Related papers: Symmetrically Constrained Compositions
Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition…
We show that whenever $s>k(k+1)$, then for any complex sequence $(\mathfrak a_n)_{n\in \mathbb Z}$, one has $$\int_{[0,1)^k}\left| \sum_{|n|\le N}\mathfrak a_ne(\alpha_1n+\ldots +\alpha_kn^k) \right|^{2s}\,{\rm d}{\mathbf \alpha}\ll…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
We obtain an integral inequality for asymptotically linear harmonic functions on asymptotically flat 3-manifolds with noncompact boundary, which implies positivity of a convex combination of ADM masses of two conformally related metrics…
This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…
For a vector $\mathbf a=(a_1,\ldots,a_r)$ of positive integers we prove formulas for the restricted partition function $p_{\mathbf a}(n): = $ the number of integer solutions $(x_1,\dots,x_r)$ to $\sum_{j=1}^r a_jx_j=n$ with $x_1\geq 0,…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
A conformal partition function ${\cal P}_n^m(s)$, which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with {\it self-dual symmetric polynomials} -- reciprocal ${\sf R}^{\{m\}}_ {S_n}$…
Music Structure Analysis (MSA) consists in segmenting a music piece in several distinct sections. We approach MSA within a compression framework, under the hypothesis that the structure is more easily revealed by a simplified representation…
Let \bar{M}_{0,n} be the moduli space of pointed, genus 0 curves. Let L_i denote the line bundle on \bar{M}_{0,n} associated to the i-th marked point (the fiber of L_i is the cotangent space of the pointed curve at the i-th point).…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
A composite likelihood is a combination of low-dimensional likelihood objects useful in applications where the data have complex structure. Although composite likelihood construction is a crucial aspect influencing both computing and…
We compute the supersymmetric partition function of the six-dimensional $(2,0)$ theory of type $A_{N-1}$ on $S^1 \times S^5$ in the presence of both codimension two and codimension four defects. We concentrate on a limit of the partition…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
The symmetrization map $\pi:\mathbb C^2\rightarrow \mathbb C^2$ is defined by $ \pi(z_1,z_2)=(z_1+z_2,z_1z_2). $ The closed symmetrized bidisc $\Gamma$ is the symmetrization of the closed unit bidisc $\overline{\mathbb D^2}$, that is, \[…