Examinando por Autor "Mariño, Inés P."

Mostrando 1 - 7 de 7

A Sequential Monte Carlo Method for Parameter Estimation in Nonlinear Stochastic PDE's with Periodic Boundary Conditions
(IEEE, 2023) Míguez, Joaquín; Molina-Bulla, Harold; Mariño, Inés P.
We tackle the problem of Bayesian inference for stochastic partial differential equations (SPDEs) with unknown parameters. We assume that the signal of interest can only be observed partially, possibly subject to some transformation, and contaminated by noise. For all practical purposes involving numerical computation, the SPDE has to be discretised using a numerical scheme that depends itself on an additional set of parameters (e.g., the number of coefficients and the time step for a spectral decomposition method). Within this setup, we address the Bayesian estimation of the complete parameter set, including both the SPDE parameters and the numerical scheme parameters, using a nested particle filter. A simple version of the proposed methodology is described and numerically demonstrated for a Kuramoto-Sivashinsky SPDE with periodic boundary conditions and a Fourier spectraldecomposition numerical scheme.
An Interpretable Machine Learning Method for the Detection of Schizophrenia Using EEG Signals
(Frontiers Media, 2021-05-28) Vázquez, Manuel A.; Maghsoudi, Arash; Mariño, Inés P.
In this work we propose a machine learning (ML) method to aid in the diagnosis of schizophrenia using electroencephalograms (EEGs) as input data. The computational algorithm not only yields a proposal of diagnostic but, even more importantly, it provides additional information that admits clinical interpretation. It is based on an ML model called random forest that operates on connectivity metrics extracted from the EEG signals. Specifically, we use measures of generalized partial directed coherence (GPDC) and direct directed transfer function (dDTF) to construct the input features to the ML model. The latter allows the identification of the most performance-wise relevant features which, in turn, provide some insights about EEG signals and frequency bands that are associated with schizophrenia. Our preliminary results on real data show that signals associated with the occipital region seem to play a significant role in the diagnosis of the disease. Moreover, although every frequency band might yield useful information for the diagnosis, the beta and theta (frequency) bands provide features that are ultimately more relevant for the ML classifier that we have implemented.
Bayesian Computation Methods for Inference in Stochastic Kinetic Models
(Wiley, 2019-01-20) Koblents, Eugenia; Mariño, Inés P.; Míguez, Joaquín
In this paper we investigate Monte Carlo methods for the approximation of the posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in biological systems according to a set of usually unknown parameters. The tracking of the species populations together with the estimation of the interaction parameters is a Bayesian inference problem for which Markov chain Monte Carlo (MCMC) methods have been a typical computational tool. Specifically, the particle MCMC (pMCMC) method has been shown to be effective, while computationally demanding method applicable to this problem. Recently, it has been shown that an alternative approach to Bayesian computation, namely, the class of adaptive importance samplers, may be more efficient than classical MCMC-like schemes, at least for certain applications. For example, the nonlinear population Monte Carlo (NPMC) algorithm has yielded promising results with a low dimensional SKM (the classical predator-prey model). In this paper we explore the application of both pMCMC and NPMC to analyze complex autoregulatory feedback networks modelled by SKMs. We demonstrate numerically how the populations of the relevant species in the network can be tracked and their interaction rates estimated, even in scenarios with partial observations. NPMC schemes attain an appealing trade-off between accuracy and computational cost that can make them advantageous in many practical applications.
Controlling chaos in a fluid flow past a movable cylinder
(Elsevier, 2003) Vallejo, Juan C.; Mariño, Inés P.; Sanjuán, Miguel A.F.; Kurths, Juergen
The model of a two-dimensional fluid flow past a cylinder is a relatively simple problem with a strong impact in many applied fields, such as aerodynamics or chemical sciences, although most of the involved physical mechanisms are not yet well known. This paper analyzes the fluid flow past a cylinder in a laminar regime with Reynolds number, Re, around 200, where two vortices appear behind the cylinder, by using an appropriate time-dependent stream function and applying non-linear dynamics techniques. The goal of the paper is to analyze under which circumstances the chaoticity in the wake of the cylinder might be modified, or even suppressed. And this has been achieved with the help of some indicators of the complexity of the trajectories for the cases of a rotating cylinder and an oscillating cylinder.
Master-slave coupling scheme for synchronization and parameter estimation in the generalized Kuramoto-Sivashinsky equation
(American Physical Society, 2024-11-06) Míguez, Joaquín; Molina-Bulla, Harold; Mariño, Inés P.
The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics, and statistics. This is motivated by the various physical applications of the equation and also because it often serves as a test model for the study of space-time pattern formation. Remarkably, most existing inference techniques rely on statistical tools, which are computationally very costly yet do not exploit the dynamical features of the system. In this paper, we introduce a simple, online parameter estimation method that relies on the synchronization properties of the KS equation. In particular, we describe a master-slave setup where the slave model is driven by observations from the master system. The slave dynamics are data-driven and designed to continuously adapt the model parameters until identical synchronization with the master system is achieved. We provide a simple analysis that supports the proposed approach and also present and discuss the results of an extensive set of computer simulations. Our numerical study shows that the proposed method is computationally fast and also robust to initialization errors, observational noise, and variations in the spatial resolution of the numerical scheme used to integrate the KS equation.
Multilayer Models of Random Sequences: Representability and Inference via Nonlinear Population Monte Carlo
(IEEE, 2019) Míguez, Joaquín; Lacasa, Lucas; Martínez-Ordoñez, José A.; Mariño, Inés P.
We investigate a class of dynamical models with a multilayer structure for the representation of discrete-time sequences. Each layer is a first-order, discrete-time Markov process, either on a discrete state space (i.e., a Markov chain) or on a general state space. The transition kernel for each layer is different (hence it yields different stochastic dynamics) and at each time there is a single active layer. The active layers are selected over time according to a first-order Markov chain. This simple description includes many types of interacting multiple models, of interest in target tracking applications. It also fits many real-world systems that display a variety of dynamical patterns over time without any observable switching mechanism (examples abound in financial time series). In this paper we show that the family of multilayer models described above can represent a broad class of random sequences, including Markov chains of order M >1 on discrete spaces or auto-regressive process (again, of order M > 1) on general state spaces. We also propose a general nonlinear population Monte Carlo scheme that can be employed for model selection and model inference. Numerical examples are given for the case of multilayer models with discrete observations.
The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging
(Frontiers Media, 2020-05-25) Whitwell, Harry J.; Bacalini, Maria Giulia; Blyuss, Oleg; Chen, Shangbin; Garagnani, Paolo; Gordleeva, Susan Yu; Jalan, Sarika; Ivanchenko, Mikhail; Kanakov, Oleg; Kustikova, Valentina; Mariño, Inés P.; Meyerov, Iosif; Ullner, Ekkehard; Franceschi, Claudio; Zaikin, Alexey
Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks—e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called “seven pillars of aging” combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.