Related papers: Shape theory via polar decomposition
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…
A fast and general Bayesian inference framework to infer the physical properties of dichroic polarization using mid-infrared imaging- and spectro-polarimetric observations is presented. The Bayesian approach is based on a hierarchical…
Polaritonic lattices offer a unique testbed for studying nonlinear driven-dissipative physics. They show qualitative changes of a steady state as a function of system parameters, which resemble non-equilibrium phase transitions. Unlike…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Pulsar radio emission is modelled as a sum of two completely polarized non-orthogonal modes with the randomly varying Stokes parameters and intensity ratio. The modes are the result of polarization evolution of the original natural waves in…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
We study lepton polarization asymmetries in the (Lambda_b -> Lambda l^+ l^-) decay using the most general model independent effective Hamiltonian. The dependence of the lepton polarizations and their combinations on the new Wilson…
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…
We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
The shape influence of decaying thermalized source on various characteristics of multifragmentation as well as its interplay with effects of angular momentum and collective expansion are first studied and the most pertinent variables are…
A new method for analyzing the morphological features of point patterns is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of anisotropic distributions.…
Polarization is well known for its ability to decompose diffuse and specular reflections. However, the existing decomposition methods only focus on direct reflection and overlook multiple reflections, especially specular inter-reflection.…
Statistical shape modeling (SSM) directly from 3D medical images is an underutilized tool for detecting pathology, diagnosing disease, and conducting population-level morphology analysis. Deep learning frameworks have increased the…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…