A semiclassical calculation of particle production by a scalar field in a potential is performed. We focus on the particular case of production of fermions by a NambuGoldstone boson θ. We have derived a (non)local equation of motion for the θ-field with the backreaction of the produced particles taken into account. The equation is solved in some special cases, namely for purely Nambu-Goldstone ...

cos nθ cos mθ = 2 cos(n − m)θ + 2 cos(n + m)θ. Certain classical orthogonal polynomials admit explicit computation of the coefficients c(n,m, k). For example, they are known explicitly for the ultraspherical polynomials along with their q-analogs [8]. However, they are not available in a simple form for the nonsymmetric Jacobi polynomials (see [7]). The first general criterion for nonnegativity...

Quantum metrology bears a great promise in enhancing measurement precision, but is unlikely to become practical in the near future. Its concepts can nevertheless inspire classical or hybrid methods of immediate value. Here we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a 'photonic gear', converting, for each photon, a mechanical rot...

We re-analyze the predictions of chiral-soliton models for the masses and decay widths of baryons in the exotic antidecuplet of flavour SU(3). The calculated ranges of the chiral-soliton moment of inertia and the π-nucleon scattering ΣπN term are used together with the observed baryon octet and decuplet mass splittings to estimate 1430MeV < mΘ+ < 1660MeV and 1790 MeV < mΞ−− < 1970MeV. These are...

We investigate the mass spectrum of pentaquark baryons in quenched lattice QCD with exact chiral symmetry. Using interpolating operators based on the diquark-diquark-antiquark picture in the Jaffe-Wilzcek model, we measure time correlation functions for 70 gauge configurations generated with Wilson gauge action at β = 6.1 on the 203 × 40 lattice, and extract the masses of even and odd parity st...

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space of inputs, a class of learning problems that is not handled by prior work. This extension is based on a measure of how matrices amplify the 2-norms of probabi...

Abstract: Consider a random vector (X, Y ) and let m(x) = E(Y |X = x). We are interested in testing H0 : m ∈ MΘ,G = {γ(·, θ, g) : θ ∈ Θ, g ∈ G} for some known function γ, some compact set Θ ⊂ IR and some function set G of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linear model, a partial linear model, a si...

Convolutional neural networks have significantly boosted the performance of face recognition in recent years due to its high capacity in learning discriminative features. To enhance the discriminative power of the Softmax loss, multiplicative angular margin [23] and additive cosine margin [44, 43] incorporate angular margin and cosine margin into the loss functions, respectively. In this paper,...

Dimer models are introduced by string theorists (see e.g. [11, 12, 13, 16, 17, 18]) to study supersymmetric quiver gauge theories in four dimensions. A dimer model is a bicolored graph on a 2-torus encoding the information of a quiver with relations. If a dimer model is non-degenerate, then the moduli space Mθ of stable representations of the quiver with dimension vector (1, . . . , 1) with res...

Accurate numerical solution of the five-body Schrödinger equation is effected via variational Monte Carlo in a correlated quark model. The spectrum is assumed to exhibit a narrow resonance with strangeness S = +1. A fully antisymmetrized and pair-correlated five-quark wave function is obtained for the assumed non-relativistic Hamiltonian which has spin, isospin, and color dependent pair interac...