Automatic contour extraction from 2D neuron images

This work describes a novel methodology for automatic contour extraction from 2D images of 3D neurons (e.g. camera lucida images and other types of 2D microscopy). Most contour-based shape analysis methods cannot be used to characterize such cells because of overlaps between neuronal processes. The proposed framework is specifically aimed at the problem of contour following even in presence of multiple overlaps. First, the input image is preprocessed in order to obtain an 8-connected skeleton with one-pixel-wide branches, as well as a set of critical regions (i.e., bifurcations and crossings). Next, for each subtree, the tracking stage iteratively labels all valid pixel of branches, tip to a critical region, where it determines the suitable direction to proceed. Finally, the labeled skeleton segments are followed in order to yield the parametric contour of the neuronal shape under analysis. The reported system was successfully tested with respect to several images and the results from a set of three neuron images are presented here, each pertaining to a different class, i.e. alpha, delta and epsilon ganglion cells, containing a total of 34 crossings. The algorithms successfully got across all these overlaps. The method has also been found to exhibit robustness even for images with close parallel segments. The proposed method is robust and may be implemented in an efficient manner. The introduction of this approach should pave the way for more systematic application of contour-based shape analysis methods in neuronal morphology. (C) 2008 Elsevier B.V. All rights reserved.

A multi-GPU algorithm for large-scale neuronal networks

Large-scale simulations of parts of the brain using detailed neuronal models to improve our understanding of brain functions are becoming a reality with the usage of supercomputers and large clusters. However, the high acquisition and maintenance cost of these computers, including the physical space, air conditioning, and electrical power, limits the number of simulations of this kind that scientists can perform. Modern commodity graphical cards, based on the CUDA platform, contain graphical processing units (GPUs) composed of hundreds of processors that can simultaneously execute thousands of threads and thus constitute a low-cost solution for many high-performance computing applications. In this work, we present a CUDA algorithm that enables the execution, on multiple GPUs, of simulations of large-scale networks composed of biologically realistic Hodgkin-Huxley neurons. The algorithm represents each neuron as a CUDA thread, which solves the set of coupled differential equations that model each neuron. Communication among neurons located in different GPUs is coordinated by the CPU. We obtained speedups of 40 for the simulation of 200k neurons that received random external input and speedups of 9 for a network with 200k neurons and 20M neuronal connections, in a single computer with two graphic boards with two GPUs each, when compared with a modern quad-core CPU. Copyright (C) 2010 John Wiley & Sons, Ltd.

Intrinsically Multivariate Predictive Genes

Canalizing genes possess such broad regulatory power, and their action sweeps across a such a wide swath of processes that the full set of affected genes are not highly correlated under normal conditions. When not active, the controlling gene will not be predictable to any significant degree by its subject genes, either alone or in groups, since their behavior will be highly varied relative to the inactive controlling gene. When the controlling gene is active, its behavior is not well predicted by any one of its targets, but can be very well predicted by groups of genes under its control. To investigate this question, we introduce in this paper the concept of intrinsically multivariate predictive (IMP) genes, and present a mathematical study of IMP in the context of binary genes with respect to the coefficient of determination (CoD), which measures the predictive power of a set of genes with respect to a target gene. A set of predictor genes is said to be IMP for a target gene if all properly contained subsets of the predictor set are bad predictors of the target but the full predictor set predicts the target with great accuracy. We show that logic of prediction, predictive power, covariance between predictors, and the entropy of the joint probability distribution of the predictors jointly affect the appearance of IMP genes. In particular, we show that high-predictive power, small covariance among predictors, a large entropy of the joint probability distribution of predictors, and certain logics, such as XOR in the 2-predictor case, are factors that favor the appearance of IMP. The IMP concept is applied to characterize the behavior of the gene DUSP1, which exhibits control over a central, process-integrating signaling pathway, thereby providing preliminary evidence that IMP can be used as a criterion for discovery of canalizing genes.

Automatic camera control in virtual environments augmented using multiple sparse videos

Automated virtual camera control has been widely used in animation and interactive virtual environments. We have developed a multiple sparse camera based free view video system prototype that allows users to control the position and orientation of a virtual camera, enabling the observation of a real scene in three dimensions (3D) from any desired viewpoint. Automatic camera control can be activated to follow selected objects by the user. Our method combines a simple geometric model of the scene composed of planes (virtual environment), augmented with visual information from the cameras and pre-computed tracking information of moving targets to generate novel perspective corrected 3D views of the virtual camera and moving objects. To achieve real-time rendering performance, view-dependent textured mapped billboards are used to render the moving objects at their correct locations and foreground masks are used to remove the moving objects from the projected video streams. The current prototype runs on a PC with a common graphics card and can generate virtual 2D views from three cameras of resolution 768 x 576 with several moving objects at about 11 fps. (C)2011 Elsevier Ltd. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Inferential Implications of Over-Parametrization: A Case Study in Incomplete Categorical Data

P>In the context of either Bayesian or classical sensitivity analyses of over-parametrized models for incomplete categorical data, it is well known that prior-dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over-parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior-dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over-parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.Resume Que ce soit dans un cadre Bayesien ou classique, il est bien connu que la surparametrisation, dans les modeles pour donnees categorielles incompletes, peut conduire a des conclusions erronees. Cependant, certains auteurs persistent a negliger les problemes lies a la presence de parametres non identifies. Nous passons en revue la litterature dans ce domaine, et considerons quelques exemples surparametres simples dans lesquels les elements subjectifs influencent de facon non negligeable les resultats, independamment de la taille des echantillons. Plus precisement, nous montrons comment des a priori consideres comme peu ou non-informatifs peuvent se reveler extremement informatifs en ce qui concerne les parametres non identifies, et que le recours a des modeles surparametres peut avoir sur les conclusions finales un impact considerable. Ceci suggere un examen tres attentif de l`impact potentiel des a priori.

Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data the local influence curvatures are derived and some diagnostic graphics are proposed A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors The local influence approach is used to compare the sensitivity of the model estimates (C) 2010 Elsevier B V All rights reserved

Comparing diagnostic tests with missing data

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows LIS to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other. (C) 2009 Elsevier B.V. All rights reserved.

A semi-Markov multistate model for estimation of the mean quality-adjusted survival for non-progressive processes

We discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models. We generalize an earlier work, considering the sojourn times in health states are not identically distributed, for a given vector of covariates. Approaches based on semiparametric and parametric (exponential and Weibull distributions) methodologies are considered. A simulation study is conducted to evaluate the performance of the proposed estimator and the jackknife resampling method is used to estimate the variance of such estimator. An application to a real data set is also included.