Related papers: On the classification of CW complexes with prescri…
By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
This review was written for the Encyclopedia of Complexity and System Science (Springer-Verlag, Berlin, 2008), and is intended as a guide to the growing literature which approaches the phenomena of cell biology from a more theoretical point…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
In this paper we present the complete classification of caps in PG(4,2). These results have been obtained using a computer based exhaustive search that exploits projective equivalence.
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal…
The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
A vast variety of biological, social, and economical networks shows topologies drastically differing from random graphs; yet the quantitative characterization remains unsatisfactory from a conceptual point of view. Motivated from the…
Complex networks are graphs representing real-life systems that exhibit unique characteristics not found in purely regular or completely random graphs. The study of such systems is vital but challenging due to the complexity of the…
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
The occurrence of unknown words in texts significantly hinders reading comprehension. To improve accessibility for specific target populations, computational modelling has been applied to identify complex words in texts and substitute them…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still…