1,459 research outputs found
Extraction of cylinders and cones from minimal point sets
We propose new algebraic methods for extracting cylinders and cones from
minimal point sets, including oriented points. More precisely, we are
interested in computing efficiently cylinders through a set of three points,
one of them being oriented, or through a set of five simple points. We are also
interested in computing efficiently cones through a set of two oriented points,
through a set of four points, one of them being oriented, or through a set of
six points. For these different interpolation problems, we give optimal bounds
on the number of solutions. Moreover, we describe algebraic methods targeted to
solve these problems efficiently
Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems
In this article, we discuss the stability of soft quasicrystalline phases in
a coupled-mode Swift-Hohenberg model for three-component systems, where the
characteristic length scales are governed by the positive-definite gradient
terms. Classic two-mode approximation method and direct numerical minimization
are applied to the model. In the latter approach, we apply the projection
method to deal with the potentially quasiperiodic ground states. A variable
cell method of optimizing the shape and size of higher-dimensional periodic
cell is developed to minimize the free energy with respect to the order
parameters. Based on the developed numerical methods, we rediscover decagonal
and dodecagonal quasicrystalline phases, and find diverse periodic phases and
complex modulated phases. Furthermore, phase diagrams are obtained in various
phase spaces by comparing the free energies of different candidate structures.
It does show not only the important roles of system parameters, but also the
effect of optimizing computational domain. In particular, the optimization of
computational cell allows us to capture the ground states and phase behavior
with higher fidelity. We also make some discussions on our results and show the
potential of applying our numerical methods to a larger class of mean-field
free energy functionals.Comment: 26 pages, 13 figures; accepted by Communications in Computational
Physic
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Revealing Dynamic Mechanisms of Cell Fate Decisions From Single-Cell Transcriptomic Data.
Cell fate decisions play a pivotal role in development, but technologies for dissecting them are limited. We developed a multifunction new method, Topographer, to construct a "quantitative" Waddington's landscape of single-cell transcriptomic data. This method is able to identify complex cell-state transition trajectories and to estimate complex cell-type dynamics characterized by fate and transition probabilities. It also infers both marker gene networks and their dynamic changes as well as dynamic characteristics of transcriptional bursting along the cell-state transition trajectories. Applying this method to single-cell RNA-seq data on the differentiation of primary human myoblasts, we not only identified three known cell types, but also estimated both their fate probabilities and transition probabilities among them. We found that the percent of genes expressed in a bursty manner is significantly higher at (or near) the branch point (~97%) than before or after branch (below 80%), and that both gene-gene and cell-cell correlation degrees are apparently lower near the branch point than away from the branching. Topographer allows revealing of cell fate mechanisms in a coherent way at three scales: cell lineage (macroscopic), gene network (mesoscopic), and gene expression (microscopic)
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