相关论文: InfoMod: A visual and computational approach to Ga…

A lot of work has gone into computing images of Galois representations coming from elliptic curves. This article presents an algorithm to determine the image of the mod-$3$ Galois representation associated to a principally polarized abelian…

There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…

In this paper, we present an InfoVis tool based on Sankey diagrams for the exploration of large combinatorial combinations of IR components - the Grid of Points (GoP). The goal of this tool is to ease the comprehension of the behavior of…

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…

Self-driving vehicles rely on urban street maps for autonomous navigation. In this paper, we introduce Pix2Map, a method for inferring urban street map topology directly from ego-view images, as needed to continually update and expand…

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…

Retrieval-augmented generation (RAG) enables large language models (LLMs) to dynamically access external information, which is powerful for answering questions over previously unseen documents. Nonetheless, they struggle with high-level…

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d N=1 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning…

In this paper, we propose UniGS, a unified map representation and differentiable framework for high-fidelity multimodal 3D reconstruction based on 3D Gaussian Splatting. Our framework integrates a CUDA-accelerated rasterization pipeline…

We present BALDUR, a novel Bayesian algorithm designed to deal with multi-modal datasets and small sample sizes in high-dimensional settings while providing explainable solutions. To do so, the proposed model combines within a common latent…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic…

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex…

This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length…

In this paper, we present a novel algorithm for probabilistically updating and rasterizing semantic maps within 3D Gaussian Splatting (3D-GS). Although previous methods have introduced algorithms which learn to rasterize features in 3D-GS…

We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least $2$ associated with representations whose kernel is a congruence…

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…

Infographics are documents designed to effectively communicate information using a combination of textual, graphical and visual elements. In this work, we explore the automatic understanding of infographic images by using Visual Question…

Multimodal recommender systems work by augmenting the representation of the products in the catalogue through multimodal features extracted from images, textual descriptions, or audio tracks characterising such products. Nevertheless, in…