Search results for "grange"
showing 10 items of 164 documents
Assessing Causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods
2009
We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) …
The Euler–Lagrange equation for the Anisotropic least gradient problem
2016
Abstract In this paper we find the Euler–Lagrange equation for the anisotropic least gradient problem inf { ∫ Ω ϕ ( x , D u ) : u ∈ B V ( Ω ) , u | ∂ Ω = f } being ϕ a metric integrand and f ∈ L 1 ( ∂ Ω ) . We also characterize the functions of ϕ -least gradient as those whose boundary of the level set is ϕ -area minimizing in Ω .
Nonradial normalized solutions for nonlinear scalar field equations
2018
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators
2021
One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Sq…
Predictability decomposition detects the impairment of brain-heart dynamical networks during sleep disorders and their recovery with treatment
2016
This work introduces a framework to study the network formed by the autonomic component of heart rate variability (cardiac process η ) and the amplitude of the different electroencephalographic waves (brain processes δ , θ , α , σ , β ) during sleep. The framework exploits multivariate linear models to decompose the predictability of any given target process into measures of self-, causal and interaction predictability reflecting respectively the information retained in the process and related to its physiological complexity, the information transferred from the other source processes, and the information modified during the transfer according to redundant or synergistic interaction betwee…
Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability.
2007
A method for assessing Granger causal relationships in bivariate time series, based on nonlinear autoregressive (NAR) and nonlinear autoregressive exogenous (NARX) models is presented. The method evaluates bilateral interactions between two time series by quantifying the predictability improvement (PI) of the output time series when the dynamics associated with the input time series are included, i.e., moving from NAR to NARX prediction. The NARX model identification was performed by the optimal parameter search (OPS) algorithm, and its results were compared to the least-squares method to determine the most appropriate method to be used for experimental data. The statistical significance of…
Mechanically-based approach to non-local elasticity: Variational principles
2010
Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…
Credit risk transmission in the European banking sector: the case of the subprime and Eurozone debt crises
2014
El objetivo del presente trabajo es analizar en profundidad la transmisión del riesgo de crédito, aproximado por los CDS spreads, en el sector bancario europeo durante el periodo 2006-2012, intentando dar respuesta a diversas cuestiones: (i) ¿existe evidencia de transmisión del riesgo de crédito entre las entidades financieras europeas de la Eurozona y las que no pertenecen a dicha zona?, (ii) ¿es esta transmisión bidireccional o unidireccional?, (iii) concretamente, ¿qué países han liderado dicha transmisión?, y (iv) ¿cómo se ha visto afectada dicha transmisión con las recientes crisis financieras? Los resultados indican un cambio significativo en la transmisión del riesgo de crédito con e…
Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions
2008
We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…