Publications related to Differential geometry applied to crystallography

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

MATHICSE Technical Report: Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

Pablo Antolin Sanchez

3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...

MATHICSE2019

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

Pablo Antolin Sanchez

3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...

2019

A Learned Shape-Adaptive Subsurface Scattering Model

Wenzel Alban Jakob, Delio Aleardo Vicini

Subsurface scattering, in which light refracts into a translucent material to interact with its interior, is the dominant mode of light transport in many types of organic materials. Accounting for this phenomenon is thus crucial for visual realism, but exp ...

ASSOC COMPUTING MACHINERY2019

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

Let A be a nonnegatively graded connected algebra over a noncommutative separable k-algebra K, and let M be a bounded below graded right A-module. If we denote by T the -coalgebra , we know that there exists an -comodule structure on over T. The structure ...

2019

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

2019

An Improved Analysis of Local Search for Max-Sum Diversification

Friedrich Eisenbrand, Rico Zenklusen, Alfonso Bolívar Cevallos Manzano

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

INFORMS2019

Embryonic lateral inhibition as optical modes: An analytical framework for mesoscopic pattern formation

Andrew Charles Oates, Jose Negrete Jr

Cellular checkerboard patterns are observed at many stages of embryonic development. We study an analytically tractable model for lateral inhibition and show that the steady states are analogous to optical phonons at the Gamma point, which have the wave nu ...

2019

High Fidelity Visualization of Large Scale Digitally Reconstructed Brain Circuitry with Signed Distance Functions

Felix Schürmann, Marwan Muhammad Ahmed Abdellah, Alessandro Enrico Foni, Sébastien Nicolas Speierer, Samuel Lieven D. Lapere, Jonas Kristofer Karlsson

We explore a first proof-of-concept application for visualizing large scale digitally reconstructed brain circuitry using signed distance functions. The significance of our method is demonstrated in comparison with using implicit geometry that is limited t ...

IEEE2019

Decompositions of dependence for high-dimensional extremes

Emeric Rolland Georges Thibaud

We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operatio ...

OXFORD UNIV PRESS2019

Differential geometry applied to crystallography

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Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

MATHICSE Technical Report: Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

A Learned Shape-Adaptive Subsurface Scattering Model

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

Dynamical Reduced Basis Methods for Hamiltonian Systems

An Improved Analysis of Local Search for Max-Sum Diversification

Embryonic lateral inhibition as optical modes: An analytical framework for mesoscopic pattern formation

High Fidelity Visualization of Large Scale Digitally Reconstructed Brain Circuitry with Signed Distance Functions

Decompositions of dependence for high-dimensional extremes

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

MATHICSE Technical Report: Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

A Learned Shape-Adaptive Subsurface Scattering Model

An Improved Analysis of Local Search for Max-Sum Diversification

Decompositions of dependence for high-dimensional extremes

Dynamical Reduced Basis Methods for Hamiltonian Systems

Embryonic lateral inhibition as optical modes: An analytical framework for mesoscopic pattern formation

High Fidelity Visualization of Large Scale Digitally Reconstructed Brain Circuitry with Signed Distance Functions