7,256 research outputs found
Electronic structure of an electron on the gyroid surface, a helical labyrinth
Previously reported formulation for electrons on curved periodic surfaces is
used to analyze the band structure of an electron bound on the gyroid surface
(the only triply-periodic minimal surface that has screw axes). We find that an
effect of the helical structure appears as the bands multiply sticking together
on the Brillouin zone boundaries. We elaborate how the band sticking is lifted
when the helical and inversion symmetries of the structure are degraded. We
find from this that the symmetries give rise to prominent peaks in the density
of states.Comment: RevTeX, 4 pages, 6 figure
Branching, Capping, and Severing in Dynamic Actin Structures
Branched actin networks at the leading edge of a crawling cell evolve via
protein-regulated processes such as polymerization, depolymerization, capping,
branching, and severing. A formulation of these processes is presented and
analyzed to study steady-state network morphology. In bulk, we identify several
scaling regimes in severing and branching protein concentrations and find that
the coupling between severing and branching is optimally exploited for
conditions {\it in vivo}. Near the leading edge, we find qualitative agreement
with the {\it in vivo} morphology.Comment: 4 pages, 2 figure
Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves
We provide a systematic test of empirical theories of covalent bonding in
solids using an exact procedure to invert ab initio cohesive energy curves. By
considering multiple structures of the same material, it is possible for the
first time to test competing angular functions, expose inconsistencies in the
basic assumption of a cluster expansion, and extract general features of
covalent bonding. We test our methods on silicon, and provide the direct
evidence that the Tersoff-type bond order formalism correctly describes
coordination dependence. For bond-bending forces, we obtain skewed angular
functions that favor small angles, unlike existing models. As a
proof-of-principle demonstration, we derive a Si interatomic potential which
exhibits comparable accuracy to existing models.Comment: 4 pages revtex (twocolumn, psfig), 3 figures. Title and some wording
(but no content) changed since original submission on 24 April 199
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
Persistent Homology Over Directed Acyclic Graphs
We define persistent homology groups over any set of spaces which have
inclusions defined so that the corresponding directed graph between the spaces
is acyclic, as well as along any subgraph of this directed graph. This method
simultaneously generalizes standard persistent homology, zigzag persistence and
multidimensional persistence to arbitrary directed acyclic graphs, and it also
allows the study of more general families of topological spaces or point-cloud
data. We give an algorithm to compute the persistent homology groups
simultaneously for all subgraphs which contain a single source and a single
sink in arithmetic operations, where is the number of vertices in
the graph. We then demonstrate as an application of these tools a method to
overlay two distinct filtrations of the same underlying space, which allows us
to detect the most significant barcodes using considerably fewer points than
standard persistence.Comment: Revised versio
Large-scale exact diagonalizations reveal low-momentum scales of nuclei
Ab initio methods aim to solve the nuclear many-body problem with controlled
approximations. Virtually exact numerical solutions for realistic interactions
can only be obtained for certain special cases such as few-nucleon systems.
Here we extend the reach of exact diagonalization methods to handle model
spaces with dimension exceeding on a single compute node. This allows
us to perform no-core shell model (NCSM) calculations for 6Li in model spaces
up to and to reveal the 4He+d halo structure of this
nucleus. Still, the use of a finite harmonic-oscillator basis implies
truncations in both infrared (IR) and ultraviolet (UV) length scales. These
truncations impose finite-size corrections on observables computed in this
basis. We perform IR extrapolations of energies and radii computed in the NCSM
and with the coupled-cluster method at several fixed UV cutoffs. It is shown
that this strategy enables information gain also from data that is not fully UV
converged. IR extrapolations improve the accuracy of relevant bound-state
observables for a range of UV cutoffs, thus making them profitable tools. We
relate the momentum scale that governs the exponential IR convergence to the
threshold energy for the first open decay channel. Using large-scale NCSM
calculations we numerically verify this small-momentum scale of finite nuclei.Comment: Minor revisions.Accepted for publication in Physical Review
Categorification of persistent homology
We redevelop persistent homology (topological persistence) from a categorical
point of view. The main objects of study are diagrams, indexed by the poset of
real numbers, in some target category. The set of such diagrams has an
interleaving distance, which we show generalizes the previously-studied
bottleneck distance. To illustrate the utility of this approach, we greatly
generalize previous stability results for persistence, extended persistence,
and kernel, image and cokernel persistence. We give a natural construction of a
category of interleavings of these diagrams, and show that if the target
category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational
Geometr
Mind the Gap: A Study in Global Development through Persistent Homology
The Gapminder project set out to use statistics to dispel simplistic notions
about global development. In the same spirit, we use persistent homology, a
technique from computational algebraic topology, to explore the relationship
between country development and geography. For each country, four indicators,
gross domestic product per capita; average life expectancy; infant mortality;
and gross national income per capita, were used to quantify the development.
Two analyses were performed. The first considers clusters of the countries
based on these indicators, and the second uncovers cycles in the data when
combined with geographic border structure. Our analysis is a multi-scale
approach that reveals similarities and connections among countries at a variety
of levels. We discover localized development patterns that are invisible in
standard statistical methods
Topological characteristics of oil and gas reservoirs and their applications
We demonstrate applications of topological characteristics of oil and gas
reservoirs considered as three-dimensional bodies to geological modeling.Comment: 12 page
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