title: Scheduling multiple divisible loads on a linear processor network

abstract:
  Min, Veeravalli, and Barlas have recently proposed strategies to minimize the
overall execution time of one or several divisible loads on a heterogeneous
linear network, using one or more installments. We show on a very simple
example that their approach does not always produce a solution and that, when
it does, the solution is often suboptimal. We also show how to find an optimal
schedule for any instance, once the number of installments per load is given.
Then, we formally state that any optimal schedule has an infinite number of
installments under a linear cost model as the one assumed in the original
papers. Therefore, such a cost model cannot be used to design practical
multi-installment strategies. Finally, through extensive simulations we
confirmed that the best solution is always produced by the linear programming
approach, while solutions of the original papers can be far away from the
optimal.


title: Study of Lorentz violation in INTEGRAL Gamma-Ray Bursts

abstract:
  We search for possible time lags caused by quantum gravitational (QG) effects
using gamma-ray bursts (GRBs) detected by INTEGRAL. The advantage of this
satellite is that we have at our disposal the energy and arrival time of every
detected single photon, which enhances the precision of the time resolution. We
present a new method for seeking time lags in unbinned data using a maximum
likelihood method and support our conclusions with Monte Carlo simulations. The
analysis of the data yields a mass scale well below the Planck mass whose value
may however increase if better statistics of GRBs were available. Furthermore,
we disagree with previous studies in which a non-monotonic function of the
redshift was used to perform a linear fit.


title: Normal zone in $YBa_2Cu_3O_{6+x}$-coated conductors

abstract:
  We consider the distribution of an electric field in YBCO-coated conductors
for a situation in which the DC transport current is forced into the copper
stabilizer due to a weak link -- a section of the superconducting film with a
critical current less than the transport current. The electric field in the
metal substrate is also discussed. The results are compared with recent
experiments on normal zone propagation in coated conductors for which the
substrate and stabilizer are insulated from each other. The potential
difference between the substrate and stabilizer, and the electric field in the
substrate outside the normal zone can be accounted for by a large screening
length in the substrate, comparable to the length of the sample. During a
quench, the electric field inside the interface between YBCO and stabilizer, as
well as in the buffer layer, can be several orders of magnitude greater than
the longitudinal macroscopic electric field inside the normal zone. We
speculate on the possibility of using possible microscopic electric discharges
caused by this large ($\sim $kV/cm) electric field as a means to detect a
quench.


title:
Matter-wave Interferometry with Phase Fluctuating Bose-Einstein
  Condensates

abstract:
  Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase
fluctuations even well below the BEC transition temperature. We demonstrate
that atom interferometers using such condensates are robust against phase
fluctuations, i.e. the relative phase of the split condensate is reproducible
despite axial phase fluctuations. However, larger phase fluctuations limit the
coherence time, especially in the presence of some asymmetries in the two wells
of the interferometer.


title: Stopped diffusion processes: boundary corrections and overshoot

abstract:
  For a stopped diffusion process in a multidimensional time-dependent domain
$\D$, we propose and analyse a new procedure consisting in simulating the
process with an Euler scheme with step size $\Delta$ and stopping it at
discrete times $(i\Delta)_{i\in\N^*}$ in a modified domain, whose boundary has
been appropriately shifted. The shift is locally in the direction of the inward
normal $n(t,x)$ at any point $(t,x)$ on the parabolic boundary of $\D$, and its
amplitude is equal to $0.5826 (...) |n^*\sigma|(t,x)\sqrt \Delta$ where
$\sigma$ stands for the diffusion coefficient of the process. The procedure is
thus extremely easy to use. In addition, we prove that the rate of convergence
w.r.t. $\Delta$ for the associated weak error is higher than without shifting,
generalizin g previous results by \cite{broa:glas:kou:97} obtained for the one
dimensional Brownian motion. For this, we establish in full generality the
asymptotics of the triplet exit time/exit position/overshoot for the discretely
stopped Euler scheme. Here, the overshoot means the distance to the boundary of
the process when it exits the domain. Numerical experiments support these
results.


title: Frame Dependence in Scalar-tensor Theory

abstract:
  Palatini variation of Jordan frame lagrangians gives an equation relating the
dilaton to the object of non-metricity and hence the existence of the dilaton
implies that the spacetime connection is more general than that given soley by
the Christoffel symbol of general relativity. Transferring from Jordan to
Einstein frame, which connection, lagrangian, field equations and stress
conservation equations occur are discussed: it is found that the Jordan frame
has more information, this can be expressed in several ways, the simplest is
that the extra information corresponds to the function multiplying the Ricci
scalar in the action. The Einstein frame has the advantages that stress
conservation implies no currents and that the field equations are easier to
work with. This is illustrated by application to Robertson-Walker spacetime.


title: PSPACE Bounds for Rank-1 Modal Logics

abstract:
  For lack of general algorithmic methods that apply to wide classes of logics,
establishing a complexity bound for a given modal logic is often a laborious
task. The present work is a step towards a general theory of the complexity of
modal logics. Our main result is that all rank-1 logics enjoy a shallow model
property and thus are, under mild assumptions on the format of their
axiomatisation, in PSPACE. This leads to a unified derivation of tight
PSPACE-bounds for a number of logics including K, KD, coalition logic, graded
modal logic, majority logic, and probabilistic modal logic. Our generic
algorithm moreover finds tableau proofs that witness pleasant proof-theoretic
properties including a weak subformula property. This generality is made
possible by a coalgebraic semantics, which conveniently abstracts from the
details of a given model class and thus allows covering a broad range of logics
in a uniform way.


title: Continuous spectrum for a class of nonhomogeneous differential operators

abstract:
  We study the boundary value problem $-{\rm div}((|\nabla
u|^{p_1(x)-2}+|\nabla u|^{p_2(x)-2})\nabla u)=\lambda|u|^{q(x)-2}u$ in
$\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded domain in
$\RR^N$ with smooth boundary, $\lambda$ is a positive real number, and the
continuous functions $p_1$, $p_2$, and $q$ satisfy $1<p_2(x)<q(x)<p_1(x)<N$ and
$\max_{y\in\bar\Omega}q(y)<\frac{N p_2(x)}{N-p_2(x)}$ for any $x\in\bar\Omega$.
The main result of this paper establishes the existence of two positive
constants $\lambda_0$ and $\lambda_1$ with $\lambda_0\leq\lambda_1$ such that
any $\lambda\in[\lambda_1,\infty)$ is an eigenvalue, while any
$\lambda\in(0,\lambda_0)$ is not an eigenvalue of the above problem.


title:
The Thermal Regulation of Gravitational Instabilities in Protoplanetary
  Disks. IV. Simulations with Envelope Irradiation

abstract:
  It is generally thought that protoplanetary disks embedded in envelopes are
more massive and thus more susceptible to gravitational instabilities (GIs)
than exposed disks. We present three-dimensional radiative hydrodynamics
simulations of protoplanetary disks with the presence of envelope irradiation.
For a disk with a radius of 40 AU and a mass of 0.07 Msun around a young star
of 0.5 Msun, envelope irradiation tends to weaken and even suppress GIs as the
irradiating flux is increased. The global mass transport induced by GIs is
dominated by lower-order modes, and irradiation preferentially suppresses
higher-order modes. As a result, gravitational torques and mass inflow rates
are actually increased by mild irradiation. None of the simulations produce
dense clumps or rapid cooling by convection, arguing against direct formation
of giant planets by disk instability, at least in irradiated disks. However,
dense gas rings and radial mass concentrations are produced, and these might be
conducive to accelerated planetary core formation. Preliminary results from a
simulation of a massive embedded disk with physical characteristics similar to
one of the disks in the embedded source L1551 IRS5 indicate a long radiative
cooling time and no fragmentation. The GIs in this disk are dominated by global
two and three-armed modes.


title: Simple derivation of the frequency dependent complex heat capacity

abstract:
  This paper gives a simple derivation of the well-known expression of the
frequency dependent complex heat capacity in modulated temperature experiments.
It aims at clarified again that the generalized calorimetric susceptibility is
only due to the non-equilibrium behaviour occurring in the vicinity of
thermodynamic equilibrium of slow internal degrees of freedom of a sample when
the temperature oscillates at a well determined frequency.


title:
Getting More From Your Multicore: Exploiting OpenMP From An Open Source
  Numerical Scripting Language

abstract:
  We introduce SLIRP, a module generator for the S-Lang numerical scripting
language, with a focus on its vectorization capabilities. We demonstrate how
both SLIRP and S-Lang were easily adapted to exploit the inherent parallelism
of high-level mathematical languages with OpenMP, allowing general users to
employ tightly-coupled multiprocessors in scriptable research calculations
while requiring no special knowledge of parallel programming. Motivated by
examples in the ISIS astrophysical modeling & analysis tool, performance
figures are presented for several machine and compiler configurations,
demonstrating beneficial speedups for real-world operations.


title: A sharpened nuclearity condition and the uniqueness of the vacuum in QFT

abstract:
  It is shown that only one vacuum state can be prepared with a finite amount
of energy and it appears, in particular, as a limit of physical states under
large timelike translations in any theory which satisfies a phase space
condition proposed in this work. This new criterion, related to the concept of
additivity of energy over isolated subsystems, is verified in massive free
field theory. The analysis entails very detailed results about the momentum
transfer of local operators in this model.


title:
Non-equilibrium heat capacity of polytetrafluoroethylene at room
  temperature

abstract:
  Polytetrafluoroethylene can be considered as a model for calorimetric studies
of complex systems with thermodynamics transitions at ambient temperature. This
polymer exhibits two phase transitions of different nature at 292 K and 303 K.
We show that sensitive ac-calorimetry measurements allow us to study the
thermodynamic behaviour of polytetrafluoroethylene when it is brought out of
thermodynamic equilibrium. Thanks to the thermal modelisation of our
calorimetric device, the frequency dependent complex heat capacity of this
polymer is extracted. The temperature and frequency variations of the real and
imaginary parts of the complex heat capacity are obtained when
polytetrafluoroethylene undergoes its first-order structural phase transition
at 292 K.


title: A novel renormalizable representation of the Yang-Mills theory

abstract:
  For a generic gauge-invariant correlator <{\cal Q}[A_{\mu}]>_{A}, we
reformulate the standard D=4 Yang-Mills theory as a renormalizable system of
two interacting fields a_{\mu} and B_{\mu} which faithfully represent high- and
low-energy degrees of freedom of the single gauge field A_{\mu} in the original
formulation. It opens a possibility to synthesize an infrared-nonsingular
weak-coupling series, employed to integrate over a_{\mu} for a given background
B_{\mu}, with qualitatively different methods. These methods are to be applied
to evaluate the resulting (after the a_{\mu}-integration) representation of
<{\cal Q}[A_{\mu}]>_{A} in terms of gauge-invariant generically non-local
low-energy observables, like Wilson loops. The latter observables are averaged
over B_{\mu} with respect to a gauge-invariant Wilsonean effective action
S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy
excitations, we implement a specific fine-tuning of the interaction between the
pair of the fields: prior to the integration over B_{\mu}, the expectation
value <a_{\mu}>_{a} vanishes, in the tree order of the loop-wise expansion, for
an arbitrary configuration of B_{\mu}.


title:
Renormalisability of the matter determinants in noncommutative gauge
  theory in the enveloping-algebra formalism

abstract:
  We consider noncommutative gauge theory defined by means of Seiberg-Witten
maps for an arbitrary semisimple gauge group. We compute the one-loop UV
divergent matter contributions to the gauge field effective action to all
orders in the noncommutative parameters $\theta$. We do this for Dirac fermions
and complex scalars carrying arbitrary representations of the gauge group. We
use path-integral methods in the framework of dimensional regularisation and
consider arbitrary invertible Seiberg-Witten maps that are linear in the matter
fields. Surprisingly, it turns out that the UV divergent parts of the matter
contributions are proportional to the noncommutative Yang-Mills action where
traces are taken over the representation of the matter fields; this result
supports the need to include such traces in the classical action of the gauge
sector of the noncommutative theory.


title: Toward the classification of cohomology-free vector fields

abstract:
  In 1984, Anatole Katok conjectured that the only closed orientable manifolds
that support cohomology-free vector fields are tori and these vector fields are
smoothly conjugated to Diophantine (constant) ones.
  In this work we present a proof of Katok conjecture for 3-manifolds.


title: The pentagon relation for the quantum dilogarithm and quantized M_{0,5}

abstract:
  We introduce and study a Schwarz space S in the space of functions on the
real line. It is a module over the algebra L of regular functions on the
(modular double of the) non-commutative q-deformation of the moduli space of
configurations of 5 cyclically ordered points on the projective line. The
algebra L has an order five automorphism corresponding to the cyclic shift of
the points. The quantum dilogarithm gives rise to an automorphism of the space
Schwarz S intertwining the automorphism of L. This easily implies the pentagon
relation for the quantum dilogarithm function.
  The triple (L, S, the automorphism) is the quantized moduli space of
configurations of 5 points on the projective line. It is the simplest example
of a quantized cluster X-variety.


title: Weighted Low-Regularity Solutions of the KP-I Initial Value Problem

abstract:
  In this paper we establish local well-posedness of the KP-I problem, with
initial data small in the intersection of the natural energy space with the
space of functions which are square integrable when multiplied by the weight y.
The result is proved by the contraction mapping principle. A similar (but
slightly weaker) result was the main Theorem in the paper " Low regularity
solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and
Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a
counterexample (included in the present paper) to the main estimate used in the
GAFA paper, which renders incorrect the proof there. The present paper thus
provides a correct proof of a strengthened version of the main result in the
GAFA paper.


title:
Photoionization of 3d electrons of Xe, Cs and Ba endohedral atoms:
  comparative analyses

abstract:
  We demonstrate rather interesting manifestations of co-existence of resonance
features in characteristics of the photoionization of 3d-electrons in Xe, Cs
and Ba endohedral atoms. It is shown that for all of the considered atoms the
reflection by the fullerene shell of photoelectrons produced by the 3d subshell
photoionization affects greatly partial photoionization cross-sections of 3d5/2
and 3d3/2 levels and respective angular anisotropy parameters, both dipole and
non-dipole adding to all of them additional maximums and minimums. The results
obtained demonstrate distinctive differences between the three atoms.
  The calculations are performed treating the 3/2 and 5/2 electrons as
electrons of different kinds with their spins "up" and "down". The effect of
C60 shell is accounted for in the frame of the "orange" skin potential model.
It is essential that in the considered photon frequency region presented
resonance features are not affected by the C60 polarization.


title: An angular momentum bound at null infinity

abstract:
  We prove an inequality relating the trace of the extrinsic curvature, the
total angular momentum, the centre of mass, and the Trautman-Bondi mass for a
class of gravitational initial data sets with constant mean curvature extending
to null infinity. As an application we obtain non-existence results for the
asymptotic Dirichlet problem for CMC hypersurfaces in stationary space-times.


title: Opinion Formation in Laggard Societies

abstract:
  We introduce a statistical physics model for opinion dynamics on random
networks where agents adopt the opinion held by the majority of their direct
neighbors only if the fraction of these neighbors exceeds a certain threshold,
p_u. We find a transition from total final consensus to a mixed phase where
opinions coexist amongst the agents. The relevant parameters are the relative
sizes in the initial opinion distribution within the population and the
connectivity of the underlying network. As the order parameter we define the
asymptotic state of opinions. In the phase diagram we find regions of total
consensus and a mixed phase. As the 'laggard parameter' p_u increases the
regions of consensus shrink. In addition we introduce rewiring of the
underlying network during the opinion formation process and discuss the
resulting consequences in the phase diagram.


title:
Precision study of K^\pm\to\pi^\pm\pi^0\pi^0 and
  K^\pm\to\pi^\pm\pi^+\pi^- Dalitz plot distributions by NA48/2

abstract:
  The NA48/2 experiment at the CERN SPS has collected an unprecedented sample
of $K^\pm\to3\pi$ decays. The high statistics and the good resolution of the
detectors allow a unique investigation of the detailed phase space
distributions of these decays. The effects of final state pion rescattering
observed in the Dalitz plot distribution of the $K^\pm\to\pi^\pm\pi^0\pi^0$
decays turned out to be a powerful tool for extraction of the S-wave $\pi\pi$
scattering lengths. The large statistics also allowed a precise measurement of
the Dalitz plot slope parameters for the $K^\pm\to3\pi^\pm$ decays.


title: Minimal $\gamma$--sheaves

abstract:
  In this note we show that finitely generated unit $O_X[\sigma]$--modules for
$X$ regular and $F$--finite have a minimal root (in the sense of [Lyubeznik,
F-modules] Definition~3.6). This problem was posed by Lyubeznik and answered by
himself in the case that $X=\Spec R$ is a complete local ring.
  One immediate consequence of this result is that the parameter test module of
tight closure theory commutes with localization. As a further application of
the methods in this paper we give new proofs of the results on discreteness and
rationality of $F$--thresholds [arXiv:0705.1210] and on $D$-module generation
[arXiv:math/0502405v1]. The new proofs are valid in a slightly more general
setting such that they also party cover the generalizations recently obtained
in [arXiv:0706.3028].


title: Equisingularite reelle : invariants locaux et conditions de regularite

abstract:
  For germs of subanalytic sets, we define two finite sequences of new
numerical invariants. The first one is obtained by localizing the classical
Lipschitz-Killing curvatures, the second one is the real analogue of the
evanescent characteristics introduced by M. Kashiwara. We show that each
invariant of one sequence is a linear combination of the invariants of the
other sequence. We then connect our invariants to the geometry of the
discriminants of all dimension. Finally we prove that these invariants are
continuous along Verdier strata of a closed subanalytic set.


title:
Universal abelian covers of rational surface singularities and
  multi-index filtrations

abstract:
  In previous papers, there were computed the Poincare series of some
(multi-index) filtrations on the ring of germs of functions on a rational
surface singularity. These Poincare series were written as the integer parts of
certain fractional power series, an interpretation of whom was not given. Here
we show that, up to a simple change of variables, these fractional power series
are specializations of the equivariant Poincare series for filtrations on the
ring of germs of functions on the universal abelian cover of the surface
singularity. We compute these equivariant Poincare series.


title: QCD and Monte Carlo generators

abstract:
  In this talk I gave a brief summary of leading order, next-to-leading order
and shower calculations. I discussed the main ideas and approximations of the
shower algorithms and the related matching schemes. I tried to focus on QCD
issues and open questions instead of making a inventory of the existing
programs.


title: Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians

abstract:
  We discuss the Hamiltonian H = p^2/2 - (ix)^{2n+1} and the mixed Hamiltonian
H = (p^2 + x^2)/2 - g(ix)^{2n+1}, which are crypto-Hermitian in a sense that,
in spite of apparent complexity of the potential, a quantum spectral problem
can be formulated such that the spectrum is real. We note first that the
corresponding classical Hamiltonian system can be treated as a gauge system,
with imaginary part of the Hamiltonian playing the role of the first class
constraint. We observe then that, on the basis of this classical problem,
several different nontrivial quantum problems can be formulated. We formulate
and solve some such problems. We find in particular that the spectrum of the
mixed Hamiltonian undergoes in certain cases rather amazing transformation when
the coupling g is sent to zero. There is an infinite set of phase transitions
in g when a couple of eigenstates of H coalesce and disappear from the
spectrum. When quantization is done in the most natural way such that gauge
constraints are imposed on quantum states, the spectrum should not be positive
definite, but must involve the negative energy states (ghosts). We speculate
that, in spite of the appearance of ghost states, unitarity might still be
preserved.


title: Observation of VHE gamma-rays from Cassiopeia A with the MAGIC telescope

abstract:
  We searched for very high energy (VHE) gamma-ray emission from the supernova
remnant Cassiopeia A. The shell-type supernova remnant Cassiopeia A was
observed with the 17 meter MAGIC telescope between July 2006 and January 2007
for a total time of 47 hours. The source was detected above an energy of 250
GeV with a significance of 5.2sigma and a photon flux above 1 TeV of
(7.3+-0.7_stat+-2.2_sys)10^-13 cm^-2s^-1. The photon spectrum is compatible
with a power law dN/dE = A E^-Gamma with a photon index
Gamma=2.3+-0.2_stat+-0.2_sys. The source is point-like within the angular
resolution of the telescope.


title: Pion spectra and HBT radii at RHIC and LHC

abstract:
  We describe RHIC pion data in central A+A collisions and make predictions for
LHC based on hydro-kinetic model, describing continuous 4D particle emission,
and initial conditions taken from Color Glass Condensate (CGC) model.


title: Partial Swapping, Unitarity and No-signalling

abstract:
  It is a well known fact that an quantum state $|\psi(\theta,\phi)>$ is
represented by a point on the Bloch sphere, characterized by two parameters
$\theta$ and $\phi$. In a recent work we already proved that it is impossible
to partially swap these quantum parameters. Here in this work we will show that
this impossibility theorem is consistent with principles like unitarity of
quantum mechanics and no signalling principle.


title:
Detection of dark energy near the Local Group with the Hubble Space
  Telescope

abstract:
  We report the detection of dark energy near the Milky Way made with precision
observations of the local Hubble flow of expansion. We estimate the local
density of dark energy and find that it is near, if not exactly equal to, the
global dark energy density. The result is independent of, compatible with, and
complementary to the horizon-scale observations in which dark energy was first
discovered. Together with the cosmological concordance data, our result forms
direct observational evidence for the Einstein antigravity as a universal
phenomenon -- in the same sense as the Newtonian universal gravity.


title:
An effective criterion and a new example for ballistic diffusions in
  random environment

abstract:
  In the setting of multidimensional diffusions in random environment, we carry
on the investigation of condition $(T')$, introduced by Sznitman [Ann. Probab.
29 (2001) 723--764] and by Schmitz [Ann. Inst. H. Poincar\'{e} Probab. Statist.
42 (2006) 683--714] respectively in the discrete and continuous setting, and
which implies a law of large numbers with nonvanishing limiting velocity
(ballistic behavior) as well as a central limit theorem. Specifically, we show
that when $d\geq2$, $(T')$ is equivalent to an effective condition that can be
checked by local inspection of the environment. When $d=1$, we prove that
condition $(T')$ is merely equivalent to almost sure transience. As an
application of the effective criterion, we show that when $d\geq4$ a
perturbation of Brownian motion by a random drift of size at most $\epsilon>0$
whose projection on some direction has expectation bigger than
$\epsilon^{2-\eta},\eta>0$, satisfies condition $(T')$ when $\epsilon$ is small
and hence exhibits ballistic behavior. This class of diffusions contains new
examples of ballistic behavior which in particular do not fulfill the condition
in [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42 (2006) 683--714], (5.4)
therein, related to Kalikow's condition.


title: Poisson-sigma model for 2D gravity with non-metricity

abstract:
  We present a Poisson-sigma model describing general 2D dilaton gravity with
non-metricity, torsion and curvature. It involves three arbitrary functions of
the dilaton field, two of which are well-known from metric compatible theories,
while the third one characterizes the local strength of non-metricity. As an
example we show that alpha' corrections in 2D string theory can generate
(target space) non-metricity.


title: Cosmology and Astrophysics of Minimal Dark Matter

abstract:
  We consider DM that only couples to SM gauge bosons and fills one gauge
multiplet, e.g. a fermion 5-plet (which is automatically stable), or a
wino-like 3-plet. We revisit the computation of the cosmological relic
abundance including non-perturbative corrections. The predicted mass of e.g.
the 5-plet increases from 4.4 TeV to 10 TeV, and indirect detection rates are
enhanced by 2 orders of magnitude. Next, we show that due to the
quasi-degeneracy among neutral and charged components of the DM multiplet, a
significant fraction of DM with energy E > 10^17 eV (possibly present among
ultra-high energy cosmic rays) can cross the Earth exiting in the charged state
and may in principle be detected in neutrino telescopes.


title: Some developments in vertex operator algebra theory, old and new

abstract:
  In this exposition, I discuss several developments in the theory of vertex
operator algebras, and I include motivation for the definition.


title:
Some generic properties of level spacing distributions of 2D real random
  matrices

abstract:
  We study the level spacing distribution $P(S)$ of 2D real random matrices
both symmetric as well as general, non-symmetric. In the general case we
restrict ourselves to Gaussian distributed matrix elements, but different
widths of the various matrix elements are admitted. The following results are
obtained: An explicit exact formula for $P(S)$ is derived and its behaviour
close to S=0 is studied analytically, showing that there is linear level
repulsion, unless there are additional constraints for the probability
distribution of the matrix elements. The constraint of having only positive or
only negative but otherwise arbitrary non-diagonal elements leads to quadratic
level repulsion with logarithmic corrections. These findings detail and extend
our previous results already published in a preceding paper. For the {\em
symmetric} real 2D matrices also other, non-Gaussian statistical distributions
are considered. In this case we show for arbitrary statistical distribution of
the diagonal and non-diagonal elements that the level repulsion exponent $\rho$
is always $\rho = 1$, provided the distribution function of the matrix elements
is regular at zero value. If the distribution function of the matrix elements
is a singular (but still integrable) power law near zero value of $S$, the
level spacing distribution $P(S)$ is a fractional exponent pawer law at small
$S$. The tail of $P(S)$ depends on further details of the matrix element
statistics. We explicitly work out four cases: the constant (box) distribution,
the Cauchy-Lorentz distribution, the exponential distribution and, as an
example for a singular distribution, the power law distribution for $P(S)$ near
zero value times an exponential tail.


title: Measurement of the Decay KL -> pi0 e+ e- gamma

abstract:
  We report on a new measurement of the branching ratio B(KL -> pi0 e+ e-
gamma) using the KTeV detector. This analysis uses the full KTeV data set
collected from 1997 to 2000. We reconstruct 139 events over a background of 14,
which results in B(KL -> pi0 e+ e- gamma) = (1.62 +/- 0.14 (stat) +/- 0.09
(syst)) x 10^{-8}. This result supersedes the earlier KTeV measurement of this
branching ratio.


title: A novel interpretation of the Klein-Gordon equation

abstract:
  The covariant Klein-Gordon equation requires twice the boundary conditions of
the Schrodinger equation and does not have an accepted single-particle
interpretation. Instead of interpreting its solution as a probability wave
determined by an initial boundary condition, this paper considers the
possibility that the solutions are determined by both an initial and a final
boundary condition. By constructing an invariant joint probability distribution
from the size of the solution space, it is shown that the usual measurement
probabilities can nearly be recovered in the non-relativistic limit, provided
that neither boundary constrains the energy to a precision near hbar/T (where T
is the time duration between the boundary conditions). Otherwise, deviations
from standard quantum mechanics are predicted.


title: Phonons in lattices with rod-like particles

abstract:
  The paper studies the modes of vibrations of a lattice with rod-like
particles, in a continuum model where the sites of the lattice are the
connections among strings and rigid rods. In these structures then,
translational and rotational degrees of freedom are strongly coupled. We will
discuss in particular two-dimensional lattices with auxetic-like behaviour.
Auxetics are materials with a negative Poisson elastic parameter, meaning that
they have a lateral extension, instead to shrink, when they are stretched. We
assume as "auxetic-like" two-dimensional structures, structures which do not
collapse, when stretched in one of the in-plane directions. The presence of
rigid rod-like particles in the lattice prevents the shrinking of the membrane.
Complete bandgaps between acoustic and optical modes are observed in analogy
with the behaviour of crystalline materials.


title:
Mapping the Evolution of Optically-Generated Rotational Wavepackets in a
  Room Temperature Ensemble of D$_2$

abstract:
  A coherent superposition of rotational states in D$_2$ has been excited by
nonresonant ultrafast (12 femtosecond) intense (2 $\times$ 10$^{14}$
Wcm$^{-2}$) 800 nm laser pulses leading to impulsive dynamic alignment.
Field-free evolution of this rotational wavepacket has been mapped to high
temporal resolution by a time-delayed pulse, initiating rapid double
ionization, which is highly sensitive to the angle of orientation of the
molecular axis with respect to the polarization direction, $\theta$. The
detailed fractional revivals of the neutral D$_2$ wavepacket as a function of
$\theta$ and evolution time have been observed and modelled theoretically.


title: Exact closed form analytical solutions for vibrating cavities

abstract:
  For one-dimensional vibrating cavity systems appearing in the standard
illustration of the dynamical Casimir effect, we propose an approach to the
construction of exact closed-form solutions. As new results, we obtain
solutions that are given for arbitrary frequencies, amplitudes and time
regions. In a broad range of parameters, a vibrating cavity model exhibits the
general property of exponential instability. Marginal behavior of the system
manifests in a power-like growth of radiated energy.


abstract:
  A generalized version of Chernoff's theorem has been obtained. Namely, the
version of Chernoff's theorem for semigroups obtained in a paper by Smolyanov,
Weizsaecker, and Wittich is generalized for a time-inhomogeneous case. The main
theorem obtained in the current paper, Chernoff's theorem for evolution
families, deals with a family of time-dependent generators of semigroups $A_t$
on a Banach space, a two-parameter family of operators $Q_{t,t+\Delta t}$
satisfying the relation: $\frac{\partial}{\partial \Delta t}Q_{t,t+\Delta
t}|_{\Delta t = 0}=A_t$, whose products $Q_{t_i,t_{i+1}}... Q_{t_{k-1},t_k}$
are uniformly bounded for all subpartitions $s = t_0 < t_1 < >... < t_n = t$.
The theorem states that $Q_{t_0,t_1}... Q_{t_{n-1},t_n}$ converges to an
evolution family $U(s,t)$ solving a non-autonomous Cauchy problem. Furthermore,
the theorem is formulated for a particular case when the generators $A_t$ are
time dependent second order differential operators. Finally, an example of
application of this theorem to a construction of time-inhomogeneous diffusions
on a compact Riemannian manifold is given.
  Keywords: Chernoff's theorem, evolution family, strongly continuous
semigroup, evolution families generated by manifold valued stochastic
processes.


title: On X-ray Optical Depth in the Coronae of Active Stars

abstract:
  We have investigated the optical thickness of the coronal plasma through the
analysis of high-resolution X-ray spectra of a large sample of active stars
observed with the High Energy Transmission Grating Spectrometer on Chandra. In
particular, we probed for the presence of significant resonant scattering in
the strong Lyman series lines arising from hydrogen-like oxygen and neon ions.
The active RS CVn-type binaries II Peg and IM Peg and the single M dwarf EV Lac
show significant optical depth. For these active coronae, the Lya/Lyb ratios
are significantly depleted as compared with theoretical predictions and with
the same ratios observed in similar active stars. Interpreting these decrements
in terms of resonance scattering of line photons out of the line-of-sight, we
are able to derive an estimate for the typical size of coronal structures, and
from these we also derive estimates of coronal filling factors. For all three
sources we find that the both the photon path length as a fraction of the
stellar radius, and the implied surface filling factors are very small and
amount to a few percent at most. The measured Lya/Lyb ratios are in good
agreement with APED theoretical predictions, thus indicating negligible optical
depth, for the other sources in our sample. We discuss the implications for
coronal structuring and heating flux requirements. For the stellar sample as a
whole, the data suggest increasing quenching of Lya relative to Lyb as function
of both L_x/L_bol and the density-sensitive MgXI forbidden to intercombination
line ratio, as might generally be expected.


title: The classification of torsion endo-trivial modules

abstract:
  This paper is a major step in the classification of endotrivial modules over
p-groups. Let G be a finite p-group and k be a field of characteristic p. A
kG-module M is an endo-trivial module if {\End_k(M)\cong k\oplus F} as
kG-modules, where F is a free module. The classification of endo-trivial
modules is the crucial step for understanding the more general class of
endo-permutation modules. The endo-permutation modules play an important role
in module theory, in particular as source modules, and in block theory where
they appear in the description of source algebras. Endo-trivial modules are
also important in the study of both derived equivalences and stable
equivalences of group algebras and block algebras.
  The collection of isomorphism classes of endo-trivial modules modulo
projectives is an abelian group under tensor product. The main result of this
paper is that this group is torsion free except in the case that G is cyclic,
quaternion or semi-dihedral. Hence for any p-group which is not cyclic,
quaternion or semi-dihedral and any finitely generated kG-module M, if M
\otimes_k M \otimes_k ... \otimes_k M \cong k \oplus P for some projective
module P and some finite number of tensor products, then M \cong k \oplus Q for
some projective module Q. The proof uses a reduction to the cases in which G is
an extraspecial or almost extraspecial p-group, proved in a previous paper of
the authors, and makes extensive use of the theory of support varieties for
modules.


title: Inf-sup estimates for the Stokes problem in a periodic channel

abstract:
  We derive estimates of the Babu\u{s}ka-Brezzi inf-sup constant $\beta$ for
two-dimensional incompressible flow in a periodic channel with one flat
boundary and the other given by a periodic, Lipschitz continuous function $h$.
If $h$ is a constant function (so the domain is rectangular), we show that
periodicity in one direction but not the other leads to an interesting
connection between $\beta$ and the unitary operator mapping the Fourier sine
coefficients of a function to its Fourier cosine coefficients. We exploit this
connection to determine the dependence of $\beta$ on the aspect ratio of the
rectangle. We then show how to transfer this result to the case that $h$ is
$C^{1,1}$ or even $C^{0,1}$ by a change of variables. We avoid non-constructive
theorems of functional analysis in order to explicitly exhibit the dependence
of $\beta$ on features of the geometry such as the aspect ratio, the maximum
slope, and the minimum gap thickness (if $h$ passes near the substrate). We
give an example to show that our estimates are optimal in their dependence on
the minimum gap thickness in the $C^{1,1}$ case, and nearly optimal in the
Lipschitz case.


title: Pulsational frequencies of the eclipsing delta-Scuti star HD 172189

abstract:
  The eclipsing delta-Scuti star HD 172189 is a probable member of the open
cluster IC 4756 and a promising candidate target for the CoRoT mission.
  The detection of pulsation modes is the first step in the asteroseismological
study of the star. Further, the calculation of the orbital parameters of the
binary system allows us to make a dynamical determination of the mass of the
star, which works as an important constraint to test and calibrate the
asteroseismological models.
  From a detailed frequency analysis of 210 hours of photometric data of HD
172189 obtained from the STEPHI XIII campaign we have identified six pulsation
frequencies with a confidence level of 99% and a seventh with a 65% confidence
level in the range between 100-300 uHz. In addiction, three eclipses were
observed during the campaign, allowing us to improve the determination of the
orbital period of the system.


title: Strong Upper Limits on Sterile Neutrino Warm Dark Matter

abstract:
  Sterile neutrinos are attractive dark matter candidates. Their parameter
space of mass and mixing angle has not yet been fully tested despite intensive
efforts that exploit their gravitational clustering properties and radiative
decays. We use the limits on gamma-ray line emission from the Galactic Center
region obtained with the SPI spectrometer on the INTEGRAL satellite to set new
constraints, which improve on the earlier bounds on mixing by more than two
orders of magnitude, and thus strongly restrict a wide and interesting range of
models.


title: A new effective interaction for the trapped Fermi gas

abstract:
  We apply the configuration-interaction method to calculate the spectra of
two-component Fermi systems in a harmonic trap, studying the convergence of the
method at the unitary interaction limit. We find that for a fixed
regularization of the two-body interaction the convergence is exponential or
better in the truncation parameter of the many-body space. However, the
conventional regularization is found to have poor convergence in the
regularization parameter, with an error that scales as a low negative power of
this parameter. We propose a new regularization of the two-body interaction
that produces exponential convergence for systems of three and four particles.
  From the systematics, we estimate the ground-state energy of the
four-particle system to be (5.05 +- 0.024)hbar omega.


title: Bulk Viscous Cosmology

abstract:
  We propose a scenario in which the dark components of the Universe are
manifestations of a single bulk viscous fluid. Using dynamical system methods,
a qualitative study of the homogeneous, isotropic background scenario is
performed in order to determine the phase space of all possible solutions. The
specific model which we investigate shares similarities with a generalized
Chaplygin gas in the background but is characterized by non-adiabatic pressure
perturbations. This model is tested against supernova type Ia and matter power
spectrum data. Different from other unified descriptions of dark matter and
dark energy, the matter power spectrum is well behaved, i.e., there are no
instabilities or oscillations on small perturbation scales. The model is
competitive in comparison with the currently most popular proposals for the
description of the cosmological dark sector.


title:
Mutually compensative pseudo solutions of primary energy spectra in the
  knee region

abstract:
  The problem of the uniqueness of solutions during the evaluation of primary
energy spectra in the knee region using an extensive air shower (EAS) data set
and the EAS inverse approach is investigated. It is shown that the unfolding of
primary energy spectra in the knee region leads to mutually compensative pseudo
solutions. These solutions may be the reason for the observed disagreements in
the elementary energy spectra of cosmic rays in the 1-100 PeV energy range
obtained from different experiments.


title:
A Study of the Type Ia/IIn Supernova 2005gj from X-ray to the Infrared:
  Paper I

abstract:
  We present extensive ugrizYHJK photometry and optical spectroscopy of SN
2005gj obtained by the SDSS-II and CSP Supernova Projects, which give excellent
coverage during the first 150 days after the time of explosion. These data show
that SN 2005gj is the second clear case, after SN 2002ic, of a thermonuclear
explosion in a dense circumstellar environment. Both the presence of singly and
doubly ionized iron-peak elements (FeIII and weak SII, SiII) near maximum light
as well as the spectral evolution show that SN 2002ic-like events are Type Ia
explosions. Independent evidence comes from the exponential decay in luminosity
of SN 2005gj, pointing to an exponential density distribution of the ejecta.
The interaction of the supernova ejecta with the dense circumstellar medium is
stronger than in SN 2002ic: (1) the supernova lines are weaker; (2) the Balmer
emission lines are more luminous; and (3) the bolometric luminosity is higher
close to maximum light. The velocity evolution of the Halpha components suggest
that the CSM around SN 2005gj is clumpy and it has a flatter density
distribution compared with the steady wind solution, in agreement with SN
2002ic. An early X-ray observation with Chandra gives an upper-limit on the
mass loss rate from the companion of < 2x10^{-4} Msun/yr.


title:
The DEEP2 Galaxy Redshift Survey: The Role of Galaxy Environment in the
  Cosmic Star-Formation History

abstract:
  Using galaxy samples drawn from the Sloan Digital Sky Survey and the DEEP2
Galaxy Redshift Survey, we study the relationship between star formation and
environment at z ~ 0.1 and z ~ 1. We estimate the total star-formation rate
(SFR) and specific star-formation rate (sSFR) for each galaxy according to the
measured [O II] nebular line luminosity, corrected using empirical calibrations
to match more robust SFR indicators. Echoing previous results, we find that in
the local Universe star formation depends on environment such that galaxies in
regions of higher overdensity, on average, have lower star-formation rates and
longer star-formation timescales than their counterparts in lower-density
regions. At z ~ 1, we show that the relationship between specific SFR and
environment mirrors that found locally. However, we discover that the
relationship between total SFR and overdensity at z ~ 1 is inverted relative to
the local relation. This observed evolution in the SFR-density relation is
driven, in part, by a population of bright, blue galaxies in dense environments
at z ~ 1. This population, which lacks a counterpart at z ~ 0, is thought to
evolve into members of the red sequence from z ~ 1 to z ~ 0. Finally, we
conclude that environment does not play a dominant role in the cosmic
star-formation history at z < 1: the dependence of the mean galaxy SFR on local
galaxy density at constant redshift is small compared to the decline in the
global SFR space density over the last 7 Gyr.


title:
Correlation in the velocity of a Brownian particle induced by frictional
  anisotropy and magnetic field

abstract:
  We study the motion of charged Brownian particles in an external magnetic
field. It is found that a correlation appears between the components of
particle velocity in the case of anisotropic friction, approaching
asymptotically zero in the stationary limit. If magnetic field is smaller
compared to the critical value, determined by frictional anisotropy, the
relaxation of the correlation is non-oscillating in time. However, in a larger
magnetic field this relaxation becomes oscillating. The phenomenon is related
to the statistical dependence of the components of transformed random force
caused by the simultaneous influence of magnetic field and anisotropic
dissipation.


title:
Multi-Wavelength Constraints on the Cosmic Star Formation History from
  Spectroscopy: the Rest-Frame UV, H-alpha, and Infrared Luminosity Functions
  at Redshifts 1.9<z<3.4

abstract:
  We use a sample of rest-frame UV selected and spectroscopically observed
galaxies at redshifts 1.9<z<3.4, combined with ground-based spectroscopic
H-alpha and Spitzer MIPS 24 micron data, to derive the most robust measurements
of the rest-frame UV, H-alpha, and infrared (IR) luminosity functions (LFs) at
these redshifts. Our sample is by far the largest of its kind, with over 2000
spectroscopic redshifts in the range 1.9<z<3.4 and ~15000 photometric
candidates in 29 independent fields covering a total area of almost a square
degree. Our method for computing the LFs takes into account a number of
systematic effects, including photometric scatter, Ly-alpha perturbations to
optical colors, and contaminants. Taking into account the latter, we find no
evidence for an excess of UV-bright galaxies over what was inferred in early
z~3 LBG studies. The UV LF appears to undergo little evolution between z~4 and
z~2. Corrected for extinction, the UV luminosity density (LD) at z~2 is at
least as large as the value at z~3 and a factor of ~9 larger than the value at
z~6, primarily reflecting an increase in the number density of bright galaxies
between z~6 and z~2. Our analysis yields the first constraints anchored by
extensive spectroscopy on the IR and bolometric LFs for faint and moderately
luminous (L[bol]<10^12 L_sun) galaxies. Adding the IR to the emergent UV
luminosity, incorporating independent measurements of the LD from ULIRGs, and
assuming realistic dust attenuation values for UV-faint galaxies, indicates
that galaxies with L[bol]<10^12 L_sun account for ~80% of the bolometric LD and
SFRD at z~2-3. Our multi-wavelength constraints on the global SFRD indicate
that approximately one-third of the present-day stellar mass density was formed
in sub-ultraluminous galaxies between redshifts z=1.9-3.4. [Abridged]


title:
Distinguishing Bulk-Diffusion from Surface-Desorption Limited Gas
  Release Processes

abstract:
  The release of a gas limited by surface desorption, or by diffusion from the
bulk of spherical pebbles is revisited. A method is proposed to identify the
release limiting process, by comparing a partial temperature ramp, up to
slightly beyond the release peak, followed by a rapid temperature drop, to a
second, full release ramp. Comparing the release curve from the second ramp to
that of the first one: i) the peak is unmoved in first order desorption
kinetics, and moves to higher temperature in the other cases, ii) as compared
to the Arrhenius analysis of the first curve, that of the second is, again,
identical in first order kinetics, in second order desorption it maintains the
slope but lowers the intercept at the reciprocal temperature origin, and it is
inapplicable in bulk diffusion kinetics.


title: New Constraints on the Lyman Continuum Escape Fraction at z~1.3

abstract:
  We examine deep far-ultraviolet (1600 Angstrom) imaging of the Hubble Deep
Field-North (HDFN) and the Hubble Ultra Deep Field (HUDF) to search for leaking
Lyman continuum radiation from starburst galaxies at z~1.3. There are 21
(primarily sub-L*) galaxies with spectroscopic redshifts between 1.1<z<1.5 and
none are detected in the far-UV. We fit stellar population templates to the
galaxies' optical/near-infrared SEDs to determine the starburst age and level
of dust attenuation, giving an accurate estimate of the intrinsic Lyman
continuum ratio, f_1500/f_700, and allowing a conversion from f_700 limits to
relative escape fractions. We show that previous high-redshift studies may have
underestimated the amplitude of the Lyman Break, and thus the relative escape
fraction, by a factor of ~2. Once the starburst age and intergalactic HI
absorption are accounted for, 18 galaxies in our sample have limits to the
relative escape fraction, f_esc,rel < 1.0 with some limits as low as f_esc,rel
< 0.10 and a stacked limit of f_esc,rel < 0.08. This demonstrates, for the
first time, that most sub-L* galaxies at high redshift do not have large escape
fractions. When combined with a similar study of more luminous galaxies at the
same redshift we show that, if all star-forming galaxies at z~1 have similar
relative escape fractions, the value must be less than 0.14 (3 sigma). We also
show that less than 20% (3 sigma) of star-forming galaxies at z~1 have relative
escape fractions near unity. These limits contrast with the large escape
fractions found at z~3 and suggest that the average escape fraction has
decreased between z~3 and z~1. (Abridged)


title: Quantum Belief Propagation

abstract:
  We present an accurate numerical algorithm, called quantum belief propagation
(QBP), for simulation of one-dimensional quantum systems at non-zero
temperature. The algorithm exploits the fact that quantum effects are
short-range in these systems at non-zero temperature, decaying on a length
scale inversely proportional to the temperature. We compare to exact results on
a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring
diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a
relative error of less than $10^{-5}$, while more elaborate calculations
further reduce the error.


title: Some Quantitative Aspects of Fractional Computability

abstract:
  Motivated by results on generic-case complexity in group theory, we apply the
ideas of effective Baire category and effective measure theory to study
complexity classes of functions which are "fractionally computable" by a
partial algorithm. For this purpose it is crucial to specify an allowable
effective density, $\delta$, of convergence for a partial algorithm. The set
$\mathcal{FC}(\delta)$ consists of all total functions $ f: \Sigma^\ast \to
\{0,1 \}$ where $\Sigma$ is a finite alphabet with $|\Sigma| \ge 2$ which are
"fractionally computable at density $\delta$". The space $\mathcal{FC}(\delta)
$ is effectively of the second category while any fractional complexity class,
defined using $\delta$ and any computable bound $\beta$ with respect to an
abstract Blum complexity measure, is effectively meager. A remarkable result of
Kautz and Miltersen shows that relative to an algorithmically random oracle
$A$, the relativized class $\mathcal{NP}^A$ does not have effective polynomial
measure zero in $\mathcal{E}^A$, the relativization of strict exponential time.
We define the class $\mathcal{UFP}^A$ of all languages which are fractionally
decidable in polynomial time at ``a uniform rate'' by algorithms with an oracle
for $A$. We show that this class does have effective polynomial measure zero in
$\mathcal{E}^A$ for every oracle $A$. Thus relaxing the requirement of
polynomial time decidability to hold only for a fraction of possible inputs
does not compensate for the power of nondeterminism in the case of random
oracles.


title:
Formation and evolution of compact binaries in globular clusters: II.
  Binaries with neutron stars

abstract:
  In this paper, the second of a series, we study the stellar dynamical and
evolutionary processes leading to the formation of compact binaries containing
neutron stars (NSs) in dense globular clusters (GCs). For this study, 70 dense
clusters were simulated independently, with a total stellar mass ~2x10^7Msun,
exceeding the total mass of all dense GCs in our Galaxy.
  We find that, in order to reproduce the empirically derived formation rate of
low-mass X-ray binaries (LMXBs), we must assume that NSs can be formed via
electron-capture supernovae (ECS) with typical natal kicks smaller than in
core-collapse supernovae. Our results explain the observed dependence of the
number of LMXBs on ``collision number'' as well as the large scatter observed
between different GCs. We predict that the number of quiescent LMXBs in
different GCs should not have a strong metallicity dependence. In our cluster
model the following mass-gaining events create populations of MSPs that do not
match the observations: (i) accretion during a common envelope event with a NS
formed through ECS, and (ii) mass transfer (MT) from a WD donor. Some processes
lead only to a mild recycling. In addition, for MSPs, we distinguish
low-magnetic-field (long-lived) and high-magnetic-field (short-lived)
populations. With this distinction and by considering only those mass-gaining
events that appear to lead to NS recycling, we obtain good agreement of our
models with the numbers and characteristics of observed MSPs in 47 Tuc and
Terzan 5, as well as with the cumulative statistics for MSPs detected in GCs of
different dynamical properties. We find that significant production of merging
double NSs potentially detectable as short gamma-ray bursts occurs only in very
dense, most likely core-collapsed GCs. (abridged)


title: Equivariant path fields on topological manifolds

abstract:
  A classical theorem of H. Hopf asserts that a closed connected smooth
manifold admits a nowhere vanishing vector field if and only if its Euler
characteristic is zero. R. Brown generalized Hopf's result to topological
manifolds, replacing vector fields with path fields. In this note, we give an
equivariant analog of Brown's theorem for locally smooth $G$-manifolds where
$G$ is a finite group.


title:
A superconductor with 4-fermion attraction perturbed by magnetic
  impurities

abstract:
  A superconductor with 4-fermion attraction, considered by Ma\'{c}kowiak and
Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic
interaction $V$ between conduction fermions and localized distinguishable spin
1/2 magnetic impurities. $V$ has the form of a reduced s-d interaction. An
upper and lower bound to the system's free energy density $f(H,\beta)$ is
derived and the two bounds are shown to coalesce in the thermodynamic limit.
The resulting mean-field equations for the gap $\Delta$ and a parameter $y$,
characterizing the impurity subsystem are solved and the solution minimizing
$f$ is found for various values of magnetic coupling constant $g$ and impurity
concentration. The phase diagrams of the system are depicted with five distinct
phases: the normal phase, unperturbed superconducting phase, perturbed
superconducting phase with nonzero gap in the excitation spectrum, perturbed
gapless superconducting phase and impurity phase with completely suppressed
superconductivity.


title: On graphs with subgraphs of large independence numbers

abstract:
  Let G be a graph on n vertices in which every induced subgraph on s=\log^3 n
vertices has an independent set of size at least t=\log n. What is the largest
q=q(n) so that every such G must contain an independent set of size at least q
? This is one of several related questions raised by Erdos and Hajnal. We show
that q(n)=\Theta(\log^2 n/\log \log n), investigate the more general problem
obtained by changing the parameters s and t, and discuss the connection to a
related Ramsey-type problem.


title: Embedding nearly-spanning bounded degree trees

abstract:
  We derive a sufficient condition for a sparse graph G on n vertices to
contain a copy of a tree T of maximum degree at most d on (1-\epsilon)n
vertices, in terms of the expansion properties of G. As a result we show that
for fixed d\geq 2 and 0<\epsilon<1, there exists a constant c=c(d,\epsilon)
such that a random graph G(n,c/n) contains almost surely a copy of every tree T
on (1-\epsilon)n vertices with maximum degree at most d. We also prove that if
an (n,D,\lambda)-graph G (i.e., a D-regular graph on n vertices all of whose
eigenvalues, except the first one, are at most \lambda in their absolute
values) has large enough spectral gap D/\lambda as a function of d and
\epsilon, then G has a copy of every tree T as above.


title: Making a K_4-free graph bipartite

abstract:
  We show that every K_4-free graph G with n vertices can be made bipartite by
deleting at most n^2/9 edges. Moreover, the only extremal graph which requires
deletion of that many edges is a complete 3-partite graph with parts of size
n/3. This proves an old conjecture of P. Erdos.


title: Ramsey numbers and the size of graphs

abstract:
  For two graph H and G, the Ramsey number r(H, G) is the smallest positive
integer n such that every red-blue edge coloring of the complete graph K_n on n
vertices contains either a red copy of H or a blue copy of G. Motivated by
questions of Erdos and Harary, in this note we study how the Ramsey number
r(K_s, G) depends on the size of the graph G. For s \geq 3, we prove that for
every G with m edges, r(K_s,G) \geq c (m/\log m)^{\frac{s+1}{s+3}} for some
positive constant c depending only on s. This lower bound improves an earlier
result of Erdos, Faudree, Rousseau, and Schelp, and is tight up to a
polylogarithmic factor when s=3. We also study the maximum value of r(K_s,G) as
a function of m.


title:
Practical Error Estimates for Reynolds' Lubrication Approximation and
  its Higher Order Corrections

abstract:
  Reynolds' lubrication approximation is used extensively to study flows
between moving machine parts, in narrow channels, and in thin films. The
solution of Reynolds' equation may be thought of as the zeroth order term in an
expansion of the solution of the Stokes equations in powers of the aspect ratio
$\epsilon$ of the domain. In this paper, we show how to compute the terms in
this expansion to arbitrary order on a two-dimensional, $x$-periodic domain and
derive rigorous, a-priori error bounds for the difference between the exact
solution and the truncated expansion solution. Unlike previous studies of this
sort, the constants in our error bounds are either independent of the function
$h(x)$ describing the geometry, or depend on $h$ and its derivatives in an
explicit, intuitive way. Specifically, if the expansion is truncated at order
$2k$, the error is $O(\epsilon^{2k+2})$ and $h$ enters into the error bound
only through its first and third inverse moments $\int_0^1 h(x)^{-m} dx$,
$m=1,3$ and via the max norms $\big\|\frac{1}{\ell!} h^{\ell-1} \partial_x^\ell
h\big\|_\infty$, $1\le\ell\le2k+2$. We validate our estimates by comparing with
finite element solutions and present numerical evidence that suggests that even
when $h$ is real analytic and periodic, the expansion solution forms an
asymptotic series rather than a convergent series.


title: Local resilience of graphs

abstract:
  In this paper, we initiate a systematic study of graph resilience. The
(local) resilience of a graph G with respect to a property P measures how much
one has to change G (locally) in order to destroy P. Estimating the resilience
leads to many new and challenging problems. Here we focus on random and
pseudo-random graphs and prove several sharp results.


title: Exact factorization of correlation functions in 2-D critical percolation

abstract:
  By use of conformal field theory, we discover several exact factorizations of
higher-order density correlation functions in critical two-dimensional
percolation. Our formulas are valid in the upper half-plane, or any conformally
equivalent region. We find excellent agreement of our results with
high-precision computer simulations. There are indications that our formulas
hold more generally.

categories: math-ph cond-mat.dis-nn cond-mat.stat-mech hep-th math.MP


title: Path-integral quantization of Galilean Fermi fields

abstract:
  The Galilei-covariant fermionic field theories are quantized by using the
path-integral method and five-dimensional Lorentz-like covariant expressions of
non-relativistic field equations. Firstly, we review the five-dimensional
approach to the Galilean Dirac equation, which leads to the Levy-Leblond
equations, and define the Galilean generating functional and Green's functions
for positive- and negative-energy/mass solutions. Then, as an example of
interactions, we consider the quartic self-interacting potential ${\lambda}
(\bar{\Psi} {\Psi})^2$, and we derive expressions for the 2- and 4-point
Green's functions. Our results are compatible with those found in the
literature on non-relativistic many-body systems. The extended manifold allows
for compact expressions of the contributions in $(3+1)$ space-time. This is
particularly apparent when we represent the results with diagrams in the
extended $(4+1)$ manifold, since they usually encompass more diagrams in
Galilean $(3+1)$ space-time.


title: Radix Sorting With No Extra Space

abstract:
  It is well known that n integers in the range [1,n^c] can be sorted in O(n)
time in the RAM model using radix sorting. More generally, integers in any
range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these
algorithms use O(n) words of extra memory. Is this necessary?
  We present a simple, stable, integer sorting algorithm for words of size
O(log n), which works in O(n) time and uses only O(1) words of extra memory on
a RAM model. This is the integer sorting case most useful in practice. We
extend this result with same bounds to the case when the keys are read-only,
which is of theoretical interest. Another interesting question is the case of
arbitrary c. Here we present a black-box transformation from any RAM sorting
algorithm to a sorting algorithm which uses only O(1) extra space and has the
same running time. This settles the complexity of in-place sorting in terms of
the complexity of sorting.


title: Event Weighted Tests for Detecting Periodicity in Photon Arrival Times

abstract:
  This paper treats the problem of detecting periodicity in a sequence of
photon arrival times, which occurs, for example, in attempting to detect
gamma-ray pulsars. A particular focus is on how auxiliary information,
typically source intensity, background intensity, and incidence angles and
energies associated with each photon arrival should be used to maximize the
detection power. We construct a class of likelihood-based tests, score tests,
which give rise to event weighting in a principled and natural way, and derive
expressions quantifying the power of the tests. These results can be used to
compare the efficacies of different weight functions, including cuts in energy
and incidence angle. The test is targeted toward a template for the periodic
lightcurve, and we quantify how deviation from that template affects the power
of detection.


title:
Structure of AlSb(001) and GaSb(001) Surfaces Under Extreme Sb-rich
  Conditions

abstract:
  We use density-functional theory to study the structure of AlSb(001) and
GaSb(001) surfaces. Based on a variety of reconstruction models, we construct
surface stability diagrams for AlSb and GaSb under different growth conditions.
For AlSb(001), the predictions are in excellent agreement with experimentally
observed reconstructions. For GaSb(001), we show that previously proposed model
accounts for the experimentally observed reconstructions under Ga-rich growth
conditions, but fails to explain the experimental observations under Sb-rich
conditions. We propose a new model that has a substantially lower surface
energy than all (nx5)-like reconstructions proposed previously and that, in
addition, leads to a simulated STM image in better agreement with experiment
than existing models. However, this new model has higher surface energy than
some of (4x3)-like reconstructions, models with periodicity that has not been
observed. Hence we conclude that the experimentally observed (1x5) and (2x5)
structures on GaSb(001) are kinetically limited rather than at the ground
state.


title: A General Search for New Phenomena at HERA

abstract:
  A model-independent search for deviations from the Standard Model prediction
is performed in $e^+ p$ and $e^- p$ collisions at HERA II using all high energy
data recorded by the H1 experiment. This corresponds to a total integrated
luminosity of 337 pb$^{-1}$. All event topologies involving isolated electrons,
photons, muons, neutrinos and jets with high transverse momenta are
investigated in a single analysis. Events are assigned to exclusive classes
according to their final state. A statistical algorithm is used to search for
deviations from the Standard Model in distributions of the scalar sum of
transverse momenta or invariant mass of final state particles and to quantify
their significance. A good agreement with the Standard Model prediction is
observed in most of the event classes. The most siginificant deviation is found
in the \mujnp channel in $e^+p$ collisions.


title:
Effect of a single impurity on the local density of states in monolayer
  and bilayer graphene

abstract:
  We use the T-matrix approximation to analyze the effect of a localized
impurity on the local density of states in mono- and bilayer graphene. For
monolayer graphene the Friedel oscillations generated by intranodal scattering
obey an inverse-square law, while the internodal ones obey an inverse law. In
the Fourier transform this translates into a filled circle of high intensity in
the center of the Brillouin zone, and empty circular contours around its
corners. For bilayer graphene both types of oscillations obey an inverse law.


title: Induced Ramsey-type theorems

abstract:
  We present a unified approach to proving Ramsey-type theorems for graphs with
a forbidden induced subgraph which can be used to extend and improve the
earlier results of Rodl, Erdos-Hajnal, Promel-Rodl, Nikiforov, Chung-Graham,
and Luczak-Rodl. The proofs are based on a simple lemma (generalizing one by
Graham, Rodl, and Rucinski) that can be used as a replacement for Szemeredi's
regularity lemma, thereby giving much better bounds. The same approach can be
also used to show that pseudo-random graphs have strong induced Ramsey
properties. This leads to explicit constructions for upper bounds on various
induced Ramsey numbers.


title: Effective Termination of Kohn's Algorithm for Subelliptic Multipliers

abstract:
  This note discusses the problem of the effective termination of Kohn's
algorithm for subelliptic multipliers for bounded smooth weakly pseudoconvex
domains of finite type. We give a complete proof for the case of special
domains of finite type and indicate briefly how this method is to be extended
to the case of general bounded smooth weakly pseudoconvex domains of finite
type.


title: Searches for New Physics at HERA

abstract:
  The high energy programme of the HERA collider ended in March 2007. During
the whole HERA programme, a combined total integrated luminosity of 1 fb$^{-1}$
was collected by the H1 and ZEUS experiments. In this context, an overview of
the most recent results of both experiments concerning searches for new physics
is presented. The topics covered are searches for contact interactions,
leptoquarks and excited leptons, as well as studies of the isolated lepton and
multi-lepton topologies, and a general signature based search.


title: TMC-1C: an accreting starless core

abstract:
  We have mapped the starless core TMC-1C in a variety of molecular lines with
the IRAM 30m telescope. High density tracers show clear signs of
self-absorption and sub-sonic infall asymmetries are present in N2H+ (1-0) and
DCO+ (2-1) lines. The inward velocity profile in N2H+ (1-0) is extended over a
region of about 7,000 AU in radius around the dust continuum peak, which is the
most extended ``infalling'' region observed in a starless core with this
tracer. The kinetic temperature (~12 K) measured from C17O and C18O suggests
that their emission comes from a shell outside the colder interior traced by
the mm continuum dust. The C18O (2-1) excitation temperature drops from 12 K to
~10 K away from the center. This is consistent with a volume density drop of
the gas traced by the C18O lines, from ~4x10^4 cm^-3 towards the dust peak to
~6x10^3 cm^-3 at a projected distance from the dust peak of 80" (or 11,000 AU).
The column density implied by the gas and dust show similar N2H+ and CO
depletion factors (f_D < 6). This can be explained with a simple scenario in
which: (i) the TMC-1C core is embedded in a relatively dense environment (H2
~10^4 cm^-3), where CO is mostly in the gas phase and the N2H+ abundance had
time to reach equilibrium values; (ii) the surrounding material (rich in CO and
N2H+) is accreting onto the dense core nucleus; (iii) TMC-1C is older than
3x10^5 yr, to account for the observed abundance of N2H+ across the core
(~10^-10 w.r.t. H2); and (iv) the core nucleus is either much younger (~10^4
yr) or ``undepleted'' material from the surrounding envelope has fallen towards
it in the past 10,000 yr.


title: Star Formation in Molecular Clouds?

abstract:
  Using studies of nearby star formation with Spitzer, I will argue that star
formation is restricted to dense cores within molecular clouds. The nature of
these dense cores and their connection to star formation will be discussed.
Their distribution over masses and over the cloud is similar to that of stars,
and their efficiency of forming stars is much higher than that of the whole
cloud. Moving to regions forming more massive stars, we find that the mass
distribution of the dense clumps is similar to that of OB associations. The
infrared luminosity per unit mass of dense gas is high and comparable to that
seen in starburst galaxies. The relation between star formation and dense gas
appears to be linear. Understanding the Kennicutt-Schmidt law requires an
understanding of what controls the conversion of gas into the dense entities
where stars actually form.


title: Vector-Boson Production of Light Higgs Pairs in 2-Higgs Doublet Models

abstract:
  At the Large Hadron Collider, we prove the feasibility to detect pair
production of the lightest CP-even Higgs boson $h$ of Type II 2-Higgs Doublet
Models through $q q^{(')}\to q q^{(')} {hh}$ (vector-boson fusion). We also
show that, through the $hh\to 4b$ decay channel in presence of heavy-flavour
tagging, further exploiting forward/backward jet sampling, one has direct
access to the $\lambda_{Hhh}$ triple Higgs coupling -- which constrains the
form of the Higgs potential.


title:
Nonlinear Schrodinger-Helmholtz Equation as Numerical Regularization of
  the Nonlinear Schrodinger Equation

abstract:
  A regularized $\alpha-$system of the Nonlinear Schr\"{o}dinger Equation (NLS)
with $2\sigma$ nonlinear power in dimension $N$ is studied. We prove existence
and uniqueness of local solution in the case $1 \le \sigma <\frac{4}{N-2}$ and
existence and uniqueness of global solution in the case $1 \le \sigma <
\frac{4}{N}$. When $\alpha \to 0^+$, this regularized system will converge to
the classical NLS in the appropriate range. In particular, the purpose of this
numerical regularization is to shed light on the profile of the blow up
solutions of the original Nonlinear Schr\"{o}dinger Equation in the range
$\frac{2}{N}\le \sigma <\frac{4}{N}$, and in particular for the critical case
$\sigma = \frac{2}{N}$.


title:
Relating multichannel scattering and production amplitudes in a
  microscopic OZI-based model

abstract:
  Relations between scattering and production amplitudes are studied in a
microscopic multichannel model for meson-meson scattering, with coupling to
confined quark-antiquark channels. Overlapping resonances and a proper
threshold behaviour are treated exactly in the model. Under the spectator
assumption, it is found that the two-particle production amplitude shares a
common denominator with the elastic scattering amplitude, besides a numerator
consisting of a linear combination of all elastic and some inelastic matrix
elements. The coefficients in these linear combinations are shown to be
generally complex. Finally, the standard operator expressions relating
production and scattering amplitudes, viz. A=T/V and Im(A)=T*A, are fulfilled,
while in the small-coupling limit the usual isobar model is recovered.


title: Optical 'Shorting Wires'

abstract:
  Connecting lumped circuit elements in a conventional circuit is usually
accomplished by conducting wires that act as conduits for the conduction
currents with negligible potential drops. More challenging, however, is to
extend these concepts to optical nanocircuit elements. Here, following our
recent development of optical lumped circuit elements, we show how a special
class of nanowaveguides formed by a thin core with relatively large (positive
or negative) permittivity surrounded by a thin concentric shell with low
permittivity may provide the required analogy to 'wires' for optical
nano-circuits.


title:
Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin
  chain

abstract:
  We study the largest particle-number-preserving sector of the dilatation
operator in maximally supersymmetric gauge theory. After exploring one-loop
Bethe Ansatze for the underlying spin chain with psl(2|2) symmetry for simple
root systems related to several Kac-Dynkin diagrams, we use the analytic Bethe
Anzats to construct eigenvalues of transfer matrices with finite-dimensional
atypical representations in the auxiliary space. We derive closed Baxter
equations for eigenvalues of nested Baxter operators. We extend these
considerations for a non-distinguished root system with FBBF grading to all
orders of perturbation theory in 't Hooft coupling. We construct generating
functions for all transfer matrices with auxiliary space determined by Young
supertableaux (1^a) and (s) and find determinant formulas for transfer matrices
with auxiliary spaces corresponding to skew Young supertableaux. The latter
yields fusion relations for transfer matrices with auxiliary space
corresponding to representations labelled by square Young supertableaux. We
derive asymptotic Baxter equations which determine spectra of anomalous
dimensions of composite Wilson operators in noncompact psl(2|2) subsector of
N=4 super-Yang-Mills theory.


title:
Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona.
  I. Linear Force-Free Approximation

abstract:
  We self-consistently derive the magnetic energy and relative magnetic
helicity budgets of a three-dimensional linear force-free magnetic structure
rooted in a lower boundary plane. For the potential magnetic energy we derive a
general expression that gives results practically equivalent to those of the
magnetic Virial theorem. All magnetic energy and helicity budgets are
formulated in terms of surface integrals applied to the lower boundary, thus
avoiding computationally intensive three-dimensional magnetic field
extrapolations. We analytically and numerically connect our derivations with
classical expressions for the magnetic energy and helicity, thus presenting a
so-far lacking unified treatment of the energy/helicity budgets in the
constant-alpha approximation. Applying our derivations to photospheric vector
magnetograms of an eruptive and a noneruptive solar active regions, we find
that the most profound quantitative difference between these regions lies in
the estimated free magnetic energy and relative magnetic helicity budgets. If
this result is verified with a large number of active regions, it will advance
our understanding of solar eruptive phenomena. We also find that the
constant-alpha approximation gives rise to large uncertainties in the
calculation of the free magnetic energy and the relative magnetic helicity.
Therefore, care must be exercised when this approximation is applied to
photospheric magnetic field observations. Despite its shortcomings, the
constant-alpha approximation is adopted here because this study will form the
basis of a comprehensive nonlinear force-free description of the energetics and
helicity in the active-region solar corona, which is our ultimate objective.


title:
Level crossing in the three-body problem for strongly interacting
  fermions in a harmonic trap

abstract:
  We present a solution of the three-fermion problem in a harmonic potential
across a Feshbach resonance. We compare the spectrum with that of the two-body
problem and show that it is energetically unfavorable for the three fermions to
occupy one lattice site rather than two. We also demonstrate the existence of
an energy level crossing in the ground state with a symmetry change of its wave
function, suggesting the possibility of a phase transition for the
corresponding many-body case.


title: On the origin of X-ray emission in some FR Is: ADAF or jet?

abstract:
  We investigate the X-ray origin in FR Is using the radio, submillimetre,
optical, and {\em Chandra} X-ray data of a small sample consisting of eight FR
I sources. These sources are very dim, with X-ray luminosities $L_{\rm
X}/L_{\rm Edd} \sim 10^{-4}-10^{-8}$ ($L_{\rm X}$ is the X-ray luminosity
between 2-10 keV). We try to fit the multiwaveband spectrum using a coupled
accretion-jet model. In this model, the accretion flow is described by an
advection-dominated accretion flow (ADAF) while in the innermost region of ADAF
a fraction of accretion flow is transferred into the vertical direction and
forms a jet. We find that X-ray emission in the source with the highest $L_{\rm
X}$ ($\sim 1.8 \times 10^{-4}L_{\rm Edd}$) is from the ADAF. The results for
the four sources with moderate $L_{\rm X}$ ($\sim$ several $\times
10^{-6}L_{\rm Edd}$) are complicated. Two are mainly from the ADAFs, one from
the jet, and the other from the sum of the jet and ADAF. The X-ray emission in
the three least luminous sources ($L_{\rm X} \lesssim 1.0\times 10^{-6}L_{\rm
Edd}$) is dominated by the jet although for one source it can also be
interpreted by the ADAF since the quality of X-ray data is low. We conclude
that these results roughly support the predictions of Yuan & Cui (2005) where
they predict that when the X-ray luminosity of the system is below a critical
value, the X-radiation will not be dominated by the emission from the ADAF any
longer, but by the jet. We also investigate the fuel supply in these sources.
We find that the accretion rates in four sources among the five in which we can
have good constraints to their accretion rates must be higher than the Bondi
rates. This implies that other fuel supply, such as the gas released by the
stellar population inside the Bondi radius, should be important.


title: Numerical Simulation of an Electroweak Oscillon

abstract:
  Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$
electroweak Standard Model in 3+1 dimensions have demonstrated the existence of
an oscillon -- an extremely long-lived, localized, oscillatory solution to the
equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson
mass. It contains total energy roughly 30 TeV localized in a region of radius
0.05 fm. A detailed description of these numerical results is presented.


title:
Current-voltage curves for molecular junctions: the effect of
  substituents

abstract:
  We present current-voltage (I-V) curves for phenylene ethynylene oligomers
between two Au surfaces computed using a Density Functional Theory/Green's
Function approach. In addition to the parent molecule, two different
substituents are considered: one where all the hydrogens are replaced by
chlorines and a second where one H is replaced by an NO2 group. In this way, we
can study the difference between electron withdrawing and pi orbital effects.
For low biases, a reduced current for the derived species is consistent with a
shift of HOMO to lower energy due to the electron withdrawal by Cl or NO2. At
higher biases, the LUMO becomes important, and the Cl and NO2 substituted
species carry more current than the parent because the LUMO is stabilized
(shifted to lower energy) due to the withdrawal of electrons by the Cl and NO2.
In these molecules, the C2 bridging units as well as the thiol anchor group are
shown to create bottlenecks to current flow.


title: Semiclassical Density of States for the Quantum Asymmetric Top

abstract:
  In the quantization of a rotating rigid body, a {\it top,} one is concerned
with the Hamiltonian operator $L_\alpha=\alpha_0^2 L_x^2 + \alpha_1^2 L_y^2 +
\alpha_2^2 L_z^2,$ where $\alpha_0 < \alpha_1 <\alpha_2.$ An explicit formula
is known for the eigenvalues of $L_\alpha$ in the case of the spherical top
($\alpha_1 = \alpha_2 = \alpha_3$) and symmetrical top ($\alpha_1 = \alpha_2
\neq \alpha_3$) \cite{LL}. However, for the asymmetrical top, no such explicit
expression exists, and the study of the spectrum is much more complex. In this
paper, we compute the semiclassical density of states for the eigenvalues of
the family of operators $L_\alpha=\alpha_0^2 L_x^2 + \alpha_1^2 L_y^2 +
\alpha_2^2 L_z^2$ for any $\alpha_0 < \alpha_1 <\alpha_2$.


title:
A review of wildland fire spread modelling, 1990-present 2: Empirical
  and quasi-empirical models

abstract:
  In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behaviour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of
an empirical or quasi-empirical nature. These models are based solely on the
statistical analysis of experimentally obtained data with or without some
physical framework for the basis of the relations. Other papers in the series
review models of a physical or quasi-physical nature, and mathematical
analogues and simulation models. The main relations of empirical models are
that of wind speed and fuel moisture content with rate of forward spread.
Comparisons are made of the different functional relationships selected by
various authors for these variables.


title: Shape Coexistence and Mixing in 152Sm

abstract:
  Experimental studies of 152Sm using multiple-step Coulomb excitation and
inelastic neutron scattering provide key data that clarify the low-energy
collective structure of this nucleus. No candidates for two-phonon
beta-vibrational states are found. Experimental level energies of the
ground-state and first excited (0+ state) rotational bands, electric monopole
transition rates, reduced quadrupole transition rates, and the isomer shift of
the first excited 2+ state are all described within ~10% precision using
two-band mixing calculations. The basic collective structure of 152Sm is
described using strong mixing of near-degenerate coexisting quasi-rotational
bands with different deformations.


title:
A review of wildland fire spread modelling, 1990-present 3: Mathematical
  analogues and simulation models

abstract:
  In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behvaiour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of a
simulation or mathematical analogue nature. Most simulation models are
implementations of existing empirical or quasi-empirical models and their
primary function is to convert these generally one dimensional models to two
dimensions and then propagate a fire perimeter across a modelled landscape.
Mathematical analogue models are those that are based on some mathematical
conceit (rather than a physical representation of fire spread) that
coincidentally simulates the spread of fire. Other papers in the series review
models of an physical or quasi-physical nature and empirical or quasi-empirical
nature. Many models are extensions or refinements of models developed before
1990. Where this is the case, these models are also discussed but much less
comprehensively.


title: On some power sum problems of Montgomery and Turan

abstract:
  We use an estimate for character sums over finite fields of Katz to solve
open problems of Montgomery and Turan. Let h=>2 be an integer. We prove that
inf_{|z_k| => 1} max_{v=1,...,n^h} |sum_{k=1}^n z_k^v| <= (h-1+o(1)) sqrt n.
This gives the right order of magnitude for the quantity and improves on a
bound of Erdos-Renyi by a factor of the order sqrt log n.


title:
Using the Renormalization Group Functions to Uniquely Determine the
  Effective Potential in Massless Scalar Electrodynamics

abstract:
  It has been demonstrated that the effective potential V(\phi) in a massless
O(N) \lambda \phi^4_4 model is determined completely by the renormalization
group functions provided the renormalization condition \frac{d^4V}{d
\phi^4}|_{\phi=\mu}=\lambda is used. This is shown to also hold in massless
scalar electrodynamics. By employing a variant of the method of
characteristics, the sums contributing to the leading-log, next-to-leading-log
etc. contributions to V(\phi) can be evaluated.


title:
The proper motion of the Arches cluster with Keck Laser-Guide Star
  Adaptive Optics

abstract:
  We present the first measurement of the proper motion of the young, compact
Arches cluster near the Galactic center from near-infrared adaptive optics (AO)
data taken with the recently commissioned laser-guide star (LGS) at the Keck
10-m telescope. The excellent astrometric accuracy achieved with LGS-AO
provides the basis for a detailed comparison with VLT/NAOS-CONICA data taken
4.3 years earlier. Over the 4.3 year baseline, a spatial displacement of the
Arches cluster with respect to the field population is measured to be 24.0 +/-
2.2 mas, corresponding to a proper motion of 5.6 +/- 0.5 mas/yr or 212 +/- 29
km/s at a distance of 8 kpc. In combination with the known line-of-sight
velocity of the cluster, we derive a 3D space motion of 232 +/- 30 km/s of the
Arches relative to the field. The large proper motion of the Arches cannot be
explained with any of the closed orbital families observed in gas clouds in the
bar potential of the inner Galaxy, but would be consistent with the Arches
being on a transitional trajectory from x1 to x2 orbits. We investigate a
cloud-cloud collision as the possible origin for the Arches cluster. The
integration of the cluster orbit in the potential of the inner Galaxy suggests
that the cluster passes within 10 pc of the supermassive black hole only if its
true GC distance is very close to its projected distance. A contribution of
young stars from the Arches cluster to the young stellar population in the
inner few parsecs of the GC thus appears increasingly unlikely. The measurement
of the 3D velocity and orbital analysis provides the first observational
evidence that Arches-like clusters do not spiral into the GC. This confirms
that no progenitor clusters to the nuclear cluster are observed at the present
epoch.


title: Bounds on the number of real solutions to polynomial equations

abstract:
  We use Gale duality for polynomial complete intersections and adapt the proof
of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k
choose 2) n^k/4 for the number of non-zero real solutions to a system of n
polynomials in n variables having n+k+1 monomials whose exponent vectors
generate a subgroup of Z^n of odd index. This bound exceeds the bound for
positive solutions only by the constant factor (e^4+3)/(e^2+3) and it is
asymptotically sharp for k fixed and n large.


title:
Simple Two-Dimensional Model for the Elastic Origin of Cooperativity
  among Spin States of Spin-Crossover Complexes

abstract:
  We study the origin of the cooperative nature of spin crossover (SC) between
low spin (LS) and high spin (HS) states from the view point of elastic
interactions among molecules. As the size of each molecule changes depending on
its spin state, the elastic interaction among the lattice distortions provides
the cooperative interaction of the spin states. We develop a simple model of SC
with intra and intermolecular potentials which accounts for the elastic
interaction including the effect of the inhomogeneity of the spin states, and
apply constant temperature molecular dynamics based on the Nos\'e-Hoover
formalism. We demonstrate that, with increase of the strength of the
intermolecular interactions, the temperature dependence of the HS component
changes from a gradual crossover to a first-order transition.


title:
An improved method for estimating source densities using the temporal
  distribution of Cosmological Transients

abstract:
  It has been shown that the observed temporal distribution of transient events
in the cosmos can be used to constrain their rate density. Here we show that
the peak flux--observation time relation takes the form of a power law that is
invariant to the luminosity distribution of the sources, and that the method
can be greatly improved by invoking time reversal invariance and the temporal
cosmological principle. We demonstrate how the method can be used to constrain
distributions of transient events, by applying it to Swift gamma-ray burst data
and show that the peak flux--observation time relation is in good agreement
with recent estimates of source parameters. We additionally show that the
intrinsic time dependence allows the method to be used as a predictive tool.
Within the next year of Swift observation, we find a 50% chance of obtaining a
peak flux greater than that of GRB 060017 -- the highest Swift peak flux to
date -- and the same probability of detecting a burst with peak flux > 100
photons s^{-1} cm^{-2} within 6 years.


title:
Propagation Constraints and Classical Solutions in K-essence Like
  Theories

abstract:
  We consider two examples of solutions of the equations of motion of scalar
field theories with higher derivatives. These are the cosmology of the rolling
tachyon and static spherically symmetric solutions of the scalar field in flat
space. By requiring that the field equations always be hyperbolic and that the
speed of propagation of the small fluctuations are not superluminal, we find
constraints on the form of the allowed interactions in the first case and on
the choice of boundary conditions in the latter. For the rolling tachyon we
find a general class of models which have the property that at large times the
tachyon matter behaves essentially like a non-relativistic gas of dust. For the
spherically symmetric solutions we show how causality influences the choice of
boundary conditions and those which are finite at the origin are shown to have
negative energy density there.


title:
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear
  Norm Minimization

abstract:
  The affine rank minimization problem consists of finding a matrix of minimum
rank that satisfies a given system of linear equality constraints. Such
problems have appeared in the literature of a diverse set of fields including
system identification and control, Euclidean embedding, and collaborative
filtering. Although specific instances can often be solved with specialized
algorithms, the general affine rank minimization problem is NP-hard. In this
paper, we show that if a certain restricted isometry property holds for the
linear transformation defining the constraints, the minimum rank solution can
be recovered by solving a convex optimization problem, namely the minimization
of the nuclear norm over the given affine space. We present several random
ensembles of equations where the restricted isometry property holds with
overwhelming probability. The techniques used in our analysis have strong
parallels in the compressed sensing framework. We discuss how affine rank
minimization generalizes this pre-existing concept and outline a dictionary
relating concepts from cardinality minimization to those of rank minimization.


title:
Short Gamma-Ray Bursts and Binary Mergers in Spiral and Elliptical
  Galaxies: Redshift Distribution and Hosts

abstract:
  To test whether the short GRB rates, redshift distribution and host galaxies
are consistent with current theoretical predictions, we use avery large
database of population synthesis calculations to examine BH-NS and NS-NS merger
rates in the universe, factoring in (i) the star formation history of the
universe, (ii) a heterogeneous population of star-forming galaxies, including
spirals and ellipticals, and (iii) a simple flux-limited selection model for
short GRB detection. When we require our models reproduce the known short GRB
rates and redshift measurements (and, for NS-NS, the merger rates extrapolated
from binary pulsars in the Galaxy), a small fraction of models reproduce all
observations, both when we assume a NS-NS and a BH-NS origin for bursts. Most
commonly models produce mergers preferentially in spiral galaxies if short GRBs
arise from NS-NS mergers alone. Model universes where present-day binary
mergers occur preferentially in elliptical galaxies necessarily include a
significant fraction of binaries with long delay times between birth and merger
(often $O(10{\rm Gyr})$). Though long delays occur, almost all of our models
predict that a higher proportion of short GRBs should occur at moderate to high
redshift (e.g., $z>1$) than has presently been observed, in agreement with
recent observations which suggest a selection bias towards successful follow-up
of low-redshift short GRBs. Finally, if only a fraction of BH-NS mergers have
the right combination of masses and spins to make GRBs, then at best only a
small fraction of BH-NS models could be consistent with all {\em current}
available data. (Abridged)


title: Improbability of DUrca process constraints EOS

abstract:
  According to recent observational and theoretical progresses, the DUrca
process (direct Urca process) may be excluded from the category of neutron star
cooling mechanisms. This result combined with the latest nuclear symmetry
energy experiments, will provide us an independent way of testing the EOS
(equation of state) for supranormal density. For example, soft EOSs such as FPS
will probably be excluded.


title: Quark-Lepton Symmetry and Quartification in Five Dimensions

abstract:
  We outline some features of higher dimensional models possessing a
Quark-Lepton (QL) symmetry. The QL symmetric model in five dimensions is
discussed, with particular emphasis on the use of split fermions. An
interesting fermionic geography which utilises the QL symmetry to suppress the
proton decay rate and to motivate the flavor differences in the quark and
leptonic sectors is considered. We discuss the quartification model in five
dimensions and contrast the features of this model with traditional four
dimensional constructs.


title: Unified model of baryonic matter and dark components

abstract:
  We investigate an interacting two-fluid cosmological model and introduce a
scalar field representation by means of a linear combination of the individual
energy densities. Applying the integrability condition to the scalar field
equation we show that this "exotic quintessence" is driven by an exponential
potential and the two-fluid mixture can be considered as a model of three
components. These components are associated with baryonic matter, dark matter
and dark energy respectively. We use the Simon, Verde & Jimenez (2005)
determination of the redshift dependence of the Hubble parameter to constrain
the current density parameters of this model. With the best fit density
parameters we obtain the transition redshift between non accelerated and
accelerated regimes z_{acc}=0.66 and the time elapsed since the initial
singularity t_0= 19.8 Gyr. We study the perturbation evolution of this model
and find that the energy density perturbation decreases with the cosmological
time.