Related papers: Group-case commutative association schemes and the…

We extend to a scheme-theoretic context the notion of a combinatorial differential form, due to A.Kock in the framework of synthetic differential geometry. We show that group-valued combinatorial forms on a scheme may be identified, under…

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…

A key challenge for the safety of advanced AI systems is the possibility that multiple simpler agents might inadvertently form a collective agent with capabilities and goals distinct from those of any individual. More generally, determining…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

We give an explicit characterization of solvable factors in factorizations of finite classical groups of Lie type. This completes the classification of solvable factors in factorizations of almost simple groups, finishing the program…

Recurrent neural networks are nowadays successfully used in an abundance of applications, going from text, speech and image processing to recommender systems. Backpropagation through time is the algorithm that is commonly used to train…

There is increasing interest in combining information from experimental studies, including randomized and single-group trials, with information from external experimental or observational data sources. Such efforts are usually motivated by…

We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re-…

We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

Student modelling and agent classified rules learning as applied in the development of the intelligent Preassessment System has been presented in [10],[11]. In this paper, we now demystify the theory behind the development of the…

In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.

This article is concerned with the relative McKay conjecture for finite reductive groups. Let G be a connected reductive group defined over the finite field F_q of characteristic p>0 with corresponding Frobenius map F. We prove that if the…

Human knowledge is largely implicit and relational -- do we have a friend in common? can I walk from here to there? In this work, we leverage the combinatorial structure of graphs to quantify human priors over such relational data. Our…

Let $\mathbb{F}$ be an arbitrary field. In this paper, we continue studying the Terwilliger algebras of association schemes over $\mathbb{F}$ that were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [8]. We determine…

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an…

If all of the entries of a large $S_n$ character table are covered up and you are allowed to uncover one entry at a time, then how can you quickly identify all of the indexing characters and conjugacy classes? We present a fast algorithmic…

There is no much doubt that biotic interactions shape community assembly and ultimately the spatial co-variations between species. There is a hope that the signal of these biotic interactions can be observed and retrieved by investigating…

In this paper, we propose an algorithm of searching for both positive and negative itemsets of interest which should be given at the first stage for positive and negative association rules mining. Traditional association rule mining…