linked components in the limit of large order of the graph the distribution factorizes into two multipliers one of which is just the spectrum of linked components in the infinite bipartite graph the second multiplier includes the dependence on the total size of the graph both these multipliers contain information on the emergence of the giant component that forms at a critical time

pairwise network information and nonlinear correlations reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines the fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and thus can be modeled as an interaction network with simple links corresponding to pairwise interactions in principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy in many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions this has the advantage of being less computationally expensive and easier to estimate we achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations this renders our approach typically superior to other methods based on linear approximations the advantages of the proposed method are documented using oscillator networks and a resting state human brain network as generic relevant examples

assessing interrater agreement from dependent data estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods we investigate the use of a latent model proposed by qu piedmonte and medendorp 1995 biomerics 51 268 275 to estimate the correlation between raters for each method and test for their equality for each of the assessment methods these correlations can be interpreted as the variance components of random effects representing subject and rater this method is applied to an hiv study in which the amount of ectopy on a woman s cervix is measured by both direct visual assessment and a computer planimetry method

scaling and multiscaling in models of fragmentation we introduce a simple geometric model which describes the kinetics of fragmentation of d dimensional objects in one dimension our model coincides with the randon scission model and shows a simple scaling behavior in the long time limit for dg1 the volume of the fragments is characterized by a single scale 1 t while other geometric properties such as the length are characterized by an infinite number of length scales and thus exhibit multiscaling

fluctuations in coagulating systems ii in this paper we consider coagulation processes in large but finite systems and study the time dependent behavior of the nonequilibrium fluctuations in the cluster size distribution for this purpose we apply van kampen s expansion to a master equation describing coagulation processes and derive an approximate fokker planck equation for the probability distribution of the fluctuations first we consider two exactly soluble models corresponding to the choicesk i j i jandk i j 1 for the rate constants in the fokker planck equation for these models and monodisperse initial conditions we calculate the probability distribution of the fluctuations and the equal time and two time correlation functions for general initial conditions we study the behavior of the fluctuations at large cluster sizes and in the scaling limit next we consider in general homogeneous rate constants with the propertyk i j a k ai aj for alla 0 and we give asymptotic expressions for the equal time correlation functions at large cluster sizes and in the scaling limit in the scaling limit we find that the fluctuations show relatively simple scaling behavior for all homogeneous rate constantsk i j

kinetic theory of random graphs from paths to cycles the structural properties of evolving random graphs are investigated treating linking as a dynamic aggregation process rate equations for the distribution of node to node distances paths and of cycles are formulated and solved analytically at the gelation point the typical length of paths and cycles l scales with the component size k as l approximately k 1 2 dynamic and finite size scaling laws for the behavior at and near the gelation point are obtained finite size scaling laws are verified using numerical simulations

cohen s linearly weighted kappa is a weighted average of 2 2 kappas an agreement table with n 3 ordered categories can be collapsed into n 1 distinct 2 2 tables by combining adjacent categories vanbelle and albert stat methodol 6 157 163 2009c showed that the components of cohen s weighted kappa with linear weights can be obtained from these n 1 collapsed 2 2 tables in this paper we consider several consequences of this result one is that the weighted kappa with linear weights can be interpreted as a weighted arithmetic mean of the kappas corresponding to the 2 2 tables where the weights are the denominators of the 2 2 kappas in addition it is shown that similar results and interpretations hold for linearly weighted kappas for multiple raters

a causal perspective on the analysis of signal and noise correlations and their role in population coding the role of correlations between neuronal responses is crucial to understanding the neural code a framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence here we complete the list of types of independence and distinguish activity independence related to total correlations conditional independence related to noise correlations signal independence related to signal correlations coding independence related to information transmission and information independence related to redundancy for each type we identify the probabilistic criterion that defines it indicate the information theoretic measure used as statistic to test for it and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence using this causal analysis we first provide sufficiency conditions relating these types second we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification we indicate that signal and noise correlation cannot be quantified separately third we explicitly define alternative system configurations used to construct the measures in which noise correlations or noise and signal correlations are eliminated accordingly we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations fourth we compare the commonly used nonparametric approach to eliminate noise correlations with a functional model based approach showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons and implies nonlocal causal structure manipulations these results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations

unicyclic components in random graphs the distribution of unicyclic components in a random graph is obtained analytically the number of unicyclic components of a given size approaches a self similar form in the vicinity of the gelation transition at the gelation point this distribution decays algebraically uk 4k 1 for k 1 as a result the total number of unicyclic components grows logarithmically with the system size

network information and connected correlations entropy and information provide natural measures of correlation among elements in a network we construct here the information theoretic analog of connected correlation functions irreducible n point correlation is measured by a decrease in entropy for the joint distribution of n variables relative to the maximum entropy allowed by all the observed n 1 variable distributions we calculate the connected information terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source

a note on interval estimation of kappa in a series of 2 2 tables when there are confounders in reliability studies failing to stratify data to account for these confounding effects may produce a misleading estimate of the interrater agreement in this paper we focus discussion on interval estimation of kappa for measuring agreement between two raters with stratified data using monte carlo simulation we compare four asymptotic interval estimators of kappa for stratified data estimator 1 a weighted average of the stratum specific kappa estimates with weights equal to the inverse of the estimated asymptotic variances of these estimates the two estimators 2 and 3 with use of the logarithmic and the square root transformations respectively and a principle similar as used in estimator 1 estimator 4 a weighted average of the stratum specific kappa estimates with weights equal to stratum sizes we find that while the coverage probability of the first three interval estimators 1 3 can often be less than the desired confidence level the fourth interval estimator 4 consistently performs well in all the situations considered here we further find that when the underlying kappa is moderate 0 30 kappa 0 50 we can substantially improve the performance of the first three estimators by using a point estimator recently proposed elsewhere for kappa in estimation of weights because interval estimator 4 outperforms the other three estimators in a variety of situations we recommend this estimator for general use

statistical mechanics of letters in words we consider words as a network of interacting letters and approximate the probability distribution of states taken on by this network despite the intuition that the rules of english spelling are highly combinatorial and arbitrary we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of words capturing ensuremath sim 92 mathrm of the multi information in four letter words and even discovering words that were not represented in the data these maximum entropy models incorporate letter interactions through a set of pairwise potentials and thus define an energy landscape on the space of possible words guided by the large letter redundancy we seek a lower dimensional encoding of the letter distribution and show that distinctions between local minima in the landscape account for ensuremath sim 68 mathrm of the four letter entropy we suggest that these states provide an effective vocabulary which is matched to the frequency of word use and much smaller than the full lexicon

measuring agreement for multinomial data a kappa like statistic is proposed as a measure of agreement for a set of multinomial random variables arrayed in a two way layout this statistic is shown to arise either via the chancecorrection of a certain proportion of agreement or via an analysis of variance for a two way layout the asymptotic standard error is derived under the assumption of complete independence among the random variables

kinetics of ring formation we study reversible polymerization of rings in this stochastic process two monomers bond and as a consequence two disjoint rings may merge into a compound ring or a single ring may split into two fragment rings this aggregation fragmentation process exhibits a percolation transition with a finite ring phase in which all rings have microscopic length and a giant ring phase where macroscopic rings account for a finite fraction of the entire mass interestingly while the total mass of the giant rings is a deterministic quantity their total number and their sizes are stochastic quantities the size distribution of the macroscopic rings is universal although the span of this distribution increases with time moreover the average number of giant rings scales logarithmically with system size we introduce a card shuffling algorithm for efficient simulation of the ring formation process and we present numerical verification of the theoretical predictions

random planar lattices and integrated superbrownian excursion in this paper a surprising connection is described between a specific brand of random lattices namely planar quadrangulations and aldous integrated superbrownian excursion ise as a consequence the radius r n of a random quadrangulation with n faces is shown to converge up to scaling to the width r r l of the support of the one dimensional ise or precisely more generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ise shifted to set the minimum of its support in zero the first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half line reminiscent of cori and vauquelin s well labelled trees the second step relates these trees to embedded discrete trees in the sense of aldous via the conjugation of tree principle an analogue for trees of vervaat s construction of the brownian excursion from the bridge from probability theory we need a new result of independent interest the weak convergence of the encoding of a random embedded plane tree by two contour walks to the brownian snake description of ise our results suggest the existence of a continuum random map describing in term of ise the scaled limit of the dynamical triangulations considered in two dimensional pure quantum gravity

ensemble inhibition and excitation in the human cortex an ising model analysis with uncertainties the pairwise maximum entropy model also known as the ising model has been widely used to analyze the collective activity of neurons however controversy persists in the literature about seemingly inconsistent findings whose significance is unclear due to lack of reliable error estimates we therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive markov chain monte carlo after the convergence of the main optimization algorithm we apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake sleep cycle our analysis shows that the ising model captures neuronal collective behavior much better than the independent model during wakefulness light sleep and deep sleep when both excitatory e and inhibitory i neurons are modeled ignoring the inhibitory effects of i neurons dramatically overestimates synchrony among e neurons furthermore information theoretic measures reveal that the ising model explains about 80 95 of the correlations depending on sleep state and neuron type thermodynamic measures show signatures of criticality although we take this with a grain of salt as it may be merely a reflection of long range neural correlations

stochastic aggregation scaling properties we study the scaling properties of stochastic aggregation processes in one dimension numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent non trivial exponents corresponding to the survival probability of particles and monomers the overall behaviour agrees qualitatively with the mean field theory this theory also provides a useful approximation for the decay exponents as well as the limiting mass distribution

using association models to analyse agreement data two examples two examples demonstrate how one can use association models to analyse agreement data the first example concerns intra rater variability in the classification of sputum cytology slides and the second deals with variability associated with the reporting of passive smoking histories the paper emphasizes models in which one estimates category scores from the data that is models that are not in the log linear family of models such models have use in assessment of category distinguishability and provide insights not easily obtained with log linear models

a comparison of methods for calculating a stratified kappa investigators use the kappa coefficient to measure chance corrected agreement among observers in the classification of subjects into nominal categories the marginal probability of classification may depend however on one or more confounding variables we consider assessment of interrater agreement with subjects grouped into strata on the basis of these confounders we assume overall agreement across strata is constant and consider a stratified index of agreement or stratified kappa based on weighted summations of the individual kappas we use three weighting schemes 1 equal weighting 2 weighting by the size of the table and 3 weighting by the inverse of the variance in a simulation study we compare these methods under differing probability structures and differing sample sizes for the tables we find weighting by sample size moderately efficient under most conditions we illustrate the techniques by assessing agreement between surgeons and graders of fundus photographs with respect to retinal characteristics with stratification by initial severity of the disease

universal distribution of masses in a one dimensional sticky gas abstract agglomeration of particles by perfectly inelastic collisions is studied in the case of a one dimensional gas particles move freely between collisions both mass and momentum are conserved at binary encounters it is shown that under a weak mean field like hypothesis admitting the existence of correlations between the velocities of colliding particles the dynamics drives the system towards a scaling regime with a universal exponential distribution of masses

market structure explained by pairwise interactions financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features here we give empirical evidence by making as few assumptions as possible that the market microstructure capturing almost all of the available information in the data of stock markets does not involve higher order than pairwise interactions we give an economic interpretation of this pairwise model we show that it accurately recovers the empirical correlation coefficients thus the collective behaviors are quantitatively described by models that capture the observed pairwise correlations but no higher order interactions furthermore we show that an order disorder transition occurs as predicted by the pairwise model last we make the link with the graph theoretic description of stock markets recovering the non random and scale free topology shrinking length during crashes and meaningful clustering features as expected

aggregation with multiple conservation laws aggregation processes with an arbitrary number of conserved quantities are investigated on the mean field level an exact solution for the size distribution is obtained the asymptotic form of this solution exhibits nontrivial double scaling while processes with one conserved quantity are governed by a single scale processes with multiple conservation laws exhibit an additional diffusion like scale the theory is applied to ballistic aggregation with mass and momentum conserving collisions and to diffusive aggregation with multiple species

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