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Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…

Methodology · Statistics 2022-04-26 Chunya Li , Xiaojun Cui , Shifeng Xiong

Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions that facilitates the efficient search for new materials and material properties. We prove invariance under isometries, continuity, and…

Computational Geometry · Computer Science 2021-06-28 Herbert Edelsbrunner , Teresa Heiss , Vitaliy Kurlin , Philip Smith , Mathijs Wintraecken

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…

Methodology · Statistics 2019-06-17 Francois-Xavier Briol , Alessandro Barp , Andrew B. Duncan , Mark Girolami

By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…

High Energy Physics - Phenomenology · Physics 2023-08-11 Andrew J. Larkoski , Jesse Thaler

Detecting structure in data is the first step to arrive at meaningful representations for systems. This is particularly challenging for dislocation networks evolving as a consequence of plastic deformation of crystalline systems. Our study…

Materials Science · Physics 2024-06-24 Benjamin Udofia , Tushar Jogi , Markus Stricker

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…

Machine Learning · Statistics 2007-06-26 Bharath K. Sriperumbudur , Gert R. G. Lanckriet

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…

Computational Geometry · Computer Science 2019-01-28 Michael Kerber , Arnur Nigmetov

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Machine Learning · Computer Science 2019-05-10 Charlie Frogner , Farzaneh Mirzazadeh , Justin Solomon

Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a…

Methodology · Statistics 2017-05-10 Matthias Killiches , Daniel Kraus , Claudia Czado

Structural fingerprints and pharmacophore modeling are methodologies that have been used for at least two decades in various fields of cheminformatics: from similarity searching to machine learning (ML). Advances in silico techniques…

Quantitative Methods · Quantitative Biology 2023-11-01 Dawid Warszycki , Łukasz Struski , Marek Śmieja , Rafał Kafel , Rafał Kurczab

Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the…

Materials Science · Physics 2009-08-12 Ioan Bucataru , Michael A. Slawinski

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Statistics Theory · Mathematics 2015-03-19 Michel Broniatowski , Aida Toma , Igor Vajda

Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are…

Machine Learning · Computer Science 2021-09-07 Robert A. Murphy

We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional…

Computer Vision and Pattern Recognition · Computer Science 2017-06-15 James Damon , Ellen Gasparovic

Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curves, that includes several recently proposed metrics, for…

Differential Geometry · Mathematics 2014-10-07 Martin Bauer , Martins Bruveris , Stephen Marsland , Peter W. Michor

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

Methodology · Statistics 2024-02-28 Paromita Dubey , Yaqing Chen , Hans-Georg Müller

We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…

General Mathematics · Mathematics 2023-09-06 N. Alexia Raharinirina , Konstantin Fackeldey , Marcus Weber

A finite set of unlabelled points in Euclidean space is the simplest representation of many real objects from mineral rocks to sculptures. Since most solid objects are rigid, their natural equivalence is rigid motion or isometry maintaining…

Metric Geometry · Mathematics 2023-03-27 Vitaliy Kurlin

Molecular assembly offers a promising path to detect life beyond Earth, while minimizing assumptions based on terrestrial life. As mass spectrometers will be central to upcoming Solar System missions, predicting molecular assembly from…

Machine Learning · Computer Science 2025-07-28 Lindsay A. Rutter , Abhishek Sharma , Ian Seet , David Obeh Alobo , An Goto , Leroy Cronin

An intercomparison of microdosimetric and nanodosimetric quantities simulated Monte Carlo codes is in progress with the goal of assessing the uncertainty contribution to simulated results due to the uncertainties of the electron interaction…