title: Piecewise linear regularized solution paths

abstract:
  We consider the generic regularized optimization problem
$\hat{\mathsf{\beta}}(\lambda)=\arg
\min_{\beta}L({\sf{y}},X{\sf{\beta}})+\lambda J({\sf{\beta}})$. Efron, Hastie,
Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for
the LASSO--that is, if $L$ is squared error loss and $J(\beta)=\|\beta\|_1$ is
the $\ell_1$ norm of $\beta$--the optimal coefficient path is piecewise linear,
that is, $\partial \hat{\beta}(\lambda)/\partial \lambda$ is piecewise
constant. We derive a general characterization of the properties of (loss $L$,
penalty $J$) pairs which give piecewise linear coefficient paths. Such pairs
allow for efficient generation of the full regularized coefficient paths. We
investigate the nature of efficient path following algorithms which arise. We
use our results to suggest robust versions of the LASSO for regression and
classification, and to develop new, efficient algorithms for existing problems
in the literature, including Mammen and van de Geer's locally adaptive
regression splines.


title: $B_2$-crystals: axioms, structure, models

abstract:
  We present a list of ``local'' axioms and an explicit combinatorial
construction for the regular $B_2$-crystals (crystal graphs of highest weight
integrable modules over $U_q(sp_4)$). Also a new combinatorial model for these
crystals is developed.


title: Curves of given $p$-rank with trivial automorphism group

abstract:
  Let $k$ be an algebraically closed field of characteristic $p >0$. Suppose $g
\geq 3$ and $0 \leq f \leq g$. We prove there is a smooth projective $k$-curve
of genus $g$ and $p$-rank $f$ with no non-trivial automorphisms. In addition,
we prove there is a smooth projective hyperelliptic $k$-curve of genus $g$ and
$p$-rank $f$ whose only non-trivial automorphism is the hyperelliptic
involution. The proof involves computations about the dimension of the moduli
space of (hyperelliptic) $k$-curves of genus $g$ and $p$-rank $f$ with extra
automorphisms.


title: Supersymmetric and R symmetric vacua in Wess-Zumino models

abstract:
  In the context of supersymmetric Wess-Zumino models with an R symmetry, we
find some simple conditions on the R-charge content of the theory that imply
the presence or absence of supersymmetric and R-symmetric vacua. The main
result of this work is that the comparison between the number of R-charge 0 and
R-charge 2 superfields is essential to the properties of the model as regards
symmetry breaking. We also study possible exceptions to the Nelson-Seiberg
theorem --finding that there are supersymmetric vacua that break R symmetry in
generic models-- and the spontaneous breaking of R symmetry in
supersummetry-breaking vacua, with some insight on the Coleman-Weinberg
one-loop potential.


title: A Modified Borel Summation Technique

abstract:
  We compare and contrast three different perturbative expansions for the
quartic anharmonic oscillator wavefunction and apply a modified Borel summation
technique to determine the energy eigenvalues. In the first two expansions this
provides the energy eigenvalues directly however in the third method we tune
the wavefunctions to achieve the correct large x behaviour. This tuning
technique allows us to determine the energy eigenvalues up to an arbitrary
level of accuracy with remarkable efficiency. We give numerical evidence to
explain this behaviour. We also refine the modified Borel summation technique
to improve its accuracy. The main sources of error are investigated with
reasonable error corrections calculated.


title: Locally compact quantum groups. Radford's $S^4$ formula

abstract:
  Let $A$ be a finite-dimensional Hopf algebra. The left and the right
integrals on $A$ are related by means of a distinguished group-like element
$\delta$ of $A$. Similarly, there is this element $\hat\delta$ in the dual Hopf
algebra $\hat A$. Radford showed that
$$S^4(a)=\delta^{-1}(\hat\delta\triangleright a \triangleleft
\hat\delta^{-1})\delta$$ for all $a$ in $A$ where $S$ is the antipode of $A$
and where $\triangleright$ and $\triangleleft$ are used to denote the standard
left and right actions of $\hat A$ on $A$. The formula still holds for
multiplier Hopf algebras with integrals (algebraic quantum groups).
  In the theory of locally compact quantum groups, an analytical form of
Radford's formula can be proven (in terms of bounded operators on a Hilbert
space).
  In this talk, we do not have the intention to discuss Radford's formula as
such, but rather to use it, together with related formulas, for illustrating
various aspects of the road that takes us from the theory of Hopf algebras
(including compact quantum groups) to multiplier Hopf algebras (including
discrete quantum groups) and further to the more general theory of locally
compact quantum groups.


title: Earthquake Networks, Complex

abstract: An article for the Springer Encyclopedia of Complexity and System Science


title:
Integral-Field Spectroscopy of the Post Red Supergiant IRC +10420:
  evidence for an axi-symmetric wind

abstract:
  We present NAOMI/OASIS adaptive-optics assisted integral-field spectroscopy
of the transitional massive hypergiant IRC +10420, an extreme mass-losing star
apparently in the process of evolving from a Red Supergiant toward the
Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the
star, we study the appearance of the line-emission from the inner wind as
viewed when reflected off the surrounding nebula. We find that, contrary to
previous work, there is strong evidence for wind axi-symmetry, based on the
equivalent-width and velocity variations of H$\alpha$ and Fe {\sc ii}
$\lambda$6516. We attribute this behaviour to the appearance of the complex
line-profiles when viewed from different angles. We also speculate that the Ti
{\sc ii} emission originates in the outer nebula in a region analogous to the
Strontium Filament of $\eta$ Carinae, based on the morphology of the
line-emission. Finally, we suggest that the present-day axisymmetric wind of
IRC +10420, combined with its continued blueward evolution, is evidence that
the star is evolving toward the B[e] supergiant phase.


title:
Axisymmetric orbit models of N-body merger remnants: a dependency of
  reconstructed mass on viewing angle

abstract:
  We model mock observations of collisionless N-body disc-disc mergers with an
axisymmetric orbit superposition program that has been used to model Coma
ellipticals. The remnants sample representatively the shapes of disc-disc
mergers including prolate, triaxial and oblate objects. The aim is to better
understand how the assumption of axial symmetry affects reconstructed masses
and stellar motions of systems which are intrinsically not axisymmetric,
whether it leads to a bias and how such a potential bias can be recognised in
models of real galaxies. The mass recovery at the half-light radius depends on
viewing-angle and intrinsic shape: edge-on views allow to reconstruct total
masses with an accuracy between 20% (triaxial/prolate remnants) and 3% (oblate
remnant). Masses of highly flattened, face-on systems are underestimated by up
to 50%. Deviations in local mass densities can be larger where remnants are
strongly triaxial or prolate. Luminous M/L are sensitive to box orbits in the
remnants. Box orbits cause the central kinematics to vary with viewing-angle.
Reconstructed luminous M/L and central masses follow this variation. Luminous
M/L are always underestimated (up to a factor of 2.5). Respective dark halos in
the models can be overestimated by about the same amount, depending again on
viewing angle. Reconstructed velocity anisotropies depend on viewing angle and
on the orbital composition of the remnant. We construct N-body realisations of
the Schwarzschild models to discuss chaotic orbits and the virial equilibrium
in our models. Apparently flattened, rotating ellipticals of intermediate mass
are likely close to both, axial symmetry and edge-on orientation. Our results
imply that Schwarzschild models allow a reconstruction of their masses and
stellar anisotropies with high accuracy. (abridged)


title:
Role of electrostatics in the texture of islands in free standing
  ferroelectric liquid crystal films

abstract:
  Curved textures of ferroelectric smectic C* liquid crystals produce space
charge when they involve divergence of the spontaneous polarization field.
Impurity ions can partially screen this space charge, reducing long range
interactions to local ones. Through studies of the textures of islands on very
thin free-standing smectic films, we see evidence of this effect, in which
materials with a large spontaneous polarization have static structures
described by a large effective bend elastic constant. To address this issue, we
calculated the electrostatic free energy of a free standing film of
ferroelectric liquid crystal, showing how the screened coulomb interaction
contributes a term to the effective bend elastic constant, in the static long
wavelength limit. We report experiments which support the main features of this
model.


title: Statistical inferences for functional data

abstract:
  With modern technology development, functional data are being observed
frequently in many scientific fields. A popular method for analyzing such
functional data is ``smoothing first, then estimation.'' That is, statistical
inference such as estimation and hypothesis testing about functional data is
conducted based on the substitution of the underlying individual functions by
their reconstructions obtained by one smoothing technique or another. However,
little is known about this substitution effect on functional data analysis. In
this paper this problem is investigated when the local polynomial kernel (LPK)
smoothing technique is used for individual function reconstructions. We find
that under some mild conditions, the substitution effect can be ignored
asymptotically. Based on this, we construct LPK reconstruction-based estimators
for the mean, covariance and noise variance functions of a functional data set
and derive their asymptotics. We also propose a GCV rule for selecting good
bandwidths for the LPK reconstructions. When the mean function also depends on
some time-independent covariates, we consider a functional linear model where
the mean function is linearly related to the covariates but the covariate
effects are functions of time. The LPK reconstruction-based estimators for the
covariate effects and the covariance function are also constructed and their
asymptotics are derived. Moreover, we propose a $L^2$-norm-based global test
statistic for a general hypothesis testing problem about the covariate effects
and derive its asymptotic random expression. The effect of the bandwidths
selected by the proposed GCV rule on the accuracy of the LPK reconstructions
and the mean function estimator is investigated via a simulation study. The
proposed methodologies are illustrated via an application to a real functional
data set collected in climatology.


title: Wrapping interactions at strong coupling -- the giant magnon

abstract:
  We derive generalized Luscher formulas for finite size corrections in a
theory with a general dispersion relation. For the AdS_5xS^5 superstring these
formulas encode leading wrapping interaction effects. We apply the generalized
mu-term formula to calculate finite size corrections to the dispersion relation
of the giant magnon at strong coupling. The result exactly agrees with the
classical string computation of Arutyunov, Frolov and Zamaklar. The agreement
involved a Borel resummation of all even loop-orders of the BES/BHL dressing
factor thus providing a strong consistency check for the choice of the dressing
factor.


title: Extremality conditions for isolated and dynamical horizons

abstract:
  A maximally rotating Kerr black hole is said to be extremal. In this paper we
introduce the corresponding restrictions for isolated and dynamical horizons.
These reduce to the standard notions for Kerr but in general do not require the
horizon to be either stationary or rotationally symmetric. We consider physical
implications and applications of these results. In particular we introduce a
parameter e which characterizes how close a horizon is to extremality and
should be calculable in numerical simulations.


title: Intersection theory from duality and replica

abstract:
  Kontsevich's work on Airy matrix integrals has led to explicit results for
the intersection numbers of the moduli space of curves. In this article we show
that a duality between k-point functions on $N\times N$ matrices and N-point
functions of $k\times k$ matrices, plus the replica method, familiar in the
theory of disordered systems, allows one to recover Kontsevich's results on the
intersection numbers, and to generalize them to other models. This provides an
alternative and simple way to compute intersection numbers with one marked
point, and leads also to some new results.


title:
Optical characterization of GaN by N+ implantation into GaAs at elevated
  temperature

abstract:
  Both hexagonal wurtzite and cubic zinc blend GaN phases were synthesized in
GaAs by 50 keV N+ implantation at 400 deg C and subsequent annealing at 900 deg
C for 15 min in N2 ambient. Crystallographic structural and Raman scattering
studies revealed that GaN phases were grown for fluence above 2x1017 cm-2.
Temperature-dependent photoluminescence study showed sharp direct band-to-band
transition peak ~3.32 eV at temperature <= 200K. The intermediate bandgap
value, with respect to ~3.4 eV for hexagonal and ~3.27 eV for cubic phases of
GaN is an indicative for the formation of mixed hexagonal and cubic phases.


title: Enumerative Properties of NC^B(p,q)

abstract:
  We determine the rank generating function, the zeta polynomial and the
Moebius function for the poset NC^B(p,q) of annular non-crossing partitions of
type B, where p and q are two positive integers. We give an alternative
treatment of some of these results in the case q=1, for which this poset is a
lattice. We also consider the general case of multiannular non-crossing
partitions of type B, and prove that this reduces to the cases of non-crossing
partitions of type B in the annulus and in the disc.


title: Moderate Growth Time Series for Dynamic Combinatorics Modelisation

abstract:
  Here, we present a family of time series with a simple growth constraint.
This family can be the basis of a model to apply to emerging computation in
business and micro-economy where global functions can be expressed from local
rules. We explicit a double statistics on these series which allows to
establish a one-to-one correspondence between three other ballot-like
strunctures.


title: On the p-th root of a p-adic number

abstract:
  We give a sufficient and necessary condition for a p-adic integer to have
p-th root in the ring of p-adic integers. The same condition holds clearly for
residues modulo p^k. We give a proof that Fermat's last theorem is false for
p-adic integers and for residues mod p^k.


title:
Polarization rotation for light propagating non-parallel to a magnetic
  field in QED vacuum and in a dilute electron gas

abstract:
  The rotation of the polarization vector for light propagating perpendicular
to an external constant external magnetic field $B$, is calculated in quantum
vacuum, where it leads to different photon eigenmodes of the magnetized photon
self-energy tensor for polarizations along and orthogonal to $B$ (Cotton-Mouton
effect in QED vacuum). Its analogies and differences with Faraday effect are
discussed and both phenomena are calculated for a relativistic electron gas at
low densities, by starting from the low energy limit of the photon self-energy
eigenvalues in presence of $B$. In the Cotton-Mouton case the polarization
vector describes an ellipse whose axes vary periodically from zero to a maximum
value. By assuming an effective electron density of order $10^3$ cm$^{-3}$ the
quantum relativistic eigenvalues lead to a rotation of the polarization plane
compatible with some of the limit values reported by PVLAS experiments. Other
consequences, which are interesting for astrophysics, are also discussed.


title:
Experimental joint signal-idler quasi-distributions and photon-number
  statistics for mesoscopic twin beams

abstract:
  Joint signal-idler photoelectron distributions of twin beams containing
several tens of photons per mode have been measured recently. Exploiting a
microscopic quantum theory for joint quasi-distributions in parametric
down-conversion developed earlier we characterize properties of twin beams in
terms of quasi-distributions using experimental data. Negative values as well
as oscillating behaviour in quantum region are characteristic for the
subsequently determined joint signal-idler quasi-distributions of integrated
intensities. Also the conditional and difference photon-number distributions
are shown to be sub-Poissonian and sub-shot-noise, respectively.


title: Ferromagnetism in cobalt doped n-GaN

abstract:
  Ferromagnetic ordering is reported in the post-annealed samples of Co doped
n-GaN formed by Co+ implantation. A maximum Curie temperature ~ 250K is
recorded for the sample with 8 atomic percent Co. Particle induced x-ray
emission-channeling study confirmed the substitutional Co in Ga lattice site.
Local atomic arrangement around magnetic impurities is also analyzed using
Raman study. A disordered model with carrier mediated coupling of localized
magnetic moments is made responsible for the observed ferromagnetic ordering.


title: Tensoring with infinite-dimensional modules in $\scr O_0$

abstract:
  We show that the principal block $\scr O_0$ of the BGG category $\scr O$ for
a semisimple Lie algebra $\germ g$ acts faithfully on itself via exact
endofunctors which preserve tilting modules, via right exact endofunctors which
preserve projective modules and via left exact endofunctors which preserve
injective modules. The origin of all these functors is tensoring with arbitrary
(not necessarily finite-dimensional) modules in the category $\scr O$. We study
such functors, describe their adjoints and show that they give rise to a
natural (co)monad structure on $\scr O_0$. Furthermore, all this generalises to
parabolic subcategories of $\scr O_0$. As an example, we present some explicit
computations for the algebra $\germ{sl}_3$.


title: On the $\mathbb{L}_p$-error of monotonicity constrained estimators

abstract:
  We aim at estimating a function $\lambda:[0,1]\to \mathbb {R}$, subject to
the constraint that it is decreasing (or increasing). We provide a unified
approach for studying the $\mathbb {L}_p$-loss of an estimator defined as the
slope of a concave (or convex) approximation of an estimator of a primitive of
$\lambda$, based on $n$ observations. Our main task is to prove that the
$\mathbb {L}_p$-loss is asymptotically Gaussian with explicit (though unknown)
asymptotic mean and variance. We also prove that the local $\mathbb {L}_p$-risk
at a fixed point and the global $\mathbb {L}_p$-risk are of order $n^{-p/3}$.
Applying the results to the density and regression models, we recover and
generalize known results about Grenander and Brunk estimators. Also, we obtain
new results for the Huang--Wellner estimator of a monotone failure rate in the
random censorship model, and for an estimator of the monotone intensity
function of an inhomogeneous Poisson process.


title: HIPPARCOS Astrometric Orbit and Evolutionary Status of HR 6046

abstract:
  The previously known, 6-yr spectroscopic binary HR 6046 has been speculated
in the past to contain a compact object as the secondary. A recent study has
re-determined the orbit with great accuracy, and shown that the companion is an
evolved but otherwise normal star of nearly identical mass as the primary,
which is also a giant. The binary motion was detected by the Hipparcos mission
but was not properly accounted for in the published astrometric solution. Here
we use the Hipparcos intermediate data in combination with the spectroscopic
results to revise that solution and establish the orbital inclination angle for
the first time, and with it the absolute masses M(A) = 1.38 [-0.03,+0.09]
M(Sun) and M(B) = 1.36 [-0.02,+0.07] M(Sun). Aided by other constraints, we
investigate the evolutionary status and confirm that the primary star is
approaching the tip of the red-giant branch, while the secondary is beginning
its first ascent.


title: Nitrogen ion beam synthesis of InN in InP (100) at elevated temperature

abstract:
  InN phase is grown in crystalline InP(100) substrates by 50 keV N+
implantation at an elevated temperature of 400 deg C followed by annealing at
525 deg C in N2 ambient. Crystallographic structural and Raman scattering
studies are performed for the characterization of grown phases. Temperature-
and power-dependent photoluminescence studies show direct band-to-band
transition peak ~1.06 eV at temperatures <=150K. Implantations at an elevated
temperature with a low ion beam current and subsequent low temperature
annealing step are found responsible for the growth of high-quality InN phase.


title:
On the occurrence of oscillatory modulations in the power-law behavior
  of dynamic and kinetic processes in fractals

abstract:
  The dynamic and kinetic behavior of processes occurring in fractals with
spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the
existence of a fundamental scaling ratio (b_1). We address time-dependent
physical processes, which as a consequence of the time evolution develop a
characteristic length of the form $\xi \propto t^{1/z}$, where z is the dynamic
exponent. So, we conjecture that the interplay between the physical process and
the symmetry properties of the fractal leads to the occurrence of time DSI
evidenced by soft log-periodic modulations of physical observables, with a
fundamental time scaling ratio given by $\tau = b_1 ^z$. The conjecture is
tested numerically for random walks, and representative systems of broad
universality classes in the fields of irreversible and equilibrium critical
phenomena.


title: Tau decay and the structure of the a1

abstract:
  We analyse the decay $\tau\to\pi\pi\pi\nu$ based on the recently developed
techniques to generate axial-vector resonances dynamically. Under the
assumption that the a1 is a coupled-channel meson-molecule, the spectral
function is described surprisingly well by adjusting only one free parameter.
Including, in addition, an elementary a1 corrupts the results.


title:
Squeezed-light generation in a nonlinear planar waveguide with a
  periodic corrugation

abstract:
  Two-mode nonlinear interaction (second-harmonic and second-subharmonic
generation) in a planar waveguide with a small periodic corrugation at the
surface is studied. Scattering of the interacting fields on the corrugation
leads to constructive interference that enhances the nonlinear process provided
that all the interactions are phase matched. Conditions for the overall phase
matching are found. Compared with a perfectly quasi-phase-matched waveguide,
better values of squeezing as well as higher intensities are reached under
these conditions. Procedure for finding optimum values of parameters for
squeezed-light generation is described.


title: On equimultiple modules

abstract:
  We study the class of equimultiple modules. In particular, we prove several
criteria for an equimultiple module to be a complete intersection and prove the
openness of the equimultiple locus of an ideal module.


title:
Coupling of frustrated Ising spins to magnetic cycloid in multiferroic
  TbMnO3

abstract:
  We report on diffraction measurements on multiferroic TbMnO3 which
demonstrate that the Tb- and Mn-magnetic orders are coupled below the
ferroelectric transition TFE = 28 K. For T < TFE the magnetic propagation
vectors (tau) for Tb and Mn are locked so that tauTb = tauMn, while below TNTb
= 7 K we find that tauTb and tauMn lock-in to rational values of 3/7 b* and 2/7
b*, respectively, and obey the relation 3tauTb - tauMn = 1. We explain this
novel matching of wave vectors within the frustrated ANNNI model coupled to a
periodic external field produced by the Mn-spin order. The tauTb = tauMn
behavior is recovered when Tb magnetization is small, while the tauTb = 3/7
regime is stabilized at low temperatures by a peculiar arrangement of domain
walls in the ordered state of Ising-like Tb spins.


title:
On local $U$-statistic processes and the estimation of densities of
  functions of several sample variables

abstract:
  A notion of local $U$-statistic process is introduced and central limit
theorems in various norms are obtained for it. This involves the development of
several inequalities for $U$-processes that may be useful in other contexts.
This local $U$-statistic process is based on an estimator of the density of a
function of several sample variables proposed by Frees [J. Amer. Statist.
Assoc. 89 (1994) 517--525] and, as a consequence, uniform in bandwidth central
limit theorems in the sup and in the $L_p$ norms are obtained for these
estimators.


title: Sl(N) link homology using foams and the Kapustin-Li formula

abstract:
  We use foams to give a topological construction of a rational link homology
categorifying the slN link invariant, for N>3. To evaluate closed foams we use
the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that
for any link our homology is isomorphic to Khovanov and Rozansky's.


title: Multi-phonon Raman scattering in GaN nanowires

abstract:
  UV Raman scattering studies show longitudinal optical (LO) mode up to 4th
order in wurtzite GaN nanowire system. Frohlich interaction of electron with
the long range electrostatic field of ionic bonded GaN gives rise to
enhancement in LO phonon modes. Good crystalline quality, as indicated by the
crystallographic as well as luminescence studies, is thought to be responsible
for this significant observation. Calculated size dependence, incorporating
size corrected dielectric constants, of electron-phonon interaction energy
agrees well with measured values and also predict stronger interaction energy
than that of the bulk for diameter below ~3 nm.


title: Collection analysis for Horn clause programs

abstract:
  We consider approximating data structures with collections of the items that
they contain. For examples, lists, binary trees, tuples, etc, can be
approximated by sets or multisets of the items within them. Such approximations
can be used to provide partial correctness properties of logic programs. For
example, one might wish to specify than whenever the atom $sort(t,s)$ is proved
then the two lists $t$ and $s$ contain the same multiset of items (that is, $s$
is a permutation of $t$). If sorting removes duplicates, then one would like to
infer that the sets of items underlying $t$ and $s$ are the same. Such results
could be useful to have if they can be determined statically and automatically.
We present a scheme by which such collection analysis can be structured and
automated. Central to this scheme is the use of linear logic as a omputational
logic underlying the logic of Horn clauses.


title: Pathway parameter and thermonuclear functions

abstract:
  In the theory of thermonuclear reaction rates, analytical evaluation of
thermonuclear functions for non-resonant reactions, including cases with
cut-off and depletion of the tail of the Maxwell-Boltzmann distribution
function were considered in a series of papers by Mathai and Haubold (1988). In
the present paper we study more general classes of thermonuclear functions by
introducing a pathway parameter alpha, so that when alpha --> 1 the
thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will
also give interpretations for the pathway parameter alpha in the case of
cut-off and in terms of moments.


title: Variational quantum Monte Carlo simulations with tensor-network states

abstract:
  We show that the formalism of tensor-network states, such as the matrix
product states (MPS), can be used as a basis for variational quantum Monte
Carlo simulations. Using a stochastic optimization method, we demonstrate the
potential of this approach by explicit MPS calculations for the transverse
Ising chain with up to N=256 spins at criticality, using periodic boundary
conditions and D*D matrices with D up to 48. The computational cost of our
scheme formally scales as ND^3, whereas standard MPS approaches and the related
density matrix renromalization group method scale as ND^5 and ND^6,
respectively, for periodic systems.


title: A complement to Le Cam's theorem

abstract:
  This paper examines asymptotic equivalence in the sense of Le Cam between
density estimation experiments and the accompanying Poisson experiments. The
significance of asymptotic equivalence is that all asymptotically optimal
statistical procedures can be carried over from one experiment to the other.
The equivalence given here is established under a weak assumption on the
parameter space $\mathcal{F}$. In particular, a sharp Besov smoothness
condition is given on $\mathcal{F}$ which is sufficient for Poissonization,
namely, if $\mathcal{F}$ is in a Besov ball $B_{p,q}^{\alpha}(M)$ with $\alpha
p>1/2$. Examples show Poissonization is not possible whenever $\alpha p<1/2$.
In addition, asymptotic equivalence of the density estimation model and the
accompanying Poisson experiment is established for all compact subsets of
$C([0,1]^m)$, a condition which includes all H\"{o}lder balls with smoothness
$\alpha>0$.


title: Bose-Einstein condensation of a Knudsen gas

abstract:
  We reconcile a long-standing controversy regarding the transition temperature
of the Bose-Einstein condensation in a dilute interacting Bose gas, by showing
that there is a crossover between ideal gas and interacting gas. The former
corresponds to a Knudsen (or collisionless) regime, in which the mean-free-path
is much larger than the system dimension, while the latter corresponds to the
opposite hydrodynamic regime. The deviation of the transition temperature from
that of the non-interacting gas is proportional to the square root of a in the
Knudsen regime, and to a in the hydrodynamic regime, where a is the scattering
length. This crossover may be observable in a Bose gas trapped in a potential
or on an optical lattice.


title: Realizing modules over the homology of a DGA

abstract:
  Let A be a DGA over a field and X a module over H_*(A). Fix an
$A_\infty$-structure on H_*(A) making it quasi-isomorphic to A. We construct an
equivalence of categories between A_{n+1}-module structures on X and length n
Postnikov systems in the derived category of A-modules based on the bar
resolution of X. This implies that quasi-isomorphism classes of A_n-structures
on X are in bijective correspondence with weak equivalence classes of
rigidifications of the first n terms of the bar resolution of X to a complex of
A-modules. The above equivalences of categories are compatible for different
values of n. This implies that two obstruction theories for realizing X as the
homology of an A-module coincide.


title:
Large-order shifted 1/N expansions through the asymptotic iteration
  method

abstract:
  The perturbation technique within the framework of the asymptotic iteration
method is used to obtain large-order shifted 1/N expansions, where N is the
number of spatial dimensions. This method is contrary to the usual
Rayleigh-Schr\"{o}dinger perturbation theory, no matrix elements need to be
calculated. The method is applied to the Schr\"{o}dinger equation and the
non-polynomial potential $V(r)=r^2+\frac{b r^2}{(1+cr^2)}$ in three dimensions
is discussed as an illustrative example.


title:
A generation-based particle-hole density-matrix renormalization group
  study of interacting quantum dots

abstract:
  The particle-hole version of the density-matrix renormalization-group method
(PH-DMRG) is utilized to calculate the ground-state energy of an interacting
two-dimensional quantum dot. We show that a modification of the method, termed
generation-based PH-DMRG, leads to significant improvement of the results, and
discuss its feasibility for the treatment of large systems. As another
application we calculate the addition spectrum.


title:
Affleck-Dine leptogenesis via multiscalar evolution in a supersymmetric
  seesaw model

abstract:
  A leptogenesis scenario in a supersymmetric standard model extended with
introducing right-handed neutrinos is reconsidered. Lepton asymmetry is
produced in the condensate of a right-handed sneutrino via the Affleck-Dine
mechanism. The LH_u direction develops large value due to a negative effective
mass induced by the right-handed sneutrino condensate through the Yukawa
coupling of the right-handed neutrino, even if the minimum during the inflation
is fixed at the origin. The lepton asymmetry is nonperturbatively transfered to
the LH_u direction by this Yukawa coupling.


title:
Extension of thermonuclear functions through the pathway model including
  Maxwell-Boltzmann and Tsallis distributions

abstract:
  The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended
to cover Tsallis statistics (Tsallis, 1988) and more general cases of
distribution functions. An analytical study of respective thermonuclear
functions is being conducted with the help of statistical techniques. The
pathway model, recently introduced by Mathai (2005), is utilized for
thermonuclear functions and closed-form representations are obtained in terms
of H-functions and G-functions. Maxwell-Boltzmannian thermonuclear functions
become particular cases of the extended thermonuclear functions. A brief review
on the development of the theory of analytic representations of nuclear
reaction rates is given.


title:
Casimir-Polder interatomic potential between two atoms at finite
  temperature and in the presence of boundary conditions

abstract:
  We evaluate the Casimir-Polder potential between two atoms in the presence of
an infinite perfectly conducting plate and at nonzero temperature. In order to
calculate the potential, we use a method based on equal-time spatial
correlations of the electric field, already used to evaluate the effect of
boundary conditions on interatomic potentials. This method gives also a
transparent physical picture of the role of a finite temperature and boundary
conditions on the Casimir-Polder potential. We obtain an analytical expression
of the potential both in the near and far zones, and consider several limiting
cases of interest, according to the values of the parameters involved, such as
atom-atom distance, atoms-wall distance and temperature.


title:
Simple direct measurement of nonclassical joint signal-idler
  photon-number statistics and correlation area of twin photon beams

abstract:
  The measurement of joint signal-idler photon-number distribution of a field
obtained from spontaneous parametric downconversion using an intensified CCD
camera is presented. It is shown that a classicality criterion is violated
directly by the measured data. Characteristic dimensions of the area of
correlation are determined in the same experimental setup.


title:
Antisymmetric entangled two-photon states generated in nonlinear GaN/AlN
  photonic-band-gap structures

abstract:
  The properties of an entangled two-photon state antisymmetric in frequencies
are studied. At a beam-splitter, two entangled photons are perfectly
anti-correlated. In addition, they cannot be detected at the same time instant
despite the fact that their detection times are confined to a narrow time
window, i.e. they are temporally anti-bunched. Using nonlinear
photonic-band-gap structures made of GaN/AlN, two schemes for generating such
states are described.


title: Embedding group algebras into finite von Neumann regular rings

abstract:
  Let G be a group and let K be a field of characteristic zero. We shall prove
that KG can be embedded into a von Neumann unit-regular ring. In the course of
the proof, we shall obtain a result relevant to the Atiyah conjecture.


title: Unbiased Random Threshold Networks Are Chaotic or Critical

abstract: This paper has been withdrawn.

categories: cond-mat.dis-nn cond-mat.stat-mech nlin.CG q-bio.MN


title: Mathematical Modeling of Control Dynamical Systems

abstract: This paper has been withdrawn by the author due to a crucial mistakes.


title:
Monopoles, topology of the Standard Model, and unification of
  interactions at Tev scale

abstract:
  It is shown that unification of strong and Electroweak interactions at Tev
scale may lead to appearance of topologically stable monopoles with masses of
the order of 40 Tev. Those monopoles may play an important role in the early
Universe, at finite temperature. They may even be condensed at high enough
temperature. The lattice model for investigation of this phenomenon is
presented.


title: Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

abstract:
  We give a natural family of Bridgeland stability conditions on the derived
category of a smooth projective complex surface S and describe ``wall-crossing
behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates
Pic(S) and $C \in |H|$. If, in addition, S is a K3 or Abelian surface, we use
this description to construct a sequence of fine moduli spaces of
Bridgeland-stable objects via Mukai flops and generalized elementary
modifications of the universal coherent sheaf. We also discover a natural
generalization of Thaddeus' stable pairs for curves embedded in the moduli
spaces.


title: Observation of B0 -> K*0 K*0bar and search for B0 -> K*0 K*0

abstract:
  We report the observation of the b -> d penguin-dominated decay B0 -> K*0
K*0bar with a sample of 383.2 +/- 4.2 million BBbar pairs collected with the
BaBar detector at the PEP-II asymmetric-energy e^+e^- collider at the Stanford
Linear Accelerator Center. The measured branching fraction is Br(B0 -> K*0
K*0bar) = [1.28^{+0.35}_{-0.30} +/- 0.11] x 10^{-6} and the fraction of
longitudinal polarization f_L (B0 -> K*0 K*0bar) = 0.80^{+0.10}_{-0.12} +/-
0.06. The first error quoted is statistical and the second systematic. We also
obtain an upper limit at the 90% confidence level on the branching fraction for
Br(B0 ->K*0 K*0) < 0.41 x 10^{-6}.


title: The spin structure of the pion

abstract:
  We present the first calculation of the transverse spin structure of the pion
in lattice QCD. Our simulations are based on two flavors of non-perturbatively
improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to
(2.1 fm)^3 and lattice spacings below 0.1 fm. We find a characteristic
asymmetry in the spatial distribution of transversely polarized quarks. This
asymmetry is very similar in magnitude to the analogous asymmetry we previously
obtained for quarks in the nucleon. Our results support the hypothesis that all
Boer-Mulders functions are alike.


title: Lorentz Invariance Violation from String Theory

abstract:
  In this brief, and by no means complete, review I discuss situations in
string theory, in which Lorentz Invariance Violation may occur in a way
consistent with world-sheet conformal invariance, thereby leading to
acceptable, in principle, string backgrounds. In particular, I first discuss
spontaneous Lorentz violation in (non supersymmetric) open string field theory.
Then, I move onto a discussion of gravity-induced modified dispersion relations
in non-critical (Liouville) strings, in the sense of an induced Finsler-like
geometry depending on both coordinates and momenta, for string propagation in
non-trivial space times (such as D-particle ``foamy situations''). I pay
attention to explaining the appearance of bi-metric models from such string
theories, which could serve as examples of alternative scenaria to dark matter.
Finally, I make some comparisons with similar developments in other contexts,
such as critical strings in non-commutative space times, as well as deformed
special relativities and theories with reduced Lorentz symmetry, advocated
recently, where again Finsler geometry seems to come into play. In this latter
respect, I put the emphasis on phenomenology and attempt to answer the question
as to whether there is the possibility of experimental disentanglement of the
various approaches.


title: First real time detection of Be7 solar neutrinos by Borexino

abstract:
  This paper reports a direct measurement of the Be7 solar neutrino signal rate
performed with the Borexino low background liquid scintillator detector. This
is the first real-time spectral measurement of sub-MeV solar neutrinos. The
result for 0.862 MeV Be7 is 47 +- 7 (stat} +- 12 (sys} counts/(day x 100 ton),
consistent with predictions of Standard Solar Models and neutrino oscillations
with LMA-MSW parameters.


title: Focusing and Polarization in Intuitionistic Logic

abstract:
  A focused proof system provides a normal form to cut-free proofs that
structures the application of invertible and non-invertible inference rules.
The focused proof system of Andreoli for linear logic has been applied to both
the proof search and the proof normalization approaches to computation. Various
proof systems in literature exhibit characteristics of focusing to one degree
or another. We present a new, focused proof system for intuitionistic logic,
called LJF, and show how other proof systems can be mapped into the new system
by inserting logical connectives that prematurely stop focusing. We also use
LJF to design a focused proof system for classical logic. Our approach to the
design and analysis of these systems is based on the completeness of focusing
in linear logic and on the notion of polarity that appears in Girard's LC and
LU proof systems.


title:
The Concept of Entropy and its Concavity for a Finite Protein in its
  Environment: An exact study on a Square Lattice

abstract:
  We consider a general lattice model of a finite protein in its environment
and calculate its Boltzmann entropy SB(E) as a function of its energy E in a
microcanonical ensemble, and Gibbs entropy SG(E) as a function of its average
energy E in a canonical ensemble by exact enumeration on a square lattice. We
find that because of the finite size of the protein, (i) the two are very
different and SG(E)>SB(E), (ii) SB(E) need not be concave while SG(E) is, and
(iii) SG(E) is relevant for experiments but not SB(E), even though SB(E) is
conceptually more useful. We discuss the consequences of these differences. The
results are general and applicable to all finite systems.


title: Effective Field Theory for the Anisotropic Wilson Lattice Action

abstract:
  We construct the effective field theory appropriate for describing the low
energy behavior of anisotropic Wilson lattice actions and the O(a) improved
variant thereof. We then apply this effective field theory to the hadron
spectrum and dispersion relations, focussing on the corrections due to the
anisotropy. We point out an important feature of anisotropic lattices regarding
the Aoki-regime; for a given set of fermion masses and spatial lattice spacing,
if an isotropic action is in the QCD-phase, this does not guarantee that the
anisotropic action is outside the Aoki-regime. This may be important in the
tuning of bare parameters for anisotropic lattices using domain-wall and
overlap fermions as well as Wilson and O(a)-improved Wilson fermions.


title: A Language for Generic Programming in the Large

abstract:
  Generic programming is an effective methodology for developing reusable
software libraries. Many programming languages provide generics and have
features for describing interfaces, but none completely support the idioms used
in generic programming. To address this need we developed the language G. The
central feature of G is the concept, a mechanism for organizing constraints on
generics that is inspired by the needs of modern C++ libraries. G provides
modular type checking and separate compilation (even of generics). These
characteristics support modular software development, especially the smooth
integration of independently developed components. In this article we present
the rationale for the design of G and demonstrate the expressiveness of G with
two case studies: porting the Standard Template Library and the Boost Graph
Library from C++ to G. The design of G shares much in common with the concept
extension proposed for the next C++ Standard (the authors participated in its
design) but there are important differences described in this article.


title: Automorphisms and isomorphisms of Chevalley groups and algebras

abstract:
  An adjoint Chevalley group of rank at least 2 over a rational algebra (or a
similar ring), its elementary subgroup, and the corresponding Lie ring have the
same automorphism group. These automorphisms are explicitly described.


title:
Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong
  Coupling and Non-Markovian Regimes

abstract:
  We examine the dynamics of bipartite entanglement between a two-level atom
and the electromagnetic field. We treat the Jaynes-Cummings model with a single
field mode and examine in detail the exact time evolution of entanglement,
including cases where the atomic state is initially mixed and the atomic
transition is detuned from resonance. We then explore the effects of other
nearby modes by calculating the exact time evolution of entanglement in more
complex systems with two, three, and five field modes. For these cases we can
obtain exact solutions which include the strong coupling regimes. Finally, we
consider the entanglement of a two-level atom with the infinite collection of
modes present in the intracavity field of a Fabre-Perot cavity. In contrast to
the usual treatment of atom-field interactions with a continuum of modes using
the Born-Markov approximation, our treatment in all cases describes the full
non-Markovian dynamics of the atomic subsystem. Only when an analytic
expression for the infinite mode case is desired do we need to make a weak
coupling assumption which at long times approximates Markovian dynamics.


title: The evolution of cosmological gravitational waves in f(R) gravity

abstract:
  We give a rigorous and mathematically clear presentation of the Covariant and
Gauge Invariant theory of gravitational waves in a perturbed
Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where
the matter is described by a perfect fluid with a barotropic equation of state.
As an example of a consistent analysis of tensor perturbations in Fourth Order
Gravity, we apply the formalism to a simple background solution of R^n gravity.
We obtain the exact solutions of the perturbation equations for scales much
bigger than and smaller than the Hubble radius. It is shown that the evolution
of tensor modes is highly sensitive to the choice of n and an interesting new
feature arises. During the radiation dominated era, their exist a growing
tensor perturbation for nearly all choices of n. This occurs even when the
background model is undergoing accelerated expansion as opposed to the case of
General Relativity. Consequently, cosmological gravitational wave modes can in
principle provide a strong constraint on the theory of gravity independent of
other cosmological data sets.


title: Photometric Calibration of the Swift Ultraviolet/Optical Telescope

abstract:
  We present the photometric calibration of the Swift UltraViolet/Optical
Telescope (UVOT) which includes: optimum photometric and background apertures,
effective area curves, colour transformations, conversion factors for count
rates to flux, and the photometric zero points (which are accurate to better
than 4 per cent) for each of the seven UVOT broadband filters. The calibration
was performed with observations of standard stars and standard star fields that
represent a wide range of spectral star types. The calibration results include
the position dependent uniformity, and instrument response over the 1600-8000A
operational range. Because the UVOT is a photon counting instrument, we also
discuss the effect of coincidence loss on the calibration results. We provide
practical guidelines for using the calibration in UVOT data analysis. The
results presented here supersede previous calibration results.


title: A search for B+ --> tau+ nu with Hadronic B tags

abstract:
  We present a search for the decay B^+ --> tau^+ nu using $383 \times 10^{6}}$
BBbar pairs collected at the Upsilon(4S) resonance with the BABAR detector at
the SLAC PEP-II B Factory. We select a sample of events with one completely
reconstructed tag B in a hadronic decay mode ($B^- \to D^{(*)0} X^-$), and
examine the rest of the event to search for a B^+ --> tau^+ nu decay. We
identify the tau lepton in the following modes: tau^+ --> e^+ nu nu,tau^+ -->
mu^+ nu nu, tau^+ --> pi^+ nu and tau^+ --> pi^+ pi^0 nu. We find a 2.2 sigma
excess in data and measure a branching fraction of B(B+ --> tau^+ nu) =
(1.8^{+0.9}_{-0.8}(stat.) \pm 0.4(bkg. syst.) \pm 0.2 (other syst.)) \times
10^{4}. We calculate the product of the B meson decay constant f_{B} and
|V_{ub}| to be f_{B} |V_{ub}| =
(10.1^{+2.3}_{-2.5}(stat.)^{+1.2}_{-1.5}(syst.))\times10^{-4} GeV


title:
Association of mid-infrared solar plages with Calcium K line emissions
  and magnetic structures

abstract:
  Solar mid-IR observations in the 8-15 micrometer band continuum with moderate
angular resolution (18 arcseconds) reveal the presence of bright structures
surrounding sunspots. These plage-like features present good association with
calcium CaII K1v plages and active region magnetograms. We describe a new
optical setup with reflecting mirrors to produce solar images on the focal
plane array of uncooled bolometers of a commercial camera preceded by germanium
optics. First observations of a sunspot on September 11, 2006 show a mid-IR
continuum plage exhibiting spatial distribution closely associated with CaII
K1v line plage and magnetogram structures. The mid-IR continuum bright plage is
about 140 K hotter than the neighboring photospheric regions, consistent with
hot plasma confined by the magnetic spatial structures in and above the active
region


title: Gauge invariance in fractional field theories

abstract:
  The principle of local gauge invariance is applied to fractional wave
equations and the interaction term is determined up to order $o(\bar{g})$ in
the coupling constant $\bar{g}$. As a first application, based on the
Riemann-Liouville fractional derivative definition, the fractional Zeeman
effect is used to reproduce the baryon spectrum accurately.
  The transformation properties of the non relativistic fractional
Schr\"odinger-equation under spatial rotations are investigated and an internal
fractional spin is deduced.


title: The SN 1987A Link to Others and Gamma-Ray Bursts

abstract:
  Early measurements of SN 1987A can be interpreted in light of a beam/jet
(BJ), with a collimation factor >10,000, which impacted polar ejecta (PE) to
produce the "Mystery Spot" (MS), ~24 lt-d away. Other details of SN 1987A
suggest that it came from a merger of 2 stellar cores of a common envelope (CE)
binary, i.e. a "double degenerate" (DD) SN. Even having to penetrate the CE,
the BJ may have caused a long-soft (l)GRB upon hitting the PE, thus DD can
produce lGRBs. Because DD must be the dominant merger/SN mechanism in
elliptical galaxies (EGs), where only short, hard GRBs (sGRBs) have been
observed, DD without CE or PE must also produce sGRBs, and thus NS-NS mergers
may not make GRBs as we know them, and/or be as common as previously thought.
Millisecond pulsars (MSPs) in the non-core-collapsed globular clusters are also
99% DD-formed from WD-WD merger, consistent with their 2.10 ms minimum spin
period, the 2.14 ms signal seen from SN 1987A, and sGRBs offset from the
centers of EGs. The details of Ia's suggest that these are also DD, and the
total thermonuclear disruption paradigm is now in serious doubt as well, a
cause for concern in Ia Cosmology, because Ia's will appear to be Ic's when
viewed from their DD merger poles, given sufficient matter above that lost to
core-collapse. As a DD SN, 1987A appears to be the Rosetta Stone for 99% of
SNe, GRBs and MSPs, including all recent nearby SNe except SN 1986J, and the
more distant SN 2006gy. There is no need to invent exotica, such as
"collapsars," to account for GRBs.


title:
Influence of random roughness on the adhesion between metal surfaces due
  to capillary condensation

abstract:
  The capillary force was measured by atomic force microscopy between a gold
coated sphere mounted on a cantilever and gold surfaces with different
roughness. For smooth surfaces the capillary adhesive force surpasses in
magnitude any dispersion, e.g. van der Waals/Casimir, and/or electrostatic
forces. A substantial decrease in the capillary force was observed by
increasing the roughness ampltitude a few nanometers between 1-10 nm. From
these measurements two limits can be defined: a smooth limit where a closely
macroscopic size contact surface interacts through the capillary force, and the
rough limit where only a few asperities give a capillary contribution.


title:
Solutions of fractional reaction-diffusion equations in terms of
  Mittag-Leffler functions

abstract:
  This paper deals with the solution of unified fractional reaction-diffusion
systems. The results are obtained in compact and elegant forms in terms of
Mittag-Leffler functions and generalized Mittag-Leffler functions, which are
suitable for numerical computation. On account of the most general character of
the derived results, numerous results on fractional reaction, fractional
diffusion, and fractional reaction-diffusion problems scattered in the
literature, including the recently derived results by the authors for
reaction-diffusion models, follow as special cases.


title: The study of a new gerrymandering methodology

abstract:
  This paper is to obtain a simple dividing-diagram of the congressional
districts, where the only limit is that each district should contain the same
population if possibly. In order to solve this problem, we introduce three
different standards of the "simple" shape. The first standard is that the final
shape of the congressional districts should be of a simplest figure and we
apply a modified "shortest split line algorithm" where the factor of the same
population is considered only. The second standard is that the gerrymandering
should ensure the integrity of the current administrative area as the
convenience for management. Thus we combine the factor of the administrative
area with the first standard, and generate an improved model resulting in the
new diagram in which the perimeters of the districts are along the boundaries
of some current counties. Moreover, the gerrymandering should consider the
geographic features.The third standard is introduced to describe this
situation. Finally, it can be proved that the difference between the supporting
ratio of a certain party in each district and the average supporting ratio of
that particular party in the whole state obeys the Chi-square distribution
approximately. Consequently, we can obtain an archetypal formula to check
whether the gerrymandering we propose is fair.


title: Background Field Equations for the Duality Symmetric String

abstract:
  This paper describes the background field equations for strings in T-duality
symmetric formalisms in which the dimension of target space is doubled and the
sigma model supplemented with constraints. These are calculated by demanding
the vanishing of the beta-functional of the sigma model couplings in the
doubled target space. We demonstrate the equivalence with the background field
equations of the standard string sigma model.


title: Tropical fans and the moduli spaces of tropical curves

abstract:
  We give a rigorous definition of tropical fans (the "local building blocks
for tropical varieties") and their morphisms. For such a morphism of tropical
fans of the same dimension we show that the number of inverse images (counted
with suitable tropical multiplicities) of a point in the target does not depend
on the chosen point - a statement that can be viewed as the beginning of a
tropical intersection theory. As an application we consider the moduli spaces
of rational tropical curves (both abstract and in some R^r) together with the
evaluation and forgetful morphisms. Using our results this gives new, easy, and
unified proofs of various tropical independence statements, e.g. of the fact
that the numbers of rational tropical curves (in any R^r) through given points
are independent of the points.


title: Quasi-periodic stability of normally resonant tori

abstract:
  We study quasi-periodic tori under a normal-internal resonance, possibly with
multiple eigenvalues. Two non-degeneracy conditions play a role. The first of
these generalizes invertibility of the Floquet matrix and prevents drift of the
lower dimensional torus. The second condition involves a Kolmogorov-like
variation of the internal frequencies and simultaneously versality of the
Floquet matrix unfolding. We focus on the reversible setting, but our results
carry over to the Hamiltonian and dissipative contexts.


title: Capacity of the Degraded Half-Duplex Relay Channel

abstract:
  A discrete memoryless half-duplex relay channel is constructed from a
broadcast channel from the source to the relay and destination and a multiple
access channel from the source and relay to the destination. When the relay
listens, the channel operates in the broadcast mode. The channel switches to
the multiple access mode when the relay transmits. If the broadcast component
channel is physically degraded, the half-duplex relay channel will also be
referred to as physically degraded. The capacity of this degraded half-duplex
relay channel is examined. It is shown that the block Markov coding suggested
in the seminal paper by Cover and El Gamal can be modified to achieve capacity
for the degraded half-duplex relay channel. In the code construction, the
listen-transmit schedule of the relay is made to depend on the message to be
sent and hence the schedule carries information itself. If the schedule is
restricted to be deterministic, it is shown that the capacity can be achieved
by a simple management of information flows across the broadcast and multiple
access component channels.


title:
Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the
  equation d/dx(pdu/dx)+qu=0

abstract:
  We give a simple solution of the equation d/dx(pdu/dx)+qu=cu whenever a
nontrivial solution of d/dx(pdu/dx)+qu=0 is known. The method developed for
obtaining this result is based on the theory of pseudoanalytic functions and
their relationship with solutions of the stationary two-dimensional Schrodinger
equation. The final result, that is the formula for the general solution of the
equation d/dx(pdu/dx)+qu=cu has a simple and easily verifiable form.


title: Reflecting magnons

abstract:
  We study the worldsheet reflection matrix of a string attached to a D-brane
in $AdS_5 \times S^5$. The D-brane corresponds to a maximal giant graviton and
it wraps an $S^3$ inside $S^5$. In the gauge theory, the open string is
described by a spin chain with boundaries. We study an open string with a large
SO(6) charge, which allows us to focus on one boundary at a time and to define
an asymptotic boundary reflection matrix. We consider two cases corresponding
to two possible relative orientations for the charges of the giant graviton and
the open string. Using the symmetries of the problem we compute the boundary
reflection matrix up to a phase. These matrices obey the boundary Yang Baxter
equation. A crossing equation is derived for the overall phase. We perform weak
coupling computations up to two loops and obtain results that are consistent
with integrability. Finally, we determine the phase factor at strong coupling
using classical solutions.


title:
Opportunism in Multiuser Relay Channels: Scheduling, Routing and
  Spectrum Reuse

abstract:
  In order to understand the key merits of multiuser diversity techniques in
relay-assisted cellular multihop networks, this paper analyzes the spectral
efficiency of opportunistic (i.e., channel-aware) scheduling algorithms over a
fading multiuser relay channel with $K$ users in the asymptotic regime of large
(but finite) number of users. Using tools from extreme-value theory, we
characterize the limiting distribution of spectral efficiency focusing on Type
I convergence and utilize it in investigating the large system behavior of the
multiuser relay channel as a function of the number of users and physical
channel signal-to-noise ratios (SNRs). Our analysis results in very accurate
formulas in the large (but finite) $K$ regime, provides insights on the
potential performance enhancements from multihop routing and spectrum reuse
policies in the presence of multiuser diversity gains from opportunistic
scheduling and helps to identify the regimes and conditions in which
relay-assisted multiuser communication provides a clear advantage over direct
multiuser communication.


title: The first rotation periods in Praesepe

abstract:
  The cluster Praesepe (age 650 Myr) is an ideal laboratory to study stellar
evolution. Specifically, it allows us to trace the long-term decline of
rotation and activity on the main-sequence. Here we present rotation periods
measured for five stars in Praesepe with masses of 0.1-0.5Ms -- the first
rotation periods for members of this cluster. Photometric periodicities were
found from two extensive monitoring campaigns, and are confirmed by multiple
independent test procedures. We attribute these variations to magnetic spots
co-rotating with the objects, thus indicating the rotation period. The five
periods, ranging from 5 to 84h, show a clear positive correlation with object
mass, a trend which has been reported previously in younger clusters. When
comparing with data for F-K stars in the coeval Hyades, we find a dramatic drop
in the periods at spectral type K8-M2 (corresponding to 0.4-0.6Ms). A
comparison with periods of VLM stars in younger clusters provides a constraint
on the spin-down timescale: We find that the exponential rotational braking
timescale is clearly longer than 200 Myr, most likely 400-800 Myr. These
results are not affected by the small sample size in the rotation periods. Both
findings, the steep drop in the period-mass relation and the long spin-down
timescale, indicate a substantial change in the angular momentum loss mechanism
for very low mass objects, possibly the breakdown of the solar-type (Skumanich)
rotational braking. While the physical origin for this behaviour is unclear, we
argue that parts of it might be explained by the disappearance of the radiative
core and the resulting breakdown of an interface-type dynamo in the VLM regime.
Rotational studies in this mass range hold great potential to probe magnetic
properties and interior structure of main-sequence stars.


title:
Completeness of the classical 2D Ising model and universal quantum
  computation

abstract:
  We prove that the 2D Ising model is complete in the sense that the partition
function of any classical q-state spin model (on an arbitrary graph) can be
expressed as a special instance of the partition function of a 2D Ising model
with complex inhomogeneous couplings and external fields. In the case where the
original model is an Ising or Potts-type model, we find that the corresponding
2D square lattice requires only polynomially more spins w.r.t the original one,
and we give a constructive method to map such models to the 2D Ising model. For
more general models the overhead in system size may be exponential. The results
are established by connecting classical spin models with measurement-based
quantum computation and invoking the universality of the 2D cluster states.


title: Heterotic twistor-string theory

abstract:
  We reformulate twistor-string theory as a heterotic string based on a twisted
(0,2) model. The path integral localizes on holomorphic maps, while the (0,2)
moduli naturally correspond to the states of N=4 super Yang-Mills and conformal
supergravity under the Penrose transform. We show how the standard
twistor-string formulae of scattering amplitudes as integrals over the space of
curves in supertwistor space may be obtained from our model. The corresponding
string field theory gives rise to a twistor action for N=4 conformal
supergravity coupled to super Yang-Mills. The model helps to explain how the
twistor-strings of Witten and Berkovits are related and clarifies various
aspects of each of these models.


title:
A Chandra Observation of Abell 13: Investigating the Origin of the Radio
  Relic

abstract:
  We present results from the Chandra X-ray observation of Abell 13, a galaxy
cluster that contains an unusual noncentral radio source, also known as a radio
relic. This is the first pointed X-ray observation of Abell 13, providing a
more sensitive study of the properties of the X-ray gas. The X-ray emission
from Abell 13 is extended to the northwest of the X-ray peak and shows
substructure indicative of a recent merger event. The cluster X-ray emission is
centered on the bright galaxy H of Slee et al. 2001. We find no evidence for a
cooling flow in the cluster. A knot of excess X-ray emission is coincident with
the other bright elliptical galaxy F. This knot of emission has properties
similar to the enhanced emission associated with the large galaxies in the Coma
cluster.
  With these Chandra data we are able to compare the properties of the hot
X-ray gas with those of the radio relic from VLA data, to study the interaction
of the X-ray gas with the radio emitting electrons. Our results suggest that
the radio relic is associated with cooler gas in the cluster. We suggest two
explanations for the coincidence of the cooler gas and radio source. First, the
gas may have been uplifted by the radio relic from the cluster core.
Alternatively, the relic and cool gas may have been displaced from the central
galaxy during the cluster merger event.


title:
Weighted hyperprojective spaces and homotopy invariance in orbifold
  cohomology

abstract:
  We show that Chen-Ruan cohomology is a homotopy invariant in certain cases.
We introduce the notion of a T-representation homotopy, which is a stringent
form of homotopy under which Chen-Ruan cohomology is invariant. We show that
while hyperkahler quotients of the cotangent bundle to a complex vector space
by a circle S^1 (here termed weighted hyperprojective spaces) are homotopy
equivalent to weighted projective spaces, they are not S^1-representation
homotopic. Indeed, we show that their Chen-Ruan cohomology rings (over the
rationals) are distinct.


title:
Relating gravitational wave constraints from primordial nucleosynthesis,
  pulsar timing, laser interferometers, and the CMB: implications for the early
  universe

abstract:
  We derive a general master equation relating the gravitational-wave
observables r and Omega_gw(f). Here r is the tensor-to-scalar ratio,
constrained by cosmic-microwave-background (CMB) experiments; and Omega_gw(f)
is the energy spectrum of primordial gravitational-waves, constrained e.g. by
pulsar-timing measurements, laser-interferometer experiments, and Big Bang
Nucleosynthesis (BBN). Differentiating the master equation yields a new
expression for the tilt d(ln Omega_gw(f))/d(ln f). The relationship between r
and Omega_gw(f) depends sensitively on the uncertain physics of the early
universe, and we show that this uncertainty may be encapsulated (in a
model-independent way) by two quantities: w_hat(f) and nt_hat(f), where
nt_hat(f) is a certain logarithmic average over nt(k) (the primordial tensor
spectral index); and w_hat(f) is a certain logarithmic average over w_tilde(a)
(the effective equation-of-state in the early universe, after horizon
re-entry). Here the effective equation-of-state parameter w_tilde(a) is a
combination of the ordinary equation-of-state parameter w(a) and the bulk
viscosity zeta(a). Thus, by comparing constraints on r and Omega_gw(f), one can
obtain (remarkably tight) constraints in the [w_hat(f), nt_hat(f)] plane. In
particular, this is the best way to constrain (or detect) the presence of a
``stiff'' energy component (with w > 1/3) in the early universe, prior to BBN.
Finally, although most of our analysis does not assume inflation, we point out
that if CMB experiments detect a non-zero value for r, then we will immediately
obtain (as a free by-product) a new upper bound w_hat < 0.55 on the
logarithmically averaged effective equation-of-state parameter during the
``primordial dark age'' between the end of inflation and the start of BBN.


title:
Minimal Number of Generators and Minimum Order of a Non-Abelian Group
  whose Elements Commute with Their Endomorphic Images

abstract:
  A group in which every element commutes with its endomorphic images is called
an $E$-group. If $p$ is a prime number, a $p$-group $G$ which is an $E$-group
is called a $pE$-group. Every abelian group is obviously an $E$-group. We prove
that every 2-generator $E$-group is abelian and that all 3-generator $E$-groups
are nilpotent of class at most 2. It is also proved that every infinite
3-generator $E$-group is abelian. We conjecture that every finite 3-generator
$E$-group should be abelian. Moreover we show that the minimum order of a
non-abelian $pE$-group is $p^8$ for any odd prime number $p$ and this order is
$2^7$ for $p=2$. Some of these results are proved for a class wider than the
class of $E$-groups.


title: A lower bound for the number of conjugacy classes of finite groups

abstract:
  In 2000, L. H\'{e}thelyi and B. K\"{u}lshammer proved that if $p$ is a prime
number dividing the order of a finite solvable group $G$, then $G$ has at least
$2\sqrt{p-1}$ conjugacy classes. In this paper we show that if $p$ is large,
the result remains true for arbitrary finite groups.


title: Minimal blocking sets in PG(n,2) and covering groups by subgroups

abstract:
  In this paper we prove that a set of points $B$ of PG(n,2) is a minimal
blocking set if and only if $<B>=PG(d,2)$ with $d$ odd and $B$ is a set of
$d+2$ points of $PG(d,2)$ no $d+1$ of them in the same hyperplane. As a
corollary to the latter result we show that if $G$ is a finite 2-group and $n$
is a positive integer, then $G$ admits a $\mathfrak{C}_{n+1}$-cover if and only
if $n$ is even and $G\cong (C_2)^{n}$, where by a $\mathfrak{C}_m$-cover for a
group $H$ we mean a set $\mathcal{C}$ of size $m$ of maximal subgroups of $H$
whose set-theoretic union is the whole $H$ and no proper subset of
$\mathcal{C}$ has the latter property and the intersection of the maximal
subgroups is core-free. Also for all $n<10$ we find all pairs $(m,p)$ ($m>0$ an
integer and $p$ a prime number) for which there is a blocking set $B$ of size
$n$ in $PG(m,p)$ such that $<B>=PG(m,p)$.


title: On quasi-Baer rings of Ore extensions

abstract:
  Let $R$ be a ring and $S=R[x;\sigma,\delta]$ its Ore extension. We prove
under some conditions that $R$ is a quasi-Baer ring if and only if the Ore
extension $R[x;\sigma,\delta]$ is a quasi-Baer ring. Examples are provided to
illustrate and delimit our results.


title: The Role of MHD in the ICM and its Interactions with AGN Outflows

abstract:
  Magnetic fields probably play a central role in the dynamics and
thermodynamics of ICMs and their interactions with AGNs, despite the fact that
the fields usually contribute relatively little pressure; i.e., the ICM is a
``high-$\beta$'' plasma. More typically, the roles of magnetic fields come
through ``microscopic'' influences on charged particle behaviors, and through
magnetic tension, which can still be significant in subsonic, high-$\beta$
flows. I briefly review these issues, while exploring the underlying question
of using the commonly-applied magnetohydrodynamics model in the ICM when
Coulomb scattering mean free paths can sometimes exceed tens of kiloparsecs.


title: Mapping an Island in the Landscape

abstract:
  We provide a complete classification and statistical analysis of all type IIA
orientifold compactifications with intersecting D6-branes on the orbifold
T^6/Z'_6. The total number of four dimensional N=1 supersymmetric models is
found to be O(10^23). After a statistical analysis of the gauge sector
properties of all possible solutions, we study three subsets of configurations
which contain the chiral matter sector of the standard model, a Pati-Salam or
SU(5) GUT model, respectively. We find O(10^15) compactifications with an MSSM
and O(10^11) models with a Pati-Salam sector. Along the way we derive an
explicit algebraic formulation for the computation of the non-chiral matter
spectrum for all Z_N orbifolds.


title:
Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields
  in Dipolar Spin Glasses with Strong Single-Ion Anisotropy

abstract:
  We present analytical and numerical evidence for the validity of an effective
S=1/2 approach to the description of random field generation in S>=1, and
especially in an S=1, dipolar spin glass models with strong uniaxial Ising
anisotropy and subject to weak external magnetic field Bx transverse to the
Ising direction. Explicitely Bx-dependent random fields are shown to naturally
emerge in the effective low-energy description of a microscopic S=1 toy model.
We discuss our results in relation to recent theoretical studies pertaining to
the topic of Bx-induced random fields in the LiHo$_x$Y$_{1-x}$F$_4$ magnetic
materials with the Ho$^{3+}$ Ising moments subject to a transverse field. We
show that the S_{eff}=1/2 approach is able to capture both the qualitative and
quantitative aspects of the physics at small Bx, giving results that agree with
those obtained using conventional second order perturbation theory.


title: Q7-branes and their coupling to IIB supergravity

abstract:
  We show how, by making use of a new basis of the IIB supergravity
axion-dilaton coset, SL(2,R)/SO(2), 7-branes that belong to different conjugacy
classes of the duality group SL(2,R) naturally couple to IIB supergravity with
appropriate source terms characterized by an SL(2,R) charge matrix Q. The
conjugacy classes are determined by the value of the determinant of Q. The
(p,q) 7-branes are the branes in the conjugacy class detQ = 0. The 7-branes in
the conjugacy class detQ > 0 are labelled by three numbers (p,q,r) which
parameterize the matrix Q and will be called Q7-branes. We construct the full
bosonic Wess--Zumino term for the Q7-branes. In order to realize a gauge
invariant coupling of the Q7-brane to the gauge fields of IIB supergravity it
is necessary to introduce an SL(2,R) doublet of two distinct Born--Infeld
fields on the Q7-brane world-volume.


title: Scalar Trefoils

abstract:
  The knot model is extended by assuming that the trefoils are realized as
either chiral fermions or as scalar bosons. There are then four scalar trefoils
with electric charges (0, -1,2/3,-1/3) that may be classified in the same way
as the chiral fermions: as two isotopic doublets where the two doublets have
different hypercharge and the two members of the doublets have different t_3.
Only the neutral scalar plays the role of the standard Higgs in fixing the mass
ratios of the vector bosons, wile the charged scalars, in addition to having
the usual electromagnetic interactions of scalar particles, fix the mass
spectrum of the fermions. The extended model would suggest a search for the
charged scalars.


title:
Definitive Evidence of Interlayer Coupling Between (Ga,Mn)As Layers
  Separated by a Nonmagnetic Spacer

abstract:
  We have used polarized neutron reflectometry to study the structural and
magnetic properties of the individual layers in a series of
(Al,Be,Ga)As/(Ga,Mn)As/GaAs/(Ga,Mn)As multilayer samples. Structurally, we
observe that the samples are virtually identical except for the GaAs spacer
thickness (which varies from 3-12 nm), and confirm that the spacers contain
little or no Mn. Magnetically, we observe that for the sample with the thickest
spacer layer, modulation doping by the(Al,Be,Ga)As results in (Ga,Mn)As layers
with very different temperature dependent magnetizations. However, as the
spacer layer thickness is reduced, the temperature dependent magnetizations of
the top an bottom (Ga,Mn)As layers become progressively more similar - a trend
we find to be independent of the crystallographic direction along which spins
are magnetized. These results definitively show that (Ga,Mn)As layers can
couple across a non-magnetic spacer, and that such coupling depends on spacer
thickness.


title: MASA's and certain type I closed faces of C*-algebras

abstract:
  A result of Akemann, Anderson, and Pedersen states that if a sequence of pure
states of a C*-algebra A approaches infinity in a certain sense, then there is
a MASA B such that each of the states has the unique extension property with
respect to B. We generalize this in two ways: We prove that B can be required
to contain an approximate identity of A, and we show that the discrete space
which underlies the result cited can be replaced with a totally disconnected
space.
  We consider two special kinds of type I closed faces, both related to the
above, atomic closed faces and closed faces with nearly closed extreme
boundary. One specific question is whether an atomic closed face always has an
"isolated point". We give a counterexample for this and also show that the
answer is yes if the the atomic face has nearly closed extreme boundary.
  We prove a complement to Glimm's theorem on type I C*-algebras which arises
from the theory of type I closed faces. One of our examples is a type I closed
face which is isomorphic to a closed face of every non-type I separable
C*-algebra and which is not isomorphic to a closed face of any type I
C*-algebra.


title: The WEBT Campaign on the Blazar 3C279 in 2006

abstract:
  The quasar 3C279 was the target of an extensive multiwavelength monitoring
campaign from January through April 2006, including an optical-IR-radio
monitoring campaign by the Whole Earth Blazar Telescope (WEBT) collaboration.
In this paper we focus on the results of the WEBT campaign. The source
exhibited substantial variability of optical flux and spectral shape, with a
characteristic time scale of a few days. The variability patterns throughout
the optical BVRI bands were very closely correlated with each other. In
intriguing contrast to other (in particular, BL Lac type) blazars, we find a
lag of shorter- behind longer-wavelength variability throughout the RVB ranges,
with a time delay increasing with increasing frequency. Spectral hardening
during flares appears delayed with respect to a rising optical flux. This, in
combination with the very steep IR-optical continuum spectral index of ~ 1.5 -
2.0, may indicate a highly oblique magnetic field configuration near the base
of the jet. An alternative explanation through a slow (time scale of several
days) acceleration mechanism would require an unusually low magnetic field of <
0.2 G, about an order of magnitude lower than inferred from previous analyses
of simultaneous SEDs of 3C279 and other FSRQs with similar properties.


title: Multiscale Analysis and Localization of Random Operators

abstract:
  A discussion of the method of multiscale analysis in the study of
localization of random operators based on lectures given at \emph{Random
Schr\"odinger operators: methods, results, and perspectives}, \'Etats de la
recherche, Universit\'e Paris 13, June 2002


title: Localization for a continuum Cantor-Anderson Hamiltonian

abstract:
  We prove localization at the bottom of the spectrum for a random
Schr\"odinger operator in the continuum with a single-site potential
probability distribution supported by a Cantor set of zero Lebesgue measure.
This distribution is too singular to be treated by the usual methods. In
particular, an "a priori" Wegner estimate is not available. To prove the result
we perform a multiscale analysis following the work of Bourgain and Kenig for
the Bernoulli-Anderson Hamiltonian, and obtain the required Wegner estimate
scale by scale. To do so, we generalize their argument based on Sperner's Lemma
by resorting to the LYM inequality for multisets, and combine it with the
concept of scale dependent equivalent classes of configurations introduced by
Germinet, Hislop and Klein for the study of Poisson Hamiltonians.


title: A probabilistic regulatory network for the human immune system

abstract:
  In this paper we made a review of some papers about probabilistic regulatory
networks (PRN), in particular we introduce our concept of homomorphisms of PRN
with an example of projection of a regulatory network to a smaller one. We
apply the model PRN (or Probabilistic Boolean Network) to the immune system,
the PRN works with two functions. The model called ""The B/T-cells
interaction"" is Boolean, so we are really working with a Probabilistic Boolean
Network. Using Markov Chains we determine the state of equilibrium of the
immune response.


title: Product-free subsets of groups, then and now

abstract:
  A subset of a group is product-free if it does not contain elements a, b, c
such that ab = c. We review progress on the problem of determining the size of
the largest product-free subset of an arbitrary finite group, including a lower
bound due to the author, and a recent upper bound due to Gowers. The bound of
Gowers is more general; it allows three different sets A, B, C such that one
cannot solve ab = c with a in A, b in B, c in C. We exhibit a refinement of the
lower bound construction which shows that for this broader question, the bound
of Gowers is essentially optimal.


title:
Linking Jet Emission, X-ray States and Hard X-ray Tails in the Neutron
  Star X-ray Binary GX 17+2

abstract:
  We present the results from simultaneous radio (Very Large Array) and X-ray
(Rossi-X-ray Timing Explorer) observations of the Z-type neutron star X-ray
binary GX~17+2. The aim is to assess the coupling between X-ray and radio
properties throughout its three rapidly variable X-ray states and during the
time-resolved transitions. These observations allow us, for the first time, to
investigate quantitatively the possible relations between the radio emission
and the presence of the hard X-ray tails and the X-ray state of the source. The
observations show: 1) a coupling between the radio jet emission and the X-ray
state of the source, i.e. the position in the X-ray hardness-intensity diagram
(HID); 2) a coupling between the presence of a hard X-ray tail and the position
in the HID, qualitatively similar to that found for the radio emission; 3) an
indication for a quantitative positive correlation between the radio flux
density and the X-ray flux in the hard-tail power law component; 4) evidence
for the formation of a radio jet associated with the Flaring Branch-to-Normal
Branch X-ray state transition; 5) that the radio flux density of the
newly-formed jet stabilizes when also the normal-branch oscillation (NBO) in
the X-ray power spectrum stabilizes its characteristic frequency, suggesting a
possible relation between X-ray variability associated to the NBO and the jet
formation. We discuss our results in the context of jet models.


title:
Densities, Parton Distributions, and Measuring the Non-Spherical Shape
  of the Nucleon

abstract:
  Spin-dependent quark densities, matrix elements of specific density operators
in proton states of definite spin-polarization, indicate that the nucleon may
harbor an infinite variety of non-spherical shapes. We show that these matrix
elements are closely related to specific transverse momentum dependent parton
distributions accessible in the angular dependence of the semi-inclusive
processes electron plus proton goes to electron plus pion plus anything, and
the Drell-Yan reaction proton plus proton goes to a lepton anti-lepton pair
plus anything. New measurements or analyses would allow the direct exhibition
of the non-spherical nature of the proton.


title:
The Number of Different Binary Functions Generated by NK-Kauffman
  Networks and the Emergence of Genetic Robustness

abstract:
  We determine the average number $ \vartheta (N, K) $, of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for $ N \gg
1 $, there exists a connectivity critical value $ K_c $ such that $
\vartheta(N,K) \approx e^{\phi N} $ ($ \phi > 0 $) for $ K < K_c $ and
$\vartheta(N,K) \approx 1 $ for $ K > K_c $. We find that $ K_c $ is not a
constant, but scales very slowly with $ N $, as $ K_c \approx \log_2 \log_2 (2N
/ \ln 2) $. The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.


title:
Global well-posedness for the radial defocusing cubic wave equation on
  $\mathbb{R}^{3}$ and for rough data

abstract:
  We prove global well-posedness for the $3D$ radial defocusing cubic wave
equation with data in $H^{s} \times H^{s-1}$, $1>s>{7/10}$.


title: Observation of Ferromagnetic Clusters in Bi0.125Ca0.875MnO3

abstract:
  The electron doped manganite system, Bi0.125Ca0.875MnO3, exhibits large bulk
magnetization of unknown origin. To select amongst possible magnetic ordering
models, we have conducted temperature and magnetic field dependent small-angle
neutron scattering measurements. Nontrivial spin structure has been revealed.
Ferromagnetic spin clusters form in the antiferromagnetic background when
temperature is decreased to Tc~108K. With a further reduction in temperature or
the application of external magnetic field, the clusters begin to form in
larger numbers, which gives an overall enhancement of magnetization below Tc.


title:
Ti-rich and Cu-poor grain-boundary layers of CaCu$_3$Ti$_4$O$_{12}$
  detected by x-ray photoelectron spectroscopy

abstract:
  Cleaved and polished surfaces of CaCu$_3$Ti$_4$O$_{12}$ ceramics have been
investigated by x-ray photoelectron spectroscopy (XPS) and energy dispersive
x-ray spectroscopy (EDX), respectively. While EDX technique shows the identical
CaCu$_3$Ti$_4$O$_{12}$ stoichiometry for the two surfaces, XPS indicates that
the cleaved surface with grain-boundary layers is remarkably Ti-rich and
Cu-poor. The core-level spectrum of Cu 2$p$ unambiguously shows the existence
of monovalent copper only for the cleaved surface. Possible grain-boundary
structure and its formation are discussed.


title: Nondestructive interaction-free atom-photon controlled-NOT gate

abstract:
  We present a probabilistic (ideally 50%) nondestructive interaction-free
atom-photon controlled-NOT gate, where nondestructive means that all four
outgoing target photon modes of the gate are available and feed-forwardable.
Individual atoms are controlled by a stimulated Raman adiabatic passage
transition and photons by a ring resonator with two outgoing ports. Realistic
estimates we obtain for ions confined in a Paul trap around which the resonator
is mounted show that a strong atom-photon coupling can be achieved. It is also
shown how the resonator can be used for controlling superposition of atom
states.


title: Compositional Semantics Grounded in Commonsense Metaphysics

abstract:
  We argue for a compositional semantics grounded in a strongly typed ontology
that reflects our commonsense view of the world and the way we talk about it in
ordinary language. Assuming the existence of such a structure, we show that the
semantics of various natural language phenomena may become nearly trivial.


title: Inverse problems for linear forms over finite sets of integers

abstract:
  Let f(x_1,x_2,...,x_m) = u_1x_1+u_2 x_2+... + u_mx_m be a linear form with
positive integer coefficients, and let N_f(k) = min{|f(A)| : A \subseteq Z and
|A|=k}. A minimizing k-set for f is a set A such that |A|=k and |f(A)| =
N_f(k). A finite sequence (u_1, u_2,...,u_m) of positive integers is called
complete if {\sum_{j\in J} u_j : J \subseteq {1,2,..,m}} = {0,1,2,..., U},
where $U = \sum_{j=1}^m u_j.$ It is proved that if f is an m-ary linear form
whose coefficient sequence (u_1,...,u_m) is complete, then N_f(k) = Uk-U+1 and
the minimizing k-sets are precisely the arithmetic progressions of length k.
Other extremal results on linear forms over finite sets of integers are
obtained.


title: Abnormal Electronic Transport in Disordered Graphene Nanoribbon

abstract:
  We investigate the conductivity $\sigma$ of graphene nanoribbons with zigzag
edges as a function of Fermi energy $E_F$ in the presence of the impurities
with different potential range. The dependence of $\sigma(E_F)$ displays four
different types of behavior, classified to different regimes of length scales
decided by the impurity potential range and its density. Particularly, low
density of long range impurities results in an extremely low conductance
compared to the ballistic value, a linear dependence of $\sigma(E_F)$ and a
wide dip near the Dirac point, due to the special properties of long range
potential and edge states. These behaviors agree well with the results from a
recent experiment by Miao \emph{et al.} (to appear in Science).


title: Effects of impurities on Tamm-like lanthanide-metal surface states

abstract:
  The effects of isolated residual-gas adsorbates on the local electronic
structure of the Dy(0001) surface were spatially mapped by scanning tunneling
microscopy and spectroscopy at 12 K. Less than 15 A away from an adsorbate, a
strong reduction of the intensity and a significant increase of the width of
the majority component of the surface state due to impurity scattering were
observed, with essentially no change of the minority component; this reflects a
high lateral localization of the Tamm-like surface state. Furthermore, an
adsorbate-induced state was found that behaves metastable.


title: Small value estimates for the additive group

abstract:
  We generalize Gel'fond's criterion of algebraic independence to the context
of a sequence of polynomials whose first derivatives take small values on large
subsets of a fixed subgroup of the additive group of complex numbers, instead
of just one point. We also provide one extension dealing with a subgroup of the
multiplicative group of non-zero complex numbers.


title: Intermittent dynamics and 1/f^beta noise in single cardiac muscle cells

abstract:
  Fluctuations in the spontaneous beating activity of isolated cardiac cells
were studied over a timescale of six decades. The beat dynamics of single
cardiac cells were heterogeneous and intermittent. The interbeat intervals
(IBIs) were power-law distributed in a long-time regime. Furthermore, for long
timescales up to the experimental window, the autocorrelation of IBIs exhibits
a scaling behavior of 1/f^beta-noise type. These observations suggest that
1/f^beta noise is an intrinsic characteristic of spontaneous activity of single
cardiac cells.


title: On Compact Routing for the Internet

abstract:
  While there exist compact routing schemes designed for grids, trees, and
Internet-like topologies that offer routing tables of sizes that scale
logarithmically with the network size, we demonstrate in this paper that in
view of recent results in compact routing research, such logarithmic scaling on
Internet-like topologies is fundamentally impossible in the presence of
topology dynamics or topology-independent (flat) addressing. We use analytic
arguments to show that the number of routing control messages per topology
change cannot scale better than linearly on Internet-like topologies. We also
employ simulations to confirm that logarithmic routing table size scaling gets
broken by topology-independent addressing, a cornerstone of popular
locator-identifier split proposals aiming at improving routing scaling in the
presence of network topology dynamics or host mobility. These pessimistic
findings lead us to the conclusion that a fundamental re-examination of
assumptions behind routing models and abstractions is needed in order to find a
routing architecture that would be able to scale ``indefinitely.''


title: Benefiting from Disorder: Source Coding for Unordered Data

abstract:
  The order of letters is not always relevant in a communication task. This
paper discusses the implications of order irrelevance on source coding,
presenting results in several major branches of source coding theory: lossless
coding, universal lossless coding, rate-distortion, high-rate quantization, and
universal lossy coding. The main conclusions demonstrate that there is a
significant rate savings when order is irrelevant. In particular, lossless
coding of n letters from a finite alphabet requires Theta(log n) bits and
universal lossless coding requires n + o(n) bits for many countable alphabet
sources. However, there are no universal schemes that can drive a strong
redundancy measure to zero. Results for lossy coding include distribution-free
expressions for the rate savings from order irrelevance in various high-rate
quantization schemes. Rate-distortion bounds are given, and it is shown that
the analogue of the Shannon lower bound is loose at all finite rates.


title: Phase Transition Dynamics and Its Alpha' Corrections

abstract:
  We study the dynamics of the first order phase transition in the holographic
hard wall model, namely, Polchinski-Strassler's model and come to the
conclusion that the phase transition is incomplete in large N limit with the
natural boundary condition. We also consider the string length corrections to
both hard wall model and Witten's model, and find that the interesting
transition configuration is preserved under the alpha' corrections.


title: Markov bases for two-way subtable sum problems

abstract:
  It has been well-known that for two-way contingency tables with fixed row
sums and column sums the set of square-free moves of degree two forms a Markov
basis. However when we impose an additional constraint that the sum of a
subtable is also fixed, then these moves do not necessarily form a Markov
basis. Thus, in this paper, we show a necessary and sufficient condition on a
subtable so that the set of square-free moves of degree two forms a Markov
basis.


title:
Comparative study of electron and hole doped High-Tc compounds in
  pseudogap regime: LDA+DMFT+Sk approach

abstract:
  Pseudogap regime for the prototype high-Tc compounds hole doped
Bi2Sr2CaCu2O8-x (Bi2212) and electron doped Nd2-xCexCuO4 (NCCO) is described by
means of novel generalized LDA+DMFT+Sk approach. Here conventional dynamical
mean-field theory (DMFT) equations are supplied with additional (momentum
dependent) self-energy Sk. In the present case Sk describes non-local dynamical
correlations induced by short-ranged collective Heisenberg-like
antiferromagnetic spin fluctuations. Material specific model parameters of two
neighboring CuO2 layers of Bi2212 and single CuO2 layer of NCCO were obtained
within local density approximation (LDA) and constrained LDA method. We show
that Fermi surface in presence of the pseudogap fluctuations have perfectly
visible "hot-spots" for NCCO while in Bi2212 there is just rather broad region
with strong antiferromagnetic scattering. Results obtained are in good
agreement with recent ARPES and optical experiments.


title:
Spectacular Trailing Streamers near LMC X-1: The First Evidence of a
  Jet?

abstract:
  We report VIMOS integral field spectroscopy of the N159F nebula surrounding
LMC X-1. Our observations reveal a rich, extended system of emission line
filaments lining the boundary of a large conical cavity identified in Spitzer
mid-IR imaging. We find that X-ray photoionization cannot be solely responsible
for the observed ionization structure of N159F. We propose that the extended
filamentary emission is produced primarily by ionization from a shock driven by
a presently unobserved jet from LMC X-1. We infer a shock velocity of v_s ~ 90
km/s and conclude that the jet responsible for the bow shock is presently
undetected because it has switched off, rather than because it has a low
surface brightness. This interpretation is consistent with the present soft
X-ray spectral state of LMC X-1 and suggests the jet is intermittent.


title: Conformal representations of Leibniz algebras

abstract:
  In this note we present a more detailed and explicit exposition of the
definition of a conformal representation of a Leibniz algebra. Recall
(arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The
idea is based on the general fact that every dialgebra that belongs to a
variety $\Var $ can be embedded into a conformal algebra of the same variety.
In particular, we prove that an arbitrary (finite dimensional) Leibniz algebra
has a (finite) faithful conformal representation. As a corollary, we deduce the
analogue of the PBW-theorem for Leibniz algebras.


title: Generalized rational blow-down, torus knots, and Euclidean algorithm

abstract:
  We construct a Kirby diagram of the rational homology ball used in
"generalized rational blow-down" developed by Jongil Park. The diagram consists
of a dotted circle and a torus knot. The link is simpler, but the parameters
are a little complicate. Euclidean Algorithm is used three times in the
construction and the proof.


title:
Effects of nuclear molecular configurations on the astrophysical
  S-factor for $^{16}$O + $^{16}$O

abstract:
  The impact of nuclear molecular configurations on the astrophysical S-factor
for $^{16}$O + $^{16}$O is investigated within the realistic two-center shell
model based on Woods-Saxon potentials. These molecular effects refer to the
formation of a neck between the interacting nuclei and the radial dependent
collective mass parameter. It is demonstrated that the former is crucial to
explain the current experimental data with high accuracy and without any free
parameter, whilst in addition the latter predicts a pronounced maximum in the
S-factor. In contrast to very recent results by Jiang et al., the S-factor does
not decline towards extremely low values as energy decreases.


title:
Electronic structures of hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin
  films

abstract:
  We investigated the electronic structure of multiferroic hexagonal RMnO3 (R =
Gd, Tb, Dy, and Ho) thin films using both optical spectroscopy and
first-principles calculations. Using artificially stabilized hexagonal RMnO3,
we extended the optical spectroscopic studies on the hexagonal multiferroic
manganite system. We observed two optical transitions located near 1.7 eV and
2.3 eV, in addition to the predominant absorption above 5 eV. With the help of
first-principles calculations, we attribute the low-lying optical absorption
peaks to inter-site transitions from the oxygen states hybridized strongly with
different Mn orbital symmetries to the Mn 3d3z2-r2 state. As the ionic radius
of the rare earth ion increased, the lowest peak showed a systematic increase
in its peak position. We explained this systematic change in terms of a
flattening of the MnO5 triangular bipyramid.