Related papers: Interactions between Digital Geometry and Combinat…
Vector representations of words have heralded a transformational approach to classical problems in NLP; the most popular example is word2vec. However, a single vector does not suffice to model the polysemous nature of many (frequent) words,…
Interpretable topic modeling is essential for tracking how research interests evolve within co-author communities. In scientific corpora, where novelty is prized, identifying underrepresented niche topics is particularly important. However,…
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations,…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…
Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the…
We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli…
We use the techniques of birational algebraic geometry and some combinatorial arguments related to weighted trees to study the structure of resolutions of compactifications of hypothetical counterexamples to the two-dimensional Jacobian…
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…
On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization…
This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
For many computational problems involving randomness, intricate geometric features of the solution space have been used to rigorously rule out powerful classes of algorithms. This is often accomplished through the lens of the multi Overlap…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…