Related papers: A database of rigorous Maass forms

We discuss an arithmetic approach to some congruence properties of Siegel theta series of even positive definite unimodular quadratic forms.

We study graded rings of modular forms over congruence subgroups, with coefficients in a subring $A$ of $\mathbb{C}$, and specifically the highest weight needed to generate these rings as $A$-algebras. In particular, we determine upper…

We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…

The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…

This paper introduces the recent work of Nebula Graph, an open-source, distributed, scalable, and native graph database. We present a system design trade-off and a comprehensive overview of Nebula Graph internals, including graph data…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy…

We consider here the problem of obtaining reliable, consistent information from inconsistent databases -- databases that do not have to satisfy given integrity constraints. We use the notion of consistent query answer -- a query answer…

In 2012 we announced the House of Graphs (https://houseofgraphs.org) [Discrete Appl. Math. 161 (2013), 311-314], which was a new database of graphs. The House of Graphs hosts complete lists of graphs of various graph classes, but its main…

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

Recently, a method [7] was proposed to generate contrastive explanations for differentiable models such as deep neural networks, where one has complete access to the model. In this work, we propose a method, Model Agnostic Contrastive…

A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…

We exhibit an algorithm to compute a Dirichlet domain for a cofinite Fuchsian group Gamma. As a consequence, we compute the invariants of Gamma, including an explicit finite presentation for Gamma.

This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…

We train deep learning models on thousands of galaxy catalogues from the state-of-the-art hydrodynamic simulations of the CAMELS project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to…

"GRAMA" is a Mathematica package for doing symbolic tensor computations and complicated algebraic manipulations in 10-dimensional (D=10) simple (N=1) supergravity. The main new ingredients of this package inside the general Mathematica…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…