Related papers: Measuring Lattices
Biomolecular condensates form on timescales of seconds in cells upon environmental or compositional changes. Condensate formation is thus argued to act as a mechanism for sensing such changes and quickly initiating downstream processes,…
Dislocations - linear defects within the crystal lattice of, e.g., metals - already have been directly observed and analyzed for nearly a century. While experimental characterization methods can nowadays reconstruct three-dimensional…
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear…
New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent…
Parallax measurements allow distances to celestial objects to be determined. Coupled with measurement of their position on the celestial sphere, it gives a full three-dimensional picture of the location of the objects relative to the…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
We show how a filtration of Delaunay complexes can be used to approximate the persistence diagram of the distance to a point set in $R^d$. Whereas the full Delaunay complex can be used to compute this persistence diagram exactly, it may…
Motivated by an application in cell biology, we consider spatial sorting processes defined by particles moving from an initial to a final configuration. We describe an algorithm for constructing a cell complex in space-time, called the…
It is proposed to search for scintillation of extragalactic sources through the last unknown baryonic structures. Appropriate observation of the scintillation process described here should allow one to detect column density stochastic…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…
We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact…
In ab-initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. "Ab-initio" means a process performed without any good…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty…
We consider causal 3-dimensional triangulations with the topology of $S^2\times [0,1]$ or $D^2\times [0,1]$ where $S^2$ and $D^2$ are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that…
Computation of biological processes creates great promise for everyday life and great challenges for physical scientists. Simulations of molecular dynamics appeal to biologists as a natural extension of structural biology. Once biologists…
Despite more than 100 years of study, it is unclear if the movement of proteins inside the cell is best described as a mosh pit or an exquisitely choreographed dance. Recent studies suggest the latter. Local interactions induce molecular…
The accurate segmentation and tracking of cells in microscopy image sequences is an important task in biomedical research, e.g., for studying the development of tissues, organs or entire organisms. However, the segmentation of touching…