Related papers: A proof algorithm associated with the dipole split…
In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed…
In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth…
Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…
Finding the optimal solution is often the primary goal in combinatorial optimization (CO). However, real-world applications frequently require diverse solutions rather than a single optimum, particularly in two key scenarios. The first…
In this publication the construction of an automatic algorithm to subtract infrared divergences in real QCD corrections through the Catani-Seymour dipole subtraction method [arXiv:hep-ph/9605323] is reported. The resulting computer code has…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
We present an NNLO-compatible subtraction scheme for computing QCD jet cross sections of hadron-initiated processes at NLO accuracy. The scheme is constructed specifically with those complications in mind, that emerge when extending the…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…
We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ "anchors" lead to a global solution and a…
We point out an issue with Lemma 8.6 of [1]. This lemma specifies the required sample complexity for recovering the delay-Doppler pairs in radar systems. In this lemma, it is claimed that the required sample complexity is linearly related…
We present the implementation of the dipole subtraction formalism for the real radiation contributions to any next-to-leading order QCD process in the MadGraph/MadEvent framework. Both massless and massive dipoles are considered. Starting…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…