role of the admittance operator in rough surface scattering the linear operator that relates the normal gradient of a wave field to its values on an irregular surface is the basis for a new formulation of the rough surface scattering problem this formulation has led to a class of approximations that surpass traditional methods in accuracy and efficiency the connection between this approach and the standard formulation by means of a boundary integral equation is the subject of this paper while equivalent in all respects the admittance operator formulation provides helpful new perspectives on the physics of surface scattering and lends itself naturally to more elaborate problems for example at a rough boundary between dissimilar media the operators compose themselves into generalized reflection and transmission operators while at a random surface the operator terms lead to analytic forms for the scattered field moments

frequency domain elastic wave modeling by finite differences a tool for crosshole seismic imaging the migration imaging or inversion of wide aperture cross hole data depends on the ability to model wave propagation in complex media for multiple source positions computational costs can be considerably reduced in frequency domain imaging by modeling the frequency domain steady state equations rather than the time domain equations of motion i develop a frequency domain approach in this note that is competitive with time domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required

effect of intermodular connection on fast sparse synchronization in clustered small world neural networks we consider a clustered network with small world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength j inter and the average number of intermodular links per interneuron m syn inter in contrast to the case of nonclustered networks two kinds of sparsely synchronized states such as modular and global synchronization are found for the case of modular sparse synchronization the population behavior reveals the modular structure because the intramodular dynamics of subnetworks make some mismatching on the other hand in the case of global sparse synchronization the population behavior is globally identical independently of the cluster structure because the intramodular dynamics of subnetworks make perfect matching we introduce a realistic cross correlation modularity measure representing the matching degree between the instantaneous subpopulation spike rates of the subnetworks and examine whether the sparse synchronization is global or modular depending on its magnitude the intermodular coupling strength j inter seems to play dual roles for the pacing between spikes in each subnetwork for large j inter due to strong inhibition it plays a destructive role to spoil the pacing between spikes while for small j inter it plays a constructive role to favor the pacing between spikes through competition between the constructive and the destructive roles of j inter there exists an intermediate optimal j inter at which the pacing degree between spikes becomes maximal in contrast the average number of intermodular links per interneuron m syn inter seems to play a role just to favor the pacing between spikes with increasing m syn inter the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes furthermore we employ the realistic sub and whole population order parameters based on the instantaneous sub and whole population spike rates to determine the threshold values for the synchronization unsynchronization transition in the sub and whole populations and the degrees of global and modular sparse synchronization are also measured in terms of the realistic sub and whole population statistical mechanical spiking measures defined by considering both the occupation and the pacing degrees of spikes it is expected that our results could have implications for the role of the brain plasticity in some functional behaviors associated with population synchronization

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

a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

mean field approximations for coupled populations of generalized linear model spiking neurons with markov refractoriness there has recently been a great deal of interest in inferring network connectivity from the spike trains in populations of neurons one class of useful models that can be fit easily to spiking data is based on generalized linear point process models from statistics once the parameters for these models are fit the analyst is left with a nonlinear spiking network model with delays which in general may be very difficult to understand analytically here we develop mean field methods for approximating the stimulus driven firing rates in both the time varying and steady state cases auto and cross correlations and stimulus dependent filtering properties of these networks these approximations are valid when the contributions of individual network coupling terms are small and hence the total input to a neuron is approximately gaussian these approximations lead to deterministic ordinary differential equations that are much easier to solve and analyze than direct monte carlo simulation of the network activity these approximations also provide an analytical way to evaluate the linear input output filter of neurons and how the filters are modulated by network interactions and some stimulus feature finally in the case of strong refractory effects the mean field approximations in the generalized linear model become inaccurate therefore we introduce a model that captures strong refractoriness retains all of the easy fitting properties of the standard generalized linear model and leads to much more accurate approximations of mean firing rates and cross correlations that retain fine temporal behaviors

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

semistability at the end of a group extension a 1 ended cw complex q is semistable at oo if all proper maps r 0 oo q are properly homotopic if xi and x2 are finite cw complexes with isomorphic fundamental groups then the universal cover of xi is semistable at oo if and only if the universal cover of x2 is semistable at oo hence the notion of a finitely presented group being semistable at oo is well defined we prove main theorem let 1 h g k 1 be a short exact sequence of finitely generated infinite groups if g is finitely presented then g is semistable at cc theorem if a and b are locally compact connected noncompact cw complexes then a x b is semistable at oo theorem x y xy xi y c b and c nonzero integers is semistable at oo the proofs are geometrical in nature and the main tool is covering space theory

derivation of closed form expressions for the t matrices of rayleigh rice and extinction theorem perturbation theories closed form expressions are derived for the rayleigh rice and extinction theorem perturbation theories for the case of dirichlet boundary conditions it is shown that the two theories are related through the reciprocity transformation to all orders it follows that a proof of invariance of either of the theories with respect to the reciprocity transformation would imply the formal equivalence of the two theories using the reciprocity relationship between the two theories a recursion relation is derived for an nth order term of the extinction theorem perturbation theory similar to the one for the rayleigh rice perturbation theory in spite of considerable effort no general proof of invariance of the terms of the two perturbation series with respect to the reciprocity transformation was obtained two possible approaches to such a proof are suggested while the question of convergence of the two series is not examined in this work it is possible that the formulas derived here will prove useful in such a study

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

using subnormality to show the simple connectivity at infinity of a finitely presented group a cw complex x is simply connected at infinity if for each compact c in x there exists a compact d in x such that loops in x d are homotopically trivial in x c let g be a finitely presented group and x a finite cw complex with fundamental group g g is said to be simply connected at infinity if the universal cover of x is simply connected at infinity b jackson and c m houghton have independently shown that if g and a normal subgroup h are infinite finitely presented groups with g h infinite and either h or g h 1 ended then g is simply connected at infinity in the case where h is 1 ended we exhibit a class of groups showing that the finitely presented hypothesis on h cannot be reduced to finitely generated we address the question if n is normal in h and h is normal in g and these are infinite groups with n and g finitely presented and either n or g h is 1 ended is g simply connected at infinity in the case that n is 1 ended the answer is shown to be yes in the case that g h is 1 ended we exhibit a class of such groups that are not simply connected at infinity

information geometry of interspike intervals in spiking neurons an information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time variant spike rate and a fixed shape parameter we formulate the problem of characterization as a semiparametric statistical estimation where the spike rate is a nuisance parameter we derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation and we show that some existing measures such as the coefficient of variation and the local variation are expressed as estimators of certain functions under the same assumptions

on analyticity of linear waves scattered by a layered medium abstract the scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering in this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of high order perturbation of surfaces methods for simulating such waves more specifically we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions this result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of operator expansions field expansions and transformed field expansions

singularities affect dynamics of learning in neuromanifolds the parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units a parameter space forms a geometrical manifold called the neuromanifold in the case of neural networks such a model is identified with a statistical model and a riemannian metric is given by the fisher information matrix however the matrix degenerates at singularities such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities arma time series model and many other cases the standard statistical paradigm of the cramer rao theorem does not hold and the singularity gives rise to strange behaviors in parameter estimation hypothesis testing bayesian inference model selection and in particular the dynamics of learning from examples prevailing theories so far have not paid much attention to the problem caused by singularity relying only on ordinary statistical theories developed for regular nonsingular models only recently have researchers remarked on the effects of singularity and theories are now being developed this article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures we demonstrate our recent results on these problems simple toy models are also used to show explicit solutions we explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically because the fisher information matrix degenerates that the model selection criteria such as aic bic and mdl fail to hold in these models that a smooth bayesian prior becomes singular in such models and that the trajectories of dynamics of learning are strongly affected by the singularity causing plateaus or slow manifolds in the parameter space the natural gradient method is shown to perform well because it takes the singular geometrical structure into account the generalization error and the training error are studied in some examples

response to comments on reflection from a corrugated surface revisited j acoust soc am 96 1116 1129 1994 the comments of kazandjian j acoust soc am 98 1813 1814 1995 concerning the paper j acoust soc am 96 1116 1129 1994 are discussed notably those concerning the equivalence of the rayleigh and extinction methods the identity and convergence of perturbation series deriving from these methods and the pertinence of numerical computations as indicators of the validity of theoretical predictions

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

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

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

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

stability of high order perturbative methods for the computation of dirichlet neumann operators abstract in this paper we present results on the stability of perturbation methods for the evaluation of dirichlet neumann operators dno defined on domains that are viewed as complex deformations of a basic simple geometry in such cases geometric perturbation methods based on variations of the spatial domains of definition have long been recognized to constitute efficient and accurate means for the approximation of dno and in fact several numerical implementations have been previously proposed inspired by our recent analytical work here we demonstrate that the convergence of these algorithms is quite generally limited by numerical instability indeed we show that these standard perturbative methods for the calculation of dno suffer from significant ill conditioning which is manifest even for very smooth boundaries and whose severity increases with boundary roughness moreover and again motivated by our previous work we introduce an alternative perturbative approach that we show to be numerically stable this approach can be interpreted as a reformulation of classical perturbative algorithms in suitable independent variables and thus it allows for both direct comparison and the possibility of analytic continuation of the perturbation series it can also be related to classical preconditioned spectral approaches and as such it retains in finite arithmetic the spectral convergence properties of classical perturbative methods albeit at a higher computational cost as it does not take advantage of possible dimensional reductions still as we show an alternative approach such as the one we propose may be mandated in cases where substantial information is contained in high order harmonics and or perturbation coefficients of the solution

impact of correlated inputs on the output of the integrate and fire model for the integrate and fire model with or without reversal potentials we consider how correlated inputs affect the variability of cellular output for both models the variability of efferent spike trains measured by coefficient of variation cv of the interspike interval is a nondecreasing function of input correlation when the correlation coefficient is greater than 0 09 the cv of the integrate and fire model without reversal potentials is always above 0 5 no matter how strong the inhibitory inputs when the correlation coefficient is greater than 0 05 cv for the integrateand fire model with reversal potentials is always above 0 5 independent of the strength of the inhibitory inputs under a given condition on correlation coefficients we find that correlated poisson processes can be decomposed into independent poisson processes we also develop a novel method to estimate the distribution density of the first passage time of the integrate and fire model

stochastic dynamics of a finite size spiking neural network we present a simple markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite size spiking neural network we give closed form estimates for the equilibrium distribution mean rate variance and autocorrelation function of the network activity the model is applicable to any network where the probability of firing of a neuron in the network depends on only the number of neurons that fired in a previous temporal epoch networks with statistically homogeneous connectivity and membrane and synaptic time constants that are not excessively long could satisfy these conditions our model completely accounts for the size of the network and correlations in the firing activity it also allows us to examine how the network dynamics can deviate from mean field theory we show that the model and solutions are applicable to spiking neural networks in biophysically plausible parameter regimes

conversion of temporal correlations between stimuli to spatial correlations between attractors it is shown that a simple modification of synaptic structures of the hopfield type constructed to produce autoassociative attractors produces neural networks whose attractors are correlated with several learned patterns used in the construction of the matrix the modification stores in the matrix a fixed sequence of uncorrelated patterns the network then has correlated attractors provoked by the uncorrelated stimuli thus the network converts the temporal order or temporal correlation expressed by the sequence of patterns into spatial correlations expressed in the distributions of neural activities in attractors the model captures phenomena observed in single electrode recordings in performing monkeys by miyashita et al the correspondence is as close as to reproduce the fact that given uncorrelated patterns as sequentially learned stimuli the attractors produced are significantly correlated up to a separation of 5 five in the sequence this number 5 is universal in a range of parameters and requires essentially no tuning we then discuss learning scenarios that could lead to this synaptic structure as well as experimental predictions following from it finally we speculate on the cognitive utility of such an arrangement

asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons we investigate theoretically the conditions for the emergence of synchronous activity in large networks consisting of two populations of extensively connected neurons one excitatory and one inhibitory the neurons are modeled with quadratic integrate and fire dynamics which provide a very good approximation for the subthreshold behavior of a large class of neurons in addition to their synaptic recurrent inputs the neurons receive a tonic external input that varies from neuron to neuron because of its relative simplicity this model can be studied analytically we investigate the stability of the asynchronous state as of the network with given average firing rates of the two populations first we show that the as can remain stable even if the synaptic couplings are strong then we investigate the conditions under which this state can be destabilized we show that this can happen in four generic ways the first is a saddle node bifurcation which leads to another state with different average firing rates this bifurcation which occurs for strong enough recurrent excitation does not correspond to the emergence of synchrony in contrast in the three other instability mechanisms hopf bifurcations which correspond to the emergence of oscillatory synchronous activity occur we show that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations we also show that besides these codimension 1 bifurcations the system can display several codimension 2 bifurcations takens bogdanov gavrielov guckenheimer and double hopf bifurcations

a master equation formalism for macroscopic modeling of asynchronous irregular activity states many efforts have been devoted to modeling asynchronous irregular ai activity states which resemble the complex activity states seen in the cerebral cortex of awake animals most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which ai states are sustained through recurrent sparse connectivity with or without external input in this letter we propose a mesoscopic description of such ai states using master equation formalism we derive a second order mean field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks this formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized we compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces considering the randomly connected network as a unit this approach could be used to build large scale networks of such connected units with an aim to model activity states constrained by macroscopic measurements such as voltage sensitive dye imaging

parabolic and quasiparabolic subgroups of free partially commutative groups let be a finite graph and g be the corresponding free partially commutative group in this paper we study subgroups generated by vertices of the graph which we call canonical parabolic subgroups a natural extension of the definition leads to canonical quasiparabolic subgroups it is shown that the centralisers of subsets of g are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions

a reduced order representation of the poincare steklov operator an application to coupled multi physics problems this work investigates a model reduction method applied to coupled multi physics systems the case in which a system of interest interacts with an external system is considered an approximation of the poinste operator is computed by simulating in an offline phase the external problem when the inputs are the laplace beltrami eigenfunctions defined at the interface in the online phase only the reduced representation of the operator is needed to account for the influence of the external problem on the main system an online basis enrichment is proposed in order to guarantee a precise reduced order computation several test cases are proposed on different fluid structure couplings

comparison of perturbation theories for rough surface scattering rayleigh rice perturbation theory is compared with the more rigorously derived perturbation theory based on the extinction theorem or extended boundary condition for the case of dirichlet boundary conditions numerical calculations for a sinusoidal surface profile show that the two theories give identical results when carried out to high order this is true even when the two series do not seem to converge numerically numerical convergence of the two series is found in several cases including some cases in which the rayleigh hypothesis is invalid for surfaces of arbitrary shape the two perturbation series appear superficially to differ at third and higher order it is shown however that a reciprocity transformation of one series makes it identical to the other through fifth order finally it is shown that reciprocity holds in both perturbation theories establishing analytically the equivalence of the two theories at least through fifth order these results are surprising given the limited regime

efficient enforcement of far field boundary conditions in the transformed field expansions method the method of transformed field expansions tfe has been demonstrated to be a robust and highly accurate numerical scheme for simulating solutions of boundary value and free boundary problems from the sciences and engineering as a boundary perturbation method it builds highly accurate solutions based upon exact solutions in a simple canonical geometry and corrects these via taylor series to fit the actual geometry at hand the tfe method has significantly enhanced stability properties when compared with other boundary perturbation approaches however this comes at the cost of requiring a full volumetric discretization as opposed the surface formulation that other methods can realize in this paper we outline two techniques for ameliorating this shortcoming first by employing a legendre spectral element method to implement efficient graded meshes and second by utilizing an artificial boundary with a transparent boundary condition placed quite close to the boundary of the domain in this contribution we focus on the specific problem of simulating the dirichlet neumann operator associated to laplace s equation on a periodic cell which arises in the water wave problem while the details of our results are specific to this problem the general conclusions are valid for the wider class of problems to which the tfe method can be applied for each technique we discuss implementation details and display numerical results which support the conclusion that each of these techniques can greatly reduce the computational cost of using the tfe method

intrinsic graph structure estimation using graph laplacian a graph is a mathematical representation of a set of variables where some pairs of the variables are connected by edges common examples of graphs are railroads the internet and neural networks it is both theoretically and practically important to estimate the intensity of direct connections between variables in this study a problem of estimating the intrinsic graph structure from observed data is considered the observed data in this study are a matrix with elements representing dependency between nodes in the graph the dependency represents more than direct connections because it includes influences of various paths for example each element of the observed matrix represents a co occurrence of events at two nodes or a correlation of variables corresponding to two nodes in this setting spurious correlations make the estimation of direct connection difficult to alleviate this difficulty a digraph laplacian is used for characterizing a graph a generative model of this observed matrix is proposed and a parameter estimation algorithm for the model is also introduced the notable advantage of the proposed method is its ability to deal with directed graphs while conventional graph structure estimation methods such as covariance selections are applicable only to undirected graphs the algorithm is experimentally shown to be able to identify the intrinsic graph structure

dynamics of learning in multilayer perceptrons near singularities the dynamical behavior of learning is known to be very slow for the multilayer perceptron being often trapped in the plateau it has been recently understood that this is due to the singularity in the parameter space of perceptrons in which trajectories of learning are drawn the space is riemannian from the point of view of information geometry and contains singular regions where the riemannian metric or the fisher information matrix degenerates this paper analyzes the dynamics of learning in a neighborhood of the singular regions when the true teacher machine lies at the singularity we give explicit asymptotic analytical solutions trajectories both for the standard gradient sgd and natural gradient ngd methods it is clearly shown in the case of the sgd method that the plateau phenomenon appears in a neighborhood of the critical regions where the dynamical behavior is extremely slow the analysis of the ngd method is much more difficult because the inverse of the fisher information matrix diverges we conquer the difficulty by introducing the blow down technique used in algebraic geometry the ngd method works efficiently and the state converges directly to the true parameters very quickly while it staggers in the case of the sgd method the analytical results are compared with computer simulations showing good agreement the effects of singularities on learning are thus qualitatively clarified for both standard and ngd methods

population coding and decoding in a neural field a computational study this study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable a general prototype model for the encoding process is proposed in which neural responses are correlated with strength specified by a gaussian function of their difference in preferred stimuli based on the model we study the effect of correlation on the fisher information compare the performances of three decoding methods that differ in the amount of encoding information being used and investigate the implementation of the three methods by using a recurrent network this study not only rediscovers main results in existing literatures in a unified way but also reveals important new features especially when the neural correlation is strong as the neural correlation of firing becomes larger the fisher information decreases drastically we confirm that as the width of correlation increases the fisher information saturates and no longer increases in proportion to the number of neurons however we prove that as the width increases further wider than 2 times the effective width of the turning function the fisher information increases again and it increases without limit in proportion to the number of neurons furthermore we clarify the asymptotic efficiency of the maximum likelihood inference mli type of decoding methods for correlated neural signals it shows that when the correlation covers a nonlocal range of population excepting the uniform correlation and when the noise is extremely small the mli type of method whose decoding error satisfies the cauchy type distribution is not asymptotically efficient this implies that the variance is no longer adequate to measure decoding accuracy

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

stochastic neural field theory and the system size expansion we analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of n identical neurons the state of the network is specified by the fraction of active or spiking neurons in each population and transition rates are chosen so that in the thermodynamic or deterministic limit n rightarrow infty we recover standard activity based or voltage based rate models we derive the lowest order corrections to these rate equations for large but finite n using two different approximation schemes one based on the van kampen system size expansion and the other based on path integral methods both methods yield the same series expansion of the moment equations which at mathcal o 1 n can be truncated to form a closed system of equations for the first and second order moments taking a continuum limit of the moment equations while keeping the system size n fixed generates a system of integrodifferential equations for the

comparison of the rayleigh fourier and extinction theorem methods applied to scattering and transmission at a rough solid solid interface the rayleigh fourier and extinction theorem mathematical formalisms are established and compared in the case of scattering from and transmission through a rough solid solid interface by using the reciprocity properties of the solution resulting from the extinction theorem formalism it is shown that if they have unique solutions the two formalisms are theoretically equivalent when used to obtain the displacement fields beyond the maximum excursions of the rough interface as a result the perturbation approaches of the two formalisms yield identical results from a numerical point of view it is shown that the two methods can give close results regardless of the verification of the rayleigh hypothesis the closeness of the two approaches which has already been established and numerically confirmed in the case of a fluid solid interface does not seem to be known or even conjectured in the literature in the case of a solid solid interface it is indicated that with the mathematics included in this pap

reflection from a corrugated surface revisited the problem of scattering of a plane sonic wave from a soft surface with periodic sinusoidal unevenness along one direction is examined by means of the rayleigh plane wave expansion and the waterman extinction methods numerically implemented by fourier projection and expansion respectively the computations are done with real double precision stochastic arithmetic instead of the usual complex double precision floating point arithmetic in order to precisely evaluate the numerical accuracy of the results conditioned by round off errors it is shown that the low order plane wave coefficients obtained by the rayleigh and waterman methods are identical when obtained from matrix systems that are large enough to give convergence of these coefficients for the same matrix size the higher order coefficients differ the higher the diffraction order it is also shown that the waterman fourier series computation of the near field is generally meaningful whereas that of rayleigh involving summation of t

generation of correlated spike trains neuronal spike trains display correlations at diverse timescales throughout the nervous system the functional significance of these correlations is largely unknown and computational investigations can help us understand their role in order to generate correlated spike trains with given statistics several case specific methods have been described in the litterature this letter presents two general methods to generate sets of spike trains with given firing rates and pairwise correlation functions along with efficient simulation algorithms

theory of correlations in stochastic neural networks one of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity in general however the interpretation of the observed correlations is difficult since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong thus a comparison between the observed correlations and the predictions from specific model networks is needed in this paper we develop a theory of neuronal correlation functions in large networks comprising several highly connected subpopulations and obeying stochastic dynamic rules when the networks are in asynchronous states the cross correlations are relatively weak i e their amplitude relative to that of the autocorrelations is of order of 1 n n being the size of the interacting populations using the weakness of the cross correlations general equations that express the matrix of cross correlations in terms of the mean neuronal activities and the effective interaction matrix are presented the effective interactions are the synaptic efficacies multiplied by the gain of the postsynaptic neurons the time delayed cross correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the nonorthogonal eigenvectors of the effective interaction matrix the theory is extended to networks with random connectivity such as randomly dilute networks this allows for a comparison between the contribution from the internal common input and that from the direct interactions to the correlations of monosynaptically coupled pairs a closely related quantity is the linear response of the neurons to external time dependent perturbations we derive the form of the dynamic linear response function of neurons in the above architecture in terms of the eigenmodes of the effective interaction matrix the behavior of the correlations and the linear response when the system is near a bifurcation point is analyzed near a saddle node bifurcation the correlation matrix is dominated by a single slowly decaying critical mode near a hopf bifurcation the correlations exhibit weakly damped sinusoidal oscillations the general theory is applied to the case of a randomly dilute network consisting of excitatory and inhibitory subpopulations using parameters that mimic the local circuit of 1 mathrm mm 3 of the rat neocortex both the effect of dilution as well as the influence of a nearby bifurcation to an oscillatory state are demonstrated

higher order statistics of input ensembles and the response of simple model neurons pairwise correlations among spike trains recorded in vivo have been frequently reported it has been argued that correlated activity could play an important role in the brain because it efficiently modulates the response of a postsynaptic neuron we show here that a neuron s output firing rate critically depends on the higher order statistics of the input ensemble we constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations but differed with regard to the higher order interactions within the population the first ensemble was characterized by clusters of spikes synchronized over the whole population in the second ensemble the size of spike clusters was on average proportional to the pairwise correlation for both input models we assessed the role of the size of the population the firing rate and the pairwise correlation on the output rate of two simple model neurons a continuous firing rate model and a conductance based leaky integrate and fire neuron an approximation to the mean output rate of the firing rate neuron could be derived analytically with the help of shot noise theory interestingly the essential features of the mean response of the two neuron models were similar for both neuron models the three input parameters played radically different roles with respect to the postsynaptic firing rate depending on the interaction structure of the input for instance in the case of an ensemble with small and distributed spike clusters the output firing rate was efficiently controlled by the size of the input population in addition to the interaction structure the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate

a method for selecting the bin size of a time histogram the time histogram method is the most basic tool for capturing a time dependent rate of neuronal spikes generally in the neurophysiological literature the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers here we propose a method for objectively selecting the bin size from the spike count statistics alone so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate for a small number of spike sequences generated from a modestly fluctuating rate the optimal bin size may diverge indicating that any time histogram is likely to capture a spurious rate given a paucity of data the method presented here can nevertheless suggest how many experimental trials should be added in order to obtain a meaningful time dependent histogram with the required accuracy

euler classes and bredon cohomology for groups with restricted families of finite subgroups we explore some of the special features with respect to bredon cohomology for groups whose finite subgroups are all either nilpotent or p groups or cyclic p groups we get some results on dimensions and also a formula for the equivariant euler class for certain groups we consider the generalization for bredon cohomology of the properties of being duality or poincare duality and study their behavior under p power index extensions with coefficients in a field of characteristic p

recurrent biological neural networks the weak and noisy limit a perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network a series expansion is constructed that converges for networks with noisy membrane potential and weak synaptic connectivity the terms of the series can be interpreted as loops of interactions between neurons so the technique is called a loop expansion a diagrammatic method is introduced that allows for construction of analytic expressions for the parameter dependencies of the spike probability function and correlation functions an analytic expression is obtained to predict the effect of the surrounding network on a neuron during an intracellular current injection the analytic results are compared with simulations to test the range of their validity and significant effects of the the recurrent connections in network are accurately predicted by the loop expansion

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

traveling water waves we present a numerical continuation method for traveling wave solutions to the full water wave problem using a spectral collocation discretization the water wave problem is reformulated in terms of surface variables giving rise to the zakharov craig sulem formulation and traveling waves are studied by introducing a phase velocity vector as a parameter we follow non trivial solution branches bifurcating from the trivial solution branch via numerical continuation methods techniques such as projections and filtering allow the computation to proceed for greater distances up the branch and parallelism allows the computation of larger problems we conclude with results including the formation of hexagonal patterns for the three dimensional problem

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

conditional mixture model for correlated neuronal spikes analysis of correlated spike trains is a hot topic of research in computational neuroscience a general model of probability distributions for spikes includes too many parameters to be of use in analyzing real data instead we need a simple but powerful generative model for correlated spikes we developed a class of conditional mixture models that includes a number of existing models and analyzed its capabilities and limitations we apply the model to dynamical aspects of neuron pools when hebbian cell assemblies coexist in a pool of neurons the condition is specified by these assemblies such that the probability distribution of spikes is a mixture of those of the component assemblies the probabilities of activation of the hebbian assemblies change dynamically we used this model as a basis for a competitive model governing the states of assemblies

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

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

an improved formalism for wave scattering from rough surfaces the scattered field and its normal gradient obey a mutual linear relation at the scattering surface that is distinct from the physical boundary condition connecting either quantity to the incident radiation on a moderately rough surface this relation can be represented by an operator whose series expansion in surface slope converges nicely even for large values of the rayleigh parameter this allows the helmholtz integral for scattering amplitude to be written as a series of readily computable terms one or two of which provide good approximations for surfaces too irregular for the usual bragg expansion this formulation reproduces the bragg series for small surface elevations and in the limit of low roughness wavenumber gives the kirchhoff approximation with an explicit correction term in surface curvature the usual results for a composite surface also emerge naturally on several test profiles the method produces better overall accuracy than other multiscale approximations at comparable efficiency

connectivity at infinity for right angled artin groups we establish sufficient conditions implying semistability and connectivity at infinity properties for cat 0 cubical complexes we use this along with the geometry of cubical k 1 s to give a complete description of the higher connectivity at infinity properties of right angled artin groups among other things this determines which right angled artin groups are duality groups applications to group extensions are also included

estimating spiking irregularities under changing environments we considered a gammadistribution of interspike intervals as a statistical model for neuronal spike generation a gamma distribution is a natural extension of the poisson process taking the effect of a refractory period into account the model is specified by two parameters a time dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons because the environment changes over time observed data are generated from a model with a time dependent firing rate which is an unknown function a statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve we used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function we obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate this estimation is efficient without fisher information loss and better than maximum likelihood estimation we suggest a measure of spiking irregularity based on the estimating function which may be useful for characterizing individual neurons in changing environments

groups quasi isometric to right angled artin groups we characterize groups quasi isometric to a right angled artin group raag g with finite outer automorphism group in particular all such groups admit a geometric action on a cat 0 cube complex that has an equivariant fibering over the davis building of g this characterization will be used in forthcoming work of the first author to give a commensurability classification of the groups quasi isometric to certain raags

the submonoid and rational subset membership problems for graph groups abstract we show that the membership problem in a finitely generated submonoid of a graph group also called a right angled artin group or a free partially commutative group is decidable if and only if the independence graph commutation graph is a transitive forest as a consequence we obtain the first example of a finitely presented group with a decidable generalized word problem that does not have a decidable membership problem for finitely generated submonoids we also show that the rational subset membership problem is decidable for a graph group if and only if the independence graph is a transitive forest answering a question of kambites silva and the second author m kambites p v silva b steinberg on the rational subset problem for groups j algebra 309 2 2007 622 639 finally we prove that for certain amalgamated free products and hnn extensions the rational subset and submonoid membership problems are recursively equivalent in particular this applies to finitely generated groups with two or more ends that are either torsion free or residually finite

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

efficient learning in boltzmann machines using linear response theory the learning process in boltzmann machines is computationally very expensive the computational complexity of the exact algorithm is exponential in the number of neurons we present a new approximate learning algorithm for boltzmann machines based on mean field theory and the linear response theorem the computational complexity of the algorithm is cubic in the number of neurons in the absence of hidden units we show how the weights can be directly computed from the fixed point equation of the learning rules thus in this case we do not need to use a gradient descent procedure for the learning process we show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role finally we apply the method to a pattern completion task and show good performance for networks up to 100 neurons

temporal correlations in stochastic networks of spiking neurons the determination of temporal and spatial correlations in neuronal activity is one of the most important neurophysiological tools to gain insight into the mechanisms of information processing in the brain its interpretation is complicated by the difficulty of disambiguating the effects of architecture single neuron properties and network dynamics we present a theory that describes the contribution of the network dynamics in a network of spiking neurons for a simple neuron model including refractory properties we calculate the temporal cross correlations in a completely homogeneous excitatory fully connected network in a stable stationary state for stochastic dynamics in both discrete and continuous time we show that even for this simple network architecture the crosscorrelations exhibit a large variety of qualitatively different properties strongly dependent on the level of noise the decay constant of the refractory function and the network activity at the critical point the crosscorrelations oscillate with a frequency that depends on the refractory properties or decay exponentially with a diverging damping constant for weak refractory properties we also investigate the effect of the synaptic time constants it is shown that these time constants may apart from their influence on the asymmetric peak arising from the direct synaptic connection also affect the long term properties of the cross correlations

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

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

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

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

analytic continuation of dirichlet neumann operators the analytic dependence of dirichlet neumann operators dno with respect to variations of their domain of definition has been successfully used to devise diverse computational strategies for their estimation these strategies have historically proven very competitive when dealing with small deviations from exactly solvable geometries as in this case the perturbation series of the dno can be easily and recursively evaluated in this paper we introduce a scheme for the enhancement of the domain of applicability of these approaches that is based on techniques of analytic continuation we show that in fact dno depend analytically on variations of arbitrary smooth domains in particular this implies that they generally remain analytic beyond the disk of convergence of their power series representations about a canonical separable geometry and this in turn guarantees that alternative summation mechanisms such as pade approximation can be effectively used to numerically access this extended domain of analyticity our method of proof is motivated by our recent development of stable recursions for the coefficients of the perturbation series here we again utilize this recursion as we compare and contrast the performance of our new algorithms with that of previously advanced perturbative methods the numerical results clearly demonstrate the beneficial effect of incorporating analytic continuation procedures into boundary perturbation methods moreover the results also establish the superior accuracy and applicability of our new approach which as we show allows for precise calculations corresponding to very large perturbations of a basic geometry

theory of correlation in a network with synaptic depression synaptic depression affects not only the mean responses of neurons but also the correlation of response variability in neural populations although previous studies have constructed a theory of correlation in a spiking neuron model by using the mean field theory framework synaptic depression has not been taken into consideration we expanded the previous theoretical framework in this study to spiking neuron models with short term synaptic depression on the basis of this theory we analytically calculated neural correlations in a ring attractor network with mexican hat type connectivity which was used as a model of the primary visual cortex the results revealed that synaptic depression reduces neural correlation which could be beneficial for sensory coding furthermore our study opens the way for theoretical studies on the effect of interaction change on the linear response function in large stochastic networks

the topology at infinity of out fn we construct a bordification of outer space analogous to the borel serre bordification of symmetric spaces as an application we show that out fn is 2n 5 connected at infinity and that it is a virtual duality group of dimension 2n 3

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

an operator expansion method for computing nonlinear surface waves on a ferrofluid jet we present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet it is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to do so we describe the associated dirichlet neumann operator in terms of a taylor series expansion where each term can be efficiently computed by a pseudo spectral scheme using the fast fourier transform we show detailed numerical tests on the convergence of this operator and to illustrate the performance of our method we simulate the long time propagation and pairwise collisions of axisymmetric solitary waves both depression and elevation waves are examined by varying the magnetic field comparisons with weakly nonlinear predictions are also provided accurate and efficient numerical solver for the full nonlinear problem reduction of the original problem to a lower dimensional system of equations series expansion for the dirichlet neumann operator in the axisymmetric case study of head on and overtaking collisions of axisymmetric solitary waves

an operator expansions method for computing dirichlet neumann operators in linear elastodynamics abstract the propagation of linear elastic waves arises in a wide array of applications for instance in mechanical engineering materials science and the geosciences many configurations of interest can be effectively modeled as layers of isotropic homogeneous materials separated by thin interfaces across which material properties vary rapidly in the frequency domain one must solve a system of coupled elliptic partial differential equations however this can be greatly simplified in the instance of layered media by considering interface unknowns to realize this one must be able to produce normal stresses tractions at these interfaces and dirichlet neumann operators accomplish this in this contribution we discuss a novel boundary perturbation approach to compute these operators in a rapid high order and robust fashion

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