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We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular VAR models appear, for example, as solutions of…

We investigate the cosmological reconstruction in modified f(R,T) gravity, where R is the Ricci scalar and T the trace of the stress-energy tensor. Special attention is attached to the case in which the function f is given by f (R, T) = f1…

We establish weak well-posedness for critical symmetric stable driven SDEs in R d with additive noise Z, d $\ge$ 1. Namely, we study the case where the stable index of the driving process Z is $\alpha$ = 1 which exactly corresponds to the…

This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a $p$-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of…

Relativity and quantum mechanics are two cornerstones of modern physics, yet their unification within a single-particle path integral and a dynamical explanation of quantum measurement remain unresolved. Historically, these two problems…

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…

This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the…

The non-equilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable…

Non-negative matrix factorization (NMF) is widely used for parts-based representations, yet formal inference for covariate effects is rarely available when the basis is learned under non-negativity. We introduce non-negative matrix…

Collinear factorization and color-glass condensate (CGC) effective field theory are generally treated as separate approaches for calculating scattering amplitudes, valid in different kinematic regimes. For deep inelastic scattering at high…

In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self-force problem of classical electrodynamics is properly solved, it becomes a plausible ontology underlying the statistical description of…

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization…

We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_g where F_g scales…

We have studied numerically the dynamics of sliding charge-density waves (CDWs) in the presence of impurities in d=1,2. The model considered exhibits a first order dynamical transition at a critical driving force $F_c$ between ``rough''…

The review is devoted to consideration of possible observational consequences of modified gravity theories, suggested for explanation of the contemporary accelerated expansion of the universe. The major attention is paid to F(R)-models. It…

This paper considers estimation of large dynamic factor models with common and idiosyncratic trends by means of the Expectation Maximization algorithm, implemented jointly with the Kalman smoother. We show that, as the cross-sectional…

In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…

The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous…

Over the past couple of years we have had significant progress in determining long-distance singularities in gauge-theory scattering amplitudes of massless particles beyond the planar limit. Upon considering all kinematic invariants much…