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

We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…

Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…

We present a means of formulating and solving the well known structure-and-motion problem in computer vision with probabilistic graphical models. We model the unknown camera poses and 3D feature coordinates as well as the observed 2D…

An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information…

For each of the groups PSL2(F25), PSL2(F32), PSL2(F49), PGL2(F25), and PGL2(F27), we display the first explicitly known polynomials over Q having that group as Galois group. Each polynomial is related to a Galois representation associated…

Multimodal learning from document data has achieved great success lately as it allows to pre-train semantically meaningful features as a prior into a learnable downstream task. In this paper, we approach the document classification problem…

We introduce a procedure based on computational algebraic geometry to determine whether two algebras are isomorphic. We then apply it to show that if $R$ is a commutative unital ring in which $2$ is not invertible, $G$ is a group of order…

Informed learning is an emerging field in machine learning that aims to compensate for insufficient data with prior knowledge. Shape knowledge covers many types of prior knowledge concerning the relationship of a function's output with…

Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning,…

This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame,…

A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…

Moving object detection (MOD) is a significant problem in computer vision that has many real world applications. Different categories of methods have been proposed to solve MOD. One of the challenges is to separate moving objects from…

Modular object-centric representations are essential for *human-like reasoning* but are challenging to obtain under spatial ambiguities, *e.g. due to occlusions and view ambiguities*. However, addressing challenges presents both theoretical…

As Large Language Models (LLMs) become popular, there emerged an important trend of using multimodality to augment the LLMs' generation ability, which enables LLMs to better interact with the world. However, there lacks a unified perception…

This letter describes an incremental multimodal surface mapping methodology, which represents the environment as a continuous probabilistic model. This model enables high-resolution reconstruction while simultaneously compressing spatial…

We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…

We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal…

In recent years, the research community has shown a lot of interest to panoramic images that offer a 360-degree directional perspective. Multiple data modalities can be fed, and complimentary characteristics can be utilized for more robust…