Related papers: Faster multivariate integration in D-modules
We establish some cohomological bounds in D-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the b-function lemma for non-holonomic D-modules.
We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated $\mathcal{D}$-modules, based on Griffiths-Dwork reduction. By…
In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple…
Let $X$ be an algebraic variety, $f$ a regular function, $j:U\subset X$ the complement to the locus of vanishing of $f$, and $M$ a holonomic D-module on $U$. Consider the $D_U[s]$-module $M\otimes "f^s"$. The goal of this note is to…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…
We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with…
We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Shape compactness is a key geometrical property to describe interesting regions in many image segmentation tasks. In this paper, we propose two novel algorithms to solve the introduced image segmentation problem that incorporates a…
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes address the more general case when the coefficients are…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
The holonomic gradient method gives an algorithm to efficiently and accurately evaluate normalizing constants and their derivatives. We apply the holonomic gradient method in the case of the conditional Poisson or multinomial distribution…
Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually.…
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…