Related papers: Measuring Lattices
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…
Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we…
Distance measurement is crucial to astronomy. Here we suggest a new conceptual method to measure the distance by using a local instrument. By engaging the double-slit interference and by considering the phase information of the light, the…
Programmable unitary converters are powerful tools for realizing unitary transformations, advancing fields of computing and communication. The accuracy of these unitary transformations is crucial for maintaining high fidelity in such…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
A 3-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of…
We propose a 3D convolutional neural network to simultaneously segment and detect cell nuclei in confocal microscopy images. Mirroring the co-dependency of these tasks, our proposed model consists of two serial components: the first part…
The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…
The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be…
We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal…
Estimating decay parameters in lattice simulations is a computationally demanding problem, requiring several volumes and momenta. We explore an alternative approach, where the transition amplitude can be extracted from the spectral…
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study…
The use of a method of spectra disentangling for telluric lines is explained in detail, with a particular emphasis on high-precision radial-velocity measurements for the search for extrasolar planets. New improvements to the method are…
Electro-optical properties of deformed helix ferroelectric liquid crystal (DHFLC) cells are studied by using a general theoretical approach to polarization gratings in which the transmission and reflection matrices of diffraction orders are…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
Cell counting in microscopy images is vital in medicine and biology but extremely tedious and time-consuming to perform manually. While automated methods have advanced in recent years, state-of-the-art approaches tend to increasingly…