three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

calculation of entropy from data of motion we discuss the question of determining the entropy given the phase space trajectory which describes the detailed history of a many body system over a period of observation our viewpoint is that the determination of entropy as well as all other thermodynamic properties should require no concepts or information other than those given and defined by the trajectory the counting of coincidence or repetition of states along the trajectory is presented as a way to determine entropy given the trajectory an illustrative program based on the kinetic ising model is described in detail

on a generalization of a normal map and equation the class of normal maps was recently investigated by robinson and ralph in connection with the study of a variational inequality defined on a polyhedral set in this paper a generalization of such a map is considered and the associated generalized normal equation is studied the latter provides a unified formulation of several generalized variational inequality and complementarity problems using degree theory some sufficient conditions for the existence of a zero of a generalized normal map are established and the stability of a generalized normal equation at a solution is analyzed specializations of the results to various applications are discussed

new results on the algebraic theory of linear systems the solution of the cover problems abstract we give the complete solution of a large class of problems in linear system theory the so called cover problems these problems are formulated and solved both in the state space and in the input output frameworks the key concept which allows the effective parametrization of all solutions of the cover problems is that of the partial realizations of a sequence of matrices it is shown that the solutions of the state space cover problems can be expressed as state spaces of the partial realizations of appropriately defined sequences of matrices and the solution of the input output cover problems can be expressed as a simple function of the functions of the partial realizations of the sequences of mentioned above

scaling and universality in proportional elections a most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics a necessary step in this line of endeavor is to find regularities in data referring to large scale social phenomena such as scaling and universality we show that in proportional elections the distribution of the number of votes received by candidates is a universal scaling function identical in different countries and years this finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical political and or economical context where voters operate a simple dynamical model for the behavior of voters similar to a branching process reproduces the universal distribution

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

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

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

gap functions and error bounds for inverse quasi variational inequality problems abstract this paper is dedicated to inverse quasi variational inequalities which correspond to a mixture of quasi variational inequalities and inverse variational inequalities our aim is to obtain local global error bounds for inverse quasi variational inequality problems in terms of different gap functions merit functions i e the residual gap function the regularized gap function and the d gap function these bounds provide effective estimated distances between a specific point and the exact solution of the inverse quasi variational inequality problem since the class of inverse quasi variational inequalities includes the classes of general quasi variational inequalities and variational inequalities our results cover and extend similar results for these problems

further applications of a splitting algorithm to decomposition in variational inequalities and convex programming a classical method for solving the variational inequality problem is the projection algorithm we show that existing convergence results for this algorithm follow from one given by gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators moreover we extend the projection algorithm to solveany monotone affine variational inequality problem when applied to linear complementarity problems we obtain a matrix splitting algorithm that is simple and for linear quadratic programs massively parallelizable unlike existing matrix splitting algorithms this algorithm converges under no additional assumption on the problem when applied to generalized linear quadratic programs we obtain a decomposition method that unlike existing decomposition methods can simultaneously dualize the linear constraints and diagonalize the cost function this method gives rise to highly parallelizable algorithms for solving a problem of deterministic control in discrete time and for computing the orthogonal projection onto the intersection of convex sets

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

self adaptive projection method for co coercive variational inequalities in some real world problems the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables in this case if the mapping is co coercive the basic projection method is applicable however in order to determine the step size the existing basic projection method needs to know the co coercive modulus in advance in practice usually even if the mapping can be characterized co coercive it is difficult to evaluate the modulus and a conservative estimation will lead an extremely slow convergence in view of this point this paper presents a self adaptive projection method without knowing the co coercive modulus we also give a real life example to demonstrate the practicability of the proposed method

on a connection between spectral factorization and geometric control theory we investigate here how the geometric control theory of basile marro and wonham can be obtained in a hilbert space context as the byproduct of the factorization of a spectral density with no zeros on the imaginary axis we show how controlled invariant subspaces can be obtained as images of orthogonal projections of co invariant subspaces onto a semi invariant markovian subspace of the hardy space of square integrable functions analytic in the right half plane output nulling subspaces are then related to a particular spectral factorization problem a similar construction is presented for controllability subspaces and a new algorithm for the computation of these subspaces is presented

maximum entropy approach for deducing amino acid interactions in proteins we present a maximum entropy approach for inferring amino acid interactions in proteins subject to constraints pertaining to the mean numbers of various types of equilibrium contacts for a given sequence or a set of sequences we have carried out several kinds of tests for a two dimensional lattice model with just two types of amino acids with very promising results we also show that the method works very well even when the mean numbers of contacts are not known and therefore can be applied to real proteins

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

a parallel splitting method for coupled monotone inclusions a parallel splitting method is proposed for solving systems of coupled monotone inclusions in hilbert spaces and its convergence is established under the assumption that solutions exist unlike existing alternating algorithms which are limited to two variables and linear coupling our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes the breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions variational problems best approximation and network flows

duality in polynomial models with some applications to geometric control theory duality is studied in the context of polynomial models for linear systems the output injection group the dual of the feedback group is studied and a polynomial characterization of c a invariant subspaces as well as of the maximal reachability subspaces contained in ker c is given

minimal factorizations of rational matrix functions in terms of polynomial models the problem of minimal factorization of rational bicausal matrices is considered using polynomial models the factors are given explicitly in terms of polynomial matrices

the algebraic riccati equation a polynomial approach abstract polynomial models are used to give a unified approach to the problem of classifying the set of all real symmetric solutions of the algebraic riccati equation

inverse variational inequalities with projection based solution methods abstract an inverse variational inequality is defined as to find a vector u r n such that f u v f u t u 0 v if an inverse function u f 1 x exists the above inverse variational inequality could be transformed as a regular variational inequality however in reality it is not uncommon that the inverse function of f 1 x does not have explicit form although its functional values can be observed existing line search algorithms cannot be applied directly to solve such inverse variational inequalities in this paper we propose two projection based methods using the co coercivity of mapping f a self adaptive strategy is developed to determine the step sizes efficiently when the co coercivity modulus is unknown the convergence of the proposed methods is proved rigorously

estimation of entropy and mutual information we present some new results on the nonparametric estimation of entropy and mutual information first we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators the setup is related to grenander s method of sieves and places no assumptions on the underlying probability measure generating the data second we prove a converse to these consistency theorems demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information even given unlimited data this inconsistency theorem leads to an analytical approximation of the bias valid in surprisingly small sample regimes and more accurate than the usual 1 n formula of miller and madow over a large region of parameter space the two most practical implications of these results are negative 1 information estimates in a certain data regime are likely contaminated by bias even if bias corrected estimators are used and 2 confidence intervals calculated by standard techniques drastically underestimate the error of the most common estimation methods finally we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem by casting bias calculation problems in this approximation theory framework we obtain the best possible generalization of known asymptotic bias results more interesting this framework leads to an estimator with some nice properties the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions and this maximum error turns out to be surprisingly small we demonstrate the application of this new estimator on both real and simulated data

a bundle method for solving equilibrium problems we present a bundle method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle first we consider a general algorithm that we prove to be convergent then we explain how to make this algorithm implementable the strategy is to approximate the nonsmooth convex functions by piecewise linear convex functions in such a way that the subproblems are easy to solve and the convergence is preserved in particular we introduce a stopping criterion which is satisfied after finitely many iterations and which gives rise to stationary points finally we apply our implementable algorithm for solving the particular case of singlevalued and multivalued variational inequalities and we find again the results obtained recently by salmon et al 18

statistical mechanics for natural flocks of birds flocking is a typical example of emergent collective behavior where interactions between individuals produce collective patterns on the large scale here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data we construct the minimally structured maximum entropy model consistent with experimental correlations in large flocks of starlings the maximum entropy model shows that local pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings with no free parameters we also find that the number of interacting neighbors is independent of flock density confirming that interactions are ruled by topological rather than metric distance finally by comparing flocks of different sizes the model correctly accounts for the observed scale invariance of long range correlations among the fluctuations in flight direction