Related papers: Empirical Chaos Processes and Blind Deconvolution
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…
We examine the {combinatorial} or {probabilistic} definition ("Boltzmann's principle") of the entropy or cross-entropy function $H \propto \ln \mathbb{W}$ or $D \propto - \ln \mathbb{P}$, where $\mathbb{W}$ is the statistical weight and…
Einstein-Weyl geometry is a triple (D,g,w), where D is a symmetric connection, [g] is a conformal structure and w is a covector such that: (i) connection D preserves the conformal class [g], that is, Dg=wg; (ii) trace-free part of the…
The technique of $Q$-polinomials are used to derive the $w$- constraints in the two-matrix and Kontsevich-like model at finite $N$. These constraints are closed and form Lie algebra. They are associated with the matrices, $\lambda…
Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit…
Abrupt and rapid high-amplitude changes in a dynamical system's states known as extreme event appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…
We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate…
We discuss the possibility of colour rearrangement in $\ee \to \W^+ \W^- \to \q_1 \qbar_2 \q_3 \qbar_4$ events, i.e.\ that the original colour singlets $\q_1 \qbar_2$ and $\q_3 \qbar_4$ may be transmuted, for instance, into new singlets…
We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass $M$ in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of…
In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix…
The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…
We have presented a theoretical study of exclusive rare $W$-boson decays, $W\to V\ell\bar{\nu}_\ell$ with $V$ denoting a neutral vector meson and $\ell=e$ or $\mu$, in the standard model. The leading-order contributions to these processes…
Estimating conditional means using only the marginal means available from aggregate data is commonly known as the ecological inference problem (EI). We provide a reassessment of EI, including a new formalization of identification conditions…
Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement…
We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic…
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\mathbb{R}^2$) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys.…
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are constructed by using the algebra of Dirac $\gamma$ matrices in the space-time of arbitrary dimension $d$, where the first kind can detect some BSD relativistic and…
We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…