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We study the Dirichlet problem for the semilinear equations involving the pseudo-relativistic operator on a bounded domain, (\sqrt{-\Delta + m^2} - m)u =|u|^{p-1}u \quad \textrm{in}~\Omega, with the Dirichlet boundary condition $u=0$ on…
In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state…
Relation extraction (RE) plays an important role in extracting knowledge from unstructured text but requires a large amount of labeled corpus. To reduce the expensive annotation efforts, semisupervised learning aims to leverage both labeled…
We investigate the following longstanding open questions raised by Kraj\'i\v{c}ek and Pudl\'ak (J. Symb. L. 1989), Sadowski (FCT 1997), K\"obler and Messner (CCC 1998) and Messner (PhD 2000). Q1: Does TAUT have (p-)optimal proof systems?…
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
A rectangular dual of a graph $G$ is a contact representation of $G$ by axis-aligned rectangles such that (i)~no four rectangles share a point and (ii)~the union of all rectangles is a rectangle. The partial representation extension problem…
This is the third article in a series of four articles dealing with the P vs. NP question. The purpose of this work is to demonstrate that the methods used in the first two articles of this series are not affected by oracle relativizations.…
Representational similarity analysis (RSA) is a multivariate technique to investigate cortical representations of objects or constructs. While avoiding ill-posed matrix inversions that plague multivariate approaches in the presence of many…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
A k-ary semi-algebraic relation E on R^d is a subset of R^{kd}, the set of k-tuples of points in R^d, which is determined by a finite number of polynomial equations and inequalities in kd real variables. The description complexity of such a…
In parameterized complexity, it is a natural idea to consider different generalizations of classic problems. Usually, such generalization are obtained by introducing a "relaxation" variable, where the original problem corresponds to setting…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…