Search results for "modeling"
showing 10 items of 4489 documents
ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS
2007
International audience; An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh-Nagumo model.
Pruning Incremental Linear Model Trees with Approximate Lookahead
2014
Incremental linear model trees with approximate lookahead are fast, but produce overly large trees. This is due to non-optimal splitting decisions boosted by a possibly unlimited number of examples obtained from a data source. To keep the processing speed high and the tree complexity low, appropriate incremental pruning techniques are needed. In this paper, we introduce a pruning technique for the class of incremental linear model trees with approximate lookahead on stationary data sources. Experimental results show that the advantage of approximate lookahead in terms of processing speed can be further improved by producing much smaller and consequently more explanatory, less memory consumi…
Cross Correlations in Scaling Analyses of Phase Transitions
2008
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced …
Spatio‐temporal classification in point patterns under the presence of clutter
2019
We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. In previous studies, related to the spatial context, Kth nearest-neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation-maximization algorithm. This paper extends this methodology to the spatio-temporal context by considering the properties of the spatio-temporal Kth nearest-neighbor distances. For this purpose, we make use of a couple of spatio-temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions o…
Conflict and segregation in networks: An experiment on the interplay between individual preferences and social influence
2016
We examine the interplay between a person's individual preference and the social influence others exert. We provide a model of network relationships with conflicting preferences, where individuals are better off coordinating with those around them, but where not all have a preference for the same action. We test our model in an experiment, varying the level of conflicting preferences between individuals. Our findings suggest that preferences are more salient than social influence, under conflicting preferences: subjects relate mainly with others who have the same preferences. This leads to two undesirable outcomes: network segregation and social inefficiency. The same force that helps peopl…
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…
Wronskian and Casorati determinant representations for Darboux–Pöschl–Teller potentials and their difference extensions
2009
We consider some special reductions of generic Darboux?Crum dressing formulae and of their difference versions. As a matter of fact, we obtain some new formulae for Darboux?P?schl?Teller (DPT) potentials by means of Wronskian determinants. For their difference deformations (called DDPT-I and DDPT-II potentials) and the related eigenfunctions, we obtain new formulae described by the ratios of Casorati determinants given by the functional difference generalization of the Darboux?Crum dressing formula.
A Bayesian Sequential Look at u-Control Charts
2005
We extend the usual implementation of u-control charts (uCCs) in two ways. First, we overcome the restrictive (and often inadequate) assumptions of the Poisson model; next, we eliminate the need for the questionable base period by using a sequential procedure. We use empirical Bayes(EB) and Bayes methods and compare them with the traditional frequentist implementation. EB methods are somewhat easy to implement, and they deal nicely with extra-Poisson variability (and, at the same time, informally check the adequacy of the Poisson assumption). However, they still need the base period. The sequential, full Bayes approach, on the other hand, also avoids this drawback of traditional u-charts. T…
Using mathematical morphology for unsupervised classification of functional data
2011
This paper is concerned with the unsupervised classification of functional data by using mathematical morphology. Different morphological operators are used to extract relevant structures of the functions (considered as sets through their subgraph representations). These operators can be considered as preprocessing tools whose outputs are also functional data. We explore some dissimilarity measures and clustering methods for the classification of the transformed data. Our approach is illustrated through a detailed analysis of two data sets. These techniques, which have mainly been used in image processing, provide a flexible and robust toolbox for improving the results in unsupervised funct…
Weighted bounded mean oscillation applied to backward stochastic differential equations
2015
Abstract We deduce conditional L p -estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution ( Y , Z ) on subintervals of [ 0 , T ] . Some new results for the decoupling technique introduced in Geiss and Ylinen (2019) are obtained as well and some applications of the tail estimates are given.