estimating a state space model from point process observations a widely used signal processing paradigm is the state space model the state space model is defined by two equations an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit latent stimulus we develop an algorithm to estimate a state space model observed through point process measurements we represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus given the latent process neural spiking activity is characterized as a general point process defined by its conditional intensity function we develop an approximate expectation maximization em algorithm to estimate the unobservable state space process its parameters and the parameters of the point process the em algorithm combines a point process recursive nonlinear filter algorithm the fixed interval smoothing algorithm and the state space covariance algorithm to compute the complete data log likelihood efficiently we use a kolmogorov smirnov test based on the time rescaling theorem to evaluate agreement between the model and point process data we illustrate the model with two simulated data examples an ensemble of poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local bernoulli process

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

forecasting synchronizability of complex networks from data given a complex networked system whose topology and dynamical equations are unknown is it possible to foresee that a certain type of collective dynamics can potentially emerge in the system provided that only time series measurements are available we address this question by focusing on a commonly studied type of collective dynamics namely synchronization in coupled dynamical networks we demonstrate that using the compressive sensing paradigm even when the coupling strength is not uniform so that the network is effectively weighted the full topology the coupling weights and the nodal dynamical equations can all be uncovered accurately the reconstruction accuracy and data requirement are systematically analyzed in a process that includes a validation of the reconstructed eigenvalue spectrum of the underlying coupling matrix a master stability function msf the fundamental quantity determining the network synchronizability can then be calculated based on the reconstructed dynamical system the accuracy of which can be assessed as well with the coupling matrix and msf fully uncovered the emergence of synchronous dynamics in the network can be anticipated and controlled to forecast the collective dynamics on complex networks is an extremely challenging problem with significant applications in many disciplines and our work represents an initial step in this important area

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

a distortion theorem for biholomorphic mappings in c 2 the classical distortion theorems for families of univalent functions have been studied not later than 1907 when kbe discovered his verzerrangsatz

linear invariance of locally biholomorphic mappings in the unit ball of a jb triple abstract we study the notion of linear invariance on the unit ball of a j b triple x and we obtain some connection between the norm order of a linear invariant family and the starlikeness of order 1 2 also we give some result concerning the radius of univalence of some linear invariant families finally if the dimension of x is finite and if the norm order of a linear invariant family is finite then we prove the normality of the linear invariant family and we also obtain upper bounds on the distortion and the growth of mappings in a linear invariant family with specified norm order in particular our results are valid for the classical cartan domains and the unit polydisc

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

a set probability technique for detecting relative time order across multiple neurons with the development of multielectrode recording techniques it is possible to measure the cell firing patterns of multiple neurons simultaneously generating a large quantity of data identification of the firing patterns within these large groups of cells is an important and a challenging problem in data analysis here we consider the problem of measuring the significance of a repeat in the cell firing sequence across arbitrary numbers of cells in particular we consider the question given a ranked order of cells numbered 1 to n what is the probability that another sequence of length n contains j consecutive increasing elements assuming each element of the sequence is drawn with replacement from the numbers 1 through n we derive a recursive formula for the probability of the sequence of length j or more for n 2j a closed form solution is derived for n 2j we obtain upper and lower bounds for these probabilities for various combinations of parameter values these can be computed very quickly for a typical case with small n 10 and large n 3000 sequences of 7 and 8 are statistically very unlikely a potential application of this technique is in the detection of repeats in hippocampal place cell order during sleep unlike most previous articles on increasing runs in random lists we use a probability approach based on sets of overlapping sequences

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

global existence for nonlinear klein gordon equations in infinite homogeneous waveguides in two dimensions in this paper we prove a global existence result for nonlinear klein gordon equations with small data in infinite homogeneous waveguids r2 m where m m g is a zoll manifold the method is based on the normal forms the eigenfunction expansion for m and the special distribution of eigenvalues of laplace beltrami on zoll manifold

the number of synaptic inputs and the synchrony of large sparse neuronal networks the prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons we study synchronization in models of large networks of spiking neurons with random sparse connectivity synchrony occurs only when the average number of synapses m that a cell receives is larger than a critical value mc below mc the system is in an asynchronous state in the limit of weak coupling assuming identical neurons we reduce the model to a system of phase oscillators that are coupled via an effective interaction in this framework we develop an approximate theory for sparse networks of identical neurons to estimate mc analytically from the fourier coefficients of our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it we apply this theory to compute mc for a model of inhibitory networks of integrate and fire i f neurons as a function of the intrinsic neuronal properties e g the refractory period tr the synaptic time constants and the strength of the external stimulus iext the number mc is found to be nonmonotonous with the strength of iext for tr 0 we estimate the minimum value of mc over all the parameters of the model to be 363 8 above mc the neurons tend to fire in smeared one cluster states at high firing rates and smeared two or more cluster states at low firing rates refractoriness decreases mc at intermediate and high firing rates these results are compared to numerical simulations we show numerically that systems with different sizes n behave in the same way provided the connectivity m is such that 1 meff 1 m 1 n remains constant when n varies this allows extrapolating the large n behavior of a network from numerical simulations of networks of relatively small sizes n 800 in our case we find that our theory predicts with remarkable accuracy the value of mc and the patterns of synchrony above mc provided the synaptic coupling is not too large we also study the strong coupling regime of inhibitory sparse networks all of our simulations demonstrate that increasing the coupling strength reduces the level of synchrony of the neuronal activity above a critical coupling strength the network activity is asynchronous we point out a fundamental limitation for the mechanisms of synchrony relying on inhibition alone if heterogeneities in the intrinsic properties of the neurons and spatial fluctuations in the external input are also taken into account

high order events in cortical networks a lower bound it is commonly believed that information processing in cortical networks involves the collective spikingactivity of neuronal assemblies nevertheless due to current technical limitations in multielectrodes recordingmethods it is not possible to tackle this issue with direct experimental measurements in this study we simulatespiking activity of large ensembles of cells focusing on the temporal correlation properties of the neuronaldynamics and demonstrate that transient fast synchronization of large groups of cells is a natural phenomenonof the cortical activity to prove this result we use a statistical approach based on combinatorics andknowledge derived from a previous research work a benucci et al phys rev e 68 041905 2003 wequantify the degree of synchronous activity by computing a lower bound for the fraction of cells participatingin fast few milliseconds synchronous events finally we discuss the implications of the results found in termsof cortical coding mechanisms doi 10 1103 physreve 70 051909 pacs number s 87 19 lai introduction

jordan triples and riemannian symmetric spaces we introduce a class of real jordan triple systems called jh triples and show via the tits kantor koecher construction of lie algebras that they correspond to a class of riemannian symmetric spaces including the hermitian symmetric spaces and the symmetric r spaces

a semiparametric bayesian model for detecting synchrony among multiple neurons we propose a scalable semiparametric bayesian model to capture dependencies among multiple neurons by detecting their cofiring possibly with some lag time patterns over time after discretizing time so there is at most one spike at each interval the resulting sequence of 1s spike and 0s silence for each neuron is modeled using the logistic function of a continuous latent variable with a gaussian process prior for multiple neurons the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model the advantages of our approach are as follows the nonparametric component i e the gaussian process model provides a flexible framework for modeling the underlying firing rates and the parametric component i e the copula model allows us to make inferences regarding both contemporaneous and lagged relationships among neurons using the copula model we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of a dependence structure among variables our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems using simulated data we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons we also apply our model to spike train data obtained from prefrontal cortical areas

on the precise growth covering and distortion theorems for normalized biholomorphic mappings abstract in this paper we consider a normalized biholomorphic mapping f x defined on the unit ball in a complex banach space where the origin 0 is a zero of order k 1 of f x x the precise growth and covering theorem for f x is obtained when f x is a starlike mapping or a starlike mapping of order especially the precise growth and covering theorem for f x is also established when f x is a quasi convex mapping moreover the precise distortion theorem for f x is given when f x is a convex mapping our result includes many known results

information geometric measures as robust estimators of connection strengths and external inputs information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains among several advantages of this approach a significant property is the close link between information geometric measures and neural network architectures previous modeling studies established that the first and second order information geometric measures corresponded to the number of external inputs and the connection strengths of the network respectively this relationship was however limited to a symmetrically connected network and the number of neurons used in the parameter estimation of the log linear model needed to be known recently simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections inspired by these studies we analytically investigated the link between the information geometric measures and the neural network structure with asymmetrically connected networks of n neurons we focused on the information geometric measures of orders one and two which can be derived from the two neuron log linear model because unlike higher order measures they can be easily estimated experimentally considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics we analytically showed that the corrected first and second order information geometric measures provided robust and consistent approximation of the external inputs and connection strengths respectively these results suggest that information geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system level neuroscience

trace order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional jb triple abstract we give a distortion theorem for linearly invariant families on the unit ball b of a finite dimensional jb triple x by using the trace order the exponents in the distortion bounds depend on the bergman metric at 0 further we introduce a new definition for the trace order of a linearly invariant family on b based on a jacobian argument we also construct an example of a linearly invariant family on b which has minimum trace order and is not a subset of the normalized convex mappings of b for dim x 2 finally we prove a regularity theorem for linearly invariant families on b all four types of classical cartan domains are the open unit balls of jb triples and the same holds for any finite product of these domains thus the unit balls of jb triples are natural generalizations of the unit disc in c and we have a setting in which a large number of bounded symmetric homogeneous domains may be studied simultaneously

on the convexity of a solution of liouville s equation the main purpose of the present note is to give a simple complex variable proof of the fact 3 10 11 that h z is convex whenever is convex the major step in our proof can be formulated as a coefficient inequality for convex univalent functions

distortion theorems for biholomorphic convex mappings in cn abstract in the paper the problem of sharp lower estimation for df z in the class of normalized biholomorphic mappings f between the open unit ball b n and convex domains in c n has been considered

relations among starlikeness convexity and k fold symmetry of locally biholomorphic mappings in cn abstract the subject of the paper concerns the existence of different inclusions between families s t s c of c n biholomorphic starlike or convex mappings and a family s k k 2 of c n locally biholomorphic mappings in the definition of s k we used a combination of a kikuchi matsuno suffridge s starlikeness condition and a property of j k symmetrical mappings in c n this definition generalizes a notion of planar sakaguchi s functions onto n dimensional case a motivation for the family s k comes from the paper 11 of the second author and the paper 6 of hamada and kohr the family s k is a superset of a family which is connected with a problem posed in the first paper and solved in the second one

long time existence for semi linear klein gordon equations with small cauchy data on zoll manifolds we prove a long time existence result for semi linear klein gordon equations with small cauchy data on zoll manifolds this generalizes a preceding result concerning the case of spheres obtained in an earlier paper by the authors the proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds

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

roper suffridge extension operator and the lower bound for the distortion abstract liczberski starkov gave a sharp lower bound for d n f z near the origin where n is the roper suffridge extension operator and f is a normalized convex mapping on the unit disk in c they gave a conjecture that the sharp lower bound holds on the euclidean unit ball b n in c n in this paper we will give a sharp lower bound on b n for a more general extension operator and for normalized univalent mappings f or normalized convex mappings f we will give a lower bound for mappings f in a linear invariant family we will also give a similar sharp lower bound on bounded convex complete reinhardt domains in c n

global solutions for nonlinear klein gordon equations in infinite homogeneous waveguides abstract in this paper we prove a global existence result for nonlinear klein gordon equations in infinite homogeneous waveguides r m with smooth small data where m m g is a zoll manifold or a compact revolution hypersurface the method is based on normal forms eigenfunction expansion and the special distribution of eigenvalues of the laplace beltrami on such manifolds

distortion of locally biholomorphic bloch mappings on bounded symmetric domains abstract we generalize bonk s distortion theorem on the unit disc in the complex plane to locally biholomorphic mappings on finite dimensional bounded symmetric domains as an application we obtain a lower bound for the bloch constant for various classes of locally biholomorphic bloch mappings

an application from partial sums of e z to a problem in several complex variables abstract let b n r z c n z where is the euclidean norm and for x c n let h x denote the closed convex hull of x in c n in 1990 graham showed that if f is a normalized holomorphic map from bn1 into c n and if f is either an open map or a polynomial map then there is a sharp uniform constant a a given by ae1 a 1 such that h f bn1 bna graham posed the question to find for normalized polynomial maps f of degree m the best constant am so that h f bn1 bnam we answer this question and obtain for each m the sharp constant a m a a ln m 2 1 a m a ln 2 1 a a 1 a m 1 m m we also note that this solution extends an old result of polya and szeg

the generalized roper suffridge extension operator abstract let f z be a normalized convex starlike function on the unit disc d let z c n z 1 2 z 2 p 2 z n p n where z z1 z2 zn z1 d z 2 z n c n 1 pi 1 i 2 n are real numbers in this note we prove that f z f z1 f z1 1 p2z2 f z1 1 pnzn is a normalized convex starlike mapping on where we choose the power function such that f z1 1 pi z1 0 1 i 2 n some other related results are proved

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

loewner chains and the roper suffridge extension operator abstract let f be a locally univalent function on the unit disc and let 0 1 2 we consider the family of operators extending f to a holomorphic map from the unit ball b in cn to cn given by n f z f z1 z f z1 where z z2 zn when 1 2 we obtain the roper suffridge extension operator we show that if f s then n f can be imbedded in a loewner chain our proof shows that if f s then n f is starlike and if f with 2 then n f is a spirallike map of type in particular we obtain a new proof that the roper suffridge operator preserves starlikeness we also obtain the radius of starlikeness of n s and the radius of convexity of n 1 2 s we show that if f is a normalized univalent bloch function on u then n f is a bloch mapping on b finally we show that if f belongs to a class of univalent functions which satisfy growth and distortion results then n f satisfies related growth and covering results

discovering the false discovery rate summary i describe the background for the paper controlling the false discovery rate a new and powerful approach to multiple comparisons by benjamini and hochberg that was published in the journal of the royal statistical society series b in 1995 i review the progress since made on the false discovery rate as well as the major conceptual developments that followed

distortion theorems for convex mappings on homogeneous balls abstract let b be the open unit ball of a complex banach space x and let b be homogeneous we prove distortion results for normalized convex mappings f b x which generalize various finite dimensional distortion theorems and improve some infinite dimensional ones in particular our results are valid for the open unit balls of complex hilbert spaces and the cartan domains

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

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

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

bloch functions on bounded symmetric domains we introduce and characterize bloch functions on bounded symmetric domains which may be infinite dimensional by extending several well known equivalent conditions for bloch functions on the open unit disc u in cc we also generalize a number of results concerning bloch functions on u to bounded symmetric domains given a holomorphic mapping between bounded symmetric domains bxbx and byby we derive criteria for boundedness and compactness of the composition operator c c between the bloch spaces b by b by and b bx b bx extending several known results for finite dimensional domains

a generalization of half plane mappings to the ball in mathbb c n let f be a normalized f 0 0 df 0 i biholomorphic mapping of the unit ball b c c onto a convex domain c c that is the union of lines parallel to some unit vector u c we consider the situation in which there is one infinite singularity of f on b in one case with a simple change of variables we classify all convex mappings of b that are half plane mappings in the first coordinate in the more complicated case when u is not in the span of the infinite singularity we derive a form of the mappings in dimension n 2

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

the time rescaling theorem and its application to neural spike train data analysis measuring agreement between a statistical model and a spike train data series that is evaluating goodness of fit is crucial for establishing the model s validity prior to using it to make inferences about a particular neural system assessing goodness of fit is a challenging problem for point process neural spike train models especially for histogram based models such as perstimulus time histograms psth and rate functions estimated by spike train smoothing the time rescaling theorem is a well known result in probability theory which states that any point process with an integrable conditional intensity function may be transformed into a poisson process with unit rate we describe how the theorem may be used to develop goodness of fit tests for both parametric and histogram based point process models of neural spike trains we apply these tests in two examples a comparison of psth inhomogeneous poisson and inhomogeneous markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers inhomogeneous poisson inhomogeneous gamma and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity to help make the logic behind the time rescaling theorem more accessible to researchers in neuroscience we present a proof using only elementary probability theory arguments we also show how the theorem may be used to simulate a general point process model of a spike train our paradigm makes it possible to compare parametric and histogram based neural spike train models directly these results suggest that the time rescaling theorem can be a valuable tool for neural spike train data analysis

measure of correlation orthogonal to change in firing rate there are a number of measures of correlation for spikes of two neurons and for spikes at two successive time bins in one neuron covariance correlation coefficient mutual information and information geometric measure in the log linear model it is desirable to have a measure that is not affected by change in the firing rates of neurons we explain the superiority of the information geometric measure from the point of view of geometry by which the correlation and firing rates are separated orthogonally that is without correlation we then analyze characteristics of other measures and show analytically how they are related to firing rates

global existence of small solutions for quadratic quasilinear klein gordon systems in two space dimensions consider a quasi linear system of two klein gordon equations with masses m1 m2 we prove that when m1a2m2 and m2a2m1 such a system has global solutions for small smooth compactly supported cauchy data this extends a result proved by sunagawa j differential equations 192 2 2003 308 in the semi linear case moreover we show that global existence holds true also when m1 2m2 and a convenient null condition is satisfied by the nonlinearities

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

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

growth and distortion theorems for linearly invariant families on homogeneous unit balls in cn abstract let b be a homogeneous unit ball in x c n in this paper we obtain growth and distortion theorems for linearly invariant families f of locally biholomorphic mappings on the unit ball b with finite norm order ord e 1 f we use the euclidean norm for the target space instead of the norm of x because we are able to obtain lower bounds in the two point distortion theorems for linearly invariant families on any homogeneous unit ball in c n we also obtain similar results for affine and linearly invariant families a l i f s of pluriharmonic mappings of the unit ball b into c n again in most of these results we use the euclidean norm for the target space to obtain lower bounds in the two point distortion theorems for a l i f s on b these results are generalizations to homogeneous unit balls of recent results due to graham kohr and pfaltzgraff the authors of this paper and duren hamada and kohr in the last section we consider two point distortion theorems for l i f s and a l i f s on the unit polydisc u n in c n

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

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

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