title: Ground state energy of the low density Hubbard model

abstract:
  We derive a lower bound on the ground state energy of the Hubbard model for
given value of the total spin. In combination with the upper bound derived
previously by Giuliani, our result proves that in the low density limit, the
leading order correction compared to the ground state energy of a
non-interacting lattice Fermi gas is given by $8\pi a \rho_u \rho_d$, where
$\rho_{u(d)}$ denotes the density of the spin-up (down) particles, and $a$ is
the scattering length of the contact interaction potential. This result extends
previous work on the corresponding continuum model to the lattice case.


title: A Note on Quantum Field Theories with a Minimal Length Scale

abstract:
  The aim of this note is to address the low energy limit of quantum field
theories with a minimal length scale. The essential feature of these models is
that the minimal length acts as a regulator in the asymptotic high energy limit
which is incorporated through an infinite series of higher order derivatives.
If one investigates a perturbative expansion in inverse powers of the Planck
mass, one generically obtains extra poles in the propagator, and instabilities
connected with the higher order derivative Lagrangian, that are however
artifacts of truncating the series.


title:
Prescribing valuations of the order of a point in the reductions of
  abelian varieties and tori

abstract:
  Let G be the product of an abelian variety and a torus defined over a number
field K. Let R be a K-rational point on G of infinite order. Call n_R the
number of connected components of the smallest algebraic K-subgroup of G to
which R belongs. We prove that n_R is the greatest positive integer which
divides the order of (R mod p) for all but finitely many primes p of K.
Furthermore, let m>0 be a multiple of n_R and let S be a finite set of rational
primes. Then there exists a positive Dirichlet density of primes p of K such
that for every l in S the l-adic valuation of the order of (R mod p) equals
v_l(m).


title: On pairs of commuting nilpotent matrices

abstract:
  Let $B$ be a nilpotent matrix and suppose that its Jordan canonical form is
determined by a partition $\lambda$. Then it is known that its nilpotent
commutator $N_B$ is an irreducible variety and that there is a unique partition
$\mu$ such that the intersection of the orbit of nilpotent matrices
corresponding to $\mu$ with $N_B$ is dense in $N_B$. We prove that map $D$
given by $D(\lambda)=\mu$ is an idempotent map. This answers a question of
Basili and Iarrobino and gives a partial answer to a question of Panyushev. In
the proof, we use the fact that for a generic matrix $A \in N_B$ the algebra
generated by $A$ and $B$ is a Gorenstein algebra. Thus, a generic pair of
commuting nilpotent matrices generates a Gorenstein algebra. We also describe
$D(\lambda)$ in terms of $\lambda$ if $D(\lambda)$ has at most two parts.


title: Proximity effect-assisted absorption of spin currents in superconductors

abstract:
  The injection of pure spin current into superconductors by the dynamics of a
ferromagnetic contact is studied theoretically. Taking into account suppression
of the order parameter at the interfaces (inverse proximity effect) and the
energy-dependence of spin-flip scattering, we determine the
temperature-dependent ferromagnetic resonance linewidth broadening. Our results
agree with recent experiments in Nb|permalloy bilayers [C. Bell et al.,
arXiv:cond-mat/0702461].


title:
Two variants of the support problem for products of abelian varieties
  and tori

abstract:
  Let G be the product of an abelian variety and a torus defined over a number
field K. Let P and Q be K-rational points on G. Suppose that for all but
finitely many primes p of K the order of (Q mod p) divides the order of (P mod
p). Then there exist a K-endomorphism f of G and a non-zero integer c such that
f(P)=cQ. Furthermore, we are able to prove the above result with weaker
assumptions: instead of comparing the order of the points we only compare the
radical of the order (radical support problem) or the l-adic valuation of the
order for some fixed rational prime l (l-adic support problem).


title:
Coverage processes on spheres and condition numbers for linear
  programming

abstract:
  This paper has two agendas. Firstly, we exhibit new results for coverage
processes. Let $p(n,m,\alpha)$ be the probability that $n$ spherical caps of
angular radius $\alpha$ in $S^m$ do not cover the whole sphere $S^m$. We give
an exact formula for $p(n,m,\alpha)$ in the case $\alpha\in[\pi/2,\pi]$ and an
upper bound for $p(n,m,\alpha)$ in the case $\alpha\in [0,\pi/2]$ which tends
to $p(n,m,\pi/2)$ when $\alpha\to\pi/2$. In the case $\alpha\in[0,\pi/2]$ this
yields upper bounds for the expected number of spherical caps of radius
$\alpha$ that are needed to cover $S^m$. Secondly, we study the condition
number ${\mathscr{C}}(A)$ of the linear programming feasibility problem
$\exists x\in\mathbb{R}^{m+1}Ax\le0,x\ne0$ where
$A\in\mathbb{R}^{n\times(m+1)}$ is randomly chosen according to the standard
normal distribution. We exactly determine the distribution of
${\mathscr{C}}(A)$ conditioned to $A$ being feasible and provide an upper bound
on the distribution function in the infeasible case. Using these results, we
show that $\mathbf{E}(\ln{\mathscr{C}}(A))\le2\ln(m+1)+3.31$ for all $n>m$, the
sharpest bound for this expectancy as of today. Both agendas are related
through a result which translates between coverage and condition.


title:
On the motivic spectra representing algebraic cobordism and algebraic
  K-theory

abstract:
  We show that the motivic spectrum representing algebraic $K$-theory is a
localization of the suspension spectrum of $\mathbb{P}^\infty$, and similarly
that the motivic spectrum representing periodic algebraic cobordism is a
localization of the suspension spectrum of $BGL$. In particular, working over
$\mathbb{C}$ and passing to spaces of $\mathbb{C}$-valued points, we obtain new
proofs of the topological versions of these theorems, originally due to the
second author. We conclude with a couple of applications: first, we give a
short proof of the motivic Conner-Floyd theorem, and second, we show that
algebraic $K$-theory and periodic algebraic cobordism are $E_\infty$ motivic
spectra.


title:
The formation, disruption and properties of pressure-supported stellar
  systems and implications for the astrophysics of galaxies

abstract:
  Most stars form in dense star clusters deeply embedded in residual gas. These
objects must therefore be seen as the fundamental building blocks of galaxies.
With this contribution some physical processes that act in the very early and
also later dynamical evolution of dense stellar systems in terms of shaping
their later appearance and properties, and the impact they have on their host
galaxies, are highlighted. Considering dense systems with increasing mass, it
turns out that near 10^6 Msol their properties change fundamentally: stellar
populations become complex, a galaxial mass--radius relation emerges and the
median two-body relaxation time becomes longer than a Hubble time.
Intriguingly, only systems with a two-body relaxation time longer than a Hubble
time show weak evidence for dark matter, whereby dSph galaxies form total
outliers.


title:
The spin expansion for binary black hole merger: new predictions and
  future directions

abstract:
  In a recent paper arXiv:0709.0299, we introduced a spin expansion that
provides a simple yet powerful way to understand aspects of binary black hole
(BBH) merger. This approach relies on the symmetry properties of initial and
final quantities like the black hole mass m, kick velocity {\bf k}, and spin
vector {\bf s}, rather than a detailed understanding of the merger dynamics. In
this paper, we expand on this proposal, examine how well its predictions agree
with current simulations, and discuss several future directions that would make
it an even more valuable tool. The spin expansion yields many new predictions,
including several exact results that may be useful for testing numerical codes.
Some of these predictions have already been confirmed, while others await
future simulations. We explain how a relatively small number of simulations --
10 equal-mass simulations, and 16 unequal-mass simulations -- may be used to
calibrate all of the coefficients in the spin expansion up to second order at
the minimum computational cost. For a more general set of simulations of given
covariance, we derive the minimum-variance unbiased estimators for the spin
expansion coefficients. We discuss how this calibration would be interesting
and fruitful for general relativity and astrophysics. Finally, we sketch the
extension to eccentric orbits.


title: The Production Rate and Employment of Ph.D. Astronomers

abstract:
  In an effort to encourage self-regulation of the astronomy job market, I
examine the supply of, and demand for, astronomers over time. On the supply
side, I document the production rate of Ph.D. astronomers from 1970 to 2006
using the UMI Dissertation Abstracts database, along with data from other
independent sources. I compare the long-term trends in Ph.D. production with
federal astronomy research funding over the same time period, and I demonstrate
that additional funding is correlated with higher subsequent Ph.D. production.
On the demand side, I monitor the changing patterns of employment using
statistics about the number and types of jobs advertised in the AAS Job
Register from 1984 to 2006. Finally, I assess the sustainability of the job
market by normalizing this demand by the annual Ph.D. production. The most
recent data suggest that there are now annual advertisements for about one
postdoctoral job, half a faculty job, and half a research/support position for
every new domestic Ph.D. recipient in astronomy and astrophysics. The average
new astronomer might expect to hold up to 3 jobs before finding a steady
position.


title: Cascading Gravity and Degravitation

abstract:
  We construct a cascading brane model of gravity in which the behavior of the
gravitational force law interpolates from (n+4)-dimensional to
(n+3)-dimensional all the way down to 4-dimensional from longer to shorter
length scales. We show that at the linearized level, this model exhibits the
features necessary for degravitation of the cosmological constant. The model is
shown to be ghost free with the addition of suitable brane kinetic operators,
and we demonstrate this using a number of independent procedures. Consequently
this is a consistent IR modification of gravity, providing a promising
framework for a dynamical, degravitating solution of the cosmological constant
problem.


title: Classical Effective Field Theory and Caged Black Holes

abstract:
  Matched asymptotic expansion is a useful technique in General Relativity and
other fields whenever interaction takes place between physics at two different
length scales. Here matched asymptotic expansion is argued to be equivalent
quite generally to Classical Effective Field Theory (CLEFT) where one (or more)
of the zones is replaced by an effective theory whose terms are organized in
order of increasing irrelevancy, as demonstrated by Goldberger and Rothstein in
a certain gravitational context. The CLEFT perspective has advantages as the
procedure is clearer, it allows a representation via Feynman diagrams, and
divergences can be regularized and renormalized in standard field theoretic
methods. As a side product we obtain a wide class of classical examples of
regularization and renormalization, concepts which are usually associated with
Quantum Field Theories.
  We demonstrate these ideas through the thermodynamics of caged black holes,
both simplifying the non-rotating case, and computing the rotating case. In
particular we are able to replace the computation of six two-loop diagrams by a
single factorizable two-loop diagram, as well as compute certain new three-loop
diagrams. The results generalize to arbitrary compactification manifolds. For
caged rotating black holes we obtain the leading correction for all
thermodynamic quantities. The angular momentum is found to non-renormalize at
leading order.


title: The Outermost Ejecta of Type Ia Supernovae

abstract:
  The properties of the highest velocity ejecta of normal Type Ia supernovae
(SNe Ia) are studied via models of very early optical spectra of 6 SNe. At
epochs earlier than 1 week before maximum, SNe with a rapidly evolving Si II
6355 line velocity (HVG) have a larger photospheric velocity than SNe with a
slowly evolving Si II 6355 line velocity (LVG). Since the two groups have
comparable luminosities, the temperature at the photosphere is higher in LVG
SNe. This explains the different overall spectral appearance of HVG and LVG
SNe. However, the variation of the Ca II and Si II absorptions at the highest
velocities (v >~ 20,000 km/s) suggests that additional factors, such as
asphericity or different abundances in the progenitor white dwarf, affect the
outermost layers. The C II 6578 line is marginally detected in 3 LVG SNe,
suggesting that LVG undergo less intense burning. The carbon mass fraction is
small, only less than 0.01 near the photosphere, so that he mass of unburned C
is only <~ 0.01 Msun. Radioactive 56Ni and stable Fe are detected in both LVG
and HVG SNe. Different Fe-group abundances in the outer layers may be one of
the reasons for spectral diversity among SNe Ia at the earliest times. The
diversity among SNe Ia at the earliest phases could also indicate an intrinsic
dispersion in the width-luminosity relation of the light curve.


title:
Localization of gauge theory on a four-sphere and supersymmetric Wilson
  loops

abstract:
  We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which
relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric
Yang-Mills theory with a Gaussian matrix model. We also compute the partition
function and give a new matrix model formula for the expectation value of a
supersymmetric circular Wilson loop operator for the pure N=2 and the N=2*
supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2
superconformal gauge theory is treated similarly.


title: The Milky Way as a Kiloparsec-Scale Axionscope

abstract:
  Very high energy gamma-rays are expected to be absorbed by the extragalactic
background light over cosmological distances via the process of
electron-positron pair production. Recent observations of cosmologically
distant gamma-ray emitters by ground based gamma-ray telescopes have, however,
revealed a surprising degree of transparency of the universe to very high
energy photons. One possible mechanism to explain this observation is the
oscillation between photons and axion-like-particles (ALPs). Here we explore
this possibility further, focusing on photon-ALP conversion in the magnetic
fields in and around gamma-ray sources and in the magnetic field of the Milky
Way, where some fraction of the ALP flux is converted back into photons. We
show that this mechanism can be efficient in allowed regions of the ALP
parameter space, as well as in typical configurations of the Galactic Magnetic
Field. As case examples, we consider the spectrum observed from two HESS
sources: 1ES1101-232 at redshift z=0.186 and H 2356-309 at z=0.165. We also
discuss features of this scenario which could be used to distinguish it from
standard or other exotic models.


title:
Using BBN in cosmological parameter extraction from CMB: a forecast for
  Planck

abstract:
  Data from future high-precision Cosmic Microwave Background (CMB)
measurements will be sensitive to the primordial Helium abundance $Y_p$. At the
same time, this parameter can be predicted from Big Bang Nucleosynthesis (BBN)
as a function of the baryon and radiation densities, as well as a neutrino
chemical potential. We suggest to use this information to impose a
self-consistent BBN prior on $Y_p$ and determine its impact on parameter
inference from simulated Planck data. We find that this approach can
significantly improve bounds on cosmological parameters compared to an analysis
which treats $Y_p$ as a free parameter, if the neutrino chemical potential is
taken to vanish. We demonstrate that fixing the Helium fraction to an arbitrary
value can seriously bias parameter estimates. Under the assumption of
degenerate BBN (i.e., letting the neutrino chemical potential $\xi$ vary), the
BBN prior's constraining power is somewhat weakened, but nevertheless allows us
to constrain $\xi$ with an accuracy that rivals bounds inferred from present
data on light element abundances.


title: Approximate square-root-time relaxation in glass-forming liquids

abstract:
  We present data for the dielectric relaxation of 43 glass-forming organic
liquids, showing that the primary (alpha) relaxation is often close to
square-root-time relaxation. The better an inverse power-law description of the
high-frequency loss applies, the more accurately is square-root-time relaxation
obeyed. These findings suggest that square-root-time relaxation is generic to
the alpha process, once a common view, but since long believed to be incorrect.
Only liquids with very large dielectric losses deviate from this picture by
having consistently narrower loss peaks. As a further challenge to the
prevailing opinion, we find that liquids with accurate square-root-time
relaxation cover a wide range of fragilities.


title: GRB070125: The First Long-Duration Gamma-Ray Burst in a Halo Environment

abstract:
  We present the discovery and high signal-to-noise spectroscopic observations
of the optical afterglow of the long-duration gamma-ray burst GRB070125. Unlike
all previously observed long-duration afterglows in the redshift range 0.5 < z
< 2.0, we find no strong (rest-frame equivalent width W > 1.0 A) absorption
features in the wavelength range 4000 - 10000 A. The sole significant feature
is a weak doublet we identify as Mg II 2796 (W = 0.18 +/- 0.02 A), 2803 (W =
0.08 +/- 0.01) at z = 1.5477 +/- 0.0001. The low observed Mg II and inferred H
I column densities are typically observed in galactic halos, far away from the
bulk of massive star formation. Deep ground-based imaging reveals no host
directly underneath the afterglow to a limit of R > 25.4 mag. Either of the two
nearest blue galaxies could host GRB070125; the large offset (d >= 27 kpc)
would naturally explain the low column density. To remain consistent with the
large local (i.e. parsec scale) circum-burst density inferred from broadband
afterglow observations, we speculate GRB070125 may have occurred far away from
the disk of its host in a compact star-forming cluster. Such distant stellar
clusters, typically formed by dynamical galaxy interactions, have been observed
in the nearby universe, and should be more prevalent at z>1 where galaxy
mergers occur more frequently.


title: Azimuthal Asymmetry of Prompt Photons in Nuclear Collisions

abstract:
  The azimuthal elliptic asymmetry v2 observed in heavy ion collisions, is
usually associated with properties of the medium created in the final state. We
compute the azimuthal asymmetry which is due to multiple interactions of
partons at the initial stage of nuclear collisions, and which is also present
in $pA$ collisions. In our approach the main source of azimuthal asymmetry is
the combination of parton multiple interactions with the steep variation of the
nuclear density at the edge of nuclei. We apply the light-cone dipole formalism
to compute the azimuthal asymmetry of prompt photons yield from parton-nucleus,
proton-nucleus and nucleus-nucleus collisions at the RHIC energy.


title:
Spectra and symmetric eigentensors of the Lichnerowicz Laplacian on
  $P^n(\comp)$

abstract:
  We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian
acting on the space of complex symmetric covariant tensor fields on the complex
projective space $P^n(\comp)$. The spaces of symmetric eigentensors are
explicitly given.


title:
Static plane symmetric relativistic fluids and empty repelling singular
  boundaries

abstract:
  We present a detailed analysis of the general exact solution of Einstein's
equation corresponding to a static and plane symmetric distribution of matter
with density proportional to pressure. We study the geodesics in it and we show
that this simple spacetime exhibits very curious properties. In particular, it
has a free of matter repelling singular boundary and all geodesics bounce off
it.


title: The Surface Detector System of the Pierre Auger Observatory

abstract:
  The Pierre Auger Observatory is designed to study cosmic rays with energies
greater than 10^{19} eV. Two sites are envisaged for the observatory, one in
each hemisphere, for complete sky coverage. The southern site of the Auger
Observatory, now approaching completion in Mendoza, Argentina, features an
array of 1600 water-Cherenkov surface detector stations covering 3000 km^2,
together with 24 fluorescence telescopes to record the air shower cascades
produced by these particles. The two complementary detector techniques together
with the large collecting area form a powerful instrument for these studies.
Although construction is not yet complete, the Auger Observatory has been
taking data stably since January 2004 and the first physics results are being
published. In this paper we describe the design features and technical
characteristics of the surface detector stations of the Pierre Auger
Observatory.


title:
Time-varying tip-sample force measurements confirm steady-state dynamics
  in tapping-mode atomic force microscopy

abstract:
  Direct time-varying tip-sample force measurements by torsional harmonic
cantilevers facilitate detailed investigations of the cantilever dynamics in
tapping-mode atomic force microscopy. Here we report experimental evidence that
the mathematical relationships describing the steady state dynamics are
quantitatively satisfied by the independent measurements of tip-sample forces
over a broad range of experimental conditions. These results confirm the
existing understanding of the tapping-mode atomic force microscopy and build
confidence on the reliability of time-varying tip-sample force measurements by
the torsional harmonic cantilevers.


title: Microscopic origin of low frequency flux noise in Josephson circuits

abstract:
  We analyze the data and discuss their implications for the microscopic origin
of the low frequency flux noise in superconducting circuits. We argue that this
noise is produced by spins at the superconductor insulator boundary whose
dynamics is due to RKKY interaction. We show that this mechanism explains size
independence of the noise, different frequency dependences of the spectra
reported in large and small SQUIDs and gives the correct intensity for
realistic parameters.


title:
The contribution of UVES@VLT to the new era of QSO absorption line
  studies

abstract:
  We briefly review the main results obtained in the field of QSO absorption
line studies with the UVES high resolution spectrograph mounted on the Kueyen
unit of the ESO Very Large Telescope (Paranal, Chile).


title: Importance of on-site interaction in graphene

abstract:
  We use the Gutzwiller method to investigate the importance of the on-site
Coulomb interaction in graphene. We apply it to Hubbard Hamiltonian to study
the renormalization of the kinetic energy in graphene due to the on-site
Coulomb interaction. We find that a reasonable strength of the interaction has
a very weak effect in reducing the kinetic energy. Hence we predict that the
Brinkmann-Rice metal-insulator transition in graphene is not possible. The
effect is understood in terms of the high kinetic energy in graphene.


title: Voting, the symmetric group, and representation theory

abstract:
  We show how voting may be viewed naturally from an algebraic perspective by
viewing voting profiles as elements of certain well-studied
$\mathbb{Q}S_n$-modules. By using only a handful of simple combinatorial
objects (e.g., tabloids) and some basic ideas from representation theory (e.g.,
Schur's Lemma), this allows us to recast and extend some well-known results in
the field of voting theory.


title:
Kinks and Mid-Infrared Optical Conductivity from Strong Electron
  Correlation

abstract:
  We compute the one-particle spectral function and the optical conductivity
for the 2-d Hubbard model on a square lattice. The computational method is
cellular dynamical mean-field theory (CDMFT) in which a 4-site Hubbard
plaquette is embedded in a self-consistent bath. We obtain a `kink' feature in
the dispersion of the spectral function and a mid-infrared (mid-IR) absorption
peak in the optical conductivity, consistent with experimental data. Of the 256
plaquette states, only a single state which has d$_{x^2-y^2}$ symmetry
contributes to the mid-IR, thereby suggesting a direct link with the pseudogap.
Local correlations between doubly and singly occupied sites which lower the
kinetic energy of a hole are the efficient cause of this effect.


title:
Exact time-average distribution for a stationary non-Markovian massive
  Brownian particle coupled to two heat baths

abstract:
  Using a time-averaging technique we obtain exactly the probability
distribution for position and velocity of a Brownian particle under the
influence of two heat baths at different temperatures. These baths are
expressed by a white noise term, representing the fast dynamics, and a colored
noise term, representing the slow dynamics. Our exact solution scheme accounts
for inertial effects, that are not present in approaches that assume the
Brownian particle in the over-damped limit. We are also able to obtain the
contribution associated with the fast noise that are usually neglected by other
approaches.


title: Electronic Energy Spectra of Square and Cubic Fibonacci Quasicrystals

abstract:
  Understanding the electronic properties of quasicrystals, in particular the
dependence of these properties on dimension, is among the interesting open
problems in the field of quasicrystals. We investigate an off-diagonal
tight-binding Hamiltonian on the separable square and cubic Fibonacci
quasicrystals. We use the well-studied singular-continuous energy spectrum of
the 1-dimensional Fibonacci quasicrystal to obtain exact results regarding the
transitions between different spectral behaviors of the square and cubic
quasicrystals. We use analytical results for the addition of 1d spectra to
obtain bounds on the range in which the higher-dimensional spectra contain an
absolutely continuous component. We also perform a direct numerical study of
the spectra, obtaining good results for the square Fibonacci quasicrystal, and
rough estimates for the cubic Fibonacci quasicrystal.


title:
Hidden Charge 2e Boson: Experimental Consequences for Doped Mott
  Insulators

abstract:
  We show here that many of the normal state properties of the cuprates can
result from the new charge 2e bosonic field which we have recently (Phys. Rev.
Lett. {\bf 99}, 46404 (2007) and Phys. Rev. B 77, 014512 (2008)) shown to exist
in the exact low-energy theory of a doped Mott insulator. In particular, the 1)
mid-infrared band including the non-vanishing of the restricted f-sum rule in
the Mott insulator, 2) the $T^2$ contribution to the thermal conductivity, 3)
the pseudogap, 4) the bifurcation of the electron spectrum below the chemical
potential as recently seen in angle-resolved photoemission, 5) insulating
behaviour away from half-filling, 6) the high and low-energy kinks in the
electron dispersion and 7) T-linear resistivity all derive from the charge 2e
bosonic field.
  We also calculate the inverse dielectric function and show that it possesses
a sharp quasiparticle peak and a broad particle-hole continuum. The sharp peak
is mediated by a new charge e composite excitation formed from the binding of a
charge 2e boson and a hole and represents a distinctly new prediction of this
theory. It is this feature that is responsible for dynamical part of the
spectral weight transferred across the Mott gap. We propose that electron
energy loss spectroscopy at finite momentum and frequency can be used to probe
the existence of such a sharp feature.


title: Coherent effects in a thin film of metamaterial

abstract:
  The refraction is theoretically considered of ultimately short pulses at
interface of two dielectrics that contains a thin film of nonlinear
metamaterial. For the model of metamaterial composed of nanoparticles and
magnetic nanocircuits (split-ring resonators) the equations are obtained
suitable for describing the coherent responses of such film. The numerical
simulation demonstrates the emergence of oscillatory echo in inhomogeneous
system of meta-atoms. It is supposed that the reported methods are applicable
for investigation of thin metamaterial films.


title:
Correlation of the highest-energy cosmic rays with the positions of
  nearby active galactic nuclei

abstract:
  Data collected by the Pierre Auger Observatory provide evidence for
anisotropy in the arrival directions of the cosmic rays with the highest
energies, which are correlated with the positions of relatively nearby active
galactic nuclei (AGN) \cite{science}. The correlation has maximum significance
for cosmic rays with energy greater than ~ 6x10^{19}$ eV and AGN at a distance
less than ~ 75 Mpc. We have confirmed the anisotropy at a confidence level of
more than 99% through a test with parameters specified {\em a priori}, using an
independent data set. The observed correlation is compatible with the
hypothesis that cosmic rays with the highest energies originate from
extra-galactic sources close enough so that their flux is not significantly
attenuated by interaction with the cosmic background radiation (the
Greisen-Zatsepin-Kuz'min effect). The angular scale of the correlation observed
is a few degrees, which suggests a predominantly light composition unless the
magnetic fields are very weak outside the thin disk of our galaxy. Our present
data do not identify AGN as the sources of cosmic rays unambiguously, and other
candidate sources which are distributed as nearby AGN are not ruled out. We
discuss the prospect of unequivocal identification of individual sources of the
highest-energy cosmic rays within a few years of continued operation of the
Pierre Auger Observatory.


title:
Transfinite diameter notions in C^N and integrals of Vandermonde
  determinants

abstract:
  We provide a general framework and indicate relations between the notions of
transfinite diameter, homogeneous transfinite diameter, and weighted
transfinite diameter for sets in C^N. An ingredient is a formula of Rumely
which relates the Robin function and the transfinite diameter of a compact set.
We also prove limiting formulas for integrals of generalized Vandermonde
determinants with varying weights for a general class of compact sets and
measures in C^N. Our results extend to certain weights and measures defined on
cones in R^N.


title:
D-brane instanton effects in Type II orientifolds: local and global
  issues

abstract:
  We review how D-brane instantons can generate open string couplings of
stringy hierarchy in the superpotential which violate global abelian symmetries
and are therefore perturbatively forbidden. We discuss the main ingredients of
this mechanism, focussing for concreteness on Euclidean $D2$-branes in Type IIA
orientifold compactifications. Special emphasis is put on a careful analysis of
instanton zero modes and a classification of situations leading to
superpotential or higher fermionic F-terms. This includes the discussion of
chiral and non-chiral instanton recombination, viewed as a multi-instanton
effect. As phenomenological applications we discuss the generation of
perturbatively forbidden Yukawa couplings in SU(5) GUT models and Majorana
masses for right-handed neutrinos. Finally we analyse the mirror dual
description of $D1$-instantons in Type I compactifications with $D9$-branes and
stable holomorphic bundles. We present globally defined semi-realistic string
vacua on an elliptically fibered Calabi-Yau realising the non-perturbative
generation of Majorana masses.


title: Three-body scattering from nonperturbative flow equations

abstract:
  We consider fermion-dimer scattering in the presence of a large positive
scattering length in the frame of functional renormalization group equations. A
flow equation for the momentum dependent fermion-dimer scattering amplitude is
derived from first principles in a systematic vertex expansion of the exact
flow equation for the effective action. The resummation obtained from the
nonperturbative flow is shown to be equivalent to the one performed by the
integral equation by Skorniakov and Ter-Martirosian (STM). The flow equation
approach allows to integrate out fermions and bosons simultaneously, in line
with the fact that the bosons are not fundamental but build up gradually as
fluctuation induced bound states of fermions. In particular, the STM result for
atom-dimer scattering is obtained by choosing the relative cutoff scales of
fermions and bosons such that the fermion fluctuations are integrated out
already at the initial stage of the RG evolution.


title:
Nucleosynthesis in early supernova winds III: No significant
  contribution from neutron-rich pockets

abstract:
  Recent nucleosynthesis calculations of Type II supernovae using advanced
neutrino transport determine that the early neutrino winds are proton-rich.
However, a fraction of the ejecta emitted at the same time is composed of
neutron-rich pockets. In this paper we calculate the nucleosynthesis
contribution from the neutron-rich pockets in the hot convective bubbles of a
core-collapse supernova and show that they do not contribute significantly to
the total nucleosynthesis.


title:
Vector electromagnetic theory of transition and diffraction radiation
  with application to the measurement of longitudinal bunch size

abstract:
  We have developed a novel method based on vector electromagnetic theory and
Schellkunoff's principles to calculate the spectral and angular distributions
of transtion radiation (TR) and diffraction radiation (DR) produced by a
charged particle interacting with an arbitrary target. The vector method
predicts the polarization and spectral angular distributions of the radiation
at an arbitrary distance form the source, i.e. in both the near and far fields,
and in any direction of observation. The radiation fields of TR and DR
calculated with the commonly used scalar Huygens model are shown to be limiting
forms of those predicted by the vector theory and the regime of validity of the
scalar theory is explicitly shown. Calculations of TR and DR done using the
vector model are compared to results available in the literature for various
limiting cases and for cases of more general interest. Our theory has important
applications in the design of TR and DR diagnostics particularly those that
utilize coherent TR or DR to infer the longitudinal bunch size and shape. A new
technique to determine the bunch length using the angular distribution of
coherent TR or DR is proposed.


title: Random walk on a population of random walkers

abstract:
  We consider a population of $N$ labeled random walkers moving on a substrate,
and an excitation jumping among the walkers upon contact. The label
$\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be
viewed as a stochastic process, where the transition probabilities are a
stochastic process themselves. Upon mapping onto two simpler processes, the
quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of
long times and low walkers density. The results are compared with numerical
simulations. Several different topologies for the substrate underlying
diffusion are considered.


title: Expanding and Improving the Search for Habitable Worlds

abstract:
  This review focuses on recent results in advancing our understanding of the
location and distribution of habitable exo-Earth environments. We first review
the qualities that define a habitable planet/moon environment. We extend these
concepts to potentially habitable environments in our own Solar System and the
current and future searches for biomarkers there, focusing on the primary
targets for future exploratory missions: Mars, Europa, and Enceladus. We
examine our current knowledge on the types of planetary systems amenable to the
formation of habitable planets, and review the current state of searches for
extra-solar habitable planets as well as expected future improvements in
sensitivity and preparations for the remote detection of the signatures of life
outside our Solar System.


title: Recent BES results and the BESIII upgrade

abstract:
  Using 58 million $J/\psi$ and 14 million $\psi(2S)$ events collected by the
BESII detector at the BEPC, branching fractions or upper limits for the decays
$J/\psi$ and $\psi(2S) \to \Lambda \bar{\Lambda} \pi^0$ and $\Lambda
\bar{\Lambda} \eta$ are measured, and the decays of $J/\psi$ and $\psi(2S)$ to
$n K^0_S \bar{\Lambda}+c.c.$ are observed and measured for the first time.
Finally, $R$ measurement data taken with the BESII detector at center-of-mass
energies between 3.7 and 5.0 GeV are fitted to determine resonance parameters
of the high mass charmonium states, $\psi(3770)$, $\psi(4040)$, $\psi(4160)$,
and $\psi(4415)$.
  The Beijing Electron Collider is being upgraded to a two-ring collider
(BEPCII) with a design luminosity of $1 \times 10^{33}$cm$^{-2}$ s$^{-1}$ at
3.89 GeV and will operate between 2 and 4.2 GeV in the center of mass. With
this luminosity, the new BESIII detector will beable to collect, for example,
10 billion $J/\psi$ events in one year of running. BEPCII and BESIII are
currently nearing completion, and commissioning of both is expected to begin in
mid-2008.


title:
Stellar populations, neutral hydrogen and ionised gas in field
  early-type galaxies

abstract:
  We present a study of the stellar populations of a sample of 39 local, field
early-type galaxies whose HI properties are known from interferometric data.
Our aim is to understand whether stellar age and chemical composition depend on
the HI content of galaxies. As a by-product of our analysis, we also study
their ionised gas content and how it relates to the neutral hydrogen gas.
Stellar populations and ionised gas are studied from optical long-slit spectra.
We determine stellar age, metallicity and alpha-to-iron ratio by analysing a
set of Lick/IDS line-strength indices measured from the spectra after modelling
and subtracting the ionised-gas emission. We do not find any trend in the
stellar populations parameters with M(HI). However, we do find that, at stellar
velocity dispersion below 230 km/s, 2/3 of the galaxies with less than 100
million solar masses of HI are centrally rejuvenated, while none of the
HI-richer systems are. Furthermore, none of the more massive
(velocity-dispersion>230 km/s) objects are centrally rejuvenated independently
on their HI mass. Concerning the ionised gas, we detect emission in 60% of the
sample. This is generally extended and always carachterised by LINER-like
emission-line ratios at any radius. We find that a large HI mass is necessary
(but not sufficient) for a galaxy to host bright ionised-gas emission. A
plausible interpretation of our results is that gas-rich mergers play a
significant role in E/S0 formation, especially at lower mass. Within this
picture, HI-poor, centrally-rejuvenated objects could form in mergers where gas
angular-momentum removal (and therefore inflow) is efficient; HI-rich galaxies
with no significant age gradients (but possibly uniformly young) could be
formed in interactions characterised by high-angular momentum gas.


title: On the Lego-Teichmuller game for finite $G$ cover

abstract:
  Given a smooth, oriented, closed surface $\Sigma$ of genus zero, possibly
with boundary, let $\tilde{\Sigma} \longrightarrow \Sigma$ be a given $G$-cover
of $\Sigma$, where $G$ is a given finite group. Let $S_{n}$ denote the standard
sphere with $n$ holes. There are many ways of gluing together several $G$-cover
of $S_{n}$ to construct the $G$-cover $\ts \longrightarrow \Sigma$, of
$\Sigma$. We let $M(\tilde{\Sigma} ,\Sigma)$ be the set of all ways to
construct the given $G$-cover, $\tilde{\Sigma} \longrightarrow \Sigma$, of
$\Sigma$ from gluing of several $G$-covers of $S_{n}$, here $n$ may vary. In
this paper, we define some simple moves and relation which will turn
$M(\tilde{\Sigma} ,\Sigma)$ into a connected and simply-connected complex. This
will be used in the future paper to construct $G$-equivariant Modular Functor.
This $G$-equivariant Modular Functor will be an extension of the usual Modular
Functor.


title:
Perception and recognition in a neural network theory in which neurons
  exhibit hysteresis

abstract:
  A neural network theory of visual perception and recognition is presented.
Information flows both from the retina to the brain and from the brain to the
retina. A report that when a scene is perceived 50 retinal cells are much more
active than any of the other retinal cells is ascribed significance in the
theory. The theory involves neurons that exhibit hysteresis, without the need
for any changes in synaptic connection strengths during learning. The fact that
the brain is able to recognize faces and other objects very rapidly is
discussed in the context of the theory. The theory can be epitomized as "We see
with our eyes and remember with our brains".


title:
Variation of the magnetic ordering in GdT$_2$Zn$_{20}$ (T= Fe, Ru, Os,
  Co, Rh and Ir) and its correlation with the electronic structure of
  isostructural YT$_2$Zn$_{20}$

abstract:
  Magnetization, resistivity and specific heat measurements were performed on
the solution-grown, single crystals of six GdT$_2$Zn$_{20}$ (T = Fe, Ru, Os,
Co, Rh and Ir) compounds, as well as their Y analogues. For the Gd compounds,
the Fe column members manifest a ferromagnetic (FM) ground state (with an
enhanced Curie temperature, $T_{\mathrm{C}}$, for T = Fe and Ru), whereas the
Co column members manifest an antiferromagnetic (AFM) ground state.
Thermodynamic measurements on the YT$_2$Zn$_{20}$ revealed that the enhanced
$T_{\mathrm{C}}$ for GdFe$_2$Zn$_{20}$ and GdRu$_2$Zn$_{20}$ can be understood
within the framework of Heisenberg moments embedded in a nearly ferromagnetic
Fermi liquid. Furthermore, electronic structure calculations indicate that this
significant enhancement is due to large, close to the Stoner FM criterion,
transition metal partial density of states at Fermi level, whereas the change
of FM to AFM ordering is associated with filling of electronic states with two
additional electrons per formula unit. The degree of this sensitivity is
addressed by the studies of the pseudo-ternary compounds
Gd(Fe$_x$Co$_{1-x}$)$_2$Zn$_{20}$ and Y(Fe$_x$Co$_{1-x}$)$_2$Zn$_{20}$ which
clearly reveal the effect of 3d band filling on their magnetic properties.


title:
The Variable X-ray and Near-IR Behavior of the Particularly Anomaloux
  X-ray Pulsar 1E 1048.1-5937

abstract:
  We present the results of X-ray and near-IR observations of the anomalous
X-ray pulsar 1E 1048.1-5937, believed to be a magnetar. This AXP underwent a
period of extreme variability during 2001-2004, but subsequently entered an
extended and unexpected quiescence in 2004-2006, during which we monitored it
with RXTE, CXO, and HST. Its timing properties were stable for >3 years
throughout the quiescent period. 1E 1048.1-5937 again went into outburst in
March 2007, which saw a factor of >7 total X-ray flux increase which was
anti-correlated with a pulsed fraction decrease, and correlated with spectral
hardening, among other effects. The near-IR counterpart also brightened
following the 2007 event. We discuss our findings in the context of the
magnetar and other models.


title: Single-Exclusion Number and the Stopping Redundancy of MDS Codes

abstract:
  For a linear block code C, its stopping redundancy is defined as the smallest
number of check nodes in a Tanner graph for C, such that there exist no
stopping sets of size smaller than the minimum distance of C. Schwartz and
Vardy conjectured that the stopping redundancy of an MDS code should only
depend on its length and minimum distance.
  We define the (n,t)-single-exclusion number, S(n,t) as the smallest number of
t-subsets of an n-set, such that for each i-subset of the n-set, i=1,...,t+1,
there exists a t-subset that contains all but one element of the i-subset. New
upper bounds on the single-exclusion number are obtained via probabilistic
methods, recurrent inequalities, as well as explicit constructions. The new
bounds are used to better understand the stopping redundancy of MDS codes. In
particular, it is shown that for [n,k=n-d+1,d] MDS codes, as n goes to
infinity, the stopping redundancy is asymptotic to S(n,d-2), if d=o(\sqrt{n}),
or if k=o(\sqrt{n}) and k goes to infinity, thus giving partial confirmation of
the Schwartz-Vardy conjecture in the asymptotic sense.


title:
Threshold and Flavour Effects in the Renormalization Group Equations of
  the MSSM I: Dimensionless Couplings

abstract:
  In a theory with broken supersymmetry, gaugino couplings renormalize
differently from gauge couplings, as do higgsino couplings from Higgs boson
couplings. As a result, we expect the gauge (Higgs boson) couplings and the
corresponding gaugino (higgsino) couplings to evolve to different values under
renormalization group evolution. We re-examine the renormalization group
equations (RGEs) for these couplings in the Minimal Supersymmetric Standard
Model (MSSM). To include threshold effects, we calculate the $\beta$-functions
using a sequence of (non-supersymmetric) effective theories with heavy
particles decoupled at the scale of their mass. We find that the difference
between the SM couplings and their SUSY cousins that is ignored in the
literature may be larger than two-loop effects which are included, and further
that renormalization group evolution induces a non-trivial flavour structure in
gaugino interactions. We present here the coupled set of RGEs for these
dimensionless gauge and "Yukawa"-type couplings. The RGEs for the dimensionful
SSB parameters of the MSSM will be presented in a companion paper.


title: Weak Gravity Conjecture for the Effective Field Theories with N Species

abstract:
  We conjecture an intrinsic UV cutoff for the validity of the effective field
theory with a large number of species coupled to gravity. In four dimensions
such a UV cutoff takes the form $\Lambda=\sqrt{\lambda/ N}M_p$ for $N$ scalar
fields with the same potential $\lambda \phi_i^4$, $i=1,...,N$. This conjecture
implies that the assisted chaotic inflation or N-flation might be in the
swampland, not in the landscape. Similarly a UV cutoff $\Lambda=gM_p/\sqrt{N}$
is conjectured for the U(1) gauge theory with $N$ species.


title:
Type II Small Stringy Black Holes, Probe Branes and Higher Derivative
  Interactions

abstract:
  The near horizon geometry of a fundamental string wrapped around an S1
reduced to four dimensions is expected to be AdS2 x S2. A probe string analysis
suggests a no-force condition indicating supersymmetry, which coincides with
the condition that the AdS2 is embedded in AdS3. We therefore consider the bulk
string theory in terms of a WZW model on AdS3 following recent proposals by
Dabholkar et. al and Giveon et. al. We find that conformal symmetry of the
model naturally leads to the no-force constraints obtained from the probes.
Moreover, we are able to extract the values of the moduli that account for the
value of the microscopic entropy. We also investigate higher derivative
corrections of the form alpha'^3 R^4 + flux terms to the horizon, in the
context of type IIB supergravity. Imposing the no-force condition from the
probe analysis leads to a striking simplification of the equations of motion at
this order in alpha'. However, we argue that the value of the entropy can only
be determined by considering all orders in alpha'.


title:
A Reexamination of the Canonical Structure of the Einstein-Hilbert
  Action in First-Order Form

abstract:
  A canonical analysis of the Einstein-Hilbert action S_d (d>2) is considered,
using the first order form with the metric and affine connection as independent
fields. We adopt a conservative approach to using the Dirac constraint
formalism; we do not use equations of motion which are independent of time
derivatives and correspond to first class constraints to eliminate fields.
Applying the Dirac procedure, we find that the primary constraints lead to
secondary constraints which are equations of motion not involving time
derivatives, and that those secondary constraints which are first class imply
novel tertiary constraints which are also first class. Once the constraints and
their associated gauge conditions are used to eliminate the non-dynamical
degrees of freedom in S_d, there are d(d-3) degrees of freedom left in phase
space. We also consider the simpler limiting case of the non-interacting
graviton in the first order formalism as well as the effect of adding the
action for a massless scalar field to the Einstein-Hilbert action.


title: Revealing Cosmic Magnetism with Radio Polarimetry

abstract:
  While gravitation sustains the on-going evolution of the cosmos, it is
magnetism that breaks gravity's symmetry and that provides the pathway to the
non-thermal Universe. By enabling processes such as anisotropic pressure
support, particle acceleration, and jet collimation, magnetism has for billions
of years regulated the feedback vital for returning matter to the interstellar
and intergalactic medium. After reviewing recent results that demonstrate the
unique view of magnetic fields provided by radio astronomy, I explain how the
Square Kilometre Array will provide data that will reveal what cosmic magnets
look like, how they formed, and what role they have played in the evolving
Universe.


title: The Skorokhod problem in a time-dependent interval

abstract:
  We consider the Skorokhod problem in a time-varying interval. We prove
existence and uniqueness for the solution. We also express the solution in
terms of an explicit formula. Moving boundaries may generate singularities when
they touch. We establish two sets of sufficient conditions on the moving
boundaries that guarantee that the variation of the local time of the
associated reflected Brownian motion is, respectively, finite and infinite. We
also apply these results to study the semimartingale property of a class of
two-dimensional reflected Brownian motions.


title:
Measurement of the Top Quark Mass in the Dilepton Channel using a Matrix
  Element Method and Neuroevolution Selection with 2.0 fb$^{-1}$

abstract:
  This paper has been removed from the preprint server pursuent to
collaboration policy, and is available elsewhere.


title:
New Frontiers in Cosmology and Galaxy Formation: Challenges for the
  Future

abstract:
  (Abridged) Cosmology faces three distinct challenges in the next decade. (1)
The dark sector, both dark matter and dark energy, dominates the Universe. Key
questions include determining the nature of both. Improved observational probes
are crucial. (2) Galaxy formation was initiated at around the epoch of
reionization: we need to understand how and when as well as to develop probes
of earlier epochs. (3) Our simple dark matter-driven picture of galaxy assembly
is seemingly at odds with several observational results, including the presence
of ULIRGS at high z, the `downsizing' signature, chemical signatures of
alpha-element ratios and suggestions that merging may not be important in
defining the Hubble sequence. Understanding the physical implications is a
major challenge for theorists and refiniing the observational uncertainties a
major goal for observers.


title: On Ext-indices of ring extensions

abstract:
  In this paper we are concerned with the finiteness property of Ext-indices of
several ring extensions. In this direction, we introduce some conjectures and
discuss the relationship of them. Also we give affirmative answers to these
conjectures in some special cases. Furthermore, we prove that the trivial
extension of an Artinian local ring by its residue class field is always of
finite Ext-index and we show that the Auslander-Reiten conjecture is true for
this type of rings.


title: Magic N=2 supergravities from hyper-free superstrings

abstract:
  We show by explicit construction the existence of various four dimensional
models of type II superstrings with N=2 supersymmetry, purely vector multiplet
spectrum and no hypermultiplets. Among these, two are of special interest, at
the field theory level they correspond to the two exceptional N=2
supergravities of the magic square that have the same massless scalar field
content as pure N=6 supergravity and N=3 supergravity coupled to three extra
vector multiplets. The N=2 model of the magic square that is associated to N=6
supergravity is very peculiar since not only the scalar degrees of freedom but
all the bosonic massless degrees of freedom are the same in both theories.
  All presented hyper-free N=2 models are based on asymmetric orbifold
constructions with N=(4,1) world-sheet superconformal symmetry and utilize the
2d fermionic construction techniques. The two exceptional N=2 models of the
magic square are constructed via a "twisting mechanism" that eliminates the
extra gravitini of the N=6 and N=3 extended supergravities and creates at the
same time the extra spin-1/2 fermions and spin-1 gauge bosons which are
necessary to balance the numbers of bosons and fermions. Theories of the magic
square with the same amount of supersymmetry in three and five space-time
dimensions are constructed as well, via stringy reduction and oxidation from
the corresponding four-dimensional models.


title: The Two-Impurity Anderson Model at Quantum Criticality

abstract:
  We propose a realization of the two-impurity Anderson model in a double
quantum-dot device. When charge transfer between the dots is suppressed the
system exhibits a quantum phase transition, controlled by a surface of
non-Fermi liquid fixed points parameterized by the charge valences of the dots.
Employing conformal field theory techniques, we identify the scaling exponents
that govern transport and thermodynamics close to criticality. We also
determine the dynamical exponents that set the time scale for buildup of the
non-Fermi liquid state after the system is suddenly shifted into the critical
region, e.g. by a change of a nearby gate voltage.


title: Density estimation in linear time

abstract:
  We consider the problem of choosing a density estimate from a set of
distributions F, minimizing the L1-distance to an unknown distribution
(Devroye, Lugosi 2001). Devroye and Lugosi analyze two algorithms for the
problem: Scheffe tournament winner and minimum distance estimate. The Scheffe
tournament estimate requires fewer computations than the minimum distance
estimate, but has strictly weaker guarantees than the latter.
  We focus on the computational aspect of density estimation. We present two
algorithms, both with the same guarantee as the minimum distance estimate. The
first one, a modification of the minimum distance estimate, uses the same
number (quadratic in |F|) of computations as the Scheffe tournament. The second
one, called ``efficient minimum loss-weight estimate,'' uses only a linear
number of computations, assuming that F is preprocessed.
  We also give examples showing that the guarantees of the algorithms cannot be
improved and explore randomized algorithms for density estimation.


title: The source coding game with a cheating switcher

abstract:
  Motivated by the lossy compression of an active-vision video stream, we
consider the problem of finding the rate-distortion function of an arbitrarily
varying source (AVS) composed of a finite number of subsources with known
distributions. Berger's paper `The Source Coding Game', \emph{IEEE Trans.
Inform. Theory}, 1971, solves this problem under the condition that the
adversary is allowed only strictly causal access to the subsource realizations.
We consider the case when the adversary has access to the subsource
realizations non-causally. Using the type-covering lemma, this new
rate-distortion function is determined to be the maximum of the IID
rate-distortion function over a set of source distributions attainable by the
adversary. We then extend the results to allow for partial or noisy
observations of subsource realizations. We further explore the model by
attempting to find the rate-distortion function when the adversary is actually
helpful.
  Finally, a bound is developed on the uniform continuity of the IID
rate-distortion function for finite-alphabet sources. The bound is used to give
a sufficient number of distributions that need to be sampled to compute the
rate-distortion function of an AVS to within a certain accuracy. The bound is
also used to give a rate of convergence for the estimate of the rate-distortion
function for an unknown IID finite-alphabet source .


title: Smooth and palindromic Schubert varieties in affine Grassmannians

abstract:
  Let G be a simply-connected simple compact Lie group over the complex
numbers. The affine Grassmannian is a projective ind-variety,
homotopy-equivalent to the loop space of G and closely analogous to a maximal
flag variety of the classical Grassmannian manifold. It has a Schubert cell
decomposition indexed by the coroot lattice or equivalently by the minimal
length coset representatives for the affine Weyl group modulo the Weyl group
for G. The closure of an affine Schubert cell is a finite dimensional
projective variety that we call an affine Schubert variety. In this paper we
completely determine the smooth and palindromic (rationally smooth) affine
Schubert varieties.


title: Low SNR Capacity of Noncoherent Fading Channels

abstract:
  Discrete-time Rayleigh fading single-input single-output (SISO) and
multiple-input multiple-output (MIMO) channels are considered, with no channel
state information at the transmitter or the receiver. The fading is assumed to
be stationary and correlated in time, but independent from antenna to antenna.
Peak-power and average-power constraints are imposed on the transmit antennas.
For MIMO channels, these constraints are either imposed on the sum over
antennas, or on each individual antenna. For SISO channels and MIMO channels
with sum power constraints, the asymptotic capacity as the peak signal-to-noise
ratio tends to zero is identified; for MIMO channels with individual power
constraints, this asymptotic capacity is obtained for a class of channels
called transmit separable channels. The results for MIMO channels with
individual power constraints are carried over to SISO channels with delay
spread (i.e. frequency selective fading).


title: Towards a Physical Theory of Subjective Mental States

abstract:
  Any complete theory of physical reality must allow for the ubiquitous
phenomenon of subjective experience at some level, or risk being conceptually
incoherent. However, as long as the ontological status of subjectivity itself
remains unresolved, the topic will be seen as more within the purview of
philosophy than of physics. Towards a resolution of this issue within
empirically motivated physical theory, this article introduces an operational
definition that ultilizes the general consensus that subjective mental states,
whatever else is controversial about them, at least correlate in some way to
physical states. It is shown here that implementing this underappreciated
assumption within the framework of a physical theory in fact leads to
wide-ranging consequences. In particular, a correlation requires there exist a
well-defined mapping from a space of subjective mental states onto a space of
information-bearing elements of some physical theory. Given the peculiar nature
of subjective states as inherently private appearances, any empirical
identification of states must be performed by the experiencing subject. It is
argued that such an operationally defined 'self-measuring' act leads
unavoidably to an 'uncertainty principle' that is analogous in some intriguing
ways to Heisenberg's principle for quantum mechanics. A model is then
introduced for subjective states as algorithmically incomputable numbers.
Additionaally, an inequality similar to Bell's theorem may be derived,
indicating an analogy with the violations of local reality and the ontology of
observables within quantum mechanics.


title: Weibel Instabilities in Dense Quantum Plasmas

abstract:
  The quantum effect on the Weibel instability in an unmagnetized plasma is
presented. Our analysis shows that the quantum effect tends to stabilize the
Weibel instability in the hydrodynamic regime, whereas it produces a new
oscillatory instability in the kinetic regime. A novel effect the quantum
damping, which is associated with the Landau damping, is disclosed. The new
quantum Weibel instability may be responsible for the generation of
non-stationary magnetic fields in compact astrophysical objects as well as in
the forthcoming intense laser-solid density plasma experiments.


title:
Exploring Parameter Constraints on Quintessential Dark Energy: the
  Albrecht-Skordis model

abstract:
  We consider the effect of future dark energy experiments on
``Albrecht-Skordis'' (AS) models of scalar field dark energy using the
Monte-Carlo Markov chain method. We deal with the issues of parameterization of
these models, and have included spatial curvature as a parameter, finding it to
be important. We use the Dark Energy Task Force (DETF) simulated data to
represent future experiments and report our results in the form of likelihood
contours in the chosen parameter space. Simulated data is produced for cases
where the background cosmology has a cosmological constant, as well as cases
where the dark energy is provided by the AS model. The latter helps us
demonstrate the power of DETF Stage 4 data in the context of this specific
model. Though the AS model can produce equations of state functions very
different from what is possible with the $w_0-w_a$ parametrization used by the
DETF, our results are consistent with those reported by the DETF.


title: Addressing the Crisis in Fundamental Physics

abstract:
  I present the case for fundamental physics experiments in space playing an
important role in addressing the current "dark energy'' crisis. If cosmological
observations continue to favor a value of the dark energy equation of state
parameter w=-1, with no change over cosmic time, then we will have difficulty
understanding this new fundamental physics. We will then face a very real risk
of stagnation unless we detect some other experimental anomaly. The advantages
of space-based experiments could prove invaluable in the search for the a more
complete understanding of dark energy. This talk was delivered at the start of
the Fundamental Physics Research in Space Workshop in May 2006.


title: An X-ray, IR, and Submillimeter Flare of Sagittarius A*

abstract:
  Energetic flares are observed in the Galactic supermassive black hole
Sagittarius A* from radio to X-ray wavelengths. On a few occasions,
simultaneous flares have been detected in IR and X-ray observations, but clear
counterparts at longer wavelengths have not been seen. We present a flare
observed over several hours on 2006 July 17 with the Chandra X-Ray Observatory,
the Keck II telescope, the Caltech Submillimeter Observatory, and the
Submillimeter Array. All telescopes observed strong flare events, but the
submillimeter peak is found to occur nearly 100 minutes after the X-ray peak.
Submillimeter polarization data show linear polarization in the excess flare
emission, increasing from 9% to 17% as the flare passes through its peak,
consistent with a transition from optically thick to thin synchrotron emission.
The temporal and spectral behavior of the flare require that the energetic
electrons responsible for the emission cool faster than expected from their
radiative output. This is consistent with adiabatic cooling in an expanding
emission region, with X-rays produced through self-Compton scattering, although
not consistent with the simplest model of such expansion. We also present a
submillimeter flare that followed a bright IR flare on 2005 July 31. Compared
to 2006, this event had a larger peak IR flux and similar submillimeter flux,
but it lacked measurable X-ray emission. It also showed a shorter delay between
the IR and submillimeter peaks. Based on these events we propose a synchrotron
and self-Compton model to relate the submillimeter lag and the variable
IR/X-ray luminosity ratio.


title: Mean-field dynamo in partially ionized plasmas-I

abstract:
  There are several astrophysical situations where one needs to study the
dynamics of magnetic flux in partially ionized turbulent plasmas. In a
partially ionized plasma the magnetic induction is subjected to the ambipolar
diffusion and the Hall effect in addition to the usual resistive dissipation.
In this paper we initiate the study of the kinematic dynamo in a partially
ionized turbulent plasma. The Hall effect arises from the treatment of the
electrons and the ions as two separate fluids and the ambipolar diffusion due
to the inclusion of neutrals as the third fluid. It is shown that these
nonideal effects modify the so called $\alpha$ effect and the turbulent
diffusion coefficient $\beta$ in a rather substantial way. The Hall effect may
enhance or quench the dynamo action altogether. The ambipolar diffusion brings
in an $\alpha$ which depends on the mean magnetic field. The new correlations
embodying the coupling of the charged fluids and the neutral fluid appear in a
decisive manner. The turbulence is necessarily magnetohydrodynamic with new
spatial and time scales. The nature of the new correlations is demonstrated by
taking the Alfv\'enic turbulence as an example.


title:
Exploring Parameter Constraints on Quintessential Dark Energy: the
  Pseudo-Nambu Goldstone Boson Model

abstract:
  We analyze the constraining power of future dark energy experiments for
Pseudo-Nambu Goldstone Boson (PNGB) quintessence. Following the Dark Energy
Task Force methodology, we forecast data for three experimental ``stages'':
Stage 2 represents in-progress projects relevant to dark energy; Stage 3 refers
to medium sized experiments; Stage 4 comprises larger projects. We determine
the posterior probability distribution for the parameters of the PNGB model
using Markov Chain Monte Carlo analysis. Utilizing data generated on a $\Lambda
CDM$ cosmology, we find that the relative power of the different data stages on
PNGB quintessence is roughly comparable to the DETF results for the $w_0-w_a$
parametrization of dark energy. We also generate data based on a PNGB
cosmological model that is consistent with a $\Lambda CDM$ fiducial model at
Stage 2. We find that Stage 4 data based on this PNGB fiducial model will rule
out a cosmological constant by at least $3 \sigma$.


title: The evolution of the mass-metallicity relation at z~3

abstract:
  We present preliminary results of an ESO-VLT large programme (AMAZE) aimed at
determining the evolution of the mass-metallicity relation at z~3 by means of
deep near-IR spectroscopy. Gas metallicities and stellar masses are measured
for an initial sample of nine star forming galaxies at z~3.3. When compared
with previous surveys, the mass-metallicity relation inferred at z~3.3 shows an
evolution significantly stronger than observed at lower redshifts. There are
also some indications that the metallicity evolution of low mass galaxies is
stronger relative to high mass systems, an effect which can be considered as
the chemical version of the galaxy downsizing. The mass-metallicity relation
observed at z~3.3 is difficult to reconcile with the predictions of some
hierarchical evolutionary models. We shortly discuss the possible implications
of such discrepancies.


title: From quasi-entropy to skew information

abstract:
  This paper gives an overview about particular quasi-entropies, generalized
quantum covariances, quantum Fisher informations, skew-informations and their
relations. The point is the dependence on operator monotone functions. It is
proven that a skew-information is the Hessian of a quasi-entropy. The
skew-information and some inequalities are extended to a von Neumann algebra
setting.


title:
Simultaneous Chandra, CSO and VLA Observations of Sgr A*: The Nature of
  Flaring Activity

abstract:
  Sgr A*, the massive black hole at the center of the Galaxy, varies in radio
through X-ray emission on hourly time scales. The flare activity is thought to
arise from the innermost region of an accretion flow onto Sgr A*. We present
simultaneous light curves of Sgr A* in radio, sub-mm and X-rays that show a
possible time delay of 110$\pm17$ minutes between X-ray and 850 $\mu$m
suggesting that the sub-mm flare emission is optically thick. At radio
wavelengths, we detect time lags of of $20.4\pm6.8, 30\pm12$ and 20$\pm6$
minutes between the flare peaks observed at 13 and 7 mm (22 and 43 GHz) in
three different epochs using the VLA. Linear polarization of 1$\pm0.2$% and
0.7$\pm0.1$% is detected at 7 and 13 mm, respectively, when averaged over the
entire observation on 2006 July 17. A simple model of a bubble of synchrotron
emitting electrons cooling via adiabatic expansion can explain the time delay
between various wavelengths, the asymmetric shape of the light curves, and the
observed polarization of the flare emission at 43 and 22 GHz. The derived
physical quantities that characterize the emission give an expansion speed of
v$_{exp} \sim 0.003-0.1$c, magnetic field of B$\sim$10-70 Gauss and particle
spectral index p$\sim$1-2. These parameters suggest that the associated plasma
cannot escape from Sgr A* unless it has a large bulk motion.


title:
The impact of the 18F(a,p)21Ne reaction on asymptotic giant branch
  nucleosynthesis

abstract:
  We present detailed models of low and intermediate-mass asymptotic giant
branch (AGB) stars with and without the 18F(a,p)21Ne reaction included in the
nuclear network, where the rate for this reaction has been recently
experimentally evaluated for the first time. The lower and recommended measured
rates for this reaction produce negligible changes to the stellar yields,
whereas the upper limit of the rate affects the production of 19F and 21Ne. The
stellar yields increase by ~50% to up to a factor of 4.5 for 19F, and by
factors of ~2 to 9.6 for 21Ne. While the 18}F(a,p)21Ne reaction competes with
18O production, the extra protons released are captured by 18O to facilitate
the 18O(p,a)15N(a,g)19F chain. The higher abundances of 19F obtained using the
upper limit of the rate helps to match the [F/O] ratios observed in AGB stars,
but only for large C/O ratios. Extra-mixing processes are proposed to help to
solve this problem. Some evidence that the 18F(a,p)21Ne rate might be closer to
its upper limit is provided by the fact that the higher calculated 21Ne/22Ne
ratios in the He intershell provide an explanation for the Ne isotopic
composition of silicon-carbide grains from AGB stars. This needs to be
confirmed by future experiments of the 18F(a,p)21Ne reaction rate. The
availability of accurate fluorine yields from AGB stars will be fundamental for
interpreting observations of this element in carbon-enhanced metal-poor stars.


title:
Exploring Parameter Constraints on Quintessential Dark Energy: The
  Exponential Model

abstract:
  We present an analysis of a scalar field model of dark energy with an
exponential potential using the Dark Energy Task Force (DETF) simulated data
models. Using Markov Chain Monte Carlo sampling techniques we examine the
ability of each simulated data set to constrain the parameter space of the
exponential potential for data sets based on a cosmological constant and a
specific exponential scalar field model. We compare our results with the
constraining power calculated by the DETF using their ``$w_0-w_a$''
parametrization of the dark energy. We find that respective increases in
constraining power from one stage to the next produced by our analysis give
results consistent with DETF results. To further investigate the potential
impact of future experiments, we also generate simulated data for an
exponential model background cosmology which can not be distinguished from a
cosmological constant at DETF ``Stage 2'', and show that for this cosmology
good DETF Stage 4 data would exclude a cosmological constant by better than
3$\sigma$.


title: BAT X-ray Survey - I: Methodology and X-ray Identification

abstract:
  We applied the Maximum Likelihood method, as an image reconstruction
algorithm, to the BAT X-ray Survey (BXS). This method was specifically designed
to preserve the full statistical information in the data and to avoid
mosaicking of many exposures with different pointing directions, thus reducing
systematic errors when co-adding images. We reconstructed, in the 14-170 keV
energy band, the image of a 90x90 deg$^2$ sky region, centered on
(RA,DEC)=105$^{\circ}$,-25$^{\circ}$, which BAT surveyed with an exposure time
of $\sim1$ Ms (in Nov. 2005). The best sensitivity in our image is $\sim0.85$
mCrab or $2.0\times 10^{-11}$ erg cm$^{-2}$. We detect 49 hard X-ray sources
above the 4.5 $\sigma$ level; of these, only 12 were previously known as hard
X-ray sources ($>$15 keV). Swift/XRT observations allowed us to firmly identify
the counterparts for 15 objects, while 2 objects have Einstein IPC counterparts
\citep{harris90}; in addition to those, we found a likely counterpart for 13
objects by correlating our sample with the ROSAT All-Sky Survey Bright Source
Catalog \citep{voges99}. 7 objects remain unidentified. Analysis of the noise
properties of our image shows that $\sim75$% of the area is surveyed to a flux
limit of $\sim$1 mCrab. This study shows that the coupling of the Maximum
Likelihood method to the most sensitive, all-sky surveying, hard X-ray
instrument, BAT, is able to probe for the first time the hard X-ray sky to the
mCrab flux level. The successful application of this method to BAT demonstrates
that it could also be applied with advantage to similar instruments like
INTEGRAL-IBIS.


title: Self-consistent quasiparticle model for 2, 3 and (2+1) flavor QGP

abstract:
  Quasi-particle model of quark gluon plasma is the statistical mechanics of
particles with medium dependent mass, related to plasma frequency, which was
proposed to describe the thermodynamics of the medium itself. At relativistic
limit the plasma frequency depends on number density and temperature. The
number density is a thermodynamic quantity of the medium which in turn depends
on plasma frequency. Hence, one need to solve this problem self-consistently,
instead of using perturbative expressions for plasma frequency. Here we carry
out such a self-consistent calculations using our, recently developed, a new
formulations of quasiparticle model. By adjusting a single parameter for each
system, a remarkably good fit to lattice QCD results are obtained for 2, 3 and
(2+1) flavor quark gluon plasma systems, first, with zero chemical potential.
Then, it is extended to systems with finite chemical potential and fits very
well the lattice results without any new parameter.


title: Approximation of the joint spectral radius using sum of squares

abstract:
  We provide an asymptotically tight, computationally efficient approximation
of the joint spectral radius of a set of matrices using sum of squares (SOS)
programming. The approach is based on a search for an SOS polynomial that
proves simultaneous contractibility of a finite set of matrices. We provide a
bound on the quality of the approximation that unifies several earlier results
and is independent of the number of matrices. Additionally, we present a
comparison between our approximation scheme and earlier techniques, including
the use of common quadratic Lyapunov functions and a method based on matrix
liftings. Theoretical results and numerical investigations show that our
approach yields tighter approximations.


title: Quantum serial turbo-codes

abstract:
  We present a theory of quantum serial turbo-codes, describe their iterative
decoding algorithm, and study their performances numerically on a
depolarization channel. Our construction offers several advantages over quantum
LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that
deteriorate the performances of iterative decoding. Secondly, the iterative
decoder makes explicit use of the code's degeneracy. Finally, there is complete
freedom in the code design in terms of length, rate, memory size, and
interleaver choice.
  We define a quantum analogue of a state diagram that provides an efficient
way to verify the properties of a quantum convolutional code, and in particular
its recursiveness and the presence of catastrophic error propagation. We prove
that all recursive quantum convolutional encoder have catastrophic error
propagation. In our constructions, the convolutional codes have thus been
chosen to be non-catastrophic and non-recursive. While the resulting families
of turbo-codes have bounded minimum distance, from a pragmatic point of view
the effective minimum distances of the codes that we have simulated are large
enough not to degrade the iterative decoding performance up to reasonable word
error rates and block sizes. With well chosen constituent convolutional codes,
we observe an important reduction of the word error rate as the code length
increases.


title: Constraining Charming Penguins in Charmless B Decays

abstract:
  We discuss the correlations of charming penguin contributions to
$B\to\pi\pi$, $\pi K$ and KK using approximate flavor SU(3) symmetry. Strong
constraints are found from the direct CP asymmetries especially in $\pi K$
modes. We make a global fit to the latest data and find that only a small
charming penguin is allowed, and the size of color-suppressed tree amplitude
(C) relative to tree amplitudes (T) remains large $C/T\simeq0.6$, which
disfavors the possibility of a large charming penguin as an explanation for the
$\pi\pi$ puzzle. We show that a small charming penguin can still have sizable
effect in the time-dependence CP asymmetries in KK mode.


title:
A new approach for testing variations of fundamental constants over
  cosmic epochs using FIR fine-structure lines

abstract:
  Aims. To obtain limits on the variation of the fine-structure constant alpha
and the electron-to-proton mass ratio mu over different cosmological epochs.
Methods. A new approach based on the comparison of redshifts of far infrared
(FIR) fine-structure lines and low-lying rotational transitions in CO is
proposed which is in principle more sensitive by a factor of 10 compared to QSO
metal absorption lines. Results. Estimations of the quotient F = alpha^2/mu
obtained for two distant quasars J1148+5251 (z = 6.42) and BR1202-0725 (z =
4.69) provide Delta F/F = (0.1+/-1.0)10^{-4} and (1.4+/-1.5)10^{-4},
respectively. The obtained limits are consistent with no variation of physical
constants at the level of 0.01% over a period of 13 Gyr. Conclusions. Upcoming
observations of quasars and distant galaxies in FIR fine-structure lines of
different species and in CO low rotational lines at the SOFIA, HSO, and ALMA
are expected to improve the current limit by, at least, an order of magnitude.


title: On homotopy of volterrian quadratic stochastic operators

abstract:
  In the present paper we introduce a notion of homotopy of two Volterra
operators which is related to fixed points of such operators. It is establish a
criterion when two Volterra operators are homotopic, as a consequence we obtain
that the corresponding tournaments of that operators are the same. This, due to
\cite{Ga1}, gives us a possibility to know some information about the
trajectory of homotopic Volterra operators. Moreover, it is shown that any
Volterra q.s.o. given on a face has at least two homotopic extension to the
whole simplex.


title: Hilbert schemes of finite abelian group orbits and Grobner fans

abstract:
  Let $G$ be a finite abelian subgroup of
$PGL(r-1,K)=\mathrm{Aut}(\P^{r-1}_K)$. In this paper, we prove that the
normalization of the $G$-orbit Hilbert scheme $\Hilb^G(\P^{r-1})$ is described
as a toric variety, which corresponds to the Gr\"obner fan for some homogeneous
ideal $I$ of $K[x_1, ..., x_r]$.


title:
Extended Thermodynamics for dense gases and macromolecular fluids,
  obtained through a non relativistic limit

abstract:
  In this paper we consider the 14 moments model of Extended Thermodynamics for
dense gases and macromolecular fluids. Solutions of the restrictions imposed by
the entropy principle and that of Galilean relativity for such a model have
been until now obtained in literature only in an approximate manner up to a
certain order with respect to thermodynamic equilibrium; for more restrictive
models they have been obtained up to whatever order, but by using Taylor
expansions around equilibrium and without proving convergence. Here we have
found an exact solution without using expansions. The idea has been to write
firstly a relativistic model, for which it is easy to impose the Einsteinian
relativity principle, and then taking its non relativistic limit.


title: A D-dimensional Heckmann-like solution of Jordan-Brans-Dicke theory

abstract:
  In this short letter we present a some rigorous vacuum solutions of the
D-dimensional Jordan-Brans-Dicke field equations. In contrast with the well
known Brans-Dicke solutions, to the search of static and spherically symmetric
space-time we choose the widespread Hilbert coordinates.


title:
Electroweak and QCD corrections to Higgs-boson production in
  vector-boson fusion at the LHC

abstract:
  Radiative corrections of strong and electroweak interactions are presented at
next-to-leading order for Higgs-boson production in the weak-boson-fusion
channel at the LHC. The calculation includes all weak-boson fusion and
quark-antiquark annihilation diagrams as well as all related interferences. The
electroweak corrections, which also include real corrections from incoming
photons and leading heavy-Higgs-boson effects at two-loop order, are of the
same size as the QCD corrections, viz. typically at the level of 5-10% for a
Higgs-boson mass up to \sim 700 GeV. In general, they do not simply rescale
differential distributions, but induce distortions at the level of 10%. The
discussed corrections have been implemented in a flexible Monte Carlo event
generator.


title: Dynamics Of Proton Spin : Role Of $qqq$ Force

abstract:
  The analytic structure of the $qqq$ wave function, obtained recently in the
high momentum regime of QCD, is employed for the formulation of baryonic
transition amplitudes via quark loops. A new aspect of this study is the role
of a direct ($Y$-shaped, Mercedes-Benz type) $qqq$ force in generating the
$qqq$ wave function. The dynamics is that of a Salpeter-like equation (3D
support for the kernel) formulated covariantly on the light front, a la
Markov-Yukawa Transversality Principle (MYTP) which warrants a 2-way
interconnection between the 3D and 4D Bethe-Salpeter (BSE) forms for 2 as well
as 3 fermion quarks. The dynamics of this 3-body force shows up through a
characteristic singularity in the hypergeometric differential equation for the
3D wave function $\phi$, corresponding to a $negative$ eigenvalue of the spin
operator $i \sigma_1.\sigma_2\times \sigma_3$ which is an integral part of the
$qqq$ force. As a first application of this wave function to the problem of the
proton spin anomaly, the two-gluon contribution to the anomaly yields an
estimate of the right sign, although somewhat smaller in magnitude.
  Keywords: 3bodyforce; proton-spin; 2gluon anomaly; fractional correction
$\theta$


title:
Origins of anomalous electronic structures of epitaxial graphene on
  silicon carbide

abstract:
  On the basis of first-principles calculations, we report that a novel
interfacial atomic structure occurs between graphene and the surface of silicon
carbide, destroying the Dirac point of graphene and opening a substantial
energy gap there. In the calculated atomic structures, a quasi-periodic
$6\times 6$ domain pattern emerges out of a larger commensurate
$6\sqrt{3}\times6\sqrt{3}R30^\circ$ periodic interfacial reconstruction,
resolving a long standing experimental controversy on the periodicity of the
interfacial superstructures. Our theoretical energy spectrum shows a gap and
midgap states at the Dirac point of graphene, which are in excellent agreement
with the recently-observed anomalous angle-resolved photoemission spectra.
Beyond solving unexplained issues of epitaxial graphene, our atomistic study
may provide a way to engineer the energy gaps of graphene on substrates.


title:
A study of supervised classification of Hipparcos variable stars using
  PCA and Support Vector Machines

abstract:
  We report on the automated classification of Hipparcos variable stars by a
supervised classification algorithm known as Support Vector Machines. The
dataset comprised about 3200 stars, each characterized by 51 features. These
are the B-V and V-I colours, the skewness of the lightcurve, the median
subtracted 10-percentiles and forty bins from the Fourier envelope of the
lightcurve. We also tested whether the classification performance can be
improved by using the most significant principal components calculated from
this dataset. We show that the overall classification performance (as measured
by the fraction of true positives) on the original dataset is of the order of
62%. For about 9 of the 18 different variability classes, the classification
accuracy is significantly larger than 60% (up to 98%). Introducing principal
components does not significantly improve this result. We further find that
many of the different variability classes are not very distinct and possibly
poorly defined, i.e. there exists a considerable class overlap. It is concluded
that this `contamination' of the template set implies minimum errors and thus
degrades the overall performance.


title:
Fusion of necklace-ring patterns into vortex and fundamental solitons in
  dissipative media

abstract:
  We demonstrate that necklace-shaped arrays of localized spatial beams can
merge into stable fundamental or vortex solitons in a generic model of laser
cavities, based on the two-dimensional complex Ginzburg-Landau equation with
the cubic-quintic nonlinearity. The outcome of the fusion is controlled by the
number of beads in the initial necklace, 2N, and its topological charge, M. We
predict and confirm by systematic simulations that the vorticity of the
emerging soliton is the absolute value of difference of N and M. Threshold
characteristics of the fusion are found and explained too. If the initial
radius of the array (R0) is too large, it simply keeps the necklace shape (if
R0 is somewhat smaller, the necklace features a partial fusion), while, if R0
is too small, the array disappears.


title:
Classification of integrable Volterra type lattices on the sphere.
  Isotropic case

abstract:
  The symmetry approach is used for classification of integrable isotropic
vector Volterra lattices on the sphere. The list of integrable lattices
consists mainly of new equations. Their symplectic structure and associated PDE
of vector NLS-type are discussed.


title: Phase-Separation Transition in Liquid Mixtures Near Charged Objects

abstract:
  We study the thermodynamic behavior of nonpolar liquid mixtures in the
vicinity of curved charged objects, such as electrodes or charged colloids. For
small enough charge on the object, or equivalently, small potential, the
dielectrophoretic force leads to enrichment of the more polar liquid close the
colloid. However, there is a critical value of charge (or potential), above
which a phase-separation transition occurs, and the interface between high- and
low-dielectric constant components becomes sharp. Analytical and numerical
composition profile are given, and the equilibrium front location as a function
of charge or voltage is found. We further employ a simple Cahn-Hilliard type
equation to study the dynamics of phase-separation in spatially nonuniform
electric fields. We find an exponential relaxation of the composition front
location, with a characteristic time depending on the charge, mixture
composition and ambient temperature.


title: Variable VHE gamma-ray emission from non-blazar AGNs

abstract:
  The observation of rapidly variable very high energy (VHE) gamma-rays from
non-aligned active galactic nuclei (AGNs), as reported from M87, proves
challenging for conventional theoretical acceleration and emission models. We
re-examine the centrifugal acceleration of particles by rotating jet
magnetospheres in the vicinity of accreting supermassive black hole systems and
analyze the energy constraints imposed for highly underluminous systems.
Applications are presented for conditions expected to be present in the radio
galaxy M87, assuming accretion onto the central black hole to occur in an
advection-dominated (ADAF) mode. We show that for a highly underluminous source
like M87, centrifugally accelerated electrons may reach Lorentz factors up to
$\gamma \sim (10^7-10^8)$, allowing inverse Compton (Thomson) upscattering of
sub-mm disk photons to the TeV regime. Upscattering of Comptonized disk photons
results in a flat TeV spectrum $L_{\nu} \propto \nu^{-\alpha_c}$ with spectral
index $\alpha_c \simeq 1.2$. The characteristic variability time scale is of
the order $r_{\rm L}/c$, which in the case of M87 corresponds to $\simeq 1.7$ d
for a typical light cylinder radius of $r_{\rm L} \simeq 5 r_{\rm s}$.
Centrifugal acceleration could thus provide a natural explanation for the
challenging VHE emission features in M87. Our results suggest that some
advection-dominated accreting (non-blazar) AGNs could well be observable VHE
emitting sources. (abridged)


title:
An alternative NMSSM phenomenology with manifest perturbative
  unification

abstract:
  Can supersymmetric models with a moderate stop mass be made consistent with
the negative Higgs boson searches at LEP, while keeping perturbative
unification manifest? The NMSSM achieves this rather easily, but only if extra
matter multiplets filling complete SU(5) representations are present at
intermediate energies. As a concrete example which makes use of this feature,
we give an analytic description of the phenomenology of a constrained NMSSM
close to a Peccei-Quinn symmetry point. The related pseudo-Goldstone boson
appears in decays of the Higgs bosons and possibly of the lightest neutralino,
and itself decays into (b anti-b) and (tau anti-tau).


title: Random matrices, free probability, planar algebras and subfactors

abstract:
  Using a family of graded algebra structures on a planar algebra and a family
of traces coming from random matrix theory, we obtain a tower of
non-commutative probability spaces, naturally associated to a given planar
algebra. The associated von Neumann algebras are II$_{1}$ factors whose
inclusions realize the given planar algebra as a system of higher relative
commutants. We thus give an alternative proof to a result of Popa that every
planar algebra can be realized by a subfactor.


title:
Fractal Dimensions of a Weakly Clustered Distribution and the Scale of
  Homogeneity

abstract:
  Homogeneity and isotropy of the universe at sufficiently large scales is a
fundamental premise on which modern cosmology is based. Fractal dimensions of
matter distribution is a parameter that can be used to test the hypothesis of
homogeneity. In this method, galaxies are used as tracers of the distribution
of matter and samples derived from various galaxy redshift surveys have been
used to determine the scale of homogeneity in the Universe. Ideally, for
homogeneity, the distribution should be a mono-fractal with the fractal
dimension equal to the ambient dimension. While this ideal definition is true
for infinitely large point sets, this may not be realised as in practice, we
have only a finite point set. The correct benchmark for realistic data sets is
a homogeneous distribution of a finite number of points and this should be used
in place of the mathematically defined fractal dimension for infinite number of
points (D) as a requirement for approach towards homogeneity. We derive the
expected fractal dimension for a homogeneous distribution of a finite number of
points. We show that for sufficiently large data sets the expected fractal
dimension approaches D in absence of clustering. It is also important to take
the weak, but non-zero amplitude of clustering at very large scales into
account. In this paper we also compute the expected fractal dimension for a
finite point set that is weakly clustered. Clustering introduces departures in
the Fractal dimensions from D and in most situations the departures are small
if the amplitude of clustering is small. Features in the two point correlation
function, like those introduced by Baryon Acoustic Oscillations (BAO) can lead
to non-trivial variations in the Fractal dimensions where the amplitude of
clustering and deviations from D are no longer related in a monotonic manner.


title: Local Quantum Pure-state Identification without Classical Knowledge

abstract:
  Suppose we want to distinguish two quantum pure states. We consider the case
in which no classical knowledge on the two states is given and only a pair of
samples of the two states is available. This problem is called quantum
pure-state identification problem. Our task is to optimize the mean
identification success probability, which is averaged over an independent
unitary invariant distribution of the two reference states. In this paper, the
two states are assumed bipartite states which are generally entangled. The
question is whether the maximum mean identification success probability can be
attained by means of an LOCC (Local Operations and Classical Communication)
measurement scheme. We will show that this is possible by constructing a POVM
which respects the conditions of LOCC.


title: STM tunneling through a quantum wire with a side-attached impurity

abstract:
  The STM tunneling through a quantum wire (QW) with a side-attached impurity
(atom, island) is investigated using a tight-binding model and the
nonequilibrium Keldysh Green function method. The impurity can be coupled to
one or more QW atoms. The presence of the impurity strongly modifies the local
density of states of the wire atoms, thus influences the STM tunneling through
all the wire atoms. The transport properties of the impurity itself are also
investigated mainly as a function of the wire length and the way it is coupled
to the wire. It is shown that the properties of the impurity itself and the way
it is coupled to the wire strongly influence the STM tunneling which is
reflected in the density of states and differential conductance.


title: The Cops & Robber game on series-parallel graphs

abstract:
  The Cops and Robber game is played on undirected finite graphs. $k$ cops and
one robber are positioned on vertices and take turn in moving along edges. The
cops win if, after a move, a cop and the robber are on the same vertex. A graph
is called $k$-copwin, if the cops have a winning strategy.
  It is known that planar graphs are 3-copwin (Aigner & Fromme, 1984) and that
outerplanar graphs are 2-copwin (Clarke, 2002). In this short note, we prove
that series-parallel (i.e., graphs with no $K_4$ minor) graphs are 2-copwin.
  It is a well-known trick in the literature of cops & robber games to define
variants of the game which impose restrictions on the possible strategies of
the cops (see Clarke, 2002). For our proof, we define the ``cops & robber game
with exits''.
  Our proof yields a winning strategy for the cops.


title: Initial conditions for massive star formation

abstract:
  In this contribution, our knowledge of the initial conditions under which
massive star formation takes place is reviewed. Massive stars are born in
massive clumps of giant molecular clouds (GMCs), hence first the properties of
GMCs are summarized. As a potentially early stage of molecular clouds, infrared
dark clouds have been discovered a decade ago as dark patches in mid-infrared
(MIR) images of the Galactic plane and many studies of the physical conditions
within them have been conducted recently. Without the guidance of MIR
absorption, large scale, unbiased cold dust surveys can be used as well to
identify massive cold clumps. In the absence of indicators of ongoing massive
star formation, like compact HII regions and bright IR sources, these clumps
are the most promising objects for the study of the initial conditions of
massive star formation. Current observational approaches to find IR quiet
clumps and their physical and chemical properties are summarized.


title: Applications of physical methods in high-frequency futures markets

abstract:
  In the present work we demonstrate the application of different physical
methods to high-frequency or tick-by-tick financial time series data. In
particular, we calculate the Hurst exponent and inverse statistics for the
price time series taken from a range of futures indices. Additionally, we show
that in a limit order book the relaxation times of an imbalanced book state
with more demand or supply can be described by stretched exponential laws
analogous to those seen in many physical systems.


title:
Ground State and Charge Renormalization in a Nonlinear Model of
  Relativistic Atoms

abstract:
  We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to
describe relativistic electrons interacting with the Dirac sea, in an external
electrostatic potential. The model can be seen as a mean-field approximation of
Quantum Electrodynamics (QED) where photons and the so-called exchange term are
neglected. A state of the system is described by its one-body density matrix,
an infinite rank self-adjoint operator which is a compact perturbation of the
negative spectral projector of the free Dirac operator (the Dirac sea).
  We study the minimization of the reduced BDF energy under a charge
constraint. We prove the existence of minimizers for a large range of values of
the charge, and any positive value of the coupling constant $\alpha$. Our
result covers neutral and positively charged molecules, provided that the
positive charge is not large enough to create electron-positron pairs. We also
prove that the density of any minimizer is an $L^1$ function and compute the
effective charge of the system, recovering the usual renormalization of charge:
the physical coupling constant is related to $\alpha$ by the formula
$\alpha_{\rm phys}\simeq \alpha(1+2\alpha/(3\pi)\log\Lambda)^{-1}$, where
$\Lambda$ is the ultraviolet cut-off. We eventually prove an estimate on the
highest number of electrons which can be bound by a nucleus of charge $Z$. In
the nonrelativistic limit, we obtain that this number is $\leq 2Z$, recovering
a result of Lieb.
  This work is based on a series of papers by Hainzl, Lewin, Sere and Solovej
on the mean-field approximation of no-photon QED.