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Chirality, the lack of inversion symmetry, is a geometrical property critical to chemistry, biology and material sciences. In the three-dimensional Euclidean space $\mathbb{R}^3$ chriality can ususally be characterized with four-point…
The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…
Chirality refers to the asymmetry of objects that cannot be superimposed on their mirror image. It is a concept that exists in various scientific fields and has profound consequences. Although these are perhaps most widely recognized within…
Chirality information (i.e. information that allows distinguishing left from right) is ubiquitous for various data modes in computer vision, including images, videos, point clouds, and meshes. While chirality has been extensively studied in…
Chirality is one of the important assymmetrical property in wide area of natural science, which has been studied to predict molecular behavior. One of good methods to analyze molecules with complex structures is representing them as graphs…
Chirality is a fundamental symmetry concept describing discrete states, i.e., left-handed, right-handed, or achiral, and existing at disparate scales and in many categories of scientific fields. Even though symmetry breaking is…
Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here the description of central chirality for tetrahedral molecules using a geometrical approach based on…
Molecular chirality, a form of stereochemistry most often describing relative spatial arrangements of bonded neighbors around tetrahedral carbon centers, influences the set of 3D conformers accessible to the molecule without changing its 2D…
We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of…
The requirements of N=1 superconformal invariance for the correlation functions of chiral superfields are analysed. Complete expressions are found for the three point function for the general spin case and for the four point function for…
An intriguing feature of the Standard Model is that the representations of the unbroken gauge symmetries are vector-like whereas those of the spontaneously broken gauge symmetries are chiral. Here we provide a toy model which shows that a…
Chirality, a pervasive phenomenon in nature, is widely studied across diverse fields including the origins of life, chemical catalysis, drug discovery, and physical optoelectronics. The investigations of natural chiral materials have been…
Chirality in condensed matter is now a topic of the utmost importance because of its significant role in the understanding and mastering of a large variety of new fundamental physicals mechanisms. Versatile experimental approaches, capable…
The presence of chirality in the main molecules of life may well be not just a structural artifact, but of pure biological advantage. The possibility of the existence of a phenomenon of a special mode of interaction, labeled as "chiral…
The chiral structure of liquid crystalline phases arises due to the intrinsic chirality of the constituent mesogens. While it is seemingly straightforward to quantify the macroscopic chirality by using, for instance, the cholesteric pitch…
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Chiral objects rotate when placed in a collimated flow or wind. We exploit this hydrodynamic intuition to construct a tensorial chirality measure for rigid filaments and curves. This tensor is trace-free, so if a curve has a right-handed…
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of…
Chirality is not just a structural artifact in biology but it may provide for a genuine biological advantage. This is due to the phenomenon of chiral interaction (CI) which is described here for mechanical-chiral devices. The main…