finite state automata and simple recurrent networks we explore a network architecture introduced by elman 1988 for predicting successive elements of a sequence the network uses the pattern of activation over a set of hidden units from time step t1 together with element t to predict element t 1 when the network is trained with strings from a particular finite state grammar it can learn to be a perfect finite state recognizer for the grammar when the network has a minimal number of hidden units patterns on the hidden units come to correspond to the nodes of the grammar although this correspondence is not necessary for the network to act as a perfect finite state recognizer we explore the conditions under which the network can carry information about distant sequential contingencies across intervening elements such information is maintained with relative ease if it is relevant at each intermediate step it tends to be lost when intervening elements do not depend on it at first glance this may suggest that such networks are not relevant to natural language in which dependencies may span indefinite distances however embeddings in natural language are not completely independent of earlier information the final simulation shows that long distance sequential contingencies can be encoded by the network even if only subtle statistical properties of embedded strings depend on the early information

using polygons to recognize and locate partially occluded objects we present computer vision algorithms that recognize and locate partially occluded objects the scene may contain unknown objects that may touch or overlap giving rise to partial occlusion the algorithms revolve around a generate test paradigm the paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects polygon representations of the object s boundary guide the hypothesis generation scheme choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification special vertices of the polygon called corners help detect and locate the model in the scene polygon moment calculations lead to estimates of the dissimilarity between scene and model corners and determine the model corner location in the scene an association graph represents the matches and compatibility constraints extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis using a coordinate transform that maps the model onto the scene the hypothesis gives the proposed model s location and orientation hypothesis verification requires checking for region consistency the union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene experimental results give examples of all phases of recognizing and locating the objects

using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

convergence of the nelder mead simplex method to a nonstationary point this paper analyzes the behavior of the nelder mead simplex method for a family of examples which cause the method to converge to a nonstationary point all the examples use continuous functions of two variables the family of functions contains strictly convex functions with up to three continuous derivatives in all the examples the method repeatedly applies the inside contraction step with the best vertex remaining fixed the simplices tend to a straight line which is orthogonal to the steepest descent direction it is shown that this behavior cannot occur for functions with more than three continuous derivatives the stability of the examples is analyzed

a multivariate analysis of evoked responses in eeg and meg data this paper presents a multivariate analysis of evoked responses and their spatiotemporal dynamics as measured with electro or magnetoencephalography this analysis uses standard techniques mancova to make possible statistical inference about differential responses after the data have been transformed using singular value decomposition the generality of this approach is limited only by the assumptions implicit in the general linear model and can range from simple analyses like hotelling s t2 test in comparing evoked responses among different conditions to complex analyses of a multivariate regression type e g characterizing the response components associated with a behavioral or psychophysical parameter to illustrate the technique we have characterized time dependent changes both within and between trials in magnetic fields evoked by self paced movements our illustrative analysis showed that movement evoked components were less prone to adaptation than premovement components suggesting that functionally distinct preparatory and early executive biomagnetic signals show differential adaptation

fortified descent simplicial search method a general approach we propose a new simplex based direct search method for unconstrained minimization of a real valued function f of n variables as in other methods of this kind the intent is to iteratively improve an n dimensional simplex through certain reflection expansion contraction steps the method has three novel features first a user chosen integer bar m k specifies the number of good vertices to be retained in constructing the initial trial simplices reflected then either expanded or contracted at iteration k second a trial simplex is accepted only when it satisfies the criteria of fortified descent which are stronger than the criterion of strict descent used in most direct search methods third the number of additional function evaluations needed to check a trial reflected expanded simplex for fortified descent can be controlled if one of the initial trial simplices satisfies the fortified descent criteria it is accepted as the new simplex otherwise the simplex is shrunk a fraction of the way toward a best vertex and the process is restarted etc until either a trial simplex is accepted or the simplex effectively has shrunk to a single point we prove several theoretical properties of the new method if f is continuously differentiable bounded below and uniformly continuous on its lower level set and we choose bar m k with the same value at all iterations k then every cluster point of the generated sequence of iterates is a stationary point the same conclusion holds if the function is continuously differentiable bounded below and we choose bar m k 1 at all iterations k

percolation theory and fragmentation measures in social networks abstract we study the statistical properties of a recently proposed social networks measure of fragmentation f after removal of a fraction q of nodes or links from the network the measure f is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network we compare this measure with the one traditionally used in percolation theory p the fraction of nodes in the largest cluster relative to the total number of nodes using both analytical and numerical methods we study erd s renyi er and scale free sf networks under various node removal strategies we find that for a network obtained after removal of a fraction q of nodes above criticality p 1 f 1 2 for fixed p and close to criticality we show that 1 f better reflects the actual fragmentation for a given p 1 f has a broad distribution and thus one can improve significantly the fragmentation of the network we also study and compare the fragmentation measure f and the percolation measure p for a real national social network of workplaces linked by the households of the employees and find similar results

robust partial shape classification using invariant breakpoints and dynamic alignment abstract a system for classifying partially occluded noisy shapes in varying positions orientations and dimensions is described an iterative algorithm derived from the colinearity principle is developed to locate invariant breakpoints on a shape contour the set of invariant breakpoints partitions the contour into a sequence of contour segments each contour segment is described by an ordered sequence that represents the euclidean distance between the pixels in the contour segment and the centroid of the region formed by connecting the end points of the contour segment by a straight line two stages of dynamic alignment with the appropriate constraints are formulated to determine shape similarity the first stage gives a distance measure of contour segment similarity and in the second stage the intersegment distances are used to optimally align contour segments so that a final measure of shape similarity is obtained the performance of the system is demonstrated by considering the classification of aircraft shapes belonging to four classes and classification results are presented as functions of noise and occlusion levels the results indicate that reasonable classification is obtained for noisy shapes with 0 to 30 occlusion

non linear alignment of neural net outputs for partial shape classification abstract a neural network approach to the partial shape classification problem is derived although neural networks are generally robust static pattern classifiers they are not effective in classifying patterns with inherent temporal variations in order to compensate for temporal variations resulting from random partial occlusion a multi neural network system which includes a dynamic alignment procedure at the neural net outputs is proposed in formulating the dynamic alignment stage a similarity measure between an input and the neural net outputs is defined combining the robustness of neural networks with the non linear alignment capability of dynamic alignment results in a classifier which can tolerate high degrees of random noise and random occlusion in shapes

on the roots of certain polynomials arising from the analysis of the nelder mead simplex method abstract the study of the effect of dimensionality on the nelder mead simplex method for unconstrained optimization leads us to the study of a two parameter family of polynomials of the form p n z b az az n 1 z n we show that provided that a a b is real it is possible to use primarily the schur cohn criterion in order to determine the configuration of the roots of p n z with respect to the unit circle

optimal allocation and sizing of capacitors to minimize the transmission line loss and to improve the voltage profile in this paper a modified discrete particle swarm optimization is presented to find the optimal placement and size of capacitors in a distribution system the objective function is composed of the line loss and the capacitors investment cost the bus voltage and the feeder current as constraints are included in the objective function by a constraint penalty factor to validate the proposed method the 18 bus ieee distribution system and the semi urban distribution system which is connected to bus 2 of the roy billinton test system are used the proposed method is applied to the problem and its robustness and accuracy are studied the results are compared with pure dpso genetic algorithm and nonlinear programming it is illustrated in two examples that the proposed optimization method is more accurate and particularly more robust than others for the planning of capacitors

on the convergence of pattern search algorithms we introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems our definition unifies an important collection of optimization methods that neither compute nor explicitly approximate derivatives we exploit our characterization of pattern search methods to establish a global convergence theory that does not enforce a notion of sufficient decrease our analysis is possible because the iterates of a pattern search method lie on a scaled translated integer lattice this allows us to relax the classical requirements on the acceptance of the step at the expense of stronger conditions on the form of the step and still guarantee global convergence

extremal properties of the determinant of the laplacian in the bergman metric on the moduli space of genus two riemann surfaces we study extremal properties of the determinant of the laplacian in the bergman metric on the moduli space of compact genus two riemann surfaces by a combination of analytical and numerical methods we identify four non degenerate critical points of this function and compute the signature of the hessian at these points the curve with the maximal number of automorphisms the burnside curve turns out to be the point of the absolute maximum our results agree with the mass formula for virtual euler characteristics of the moduli space a similar analysis is performed for bolza s strata of symmetric riemann surfaces of genus two

eigenvalue solution for the convected wave equation in a circular soft wall duct abstract a numerical approach to find the eigenvalues of the wave equation applied in a circular duct with convective flow and soft wall boundary conditions is proposed the characteristic equation is solved in the frequency domain as a function of a locally reacting acoustic impedance and the flow mach number in addition the presence of the convective flow couples the solution of the eigenvalues with the axial propagation constants the unknown eigenvalues are also related to these propagation constants by a quadratic expression that leads to two solutions these two solutions replaced into the characteristic equation generate two separate eigenvalue problems depending on the direction of propagation given that the resulting nonlinear complex valued equations do not provide the solution explicitly a numerical technique must be used the proposed approach is based on the minimization of the absolute value of the characteristic equation by the nelder mead simplex method the main advantage of this method is that it only uses function evaluations rather than derivatives and geometric reasoning the minimization is performed starting from very low frequencies and increasing by small steps to the particular frequency of interest the initial guess for the first frequency of calculation is provided as the hard wall eigenvalue solution then the solution from the previous step is used as the initial value for the next calculation this approach was specifically developed for applications with resonator type liners commonly used in the commercial aviation industry where the low frequency behavior resembles that of a hard wall and agrees with the first initial guess for the first frequency of calculation the numerical technique was found to be very robust in terms of convergence and stability also the method provides a physical meaning for each eigenvalue since the variation as a function of frequency can be clearly followed with respect to the values that are originally linked to the hard wall modes

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

on estimation of intermodulated frequencies for sinusoidal signals with unknown fundamental frequencies in this correspondence the problem of estimating the intermodulated frequencies of sinusoidal signals with unknown fundamental frequencies is investigated it is shown that by formulating the intermodulation structure as a constraint in the estimation of these frequencies a smaller cramer rao lower bound crlb can be obtained that is a more accurate estimate of these frequencies can be obtained the steps in the proposed estimation procedure are i obtaining initial estimate of the frequencies using existing methods ii establishing the intermodulation structure from the initial estimate of the frequencies and iii refining the initial estimate using the intermodulation structure the implementation and performance of the proposed estimation procedure is demonstrated by a simulation example

on designing an isotropic fiducial mark the crame spl acute r rao lower bound crlb of image registration error using an isotropic fiducial mark is derived the derived crlb is a function of the intensity profile of the fiducial mark following the development of the crlb a new method for designing an isotropic fiducial mark suitable for digital image registration is presented a parameterization method of the fiducial intensity profile is introduced which guarantees no aliasing effect when the fiducial mark is digitized with the proper sampling rate a method for computing the fiducial intensity profile based on minimization of the crlb registration error and subject to certain practical constraints is developed for imaging systems with a significant low pass effect it is proposed to pre emphasize the high frequency components of the fiducial mark by converting the designed gray scale fiducial marks into binary fiducial marks experimental results show that the designed fiducial mark can provide very accurate registration results and that the registration accuracy is independent of its location

using variance information in magnetoencephalography measures of functional connectivity the use of magnetoencephalography meg to assess long range functional connectivity across large scale distributed brain networks is gaining popularity recent work has shown that electrodynamic networks can be assessed using both seed based correlation or independent component analysis ica applied to meg data and further that such metrics agree with fmri studies to date techniques for meg connectivity assessment have typically used a variance normalised approach either through the use of pearson correlation coefficients or via variance normalisation of envelope timecourses prior to ica here we show that the use of variance information i e data that have not been variance normalised in source space projected hilbert envelope time series yields important spatial information and is of significant functional relevance further we show that employing this information in functional connectivity analyses improves the spatial delineation of network nodes using both seed based and ica approaches the use of variance is particularly important in meg since the non independence of source space voxels brought about by the ill posed meg inverse problem means that spurious signals can exist in areas of low signal variance we therefore suggest that this approach be incorporated into future studies

robust identification of harmonic oscillator parameters using the adjoint fokker planck equation we present a model based output only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators in this context suitable models of the oscillator s damping and stiffness properties are postulated guided by physical understanding of the oscillatory phenomena the temporal dynamics and the probability density function of the oscillation amplitude are described by a langevin equation and its associated fokker planck equation respectively one method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values obtained from data processing by taking the short time limit of the first two transition moments however this limit estimation loses robustness in some situations for instance when the data are band pass filtered to isolate the spectral contents of the oscillatory phenomena of interest in this paper we use a robust alternative where the adjoint fokker planck equation is solved to compute kramers moyal coefficients exactly and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales the method is illustrated with a stochastic van der pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors where system identification is highly relevant to control

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

numerical study of blow up and dispersive shocks in solutions to generalized korteweg de vries equations abstract we present a detailed numerical study of solutions to general korteweg de vries equations with critical and supercritical nonlinearity both in the context of dispersive shocks and blow up we study the stability of solitons and show that they are unstable against being radiated away and blow up in the l 2 critical case the blow up mechanism by martel merle and raphael can be numerically identified in the limit of small dispersion it is shown that a dispersive shock always appears before an eventual blow up in the latter case always the first soliton to appear will blow up it is shown that the same type of blow up as for the perturbations of the soliton can be observed which indicates that the theory by martel merle and raphael is also applicable to initial data with a mass much larger than the soliton mass we study the scaling of the blow up time t in dependence of the small dispersion parameter and find an exponential dependence t and that there is a minimal blow up time t 0 greater than the critical time of the corresponding hopf solution for 0 to study the cases with blow up in detail we apply the first dynamic rescaling for generalized korteweg de vries equations this allows to identify the type of the singularity

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

measuring functional connectivity using meg methodology and comparison with fcmri functional connectivity fc between brain regions is thought to be central to the way in which the brain processes information abnormal connectivity is thought to be implicated in a number of diseases the ability to study fc is therefore a key goal for neuroimaging functional connectivity fc mri has become a popular tool to make connectivity measurements but the technique is limited by its indirect nature a multimodal approach is therefore an attractive means to investigate the electrodynamic mechanisms underlying hemodynamic connectivity in this paper we investigate resting state fc using fcmri and magnetoencephalography meg in fcmri we exploit the advantages afforded by ultra high magnetic field in meg we apply envelope correlation and coherence techniques to source space projected meg signals we show that beamforming provides an excellent means to measure fc in source space using meg data however care must be taken when interpreting these measurements since cross talk between voxels in source space can potentially lead to spurious connectivity and this must be taken into account in all studies of this type we show good spatial agreement between fc measured independently using meg and fcmri fc between sensorimotor cortices was observed using both modalities with the best spatial agreement when meg data are filtered into the band this finding helps to reduce the potential confounds associated with each modality alone while it helps reduce the uncertainties in spatial patterns generated by meg brought about by the ill posed inverse problem addition of electrodynamic metric confirms the neural basis of fcmri measurements finally we show that multiple meg based fc metrics allow the potential to move beyond what is possible using fcmri and investigate the nature of electrodynamic connectivity our results extend those from previous studies and add weight to the argument that neural oscillations are intimately related to functional connectivity and the bold response

an efficient technique to find semi analytical solutions for higher order multi point boundary value problems abstract a new semi analytical algorithm is presented to solve general multi point boundary value problems this method can be applied on nth order linear nonlinear singular and nonsingular multi point boundary value problems mathematical base of the method is presented convergence of the method is proved also the algorithm is applied to solve multi point boundary value problems including nonlinear sixth order nonlinear singular second order five point boundary value problems and a singularly perturbed boundary value problem comparison results show that the new method works more accurate than the other methods

direct search methods on parallel machines direct search methods are methods designed to solve unconstrained minimization problems of the form mathop min limits x in mathbb r n f x where f n these methods are distinguished by the fact that they neither use nor require explicit derivative information the search for a local minimizer is driven solely by function information popular methods in this class include the factorial design algorithm of box 1 the pattern search algorithm of hooke and jeeves 4 and the simplex method of neider and mead 5

the effect of dropout on the efficiency of d optimal designs of linear mixed models dropout is often encountered in longitudinal data optimal designs will usually not remain optimal in the presence of dropout in this paper we study d optimal designs for linear mixed models where dropout is encountered moreover we estimate the efficiency loss in cases where a d optimal design for complete data is chosen instead of that for data with dropout two types of monotonically decreasing response probability functions are investigated to describe dropout our results show that the location of d optimal design points for the dropout case will shift with respect to that for the complete and uncorrelated data case owing to this shift the information collected at the d optimal design points for the complete data case does not correspond to the smallest variance we show that the size of the displacement of the time points depends on the linear mixed model and that the efficiency loss is moderate

classification of temporal sequences via prediction using the simple recurrent neural network abstract an approach to classify temporal sequences using the simple recurrent neural network srnn is developed in this paper a classification problem is formulated as a component prediction problem and two training methods are described to train a single srnn to predict the components of temporal sequences belonging to multiple classes issues related to the selection of the dimension of the context vector and the influence of the context vector on classification are identified and investigated the use of a different initial context vector for each class is proposed as a means to improve classification and a classification rule which incorporates the different initial context vectors is formulated a systematic method in which the srnn is trained with noisy exemplars is developed to enhance the classification performance of the network a 4 class localized object classification problem is selected to demonstrate that a a single srnn can be trained to classify real multi class sequences via component prediction b the classification accuracy can be improved by using a distinguishing initial context vector for each class and c the classification accuracy of the srnn can be improved significantly by using the distinguishing initial context vector in conjunction with the systematic re training method it is concluded that through the approach developed in this paper the srnn can robustly classify temporal sequences which may have an unequal number of components

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

source stability index a novel beamforming based localisation metric many experimental studies into human brain function now use magnetoencephalography meg to non invasively investigate human neuronal activity a number of different analysis techniques use the observed magnetic fields outside of the head to estimate the location and strength of the underlying neural generators one such technique a spatial filtering method known as beamforming produces whole head volumetric images of activation typically a differential power map throughout the head is generated between a time window containing the response to a stimulus of interest and a window containing background brain activity a statistical test is normally performed to reveal locations which show a significantly different response in the presence of the stimulus despite this being a widely used measure for both phase locked and non phase locked information it requires a number of assumptions namely that the baseline activity defined is stable and also that a change in total power is the most effective way of revealing the neuronal sources required for the task this paper introduces a metric which evaluates the consistency of the response at each location within a cortical volume such a method of localisation negates the need for a baseline period of activity to be defined and also moves away from simply considering the energy content of brain activity the paper presents both simulated and real data it demonstrates that this new metric of stability is able to more accurately and crucially more reliably draw inferences about neuronal sources of interest

detection and remediation of stagnation in the nelder mead algorithm using a sufficient decrease condition the nelder mead algorithm can stagnate and converge to a nonoptimal point even for very simple problems in this note we propose a test for sufficient decrease which if passed for all iterations will guarantee convergence of the nelder mead iteration to a stationary point if the objective function is smooth and the diameters of the nelder mead simplices converge to zero failure of this condition is an indicator of potential stagnation as a remedy we propose a new step which we call an oriented restart that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point we also give results that apply when the objective function is a low amplitude perturbation of a smooth function we illustrate our results with some numerical examples

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

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

video denoising deblocking and enhancement through separable 4 d nonlocal spatiotemporal transforms we propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences the algorithm implements the paradigm of nonlocal grouping and collaborative filtering where a higher dimensional transform domain representation of the observations is leveraged to enforce sparsity and thus regularize the data 3 d spatiotemporal volumes are constructed by tracking blocks along trajectories defined by the motion vectors mutually similar volumes are then grouped together by stacking them along an additional fourth dimension thus producing a 4 d structure termed group where different types of data correlation exist along the different dimensions local correlation along the two dimensions of the blocks temporal correlation along the motion trajectories and nonlocal spatial correlation i e self similarity along the fourth dimension of the group collaborative filtering is then realized by transforming each group through a decorrelating 4 d separable transform and then by shrinkage and inverse transformation in this way the collaborative filtering provides estimates for each volume stacked in the group which are then returned and adaptively aggregated to their original positions in the video the proposed filtering procedure addresses several video processing applications such as denoising deblocking and enhancement of both grayscale and color data experimental results prove the effectiveness of our method in terms of both subjective and objective visual quality and show that it outperforms the state of the art in video denoising

exploring the 3d geometry of the diffusion kurtosis tensor impact on the development of robust tractography procedures and novel biomarkers diffusion kurtosis imaging dki is a diffusion weighted technique which overcomes limitations of the commonly used diffusion tensor imaging approach this technique models non gaussian behaviour of water diffusion by the diffusion kurtosis tensor kt which can be used to provide indices of tissue heterogeneity and a better characterisation of the spatial architecture of tissue microstructure in this study the geometry of the kt is elucidated using synthetic data generated from multi compartmental models where diffusion heterogeneity between intra and extra cellular media is taken into account as well as the sensitivity of the results to each model parameter and to synthetic noise furthermore based on the assumption that the maxima of the kt are distributed perpendicularly to the direction of well aligned fibres a novel algorithm for estimating fibre direction directly from the kt is proposed and compared to the fibre directions extracted from dki based orientation distribution function odf estimates previously proposed in the literature synthetic data results showed that for fibres crossing at high intersection angles direction estimates extracted directly from the kt have smaller errors than the dki based odf estimation approaches dki odf nevertheless the proposed method showed smaller angular resolution and lower stability to changes of the simulation parameters on real data tractography performed on these kt fibre estimates suggests a higher sensitivity than the dki based odf in resolving lateral corpus callosum fibres reaching the pre central cortex when diffusion acquisition is performed with five b values using faster acquisition schemes kt based tractography did not show improved performance over the dki odf procedures nevertheless it is shown that direct kt fibre estimates are more adequate for computing a generalised version of radial kurtosis maps

an analysis of noise in recurrent neural networks convergence and generalization concerns the effect of noise on the performance of feedforward neural nets we introduce and analyze various methods of injecting synaptic noise into dynamically driven recurrent nets during training theoretical results show that applying a controlled amount of noise during training may improve convergence and generalization performance we analyze the effects of various noise parameters and predict that best overall performance can be achieved by injecting additive noise at each time step noise contributes a second order gradient term to the error function which can be viewed as an anticipatory agent to aid convergence this term appears to find promising regions of weight space in the beginning stages of training when the training error is large and should improve convergence on error surfaces with local minima the first order term is a regularization term that can improve generalization specifically it can encourage internal representations where the state nodes operate in the saturated regions of the sigmoid discriminant function while this effect can improve performance on automata inference problems with binary inputs and target outputs it is unclear what effect it will have on other types of problems to substantiate these predictions we present simulations on learning the dual parity grammar from temporal strings for all noise models and present simulations on learning a randomly generated six state grammar using the predicted best noise model

a general linear model for meg beamformer imaging a new general linear model glm beamformer method is described for processing magnetoencephalography meg data a standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space a hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band not necessary in the case of sustained dc fields enabling the general linear model to be applied and a volumetric t statistic image to be determined the new method is illustrated by a two source simulation sustained field and 20 hz and is shown to provide accurate localization the method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes respectively in the case of a scintillating scotoma the new method brings the advantages of the general linear model to the analysis of meg data and should prove useful for the localization of changing patterns of activity across all frequency ranges including dc sustained fields

wiener system modelling by exponentially weighted aggregation abstractin the paper the aggregation algorithm for wiener system modelling is proposed the method uses exponential weights to combine aggregate models from a given collection of d linear dynamic and dm nonlinear static models of the genuine system blocks that can be a priori hypotheses other system identification outcomes etc the resulting model has a noteworthy property it is almost as accurate as the best hypothetical wiener model built from a given collection this is caused by the fact that the error introduced by the aggregation routine decreases in the mean squared sense with growing number of measurements n as fast as cqn 1ln dmd where c and q are known constants simulations confirm theoretical findings and demonstrate applicability of the algorithm in engineering problems for small and moderate measurement data sets

robustness in semantic networks based on cliques abstract here we present a study on how the structure of semantic networks based on cliques specifically article titles behaves when vertex removal strategies i e random and uniform vertex removal rur highest degree vertex removal hdr and highest intermediation centrality vertex removal hicr are applied to this type of network we propose a method for calculation of the average size of the small components and we identify the existence of a fraction f p where the topological structure of the network changes semantic networks based on cliques maintain the small world phenomenon when subjected to rur hdr and hicr for fractions of removed vertices less than or equal to f p

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

robust automatic target recognition using a localized boundary representation abstract a localized classification approach which includes a localized target boundary representation a set of local features to characterize parts of a target boundary and a feature matching method is developed to classify highly degraded targets each pixel on the target boundary is represented by the perpendicular euclidean distance between the boundary pixel and the chord connecting the end points of a window centered on the boundary pixel the resulting localized representation is quite robust with respect to noise and missing segments in the targets a local feature is the segment of the localized representation between two points selected on the target boundary the two points on the boundary may be specified or randomly selected the reference features of a hypothesized target class are compared with segments of the localized representation of the test target to determine a dissimilarity measure between the hypothesized target class and the test target segments of the test target may also be matched with the reference localized contour sequences of the targets the test target is assigned to a target class using a minimum mismatch rule results from a series of experiments conducted on three targets show that it is possible to classify targets experiencing high levels of noise and high percentages of missing segments in partial targets

a neural network approach to robust shape classification abstract a neural network approach for the classification of closed planar shapes is described the primary foci are the development of an effective representation for planar shapes which may be used in conjunction with neural nets the selection of a suitable neural network structure and determining training methods to increase the degree of robustness in classification a three layer perception using backpropagation is initially trained with contour sequences of noisefree reference shapes and its generalization capability is demonstrated the network is then gradually retrained with increasingly noisy data to improve the robustness of the classifier the advantages and improvement in robustness using this extended training scheme are shown and typical classification results are presented

the copula echo state network echo state networks esns constitute a novel approach to recurrent neural network rnn training with an rnn the reservoir being generated randomly and only a readout being trained using a simple computationally efficient algorithm esns have greatly facilitated the practical application of rnns outperforming classical approaches on a number of benchmark tasks this paper studies the formulation of a class of copula based semiparametric models for sequential data modeling characterized by nonparametric marginal distributions modeled by postulating suitable echo state networks and parametric copula functions that help capture all the scale free temporal dependence of the modeled processes we provide a simple algorithm for the data driven estimation of the marginal distribution and the copula parameters of our model under the maximum likelihood framework we exhibit the merits of our approach by considering a number of applications as we show our method offers a significant enhancement in the dynamical data modeling capabilities of esns without significant compromises in the algorithm s computational efficiency

automatic parameter estimation for the discrete algebraic reconstruction technique dart computed tomography ct is a technique for noninvasive imaging of physical objects in the discrete algebraic reconstruction technique dart prior knowledge about the material s densities is exploited to obtain high quality reconstructed images from a limited number of its projections in practice this prior knowledge is typically not readily available here a fully automatic method called projection distance minimization dart pdm dart is proposed in which the optimal grey level parameters are adaptively estimated during the reconstruction process to apply pdm dart only the number of different grey levels should be known in advance simulation as well as real ct experiments show that pdm dart is capable of computing reconstructed images of which the quality is similar to reconstructions computed by conventional dart based on exact prior knowledge thereby eliminating the need for tedious and error prone user interaction