Related papers: On the classification of CW complexes with prescri…

Neural link predictors are immensely useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries that arise in a number of domains, such as…

The contributions of this paper are twofold. First, we show the potential interest of Complex-Valued Neural Network (CVNN) on classification tasks for complex-valued datasets. To highlight this assertion, we investigate an example of…

An expository description of smooth cubic curves in the real or complex projective plane.

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…

We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.

Large bibliographic networks are sparse -- the average node degree is small. This is not necessarily true for their product -- in some cases, it can ``explode'' (it is not sparse, increases in time and space complexity). An approach in such…

Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

A keyword search on constrained clustering on Web-of-Science returned just under 3,000 documents. We ran automatic analyses of those, and compiled our own bibliography of 183 papers which we analysed in more detail based on their topic and…

Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are unknown) is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…

We show that the equivariant chain complex associated to a minimal CW-structure X on the complement M(A) of a hyperplane arrangement A, is independent of X. When A is a sufficiently general linear section of an aspheric arrangement, we…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate "must-link" or "cannot-link" in…

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with…

We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain first examples of so-called non-easy linear categories of…

The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is…