相关论文: Constraint Qualification for Generic Parameter Fam…

We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known…

Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

A subset $D$ of $V$ is \emph{dominating} in $G$ if every vertex of $V-D$ has at least one neighbour in $D;$ let $\gamma(G)$ be the minimum cardinality among all dominating sets in $G.$ A graph $G$ is $\gamma$-$q$-{\it critical} if the…

In the paper a set of necessary and sufficient conditions for \textit{v-}sufficiency (equiv. \textit{sv-}sufficiency) of jets of map-germs $f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is proved which generalize both the Kuiper-Kuo and the…

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient…

Variational quantum algorithms are ubiquitous in applications of noisy intermediate-scale quantum computers. Due to the structure of conventional parametrized quantum gates, the evaluated functions typically are finite Fourier series of the…

We introduce a new categorical and constructive foundation for analytic approximation based on a Contextual Choice Principle (CCP), which enforces locality and compatibility in the construction of mathematical objects. Central to our…

Large Language Models (LLMs) have demonstrated impressive performance across a wide range of applications; however, assessing their reasoning capabilities remains a significant challenge. In this paper, we introduce a framework grounded in…

We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups have at most three invariant factors equal to 1 and the…

In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…

We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…

Gradient Boosting Machines (GBM) are among the go-to algorithms on tabular data, which produce state of the art results in many prediction tasks. Despite its popularity, the GBM framework suffers from a fundamental flaw in its base…

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. A basic property of the critical ideals of graphs asserts that the graphs with at most k trivial critical ideals,…

Let $\Gamma(S)$ be the pure mapping class group of a connected orientable surface $S$ of negative Euler characteristic. For ${\mathscr C}$ a class of finite groups, let $\hat{\pi}_1(S)^{\mathscr C}$ be the pro-${\mathscr C}$ completion of…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…

During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…

Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open…