Publications related to Weakly regular subdivisions

Related publications (32)

Cochains are all you need

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

A method and system for enforcing smoothness constraints on surface meshes from a graph convolutional neural network

Pascal Fua, Pamuditha Udaranga Wickramasinghe

A method for enforcing smoothness constraints on surface meshes produced by a Graph Convolutional Neural Network (GCNN) including the steps of reading image data from a memory, the image data including two-dimensional image data representing a three-dimens ...

2023

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

On the robustness of the metric dimension of grid graphs to adding a single edge

Patrick Thiran, Gergely Odor

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

Mehrdad Kiani Oshtorjani

The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat c ...

PERGAMON-ELSEVIER SCIENCE LTD2022

Robust numerical integration on curved polyhedra based on folded decompositions

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

ELSEVIER SCIENCE SA2022

Neural-network quantum states for periodic systems in continuous space

Giuseppe Carleo, Gabriel Maria Pescia

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-n ...

AMER PHYSICAL SOC2022

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Xavier Fernandez-Real Girona

We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...

2021

On the Volume of the John-Lowner Ellipsoid

Grigory Ivanov

We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...

SPRINGER2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Capture zone models of a multi-well system in aquifers bounded with regular and irregular inflow boundaries

David Andrew Barry

Being bounded by hydrological (inflow and barrier) boundaries, natural aquifers have regular/irregular shapes. Here, we consider aquifers bounded by segmental inflow (variable head) boundaries in which water is extracted/injected by a multi-well system. St ...

2020

Tropical Ehrhart Theory and Tropical Volume

Matthias Schymura, Georg Peter Loho

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposit ...

2019

Extended Formulations from Communication Protocols in Output-Efficient Time

Yuri Faenza, Manuel Francesco Aprile

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the exten ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

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 polytopes arisi ...

SIAM Publications2018

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018

Design and Performance Evaluation of an Infotaxis-Based Three-Dimensional Algorithm for Odor Source Localization

Alcherio Martinoli, Ali Marjovi, Faezeh Rahbar

In this paper we tackle the problem of finding the source of a gaseous leak with a robot in a three-dimensional (3-D) physical space. The proposed method extends the operational range of the probabilistic Infotaxis algorithm [1] into 3-D and makes multiple ...

IEEE2018

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Martin Vetterli, Thierry Blu, Hanjie Pan

Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one dimensional methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the hori ...

2018

Non-Normal Very Ample Polytopes - Constructions and Examples

Michal Lason

We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 231 ...

Taylor & Francis Inc2017