Related papers: Planar Symmetry Detection and Quantification using…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's…
We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological…
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence.…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
Spontaneous symmetry breaking is an essential feature of modern science. We demonstrate that it also plays an important role in the physics of complex plasmas. Complex plasmas can serve as a powerful tool for observing and studying discrete…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Coherence is a defining property of quantum theory that accounts for quantum advantage in many quantum information tasks. Although many coherence quantifiers have been introduced in various contexts, the lack of efficient methods to…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
Symmetry is a powerful tool for studying dynamics in QFT: it provides selection rules, constrains RG flows, and often simplifies analysis. Currently, our understanding is that the most general form of symmetry is described by categorical…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…
In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…
This paper finds a symmetry relation (between quantiles of a random variable and its negative) that is intuitively appealing. We show this symmetry is quite useful in finding new relations for quantiles, in particular an equivariance…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
In this paper we study a new metric for comparing Betti numbers functions in bidimensional persistent homology, based on coherent matchings, i.e. families of matchings that vary in a continuous way. We prove some new results about this…