Related papers: polyDB: A Database for Polytopes and Related Objec…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
The intensive need of atomic data is expanding continuously in a wide variety of applications (e.g. fusion energy and astrophysics, laser-produced, plasma researches, and plasma processing).This paper will introduce our ongoing research…
Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…
A classification of discrete polymatroids whose independence polytopes are reflexive will be presented.
Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…
We describe a document database, developed for BTeV, which has now been adopted for use by other collaborations. A single web based database and archival system is used to maintain public and internal documents as well as documents for a…
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last…
Database Management System (DBMS) is designed to help store and process large collections of data, and is incredibly flexible to perform various kinds of optimizations as long as it achieves serializability with a high-level interface…
We define an n-dimensional polytope Pi_n(x), depending on parameters x_i>0, whose combinatorial properties are closely connected with empirical distributions, plane trees, plane partitions, parking functions, and the associahedron. In…
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…
We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…
There has been rapidly growing demand of polymeric materials coming from different aspects of modern life because of the highly diverse physical and chemical properties of polymers. Polymer informatics is an interdisciplinary research field…
Data cubes are used for analyzing large data sets usually contained in data warehouses. The most popular data cube tools use graphical user interfaces (GUI) to do the data analysis. Traditionally this was fine since data analysts were not…
Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…
We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d…
We present PyMoosh, a Python-based simulation library designed to provide a comprehensive set of numerical tools allowing to compute essentially all optical characteristics of multilayered structures, ranging from reflectance and…
The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and…
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…
A permutation polytope is the convex hull of a group of permutation matrices. In this paper we investigate the combinatorics of permutation polytopes and their faces. As applications we completely classify permutation polytopes in…
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level…