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In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to…
In this paper the response of ionic systems subjected to a spatially varying electric field is studied. Following the Nernst-Planck equation, two forces driving the mass flux are present, namely, the concentration gradient and the electric…
The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…
This article investigates how a uniform high frequency (HF) drive applied to each site of a weakly-coupled discrete nonlinear resonator array can modulate the onsite natural stiffness and damping and thereby facilitate the active tunability…
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…
Neural Radiance Fields (NeRF) has become a popular framework for learning implicit 3D representations and addressing different tasks such as novel-view synthesis or depth-map estimation. However, in downstream applications where decisions…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that entail strong discontinuities and shocks, which give rise to…
The vertex function is analyzed using covariant spectral regularization without encountering any divergence, either UV or IR. The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
Although mean field theories have been very successful to predict a wide range of properties for solids, the discovery of high temperature superconductivity in cuprates supported the idea that strongly correlated materials cannot be…
Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct…
Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions.…
Spontaneous stochasticity refers to the emergence of intrinsic randomness in deterministic systems under singular limits, a phenomenon conjectured to be fundamental in turbulence. Armstrong and Vicol recently constructed a deterministic,…
We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…
We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven…
A method for extracting the Levy stability index $\mu$ from the multi-fractal spectrum $f(\alpha)$ in high energy multiparticle production is proposed. This index is an important parameter, characterizing the non-linear behaviour of…
Power spectral density is an accepted measure of heart rate variability. Two estimators of multifractal properties: Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis are used to investigate multifractal…
This paper introduces a new conceptual framework that recasts surface roughness effects as a "ray deflection function" (RDF) which can be statistically represented through a modified Zernike-Fourier hybrid approach that directly connects…