Research Center en Matematicas

Guanajuato, Mexico

Research Center en Matematicas

Guanajuato, Mexico
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Garyfallidis E.,Université de Sherbrooke | Ocegueda O.,Research Center en Matematicas | Wassermann D.,French Institute for Research in Computer Science and Automation | Descoteaux M.,Université de Sherbrooke
NeuroImage | Year: 2015

The neuroscientific community today is very much interested in analyzing specific white matter bundles like the arcuate fasciculus, the corticospinal tract, or the recently discovered Aslant tract to study sex differences, lateralization and many other connectivity applications. For this reason, experts spend time manually segmenting these fascicles and bundles using streamlines obtained from diffusion MRI tractography. However, to date, there are very few computational tools available to register these fascicles directly so that they can be analyzed and their differences quantified across populations. In this paper, we introduce a novel, robust and efficient framework to align bundles of streamlines directly in the space of streamlines. We call this framework Streamline-based Linear Registration. We first show that this method can be used successfully to align individual bundles as well as whole brain streamlines. Additionally, if used as a piecewise linear registration across many bundles, we show that our novel method systematically provides higher overlap (Jaccard indices) than state-of-the-art nonlinear image-based registration in the white matter. We also show how our novel method can be used to create bundle-specific atlases in a straightforward manner and we give an example of a probabilistic atlas construction of the optic radiation. In summary, Streamline-based Linear Registration provides a solid registration framework for creating new methods to study the white matter and perform group-level tractometry analysis. © 2015 Elsevier Inc.

Vera J.F.,University of Granada | Macias R.,Research Center en Matematicas
Psychometrika | Year: 2017

One of the main problems in cluster analysis is that of determining the number of groups in the data. In general, the approach taken depends on the cluster method used. For K-means, some of the most widely employed criteria are formulated in terms of the decomposition of the total point scatter, regarding a two-mode data set of N points in p dimensions, which are optimally arranged into K classes. This paper addresses the formulation of criteria to determine the number of clusters, in the general situation in which the available information for clustering is a one-mode (Formula presented.) dissimilarity matrix describing the objects. In this framework, p and the coordinates of points are usually unknown, and the application of criteria originally formulated for two-mode data sets is dependent on their possible reformulation in the one-mode situation. The decomposition of the variability of the clustered objects is proposed in terms of the corresponding block-shaped partition of the dissimilarity matrix. Within-block and between-block dispersion values for the partitioned dissimilarity matrix are derived, and variance-based criteria are subsequently formulated in order to determine the number of groups in the data. A Monte Carlo experiment was carried out to study the performance of the proposed criteria. For simulated clustered points in p dimensions, greater efficiency in recovering the number of clusters is obtained when the criteria are calculated from the related Euclidean distances instead of the known two-mode data set, in general, for unequal-sized clusters and for low dimensionality situations. For simulated dissimilarity data sets, the proposed criteria always outperform the results obtained when these criteria are calculated from their original formulation, using dissimilarities instead of distances. © 2017 The Psychometric Society

Becerra H.M.,Research Center en Matematicas | Sagues C.,University of Zaragoza
IEEE Transactions on Control Systems Technology | Year: 2013

Image-based approaches for visual control are memoryless, and they depend on the information extracted from the image plane. We propose the use of dynamic pose estimation in the task of driving a mobile robot to a desired location specified by a target image. This approach reduces the dependence of the control on the quality of current visual data and facilitates the planning of complex tasks. The pose estimation exploits the 1-D trifocal tensor (TT) as measurement, which allows us to obtain a semicalibrated estimation scheme that is valid for any visual sensor obeying a central projection model. The contribution of this brief is a novel observability analysis of the estimation problem from the 1-D TT using nonlinear tools, as well as the demonstration of the validity of closed-loop control from the estimated pose by showing a separation principle in our nonlinear framework. The overall position-based scheme drives the robot to a desired pose through smooth velocities without the need of a target model, either scene reconstruction or depth information. The effectiveness of the approach is evaluated via real-world experiments. © 2012 IEEE.

Mroz A.,Research Center en Matematicas | Mroz A.,Nicolaus Copernicus University
Fundamenta Informaticae | Year: 2016

We study edge-bipartite graphs (bigraphs), a class of signed graphs, by means of the inflation algorithm which relies on performing certain elementary transformations on a given bigraph Δ, or equivalently, on the associated integral quadratic form qΔ : ℤn → ℤ, preserving Gram ℤ-congruence. The ideas are inspired by classical results of Ovsienko and recent studies of Simson started in [SIAM J. Discr. Math. 27 (2013), 827-854], concerning classifications of integral quadratic and bilinear forms, and their Coxeter spectral analysis. We provide few modifications of the inflation algorithm and new estimations of its complexity for positive and principal loop-free bigraphs. We discuss in a systematic way the behavior and computational aspects of inflation techniques. As one of the consequences we obtain relatively simple proofs of several interesting properties of quadratic forms and their roots, extending known facts. On the other hand, the results are a first step of a solution of a variant of Grothendieck group recognition, a difficult combinatorial problem arising in representation theory of finite dimensional algebras and their derived categories, which we discuss in Part II of this two parts article with the same main title.

Ponciano J.M.,University of Florida | Capistran M.A.,Research Center en Matematicas
PLoS Computational Biology | Year: 2011

In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD) incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics. © 2011 Ponciano, Capistrán.

Brian D.,University of Idaho | Ponciano J.M.,Research Center en Matematicas | Taper M.L.,Montana State University
Ecology | Year: 2010

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability. © 2010 by the Ecological Society of America.

Arita H.T.,National Autonomous University of Mexico | Christen A.,Research Center en Matematicas | Rodriguez P.,Comision Nacional para el Conocimiento y Uso de la Biodiversidad | Soberon J.,University of Kansas
Global Ecology and Biogeography | Year: 2012

Aim A great deal of information on distribution and diversity can be extracted from presence-absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range-diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity. Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co-occurrence of species and of similarity among sites. Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness. © 2011 Blackwell Publishing Ltd.

Mendizabal-Ruiz E.G.,University of Houston | Rivera M.,Research Center en Matematicas | Kakadiaris I.A.,University of Houston
Medical Image Analysis | Year: 2013

Intravascular ultrasound (IVUS) is a catheter-based medical imaging technique that produces cross-sectional images of blood vessels and is particularly useful for studying atherosclerosis. In this paper, we present a computational method for the delineation of the luminal border in IVUS B-mode images. The method is based in the minimization of a probabilistic cost function (that deforms a parametric curve) which defines a probability field that is regularized with respect to the given likelihoods of the pixels belonging to blood and non-blood. These likelihoods are obtained by a Support Vector Machine classifier trained using samples of the lumen and non-lumen regions provided by the user in the first frame of the sequence to be segmented. In addition, an optimization strategy is introduced in which the direction of the steepest descent and Broyden-Fletcher-Goldfarb-Shanno optimization methods are linearly combined to improve convergence. Our proposed method (MRK) is capable of segmenting IVUS B-mode images from different systems and transducer frequencies without the need of any parameter tuning, and it is robust with respect to changes of the B-mode reconstruction parameters which are subjectively adjusted by the interventionist. We validated the proposed method on six 20. MHz and six 40. MHz IVUS stationary sequences corresponding to regions with different degrees of stenosis, and evaluated its performance by comparing the segmentation results with manual segmentation by two observers. Furthermore, we compared our method with the segmentation results on the same sequences as provided by the authors of three other segmentation methods available in the literature. The performance of all methods was quantified using Dice and Jaccard similarity indexes, Hausdorff distance, linear regression and Bland-Altman analysis. The results indicate the advantages of our method for the segmentation of the lumen contour. © 2013 Elsevier B.V.

Ruiz U.,Research Center en Matematicas | Murrieta-Cid R.,Research Center en Matematicas | Marroquin J.L.,Research Center en Matematicas
IEEE Transactions on Robotics | Year: 2013

In this paper, we consider the problem of capturing an omnidirectional evader using a differential drive robot in an obstacle-free environment. At the beginning of this game, the evader is at a distance L > l (the capture distance) from the pursuer. The goal of the evader is to keep the pursuer farther than this capture distance for as long as possible. The goal of the pursuer is to capture the evader as soon as possible. In this paper, we make the following contributions. We present closed-form representations of the motion primitives and time-optimal strategies for each player; these strategies are in Nash equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit toward the goal of winning the game. We propose a partition of the playing space into mutually disjoint regions where the strategies of the players are well established. This partition is represented as a graph, which exhibits properties that guarantee global optimality. We also analyze the decision problem of the game and we present the conditions defining the winner. © 2004-2012 IEEE.

Hayet J.-B.,Research Center en Matematicas
Journal of Intelligent and Robotic Systems: Theory and Applications | Year: 2012

This paper studies the local nature of the shortest length paths for a differential drive robot, in the presence of two or more landmarks that the robot has to keep in its field of view. Such a system has to satisfy several types of constraint: the non-holonomy, the bounds on the sensor angle and a visibility constraint for the landmarks. We study the shape of the configuration space resulting from these constraints, the particular spiral-like curves (that we call S-curves) resulting from maintaining the sensor angle to its saturation values, and finally we provide a local analysis of the shortest length paths for this system, that involves these S-curves. We give a more general characterization of the shortest length paths for a set of N landmarks to be kept in sight. Finally, we describe a randomized planner that is based on these local primitives and for which we present planning simulations. The main application of this work can be found in the surveillance area, which is of special interest in present days for most Latin American metropolis. © 2011 Springer Science+Business Media B.V.

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