Related papers: Convolution and Combination Matrices in Non-statio…
We propose the application of graphical convolution to the analysis of the resonance phenomenon. This time-domain approach encompasses both the finally attained periodic oscillations and the initial transient period. It also provides…
Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the…
In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…
Oscillatory processes are central for the understanding of the neural bases of cognition and behaviour. To analyse these processes, time-frequency (TF) decomposition methods are applied and non-parametric cluster-based statistical procedure…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.…
We argue that time crystal properties naturally arise from phase-space noncommutative quantum mechanics. In order to exemplify our point we consider the 2-dimensional noncommutative quantum harmonic oscillator and show that it exibihits…
Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such…
It has been shown that equivariant convolution is very helpful for many types of computer vision tasks. Recently, the 2D filter parametrization technique plays an important role when designing equivariant convolutions. However, the current…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are $q$-exponentials of an appropriate potential function, are…
This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…