Related papers: Computing Symmetric Normalisers
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
For a prime $p$, we describe a protocol for handling a specific type of fusion system on a $p$-group by computer. These fusion systems contain all saturated fusion systems. This framework allows us to computationally determine whether or…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. 1. Given a permutation group G=<S>, subgroup of $S_n$, and a parameter $k$, find a permutation $\pi$ in G such that…
The entanglement of a quantum system can be valuated using Mermin polynomials. This gives us a means to study entanglement evolution during the execution of quantum algorithms. We first consider Grover's quantum search algorithm, noticing…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
We consider the problem of discovering subgroup $H$ of permutation group $S_{n}$. Unlike the traditional $H$-invariant networks wherein $H$ is assumed to be known, we present a method to discover the underlying subgroup, given that it…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism…
Renormalization group methods generate low-resolution Hamiltonians that are more diagonal and easier to solve. This chapter reviews the similarity renormalization group for nuclear Hamiltonians, which is a popular method for generating…
Recently Aragona et al. have introduced a chain of normalizers in a Sylow 2-subgroup of Sym(2^n), starting from an elementary abelian regular subgroup. They have shown that the indices of consecutive groups in the chain depend on the number…
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective…
We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.
For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classification of all (not necessarily connected) solvable…
The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism…
In this paper we present several algorithms related with the computation of the homology of groups, from a geometric perspective (that is to say, carrying out the calculations by means of simplicial sets and using techniques of Algebraic…
We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover,…