title: Solving Fermat-type equations x^5+y^5=dz^p

abstract:
  In this paper we are interested in solving the Fermat-type equations
x^5+y^5=dz^p where d is a positive integer and p a prime number $\ge 7$. We
describe a new method based on modularity theorems which allows us to improve
all the results in a previous paper of the first author. We finally discuss the
present limitations of the method by looking at the case d=3.


title:
Detecting the overlapping and hierarchical community structure of
  complex networks

abstract:
  Many networks in nature, society and technology are characterized by a
mesoscopic level of organization, with groups of nodes forming tightly
connected units, called communities or modules, that are only weakly linked to
each other. Uncovering this community structure is one of the most important
problems in the field of complex networks. Networks often show a hierarchical
organization, with communities embedded within other communities; moreover,
nodes can be shared between different communities. Here we present the first
algorithm that finds both overlapping communities and the hierarchical
structure. The method is based on the local optimization of a fitness function.
Community structure is revealed by peaks in the fitness histogram. The
resolution can be tuned by a parameter enabling to investigate different
hierarchical levels of organization. Tests on real and artificial networks give
excellent results.

categories: physics.soc-ph cond-mat.stat-mech physics.comp-ph stat.CO


title:
On Minimally-Parametric Primordial Power Spectrum Reconstruction and the
  Evidence for a Red Tilt

abstract:
  The latest cosmological data seem to indicate a significant deviation from
scale invariance of the primordial power spectrum when parameterized either by
a power law or by a spectral index with non-zero "running". This deviation, by
itself, serves as a powerful tool to discriminate among theories for the origin
of cosmological structures such as inflationary models. Here, we use a
minimally-parametric smoothing spline technique to reconstruct the shape of the
primordial power spectrum. This technique is well-suited to search for smooth
features in the primordial power spectrum such as deviations from scale
invariance or a running spectral index, although it would recover sharp
features of high statistical significance. We use the WMAP 3 year results in
combination with data from a suite of higher resolution CMB experiments
(including the latest ACBAR 2008 release), as well as large-scale structure
data from SDSS and 2dFGRS. We employ cross-validation to assess, using the data
themselves, the optimal amount of smoothness in the primordial power spectrum
consistent with the data. This minimally-parametric reconstruction supports the
evidence for a power law primordial power spectrum with a red tilt, but not for
deviations from a power law power spectrum. Smooth variations in the primordial
power spectrum are not significantly degenerate with the other cosmological
parameters.


title: Complexity of Decoding Positive-Rate Reed-Solomon Codes

abstract:
  The complexity of maximal likelihood decoding of the Reed-Solomon codes
$[q-1, k]_q$ is a well known open problem. The only known result in this
direction states that it is at least as hard as the discrete logarithm in some
cases where the information rate unfortunately goes to zero. In this paper, we
remove the rate restriction and prove that the same complexity result holds for
any positive information rate. In particular, this resolves an open problem
left in [4], and rules out the possibility of a polynomial time algorithm for
maximal likelihood decoding problem of Reed-Solomon codes of any rate under a
well known cryptographical hardness assumption. As a side result, we give an
explicit construction of Hamming balls of radius bounded away from the minimum
distance, which contain exponentially many codewords for Reed-Solomon code of
any positive rate less than one. The previous constructions only apply to
Reed-Solomon codes of diminishing rates. We also give an explicit construction
of Hamming balls of relative radius less than 1 which contain subexponentially
many codewords for Reed-Solomon code of rate approaching one.


title: Immirzi parameter and fermions with non-minimal coupling

abstract:
  We clarify the role played by the Immirzi parameter in classical gravity
coupled to fermions. Considering the general non-minimal coupling, we show
that, although the torsion depends explicitly on the Immirzi parameter, in a
suitable parametrization the effective action obtained by integrating out the
spin-connection is independent of it. Thus the Immirzi parameter is not
detectable in classical theory even after coupling of fermions.


title: S-wave and p-wave scattering in a cold gas of Na and Rb atoms

abstract:
  Using improved experimentally based $X{}^1\Sigma^+$ and $a{}^3\Sigma^+$
molecular potentials of NaRb, we apply the variable phase method to compute new
data for low energy scattering of $^{23}$Na atoms by $^{85}$Rb atoms and
$^{87}$Rb atoms. These are the scattering lengths and volumes, numbers of bound
states and effective ranges, which we use to obtain the low energy spin-change
cross section as functions of the system temperature and the isotope masses.
  From an analysis of the contributions of s-wave and p-wave scatterings to the
elastic cross section we estimate temperatures below which only s-wave
scattering is dominant. We compare our quantal results to data obtained from
the semiclassical approximation. We supply evidence for the existence of a near
zero energy p-wave bound state supported by the singlet molecular potential.


title:
Determinants of bistability in induction of the Escherichia coli lac
  operon

abstract:
  We have developed a mathematical model of regulation of expression of the
Escherichia coli lac operon, and have investigated bistability in its
steady-state induction behavior in the absence of external glucose. Numerical
analysis of equations describing regulation by artificial inducers revealed two
natural bistability parameters that can be used to control the range of inducer
concentrations over which the model exhibits bistability. By tuning these
bistability parameters, we found a family of biophysically reasonable systems
that are consistent with an experimentally determined bistable region for
induction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). The
model predicts that bistability can be abolished when passive transport or
permease export becomes sufficiently large; the former case is especially
relevant to induction by isopropyl-beta, D-thiogalactopyranoside. To model
regulation by lactose, we developed similar equations in which allolactose, a
metabolic intermediate in lactose metabolism and a natural inducer of lac, is
the inducer. For biophysically reasonable parameter values, these equations
yield no bistability in response to induction by lactose; however, systems with
an unphysically small permease-dependent export effect can exhibit small
amounts of bistability for limited ranges of parameter values. These results
cast doubt on the relevance of bistability in the lac operon within the natural
context of E. coli, and help shed light on the controversy among existing
theoretical studies that address this issue. The results also suggest an
experimental approach to address the relevance of bistability in the lac operon
within the natural context of E. coli.


title:
Quantum Communication through Spin Chain Dynamics: an Introductory
  Overview

abstract:
  We present an introductory overview of the use of spin chains as quantum
wires, which has recently developed into a topic of lively interest. The
principal motivation is in connecting quantum registers without resorting to
optics. A spin chain is a permanently coupled 1D system of spins. When one
places a quantum state on one end of it, the state will be dynamically
transmitted to the other end with some efficiency if the spins are coupled by
an exchange interaction. No external modulations or measurements on the body of
the chain, except perhaps at the very ends, is required for this purpose. For
the simplest (uniformly coupled) chain and the simplest encoding (single qubit
encoding), however, dispersion reduces the quality of transfer. We present a
variety of alternatives proposed by various groups to achieve perfect quantum
state transfer through spin chains. We conclude with a brief discussion of the
various directions in which the topic is developing.

categories: cond-mat.other cond-mat.stat-mech cond-mat.str-el quant-ph


title: Stochastic master equation for a probed system in a cavity

abstract:
  We present a detailed derivation of the stochastic master equation
determining the time evolution of the state of a general quantum system, which
is placed inside a cavity and subjected to indirect measurements by monitoring
the state of electromagnetic radiation transmitted through the cavity. The
derivation is based on the physics involved and the final result is stated in
terms of the physical parameters of the setup. To illustrate the predictions
contained in the equation, we solve it analytically for a specific system, and
we demonstrate quantum jumps and freezing of the internal coherent dynamics of
the system as a result of continued measurements.


title:
Lower Bounds for Complementation of omega-Automata Via the Full Automata
  Technique

abstract:
  In this paper, we first introduce a lower bound technique for the state
complexity of transformations of automata. Namely we suggest first considering
the class of full automata in lower bound analysis, and later reducing the size
of the large alphabet via alphabet substitutions. Then we apply such technique
to the complementation of nondeterministic \omega-automata, and obtain several
lower bound results. Particularly, we prove an \omega((0.76n)^n) lower bound
for B\"uchi complementation, which also holds for almost every complementation
or determinization transformation of nondeterministic omega-automata, and prove
an optimal (\omega(nk))^n lower bound for the complementation of generalized
B\"uchi automata, which holds for Streett automata as well.


title:
Weak type estimates for spherical multipliers on noncompact symmetric
  spaces

abstract:
  In this paper we prove sharp weak type 1 estimates for spherical Fourier
multipliers on symmetric spaces of the noncompact type. This complements
earlier results of J.-Ph. Anker and A.D. Ionescu.


title: A generalization of the duality for multiple harmonic sums

abstract:
  The duality is a fundamental property of the finite multiple harmonic sums
(MHS). In this paper, we prove a duality result for certain generalizations of
MHS which appear naturally as the differences of MHS. We also prove a formula
for the differences of these generalized MHS.


title: Rate of decoherence for an electron weakly coupled to a phonon gas

abstract:
  We study the dynamics of an electron weakly coupled to a phonon gas. The
initial state of the electron is the superposition of two spatially localized
distant bumps moving towards each other, and the phonons are in a thermal
state. We investigate the dynamics of the system in the kinetic regime and show
that the time evolution makes the non-diagonal terms of the density matrix of
the electron decay, destroying the interference between the two bumps. We show
that such a damping effect is exponential in time, and the related decay rate
is proportional to the total scattering cross section of the electron-phonon
interaction.


title: Radiative energy loss in a finite dynamical QCD medium

abstract:
  The radiative energy loss of a quark jet traversing a finite size QCD medium
with dynamical constituents is calculated to first order in opacity. Although
finite size corrections reduce the energy loss relative to an infinite
dynamical QCD medium, under realistic conditions it remains significantly
larger than in a static medium. Quantitative predictions of jet suppression in
relativistic heavy ion collisions must therefore account for the dynamics of
the medium's constituents. Finite size effects are shown to induce a non-linear
path length dependence of the energy loss. Our results suggest a simple general
mapping between energy loss expressions for static and dynamical QCD media.


title: On the spectrum of unitary finite-Euclidean graphs

abstract:
  We consider unitary graphs attached to Z_d^n using an analogue of the
Euclidean distance. These graphs are shown to be integral when n is odd or the
dimension d is even.


title:
QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large
  r(S_1) with Double-Trace Deformations

abstract:
  We consider QCD-like theories with one massless fermion in various
representations of the gauge group SU$(N)$. The theories are formulated on
$R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these
theories are characterized by confinement, mass gap and spontaneous breaking of
a (discrete) chiral symmetry ($\chi$SB). At small $r(S_1)$, in order to
stabilize the vacua of these theories at a center-symmetric point, we suggest
to perform a double trace deformation. With these deformation, the theories at
hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features of
the large-$r(S_1)$ limit: confinement and $\chi$SB. We calculate the string
tension, mass gap, bifermion condensates and $\theta$ dependence. The
double-trace deformation becomes dynamically irrelevant at large $r(S_1)$.
Despite the fact that at small $r(S_1)$ confinement is Abelian, while it is
expected to be non-Abelian at large $r(S_1)$, we argue that small and
large-$r(S_1)$ physics are continuously connected. If so, one can use
small-$r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on
$R_4$.


title: Algebraic Degree of Polynomial Optimization

abstract:
  Consider the polynomial optimization problem whose objective and constraints
are all described by multivariate polynomials. Under some genericity
assumptions, %% on these polynomials, we prove that the optimality conditions
always hold on optimizers, and the coordinates of optimizers are algebraic
functions of the coefficients of the input polynomials. We also give a general
formula for the algebraic degree of the optimal coordinates. The derivation of
the algebraic degree is equivalent to counting the number of all complex
critical points. As special cases, we obtain the algebraic degrees of
quadratically constrained quadratic programming (QCQP), second order cone
programming (SOCP) and $p$-th order cone programming (pOCP), in analogy to the
algebraic degree of semidefinite programming.


title: A Matrix Convexity Approach to Some Celebrated Quantum Inequalities

abstract:
  Some of the important inequalities associated with quantum entropy are
immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A
general argument is given using matrix perspectives of operator convex
functions. A matrix analogue of Mar\'{e}chal's extended perspectives provides
additional inequalities, including a $p+q\leq 1$ result of Lieb.


title:
Direct and bulk-scattered forward-shock emissions: sources of X-ray
  afterglow diversity

abstract:
  I describe the modifications to the standard forward-shock model required to
account for the X-ray light-curve features discovered by Swift in the early
afterglow emission and propose that a delayed, pair-enriched, and highly
relativistic outflow, which bulk-scatters the forward-shock synchrotron
emission, yields sometimes a brighter X-ray emission, producing short-lived
X-ray flares, X-ray light-curve plateaus ending with chromatic breaks, and fast
post-plateau X-ray decays.


title: ^{7}Li NMR Study of Heavy Fermion LiV2O4 Containing Magnetic Defects

abstract:
  We present a systematic study of the variations of the ^{7}Li NMR properties
versus magnetic defect concentration up to 0.83 mol% within the spinel
structure of polycrystalline powder samples and a collection of small single
crystals of LiV2O4 in the temperature range from 0.5 to 4.2 K. We also report
static magnetization measurements and ac magnetic susceptibility measurements
at 14 MHz on the samples at low temperatures. Both the NMR spectrum and nuclear
spin-lattice relaxation rate are inhomogeneous in the presence of the magnetic
defects. The NMR data for the powders are well explained by assuming that (i)
there is a random distribution of magnetic point defects, (ii) the same heavy
Fermi liquid is present in the samples containing the magnetic defects as in
magnetically pure LiV2O4, and (iii) the influences of the magnetic defects and
of the Fermi liquid on the magnetization and NMR properties are separable. In
the single crystals, somewhat different behaviors are observed. Remarkably, the
magnetic defects in the powder samples show evidence of spin freezing below T ~
1.0 K, whereas in the single crystals with similar magnetic defect
concentration no spin freezing was found down to 0.5 K. Thus different types of
magnetic defects and/or interactions between them appear to arise in the
powders versus the crystals, possibly due to the substantially different
synthesis conditions of the powders and crystals.


title: Minimum Entropy Orientations

abstract:
  We study graph orientations that minimize the entropy of the in-degree
sequence. The problem of finding such an orientation is an interesting special
case of the minimum entropy set cover problem previously studied by Halperin
and Karp [Theoret. Comput. Sci., 2005] and by the current authors
[Algorithmica, to appear]. We prove that the minimum entropy orientation
problem is NP-hard even if the graph is planar, and that there exists a simple
linear-time algorithm that returns an approximate solution with an additive
error guarantee of 1 bit. This improves on the only previously known algorithm
which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).


title:
Degradation of non-maximal entanglement of scalar and Dirac fields in
  non-inertial frames

abstract:
  The entanglement between two modes of the free scalar and Dirac fields as
seen by two relatively accelerated observers has been investigated. It is found
that the same initial entanglement for an initial state parameter $\alpha$ and
its "normalized partner" $\sqrt{1-\alpha^{2}}$ will be degraded by the Unruh
effect along two different trajectories except for the maximally entangled
state, which just shows the inequivalence of the quantization for a free field
in the Minkowski and Rindler coordinates. In the infinite acceleration limit
the state doesn't have the distillable entanglement for any $\alpha$ for the
scalar field but always remains entangled to a degree which is dependent of
$\alpha$ for the Dirac field. It is also interesting to note that in this limit
the mutual information equals to just half of the initially mutual information,
which is independent of $\alpha$ and the type of field.


title: Probing the 3.6 Micron CIRB with Spitzer in 3 DIRBE Dark Spots

abstract:
  We observed three regions of the sky with Spitzer in which the Cosmic
InfraRed Background (CIRB) has been determined at 3.5 microns using the method
of subtracting 2MASS stellar fluxes from zodiacal light subtracted DIRBE maps.
For each of these regions we have obtained 270 seconds of integration time per
pixel with IRAC on Spitzer over the central square degree. We present galaxy
counts in each of these approximately 1 square degree IRAC surveys. Along with
deep galaxy counts in the Extended Groth Strip and GOODS North, we are able to
compare the galactic contribution to the CIRB with the "DIRBE minus 2MASS''
determined L-band CIRB. Using the profile-fit photometry package GIM2D, we find
a substantially larger flux contribution to the CIRB than that determined using
aperture photometry. We have also made the first rigorous analysis of the
uncertainties in determining the CIRB via galaxy counts in Spitzer images using
a Monte Carlo Markov Chain simulation of our data analysis. Using a simple
broken power law model for galaxy counts as a function of magnitude we find a
most probable contribution to the CIRB from galaxies at 3.6 microns of
10.8^{+2.1}_{-1.1} kJy/sr. Even with this restricted model, however, we find
that galaxy counting does not strongly constrain the CIRB from above. We are
able to find solutions in which the CIRB runs away to large intensities without
the need for an additional diffuse source.


title:
Function spaces and capacity related to a Sublinear Expectation:
  application to G-Brownian Motion Pathes

abstract:
  In this paper we give some basic and important properties of several typical
Banach spaces of functions of $G$-Brownian motion pathes induced by a sublinear
expectation--G-expectation. Many results can be also applied to more general
situations. A generalized version of Kolmogorov's criterion for continuous
modification of a stochastic process is also obtained. The results can be
applied to continuous time dynamic and coherent risk measures in finance in
particular for path-dependence risky positions under situations of volatility
model uncertainty.


title: Adaptive synchronization of dynamics on evolving complex networks

abstract:
  We study the problem of synchronizing a general complex network by means of
an adaptive strategy in the case where the network topology is slowly time
varying and every node receives at each time only one aggregate signal from the
set of its neighbors. We introduce an appropriately defined potential that each
node seeks to minimize in order to reach/maintain synchronization. We show that
our strategy is effective in tracking synchronization as well as in achieving
synchronization when appropriate conditions are met.


title:
Variability of the High-Magnetic Field X-ray Pulsar PSR J1846-0258
  Associated with the Supernova Remnant Kes 75 as Revealed by the Chandra X-ray
  Observatory

abstract:
  We present results from the archival Chandra observations of the 0.3 s X-ray
pulsar PSR J1846-0258 associated with the supernova remnant (SNR) Kes 75. The
pulsar has the highest spin-down luminosity (Edot = 8.3e36 erg/s) among all the
high magnetic field pulsars (HBPs) and has been classified as a Crab-like
pulsar despite its magnetic field (5e13 G) being above the quantum critical
field. It is the only HBP described by a non-thermal Crab-like spectrum,
powering a bright pulsar wind nebula (PWN). Our spectroscopic study shows
evidence of spectral softening (photon index = 1.32 to 1.97) and temporal
brightening (unabsorbed flux = 4.3e-12 to 2.7e-11 erg/cm^2/s) of the pulsar by
~6 times from 2000 to 2006. The 0.5-10 keV luminosity of the pulsar at the
revised distance of 6 kpc has also increased from 1.85e34 to 1.16e35 erg/s, and
the X-ray efficiency increased from 0.2% to 1.4%. The observed X-ray
brightening and softening of the pulsar suggests for the first time that this
HBP is revealing itself as a magnetar.


title:
The Aharonov-Casher effect for spin-1 particles in non-commutative
  quantum mechanics

abstract:
  By using a generalized Bopp's shift formulation, instead of star product
method, we investigate the Aharonov-Casher(AC) effect for a spin-1 neutral
particle in non-commutative(NC) quantum mechanics. After solving the Kemmer
equations both on a non-commutative space and a non-commutative phase space, we
obtain the corrections to the topological phase of the AC effect for a spin-1
neutral particle both on a NC space and a NC phase space.


title: Learning Balanced Mixtures of Discrete Distributions with Small Sample

abstract:
  We study the problem of partitioning a small sample of $n$ individuals from a
mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according
to their distributions. Each distribution is described by a vector of allele
frequencies in $\R^K$. Given two distributions, we use $\gamma$ to denote the
average $\ell_2^2$ distance in frequencies across $K$ dimensions, which
measures the statistical divergence between them. We study the case assuming
that bits are independently distributed across $K$ dimensions. This work
demonstrates that, for a balanced input instance for $k = 2$, a certain
graph-based optimization function returns the correct partition with high
probability, where a weighted graph $G$ is formed over $n$ individuals, whose
pairwise hamming distances between their corresponding bit vectors define the
edge weights, so long as $K = \Omega(\ln n/\gamma)$ and $Kn = \tilde\Omega(\ln
n/\gamma^2)$. The function computes a maximum-weight balanced cut of $G$, where
the weight of a cut is the sum of the weights across all edges in the cut. This
result demonstrates a nice property in the high-dimensional feature space: one
can trade off the number of features that are required with the size of the
sample to accomplish certain tasks like clustering.


title: Deformation quantization modules I:Finiteness and duality

abstract:
  We introduce the notion of being cohomologically complete for objects of the
derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then
we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove
coherency results by using the property of being cohomologically complete.
  We apply these results to the study of modules over deformation quantization
algebroids on complex Poisson manifolds. We prove in particular that under a
natural properness condition, the convolution of two coherent kernels over such
algebroids is coherent. We also construct the dualizing complexes in this
framework and show that the convolution of kernels commutes with duality.


title: Order parameter statistics in the critical quantum Ising chain

abstract:
  In quantum spin systems obeying hyperscaling, the probability distribution of
the total magnetization takes on a universal scaling form at criticality. We
obtain this scaling function exactly for the ground state and first excited
state of the critical quantum Ising spin chain. This is achieved through a
remarkable relation to the partition function of the anisotropic Kondo problem,
which can be computed by exploiting the integrability of the system.


title: Understanding heavy fermion from generalized statistics

abstract:
  Heavy electrons in superconducting materials are widely studied with the
Kondo lattice t-J model. Numerical results have shown that the Fermi surface of
these correlated particles undergoes a flattening effect according to the
coupling degree J. This behaviour is not easy to understand from the
theoretical point of view within standard Fermi-Dirac statistics and
non-standard theories such as fractional exclusion statistics for anyons and
Tsallis nonextensive statistics. The present work is an attempt to account for
the heavy electron distribution within incomplete statistics (IS) which is
developed for complex systems with interactions which make the statistics
incomplete such that sum_i p_i^q=1. The parameter q, when different from unity,
characterizes the incompleteness of the statistics. It is shown that the
correlated electrons can be described with the help of IS with q related to the
coupling constant J in the context of Kondo model


title:
A nonextensive approach to Bose-Einstein condensation of trapped
  interacting boson gas

abstract:
  In the Bose-Einstein condensation of interacting atoms or molecules such as
87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature
is not always obvious due to the interactions or zero point energy which cannot
be exactly taken into account. The S-wave collision model fails sometimes to
account for the condensation temperatures. In this work, we look at the problem
within the nonextensive statistics which is considered as a possible theory
describing interacting systems. The generalized energy Uq and the particle
number Nq of boson gas are given in terms of the nonextensive parameter q. q>1
(q<1) implies repulsive (attractive) interaction with respect to the perfect
gas. The generalized condensation temperature Tcq is derived versus Tc given by
the perfect gas theory. Thanks to the observed condensation temperatures, we
find q ~ 0.1 for 87Rb atomic gas, q ~ 0.95 for 7Li and q ~ 0.62 for 23Na. It is
concluded that the effective interactions are essentially attractive for the
three considered atoms, which is consistent with the observed temperatures
higher than those predicted by the conventional theory.


title:
The third post-Newtonian gravitational wave polarisations and associated
  spherical harmonic modes for inspiralling compact binaries in quasi-circular
  orbits

abstract:
  The gravitational waveform (GWF) generated by inspiralling compact binaries
moving in quasi-circular orbits is computed at the third post-Newtonian (3PN)
approximation to general relativity. Our motivation is two-fold: (i) To provide
accurate templates for the data analysis of gravitational wave inspiral signals
in laser interferometric detectors; (ii) To provide the associated
spin-weighted spherical harmonic decomposition to facilitate comparison and
match of the high post-Newtonian prediction for the inspiral waveform to the
numerically-generated waveforms for the merger and ringdown. This extension of
the GWF by half a PN order (with respect to previous work at 2.5PN order) is
based on the algorithm of the multipolar post-Minkowskian formalism, and
mandates the computation of the relations between the radiative, canonical and
source multipole moments for general sources at 3PN order. We also obtain the
3PN extension of the source multipole moments in the case of compact binaries,
and compute the contributions of hereditary terms (tails, tails-of-tails and
memory integrals) up to 3PN order. The end results are given for both the
complete plus and cross polarizations and the separate spin-weighted spherical
harmonic modes.


title: The Area Quantum and Snyder Space

abstract:
  We show that in the Snyder space the area of the disc and of the sphere can
be quantized. It is also shown that the area spectrum of the sphere can be
related to the Bekenstein conjecture for the area spectrum of a black hole
horizon.


title: Adiabatic limits on Riemannian Sol-manifolds

abstract:
  We obtain an asymptotic formula for the spectrum distribution function of the
Laplace operator on a compact Riemannian Sol-manifold in the adiabatic limit
determined by a one-dimensional foliation defined by the orbits of a
left-invariant flow.


title:
Spin dynamics near the critical doping in weakly-superconducting
  underdoped YBa2Cu3O6.35 (Tc=18K)

abstract:
  Using neutron scattering we have determined the magnetic structure and
fluctuations in the YBa2Cu3O6.35 superconductor (Tc=18 K). The long-range
ordered collinear spins of the insulating antiferromagnet are replaced by a
commensurate central mode arising from slow, isotropically polarized,
short-range spin correlations. The inelastic spectrum up to 30 meV is broad in
wave vector and commensurate. In contrast to the the resonance peak of higher
Tc superconductors, the spins exhibit a single overdamped spectrum whose rate
of relaxation decreases on cooling and saturates at 5 meV below 50 K. As the
relaxation rate saturates the quasi-static spin correlations grow and become
resolution limited in energy. The spin susceptibility at high temperatures
illustrates that the dominant energy scale is set by the temperature. At low
temperatures, the scale length is geometric and not linked by velocity to
dynamic widths. There is no observable suppression of the spin fluctuations or
central mode upon the onset of superconductivity. The spins respond not to
coherent charge pairs but to hole doping allowing coexistence of glassy short
range spin order with superconductivity. Since the physics of the weakly
superconducting system YBCO6.35 must connect continuously with that in more
strongly superconducting YBCO6.5, we find that neither incommensurate
stripe-like spin modulations nor a well-defined neutron spin resonance are
essential for the onset with doping of pairing in a high temperature cuprate
superconductor.


title:
Two-Field Integrable Evolutionary Systems of the Third Order and Their
  Differential Substitutions

abstract:
  A list of forty third-order exactly integrable two-field evolutionary systems
is presented. Differential substitutions connecting various systems from the
list are found. It is proved that all the systems can be obtained from only two
of them. Examples of zero curvature representations with $4 \times 4$ matrices
are presented.


title:
Low and intermediate energy electron collisions with the C$_2^-$
  molecular anion

abstract:
  Calculations are presented which use the molecular R-matrix with
pseudo-states (MRMPS) method to treat electron impact electron detachment and
electronic excitation of the carbon dimer anion. Resonances are found above the
ionisation threshold of C$_2^-$ with $^1\Sigma^+_g$, $^1\Pi_g$ and $^3\Pi_g$
symmetry. These are shape resonances trapped by the effect of an attractive
polarisation potential competing with a repulsive Coulomb interaction. The
$\Pi_g$ resonances are found to give structure in the detachment cross section
similar to that observed experimentally. Both excitation and detachment cross
sections are found to be dominated by large impact parameter collisions whose
contribution is modelled using the Born approximation.


title: The correspondence between a plane curve and its complement

abstract:
  Given two irreducible curves of the plane which have isomorphic complements,
it is natural to ask whether there exists an automorphism of the plane that
sends one curve on the other.
  This question has a positive answer for a large family of curves and
H.Yoshihara conjectured that it is true in general. We exhibit counterexamples
to this conjecture, over any ground field. In some of the cases, the curves are
isomorphic and in others not; this provides counterexamples of two different
kinds.
  Finally, we use our construction to find the existence of surprising
non-linear automorphisms of affine surfaces.


title:
On ergodic properties of convolution operators associated with compact
  quantum groups

abstract:
  Recent results of M.Junge and Q.Xu on the ergodic properties of the averages
of kernels in noncommutative L^p-spaces are applied to the analysis of the
almost uniform convergence of operators induced by the convolutions on compact
quantum groups.


title: Structure and thermodynamics of a ferrofluid bilayer

abstract:
  We present extensive Monte Carlo simulations for the thermodynamic and
structural properties of a planar bilayer of dipolar hard spheres for a wide
range of densities, dipole moments and layer separations. Expressions for the
stress and pressure tensors of the bilayer system are derived. For all
thermodynamic states considered the interlayer energy is shown to be attractive
and much smaller than the intralayer contribution to the energy. It vanishes at
layer separations of the order of two hard sphere diameters. The normal
pressure is negative and decays as a function of layer separation $h$ as
$-1/h^5$. Intralayer and interlayer pair distribution functions and angular
correlation functions are presented. Despite the weak interlayer energy strong
positional and orientational correlations exist between particles in the two
layers.


title: Bayesian Nonlinear Principal Component Analysis Using Random Fields

abstract:
  We propose a novel model for nonlinear dimension reduction motivated by the
probabilistic formulation of principal component analysis. Nonlinearity is
achieved by specifying different transformation matrices at different locations
of the latent space and smoothing the transformation using a Markov random
field type prior. The computation is made feasible by the recent advances in
sampling from von Mises-Fisher distributions.


title: Universal unfoldings of Laurent polynomials and tt* structures

abstract:
  This article surveys the relations between harmonic Higgs bundles and Saito
structures which lead to tt* geometry on Frobenius manifolds. We give the main
lines of the proof of the existence of a canonical tt* structure on the base
space of the universal unfolding of convenient and nondegenerate Laurent
polynomials.


title: A characterization of the overcoherence

abstract:
  Let $\mathcal{P}$ be a proper smooth formal $\mathcal{V}$-scheme, $X$ a
closed subscheme of the special fiber of $\mathcal{P}$, $\mathcal{E} \in
F\text{-}D ^\mathrm{b}_\mathrm{coh} (\D ^\dag_{\mathcal{P},\mathbb{Q}})$ with
support in $X$. We check that $\mathcal{E}$ is $\D ^\dag
_{\mathcal{P},\mathbb{Q}}$-overcoherent if and only if, for any morphism $f :
\mathcal{P}' \to \mathcal{P}$ of smooth formal $\mathcal{V}$-schemes, $f ^!
(\mathcal{E}) $ is $\D ^\dag_{\mathcal{P}', \mathbb{Q}}$-coherent.


title: Kinetic equation for a soliton gas and its hydrodynamic reductions

abstract:
  We introduce and study a new class of kinetic equations, which arise in the
description of nonequilibrium macroscopic dynamics of soliton gases with
elastic collisions between solitons. These equations represent nonlinear
integro-differential systems and have a novel structure, which we investigate
by studying in detail the class of $N$-component `cold-gas' hydrodynamic
reductions. We prove that these reductions represent integrable linearly
degenerate hydrodynamic type systems for arbitrary $N$ which is a strong
evidence in favour of integrability of the full kinetic equation. We derive
compact explicit representations for the Riemann invariants and characteristic
velocities of the hydrodynamic reductions in terms of the `cold-gas' component
densities and construct a number of exact solutions having special properties
(quasi-periodic, self-similar). Hydrodynamic symmetries are then derived and
investigated. The obtained results shed the light on the structure of a
continuum limit for a large class of integrable systems of hydrodynamic type
and are also relevant to the description of turbulent motion in conservative
compressible flows.


title: Latest Results from the Air Shower Simulation Programs CORSIKA and CONEX

abstract:
  Interpretation of EAS measurements strongly depends on detailed air shower
simulations. The uncertainty in the prediction of shower observables for
different primary particles and energies is currently dominated by differences
between hadronic interaction models. The new models QGSJETII-3 and EPOS 1.6,
which reproduce all major results of existing accelerator data (including
detailed data of RHIC experiments for EPOS), have been implemented in the air
shower simulation programs CORSIKA and CONEX. We show predictions of these new
models and compare them with those from older models such as QGSJET01 or
SIBYLL. Results for important air shower observables are discussed in detail.


title: Leibniz algebra deformations of a Lie algebra

abstract:
  In this note we compute Leibniz algebra deformations of the 3-dimensional
nilpotent Lie algebra $\mathfrak{n}_3$ and compare it with its Lie
deformations. It turns out that there are 3 extra Leibniz deformations. We also
describe the versal Leibniz deformation of $\mathfrak{n}_3$ with the versal
base.


title: Black Holes in Bulk Viscous Cosmology

abstract:
  We investigate the effects of the accretion of phantom energy with non-zero
bulk viscosity onto a Schwarzschild black hole and show that black holes
accreting viscous phantom energy will lose mass rapidly compared to the
non-viscous case. When matter is incorporated along with the phantom energy,
the black holes meet with the same fate as bulk viscous forces dominate matter
accretion. If the phantom energy has large bulk viscosity, then the mass of the
black hole will reduce faster than in the small viscosity case.


title: Stretching An Anisotropic DNA

abstract:
  We present a perturbation theory to find the response of an anisotropic DNA
to the external tension. It is shown that the anisotropy has a nonzero but
small contribution to the force-extension curve of the DNA. Thus an anisotropic
DNA behaves like an isotropic one with an effective bending constant equal to
the harmonic average of its soft and hard bending constants.

categories: cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech physics.bio-ph q-bio.BM


title:
Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers
  revisited

abstract:
  In this paper, we establish improved effective irrationality measures for
certain numbers of the form $\sqrt[3]{n}$, using approximations obtained from
hypergeometric functions. These results are very close to the best possible
using this method. We are able to obtain these results by determining very
precise arithmetic information about the denominators of the coefficients of
these hypergeometric functions. Improved bounds for $\theta(k,l;x)$ and
$\psi(k,l;x)$ for $k=1,3,4,6$ are also presented.


title: Cosmic Ray Astronomy

abstract:
  Cosmic ray astronomy attempts to identify and study the sources of ultrahigh
energy cosmic rays. It is unique in its reliance on charged particles as the
information carriers. While no discrete source of ultrahigh energy cosmic rays
has been identified so far, a new generation of detectors is acquiring the huge
exposure that is needed at the highest energies, where deflection by magnetic
fields is minimized and the background from distant sources is eliminated by
pion photoproduction. In this paper, we summarize the status of cosmic ray
astronomy, describing the detectors and the analysis techniques.


title:
Jet Berwald-Riemann-Lagrange Geometrization for Affine Maps between
  Finsler Manifolds

abstract:
  In this paper we introduce a natural definition for the affine maps between
two Finsler manifolds $(M, F)$ and $(N,\tilde F)$ and we give some geometrical
properties of these affine maps. Starting from the equations of the affine
maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet
space $J^1(TM;N)$, in the sense of a Berwald nonlinear connection
$\Gamma^b_jet$, a Berwald $\Gamma^b_jet$-linear d-connection $B\Gamma^b_jet$,
together with its d-torsions and d-curvatures, which geometrically
characterizes the initial affine maps between Finsler manifolds.


title: Production of Two Pions Induced by Neutrinos

abstract:
  We study the threshold production of two pions induced by neutrinos in
nucleon targets. The contribution of nucleon pole, pion and contact terms is
calculated using a chiral Lagrangian. The contribution of the Roper resonance,
neglected in earlier studies, has also been taken into account.


title: UGC 7069: The largest ring galaxy

abstract:
  We find that UGC 7069 is the largest ring galaxy known to date. In this
Letter, we present a multiwavelength study of this galaxy (combining radio,
2MASS, optical and ultraviolet data). The ring of UGC 7069, whose diameter
measures ~115 kpc, is also warped at its edges. The nucleus appears
double-peaked and hosts a possible LINER. The ultraviolet data indicate a
strong blue colour and suggest that UGC 7069 is a starburst galaxy. We also
present N-body simulation results, which indicate that galaxy collisions can
produce such huge rings. Large inclination angles between the target and the
intruder galaxy may account for the formation of warped rings. Multiwavelength
observations are highly essential to constrain our simulation results, which
will address the formation and evolution of such a rare galaxy.


title: Superconductivity from four Fermion complexes

abstract:
  Superconductivity is studied for a fermionic system with attractive four-body
interaction. Applying a Green function approach, the gap equation is derived.
  From the solution, the transition temperature is calculated. Under the
condition that the respective coupling constants are comparable, the transition
temperature of four-fermion complexes is considerably larger than the
corresponding BCS value.


title: Activation Confinement Inside Complex Networks Communities

abstract:
  In this work it is described how to enhance and generalize the equivalent
model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any
complex neuronal networks, especially those exibiting modular structure. It has
been shown that, though involving only a handful of equivalent neurons, the
modular equivalent model was capable of providing impressive predictions about
the non-linear integrate-and-fire dynamics in two hybrid modular networks. The
reported approach has also allowed the identification of the causes of
transient spiking confinement within the network communities, which correspond
to the fact that the little activation sent from the source community to the
others implies in long times for reaching the nearly-simultaneous activation of
the concentric levels at the other communities and respective avalanches.
Several other insights are reported in this work, including the smoothing of
the spiking functions, the consideration of intra-ring connections and its
effects, as well as the identification of how the weights in the equivalent
model change for different source nodes. This work has paved the way for a
number of promising developments, which are identified and discussed.
Preliminary results are also described which reveal waves induced by the
integrate-and-fire dynamics along the steady-state regime.


title: A New Algorithm For Difference Image Analysis

abstract:
  In the context of difference image analysis (DIA), we present a new method
for determining the convolution kernel matching a pair of images of the same
field. Unlike the standard DIA technique which involves modelling the kernel as
a linear combination of basis functions, we consider the kernel as a discrete
pixel array and solve for the kernel pixel values directly using linear
least-squares. The removal of basis functions from the kernel model is
advantageous for a number of compelling reasons. Firstly, it removes the need
for the user to specify such functions, which makes for a much simpler user
application and avoids the risk of an inappropriate choice. Secondly, basis
functions are constructed around the origin of the kernel coordinate system,
which requires that the two images are perfectly aligned for an optimal result.
The pixel kernel model is sufficiently flexible to correct for image
misalignments, and in the case of a simple translation between images, image
resampling becomes unnecessary. Our new algorithm can be extended to spatially
varying kernels by solving for individual pixel kernels in a grid of image
sub-regions and interpolating the solutions to obtain the kernel at any one
pixel.


title: The Invar tensor package: Differential invariants of Riemann

abstract:
  The long standing problem of the relations among the scalar invariants of the
Riemann tensor is computationally solved for all 6x10^23 objects with up to 12
derivatives of the metric. This covers cases ranging from products of up to 6
undifferentiated Riemann tensors to cases with up to 10 covariant derivatives
of a single Riemann. We extend our computer algebra system Invar to produce
within seconds a canonical form for any of those objects in terms of a basis.
The process is as follows: (1) an invariant is converted in real time into a
canonical form with respect to the permutation symmetries of the Riemann
tensor; (2) Invar reads a database of more than 6x10^5 relations and applies
those coming from the cyclic symmetry of the Riemann tensor; (3) then applies
the relations coming from the Bianchi identity, (4) the relations coming from
commutations of covariant derivatives, (5) the dimensionally-dependent
identities for dimension 4, and finally (6) simplifies invariants that can be
expressed as product of dual invariants. Invar runs on top of the tensor
computer algebra systems xTensor (for Mathematica) and Canon (for Maple).


title: Shear induced crystallization of an amorphous system

abstract:
  The influence of a stationary shear flow on the crystallization in a glassy
system is studied by means of molecular dynamics simulations and subsequent
cluster analysis. The results reveal two opposite effects of the shear flow on
the processes of topological ordering in the system. Shear promotes the
formation of separated crystallites and suppresses the appearance of the large
clusters. The shear-induced ordering proceeds in two stages, where the first
stage is related mainly with the growth of crystallites, whereas the second
stage is due to an adjustment of the created clusters and a progressive
alignment of their lattice directions. The influence of strain and shear rate
on the crystallization is also investigated. In particular, we find two
plausible phenomenological relations between the shear rate and the
characteristic time scale needed for ordering of the amorphous system under
shear.


title:
Van der Waals and Casimir interactions between atoms and carbon
  nanotubes

abstract:
  The van der Waals and Casimir interactions of a hydrogen atom (molecule) with
a single-walled and a multiwalled carbon nanotubes are compared. It is shown
that the macroscopic concept of graphite dielectric permittivity is already
applicable for nanotubes with only two or three walls. The absorption of
hydrogen atoms by a nanotube at separations below one nanometer is considered.
The lateral force due to exchange repulsion moves the atom to a position above
the cell center, where it is absorbed by the nanotube because the repulsive
force cannot balance the van der Waals attraction.


title: Lepton flavor violating Z boson decays induced by scalar unparticle

abstract:
  We predict the branching ratios of the lepton flavor violating Z boson decays
Z\to e^{\pm} \mu^{\pm}, Z\to e^{\pm} \tau^{\pm} and Z\to \mu^{\pm} \tau^{\pm}
in the case that the lepton flavor violation is carried by the scalar
unparticle mediation. We observe that their BRs are strongly sensitive to the
unparticle scaling dimension and the branching ratios can reach to the values
of the order of 10^{-8}, for the heavy lepton flavor case, for the small values
of the scaling dimension.


title:
On the nature of the variability power decay towards soft spectral
  states in X-ray binaries. Case study in Cyg X-1

abstract:
  A characteristic feature of the Fourier Power Density Spectrum (PDS) observed
from black hole X-ray binaries in low/hard and intermediate spectral states is
a broad band-limited noise, characterized by a constant below some frequency (a
``break'' frequency) and a power law above this frequency. It has been shown
that the variability of this type can be produced by the inward diffusion of
the local driving perturbations in a bounded configuration (accretion disk or
corona). In the framework of this model, the perturbation diffusion time t_0 is
related to the phenomenological break frequency, while the PDS power-law slope
above the ``break'' is determined by the viscosity distribution over the
configuration. he perturbation diffusion scenario explains the decay of the
power of X-ray variability observed in a number of compact sources (containing
black hole and neutron star) during an evolution of theses sources from
low/hard to high/soft states. We compare the model predictions with the subset
of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our
extensive analysis of the Cyg X-1 PDSs demonstrates that the observed
integrated power P_x decreases approximately as a square root of the
characteristic frequency of the driving oscillations \nu_{dr}. The RXTE
observations of Cyg X-1 allow us to infer P_{dr} and t_0 as a function of
\nu_{dr}. Using the inferred dependences of the integrated power of the driving
oscillations P_{dr} and t_0 on \nu_{dr} we demonstrate that the power predicted
by the model also decays as P_{x,diff} proportional to \nu_{dr}^{-0.5} that is
similar to the observed P_{x} behavior.


title: Properties of lexsegment ideals

abstract:
  We show that any lexsegment ideal with linear resolution has linear quotients
with respect to a suitable ordering of its minimal monomial generators. For
completely lexsegment ideals with linear resolution we show that the
decomposition function is regular. For arbitrary lexsegment ideals we compute
the depth and the dimension. As application we characterize the Cohen-Macaulay
lexsegment ideals.


title: On the shot-noise limit of a thermal current

abstract:
  The noise power spectral density of a thermal current between two macroscopic
dielectric bodies held at different temperatures and connected only at a
quantum point contact is calculated. Assuming the thermal energy is carried
only by phonons, we model the quantum point contact as a mechanical link,
having a harmonic spring potential. In the weak coupling, or weak-link limit,
we find the thermal current analog of the well-known electronic shot-noise
expression.


title:
Absence of eigenvalues for integro-differential operators with periodic
  coefficients

abstract:
  Applying perturbation theory methods, the absence of the point spectrum for
some nonselfadjoint integro-differential operators is investigated. The
considered differential operators are of arbitrary order and act in either
$\mathbf{L}_{p}(\mathbb{R}_{+})$ or $\mathbf{L}_{p}(\mathbb{R}) (1\leq
p<\infty)$. As an application of general results, new spectral properties of
the perturbed Hill operator are derived.


title:
On the multiplicity conjecture for non-Cohen-Macaulay simplicial
  complexes

abstract:
  We prove a reformulation of the multiplicity upper bound conjecture and use
that reformulation to prove it for three-dimensional simplicial complexes and
homology manifolds with many vertices. We provide necessary conditions for a
Cohen-Macaulay complex with many vertices to have a pure minimal free
resolution and a characterization of flag complexes whose minimal free
resolution is pure.


title: Deformations of associative submanifolds with boundary

abstract:
  Let $M$ be a topological $G_2$-manifold. We prove that the space of
infinitesimal associative deformations of a compact associative submanifold $Y$
with boundary in a coassociative submanifold $X$ is the solution space of an
elliptic problem. For a connected boundary $\partial Y$ of genus $g$, the index
is given by $\int_{\partial Y}c_1(\nu_X)+1-g$, where $\nu_X$ denotes the
orthogonal complement of $T\partial Y$ in $TX_{|\partial Y}$ and $c_1(\nu_X)$
the first Chern class of $\nu_X$ with respect to its natural complex structure.
Further, we exhibit explicit examples of non-trivial index.


title:
Street Hierarchies: A Minority of Streets Account for a Majority of
  Traffic Flow

abstract:
  Urban streets are hierarchically organized in the sense that a majority of
streets are trivial, while a minority of streets is vital. This hierarchy can
be simply, but elegantly, characterized by the 80/20 principle, i.e. 80 percent
of streets are less connected (below the average), while 20 percent of streets
are well connected (above the average); out of the 20 percent, there is 1
percent of streets that are extremely well connected. This paper, using a
European city as an example, examined, at a much more detailed level, such
street hierarchies from the perspective of geometric and topological
properties. Based on an empirical study, we further proved a previous
conjecture that a minority of streets accounts for a majority of traffic flow;
more accurately, the 20 percent of top streets accommodate 80 percent of
traffic flow (20/80), and the 1 percent of top streets account for more than 20
percent of traffic flow (1/20). Our study provides new evidence as to how a
city is (self-)organized, contributing to the understanding of cities and their
evolution using increasingly available mobility geographic information.


title: Patterns in the Kardar-Parisi-Zhang equation

abstract:
  We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang
equation for the kinetic growth of an interface in higher dimensions. The weak
noise approach provides a many body picture of a growing interface in terms of
a network of localized growth modes. Scaling in 1d is associated with a gapless
domain wall mode. The method also provides an independent argument for the
existence of an upper critical dimension.


title:
Dynamical Mass Generations and Collective Excitations in the
  (Supersymmetric-)Nambu$-$Jona-Lasinio Model and a Gauge Theory with
  Left-Right-Asymmetric Majorana Mass Terms

abstract:
  The structure of effective potential surface of the Nambu$-$Jona-Lasinio
(NJL) model with right-left asymmetric Majorana mass terms (corresponds to the
single-flavor type-II seesaw situation of neutrino) is investigated. After the
dynamical generation of Dirac mass, two collective modes appear similar to the
case of ordinary NJL model, and the phase mode (phason), which corresponds to
majoron or pion at vanishing Majorana mass parameter(s), has an excitation
mass. The mechanism of generation of phason as a pseudo Nambu-Goldstone boson
is examined by a mathematical manner, summarized into a theorem
  (claims as the generalized Nambu-Goldstone theorem). The mass of phason is
also evaluated in a supersymmetric version of the NJL-type model, and phason
mass takes the order of that of axion commonly accepted today. An
$SU(2_{c})$-gauge model is constructed for the context of neutrino seesaw
mechanism, and the Schwinger-Dyson equation of dynamical mass functions is
examined. Several physical implications such as decay modes of phason, a
non-linear sigma model for phason are given. It is proposed that the
method/result of this paper can be applied to an understanding on the origin of
the Kobayashi-Maskawa matrix.


title:
The diffusive influx and carrier efflux have a strong effect on the
  bistability of the lac operon in Escherichia coli

abstract:
  In the presence of gratuitous inducers, the lac operon of Escherichia coli
exhibits bistability. Most models in the literature assume that the inducer
enters the cell via the carrier (permease), and exits by a diffusion-like
process. The diffusive influx and carrier efflux are neglected. However,
analysis of the data shows that in non-induced cells, the diffusive influx is
comparable to the carrier influx, and in induced cells, the carrier efflux is 7
times the diffusive efflux. Since bistability entails the coexistence of steady
states corresponding to both non-induced and induced cells, neither one of
these fluxes can be ignored. Here, we formulate a model accounting for both
fluxes. We show that: (a) The thresholds of bistability are profoundly affected
by both fluxes. The diffusive influx reduces the on threshold by enhancing
inducer accumulation in non-induced cells. The carrier efflux increases the off
threshold by decreasing inducer accumulation in induced cells. (b) Simulations
of the model with experimentally measured parameter values are in good
agreement with the data for IPTG. However, there are discrepancies with respect
to the data for TMG. They are most likely due to two features missing from the
model, namely, the variation of the inducer exclusion effect and the specific
growth rate with the lactose enzyme levels. (c) The steady states and
thresholds obtained in the presence of both fluxes are well approximated by
simple analytical expressions, which may be useful for the preliminary design
of the lac genetic switch in synthetic biology.


title: Fractional term structure models: No-arbitrage and consistency

abstract:
  In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models
driven by fractional Brownian motions. By using support arguments we prove that
the resulting model is arbitrage free under proportional transaction costs in
the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we
obtain a drift condition which is similar in nature to the classical HJM
no-arbitrage drift restriction. The second part of this paper deals with
consistency problems related to the fractional HJM dynamics. We give a fairly
complete characterization of finite-dimensional invariant manifolds for HJM
models with fractional Brownian motion by means of Nagumo-type conditions. As
an application, we investigate consistency of Nelson-Siegel family with respect
to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case
such a family does not go well with the fractional HJM dynamics with
deterministic volatility. In fact, there is no nontrivial fractional interest
rate model consistent with the Nelson-Siegel family.


title:
Pi-eta scattering and the resummation of vacuum fluctuation in
  three-flavour ChPT

abstract:
  We discuss various aspects of resummed chiral perturbation theory, which was
developed recently in order to consistently include the possibility of large
vacuum fluctuations of the ss-pairs and the scenario with smaller value of the
chiral condensate for N_f=3. The subtleties of this approach are illustrated
using a concrete example of observables connected with pi-eta scattering. This
process seems to be a suitable theoretical laboratory for this purpose due to
its sensitivity to the values of the O(p^4) LEC's, namely to the values of the
fluctuation parameters L4 and L6. We discuss several issues in detail, namely
the choice of `good' observables and properties of their bare expansions, the
`safe' reparametrization in terms of physical observables, the implementation
of exact perturbative unitarity and exact renormalization scale independence,
the role of higher order remainders and their estimates. We make a detailed
comparison with standard chiral perturbation theory and use generalized ChPT as
well as resonance chiral theory to estimate the higher order remainders.


title: C-Functions in Lovelock Gravity

abstract:
  We present C-functions for static and spherically symmetric spacetimes in
Lovelock gravity theories. These functions are monotonically increasing
functions of the outward radial coordinate and acquire their minima when
evaluated on the horizon. Unlike the case of Einstein gravity, where there is a
single C-function, we find that this function is non-unique in the case of
Lovelock gravity. We define two C-functions, which agree at the horizon giving
the black hole entropy, and state the different energy conditions that must
hold in order for these functions to satisfy the monotonicity condition.


title: Massive Star Forming Regions: Turbulent Support or Global Collapse?

abstract:
  We present preliminary numerical evidence that the physical conditions in
high-mass star forming regions can arise from global gravitational infall, with
the velocity dispersions being caused primarily by infall motions rather than
random turbulence. To this end, we study the clumps and cores appearing in the
region of central collapse in a numerical simulation of the formation,
evolution, and subsequent collapse of a dense cloud out of a transonic
compression in the diffuse atomic ISM. The clumps have sizes $\sim 1$ pc,
masses of several hundred $M_\odot$, and three-dimensional velocity dispersions
$\sim 3$ km s$^{-1}$, in agreement with typical observed values for such
structures. The clumps break down into massive cores of sizes $\sim 0.1$ pc,
densities $\sim 10^5$, masses 2-300 $M_\odot$, with distributions of these
quantities that peak at the same values as the massive core sample in a recent
survey of the Cygnus X molecular cloud complex. Although preliminary, these
results suggest that high-mass star forming clumps may be in a state of global
gravitational collapse rather than in equilibrium supported by strong
turbulence.


title: Atomistic Origin of Urbach Tails in Amorphous Silicon

abstract:
  Exponential band edges have been observed in a variety of materials, both
crystalline and amorphous. In this paper, we infer the structural origins of
these tails in amorphous and defective crystalline Si by direct calculation
with current {\it ab initio} methods. We find that exponential tails appear in
relaxed models of diamond with suitable point defects. In amorphous silicon
(a-Si), we find that structural filaments of short bonds and long bonds exist
in the network, and that the tail states near the extreme edges of both band
tails are are also filamentary, with much localization on the structural
filaments. We connect the existence of both filament systems to structural
relaxation in the presence of defects and or topological disorder.


title: A poset structure on quasifibonacci partitions

abstract:
  In this paper, we study partitions of positive integers into distinct
quasifibonacci numbers. A digraph and poset structure is constructed on the set
of such partitions. Furthermore, we discuss the symmetric and recursive
relations between these posets. Finally, we prove a strong generalization of
Robbins' result on the coefficients of a quasifibonacci power series.


title: Multifluid Models for Cyclic Cosmology

abstract:
  Inspired by the Landau two-fluid model of superfluidity, we consider a
similar multifluid description for cosmology where two normal fluids occur for
matter and radiation respectively. For cyclic cosmology, two dark energy
superfluid components turn out to be insufficient but three superfluids can
lead to a sensible five-fluid model which in a certain limit becomes
indistinguishable from the brane-world cyclic model proposed earlier (Baum and
Frampton). Distinguishing more general five-fluid models from brane-world
models for cyclic cosmology could be feasible with more accurate observational
data.


title:
The advanced maximum principle for parabolic systems on manifolds with
  boundary

abstract:
  In this short note we extend Chow and Lu's advanced maximum principles for
parabolic systems on closed manifolds to the case of compact manifolds with
boundary, which also generalizes a Hopf type theorem of Pulemotov.


title: On quantum statistics in data analysis

abstract:
  Originally, quantum probability theory was developed to analyze statistical
phenomena in quantum systems, where classical probability theory does not
apply, because the lattice of measurable sets is not necessarily distributive.
On the other hand, it is well known that the lattices of concepts, that arise
in data analysis, are in general also non-distributive, albeit for completely
different reasons. In his recent book, van Rijsbergen argues that many of the
logical tools developed for quantum systems are also suitable for applications
in information retrieval. I explore the mathematical support for this idea on
an abstract vector space model, covering several forms of data analysis
(information retrieval, data mining, collaborative filtering, formal concept
analysis...), and roughly based on an idea from categorical quantum mechanics.
It turns out that quantum (i.e., noncommutative) probability distributions
arise already in this rudimentary mathematical framework. We show that a
Bell-type inequality must be satisfied by the standard similarity measures, if
they are used for preference predictions. The fact that already a very general,
abstract version of the vector space model yields simple counterexamples for
such inequalities seems to be an indicator of a genuine need for quantum
statistics in data analysis.


title: Dynamics of vortex glass phase in strongly type II superconductors

abstract:
  Dynamics of vortices in strongly type-II superconductors with strong disorder
is investigated within the frustrated three-dimensional XY model. For two
typical models in [Phys. Rev. Lett. {\bf 91}, 077002 (2003)] and [Phys. Rev. B
{\bf 68}, 220502(R) (2003)], a strong evidence for the finite temperature
vortex glass transition in the unscreened limit is provided by performing
large-scale dynamical simulations. The obtained correlation length exponents
and the dynamic exponents in both models are different from each other and from
those in the three-dimensional gauge glass model. In addition, a genuine
continuous depinning transition is observed at zero temperature for both
models. A scaling analysis for the thermal rounding of the depinning transition
shows a non-Arrhenius type creep motion in the vortex glass phase, contrarily
to the recent studies..


title:
Does the mass of a black hole decrease due to the accretion of phantom
  energy

abstract:
  According to Babichev et al., the accretion of a phantom test fluid onto a
Schwarzschild black hole will induce the mass of the black hole to decrease,
however the backreaction was ignored in their calculation. Using new exact
solutions describing black holes in a background Friedmann-Robertson-Walker
universe, we find that the physical black hole mass may instead increase due to
the accretion of phantom energy. If this is the case, and the future universe
is dominated by phantom dark energy, the black hole apparent horizon and the
cosmic apparent horizon will eventually coincide and, after that, the black
hole singularity will become naked in finite comoving time before the Big Rip
occurs, violating the Cosmic Censorship Conjecture.


title:
Nonlinear Realization of N=2 Superconformal Symmetry and Brane Effective
  Actions

abstract:
  Due to the incompatibility of the nonlinear realization of superconformal
symmetry and dilatation symmetry with the dilaton as the compensator field, in
the present paper it shows an alternative mechanism of spontaneous breaking the
N=2 superconformal symmetry to the N=0 case. By using the approach of nonlinear
transformations it is found that it leads to a space-filling brane theory with
Weyl scale W(1,3) symmetry. The dynamics of the resulting Weyl scale invariant
brane, along with that of other Nambu-Goldstone fields, is derived in terms of
the building blocks of the vierbein and the covariant derivative from the
Maurer-Cartan oneforms. A general coupling of the matter fields localized on
the brane world volume to these NG fields is also constructed.


title: Elastic effects on relaxation volume tensor calculations

abstract:
  Relaxation volume tensors quantify the effect of stress on diffusion of
crystal defects. Continuum linear elasticity predicts that calculations of
these parameters using periodic boundary conditions do not suffer from
systematic deviations due to elastic image effects and should be independent of
supercell size or symmetry. In practice, however, calculations of formation
volume tensors of the <110> interstitial in Stillinger-Weber silicon
demonstrate that changes in bonding at the defect affect the elastic moduli and
result in system-size dependent relaxation volumes. These vary with the inverse
of the system size. Knowing the rate of convergence permits accurate estimates
of these quantities from modestly sized calculations. Furthermore, within the
continuum linear elasticity assumptions the average stress can be used to
estimate the relaxation volume tensor from constant volume calculations.


title:
Shimura curve computations via K3 surfaces of Neron-Severi rank at least
  19

abstract:
  It is known that K3 surfaces S whose Picard number rho (= rank of the
Neron-Severi group of S) is at least 19 are parametrized by modular curves X,
and these modular curves X include various Shimura modular curves associated
with congruence subgroups of quaternion algebras over Q. In a family of such K3
surfaces, a surface has rho=20 if and only if it corresponds to a CM point on
X. We use this to compute equations for Shimura curves, natural maps between
them, and CM coordinates well beyond what could be done by working with the
curves directly as we did in ``Shimura Curve Computations'' (1998) =
<http://arxiv.org/abs/math/0005160>


title:
Large Deviation Property of Free Energy in p-Body
  Sherrington-Kirkpatrick Model

abstract:
  Cumulant generating function phi(n) and rate function Sigma(f) of the free
energy is evaluated in p-body Sherrington-Kirkpatrick model by using the
replica method with the replica number n finite. From a perturbational
argument, we show that the cumulant generating function is constant in the
vicinity of n = 0. On the other hand, with the help of two analytic properties
of phi(n), the behavior of phi(n) is derived again. However this is also shown
to be broken at a finite value of n, which gives a characteristic value in the
rate function near the thermodynamic value of the free energy. Through the
continuation of phi(n) as a function of n, we find out a way to derive the 1RSB
solution at least in this model, which is to fix the RS solution to be a
monotone increasing function.


title: On GCD-morphic sequences

abstract:
  This note is a response to one of the problems posed by Kwa\'sniewski in
[1,2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic
sequence $F$ is at the point product of primary GCD-morphic sequences and any
GCD-morphic sequence is encoded by natural number valued sequence satisfying
condition (C1). The problem of general importance - for example in number
theory was formulated in [1,2] while investigating a new class of DAG's and
their correspondent p.o. sets encoded uniquely by sequences with
combinatorially interpretable properties.


title: XMM-Newton discovery of transient X-ray pulsar in NGC 1313

abstract:
  We report on the discovery and analysis of the transient X-ray pulsar XMMU
J031747.5-663010 detected in the 2004 November 23 XMM-Newton observation of the
spiral galaxy NGC 1313. The X-ray source exhibits pulsations with a period
P~765.6 s and a nearly sinusoidal pulse shape and pulsed fraction ~38% in the
0.3-7 keV energy range. The X-ray spectrum of XMMU J031747.5-663010 is hard and
is well fitted with an absorbed simple power law of photon index ~1.5 in the
0.3-7 keV energy band. The X-ray properties of the source and the absence of an
optical/UV counterpart brighter than 20 mag allow us to identify XMMU
J031747.5-663010 as an accreting X-ray pulsar located in NGC 1313. The
estimated absorbed 0.3-7 keV luminosity of the source L~1.6\times 10^{39}
ergs/s, makes it one of the brightest X-ray pulsars known. Based on the
relatively long pulse period and transient behaviour of the source, we classify
it as a Be binary X-ray pulsar candidate. XMMU J031747.5-663010 is the second
X-ray pulsar detected outside the Local Group, after transient 18 s pulsating
source CXOU J073709.1+653544 discovered in the nearby spiral galaxy NGC 2403.


title:
Simulation study of earthquakes based on the two-dimensional
  Burridge-Knopoff model with the long-range interaction

abstract:
  Spatiotemporal correlations of the two-dimensional spring-block
(Burridge-Knopoff) models of earthquakes with the long-range inter-block
interactions are extensively studied by means of numerical computer
simulations. The long-range interaction derived from an elasticd theory, which
takes account of the effect of the elastic body adjacent to the fault plane,
falls off with distance r as 1/r^3. Comparison is made with the properties of
the corresponding short-range models studied earlier. Seismic spatiotemporal
correlations of the long-range models generally tend to be weaker than those of
the short-range models. The magnitude distribution exhibits a ``near-critical''
behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law,
for a wide parameter range with its B-value, B\simeq 0.55, insensitive to the
model parameters, in sharp contrast to that of the 2D short-range model and
those of the 1D short-range and long-range models where such a
``near-critical'' behavior is realized only by fine-tuning the model
parameters. In contrast to the short-range case, the mean stress-drop at a
seismic event of the long-range model is nearly independent of its magnitude,
consistently with the observation. Large events often accompany foreshocks
together with a doughnut-like quiescence as their precursors, while they hardly
accompany aftershocks with almost negligible seismic correlations observed
after the mainshock.


title: Network as a computer: ranking paths to find flows

abstract:
  We explore a simple mathematical model of network computation, based on
Markov chains. Similar models apply to a broad range of computational
phenomena, arising in networks of computers, as well as in genetic, and neural
nets, in social networks, and so on. The main problem of interaction with such
spontaneously evolving computational systems is that the data are not uniformly
structured. An interesting approach is to try to extract the semantical content
of the data from their distribution among the nodes. A concept is then
identified by finding the community of nodes that share it. The task of data
structuring is thus reduced to the task of finding the network communities, as
groups of nodes that together perform some non-local data processing. Towards
this goal, we extend the ranking methods from nodes to paths. This allows us to
extract some information about the likely flow biases from the available static
information about the network.


title:
On the zeros of certain modular functions for the normalizers of
  congruence subgroups of low levels I

abstract:
  We research the location of the zeros of the Eisenstein series and the
modular functions from the Hecke type Faber polynomials associated with the
normalizers of congruence subgroups which are of genus zero and of level at
most twelve.
  In Part I, we will consider the general theory of modular functions for the
normalizers.


title:
Dispersive Coupling Between the Superconducting Transmission Line
  Resonator and the Double Quantum Dots

abstract:
  Realization of controllable interaction between distant qubits is one of the
major problems in scalable solid state quantum computing. We study a
superconducting transmission line resonator (TLR) as a tunable dispersive
coupler for the double-dot molecules. A general interaction Hamiltonian of $n$
two-electron spin-based qubits and the TLR is presented, where the double-dot
qubits are biased at the large detuning region and the TLR is always empty and
virtually excited. Our analysis o the main decoherence sources indicates that
various major quantum operations can be reliably implemented with current
technology.


title: Gravitational wave detection using high precision pulsar observations

abstract:
  Pulsar timing experiments are reaching sufficient sensitivity to detect a
postulated stochastic gravitational wave background generated by merging
supermassive black hole systems in the cores of galaxies. We describe the
techniques behind the pulsar timing detection method, provide current upper
bounds on the amplitude of any gravitational wave background, describe
theoretical models predicting the existence of such a background and highlight
new techniques for providing a statistically rigorous detection of the
background.


title: Quantum Localization in Open Chaotic Systems

abstract:
  We study a quasi-Floquet state of a $\delta$-kicked rotor with absorbing
boundaries focusing on the nature of the dynamical localization in open quantum
systems. The localization lengths $\xi$ of lossy quasi-Floquet states located
near the absorbing boundaries decrease as they approach the boundary while the
corresponding decay rates $\Gamma$ are dramatically enhanced. We find the
relation $\xi \sim \Gamma^{-1/2}$ and explain it based upon the finite time
diffusion, which can also be applied to a random unitary operator model. We
conjecture that this idea is valid for the system exhibiting both the diffusion
in classical dynamics and the exponential localization in quantum mechanics.


title: Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors

abstract:
  The rapid developing area of compressed sensing suggests that a sparse vector
lying in an arbitrary high dimensional space can be accurately recovered from
only a small set of non-adaptive linear measurements. Under appropriate
conditions on the measurement matrix, the entire information about the original
sparse vector is captured in the measurements, and can be recovered using
efficient polynomial methods. The vector model has been extended to a finite
set of sparse vectors sharing a common non-zero location set. In this paper, we
treat a broader framework in which the goal is to recover a possibly infinite
set of jointly sparse vectors. Extending existing recovery methods to this
model is difficult due to the infinite structure of the sparse vector set.
Instead, we prove that the entire infinite set of sparse vectors can recovered
by solving a single, reduced-size finite-dimensional problem, corresponding to
recovery of a finite set of sparse vectors. We then show that the problem can
be further reduced to the basic recovery of a single sparse vector by randomly
combining the measurement vectors. Our approach results in exact recovery of
both countable and uncountable sets as it does not rely on discretization or
heuristic techniques. To efficiently recover the single sparse vector produced
by the last reduction step, we suggest an empirical boosting strategy that
improves the recovery ability of any given sub-optimal method for recovering a
sparse vector. Numerical experiments on random data demonstrate that when
applied to infinite sets our strategy outperforms discretization techniques in
terms of both run time and empirical recovery rate. In the finite model, our
boosting algorithm is characterized by fast run time and superior recovery rate
than known popular methods.


title: Untangling polygons and graphs

abstract:
  Untangling is a process in which some vertices of a planar graph are moved to
obtain a straight-line plane drawing. The aim is to move as few vertices as
possible. We present an algorithm that untangles the cycle graph C_n while
keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also
present an upper bound on the number of fixed vertices in the worst case. The
bound is a function of the number of vertices, maximum degree and diameter of
G. One of its consequences is the upper bound O((n log n)^{2/3}) for all
3-vertex-connected planar graphs.


title: Oxygen Vacancy Induced Ferromagnetism in V$_2$O$_{5-x}$

abstract:
  {\it Ab initio} calculations within density functional theory with
generalized gradient approximation have been performed to study the effects of
oxygen vacancies on the electronic structure and magnetism in undoped
V$_2$O$_{5-x}$ ($0 < x < 0.5$). It is found that the introduction of oxygen
vacancies would induce ferromagnetism in V$_2$O$_{5-x}$ with the magnetization
being proportional to the O vacancy concentration $x$. The calculated
electronic structure reveals that the valence electrons released by the
introduction of oxygen vacancies would occupy mainly the neighboring V
$d_{xy}$-dominant band which then becomes spin-polarized due to intra-atomic
exchange interaction, thereby giving rise to the half-metallic ferromagnetism.


title:
Second-harmonic generation and linear electro-optical coefficients of
  SiC polytypes and nanotubes

abstract:
  The second-order nonlinear optical susceptibility ($\chi_{abc}^{(2)}$) and
linear electro-optical coefficient ($r_{abc}$) of a large number of
single-walled zigzag, armchair and chiral SiC nanotubes (SiC-NTs) as well as
bulk SiC polytypes (2H-, 4H-, 6H- and 3C-SiC) and single graphitic SiC sheet
have been calculated from first-principles. The calculations are based on
density functional theory in the local density approximation and highly
accurate full-potential projector augmented-wave method is used. Both the
zigzag and chiral SiC-NTs are found to exhibit large second-order nonlinear
optical behavior with the $\chi_{abc}^{(2)}$ and $r_{abc}$ coefficients being
up to ten-times larger than that of bulk SiC polytypes, and also being up to
thirteen-times larger than the counterparts of the corresponding BN-NTs,
indicating that SiC-NTs are promising materials for nonlinear optical and
opto-electric applications. The prominant features in the spectra of
$\chi_{abc}^{(2)}(-2\omega,\omega,\omega)$ of the SiC-NTs are correlated with
the features in the linear optical dielectric function $\epsilon (\omega)$ in
terms of single-photon and two-photon resonances.


title: On search for hidden sector photons in Super-Kamiokande

abstract:
  If hidden sector photons exist, they could be produced through oscillations
of photons emitted by the Sun. We show that a search for these particles could
be performed in Super-Kamiokande due to the presence in this detector of a
large number of photomultiplier's (PMTs) with a relatively low noise and big
size. These particles would penetrate the Earth shielding and would be detected
by PMTs through their oscillations into real photons inside the PMTs vacuum
volume. This would results in an increase of the PMT counting rate and it daily
variations depending on the Earth position with respect to the Sun. The
proposed search for this effect is sensitive to the photon-hidden photon mixing
strength as small as ~10^{-6} for the hidden photon mass region ~10^{-3} -
10^{-1} eV and, in the case of nonobservation, could improve limits recently
obtained from photon regeneration laser experiments for this mass region.


title:
Stable liquid Hydrogen at high pressure by a novel ab-initio molecular
  dynamics

abstract:
  We introduce an efficient scheme for the molecular dynamics of electronic
systems by means of quantum Monte Carlo. The evaluation of the
(Born-Oppenheimer) forces acting on the ionic positions is achieved by two main
ingredients: i) the forces are computed with finite and small variance, which
allows the simulation of a large number of atoms, ii) the statistical noise
corresponding to the forces is used to drive the dynamics at finite temperature
by means of an appropriate Langevin dynamics. A first application to the
high-density phase of Hydrogen is given, supporting the stability of the liquid
phase at \simeq 300GPa and \simeq 400K.


title: A generalization of Doob's maximal identity

abstract:
  In this paper, using martingale techniques, we prove a generalization of
Doob's maximal identity in the setting of continuous nonnegative local
submartingales $(X_{t})$ of the form: $X_{t}=N_{t}+A_{t}$, where the measure
$(dA_{t})$ is carried by the set $\left\{t: X_{t}=0\right\}$. In particular, we
give a multiplicative decomposition for the Az\'ema supermartingale associated
with some last passage times related to such processes and we prove that these
non-stopping times contain very useful information. As a consequence, we obtain
the law of the maximum of a continuous nonnegative local martingale $(M_t)$
which satisfies $M_\infty=\psi(\sup_{t\geq0}M_t)$ for some measurable function
$\psi$ as well as the law of the last time this maximum is reached.


title: Quantum knots

abstract:
  It is known that besides the usual unitary mappings $\Omega =
1/\Omega^\dagger$ between the equivalent representations of the physical
Hilbert space of Quantum Mechanics (often, Fourier transformations), the
generalized non-unitary maps $\Omega \neq 1/\Omega^\dagger$ can also help to
simplify the analysis. We adapt the standard Dirac's notation and recollect the
Buslaev's and Grecchi's repulsive quartic oscillator Hamiltonian as an example.
Then we propose the whole new class of the models of the similar type,
characterized by a complexification of the path ${\cal C}$ of the (obviously,
not observable!) "coordinates". An exactly solvable potentialless
Schr\"{o}dinger equation is finally chosen for illustration. In it, the
dynamical (i.e., in our example, confining) role of the traditional potentials
$V(x)$ is shown to be taken over by the mere topologically nontrivial shape of
${\cal C}$. Our construction evokes several new open questions in physics
(${\cal PT}-$symmetric wave packets at a single energy?) as well as in
mathematics (a three-Hilbert-space generalized formulation of Quantum
Mechanics?).


title:
Asymptotic efficiency of simple decisions for the compound decision
  problem

abstract:
  We consider the compound decision problem of estimating a vector of $n$
parameters, known up to a permutation, corresponding to $n$ independent
observations, and discuss the difference between two symmetric classes of
estimators. The first and larger class is restricted to the set of all
permutation invariant estimators. The second class is restricted further to
simple symmetric procedures. That is, estimators such that each parameter is
estimated by a function of the corresponding observation alone. We show that
under mild conditions, the minimal total squared error risks over these two
classes are asymptotically equivalent up to essentially O(1) difference.


title: The Complex of Non-Crossing Diagonals of a Polygon

abstract:
  Given a convex n-gon P in the Euclidean plane, it is well known that the
simplicial complex \theta(P) with vertex set given by diagonals in P and facets
given by triangulations of P is the boundary complex of a polytope of dimension
n-3. We prove that for any non-convex polygonal region P with n vertices and
h+1 boundary components, \theta(P) is a ball of dimension n+3h-4. We also
provide a new proof that \theta(P) is a sphere when P is convex.


title: Near-infrared reddening of extra-galactic GMCs in a face-on geometry

abstract:
  [Abridged] We describe the near-infrared reddening signature of giant
molecular clouds (GMCs) in external galaxies. In particular, we examine the
E(J-H) and E(H-K) color-excesses, and the effective extinction law observed in
discrete GMC regions. We also study the effect of the relative scale height of
the GMC distribution to the color-excesses, and to the observed mass function
of GMCs. We perform Monte Carlo radiative transfer simulations with 3D models
of stellar radiation and clumpy dust distributions, resembling a face-on
geometry. The scattered light is included in the models, and near-infrared
color maps are calculated from the simulated data. The effective near-infrared
reddening law, i.e. the ratio E(J-H)/E(H-K), has a value close to unity in GMC
regions. The ratio depends on the relative scale height of GMCs, xi, and for xi
values 0.1...0.75 we find the typical ratios of 0.6...1.1. The effective
extinction law turns out to be very flat in GMC regions. We find the ratios of
apparent extinctions of A(H)/A(K)=1.35...1.55 and A(J)/A(H)=1.15. The effect of
the scattered flux on the effective reddening law, as well as on the effective
extinction law, is significant. Regarding the GMC mass function, we find no
correlation between the input and observed slopes of the mass functions.
Rather, the observed slope reflects the parameter $\xi$ and the dynamical range
of the mass function. We estimate that only a fraction of 10...20 % of the
total mass of GMCs is recovered, if the observed color-excess values are
transformed to masses using the Galactic reddening law. In the case of
individual clouds the fraction can vary between ~0...50 %.


title:
Exact solutions for standing kink modes of the longitudinally stratified
  coronal loops

abstract:
  The influence of longitudinal structuring on the fast kink modes of coronal
loops is investigated. Analytical dispersion relations and mode profiles are
derived for the second-order ordinary differential equation governing the z-
component of the perturbation in the magnetic field, $\delta B_z$. All other
components are given in terms of $\delta B_z$. Deviations from the frequencies
and mode profiles of homogenous loops are given as functions of the density
scale height. The effects of the fixed and variable column masses, negative
scale heights, and density contrasts inside and outside of the loops are
studied. The frequency ratios, mode profiles, and the antinode shifts from
those of the sine profiles of the homogenous loops, are tools to estimate solar
photospheric parameters. To this end, we have expanded the relevant factors up
to the second order in the stratification parameter. In particular, we verify
that the first overtone antinode shifts are in the Mm range and are within the
reach of the resolutions of the present day observations.


title:
The quadratic isoperimetric inequality for mapping tori of free group
  automorphisms

abstract:
  If F is a finitely generated free group and \phi is an automorphism of F then
F \rtimes_\phi Z satisfties a quadratic isoperimetric inequality.


title: Probe Annihilation process on noncommutative spacetime

abstract:
  This paper has been withdrawn by Chien-Yu, Chen due to the authors fields
error.


title: Single mode two-channel cavity QED

abstract:
  In this short communication, a new type of two-channel cavity QED model is
derived. Two-channel models are important for they often lead to quantum
interference phenomena. The previous models relied on the use of two or more
modes of the quantized electromagnetic field, partially because of energy and
parity restrictions. As it is shown in this work, such restrictions may be
overcome with the use of properly chosen configurations of atomic levels and
the aplication of classical external fields. Competing one- and two-photon
processes involving one single mode may be obtained.


title: Thermodynamic curvature and phase transitions in Kerr-Newman black holes

abstract:
  Singularities in the thermodynamics of Kerr-Newman black holes are commonly
associated with phase transitions. However, such interpretations are
complicated by a lack of stability and, more significantly, by a lack of
conclusive insight from microscopic models. Here, I focus on the later problem.
I use the thermodynamic Riemannian curvature scalar $R$ as a try to get
microscopic information from the known thermodynamics. The hope is that this
could facilitate matching black hole thermodynamics to known models of
statistical mechanics. For the Kerr-Newman black hole, the sign of $R$ is
mostly positive, in contrast to that for ordinary thermodynamic models, where
$R$ is mostly negative. Cases with negative $R$ include most of the simple
critical point models. An exception is the Fermi gas, which has positive $R$. I
demonstrate several exact correspondences between the two-dimensional Fermi gas
and the extremal Kerr-Newman black hole. $R$ diverges to $+\infty$ along curves
of diverging heat capacities $C_{J,\Phi}$ and $C_{\Omega,Q}$, but not along the
Davies curve of diverging $C_{J,Q}$. Finding statistical mechanical models with
like behavior might yield additional insight into the microscopic properties of
black holes. I also discuss a possible physical interpretation of $|R|$.


title: Exchange of Limits: Why Iterative Decoding Works

abstract:
  We consider communication over binary-input memoryless output-symmetric
channels using low-density parity-check codes and message-passing decoding. The
asymptotic (in the length) performance of such a combination for a fixed number
of iterations is given by density evolution. Letting the number of iterations
tend to infinity we get the density evolution threshold, the largest channel
parameter so that the bit error probability tends to zero as a function of the
iterations.
  In practice we often work with short codes and perform a large number of
iterations. It is therefore interesting to consider what happens if in the
standard analysis we exchange the order in which the blocklength and the number
of iterations diverge to infinity. In particular, we can ask whether both
limits give the same threshold.
  Although empirical observations strongly suggest that the exchange of limits
is valid for all channel parameters, we limit our discussion to channel
parameters below the density evolution threshold. Specifically, we show that
under some suitable technical conditions the bit error probability vanishes
below the density evolution threshold regardless of how the limit is taken.


title: Affleck-Dine Baryogenesis, Split Supersymmetry, and Inflation

abstract:
  It is shown that, in the context of split supersymmetry, a simple model with
a single complex scalar field can produce chaotic inflation and generate the
observed amount of baryon asymmetry via the Affleck-Dine mechanism. While the
inflaton quantum fluctuations give rise to curvature perturbation, we show that
quantum fluctuations of the phase of the scalar field can produce baryonic
isocurvature perturbation. Combining with constraints from WMAP data, all
parameters in the model can be determined to within a narrow range.


title: Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model

abstract:
  We study birational transformations of the projective space originating from
lattice statistical mechanics, specifically from various chiral Potts models.
Associating these models to \emph{stable patterns} and \emph{signed-patterns},
we give general results which allow us to find \emph{all} chiral $q$-state
spin-edge Potts models when the number of states $q$ is a prime or the square
of a prime, as well as several $q$-dependent family of models. We also prove
the absence of monocolor stable signed-pattern with more than four states. This
demonstrates a conjecture about cyclic Hadamard matrices in a particular case.
The birational transformations associated to these lattice spin-edge models
show complexity reduction. In particular we recover a one-parameter family of
integrable transformations, for which we give a matrix representation


title:
The strange-sea quark spin distribution in the nucleon from inclusive
  and semi-inclusive deep-inelastic scattering

abstract:
  We propose new method which allows determination of the strange-sea quark
spin distribution in the nucleon through measurement of various inclusive and
semi-inclusive polarized deep inelastic electron- or muon-proton reactions. It
is shown, that using combinations of inclusive data and semi-inclusive data
containing neutral pions in the final state, it is possible to extract the
strange-sea quark spin distribution. Similar result can be obtained for charged
pions and some other hadrons also.


title:
Magnetorotational-type instability in Couette-Taylor flow of a
  viscoelastic polymer liquid

abstract:
  We describe an instability of viscoelastic Couette-Taylor flow that is
directly analogous to the magnetorotational instability (MRI) in astrophysical
magnetohydrodynamics, with polymer molecules playing the role of magnetic field
lines. By determining the conditions required for the onset of instability and
the properties of the preferred modes, we distinguish it from the centrifugal
and elastic instabilities studied previously. Experimental demonstration and
investigation should be much easier for the viscoelastic instability than for
the MRI in a liquid metal. The analogy holds with the case of a predominantly
toroidal magnetic field such as is expected in an accretion disk and it may be
possible to access a turbulent regime in which many modes are unstable.


title:
A connection between palindromic and factor complexity using return
  words

abstract:
  In this paper we prove that for any infinite word W whose set of factors is
closed under reversal, the following conditions are equivalent:
  (I) all complete returns to palindromes are palindromes;
  (II) P(n) + P(n+1) = C(n+1) - C(n) + 2 for all n, where P (resp. C) denotes
the palindromic complexity (resp. factor complexity) function of W, which
counts the number of distinct palindromic factors (resp. factors) of each
length in W.