systems over a principal ideal domain a polynomial model approach the polynomial model approach to linear dynamical systems over a field was developed principally by p a fuhrmann starting in 1976 j franklin inst 305 1976 pp 521 540 in this paper an analogous approach is proposed for systems over a principal ideal domain when the concept of extended linear i o map is introduced fractional representations of transfer function matrices arise naturally in this theoretical framework a correspondence between fractional representations of the transfer function matrix of a given i o map and its reachable or observable realizations is established the mcmillan degree of a linear i o map is proved to be equal to the degree of the determinant of the matrix appearing as denominator in a coprime fractional representation of the associated transfer function matrix

conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

diagnostics for nonlinearity and heteroscedasticity in errors in variables regression we suggest new plotting methods for residual analysis in errors in variables regression the standard residuals analyses are based on the methods of miller and fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed by appropriate we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity the standard methods are not appropriate in this sense for skewed error distributions our methods require replication of the error prone predictors but they are appropriate for both symmetric and skewed error distributions besides residual plots we also construct hypothesis tests for heteroscedasticity in terms of power for detecting heteroscedasticity we show that the standard plot is more efficient when the residuals are normally distributed although it does not achieve its nominal level for skewed error distributions simulations are used to illustrate the results we also conside

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

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

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

on the geometry of the set of controllability subspaces of a pair a b abstract given a controllable system defined by a pair of matrices a b we investigate the geometry of the set of controllability subspaces this set is a subset of the set of a b invariant subspaces we prove that in fact it is a stratified submanifold and we compute its dimension

a quadratic kalman filter abstract we propose a new filtering and smoothing technique for non linear state space models observed variables are quadratic functions of latent factors following a gaussian var stacking the vector of factors with its vectorized outer product we form an augmented state vector whose first two conditional moments are known in closed form we also provide analytical formulae for the unconditional moments of this augmented vector our new quadratic kalman filter qkf exploits these properties to formulate fast and simple filtering and smoothing algorithms a simulation study first emphasizes that the qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70 rmses improvement of filtered values second it provides evidence that qkf based maximum likelihood estimates of model parameters always possess lower bias or lower rmses than the alternative estimators

decoupling of square linear systems with delays the aim of this paper is to exhibit matricial necessary and sufficient conditions for the decoupling problem of linear systems with commensurate delays under static nonpredictive and stable state feedbacks a matrix approach is used which is similar to the falb wolovich one for systems without delay the conditions obtained here are quite simple easily computable and less restrictive than the previous ones moreover we give the only possible design of the physically realizable control law that satisfies the problem

regular paper model matching for linear systems with delays and 2d systems model matching problem for linear systems with delays is considered via a transfer matrix approach we deal with a general class of neutral delay differential systems which is equivalent to 2d systems from a realizability point of view the solution of the problem is based on the decomposition of the ring of the causal rational functions which is not a principal ideal domain as the intersection of two suitable principal ideal domains

towards a compactification of the set of conditioned invariant subspaces a compactification of the set of conditioned invariant subspaces of fixed dimension for an observable pair c a is proposed it contains the almost conditioned invariant subspaces of the same dimension in certain cases the compactification is shown to be smooth and a complete geometric description is given in the case of a single output system

versal deformations in orbit spaces given an orbit space m and an equivalence relation defined in it by means of the action of a group g we obtain a miniversal deformation of an orbit through a miniversal deformation in m with regard to a suitable group action of g we show some applications to the perturbations of m tuples of subspaces and c a invariant subspaces

a b cyclic submodules abstract an a b cyclic submodule m is generated by the states of one single trajectory of a linear control system whose parameters come from a commutative ring m is finite when it is generated by the states of a deadbeat control process motivations and basic properties of such modules are given and among several further results it is shown that the family of finite a b cyclic submodules is an invariant which e g over polynomials can be determined by an appropriate grobner basis computation

on a b t invariant subspaces having extendible brunovsky bases we consider a by invariant subspaces having a brunovsky basis which can be extended to a brunovsky basis of the whole space we obtain a geometrical characterization of this class of a by invariant subspaces and a complete family of numerical invariants to classify them 0 elsevier science inc 1997

on feedback invariance properties for systems over a principal ideal domain simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the a b invariance property and the a bf invariance or feedback invariance property for systems over a ring this equivalence is no longer true and many results of the geometric control theory cannot be extended we present new algorithmically checkable characterizations of the a bf invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

corrected score function for errors in variables models methodology and application to generalized linear models summary statistical models whose independent variables are subject to measurement errors are often referred to as errors in variables models to correct for the effects of measurement error on parameter estimation this paper considers a correction for score functions a corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables this approach makes it possible to do inference as well as estimation of model parameters without additional assumptions the corrected score functions of some generalized linear models are obtained

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

estimation for the nonlinear functional relationship on etudie les proprietes asymptotiques de l estimateur du maximum de vraisemblance pour le modele fonctionnel implicite

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

on the geometry of the solutions of the cover problem for a given system sigma a b and a subspace maths the cover problem consists of finding all a b invariant subspaces containing maths for controllable systems the set of these subspaces can be suitably stratified in this paper necessary and sufficient conditions are given for the cover problem to have a solution on a given strata then the geometry of these solutions is studied in particular the set of the solutions is provided with a differentiable structure and a parameterization of all solutions is obtained through a coordinate atlas of the corresponding smooth manifold

the topology of the set of conditioned invariant subspaces we consider the topology of the set of conditioned invariant subspaces of an observable pair c a of a fixed dimension by fixing the observability indices of the restricted system a stratification by finitely many smooth manifolds is obtained termed brunovsky strata it is shown that each brunovsky stratum is homotopy equivalent to a generalized flag manifold from this description an effective formula for the betti numbers of the brunovsky strata can be derived

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

on the parametrization of the controllability subspaces of a controllable pair given a controllable linear control system defined by a pair of constant matrices a b the set of controllability subspaces is an stratified submanifold of the set of a b invariant subspaces we parameterize each strata by means of coordinate charts this parametrization has significant dierences to that of a b invariant subspaces showing a more complex geometric structure

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

similarity of non everywhere defined linear maps abstract the equivalence between linear maps defined only on a subspace or by duality defined modulo a subspace is studied and applied to block similarity of rectangular matrices in that way we find the complete families of invariants obtained by brunovsky and zaballa and the results of gohberg and others for this particular case also we describe explicit methods for obtaining the reduced matrix and the corresponding bases

differentiable structure of the set of controllable a b t invariant subspaces abstract given a b t hom c n c n m observable we prove that the set of a b t invariant subspaces having a fixed brunovsky kronecker structure is a connected manifold and we compute its dimension also we include some applications of these results

on the duality principle for linear dynamical systems over commutative rings abstract the main result in this paper characterizes those commutative rings r having the property that every linear dynamical system over r verifies the duality principle i e the system is observable reachable if and only if the dual system t is reachable observable this characterization is given in terms of the finitely generated faithful ideals of r and it generalizes a result due to ching and wyman for the noetherian case in case r satisfies the additional condition of being a reduced ring we prove that the duality principle holds in r if and only if the height of every finitely generated ideal of r is zero

two stage instrumental variables estimators for the nonlinear errors in variables model abstract estimation for the nonlinear functional errors in variables model is considered under the assumption that instrumental variables are available the approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived utilizing the nonlinearity of the relationship an estimator of the error covariance matrix is introduced using the error covariance matrix estimator two types of two stage instrumental variable estimators are proposed the two two stage estimators do not have the asymptotic bias due to the nonlinearity a monte carlo experiment also shows the superiority of the two stage estimators over the ordinary estimator

on the polynomial functional relationship summary a method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor for quadratic functional relationships with possibly non normal errors we present a consistent estimator when the error covariance matrix is known a large sample test of the quadratic against the linear functional relationship is also suggested in this case

feedback invariants for linear dynamical systems over a principal ideal domain abstract this paper studies the action of the feedback group f n m on m input n dimensional reachable linear dynamical systems over a principal ideal domain r for such a 2 dimensional system a complete set of invariants is given which characterizes the feedback class of in particular it is characterized in terms of these invariants when has the feedback cyclization property the particular cases r z and r r x are studied in some detail finally when n is arbitrary the feedback classification is given for the class of reachable systems f g such that g is a matrix with at least n 1 invariant factors equal to one

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

alternative tests for functional and pointwise output controllability of linear time invariant systems abstract this paper deals with the description of a new method for calculating the functional output controllability it is computed by means of the rank of a certain constant matrix which can be associated to the system moreover a new method for the pointwise output controllability determination by means of constructing the output controllability matrix associated to the system using the residues of the given linear system is developed finally a simple physical example is presented

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

measuring information loss due to inconsistencies in duration data from longitudinal surveys abstract in this paper we take a functional errors in variables approach to modeling longitudinal duration data containing observed inconsistencies this approach separates the problem into two parts an errors in variables problem and an estimation problem this approach also enables us to develop measures of the effect of the data inconsistencies on the parameter estimates from a duration model one measure is the loss in precision in the parameter estimates that results from the inconsistencies we refer to the proportion of parameter variances that is due to the inconsistencies in the data as information loss the second is a distance measure which is used to provide information about how close we are to a consistent estimator an example is provided using a four month panel of current population survey data

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

linear stochastic state space theory in the white noise space setting we study linear stochastic state space equations within the white noise space setting a commutative ring of power series in a countable number of variables plays an important role transfer functions are rational functions with coefficients in this commutative ring and are characterized in a number of ways a major feature in our approach is the observation that key characteristics of a linear time invariant stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system namely its average behavior

computation of maximal pre controllability submodules over a noetherian ring for dynamical systems with coefficient in a ring it is not always possible to compute by a finite procedure the maximal a b invariant submodule contained in the kernel of the output map c namely v kerc this difficulty prevents one from checking necessary and sufficient geometric conditions for the solvability of noninteracting control problems in this paper we will prove that for dynamical systems with coefficients in a noetherian ring it is always possible to compute by a finite procedure the maximal pre controllability submodule contained in the kernel of the output map c namely r kerc this result is useful in dealing with the block decoupling problem or the disturbance rejection problem

stratification and bundle structure of the set of conditioned invariant subspaces in the general case abstract we extend some known results on the smooth stratification of the set of conditioned invariant subspaces to a general pair c a c p n n without any assumption on the observability more precisely we prove that the set of c a conditioned invariant subspaces having a fixed brunovsky kronecker structure is a submanifold of the corresponding grassmann manifold with a fiber bundle structure relating the observable and nonobservable part and we then compute its dimension we also prove that the set of all c a conditioned invariant subspaces having a fixed dimension is connected provided that the nonobservable part of c a has at most one eigenvalue this condition is in general necessary

computation of maximal reachability submodules abstract a new and conceptually simple procedure is derived for the computation of the maximal reachability submodule of a given submodule of the state space of a linear discrete time system over a noethenian ring r the procedure is effective if r is effective and if kernels and intersections can be computed the procedure is compared with a rather different procedure by assan e a published recently

polynomial regression with errors in the variables a polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients assuming hypothetically the latent true regressor variable to be known and then adjusting for the errors if normality of the error variables can be assumed the estimator can be simplified considerably only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known if the variance of the errors in the dependent variable is also known another estimator can be constructed

estimation of the quadratic errors in variables model summary an estimator is presented for the coefficients of the quadratic functional relationship the estimator is shown to be asymptotically normally distributed as the sample size increases in deriving this result it is not assumed that replication occurs a monte carlo study is presented agreeing well with the asymptotic results an example from the earth sciences is analysed

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

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

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

the disturbance decoupling problem for systems over a ring up to now the use of geometric methods in the study of disturbance decoupling problems ddps for systems over a ring has provided only necessary conditions for the existence of solutions in this paper we study such problems considering separately the case in which only static feedback solutions are allowed and the one in which dynamic feedback solutions are admitted in the first case we give a complete geometric characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring practical procedures for testing the solvability conditions and for constructing solutions if any exist are given in the case of systems with coefficients in a principal ideal domain pid in the second case we give a complete geometric characterization of the solvability conditions for systems with coefficients in a pid

c a invariance of modules over principal ideal domains for discrete time linear systems over a principal ideal domain three types of c a invariance can be distinguished connections between these notions are investigated for pure submodules necessary and sufficient conditions for dynamic c a injection invariance are given sufficient conditions are obtained in the general case

dynamic feedback a b invariant submodules for linear systems over commutative noetherian domains abstract in this paper some basic characterizations of a b invariant submodules for linear systems over commutative noetherian domains are studied first a notion of dynamic feedback a b invariant submodules for such systems is introduced and then it is shown that this notion is equivalent to a b invariance

chaotic balanced state in a model of cortical circuits the nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are not well understood we consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells we study a network model with excitatory and inhibitory populations of simple binary units the internal feedback is mediated by relatively large synaptic strengths so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold the connectivity is random and sparse the mean number of connections per unit is large though small compared to the total number of cells in the network the network also receives a large temporally regular input from external sources we present an analytical solution of the mean field theory of this model which is exact in the limit of large network size this theory reveals a new cooperative stationary state of large networks which we term a balanced state in thi

a cellular decomposition of the manifold of observable conditioned invariant subspaces abstract given an observable system defined by a pair of matrices c a we obtain a cellular decomposition of the manifold of c a conditioned invariant subspaces with fixed observability indices of the restricted system and we apply this decomposition to compute their homology groups

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

differentiable families of subspaces abstract we show how the differentiable families of subspaces can be studied from a geometrical point of view by means of their representation as a differentiable mapping from the manifold of parameters m into the grassmann manifold gr k n of all k dimensional subspaces of k n and the consideration of principal bundles over gr k n and m in order to achieve this first we present a survey of the topology the differentiable structure and the bundle structure of gr k n in particular we show that the topology induced by the gap metric is equivalent to the usual quotient topology second we use these structures to prove two local characterizations of the differentiability of a family of subspaces and we state that these characterizations can be globalized if m is contractible finally we apply these properties to study the existence of global jordan basis of class c r

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

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

on the parametrization of conditioned invariant subspaces and observer theory the present paper is an in depth analysis of the set of conditioned invariant subspaces of a given observable pair c a we do this analysis in two different ways one based on polynomial models starting with a characterization obtained in p a fuhrmann linear operators and systems in hilbert space 1981 ieee trans automat control ac 26 1981 284 the other being a state space approach toeplitz operators projections in polynomial and rational models wiener hopf factorizations and factorization indices all appear and are tools in the characterizations we single out an important subclass of conditioned invariant subspaces namely the tight ones which already made an appearance in p a fuhrmann u helmke systems control lett 30 1997 217 a precursor of the present paper of particular importance for the study of the parametrization of the set of conditioned invariant subspaces of an observable pair c a is the structural map that associates with any reachable pair with only the input dimension constrained a uniquely determined conditioned invariant subspace the construction of this map uses polynomial models and the shift realization new objects the partial observability and reachability matrices are introduced which are needed for the state space characterizations kernel and image representations for conditioned invariant subspaces are derived uniqueness of a kernel representation of a conditioned invariant subspace is shown to be equivalent to tightness we pass on to an analysis and derivation of the kronecker hermite canonical form for full column rank rectangular polynomial matrices this extends the work of a e eckberg a characterization of linear systems via polynomial matrices and module theory ph d thesis mit cambridge ma 1974 g d forney siam j control optim 13 1973 493 and d hinrichsen h f munzner and d pratzel wolters systems

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

statistical signs of common inhibitory feedback with delay cross correlation histograms cchs sometimes exhibit an isolated central peak flanked by two troughs what can cause this pattern the absence of cch satellite peak makes an oscillatory common input doubtful it is here shown using a simple counting model that a common inhibitory feedback with delay can account for this pattern

a coordinate atlas of the manifold of observable conditioned invariant subspaces given an observable system c a k mxn x k nxn with k r or c the set of c a invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding grassmannian we obtain an explicit parametrization of it by means of an atlas of corresponding charts as an application we obtain the set of maximal dimensional outputs making solvable a generic disturbance decoupling problem

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

structural stability of c a marked subspaces abstract given an observable pair of matrices c a we consider the manifold of c a invariant subspaces having a fixed brunovsky kronecker structure using arnold techniques we obtain the explicit form of a miniversal deformation of a marked c a invariant subspace with respect to the usual equivalence relation as an application we obtain the dimension of the orbit and we characterize the structurally stable subspaces those with open orbit

block similarity invariants of restrictions to a b invariant subspaces we generalize some properties of invariant subspaces of endomorphisms to a b invariant subspaces in particular we show that in appropriate bases the pair a b can be written as

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