236 research outputs found
Enhancement of vacuum polarization effects in a plasma
The dispersive effects of vacuum polarization on the propagation of a strong
circularly polarized electromagnetic wave through a cold collisional plasma are
studied analytically. It is found that, due to the singular dielectric features
of the plasma, the vacuum effects on the wave propagation in a plasma are
qualitatively different and much larger than those in pure vacuum in the regime
when the frequency of the propagating wave approaches the plasma frequency. A
possible experimental setup to detect these effects in plasma is described.Comment: 33 pages, 3 figure
Equilibrium shapes of flat knots
We study the equilibrium shapes of prime and composite knots confined to two
dimensions. Using rigorous scaling arguments we show that, due to self-avoiding
effects, the topological details of prime knots are localised on a small
portion of the larger ring polymer. Within this region, the original knot
configuration can assume a hierarchy of contracted shapes, the dominating one
given by just one small loop. This hierarchy is investigated in detail for the
flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure
On the Dominance of Trivial Knots among SAPs on a Cubic Lattice
The knotting probability is defined by the probability with which an -step
self-avoiding polygon (SAP) with a fixed type of knot appears in the
configuration space. We evaluate these probabilities for some knot types on a
simple cubic lattice. For the trivial knot, we find that the knotting
probability decays much slower for the SAP on the cubic lattice than for
continuum models of the SAP as a function of . In particular the
characteristic length of the trivial knot that corresponds to a `half-life' of
the knotting probability is estimated to be on the cubic
lattice.Comment: LaTeX2e, 21 pages, 8 figur
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Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
A Comprehensive Workflow for General-Purpose Neural Modeling with Highly Configurable Neuromorphic Hardware Systems
In this paper we present a methodological framework that meets novel
requirements emerging from upcoming types of accelerated and highly
configurable neuromorphic hardware systems. We describe in detail a device with
45 million programmable and dynamic synapses that is currently under
development, and we sketch the conceptual challenges that arise from taking
this platform into operation. More specifically, we aim at the establishment of
this neuromorphic system as a flexible and neuroscientifically valuable
modeling tool that can be used by non-hardware-experts. We consider various
functional aspects to be crucial for this purpose, and we introduce a
consistent workflow with detailed descriptions of all involved modules that
implement the suggested steps: The integration of the hardware interface into
the simulator-independent model description language PyNN; a fully automated
translation between the PyNN domain and appropriate hardware configurations; an
executable specification of the future neuromorphic system that can be
seamlessly integrated into this biology-to-hardware mapping process as a test
bench for all software layers and possible hardware design modifications; an
evaluation scheme that deploys models from a dedicated benchmark library,
compares the results generated by virtual or prototype hardware devices with
reference software simulations and analyzes the differences. The integration of
these components into one hardware-software workflow provides an ecosystem for
ongoing preparative studies that support the hardware design process and
represents the basis for the maturity of the model-to-hardware mapping
software. The functionality and flexibility of the latter is proven with a
variety of experimental results
The Generalized Second Law implies a Quantum Singularity Theorem
The generalized second law can be used to prove a singularity theorem, by
generalizing the notion of a trapped surface to quantum situations. Like
Penrose's original singularity theorem, it implies that spacetime is null
geodesically incomplete inside black holes, and to the past of spatially
infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead,
the generalized second law requires that there only be a finite amount of
entropy producing processes in the past, unless there is a reversal of the
arrow of time. In asymptotically flat spacetime, the generalized second law
also rules out traversable wormholes, negative masses, and other forms of
faster-than-light travel between asymptotic regions, as well as closed timelike
curves. Furthermore it is impossible to form baby universes which eventually
become independent of the mother universe, or to restart inflation. Since the
semiclassical approximation is used only in regions with low curvature, it is
argued that the results may hold in full quantum gravity. An introductory
section describes the second law and its time-reverse, in ordinary and
generalized thermodynamics, using either the fine-grained or the coarse-grained
entropy. (The fine-grained version is used in all results except those relating
to the arrow of time.) A proof of the coarse-grained ordinary second law is
given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised
(4.1, 5.2), more comments on AdS. v3: major revisions including change of
title. v4: similar to published version, but with corrections to plan of
paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of
Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new
footnote
Tightness of slip-linked polymer chains
We study the interplay between entropy and topological constraints for a
polymer chain in which sliding rings (slip-links) enforce pair contacts between
monomers. These slip-links divide a closed ring polymer into a number of
sub-loops which can exchange length between each other. In the ideal chain
limit, we find the joint probability density function for the sizes of segments
within such a slip-linked polymer chain (paraknot). A particular segment is
tight (small in size) or loose (of the order of the overall size of the
paraknot) depending on both the number of slip-links it incorporates and its
competition with other segments. When self-avoiding interactions are included,
scaling arguments can be used to predict the statistics of segment sizes for
certain paraknot configurations.Comment: 10 pages, 6 figures, REVTeX
Preverbs: an introduction
The notion ‘preverb’ is a traditional descriptive notion in Indo-European linguistics. It refers to morphemes that appear
in front of a verb, and which form a close semantic unit with that verb. In many cases, the morpheme that functions as a preverb
can also function without a preverbal context, often as an adverb or an adposition. Most linguists use the notion ‘preverb’
as a cover term for preverbal words and preverbal prefixes. The preverb may be separated from the verb whilst retaining its
close cohesion with the verb, which is called ‘tmesis’. It may also develop into a bound morpheme, that is, a prefix inseparable
from the verb, with concomitant reduction of phonological form in some cases. If the preverb has become a real prefix, we
may use the more specific notion of ‘complex verb’, whereas we take the notion ‘complex predicate’ to refer generally to multi-morphemic
expressions with verbal valency. That is, we make a terminological distinction between complex predicates and complex verbs.
The latter are multi-morphemic, but behave as single grammatical words
Virus Replication as a Phenotypic Version of Polynucleotide Evolution
In this paper we revisit and adapt to viral evolution an approach based on
the theory of branching process advanced by Demetrius, Schuster and Sigmund
("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46
(1985) 239-262), in their study of polynucleotide evolution. By taking into
account beneficial effects we obtain a non-trivial multivariate generalization
of their single-type branching process model. Perturbative techniques allows us
to obtain analytical asymptotic expressions for the main global parameters of
the model which lead to the following rigorous results: (i) a new criterion for
"no sure extinction", (ii) a generalization and proof, for this particular
class of models, of the lethal mutagenesis criterion proposed by Bull,
Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18
(2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with
a quantitative prescription for its evaluation, (iv) the quantitative
description of the evolution of the expected values in in four distinct
"stages": extinction threshold, lethal mutagenesis, stationary "equilibrium"
and transient. Finally, based on these quantitative results we are able to draw
some qualitative conclusions.Comment: 23 pages, 1 figure, 2 tables. arXiv admin note: substantial text
overlap with arXiv:1110.336
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