Related papers: Characterizing co-NL by a group action

This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We introduce a graph-theoretical representation of proofs of multiplicative linear logic which yields both a denotational semantics and a notion of truth. For this, we use a locative approach (in the sense of ludics) related to game…

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There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…

We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized…

The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

Deep convolutional networks are widely used in video action recognition. 3D convolutions are one prominent approach to deal with the additional time dimension. While 3D convolutions typically lead to higher accuracies, the inner workings of…

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

Using fixed-point-free group actions, we set up a scheme to define nested classes of groups indexed over ordinals. Restricting to cellular actions on CW-complexes, we find new classes as well as new characterizations for some well-known…

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In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a…

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We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…

In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…

We define the notion of characteristic classes for supermanifolds endowed with a homological vector field $Q$. These take values in the cohomology of the Lie derivative operator $L_Q$ acting on arbitrary tensor fields. We formulate a…

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…