Related papers: Conjunctive Queries: Unique Characterizations and …

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

We study the extent to which standard machine learning algorithms rely on exchangeability and independence of data by introducing a monotone adversarial corruption model. In this model, an adversary, upon looking at a "clean" i.i.d.…

This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…

Simplicial complexes prove effective in modeling data with multiway dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces…

A good feature representation is a determinant factor to achieve high performance for many machine learning algorithms in terms of classification. This is especially true for techniques that do not build complex internal representations of…

When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining…

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into…

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely…

Architectural imperatives due to the slowing of Moore's Law, the broad acceptance of relaxed semantics and the O(n!) worst case verification complexity of generating sequential histories motivate a new approach to concurrent correctness.…

In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…

A Qualitative Constraint Network (QCN) is a constraint graph for representing problems under qualitative temporal and spatial relations, among others. More formally, a QCN includes a set of entities, and a list of qualitative constraints…

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…