相关论文: CALICO: Computing Annihilators from Linear Identit…

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane…

Feynman integral reduction by means of integration-by-parts identities is a major power gadget in a theorist toolbox indispensable for calculation of multiloop quantum effects relevant for particle phenomenology and formal theory alike. An…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple…

Derivatives of computer graphics, image processing, and deep learning algorithms have tremendous use in guiding parameter space searches, or solving inverse problems. As the algorithms become more sophisticated, we no longer only need to…

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most…

Reducibility methods, aiming to simplify systems by conjugating them to those with constant coefficients, are crucial for studying the existence of quasiperiodic solutions. In KAM theory for PDEs, these methods help address the…

Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them…

We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…

Let $F$ be a field of characteristic $p$ and let $\Omega^n(F)$ be the $F$-vector space of $n$-differential forms. In this work, we will study the annihilator of differential forms, give specific descriptions for special cases and show a…

Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…

The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here…

We study general quantum integrable Hamiltonians linear in a coupling constant and represented by finite NxN real symmetric matrices. The restriction on the coupling dependence leads to a natural notion of nontrivial integrals of motion and…

Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…

In this paper, we develop efficient and accurate evaluation for the Lyapunov operator function $\varphi_l(\mathcal{L}_A)[Q],$ where $\varphi_l(\cdot)$ is the function related to the exponential, $\mathcal{L}_A$ is a Lyapunov operator and…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

Energy Correlators (EC) are the simplest IR finite observables, which connect theories and experiments. In this paper, we provide a systematic algorithm to calculate the canonical differential equations for energy correlators at generic…

In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $V(x)=\alpha x^{-2}$. In such a way, we have described…

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…