fuzzy wavelet extreme learning machine abstract incorporating the time frequency localization properties of wavelets and the learning abilities of neural network nn the approximate reasoning characteristics of fuzzy inference system and the advantages of elm one pass learning and good generalization performance at extremely fast learning speed can exhibit their characteristics to reveal an effective solution in many applications following that this paper presents a novel structure called fuzzy wavelet extreme learning machine fw elm the main objectives of fw elm are to significantly reduce the network complexity by reducing the number of linear learning parameters and to decrease the sensitivity to random initialization procedure while the acceptable accuracy and generalization performances are preserved in the proposed structure each fuzzy rule corresponds to a sub wavelet neural network and consists of wavelets with different dilations and translations in this model in order to achieve a balance between network complexity and performance accuracy in the then part of each fuzzy rule one coefficient is considered for each two inputs in this work first the equivalence of an fw model and an slfn is proved and then elm can be directly applied to the model all free parameters of membership functions and wavelet coefficients are generated randomly and only the output weights are determined analytically using a one pass learning method to evaluate fw elm it is compared with popular fuzzy models like os fuzzy elm simpl ets anfis and several other relevant algorithms such as elm bp and svr on various benchmark datasets simulation results demonstrate the remarkable efficiency resulting from the proposed approach performance accuracy of fw elm is shown to be comparable with os fuzzy elm and better than the rest of the well known methods

computation in a single neuron hodgkin and huxley revisited a spiking neuron computes by transforming a complex dynamical input into a train of action potentials or spikes the computation performed by the neuron can be formulated as dimensional reduction or feature detection followed by a nonlinear decision function over the low dimensional space generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low dimensional features from experimental data and information theory can be used to evaluate the quality of the low dimensional approximation we apply these methods to analyze the simplest biophysically realistic model neuron the hodgkin huxley hh model using this system to illustrate the general methodological issues we focus on the features in the stimulus that trigger a spike explicitly eliminating the effects of interactions between spikes one can approximate this triggering feature space as a two dimensional linear subspace in the high dimensional space of input histories capturing in this way a substantial fraction of the mutual information between inputs and spike time we find that an even better approximation however is to describe the relevant subspace as two dimensional but curved in this way we can capture 90 of the mutual information even at high time resolution our analysis provides a new understanding of the computational properties of the hh model while it is common to approximate neural behavior as integrate and fire the hh model is not an integrator nor is it well described by a single threshold

hierarchical computation in the canonical auditory cortical circuit sensory cortical anatomy has identified a canonical microcircuit underlying computations between and within layers this feed forward circuit processes information serially from granular to supragranular and to infragranular layers how this substrate correlates with an auditory cortical processing hierarchy is unclear we recorded simultaneously from all layers in cat primary auditory cortex ai and estimated spectrotemporal receptive fields strfs and associated nonlinearities spike triggered averaged strfs revealed that temporal precision spectrotemporal separability and feature selectivity varied with layer according to a hierarchical processing model strfs from maximally informative dimension mid analysis confirmed hierarchical processing of two cooperative mids identified for each neuron the first comprised the majority of stimulus information in granular layers second mid contributions and nonlinear cooperativity increased in supragranular and infragranular layers the ai microcircuit provides a valid template for three independent hierarchical computation principles increases in processing complexity strf cooperativity and nonlinearity correlate with the synaptic distance from granular layers

from spiking neurons to rate models a cascade model as an approximation to spiking neuron models with refractoriness a neuron that is stimulated repeatedly by the same time dependent stimulus exhibits slightly different spike timing at each trial we compared the exact solution of the time dependent firing rate for a stochastically spiking neuron model with refractoriness spike response model with that of an inhomogeneous poisson process subject to the same stimulus to arrive at a mapping between the two models we used alternatively i a systematic parameter free volterra expansion of the exact solution or ii a linear filter combined with nonlinear poisson rate model linear nonlinear poisson cascade model with a single free parameter both the cascade model and the second order volterra model showed excellent agreement with the exact rate dynamics of the spiking neuron model with refractoriness even for strong and rapidly changing input cascade rate models are widely used in systems neuroscience our method could help to connect experimental rate measurements to the theory of spiking neurons

a regularized monotonic fuzzy support vector machine model for data mining with prior knowledge incorporating prior knowledge into data mining is an interesting but challenging problem and this study proposes a novel fuzzy support vector machine svm model to explore this issue it considers the fact that in many applications each input point may not be exactly labeled as one particular class and thus it applies a fuzzy membership to each input point it also utilizes expert knowledge concerning the monotonic relations between the response and predictor variables which is represented in the form of monotonicity constraints we formulate the classification problem of a monotonically constrained fuzzy svm called a monotonic fsvm derive its dual optimization problem and theoretically analyze its monotonic property the tikhonov regularization method is further applied to ensure that the solution is unique and bounded a new measure i e the frequency monotonicity rate is proposed to evaluate the ability of the model to retain the monotonicity the results of the experiments on real world and synthetic datasets show that this method which considers different contributions of each data and the prior knowledge of the monotonicity has a number of advantages with regard to predictive ability and retaining monotonicity over the original fsvm and svm models when applied to classification problems

limited reasoning in first order knowledge bases abstract in traditional formal approaches to knowledge representation agents are assumed to believe all the logical consequences of their knowledge bases as a result reasoning in the first order case becomes undecidable since real agents are constrained by resource limitations it seems appropriate to look for weaker forms of reasoning with better computational properties one way to approach the problem is by modeling belief reasoning can then be understood as the question whether a belief follows from believing the sentences in the knowledge base this paper proposes a model of belief which combines features from both possible world semantics and relevance logic among the important features of this logic are its treatment of quantifying in which allows us to distinguish between knowing that and knowing who and the decidability of the implication problem for belief the decidability result follows from a close connection between this notion of belief and an existing decidable form of first order entailment

bayesian modeling and classification of neural signals identifying and classifying action potential shapes in extracellular neural waveforms have long been the subject of research and although several algorithms for this purpose have been successfully applied their use has been limited by some outstanding problems the first is how to determine shapes of the action potentials in the waveform and second how to decide how many shapes are distinct a harder problem is that action potentials frequently overlap making difficult both the determination of the shapes and the classification of the spikes in this report a solution to each of these problems is obtained by applying bayesian probability theory by defining a probabilistic model of the waveform the probability of both the form and number of spike shapes can be quantified in addition this framework is used to obtain an efficient algorithm for the decomposition of arbitrarily complex overlap sequences this algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits

multiple kernel clustering based on centered kernel alignment multiple kernel clustering mkc which performs kernel based data fusion for data clustering is an emerging topic it aims at solving clustering problems with multiple cues most mkc methods usually extend existing clustering methods with a multiple kernel learning mkl setting in this paper we propose a novel mkc method that is different from those popular approaches centered kernel alignment an effective kernel evaluation measure is employed in order to unify the two tasks of clustering and mkl into a single optimization framework to solve the formulated optimization problem an efficient two step iterative algorithm is developed experiments on several uci datasets and face image datasets validate the effectiveness and efficiency of our mkc algorithm

estimating information rates with confidence intervals in neural spike trains information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus a related work kennel shlens abarbanel chichilnisky 2005 demonstrated how to reliably estimate with a bayesian confidence interval the entropy rate from a discrete observed time series we extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus the average and specific mutual information rates our estimator makes few assumptions about the underlying neural dynamics shows excellent performance in experimentally relevant regimes and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train we validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance finally we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder

connection methods in linear logic and proof nets construction linear logic ll is the logical foundation of some type theoretic languages and also of environments for specification and theorem proving in this paper we analyse the relationships between the proof net notion of ll and the connection notion used for efficient proof search in different logics aiming at using proof nets as a tool for automated deduction in linear logic we define a connection based characterization of provability in multiplicative linear logic mll we show that an algorithm for proof net construction can be seen as a proof search connection method this central result is illustrated with a specific algorithm that is able to construct for a provable mll sequent a set of connections a proof net and a sequent proof from these results we expect to extend to other ll fragments we analyse what happens with the additive connectives of ll by tackling the additive fragment in a similar way

feature selection in simple neurons how coding depends on spiking dynamics the relationship between a neuron s complex inputs and its spiking output defines the neuron s coding strategy this is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes and a nonlinear function that relates stimulus to firing probability in many sensory systems these two components of the coding strategy are found to adapt to changes in the statistics of the inputs in such a way as to improve information transmission here we show for two simple neuron models how feature selectivity as captured by the spike triggered average depends on both the parameters of the model and the statistical characteristics of the input

trade off between curvature tuning and position invariance in visual area v4 humans can rapidly recognize a multitude of objects despite differences in their appearance the neural mechanisms that endow high level sensory neurons with both selectivity to complex stimulus features and tolerance or invariance to identity preserving transformations such as spatial translation remain poorly understood previous studies have demonstrated that both tolerance and selectivity to conjunctions of features are increased at successive stages of the ventral visual stream that mediates visual recognition within a given area such as visual area v4 or the inferotemporal cortex tolerance has been found to be inversely related to the sparseness of neural responses which in turn was positively correlated with conjunction selectivity however the direct relationship between tolerance and conjunction selectivity has been difficult to establish with different studies reporting either an inverse or no significant relationship to resolve this we measured v4 responses to natural scenes and using recently developed statistical techniques we estimated both the relevant stimulus features and the range of translation invariance for each neuron focusing the analysis on tuning to curvature a tractable example of conjunction selectivity we found that neurons that were tuned to more curved contours had smaller ranges of position invariance and produced sparser responses to natural stimuli these trade offs provide empirical support for recent theories of how the visual system estimates 3d shapes from shading and texture flows as well as the tiling hypothesis of the visual space for different curvature values

an efficient gaussian kernel optimization based on centered kernel polarization criterion the formulated criterion has a defined geometrical significance the approximate criterion has a determined global minimum point with weaker constraints the influence of iteration parameters on the global optimal point is slight the proposed criterion is extended to solve multiclass problems the success of kernel based learning methods is heavily dependent on the choice of a kernel function and proper setting of its parameters in this paper we optimize the gaussian kernel for binary class problems by using centered kernel polarization criterion this criterion is an extension of kernel polarization and a simplified style of centered kernel alignment compared with formulated kernel polarization criterion the proposed criterion has a defined geometrical significance and it can locate the global optimal point with less influence of threshold selection furthermore the approximate criterion function can be proved to have a determined global minimum point by adopting the euler maclaurin formula under weaker conditions in addition taking the preservation of within class local structure into account we present an evaluation criterion named local multiclass centered kernel polarization in multiclass classification scenario comparative experiments are conducted on some benchmark examples with three gaussian kernel based learning methods and the results well demonstrate the effectiveness and efficiency of the proposed quality measures

characterizing responses of translation invariant neurons to natural stimuli maximally informative invariant dimensions the human visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions especially in the higher cortical areas the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations such as image translation due to the strong nonlinearities necessary to achieve both the selectivity and invariance characterizing and predicting the response patterns of these neurons represents a formidable computational challenge a related problem is that such neurons are poorly driven by randomized inputs such as white noise and respond strongly only to stimuli with complex high order correlations such as natural stimuli here we describe a novel two step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli one step in the optimization is finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image the estimates of the locations that triggered the response are updated in the next step under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position the most likely location is the one that has the largest projection on the estimate of the template the algorithm shows quick convergence during optimization and the estimation results are reliable even in the regime of small signal to noise ratios when we apply the algorithm to responses of complex cells in the primary visual cortex v1 to natural movies we find that responses of the majority of cells were significantly better described by translation invariant models based on one template compared with position specific models with several relevant features

centered kernel alignment inspired fuzzy support vector machine abstract support vector machine svm is a theoretically well motivated algorithm developed from statistical learning theory which has shown impressive performance in many fields in spite of its success it still suffers from the noise sensitivity problem originating from the assumption that each training point has equal importance or weight in the training process to relax this problem the svm was extended to the fuzzy svm fsvm by applying a fuzzy membership to each training point such that different training points can make different contributions to the learning of the decision surface although well determined fuzzy memberships can improve classification performance there are no general guidelines for their construction in this paper inspired by the centered kernel alignment cka which measures the degree of similarity between two kernels or kernel matrices we propose a new fuzzy membership function calculation method in which a heuristic function derived from the cka is used to calculate the dependence between a data point and its associated label although the cka induced fsvm is similar to the kernel target alignment kta induced fsvm there is actually a critical difference without that centering the definition of alignment does not correlate well with the performance of learning machines extensive experiments are performed on real world data sets from the uci benchmark repository and the application domain of computational biology which validate the superiority of the proposed fsvm model in terms of several classification performance measures

a phase transition in the first passage of a brownian process through a fluctuating boundary with implications for neural coding finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple looking problem of vast practical importance in physics biology chemistry neuroscience economics and industrial engineering problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding such as neuronal integrators with irregular inputs and internal noise we show that the probability p t that a gauss markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary as measured by its holder exponent h the critical value occurs when the roughness of the boundary equals the roughness of the process so for diffusive processes the critical value is hc 1 2 for smoother boundaries h 1 2 the probability density is a continuous function of time for rougher boundaries h 1 2 the probability is concentrated on a cantor like set of zero measure the probability density becomes divergent almost everywhere either zero or infinity the critical point hc 1 2 corresponds to a widely studied case in the theory of neural coding in which the external input integrated by a model neuron is a white noise process as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs we argue that this transition corresponds to a sharp boundary between rate codes in which the neural firing probability varies smoothly and temporal codes in which the neuron fires at sharply defined times regardless of the intensity of internal noise

fuzzy support vector machines a support vector machine svm learns the decision surface from two distinct classes of the input points in many applications each input point may not be fully assigned to one of these two classes in this paper we apply a fuzzy membership to each input point and reformulate the svms such that different input points can make different contributions to the learning of decision surface we call the proposed method fuzzy svms fsvms

comparison of information and variance maximization strategies for characterizing neural feature selectivity this paper compares several statistical methods for analyzing neural feature selectivity with natural stimuli despite the non gaussian character of correlations in natural stimuli several relevant stimulus dimensions can be found by maximizing either information or as is demonstrated here variance in the case of information the relevance of each dimension is quantified by a kullback leibler divergence between the full input probability distribution and that across inputs associated with positive neural responses both projected onto that dimension we demonstrate that least square matching of the nonlinear prediction based on several dimensions relevant to the recorded spike trains yields an optimization scheme similar to information maximization the relevant dimensions are found as those that capture the most variance in neural response the variance along a stimulus dimension is given by a renyi divergence of order 2 instead of the kullback leibler divergence used for maximizing information statistical errors expected for the two schemes are shown to be similar through both analytical and numerical calculations however in the asymptotic limit of large spike numbers maximizing information results in smaller errors than variance optimization numerical simulations for model cells with different noise levels show that this trend persists and possibly increases when the number of spikes decreases this makes the problem of finding relevant dimensions one of the examples where information theoretic approaches are no more data limited than the variance based measures variance and information optimization also outperform methods based on the spike triggered average for all numbers of spikes and neural noise levels

a decidable fragment of predicate calculus abstract we describe a decision procedure for what we call direct predicate calculus this fragment of predicate logic coincides with those formulas that can be proved in the gentzen sequent calculus with the rule of contraction eliminated it arose by thinking about what kinds of inferences should be considered obvious and in that sense characterizes fragments of logic by the tools available for proving results rather than by syntactic properties of formulas

a kernel fuzzy c means clustering based fuzzy support vector machine algorithm for classification problems with outliers or noises the support vector machine svm has provided higher performance than traditional learning machines and has been widely applied in real world classification problems and nonlinear function estimation problems unfortunately the training process of the svm is sensitive to the outliers or noises in the training set in this paper a common misunderstanding of gaussian function based kernel fuzzy clustering is corrected and a kernel fuzzy c means clustering based fuzzy svm algorithm kfcm fsvm is developed to deal with the classification problems with outliers or noises in the kfcm fsvm algorithm we first use the fcm clustering to cluster each of two classes from the training set in the high dimensional feature space the farthest pair of clusters where one cluster comes from the positive class and the other from the negative class is then searched and forms one new training set with membership degrees finally we adopt fsvm to induce the final classification results on this new training set the computational complexity of the kfcm fsvm algorithm is analyzed a set of experiments is conducted on six benchmarking datasets and four artificial datasets for testing the generalization performance of the kfcm fsvm algorithm the results indicate that the kfcm fsvm algorithm is robust for classification problems with outliers or noises

classification in a normalized feature space using support vector machines this paper discusses classification using support vector machines in a normalized feature space we consider both normalization in input space and in feature space exploiting the fact that in this setting all points lie on the surface of a unit hypersphere we replace the optimal separating hyperplane by one that is symmetric in its angles leading to an improved estimator evaluation of these considerations is done in numerical experiments on two real world datasets the stability to noise of this offset correction is subsequently investigated as well as its optimality

analyzing neural responses to natural signals maximally informative dimensions we propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli that are nongaussian and exhibit strong correlations we have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high dimensional stimulus space but within this subspace the responses can be arbitrarily nonlinear existing analysis methods are based on correlation functions between stimuli and responses but these methods are guaranteed to work only in the case of gaussian stimulus ensembles as an alternative to correlation functions we maximize the mutual information between the neural responses and projections of the stimulus onto low dimensional subspaces the procedure can be done iteratively by increasing the dimensionality of this subspace those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace if the dimensionality of the relevant subspace indeed is small it becomes feasible to map the neuron s input output function even under fully natural stimulus conditions these ideas are illustrated in simulations on model visual and auditory neurons responding to natural scenes and sounds respectively

dynamical response of the hodgkin huxley model in the high input regime the response of the hodgkin huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post synaptic potentials is analyzed in detail the model is examined in its three fundamental dynamical regimes silence bistability and repetitive firing its response is characterized in terms of statistical indicators interspike interval distributions and their first moments as well as of dynamical indicators autocorrelation functions and conditional entropies in the silent regime the coexistence of two different coherence resonances is revealed one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state the second one at intermediate noise variance is associated with the regularization of the sequence of spikes emitted by the neuron bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations in the repetitive firing regime a maximization of incoherence is observed at finite noise variance finally the mechanisms responsible for the different features appearing in the interspike interval distributions like multimodality and exponential tails are clearly identified in the various regimes

reduction of the hodgkin huxley equations to a single variable threshold model it is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold here we pursue the question of whether this picture can be justified and study the four dimensional neuron model of hodgkin and huxley as a concrete example the model is approximated by a response kernel expansion in terms of a single variable the membrane voltage the first order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential higher order kernels take care of nonlinear interactions between input spikes in contrast to the standard volterra expansion the kernels depend on the firing time of the most recent output spike in particular a zero order kernel that describes the shape of the spike and the typical after potential is included our model neuron fires if the membrane voltage given by the truncated response kernel expansion crosses a threshold the threshold model is tested on a spike train generated by the hodgkin huxley model with a stochastic input current we find that the threshold model predicts 90 percent of the spikes correctly our results show that to good approximation the description of a neuron as a threshold element can indeed be justified

a new fuzzy support vector machine to evaluate credit risk due to recent financial crises and regulatory concerns financial intermediaries credit risk assessment is an area of renewed interest in both the academic world and the business community in this paper we propose a new fuzzy support vector machine to discriminate good creditors from bad ones because in credit scoring areas we usually cannot label one customer as absolutely good who is sure to repay in time or absolutely bad who will default certainly our new fuzzy support vector machine treats every sample as both positive and negative classes but with different memberships by this way we expect the new fuzzy support vector machine to have more generalization ability while preserving the merit of insensitive to outliers as the fuzzy support vector machine svm proposed in previous papers we reformulate this kind of two group classification problem into a quadratic programming problem empirical tests on three public datasets show that it can have better discriminatory power than the standard support vector machine and the fuzzy support vector machine if appropriate kernel and membership generation method are chosen

logical linear operators for image curves we propose a language for designing image measurement operators suitable for early vision we refer to them as logical linear l l operators since they unify aspects of linear operator theory and boolean logic a family of these operators appropriate for measuring the low order differential structure of image curves is developed these l l operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld tangential conditions guarantee continuity while normal conditions select and categorize contrast profiles the resulting operators allow for coarse measurement of curvilinear differential structure orientation and curvature while successfully segregating edge and line like features by thus reducing the incidence of false positive responses these operators are a substantial improvement over thresholded linear operators which attempt to resolve the same class of features

multimodal transition and stochastic antiresonance in squid giant axons the experimental data of takahashi et al physica d 43 318 1990 on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the hodgkin huxley model the minimum of the firing rate as a function of the stimulus amplitude i 0 in the high frequency regime is due to the multimodal transition below this singular point only odd multiples of the driving period remain and the system is sensitive to noise the coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance the model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition a linear relation of output frequency vs i 0 above the transition is also confirmed

algorithms for learning kernels based on centered alignment this paper presents new and effective algorithms for learning kernels in particular as shown by our empirical results these algorithms consistently outperform the so called uniform combination solution that has proven to be difficult to improve upon in the past as well as other algorithms for learning kernels based on convex combinations of base kernels in both classification and regression our algorithms are based on the notion of centered alignment which is used as a similarity measure between kernels or kernel matrices we present a number of novel algorithmic theoretical and empirical results for learning kernels based on our notion of centered alignment in particular we describe efficient algorithms for learning a maximum alignment kernel by showing that the problem can be reduced to a simple qp and discuss a one stage algorithm for learning both a kernel and a hypothesis based on that kernel using an alignment based regularization our theoretical results include a novel concentration bound for centered alignment between kernel matrices the proof of the existence of effective predictors for kernels with high alignment both for classification and for regression and the proof of stability based generalization bounds for a broad family of algorithms for learning kernels based on centered alignment we also report the results of experiments with our centered alignment based algorithms in both classification and regression

a decision procedure revisited notes on direct logic linear logic and its implementation abstract this paper studies decidable fragments of predicate calculus we will focus on the structure of direct predicate calculus as defined in ketonen and weyhrauch 1984 in the light of the recent work of girard girard 1987 1988 on linear logic several graph theoretic results are used to prove correspondences between systems of natural deduction direct predicate logic and linear logic in addition the implementation of a decision procedure for direct predicate logic is sketched

proofs without syntax proofs are traditionally syntactic inductively generated objects this paper presents an abstract mathematical formulation of propositional calcu lus propositional logic in which proofs are combinatorial graph theoretic rather than syntactic it defines a combinatorial proof of a proposition 0 as a graph homomorphism h c g f where g j is a graph associated with and c is a coloured graph the main theorem is soundness and completeness f is true if and only if there exists a combinatorial proof h c g p

population encoding with hodgkin huxley neurons the recovery of weak stimuli encoded with a population of hodgkin huxley neurons is investigated in the absence of a stimulus the hodgkin huxley neurons are assumed to be tonically spiking the methodology employed calls for 1 finding an input output i o equivalent description of the hodgkin huxley neuron and 2 devising a recovery algorithm for stimuli encoded with the i o equivalent neuron s a hodgkin huxley neuron with multiplicative coupling is i o equivalent with an integrate and fire neuron with a variable threshold sequence for bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a nyquist type rate condition is satisfied a hodgkin huxley neuron with additive coupling and deterministic conductances is first order i o equivalent with a project integrate and fire neuron that integrates a projection of the stimulus on the phase response curve the stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals a hodgkin huxley neuron with additive coupling and stochastic conductances is shown to be first order i o equivalent with a project integrate and fire neuron with random thresholds for stimuli modeled as elements of sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion finally all previous recovery results of stimuli encoded with hodgkin huxley neurons with multiplicative and additive coupling and deterministic and stochastic conductances are extended to stimuli encoded with a population of hodgkin huxley neurons

application of multi class fuzzy support vector machine classifier for fault diagnosis of wind turbine this paper presents an approach for fault diagnosis of wind turbine wt based on multi class fuzzy support vector machine fsvm classifier in this method empirical mode decomposition is adopted to extract fault feature vectors from vibration signals fsvm is used for solving classification problem with outliers or noises where kernel fuzzy c means clustering algorithm and particle swarm optimization algorithm are applied to calculate fuzzy membership and optimize the parameters of kernel function of fsvm respectively in addition to study the performance of the proposed approach another two widely used methods named back propagation neural network and standard support vector machine are studied and compared discrete wavelet transform is also used to extract fault feature vectors to validate the proposed approach a direct drive wt test rig is constructed and the experiments are carried out the experimental results show that the proposed approach is an effective fault diagnosis method for wt which has a better performance and can achieve higher diagnostic accuracy a multi class fsvm classifier constructed by one against other method is used for fault diagnosis of wind turbine kfcm algorithm is extended to calculate fuzzy membership values of training samples for a multi class fsvm classifier pso algorithm is applied to optimize the parameters of the kernel function of fsvm fault diagnosis steps are presented and the effectiveness of the proposed method is validated

learning quadratic receptive fields from neural responses to natural stimuli models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high dimensional input in this review we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection that is the neuron is sensitive to the local covariance structure of the signal preceding the spike to infer this quadratic dependence in the presence of arbitrary e g naturalistic stimulus distribution we review several inference methods focusing in particular on two information theory based approaches maximization of stimulus energy and of noise entropy and two likelihood based approaches bayesian spike triggered covariance and extensions of generalized linear models we analyze the formal relationship between the likelihood based and information based approaches to demonstrate how they lead to consistent inference we demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

fast k dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding fast search algorithms are proposed and studied for vector quantization encoding using the k dimensional k d tree structure here the emphasis is on the optimal design of the k d tree for efficient nearest neighbor search in multidimensional space under a bucket voronoi intersection search framework efficient optimization criteria and procedures are proposed for designing the k d tree for the case when the test data distribution is available as in vector quantization application in the form of training data as well as for the case when the test data distribution is not available and only the voronoi intersection information is to be used the criteria and bucket voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform they are empirically observed to achieve constant search complexity for o log n tree depths and are found to be more efficient in reducing the search complexity a geometric interpretation is given for the maximum product criterion explaining reasons for its inefficiency with respect to the optimization criteria

adapting for the missing link we consider the fitting of generalized linear models in wich the link function is assumed to be unknown and propose the following computational method first estimate regression coefficients using the canonical link then estimate the link via a kernel smoother treating the direction in the predictor space determined by the regression coefficients as known then reestimate the direction using the estimated link and alternate between these two steps we show that under fairly general conditions n 1 2 consistent estimates of the direction are obtained a small monte carlo study is presented

two computational regimes of a single compartment neuron separated by a planar boundary in conductance space recent in vitro data show that neurons respond to input variance with varying sensitivities here we demonstrate that hodgkin huxley hh neurons can operate in two computational regimes one that is more sensitive to input variance differentiating and one that is less sensitive integrating a boundary plane in the 3d conductance space separates these two regimes for a reduced hh model this plane can be derived analytically from the v nullcline thus suggesting a means of relating biophysical parameters to neural computation by analyzing the neuron s dynamical system

what causes a neuron to spike the computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output white noise stimulus and reverse correlation the spike triggered average and spike triggered covariance are often used in experimental neuroscience to ask neurons which dimensions in stimulus space they are sensitive to and to characterize the nonlinearity of the response in this article we apply reverse correlation to the simplest model neuron with temporal dynamics the leaky integrate and fire model and find that for even this simple case standard techniques do not recover the known neural computation to overcome this we develop novel reverse correlation techniques by selectively analyzing only isolated spikes and taking explicit account of the extended silences that precede these isolated spikes we discuss the implications of our methods to the characterization of neural adaptation although these methods are developed in the context of the leaky integrate and fire model our findings are relevant for the analysis of spike trains from real neurons