Search results for "Nonlinear"
showing 10 items of 3684 documents
Introducing libeemd: a program package for performing the ensemble empirical mode decomposition
2016
The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the deco…
On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising
2015
Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each positive global minimum of the associated functional is one of such solutions. Moreover, we directly …
Multiscale Granger causality
2017
In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer a…
Comparative Evaluation of Community Detection Algorithms: A Topological Approach
2012
International audience; Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand Index, Normalized Mutual information, etc.). However, this type of comparison neglects the topological properties of the communities. In this article, we present a comprehensive comparative study of a representative set of commu…
Weak pseudo-bosons
2020
We show how the notion of {\em pseudo-bosons}, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with generalized eigenvectors of the multiplication and of the derivation operators. Connections with the quantum damped harmonic oscillator are also briefly considered.
Tridiagonality, supersymmetry and non self-adjoint Hamiltonians
2019
In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.
Rare events and scaling properties in field-induced anomalous dynamics
2012
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long sp…
Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system.
2018
In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce …
Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments
2015
Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…
Modular Structures on Trace Class Operators and Applications to Landau Levels
2009
The energy levels, generally known as the Landau levels, which characterize the motion of an electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator, with each level being infinitely degenerate. We show in this paper how the associated von Neumann algebra of observables displays a modular structure in the sense of the Tomita–Takesaki theory, with the algebra and its commutant referring to the two orientations of the magnetic field. A Kubo–Martin–Schwinger state can be built which, in fact, is the Gibbs state for an ensemble of harmonic oscillators. Mathematically, the modular structure is shown to arise as the natural modular structure associated with the…