Related papers: Multiple solutions in extracting physics informati…
It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda\phi^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda n,\epsilon)]$, in…
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
The existence and multiplicity and nonexistence of nontrivial radial convex solutions of systems of Monge-Amp\`ere equations are established with superlinearity or sublinearity assumptions for an appropriately chosen parameter. The proof of…
Many-body forces, and specially three-body forces, are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. As their precise structure is generally difficult to uncover or to implement,…
Two approximations are frequently used in statistical physics: the first one, which we shall name the mean values approximation, is generally (and improperly) named as "maximum term approximation". The second is the "Stirling…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Weak-scale supersymmetry is a well motivated, if speculative, theory beyond the Standard Model of particle physics. It solves the thorny issue of the Higgs mass, namely: how can it be stable to quantum corrections, when they are expected to…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$…