1,246 research outputs found
Representation Theory of Twisted Group Double
This text collects useful results concerning the quasi-Hopf algebra \D . We
give a review of issues related to its use in conformal theories and physical
mathematics. Existence of such algebras based on 3-cocycles with values in which mimic for finite groups Chern-Simons terms of gauge theories,
open wide perspectives in the so called "classification program". The
modularisation theorem proved for quasi-Hopf algebras by two authors some years
ago makes the computation of topological invariants possible. An updated,
although partial, bibliography of recent developments is provided.Comment: 15 pages, no figur
Modeling Cell-to-Cell Communication Networks Using Response-Time Distributions.
Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as "black boxes" with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps
On Dijkgraaf-Witten Type Invariants
We explicitly construct a series of lattice models based upon the gauge group
which have the property of subdivision invariance, when the coupling
parameter is quantized and the field configurations are restricted to satisfy a
type of mod- flatness condition. The simplest model of this type yields the
Dijkgraaf-Witten invariant of a -manifold and is based upon a single link,
or -simplex, field. Depending upon the manifold's dimension, other models
may have more than one species of field variable, and these may be based on
higher dimensional simplices.Comment: 18 page
A note on the capacity of the binary perceptron
Determining the capacity of the Binary Perceptron is a
long-standing problem. Krauth and Mezard (1989) conjectured an explicit value
of , approximately equal to .833, and a rigorous lower bound matching
this prediction was recently established by Ding and Sun (2019). Regarding the
upper bound, Kim and Roche (1998) and Talagrand (1999) independently showed
that < .996, while Krauth and Mezard outlined an argument which can
be used to show that < .847. The purpose of this expository note is
to record a complete proof of the bound < .847. The proof is a
conditional first moment method combined with known results on the spherical
perceptro
Localized radial roll patterns in higher space dimensions
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which these patterns resemble a periodic profile stays either bounded, in which case branches form closed bounded curves (“isolas”), or the length increases to infinity so that branches are unbounded in function space (“snaking”). In two space dimensions, numerical computations show that branches of localized rolls exhibit a more complicated structure in which both isolas and snaking occur. In this paper, we analyse the structure of branches of localized radial roll solutions in dimension 1+ε, with 0 < ε 1, through a perturbation analysis. Our analysis sheds light on some of the features visible in the planar case.http://math.bu.edu/people/mabeck/Bramburgeretal18.pdfFirst author draf
Cellular Heterogeneity: Do Differences Make a Difference?
A central challenge of biology is to understand how individual cells process information and respond to perturbations. Much of our knowledge is based on ensemble measurements. However, cell-to-cell differences are always present to some degree in any cell population, and the ensemble behaviors of a population may not represent the behaviors of any individual cell. Here, we discuss examples of when heterogeneity cannot be ignored and describe practical strategies for analyzing and interpreting cellular heterogeneity
Defect free global minima in Thomson's problem of charges on a sphere
Given unit points charges on the surface of a unit conducting sphere,
what configuration of charges minimizes the Coulombic energy ? Due to an exponential rise in good local minima, finding global
minima for this problem, or even approaches to do so has proven extremely
difficult. For \hbox{} recent theoretical work based on
elasticity theory, and subsequent numerical work has shown, that for --1000 adding dislocation defects to a symmetric icosadeltahedral lattice
lowers the energy. Here we show that in fact this approach holds for all ,
and we give a complete or near complete catalogue of defect free global minima.Comment: Revisions in Tables and Reference
Interstitial Fractionalization and Spherical Crystallography
Finding the ground states of identical particles packed on spheres has
relevance for stabilizing emulsions and a venerable history in the literature
of theoretical physics and mathematics. Theory and experiment have confirmed
that defects such as disclinations and dislocations are an intrinsic part of
the ground state. Here we discuss the remarkable behavior of vacancies and
interstitials in spherical crystals. The strain fields of isolated
disclinations forced in by the spherical topology literally rip interstitials
and vacancies apart, typically into dislocation fragments that combine with the
disclinations to create small grain boundary scars. The fractionation is often
into three charge-neutral dislocations, although dislocation pairs can be
created as well. We use a powerful, freely available computer program to
explore interstitial fractionalization in some detail, for a variety of power
law pair potentials. We investigate the dependence on initial conditions and
the final state energies, and compare the position dependence of interstitial
energies with the predictions of continuum elastic theory on the sphere. The
theory predicts that, before fragmentation, interstitials are repelled from
5-fold disclinations and vacancies are attracted. We also use vacancies and
interstitials to study low energy states in the vicinity of "magic numbers"
that accommodate regular icosadeltahedral tessellations.Comment: 21 pages, 9 figure
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