Related papers: A database of rigorous Maass forms
We present two approaches that can be used to compute modular forms on noncongruence subgroups. The first approach uses Hejhal's method for which we improve the arbitrary precision solving techniques so that the algorithm becomes about up…
We give a method to describe all congruence images of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n, \mathbb{Z})$. The method is applied to obtain efficient algorithms for solving this problem in odd prime degree $n$; if…
We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard…
This is a brief report on some recent large-scale Monte Carlo simulations for approximating the density of zeros in character tables of large symmetric groups. Previous computations suggested that a large fraction of zeros cannot be…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…
The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric…
For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set…
This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer…
The value semigroup $\Gamma$ and the value set $\Lambda$ of $1$-forms are, respectively, a topological and an analytical invariant of a plane branch. Giving a plane branch $\mathcal{C}$ with semigroup $\Gamma$ there are a finitely number of…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
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…
Given a finitely presented Graded Commutative Differential Algebra (GCDA), we present a method to compute its minimal model, together with a map that is a quasi-isomorphism up to a given degree. The method works by adding generators one by…
We continue and complete our previous paper `Lifts of projective congruence groups' [2] concerning the question of whether there exist noncongruence subgroups of $\SL_2(\Z)$ that are projectively equivalent to one of the groups…
Markov state models (MSMs)---or discrete-time master equation models---are a powerful way of modeling the structure and function of molecular systems like proteins. Unfortunately, MSMs with sufficiently many states to make a quantitative…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
We present efficient algorithms to calculate the color factors for the $SU(N)$ gauge group and to evaluate $\gamma$ traces. The aim of these notes is to give a self-contained, proved account of the basic results with particular emphasis on…
We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.