Publications related to Geometric analysis

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation o ...

Wiley2022

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Solvent-Aware Interfaces in Continuum Solvation

Nicola Marzari, Oliviero Andreussi, Francesco Nattino, Nicolas Georg Hörmann

Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of co ...

AMER CHEMICAL SOC2019

Geometric spects A of Similarity Problems

Peter Clemens Schlicht

This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the co ...

OXFORD UNIV PRESS2018

A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

Mihai Adrian Ionescu, Andrei Müller

This work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry ...

MDPI2018

Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications

Andrea Bartezzaghi

In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...

EPFL2017

The Intricate Structural Chemistry of MII2nLn-Type Assemblies

Rosario Scopelliti, Kay Severin, Farzaneh Fadaei Tirani, Philip Pattison, Euro Solari, Giacomo Cecot, Mathieu Jérémie Marmier

The reaction of cis-blocked, square-planar MII complexes with tetratopic N-donor ligands is known to give metallasupramolecular assemblies of the formula M2nLn. These assemblies typically adopt barrel-like structures, with the ligands paneling the sides of ...

2017

Geometrical Effect in 2D Nanopores

Aleksandra Radenovic, Andras Kis, Duncan Thomas Lindsay Alexander, Vasiliki Tileli, Martina Lihter, Ke Liu, Dumitru Dumcenco, Davide Deiana, Aditya Sarathy

A long-standing problem in the application of solid-state nanopores is the lack of the precise control over the geometry of artificially formed pores compared to the well-defined geometry in their biological counterpart, that is, protein nanopores. To date ...

American Chemical Society (ACS)2017

Isogeometric Analysis of geometric partial differential equations

Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi

We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...

Elsevier2016

On the geometrical interpretation of scale-invariant models of inflation

Georgios Karananas, Javier Rubio

We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions can be universal a ...

Elsevier2016

Solar reflected glare affecting visual performance

Jan Wienold

Visual comfort is important to the wellbeing of people and their productivity. However, too much light in the field of view can cause discomfort and disability glare. Under certain conditions it can even cause accidents. This paper addresses the disability ...

2014

Discovering Structured Variations via Coupled Template Matching

Mark Pauly, Duygu Ceylan, Boris Neubert, Ngoc Minh Dang

Understanding patterns of variation from raw measurement data remains a central goal of shape analysis. This understanding reveals which elements are exactly repeated, or how elements can be derived as structured variations from a common base element. We i ...

2016

Effect of realistic modeling of deep brain stimulation on the prediction of volume of active tissue

Juan Ramon Mosig, Laleh Golestanirad

Deep brain stimulation (DBS) is a well-established treatment for Parkinson's disease, essential tremor and dystonia. It has also been successfully applied to treat various other neurological and psychiatric conditions including depression and obsessive-com ...

2012

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Pascal Frossard, Daniel Kressner, Effrosyni Kokiopoulou

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

2011

Curvature Analysis of Pattern Transformation Manifolds

Pascal Frossard, Elif Vural

Transformation manifolds are quite attractive for image analysis applications that require transformation invariance properties. The geometric structure of a transformation manifold has a profound influence on the design of processing algorithm, and the cu ...

2010

Some applications of symmetries in differential geometry and dynamical systems

Oana Mihaela Dragulete

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

White matter fiber tract segmentation in DT-MRI using geometric flows

Jean-Philippe Thiran, Patric Hagmann, Reto Meuli, Xavier Bresson, Olivier Cuisenaire, Lisa Jonasson

In this paper, we present a 3D geometric flow designed to segment the main core of fiber tracts in diffusion tensor magnetic resonance images. The fundamental assumption of our fiber segmentation technique is that adjacent voxels in a tract have similar pr ...

2005