Related papers: Large systems of random linear equations with non-…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We establish from first principles a perturbative framework that allows us to compute reaction rates for processes taking place in nonequilibrium $O (N)$ linear-sigma systems in broken phase. The system of our concern is quasiuniform system…
We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones,…
In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated…
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new geometric characterization of the…
One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
In this paper, we first show the existence of solutions to the following system of nonlinear equations \begin{eqnarray*}\left\{\begin{array}{l} a_{11}x_1+a_{12}x_2+a_{13}x_3+\cdots+a_{1n}x_{n} =…
The critical line of the Riemann zeta function is studied from a new viewpoint. It is found that the ratio between the zeta function at any zero and the corresponding one at a conjugate point has a certain phase and its absolute value is…
For applications of machine learning in critical decisions, explainability is a primary concern, and often a regulatory requirement. Local linear methods for generating explanations, such as LIME and SHAP, have been criticized for being…
We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system…