# Rolando Jose Biscay LirioCentro de Investigación en Matemáticas (CIMAT) | CIMAT · Department of Probability and Statistics

Rolando Jose Biscay Lirio

## About

129

Publications

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Introduction

Additional affiliations

January 2012 - December 2014

## Publications

Publications (129)

Introduction
The maturation of electroencephalogram (EEG) effective connectivity in healthy infants during the first year of life is described.
Methods
Participants: A cross-sectional sample of 125 healthy at-term infants, from 0 to 12 months of age, underwent EEG in a state of quiet sleep. Procedures: The EEG primary currents at the source were d...

This work provides a framework based on multivariate autoregressive modeling for linear causal filtering in the sense of Granger. In its bivariate form, the linear causal filter defined here takes as input signals A and B, and it filters out the causal effect of B on A, thus yielding two new signals only containing the Granger-causal effect of A on...

This work provides a framework based on multivariate autoregressive modeling for linear causal filtering in the sense of Granger. In its bivariate form, the linear causal filter defined here takes as input signals A and B, and it filters out the causal effect of B on A, thus yielding two new signals only containing the Granger-causal effect of A on...

What is the role of each node in a system of many interconnected nodes? This can be quantified by comparing the dynamics of the nodes in the intact system, with their modified dynamics in the edited system, where one node is deleted. In detail, the spectra are calculated from a causal multivariate autoregressive model for the intact system. Next, w...

What is the role of each node in a system of many interconnected nodes? This can be quantified by comparing the dynamics of the nodes in the intact system with their modified dynamics in the edited system where one node is deleted. In detail, the spectra are calculated from a causal multivariate autoregressive model for the intact system. Next, wit...

An early result by Markus and Weerasinghe (1988) concerning the oscillatory behavior of simple harmonic oscillators driven by random forces is extended to the general class of coupled stochastic harmonic oscillators. The ability of numerical discretizations – as discrete dynamical systems – for reproducing this oscillatory property of the continuou...

Due to its low resolution, any EEG inverse solution provides a source estimate at each voxel that is a mixture of the true source values over all the voxels of the brain. This mixing effect usually causes notable distortion in estimates of source connectivity based on inverse solutions. To lessen this shortcoming, an unmixing approach is introduced...

We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of Schrödinger type. Then, we design three exponential schemes fo...

Several approaches have been proposed for face recognition in videos. Fisher vector (FV) encoding of local Scale-Invariant Feature Transforms (SIFT) is among the best performing ones. Aiming at speed up the computation time of this approach, a method based on FV encoding of binary features was recently introduced. By using Binary Robust Independent...

In this paper, we present a novel methodology to solve the classification problem, based on sparse (data-driven) regressions, combined with techniques for ensuring stability, especially useful for high-dimensional datasets and small samples number. The sensitivity and specificity of the classifiers are assessed by a stable ROC procedure, which uses...

The sharing and the transmission of information between cortical brain regions is carried out by mechanisms that are still not fully understood. A deeper understanding should shed light on how consciousness and cognition are implemented in the brain. Research activity in this field has recently been focusing on the discovery of non-conventional cou...

We develop a new approach for solving stochastic master equations with initial mixed quantum state. Thus, we deal with the numerical simulation of, for instance, continuous weak measurements on quantum systems. We focus on finite dimensional quantum state spaces. First, we obtain that the solution of the jump-diffusion stochastic master equation is...

The problem of interest here is the study of brain functional and effective connectivity based non-invasive EEG-MEG inverse solution time series. These signals generally have low spatial resolution, such that an estimated signal at any one site is an instantaneous linear mixture of the true, actual, unobserved signals across all cortical sites. Fal...

The problem of interest here is the study of brain functional and effective connectivity based non-invasive EEG-MEG inverse solution time series. These signals generally have low spatial resolution, such that an estimated signal at any one site is an instantaneous linear mixture of the true, actual, unobserved signals across all cortical sites. Fal...

In this work, previous results concerning the infinitely many zeros of single stochastic oscillators driven by random forces are extended to the general class of coupled stochastic oscillators. We focus on three main subjects: 1) the analysis of this oscillatory behavior for the case of coupled harmonic oscillators; 2) the identification of some cl...

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called the direction and norm decomposition method, proposes to approximate the required solution Xt by integrating the system of coupled SDEs that describes the evolution of the norm of Xt and its projection on the...

A new nonparametric approach for statistical calibration with functional data is studied. The practical motivation comes from calibration problems in chemometrics in which a scalar random variable Y needs to be predicted from a functional random variable X. The proposed predictor takes the form of a weighted average of the observed values of Y in t...

Methods: The proposed Multi-resolution Discrete Search (MRDS) method is based on three key ideas: 1) A MRSD to determine the PDD’s; 2) The parameter-free determination of the number of axon bundles using the Bayesian Information Criterion (BIC) and 3) A Simultaneous Denoising and Fitting (SDF) procedure to achieve robustness with respect to noise.

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system casual relations. For instance, electric cortical signals are used for studying functional connectivity between different brain areas, the directionality, the direct or indirect nature of the connections, a...

Functional connectivity is of central importance in understanding brain function. For this purpose, multiple time series of electric cortical activity can be used for assessing the properties of a network: the strength, directionality, and spectral characteristics (i.e., which oscillations are preferentially transmitted) of the connections. The par...

In this paper, we propose a data-driven model selection approach for the nonparametric estimation of covariance functions under very general moments assumptions on the stochastic process. Observing i.i.d replications of the process at fixed observation points, we select the best estimator among a set of candidates using a penalized least squares es...

A problem of great interest in real world systems, where multiple time series
measurements are available, is the estimation of the intra-system causal
relations. For instance, electric cortical signals are used for studying
functional connectivity between brain areas, their directionality, the direct
or indirect nature of the connections, and the s...

A non Bayesian predictive approach for statistical calibration with functional data is introduced. This is based on extending to the functional calibration setting the definition of non Bayesian predictive probability density proposed by Harris (1989). The new method is elaborated in detail in case of Gaussian functional linear models. It is shown...

A new approach for the construction of high order A-stable explicit
integrators for ordinary differential equations (ODEs) is theoretically
studied. Basically, the integrators are obtained by splitting, at each time
step, the solution of the original equation in two parts: the solution of a
linear ordinary differential equation plus the solution of...

We provide in this paper a fully adaptive penalized procedure to select a
covariance among a collection of models observing i.i.d replications of the
process at fixed observation points. For this we generalize previous results of
Bigot and al. and propose to use a data driven penalty to obtain an oracle
inequality for the estimator. We prove that t...

A new method for detecting activations in random fields, which may be useful for addressing the issue of multiple comparisons in neuroimaging, is presented. This method is based on some constructs of mathematical morphology - specifically, morphological erosions and dilations - that enable the detection of active regions in random fields possessing...

In this paper, we consider the Group Lasso estimator of the covariance matrix
of a stochastic process corrupted by an additive noise. We propose to estimate
the covariance matrix in a high-dimensional setting under the assumption that
the process has a sparse representation in a large dictionary of basis
functions. Using a matrix regression model,...

Scalp electric potentials (electroencephalogram; EEG) are contingent to the impressed current density unleashed by cortical pyramidal neurons undergoing post-synaptic processes. EEG neuroimaging consists of estimating the cortical current density from scalp recordings. We report a solution to this inverse problem that attains exact localization: ex...

This paper describes a computarized video-game test designed for the assessment ofcognitive functions in children. A sample of 254 children were evaluated, 129 with learningdisabilities and 125 normal children. Fisher's linear discriminant analysis gave 68.2%COTTect clasification.

An important field of research in functional neuroimaging is the discovery of integrated, distributed brain systems and networks, whose different regions need to work in unison for normal functioning.
The EEG is a non-invasive technique that can provide information for massive connectivity analyses. Cortical signals of time varying electric neurona...

In this paper a new nonparametric functional regression method is introduced for predicting a scalar random variable Y on the basis of a functional random variable X. The prediction has the form of a weighted average of the training data y i , where the weights are determined by the conditional probability density of X given Y = y i , which is assu...

A new method for detecting activations in random fields, which may be useful for addressing the issue of multiple comparisons in neuroimaging, is presented. This method is based on some constructs of mathematical morphology - specifically, morphological erosions and dilations - that enable the detection of active regions in random fields possessing...

We consider exploratory methods for the discovery of cortical functional
connectivity. Typically, data for the i-th subject (i=1...NS) is represented as
an NVxNT matrix Xi, corresponding to brain activity sampled at NT moments in
time from NV cortical voxels. A widely used method of analysis first
concatenates all subjects along the temporal dimens...

A non-Bayesian predictive approach for statistical calibration is introduced. This is based on particularizing to the calibration setting the general definition of non-Bayesian (or frequentist) predictive probability density proposed by Harris [Predictive fit for natural exponential families, Biometrika 76 (1989), pp. 675–684]. The new method is el...

For the purpose of statistical characterization of the spatio-temporal correlation structure of brain functioning from high-dimensional fMRI time series, we introduce an innovation approach. This is based on whitening the data by the Nearest-Neighbors AutoRegressive model with external inputs (NN-ARx). Correlations between the resulting innovations...

In this paper a new nonparametric functional method is introduced for predicting a scalar random variable Y from a functional random variable X. The resulting prediction has the form of a weighted average of the training data set, where the weights are determined by
the conditional probability density of X given Y, which is assumed to be Gaussian....

Understanding of normal and pathological brain function requires the identification and localization of functional connections between specialized regions. The availability of high time resolution signals of electric neuronal activity at several regions offers information for quantifying the connections in terms of information flow. When the signal...

An approach for the construction of A-stable high order explicit strong schemes for stochastic differential equations (SDEs)
with additive noise is proposed. We prove that such schemes also have the dynamical property that we call Random A-stability
(RA-stability), which ensures that, for linear equations with stationary solutions, the numerical sc...

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of the covariance function by expanding the process onto a collection of basis functions. We study the non asymp...

In this paper, we study the problem of adaptive estimation of the spectral
density of a stationary Gaussian process. For this purpose, we consider a
wavelet-based method which combines the ideas of wavelet approximation and
estimation by information projection in order to warrants that the solution is
a nonnegative function. The spectral density of...

Quantitative analyses involving instrumental signals, such as chromatograms, NIR, and MIR spectra have been successfully applied nowadays for the solution of important chemical tasks. Multivariate calibration is very useful for such purposes and the commonly used methods in chemometrics consider each sample spectrum as a sequence of discrete data p...

Conventional multivariate calibration methods have been developed in chemometrics, using linear regression techniques as principal component regression (PCR) and partial least squares (PLS). Nevertheless, nonlinear methods such as neural networks have been also introduced, and more recently support vector (SVR) based methods. This paper presents th...

The introduction of support vector regression (SVR) and least square support vector machines (LS-SVM) methods for regression purposes in the field of chemometrics has provided advantageous alternatives to the existing linear and nonlinear multivariate calibration (MVC) approaches. Relevance vector machines (RVMs) claim the advantages attributed to...

Conventional multivariate calibration methods have been developed in chemometrics, using linear regression techniques as principal component regression (PCR) and partial least squares (PLS). Nevertheless, nonlinear methods such as neural networks have been also introduced, and more recently support vector (SVR) based methods. This paper presents th...

Many regression tasks in practice dispose in low gear instance of digitized functions as predictor variables. This has motivated
the development of regression methods for functional data. In particular, Naradaya-Watson Kernel (NWK) and Radial Basis Function
(RBF) estimators have been recently extended to functional nonparametric regression models....

The local linearization (LL) approach has become an effective technique for the numerical integration of ordinary, random and stochastic differential equations. One of the reasons for this success is that the LL method achieves a convenient trade-off between numerical stability and computational cost. Besides, the LL method reproduces well the dyna...

A new variant of Local Linearization (LL) method is proposed for the numerical (strong) solution of differential equations driven by (additive) alpha-stable Lévy motions. This is studied through simulations making emphasis in comparison with the Euler method from the viewpoint of numerical stability. In particular, a number of examples of stiff equ...

The local linearization (LL) method for the integration of ordinary differential equations is an explicit one-step method that has a number of suitable dynamical properties. However, a major drawback of the LL integrator is that its order of convergence is only two. The present paper overcomes this limitation by introducing a new class of numerical...

Weak local linear (WLL) discretizations are playing an increasing role in the construction of effective numerical integrators and inference methods for stochastic differential equations (SDEs) with additive noise. However, due to limitations in the existing numerical implementations of WLL discretizations, the resulting integrators and inference me...

A new class of stable methods for solving ordinary differential equations (ODEs) is introduced. This is based on combining
the Local Linearization (LL) integrator with other extant discretization methods. For this, an auxiliary ODE is solved to
determine a correction term that is added to the LL approximation. In particular, combining the LL method...

The Local Linearization (LL) method for the integration (in the strong sense) of stochastic differential equations with Wiener noise is extended to equations driven by additive semimartingales. Furthermore, it is proved the convergence in ucp (uniform on compacts in probability) of the approximate solution to the exact one.

Weak local linear (WLL) discretizations are playing an increasing role in the construction of effective numerical integrators and inference methods for stochastic differential equations (SDEs) with additive noise. However, due to limitations in the existing numerical implementations of WLL discretizations, the resulting integrators and inference me...

En este trabajo se estudia el comportamiento de una ecuación
diferencial estocástica con ruidos de Lévy. A partir del
esquema del LL(Linealización Local) se analiza la convergencia
del método del LL para este caso. Se presenta un ejemplo y se
hace una comparación entre este esquema y el de Euler para un
caso particular

A method is introduced to estimate nonparametric autoregressive models under the additional constraint that its regression function has a stable cycle. It is based on a penalty approach that chooses a series expansion approximation taking into account both goodness-of-fit and fulfillment of the constraint. Consistency of the proposed estimator is o...

A Local Linearization (LL) method for the numerical integration of Random Differential Equations (RDE) is introduced. The classical LL approach is adapted to this type of equations, which are defined by random vector fields that are typically at most Hlder continuous with respect to the time argument. The order of strong convergence of the method i...

In this paper an overview of inference methods for continuous-time stochastic volatility models observed at discrete times is presented. It includes estimation methods for both parametric and nonparametric models that are completely or partially observed in a variety of situations where the data might be nonlinear functions of the components of the...

The purpose of this paper is to construct a class of orthogonal integrators for stochastic differential equations (SDEs). The family of SDEs with orthogonal solutions is univocally characterized. For this, a class of orthogonal integrators is introduced by imposing constrains to Runge-Kutta (RK) matrices and weights of the standard stochastic RK sc...

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal...

Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same spatiotemporal data: topographic and tomographic. Until now, statistical tests for these two situations have developed separately. This work introduces statistical tests for assessing simultaneously the significance of spatiotemporal event-related potent...

In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The A...

In this paper, an alternative method to compute the Lyapunov exponents of dynamical systems described by ordinary differential equations (ODEs) is introduced. The Lyapunov exponents are computed in terms of the solutions of two piecewise linear ODEs that approximate, respectively, the solutions of the original ODE and its associated variational equ...

This paper studies the order of uniform strong convergence of two Local Linear (LL) approximations to the solution of stochastic differential equations (SDEs) with additive noise. The results obtained cover multi-dimensional and non-autonomous SDEs, and also ordinary differential equations with random initial conditions. It is demonstrated that the...

Some dynamic properties of the local linearization LL) scheme for the numerical integration of initial-value problems in ordinary dierential equations ODEs) are in- vestigated. Speci®cally, the general conditions under which this scheme preserves the stationary points and periodic orbits of the ODEs and the local stability at these steady states...

The metric sample space of Fr ́echet curves (Fr ́echet, 1934, 1951, 1961) is based on a generalization of regular curves that covers continuous curves in full generality. This makes it possible to deal with both smooth and non–smooth, even non–rectifiable geometric curves in statistical analysis. In the present paper this sample space is further ex...

Information processing in the visual cortex depends on complex and context sensitive patterns of interactions between neuronal groups in many different cortical areas. Methods used to date for disentangling this functional connectivity presuppose either linearity or instantaneous interactions, assumptions that are not necessarily valid. In this pap...

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a n...

A method for the selection of centers for radial basis function (RBF) approximation is introduced, which reduces the computational cost of the evaluation of the approximating function. The method takes into consideration:1.the geometric information (arc length and curvature) of the approximating RBF expansion with all data points as centers, in ord...

We present here a method to compare the mathematical descriptions of DNA migration per pulse as a function of pulse time. It is based on obtaining robust estimates and variances of DNA reorientation time, migration velocities during and after DNA reorientation; and on the statistical comparisons of these estimates. We demonstrated an equal descript...

An algorithm is given that computes the covariance matrix of the noise term of the local linearization scheme for the numerical integration of stochastic differential equations. The order of convergence of the resulting approximation is studied. An example is presented that illustrates the performance of the algorithm.

To describe the spectral characteristics of the EGG development through autoregressive (AR) time series models it is necessary to perform regression analysis of the AR parameters with regards to the age of the subject. A major difficulty in this approach is the very complex nature of the admissible region of the AR coefficients, which impedes the s...

A new cross-validation criterion for selecting covariance structures in multivariate analysis is introduced. The criterion relies on the use of the Frobenius matrix distance as discrepancy function between structure-based and sample covariance matrices. Its implementation only requires to specify i) the candidate covariance structures, and ii) an a...

MANOVA and repeated measures ANOVA approaches have provided evidence of a number of limitations in several event-related potential (ERP) studies due to violations of their statistical assumptions and the typically moderate size of the available sample. Alternative, computer-intensive methods based on permutation principles have recently been develo...

An approach for the parametric representation of anatomical structures of the human body by means of trigonometric interpolating sums (TIS) is introduced. This representation is constructed on the basis of the geometric information provided by medical digital images and an arbitrarily chosen system of curvilinear coordinates. The parameterization d...