Related papers: Conjunctive Queries: Unique Characterizations and …
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…
In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power…
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of…
Uniqueness quantification ($\exists !$) is a quantifier in first-order logic where one requires that exactly one element exists satisfying a given property. In this paper we investigate the strength of uniqueness quantification when it is…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
Linearizability is the strongest correctness property for both shared memory and message passing systems. One of its useful features is the compositionality: a history (execution) is linearizable if and only if each object (component)…
This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner…
Deep neural networks have been the driving force behind the success in classification tasks, e.g., object and audio recognition. Impressive results and generalization have been achieved by a variety of recently proposed architectures, the…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map. This leads to an investigation into…
Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…
Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…