Related papers: Petz map and Python's lunch

We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is…

Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…

We consider a class of maps from integral Hankel operators to Hankel matrices, which we call restriction maps. In the simplest case, such a map is simply a restriction of the integral kernel onto integers. More generally, it is given by an…

We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be…

Recoverable robust optimization is a popular multi-stage approach, in which it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We consider recoverable robust optimization in combination with…

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…

There is a large class of problems in algebraic combinatorics which can be distilled into the same challenge: construct an explicit combinatorial bijection. Traditionally, researchers have solved challenges like these by visually inspecting…

In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…

Developers try to evaluate whether an AI system can be misused by adversaries before releasing it; for example, they might test whether a model enables cyberoffense, user manipulation, or bioterrorism. In this work, we show that…

Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for…

In the context of irreversible dynamics, associating to a physical process its intuitive reverse can result to be a quite ambiguous task. It is a standard choice to define the reverse process using Bayes' theorem, but, in general, this…

Autonomous robot-assisted feeding requires the ability to acquire a wide variety of food items. However, it is impossible for such a system to be trained on all types of food in existence. Therefore, a key challenge is choosing a…

In the pursuit of fully autonomous robotic systems capable of taking over tasks traditionally performed by humans, the complexity of open-world environments poses a considerable challenge. Addressing this imperative, this study contributes…

The peeling process, which describes a step-by-step exploration of a planar map, has been instrumental in addressing percolation problems on random infinite planar maps. Bond and face percolation on maps with faces of arbitrary degree are…

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…

The problem of autonomous indoor mapping is addressed. The goal is to minimize the time to achieve a predefined percentage of exposure with some desired level of certainty. The use of a pre-trained generative deep neural network, acting as…

This paper introduces three sets of sufficient conditions, for generating bijective simplicial mappings of manifold meshes. A necessary condition for a simplicial mapping of a mesh to be injective is that it either maintains the orientation…

MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…