Related papers: Cellular approximations of fusion systems
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
An $A$-cellular space is a space built from $A$ and its suspensions, analogously to the way that $CW$-complexes are built from $S^0$ and its suspensions. The $A$-cellular approximation of a space $X$ is an $A$-cellular space $CW_{A}X$ which…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories -- and consequently, semi-simple Hopf algebras -- of dimension $pq^2$, where $p$ and $q$ are distinct primes.…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
We prove, when $S$ is a $2$-group of order at most $2^9$, that each reduced fusion system over $S$ is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a $2$-group of order at…
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy…
The Temperley-Lieb (TL) family of algebras is well known for its role in building integrable lattice models. Even though a proof is still missing, it is agreed that these models should go to conformal field theories in the thermodynamic…
We examine the partition of a finite Coxeter group of type $B$ into cells determined by a weight function $L$. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with…
In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense…
We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably…
The classes of depth-bounded and name-bounded processes are fragments of the pi-calculus for which some of the decision problems that are undecidable for the full calculus become decidable. P is depth-bounded at level k if every reduction…
The existence and uniqueness of linking systems associated to saturated fusion systems over discrete $p$-toral groups were proved by Levi and Libman. Their proof make indirectly use of the classification of the finite simple groups. Here we…
Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for non-degenerate Brauer algebras. We generalise their construction to a wider class of…