Related papers: Measuring Lattices
We introduce and explore patterned lattices consisting of coupled isospectral cells that vary across the lattice. The isospectrality of the cells is encapsulated in the phase that characterizes each cell and can be designed at will such…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
The potential for a precise measurement of the Unitarity Triangle angle $\gamma$ in future experiments from the decay $B^0 \to DK^{*0}$ is well-known. It has recently been suggested that the sensitivity can be significantly enhanced by…
We present an in-depth investigation of a fully automated Fourier-based analysis to determine the cell size and the width of its distribution in 3D biological tissues. The results are thoroughly tested using generated images, and we offer…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
A fast, parallel algorithm for distant-dependent calculation and simulation of crystal properties is presented along with speedup results and methods of application. An illustrative example is used to compute the Lennard-Jones lattice…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of…
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of…
We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…
We calculate the lattice dispersion relation for three dimensional simulations of scalar fields. We argue that the mode frequency of scalar fields on the lattice should not be treated as a function of the magnitude of its wavevector but…
How cells reliably infer information about their environment is a fundamentally important question. While sensing and signaling generally start with cell-surface receptors, the degree of accuracy with which a cell can measure external…
The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research…
This work discusses preliminary work aimed at simulating and visualizing the growth process of a tiny structure inside the cell---the microtubule. Difficulty of recording the process lies in the fact that the tissue preparation method for…
We investigate five different models to reconstruct the 3D $\gamma$-ray hit coordinates in five large \lacls monolithic crystals optically coupled to pixelated silicon photomultipliers. These scintillators have a base surface of 50 $\times$…
Real-time deformability cytometry (RT-DC) is an established method that quantifies features like size, shape, and stiffness for whole cell populations on a single-cell level in real time. To extract the cell stiffness, a lookup table (LUT)…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…
Unitarity is a fundamental property of any theory required to ensure we work in a theoretically consistent framework. In comparison with the quark sector, experimental tests of unitarity for the 3x3 neutrino mixing matrix are considerably…
Epithelial cells form diverse structures from squamous spherical organoids to densely packed pseudostratified tissues. Quantification of cellular properties in these contexts requires high-resolution deep imaging and computational…