Related papers: A Density-Based Continuous Local Symmetry Measure
Symmetry is one of the most beautiful yet mysterious concepts in science. In chemical systems, presence of local symmetries at specific fragments often serve as driving forces behind many physicochemical properties, including stability,…
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
Optical chirality density is widely used as a scalar measure of the chiral properties of electromagnetic fields and their interaction with matter. However, in anisotropic and structured media, a single scalar quantity is generally…
A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system…
The concept of local symmetry is a powerful tool in predicting complex transport phenomena in aperiodic media. A nonlocal continuity formalism reveals how local symmetries are encoded into the dynamics of light propagation in discrete…
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is given to the examination of local dimensions of measures in…
Symmetry classification of crystal structures has been central to predicting physical properties of materials. While such structural classification identifies which physical responses are symmetry-allowed, the magnitudes of these responses…
Circular dichroism spectroscopy is an essential technique for understanding molecular structure and magnetic materials, but spatial resolution is limited by the wavelength of light, and sensitivity sufficient for single-molecule…
The paper describes a method for measuring the similarity and symmetry of an image annotated with bounding boxes indicating image objects. The latter representation became popular recently due to the rapid development of fast and efficient…
The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in…
We report an ab initio evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is…
Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…
The study of electronic transitions within a molecule connected to the absorption or emission of light is a common task in the process of the design of new materials. The transitions are complex quantum mechanical processes and a detailed…
Biological systems exhibit marked molecular asymmetry, with proteins based predominantly on L-amino acids and nucleic acids and carbohydrates largely composed of D-sugars. Explanations for homochirality include asymmetric photochemistry,…
We compare the various chirality measures most widely used in the literature to quantify chiral symmetry in extended solids, i.e., the continuous chirality measure, the Hausdorff distance, and the angular momentum. By studying these…
Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
In quantum mechanics, each conserved quantity (e.g., energy, position, linear momentum and angular momentum) is associated with a Hermitian operator. Its expected value can then be determined by performing a measurement on the wavefunction.…
In this work, we investigate the dynamics of homeomorphisms through the lens of the local shadowing theory. We study the influence of positively shadowable points and positively shadowable measures into the local entropy theory of…