Related papers: Recognising the small Ree groups in their natural …
The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…
Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution…
A connected algebraic group in characteristic 0 is uniquely determined by its Lie algebra. In this paper an algorithm is given for constructing an algebraic group in characteristic 0, given its Lie algebra. Using this an algorithm is…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When…
We describe algorithms and heuristics that allow us to express arbitrary elements of SLn (Z) and Sp2n (Z) as products of generators in particular "standard" generating sets. For elements obtained experimentally as random products, it…
We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general…
Given a finite-dimensional module, $V$, for a finite-dimensional, complex, semi-simple Lie algebra $\lie g$ and a positive integer $m$, we construct a family of graded modules for the current algebra $\lie g[t]$ indexed by simple $\CC\lie…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…
We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…
We introduce a new method to determine galaxy cluster membership based solely on photometric properties. We adopt a machine learning approach to recover a cluster membership probability from galaxy photometric parameters and finally derive…
Following the success of Word2Vec embeddings, graph embeddings (GEs) have gained substantial traction. GEs are commonly generated and evaluated extrinsically on downstream applications, but intrinsic evaluations of the original graph…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…
Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require…
The generation of molecules with Artificial Intelligence (AI) is poised to revolutionize materials discovery. Potential applications range from development of potent drugs to efficient carbon capture and separation technologies. However,…
The $2$-admissibility of a graph is a promising measure to identify real-world networks which have an algorithmically favourable structure. In contrast to other related measures, like the weak/strong $2$-colouring numbers or the maximum…
Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
Group testing algorithms are very useful tools for DNA library screening. Building on recent work by Levenshtein (2003) and Tonchev (2008), we construct in this paper new infinite classes of combinatorial structures, the existence of which…
This work presents a new meta-heuristic approach to select the structure of polynomial NARX models for regression and classification problems. The method takes into account the complexity of the model and the contribution of each term to…