2,218 research outputs found
Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results
We analyze the scaling laws for a set of two different species of long
flexible polymer chains joined together at one of their extremities (copolymer
stars) in space dimension D=2. We use a formerly constructed field-theoretic
description and compare our perturbative results for the scaling exponents with
recent conjectures for exact conformal scaling dimensions derived by a
conformal invariance technique in the context of D=2 quantum gravity. A simple
MC simulation brings about reasonable agreement with both approaches. We
analyse the remarkable multifractal properties of the spectrum of scaling
exponents.Comment: 5 page
Counting Hamilton cycles in sparse random directed graphs
Let D(n,p) be the random directed graph on n vertices where each of the
n(n-1) possible arcs is present independently with probability p. A celebrated
result of Frieze shows that if then D(n,p) typically
has a directed Hamilton cycle, and this is best possible. In this paper, we
obtain a strengthening of this result, showing that under the same condition,
the number of directed Hamilton cycles in D(n,p) is typically
. We also prove a hitting-time version of this statement,
showing that in the random directed graph process, as soon as every vertex has
in-/out-degrees at least 1, there are typically
directed Hamilton cycles
Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster
The scaling properties of self-avoiding walks on a d-dimensional diluted
lattice at the percolation threshold are analyzed by a field-theoretical
renormalization group approach. To this end we reconsider the model of Y. Meir
and A. B. Harris (Phys. Rev. Lett. 63:2819 (1989)) and argue that via
renormalization its multifractal properties are directly accessible. While the
former first order perturbation did not agree with the results of other
methods, we find that the asymptotic behavior of a self-avoiding walk on the
percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 +
110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric
description of the available MC and exact enumeration data in a wide range of
dimensions 2<=d<=6.Comment: 4 pages, 2 figure
Antagonism between FOXO and MYC Regulates Cellular Powerhouse.
Alterations in cellular metabolism are a key feature of the transformed phenotype. Enhanced macromolecule synthesis is a prerequisite for rapid proliferation but may also contribute to induction of angiogenesis, metastasis formation, and tumor progression, thereby leading to a poorer clinical outcome. Metabolic adaptations enable cancer cells to survive in suboptimal growth conditions, such as the limited supply of nutrient and oxygen often found in the tumor microenvironment. Metabolic changes, including activation of glycolysis and inhibition of mitochondrial ATP production, are induced under hypoxia to promote survival in low oxygen. FOXO3a, a transcription factor that is inhibited by the phosphatidylinositol 3-kinase/Akt pathway and is upregulated in hypoxia, has emerged as an important negative regulator of MYC function. Recent studies have revealed that FOXO3a acts as a negative regulator of mitochondrial function through inhibition of MYC. Ablation of FOXO3a prevents the inhibition of mitochondrial function induced by hypoxia and results in enhanced oxidative stress. This review will focus on the antagonism between FOXO3a and MYC and discuss their role in cellular bioenergetics, reactive oxygen metabolism, and adaptation to hypoxia, raising questions about the role of FOXO proteins in cancer
Network harness: bundles of routes in public transport networks
Public transport routes sharing the same grid of streets and tracks are often
found to proceed in parallel along shorter or longer sequences of stations.
Similar phenomena are observed in other networks built with space consuming
links such as cables, vessels, pipes, neurons, etc. In the case of public
transport networks (PTNs) this behavior may be easily worked out on the basis
of sequences of stations serviced by each route. To quantify this behavior we
use the recently introduced notion of network harness. It is described by the
harness distribution P(r,s): the number of sequences of s consecutive stations
that are serviced by r parallel routes. For certain PTNs that we have analyzed
we observe that the harness distribution may be described by power laws. These
power laws observed indicate a certain level of organization and planning which
may be driven by the need to minimize the costs of infrastructure and secondly
by the fact that points of interest tend to be clustered in certain locations
of a city. This effect may be seen as a result of the strong interdependence of
the evolutions of both the city and its PTN.
To further investigate the significance of the empirical results we have
studied one- and two-dimensional models of randomly placed routes modeled by
different types of walks. While in one dimension an analytic treatment was
successful, the two dimensional case was studied by simulations showing that
the empirical results for real PTNs deviate significantly from those expected
for randomly placed routes.Comment: 12 pages, 24 figures, paper presented at the Conference ``Statistical
Physics: Modern Trends and Applications'' (23-25 June 2009, Lviv, Ukaine)
dedicated to the 100th anniversary of Mykola Bogolyubov (1909-1992
Two-Dimensional Copolymers and Exact Conformal Multifractality
We consider in two dimensions the most general star-shaped copolymer, mixing
random (RW) or self-avoiding walks (SAW) with specific interactions thereof.
Its exact bulk or boundary conformal scaling dimensions in the plane are all
derived from an algebraic structure existing on a random lattice (2D quantum
gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW
are conformal dimensions of certain star copolymers, here calculated exactly as
non rational algebraic numbers. The associated multifractal function f(alpha)
are found to be identical for a random walk or a SAW in 2D. These are the first
examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January
199
Multifractality of Brownian motion near absorbing polymers
We characterize the multifractal behavior of Brownian motion in the vicinity
of an absorbing star polymer. We map the problem to an O(M)-symmetric
phi^4-field theory relating higher moments of the Laplacian field of Brownian
motion to corresponding composite operators. The resulting spectra of scaling
dimensions of these operators display the convexity properties which are
necessarily found for multifractal scaling but unusual for power of field
operators in field theory. Using a field-theoretic renormalization group
approach we obtain the multifractal spectrum for absorbtion at the core of a
polymer star as an asymptotic series. We evaluate these series using
resummation techniques.Comment: 18 pages, revtex, 6 ps-figure
Transportation Network Stability: a Case Study of City Traffic
The goals of this paper are to present criteria, that allow to a priori
quantify the attack stability of real world correlated networks of finite size
and to check how these criteria correspond to analytic results available for
infinite uncorrelated networks. As a case study, we consider public
transportation networks (PTN) of several major cities of the world. To analyze
their resilience against attacks either the network nodes or edges are removed
in specific sequences (attack scenarios). During each scenario the size S(c) of
the largest remaining network component is observed as function of the removed
share c of nodes or edges. To quantify the PTN stability with respect to
different attack scenarios we use the area below the curve described by S(c)
for c \in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011)
3838) as a numerical measure of network robustness. This measure captures the
network reaction over the whole attack sequence. We present results of the
analysis of PTN stability against node and link-targeted attacks.Comment: 18 pages, 7 figures. Submitted to the topical issue of the journal
'Advances in Complex Systems
The potential of the ground state of NaRb
The X state of NaRb was studied by Fourier transform
spectroscopy. An accurate potential energy curve was derived from more than
8800 transitions in isotopomers NaRb and NaRb. This
potential reproduces the experimental observations within their uncertainties
of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last
observed energy level (, ) lies at \AA, leading
to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table
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