相关论文: Characterizing co-NL by a group action

We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…

The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

For a complex quasi-projective manifold with a finite group action, we define higher order generalized Euler characteristics with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the…

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…

We define and study invariants which can be uniformly constructed for any gauge system. By a gauge system we understand an (anti-)Poisson supermanifold provided with an odd Hamiltonian self-commuting vector field called a homological vector…

Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis…

Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$,…

With the development of social platforms, people are more and more inclined to combine into groups to participate in some activities, so group recommendation has gradually become a problem worthy of research. For group recommendation, an…

This paper proposes a new method based on neural networks for computing the high-dimensional committor functions that satisfy Fokker-Planck equations. Instead of working with partial differential equations, the new method works with an…

We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115}…

In a recent paper, the author has shown how Interaction Graphs models for linear logic can be used to obtain implicit characterisations of non-deterministic complexity classes. In this paper, we show how this semantic approach to Implicit…

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the…

In this work we present the novel ASTRID method for investigating which attribute interactions classifiers exploit when making predictions. Attribute interactions in classification tasks mean that two or more attributes together provide…

We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same…

The superior performance of deep convolutional networks over high-dimensional problems have made them very popular for several applications. Despite their wide adoption, their underlying mechanisms still remain unclear with their…

We consider whether given a simple, finite description of a group in the form of an algorithm, it is possible to algorithmically determine if the corresponding group has some specified property or not. When there is such an algorithm, we…

The relevance of machine learning (ML) in our daily lives is closely intertwined with its explainability. Explainability can allow end-users to have a transparent and humane reckoning of a ML scheme's capability and utility. It will also…