title:
On Gravitational anomaly and Hawking radiation near weakly isolated
  horizon

abstract:
  Based on the idea of the work by Wilczek and his collaborators, we consider
the gravitational anomaly near weekly isolated horizon. We find that there
exists a universal choice of tortoise coordinate for any weakly isolated
horizon. Under this coordinate, the leading behavior of a quite arbitrary
scalar field near horizon is a 2-dimensional chiral scalar field. This means we
can extend the idea of Wilczek and his collaborators to more general cases and
show the relation between gravitational anomaly and Hawking radiation is a
universal property of black hole horizon.


title: Hall conductivity in the presence of spin-orbit interaction and disorder

abstract:
  Starting from the Kubo formula, we expand the Hall conductivity using a
cumulant approach which converges quickly at high temperatures (k_BT > energy
differences of initial and final scattering states) and can be extended to low
temperatures. The theory can deal with the sign, the ordinary and the anomalous
contributions to the Hall effect. When applied to include the spin-orbit
interaction to first order, we recover what is essentially the
Karplus-Luttinger result for the anomalous Hall effect. Contact is made to the
Chazalviel and Nozieres-Lewiner formulae. A side-jump type formula is obtained
by using an exact application of linear response. We show that there exists an
exact rigid Hall current which is not a Fermi level property. We introduce a
relationship between mass and diffusivity which allows us to generalize the
theory to strong disorder and even introduce a mobility edge. The formalism
provides a systematic and practical way of analyzing both ordinary and
anomalous contributions to the Hall conduction including the changes of sign,
and in the presence of serious disorder. As a byproduct of the method, we show
that the anomalous Hall coefficient can vary with resistance to the power n,
with 1 <= n <= 2 depending on the degree of coherence.


title: Fingered growth in channel geometry: A Loewner equation approach

abstract:
  A simple model of Laplacian growth is considered, in which the growth takes
place only at the tips of long, thin fingers. In a recent paper, Carleson and
Makarov used the deterministic Loewner equation to describe the evolution of
such a system. We extend their approach to a channel geometry and show that the
presence of the side walls has a significant influence on the evolution of the
fingers and the dynamics of the screening process, in which longer fingers
suppress the growth of the shorter ones.


title: Anisotropy in magnetic and transport properties of Fe1-xCoxSb2

abstract:
  Anisotropic magnetic and electronic transport measurements were carried out
on large single crystals of Fe1-xCoxSb2 (0<= x <=1). The semiconducting state
of FeSb2 evolves into metallic and weakly ferromagnetic by substitution of Fe
with Co for x<0.5. Further doping induces structural transformation from
orthorhombic Pnnm structure of FeSb2 to monoclinic P21/c structure of CoSb2
where semiconducting and diamagnetic ground state is restored again. Large
magnetoresistance and anisotropy in electronic transport were observed.


title:
Anisotropy in the magnetic and electrical transport properties of
  Fe1-xCrxSb2

abstract:
  We have investigated anisotropy in magnetic and electrical transport
properties of Fe1-xCrxSb2 (0<= x <=1) single crystals. The magnetic ground
state of the system evolves from paramagnetic to antiferromagnetic with gradual
substitution of Fe with Cr. Anisotropy in electrical transport diminishes with
increased Cr substitution and fades away by x=0.5. We find that the variable
range hopping (VRH) conduction mechanism dominates at low temperatures for
0.4<= x <=0.75.


title:
The planetary nebula NGC 1360, a test case of magnetic collimation and
  evolution after the fast wind

abstract:
  The central star of this nebula has an observed intense magnetic field and
the fast wind is no longer present, indicating that a back flow process has
probably developed. Long-slit, spatially resolved echelle spectra have been
obtained across the main body of NGC 1360 and over its system of bipolar jets.
Deep images of the knotty structures of the jets have also been obtained. The
data allow a detailed study of the structure and kinematics of this object and
the results are modeled considering the effects of a magnetic collimation
process in the development of the nebula and then switching off the fast
stellar wind to follow its evolution to its current state. The model is able to
successfully reproduce many of the key features of NGC 1360 under these
premises.


title: Quasi-orthogonal subalgebras of matrix algebras

abstract:
  We investigate pairwise quasi-orthogonal subalgebras in $M_{p^{kn}}$ which
are isomorphic to $M_{p^{k}}$ for $k \ge 1$, $n \ge 2$ and a prime number $p$
with $p \ge 3$. We prove there exist $p^{2kn}-1/p^{2k}-1$ such subalgebras and
they span $M_{p^{kn}}$.


title:
Colossal Positive Magnetoresistance in a Doped Nearly Magnetic
  Semiconductor

abstract:
  We report on a positive colossal magnetoresistance (MR) induced by
metallization of FeSb$_{2}$, a nearly magnetic or "Kondo" semiconductor with 3d
ions. We discuss contribution of orbital MR and quantum interference to
enhanced magnetic field response of electrical resistivity.


title:
Current-induced magnetization switching in MgO barrier magnetic tunnel
  junctions with CoFeB based synthetic ferrimagnetic free layers

abstract:
  We investigated the effect of using a synthetic ferrimagnetic (SyF) free
layer in MgO-based magnetic tunnel junctions (MTJs) on current-induced
magnetization switching (CIMS), particularly for application to spin-transfer
torque random access memory (SPRAM). The employed SyF free layer had a
Co40Fe40B20/ Ru/ Co40Fe40B20 and Co20Fe60B20/Ru/Co20Fe60B20 structures, and the
MTJs(100x(150-300) nm^2) were annealed at 300oC. The use of SyF free layer
resulted in low intrinsic critical current density (Jc0) without degrading the
thermal-stability factor (E/kBT, where E, kB, and T are the energy potential,
the Boltzmann constant, and temperature,respectively). When the two CoFeB
layers of a strongly antiferromagnetically coupled SyF free layer had the same
thickness, Jc0 was reduced to 2-4x10^6 A/cm^2. This low Jc0 may be due to the
decreased effective volume under the large spin accumulation at the CoFeB/Ru.
The E/kBT was over 60, resulting in a retention time of over ten years and
suppression of the write current dispersion for SPRAM. The use of the SyF free
layer also resulted in a bistable (parallel/antiparallel) magnetization
configuration at zero field, enabling the realization of CIMS without the need
to apply external fields to compensate for the offset field.


title: Cup products and L-values of cusp forms

abstract:
  In this note, we describe a conjecture, that, for an odd prime p, relates
special values of a cup product pairing on cyclotomic p-units in the pth
cyclotomic field to the L-values of newforms satisfying modulo p congruences
with Eisenstein series.


title: On maxima of periodograms of stationary processes

abstract:
  We consider the limit distribution of maxima of periodograms for stationary
processes. Our method is based on $m$-dependent approximation for stationary
processes and a moderate deviation result.


title:
A test of the Poincare dodecahedral space topology hypothesis with the
  WMAP CMB data

abstract:
  It has been suggested by Roukema and coworkers (hereafter R04) that the
topology of the Universe as probed by the ``matched circles'' method using the
first year release of the WMAP CMB data, might be that of the Poincar\'e
dodecahedral space (PDS) model. An excess in the correlation of the
``identified circles'' was reported by R04, for circles of angular radius of
~11 deg for a relative phase twist -36deg, hinting that this could be due to a
Clifford translation, if the hypothesized model were true.
  R04 did not however specify the statistical significance of the correlation
signal.
  We investigate the statistical significance of the signal using Monte Carlo
CMB simulations in a simply connected Universe, and present an updated analysis
using the three-year WMAP data. We find that our analyses of the first and
three year WMAP data provide results that are consistent with the simply
connected space at a confidence level as low as 68%.


title: Non-standard Schwinger fermionic representation of unitary group

abstract:
  The non-standard Schwinger fermionic representation of the unitary group is
studied by using $n$-fermion operators. One finds that the Schwinger fermionic
representation of the U(n) group is not unique when $n\ge 3$. In general, based
on $n$-fermion operators, the non-standard Schwinger fermionic representation
of the U(n) group can be established in a uniform approach, where all the
generators commute with the total number operators. The Schwinger fermionic
representation of $U(C^{m}_{n})$ group is also discussed.


title: On Galois groups of unramified pro-p extensions

abstract:
  Let p be an odd prime satisfying Vandiver's conjecture. We consider two
objects, the Galois group X of the maximal unramified abelian pro-p extension
of the compositum of all Z_p-extensions of the pth cyclotomic field and the
Galois group G of the unramified pro-p extension of the cyclotomic field of all
p-power roots of unity. We give a lower bound for the height of the annihilator
of X as an Iwasawa module. Under some mild assumptions on Bernoulli numbers, we
provide a necessary and sufficient condition for G to be abelian. The bound and
the condition in the two results are given in terms of the special values of a
cup product pairing on cyclotomic p-units. We obtain, in particular, that for p
less than 1000, Greenberg's conjecture on the pseudo-nullity of X holds and G
is in fact abelian.


title:
On the non-existence for quantum LDPC codes of type IEEE802.16e with
  rates 1/2 and 2/3B

abstract:
  In this paper, we discuss a construction of CSS codes derived from pairs of
practical irregular LDPC codes. Our design of irregular LDPC codes is based the
design written in the standardization of IEEE802.16e. Our research has tried to
make a CSS code with a pair of LDPC codes of type IEEE802.16e. To our regret,
we proved that it was impossible to construct a CSS code if one of classical
codes was of type IEEE802.16e with rate 1/2 and 2/3B. We would like to report
the discussion on its impossibility in this paper. This is the first paper to
analyze the possibility of a CSS code construction by using two irregular LDPC
codes which are practically useful.


title: A new key exchange cryptosystem

abstract:
  In this paper, we will present a new key exchange cryptosystem based on
linear algebra, which take less operations but weaker in security than
Diffie-Hellman's one.


title: Stepwise Spectral Swapping with Three Neutrino Flavors

abstract:
  We develop a framework for studying collective three-flavor neutrino
oscillations based on the density matrix formalism. We show how techniques
proven useful for collective two-flavor neutrino oscillations such as
corotating frames can be applied readily to three-flavor mixing. Applying two
simple assumptions and the conservation of two ``lepton numbers'' we use this
framework to demonstrate how the adiabatic/precession solution emerges. We
illustrate with a numerical example how two stepwise spectral swaps appear
naturally if the flavor evolution of the neutrino gas can be described by such
a solution. For the special case where mu and tau flavor neutrinos are equally
mixed and are produced with identical energy spectra and total numbers, we find
that one of the spectral swaps in the three-flavor scenario agrees with that in
the two-flavor scenario when appropriate mixing parameters are used. Using the
corotating frame technique we show how the adiabatic/precession solution can
obtain even in the presence of a dominant ordinary matter background. With this
solution we can explain why neutrino spectral swapping can be sensitive to
deviations from maximal 23-mixing when the ``mu-tau'' matter term is
significant.


title: An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$

abstract:
  The lattice $A_n^*$ is an important lattice because of its covering
properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an
algorithm to compute the nearest lattice point in $A_n^*$ that requires
$O(n\log{n})$ arithmetic operations. In this paper, we describe a new
algorithm. While the complexity is still $O(n\log{n})$, it is significantly
simpler to describe and verify. In practice, we find that the new algorithm
also runs faster.


title: Formation Scenario of Magnetars: The Puzzle of Isolation

abstract:
  Magnetars (SGRs and AXPs) are one of the most evolutionary paths of a neutron
star. These objects have an ultra-strong magnetic field $B \sim 10^{15}$ G at
their surface and show persistent X-ray pulsations and transient bursts. Till
date there are 14 magnetars known: 5 SGRs (4 confirmed, 1 candidate) and 9 AXPs
(7 confirmed, 2 candidates). It is an open puzzle that all these objects are
isolated and none have been found in binaries. We discuss the formation
scenario which can lead to such a situation.


title:
Klein-Gordon and Dirac particles in non-constant scalar-curvature
  background

abstract:
  The Klein-Gordon and Dirac equations are considered in a semi-infinite lab
($x > 0$) in the presence of background metrics $ds^2 =u^2(x) \eta_{\mu\nu}
dx^\mu dx^\nu$ and $ds^2=-dt^2+u^2(x)\eta_{ij}dx^i dx^j$ with $u(x)=e^{\pm
gx}$. These metrics have non-constant scalar-curvatures. Various aspects of the
solutions are studied. For the first metric with $u(x)=e^{gx}$, it is shown
that the spectrums are discrete, with the ground state energy $E^2_{min}=p^2c^2
+ g^2c^2\hbar^2$ for spin-0 particles. For $u(x)=e^{-gx}$, the spectrums are
found to be continuous. For the second metric with $u(x)=e^{-gx}$, each
particle, depends on its transverse-momentum, can have continuous or discrete
spectrum. For Klein-Gordon particles, this threshold transverse-momentum is
$\sqrt{3}g/2$, while for Dirac particles it is $g/2$. There is no solution for
$u(x)=e^{gx}$ case. Some geometrical properties of these metrics are also
discussed.


title: Computation of 2-groups of positive classes of exceptional number fields

abstract:
  We present an algorithm for computing the 2-group of the positive divisor
classes of a number field F in case F has exceptional dyadic places. As an
application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such
number fields.


title:
Formation of Hot Planets by a combination of planet scattering, tidal
  circularization, and Kozai mechanism

abstract:
  We have investigated the formation of close-in extrasolar giant planets
through a coupling effect of mutual scattering, Kozai mechanism, and tidal
circularization, by orbital integrations. We have carried out orbital
integrations of three planets with Jupiter-mass, directly including the effect
of tidal circularization. We have found that in about 30% runs close-in planets
are formed, which is much higher than suggested by previous studies. We have
found that Kozai mechanism by outer planets is responsible for the formation of
close-in planets. During the three-planet orbital crossing, the Kozai
excitation is repeated and the eccentricity is often increased secularly to
values close enough to unity for tidal circularization to transform the inner
planet to a close-in planet. Since a moderate eccentricity can remain for the
close-in planet, this mechanism may account for the observed close-in planets
with moderate eccentricities and without nearby secondary planets. Since these
planets also remain a broad range of orbital inclinations (even retrograde
ones), the contribution of this process would be clarified by more observations
of Rossiter-McLaughlin effects for transiting planets.


title: Solar supergranulation revealed by granule tracking

abstract:
  Context: Supergranulation is a pattern of the velocity field at the surface
of the Sun, which has been known about for more than fifty years, however, no
satisfactory explanation of its origin has been proposed. Aims: New
observational constraints are therefore needed to guide theoretical approaches
which hesitate between scenarios that either invoke a large-scale instability
of the surface turbulent convection or a direct forcing by buoyancy. Method:
Using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a
7.5h-long sequence of high resolution images with unprecedented field size.
Tracking granules, we have determined the velocity field at the Sun's surface
in great detail from a scale of 2.5Mm up to 250Mm.
  Results: The kinetic energy density spectrum shows that supergranulation
peaks at 36Mm and spans on scales ranging between 20Mm and 75Mm. The decrease
of supergranular flows in the small scales is close to a $k^{-2}$-power law,
steeper than the equipartition Kolmogorov one. The probability distribution
function of the divergence field shows the signature of intermittency of the
supergranulation and thus its turbulent nature.


title: Nonchaotic Stagnant Motion in a Marginal Quasiperiodic Gradient System

abstract:
  A one-dimensional dynamical system with a marginal quasiperiodic gradient is
presented as a mathematical extension of a nonuniform oscillator. The system
exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent
chaos. In fact, the density function of residence times near stagnation points
obeys an inverse-square law, due to a mechanism similar to type-I
intermittency. However, unlike intermittent chaos, in which the alternation
between long stagnant phases and rapid moving phases occurs in a random manner,
here the alternation occurs in a quasiperiodic manner. In particular, in case
of a gradient with the golden ratio, the renewal of the largest residence time
occurs at positions corresponding to the Fibonacci sequence. Finally, the
asymptotic long-time behavior, in the form of a nested logarithm, is
theoretically derived. Compared with the Pomeau-Manneville intermittency, a
significant difference in the relaxation property of the long-time average of
the dynamical variable is found.


title:
Central and $L^p$-concentration of 1-Lipschitz maps into
  $\mathbb{R}$-trees

abstract:
  In this paper, we study the L\'{e}vy-Milman concentration phenomenon of
1-Lipschitz maps from mm-spaces to $\mathbb{R}$-trees. Our main theorems assert
that the concentration to $\mathbb{R}$-trees is equivalent to the concentration
to the real line.


title: Extragalactic H3O+: Some Consequences

abstract:
  We discuss some implications of our recent detection of extragalactic H3O+:
the location of the gas in M82, the origin of energetic radiation in M82, and
the possible feedback effects of star formation on the cosmic ray flux in
galaxies.


title:
Fractional flux quanta at intrinsic metallic interfaces of
  noncentrosymmetric superconductors

abstract:
  We examine intrinsic interfaces separating crystalline twin domains of
opposite spin-orbit coupling in a noncentrosymmetric superconductor such as
CePt3Si. At these interfaces, low-energy Andreev bound states occur as a
consequence of parity-mixed Cooper pairing, and a superconducting phase which
violates time reversal symmetry can be realized. This provides an environment
allowing flux lines with fractional flux quanta to be formed at the interface.
Their presence could have strong implications on the flux creep behavior in
such superconductors.


title: The Role of the Dilaton in Dense Skyrmion Matter

abstract:
  In this note, we report on a remarkable and surprising interplay between the
omega meson and the dilaton chi in the structure of a single skyrmion as well
as in the phase structure of dense skyrmion matter which may have a potentially
important consequence on the properties of compact stars. In our continuing
effort to understand hadronic matter at high density, we have developed a
unified field theoretic formalism for dense skyrmion matter using a single
Lagrangian to describe simultaneously both matter and meson fluctuations and
studied in-medium properties of hadrons. The effective theory used is the
Skyrme model Lagrangian gauged with the vector mesons rho and omega,
implemented with the dilaton field that describes the spontaneously broken
scale symmetry of QCD, in a form consistent with the symmetries of QCD and our
expectations regarding the high density limit. We analyze the restoration of
scale invariance and chiral symmetry as the density of the system increases. In
order to preserve the restoration of scale symmetry and chiral symmetry,
signalled in our case by the vanishing of the expectation value of the dilaton,
and to be consistent with the vector manifestation of hidden local symmetry, a
density dependent omega coupling is introduced. We uncover the crucial role
played by both the dilaton and the omega meson in the phase structure of dense
medium and discover how two different phase transition regimes arise as we dial
the dilaton mass.


title: Solar system tests of brane world models

abstract:
  The classical tests of general relativity (perihelion precession, deflection
of light, and the radar echo delay) are considered for the Dadhich, Maartens,
Papadopoulos and Rezania (DMPR) solution of the spherically symmetric static
vacuum field equations in brane world models. For this solution the metric in
the vacuum exterior to a brane world star is similar to the Reissner-Nordstrom
form of classical general relativity, with the role of the charge played by the
tidal effects arising from projections of the fifth dimension. The existing
observational solar system data on the perihelion shift of Mercury, on the
light bending around the Sun (obtained using long-baseline radio
interferometry), and ranging to Mars using the Viking lander, constrain the
numerical values of the bulk tidal parameter and of the brane tension.


title: Eigenfunction expansion for Schrodinger operators on metric graphs

abstract:
  We construct an expansion in generalized eigenfunctions for Schrodinger
operators on metric graphs. We require rather minimal assumptions concerning
the graph structure and the boundary conditions at the vertices.


title: Fragility and elastic behavior of a supercooled liquid

abstract:
  A model for the supercooled liquid is considered by taking into account its
solid like properties. We focus on how the long time dynamics is affected due
to the coupling between the slowly decaying density fluctuations and the local
displacement variables in the frozen liquid. Results from our model agree with
the recent observation of Novikov and Sokolov [Nature (London) {\bf 431}, 961
(2004)] that the fragility index $m$ of a glass forming material is linearly
related to the corresponding ratio $K/G$ of the bulk and the shear moduli.


title: Dressed matter waves

abstract:
  We suggest to view ultracold atoms in a time-periodically shifted optical
lattice as a "dressed matter wave", analogous to a dressed atom in an
electromagnetic field. A possible effect lending support to this concept is a
transition of ultracold bosonic atoms from a superfluid to a Mott-insulating
state in response to appropriate "dressing" achieved through time-periodic
lattice modulation. In order to observe this effect in a laboratory experiment,
one has to identify conditions allowing for effectively adiabatic motion of a
many-body Floquet state.


title: Quantum Error-Correcting Codes with Preexisting Protected Qubits

abstract:
  We provide a systematic way of constructing entanglement-assisted quantum
error-correcting codes via graph states in the scenario of preexisting
perfectly protected qubits. It turns out that the preexisting entanglement can
help beat the quantum Hamming bound and can enhance (not only behave as an
assistance) the performance of the quantum error correction. Furthermore we
generalize the error models to the case of not-so-perfectly-protected qubits
and introduce the quantity infidelity as a figure of merit and show that our
code outperforms also the ordinary quantum error-correcting codes.


title: Structural and Superconducting Properties of RbOs2O6 Single Crystals

abstract:
  Single crystals of RbOs2O6 have been grown from Rb2O and Os in sealed quartz
ampoules. The crystal structure has been identified at room temperature as
cubic with the lattice constant a = 10.1242(12) A. The anisotropy of the
tetrahedral and octahedral networks is lower and the displacement parameters of
alkali metal atoms are smaller than for KOs2O6, so the "rattling" of the alkali
atoms in RbOs2O6 is less pronounced. Superconducting properties of RbOs2O6 in
the mixed state have been well described within the London approach and the
Ginzburg-Landau parameter kappa(0) = 31 has been derived from the reversible
magnetization. This parameter is field dependent and changes at low
temperatures from kappa = 22 (low fields) to kappa = 31 at H_{c2}. The
thermodynamic critical field H_{c}(0) = 1.3 kOe and the superconducting gap
2delta/k_{B}T_{c} = 3.2 have been estimated. These results together with
slightly different H_{c2}(T) dependence obtained for crystals and
polycrystalline RbOs2O6 proof evidently that this compound is a weak-coupling
BCS-type superconductor close to the dirty limit.


title:
Fluctuation-dissipation relations in critical coarsening: crossover from
  unmagnetized to magnetized initial states

abstract:
  We study the non-equilibrium dynamics of the spherical ferromagnet quenched
to its critical temperature, as a function of the magnetization of the initial
state. The two limits of unmagnetized and fully magnetized initial conditions
can be understood as corresponding to times that are respectively much shorter
and much longer than a magnetization timescale, as in a recent field
theoretical analysis of the $n$-vector model. We calculate exactly the
crossover functions interpolating between these two limits, for the
magnetization correlator and response and the resulting fluctuation-dissipation
ratio (FDR). For $d>4$ our results match those obtained recently from a
Gaussian field theory. For $d<4$, non-Gaussian fuctuations arising from the
spherical constraint need to be accounted for. We extend our framework from the
fully magnetized case to achieve this, providing an exact solution for the
relevant integral kernel. The resulting crossover behaviour is very rich, with
the asymptotic FDR $X^\infty$ depending non-monotonically on the scaled age of
the system. This is traced back to non-monotonicities of the two-time
correlator, themselves the consequence of large magnetization fluctuations on
the crossover timescale. We correct a trivial error in our earlier calculation
for fully magnetized initial states; the corrected FDR is {\em consistent} with
renormalization group expansions to first order in $4-d$ for the longitudinal
fluctuations of the O(n) model in the limit $n\to\infty$.


title:
Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical
  System

abstract:
  Limit theorems for the time average of some observation functions in an
infinite measure dynamical system are studied. It is known that intermittent
phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky
reaction, are described by infinite measure dynamical systems.We show that the
time average of the observation function which is not the $L^1(m)$ function,
whose average with respect to the invariant measure $m$ is finite, converges to
the generalized arcsine distribution. This result leads to the novel view that
the correlation function is intrinsically random and does not decay. Moreover,
it is also numerically shown that the time average of the observation function
converges to the stable distribution when the observation function has the
infinite mean.


title: Multifractal analysis of non-uniformly hyperbolic systems

abstract:
  We prove a multifractal formalism for Birkhoff averages of continuous
functions in the case of some non-uniformly hyperbolic maps, which includes
interval examples such as the Manneville--Pomeau map.


title: Optical properties of gold films and the Casimir force

abstract:
  Precise optical properties of metals are very important for accurate
prediction of the Casimir force acting between two metallic plates. Therefore
we measured ellipsometrically the optical responses of Au films in a wide range
of wavelengths from 0.14 mum to 33 mum. The films at various thickness were
deposited at different conditions on silicon or mica substrates. Considerable
variation of the frequency dependent dielectric function from sample to sample
was found. Detailed analysis of the dielectric functions was performed to check
the Kramers-Kronig consistency, and extract the Drude parameters of the films.
It was found that the plasma frequency varies in the range from 6.8 eV to 8.4
eV. It is suggested that this variation is related with the film density. X-ray
reflectivity measurements support qualitatively this conclusion. The Casimir
force is evaluated for the dielectric functions corresponding to our samples,
and for that typically used in the precise prediction of the force. The force
for our films was found to be 5-14% smaller at a distance of 100 nm between the
plates. Noise in the optical data is responsible for the force variation within
1%. It is concluded that prediction of the Casimir force between metals with a
precision better than 10% must be based on the material optical response
measured from visible to mid-infrared range.


title:
Microscopic calculation and LDA of the spatial dependence of the pairing
  field with bare and induced interactions

abstract:
  The bare nucleon-nucleon interaction is essential for the production of pair
correlations in nuclei, but an important contribution also arises from the
induced interaction resulting from the exchange of collective vibrations
between nucleons moving in time reversal states close to the Fermi energy. The
pairing field resulting from the summed interaction is strongly peaked at the
nuclear surface. It is possible to reproduce the detailed spatial dependence of
this field using a Local Density Approximation (LDA) and a contact interaction,
with parameters which are quite different from those commonly used in more
phenomenological approaches.


title: Kinetic proofreading of gene activation by chromatin remodeling

abstract:
  Gene activation in eukaryotes involves the concerted action of histone tail
modifiers, chromatin remodellers and transcription factors, whose precise
coordination is currently unknown. We demonstrate that the experimentally
observed interactions of the molecules are in accord with a kinetic
proofreading scheme. Our finding could provide a basis for the development of
quantitative models for gene regulation in eukaryotes based on the
combinatorical interactions of chromatin modifiers.


title:
Stability of the homogeneous Bose-Einstein condensate at large gas
  parameter

abstract:
  The properties of the uniform Bose gas is studied within the optimized
variational perturbation theory (Gaussian approximation) in a self-consistent
way. It is shown that the atomic BEC with a repulsive interaction becomes
unstable when the gas parameter gamma=rho a^3 exceeds a critical value
gamma_{crit} ~ 0.01. The quantum corrections beyond the Bogoliubov-Popov
approximation to the energy density, chemical potential and pressure in powers
of gamma expansions are presented.


title:
Time dependent density functional theory calculation of van der Waals
  coefficient C$_{6}$ of alkali-metal atoms Li, Na, K, alkali dimers Li$_{2}$,
  Na$_{2}$, K$_{2}$ and sodium clusters Na$_{n}$

abstract:
  In this paper we employ all-electron time dependent density functional theory
(TDDFT) to calculate the long range dipole-dipole dispersion coefficient (van
der Waals coefficient) $C_{6}$ of alkali-metal atoms Li, Na, K, alkali-metal
atom dimers Li$_{2}$, Na$_{2}$, K$_{2}$ and sodium clusters containing even
number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are
obtained via Casimir-Polder expression which relates it to the frequency
dependent linear polarizabilty at imaginary frequencies. The frequency
dependent polarizabilities are calculated by employing TDDFT--based complete
sum-over-states expressions for the atoms, and direct TDDFT linear response
theory for the closed shell dimers and clusters.


title: Towards the understanding of human dynamics

abstract:
  Quantitative understanding of human behaviors provides elementary
comprehension of the complexity of many human-initiated systems. A basic
assumption embedded in the previous analyses on human dynamics is that its
temporal statistics are uniform and stationary, which can be properly described
by a Poisson process. Accordingly, the interevent time distribution should have
an exponential tail. However, recently, this assumption is challenged by the
extensive evidence, ranging from communication to entertainment and work
patterns, that the human dynamics obeys non-Poisson statistics with
heavy-tailed interevent time distribution. This review article summarizes the
recent empirical explorations on human activity pattern, as well as the
corresponding theoretical models for both task-driven and interest-driven
systems. Finally, we outline some future open questions in the studies of the
statistical mechanics of human dynamics.


title: The Eulerian distribution on self evacuated involutions

abstract:
  We present an extensive study of the Eulerian distribution on the set of self
evacuated involutions, namely, involutions corresponding to standard Young
tableaux that are fixed under the Sch$\ddot{\textrm{u}}$tzenberger map. We find
some combinatorial properties for the generating polynomial of such
distribution, together with an explicit formula for its coefficients.
Afterwards, we carry out an analogous study for the subset of self evacuated
involutions without fixed points.


title:
The limiting nuclear polarization in a quantum dot under optical
  electron-spin orientation and applicability of the box-model of the
  electron-nuclear dynamics

abstract:
  For the model Hamiltonian describing the electron-nuclear dynamics of a
quantum dot, we obtained an exact expression for the limiting nuclear
polarization as a function of the number of groups of equivalent nuclei. It is
shown that the refinement of the model Hamiltonian by increasing the number of
the groups results in a slow growth of the limiting nuclear polarization. This
allowed us to put forward arguments in favor of applicability of the box-model
(with all the nuclei being equivalent) for description of the electron-nuclear
spin dynamics within the time intervals of around hundreds of periods of the
optical orientation.


title:
Fluctuation analysis of mechanochemical coupling depending on the type
  of bio-molecular motor

abstract:
  Mechanochemical coupling was studied for two different types of myosin motors
in cells: myosin V, which carries cargo over long distances by as a single
molecule; and myosin II, which generates a contracting force in cooperation
with other myosin II molecules. Both mean and variance of myosin V velocity at
various [ATP] obeyed Michaelis-Menten mechanics, consistent with tight
mechanochemical coupling. Myosin II, working in an ensemble, however, was
explained by a loose coupling mechanism, generating variable step sizes
depending on the ATP concentration and realizing a much larger step (200 nm)
per ATP hydrolysis than myosin V through its cooperative nature at zero load.
These different mechanics are ideal for the respective myosin's physiological
functions.


title:
Turbo charging time-dependent density-functional theory with Lanczos
  chains

abstract:
  We introduce a new implementation of time-dependent density-functional theory
which allows the \emph{entire} spectrum of a molecule or extended system to be
computed with a numerical effort comparable to that of a \emph{single} standard
ground-state calculation. This method is particularly well suited for large
systems and/or large basis sets, such as plane waves or real-space grids. By
using a super-operator formulation of linearized time-dependent
density-functional theory, we first represent the dynamical polarizability of
an interacting-electron system as an off-diagonal matrix element of the
resolvent of the Liouvillian super-operator. One-electron operators and density
matrices are treated using a representation borrowed from time-independent
density-functional perturbation theory, which permits to avoid the calculation
of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated
through a newly developed algorithm based on the non-symmetric Lanczos method.
Each step of the Lanczos recursion essentially requires twice as many
operations as a single step of the iterative diagonalization of the unperturbed
Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients
allows for a dramatic reduction of the number of Lanczos steps necessary to
obtain well converged spectra, bringing such number down to hundreds (or a few
thousands, at worst) in typical plane-wave pseudopotential applications. The
resulting numerical workload is only a few times larger than that needed by a
ground-state Kohn-Sham calculation for a same system. Our method is
demonstrated with the calculation of the spectra of benzene, C$_{60}$
fullerene, and of chlorofyll a.


title: XX model on the circle

abstract:
  We diagonalize the XX model with a finite number of spins and periodic
boundary conditions. We solve for the ground state, focus on the rapidity of
the convergence to the thermodynamic limit and study the features of
multipartite entanglement.


title: Scaling of disordered recursive networks

abstract:
  In this brief report, we present a disordered version of recursive networks.
Depending on the structural parameters $u$ and $v$, the networks are either
fractals with a finite fractal dimension $d_{f}$ or transfinite fractals
(transfractal) with a infinite fractal dimension. The scaling behavior of
degree and dimensionality are studied analytically and by simulations, which
are found to be different from those in ordered recursive networks. The
transfractal dimension $\tilde{d}_f$, which is recently introduced to
distinguish the differences between networks with infinite fractal dimension,
scales as $\tilde{d}_f\sim \frac{1}{u+v-1}$ for transfractal networks.
Interestingly, the fractal dimension for fractal networks with $u=v$ is found
to approach 3 in large limit of $u$, which is thought to be the effect of
disorder. We also investigate the diffusion process on this family of networks,
and the scaling behavior of diffusion time is observed numercally as $\tau\sim
N^{(d_{f}+1)/d_{f}}$ for fractal networks and $\tau\sim \frac{1}{\tilde{d}_f}N$
for transfractal ons. We think that the later relation will give a further
understanding of transfractal dimension.


title: Rationally connected $3$-folds and symplectic geometry

abstract:
  We study the following question, asked to us By Pandharipande and Starr: Let
$X$ be a rationally connected $3$-fold, and $Y$ be a compact Kaehler $3$-fold
symplectically equivalent to it. Is $Y$ rationally connected? We show that the
answer is positive if $X$ is Fano or $b_2(X)\leq2$.


title: Decay times in turnover statistics of single enzymes

abstract:
  The first passage times for enzymatic turnovers in non-equilibrium steady
state display a statistical symmetry property related to non-equilibrium
fluctuation theorems, that makes it possible to extract the chemical driving
force from single molecule trajectories in non-equilibrium steady state. Below,
we show that this system violates the general expectation that the number of
decay constants needed to fit a first passage time distribution reflects the
number of states in the escape problem. In fact, the structure of the kinetic
mechanism makes half of the decay times vanish identically from the turnover
time distribution. The terms that cancel out correspond to the eigenvalues of a
certain sub-matrix of the master equation matrix for the first exit time
problem. We discuss how these results make modeling and data analysis easier
for such systems, and how the turnovers can be measured.


title: Accelerating universe in $f({\cal R})$ brane gravity

abstract:
  We study a 5-dimensional $f({\cal R})$ brane gravity within the framework of
scalar-tensor type theories. We show that such a model predicts, for a certain
choice of $f({\cal R})$ and a spatially flat universe, an exponential
potential, leading to an accelerated expanding universe driven solely by the
curvature of the bulk space. This result is consistent with the observational
data in the cosmological scale.


title: Heterogeneous bounds of confidence: Meet, Discuss and Find Consensus!

abstract:
  Models of continuous opinion dynamics under bounded confidence show a sharp
transition between a consensus and a polarization phase at a critical global
bound of confidence. In this paper, heterogeneous bounds of confidence are
studied. The surprising result is that a society of agents with two different
bounds of confidence (open-minded and closed-minded agents) can find consensus
even when both bounds of confidence are significantly below the critical bound
of confidence of a homogeneous society.
  The phenomenon is shown by examples of agent-based simulation and by
numerical computation of the time evolution of the agents density. The result
holds for the bounded confidence model of Deffuant, Weisbuch and others
(Weisbuch, G. et al; Meet, discuss, and segregate!, Complexity, 2002, 7,
55--63), as well as for the model of Hegselmann and Krause (Hegselmann, R.,
Krause, U.; Opinion Dynamics and Bounded Confidence, Models, Analysis and
Simulation, Journal of Artificial Societies and Social Simulation, 2002, 5, 2).
  Thus, given an average level of confidence, diversity of bounds of confidence
enhances the chances for consensus. The drawback of this enhancement is that
opinion dynamics becomes suspect to severe drifts of clusters, where
open-minded agents can pull closed-minded agents towards another cluster of
closed-minded agents. A final consensus might thus not lie in the center of the
opinion interval as it happens for uniform initial opinion distributions under
homogeneous bounds of confidence. It can be located at extremal locations. This
is demonstrated by example.
  This also show that the extension to heterogeneous bounds of confidence
enriches the complexity of the dynamics tremendously.


title: Topology Changes and Quantum Phase Transition in Spin-Chain System

abstract:
  The standard Landau-Ginzburg scenario of phase transition is broken down for
quantum phase transition. It is difficult to find an order parameter to
indicate different phases for quantum fluctuations. Here, we suggest a
topological description of the quantum phase transition for the XY model. The
ground states are identified as a specialized U(1) principal bundle on the base
manifold $S^2$. And then different first Chern numbers of U(1) principal bundle
on the base manifold $S^2$ are associated to each phase of quantum
fluctuations. The particle-hole picture is used to parameterized the ground
states of the XY system. We show that a singularity of the Chern number of the
ground states occurs simultaneously with a quantum phase transition. The Chern
number is a suitable topological order of the quantum phase transition.


title: Constrained semi-analytical models of Galactic outflows

abstract:
  We present semi-analytic models of galactic outflows, constrained by
available observations on high redshift star formation and reionization.
Galactic outflows are modeled in a manner akin to models of stellar wind blown
bubbles. Large scale outflows can generically escape from low mass halos
(M<10^9 M_sun) for a wide range of model parameters but not from high mass
halos (M> 10^{11} M_sun). The gas phase metallicity of the outflow and within
the galaxy are computed. Ionization states of different metal species are
calculated and used to examine the detectability of metal lines from the
outflows. The global influence of galactic outflows is also investigated.
Models with only atomic cooled halos significantly fill the IGM at z~3 with
metals (with -2.5>[Z/Z_sun]>-3.7), the actual extent depending on the
efficiency of winds, the IMF, the fractional mass that goes through star
formation and the reionization history of the universe. In these models, a
large fraction of outflows at z~3 are supersonic, hot (T> 10^5 K) and have low
density, making metal lines difficult to detect. They may also result in
significant perturbations in the IGM gas on scales probed by the Lyman-alpha
forest. On the contrary, models including molecular cooled halos with a normal
mode of star formation can potentially volume fill the universe at z> 8 without
drastic dynamic effects on the IGM, thereby setting up a possible metallicity
floor (-4.0<[Z/Z_sun]<-3.6). Interestingly, molecular cooled halos with a
``top-heavy'' mode of star formation are not very successful in establishing
the metallicity floor because of the additional radiative feedback, that they
induce. (Abridged)


title:
Fluctuations of statistics among subregions of a turbulence velocity
  field

abstract:
  To study subregions of a turbulence velocity field, a long record of velocity
data of grid turbulence is divided into smaller segments. For each segment, we
calculate statistics such as the mean rate of energy dissipation and the mean
energy at each scale. Their values significantly fluctuate, in lognormal
distributions at least as a good approximation. Each segment is not under
equilibrium between the mean rate of energy dissipation and the mean rate of
energy transfer that determines the mean energy. These two rates still
correlate among segments when their length exceeds the correlation length. Also
between the mean rate of energy dissipation and the mean total energy, there is
a correlation characterized by the Reynolds number for the whole record,
implying that the large-scale flow affects each of the segments.


title:
The importance of magnetic-field-oriented thermal conduction in the
  interaction of SNR shocks with interstellar clouds

abstract:
  We explore the importance of magnetic-field-oriented thermal conduction in
the interaction of supernova remnant (SNR) shocks with radiative gas clouds and
in determining the mass and energy exchange between the clouds and the hot
surrounding medium. We perform 2.5D MHD simulations of a shock impacting on an
isolated gas cloud, including anisotropic thermal conduction and radiative
cooling; we consider the representative case of a Mach 50 shock impacting on a
cloud ten-fold denser than the ambient medium. We consider different
configurations of the ambient magnetic field and compare MHD models with or
without the thermal conduction. The efficiency of the thermal conduction in the
presence of magnetic field is, in general, reduced with respect to the
unmagnetized case. The reduction factor strongly depends on the initial
magnetic field orientation, and it is minimum when the magnetic field is
initially aligned with the direction of shock propagation. The thermal
conduction contributes to suppress hydrodynamic instabilities, reducing the
mass mixing of the cloud and preserving the cloud from complete fragmentation.
Depending on the magnetic field orientation, the heat conduction may determine
a significant energy exchange between the cloud and the hot surrounding medium
which, while remaining always at levels less than those in the unmagnetized
case, leads to a progressive heating and evaporation of the cloud. This
additional heating may contrast the radiative cooling of some parts of the
cloud, preventing the onset of thermal instabilities.


title:
Performance Measurements of 8-Gsps 1-bit ADCs Developed for Wideband
  Radio Astronomical Observations

abstract:
  8-Gsps 1-bit Analog-to-Digital Converters (ADCs) were newly developed toward
the realization of the wideband observation. The development of the wideband
ADCs is one of the most essential developments for the radio interferometer. To
evaluate its performance in interferometric observations, the time (phase)
stability and frequency response were measured with a noise source and a signal
generator. The results of these measurements show that the developed ADCs can
achieve the jitter time less than 0.05 psec at the time interval of 1 sec, the
passband frequency response with the slope less than 0.73 dB/GHz and the ripple
less than 1.8 dB, and the aperture time less than 20 psec. The details of the
developed ADC design, the measurement methods, and the results of these
measurements are presented in this paper.


title:
On multilinearity and skew-symmetry of certain symbols in motivic
  cohomology of fields

abstract:
  The purpose of the present article is to show the multilinearity for symbols
in Goodwillie-Lichtenbaum complex in two cases.
  The first case shown is where the degree is equal to the weight. In this
case, the motivic cohomology groups of a field are isomorphic to the Milnor's
K-groups as shown by Nesterenko-Suslin, Totaro and Suslin-Voevodsky for various
motivic complexes, but we give an explicit isomorphism for
Goodwillie-Lichtenbaum complex in a form which visibly carries multilinearity
of Milnor's symbols to our multilinearity of motivic symbols. Next, we
establish multilinearity and skew-symmetry for irreducible
Goodwillie-Lichtenbaum symbols in H^{l-1} (Spec k, Z(l)). These properties have
been expected to hold from the author's construction of a bilinear form of
dilogarithm in case k is a subfield of the field of complex numbers and l=2.
  Next, we establish multilinearity and skew-symmetry for
Goodwillie-Lichtenbaum symbols in H^{l-1} (Spec k, Z(l)). These properties have
been expected to hold from the author's construction of a bilinear form of
dilogarithm in case k is a subfield of the field of complex numbers and l=2.
  The multilinearity of symbols may be viewed as a generalization of the
well-known formula det(AB) = det(A) det(B) for tuples of commuting matrices.


title:
Modelling interstellar extinction and polarization with spheroidal
  grains

abstract:
  We calculate the wavelength dependence of the ratio of the linear
polarization degree to extinction (polarizing efficiency)
$P(\lambda)/A(\lambda)$ from the ultraviolet to near-infrared. The prolate and
oblate particles with aspect ratios from $a/b=1.1$ up to 10 are assumed to be
rotating and partially aligned with the mechanism of paramagnetic relaxation
(Davis--Greenstein). Size/shape/orientation effects are analyzed. It is found
that the wavelength dependence of $P(\lambda)/A(\lambda)$ is mainly determined
by the particle composition and size whereas the values of
$P(\lambda)/A(\lambda)$ depend on the particle shape, degree and direction of
alignment.


title: Some Issues Concerning Holographic Dark Energy

abstract:
  We study perturbation of holographic dark energy and find it be stable. We
study the fate of the universe when interacting holographic dark energy is
present, and discuss a simple phenomenological classification of the
interacting holographic dark energy models. We also discuss the cosmic
coincidence problem in the context of holographic dark energy. We find that the
coincidence problem can not be completely solved by adding an interacting term.
Inflation may provide a better solution of the coincidence problem.


title:
The Quantum Action Principle in the framework of Causal Perturbation
  Theory

abstract:
  In perturbative quantum field theory the maintenance of classical symmetries
is quite often investigated by means of algebraic renormalization, which is
based on the Quantum Action Principle. We formulate and prove this principle in
a new framework, in causal perturbation theory with localized interactions.
Throughout this work a universal formulation of symmetries is used: the Master
Ward Identity.


title: Integral points on generic fibers

abstract:
  Let P(x,y) be a rational polynomial and k in Q be a generic value. If the
curve (P(x,y)=k) is irreducible and admits an infinite number of points whose
coordinates are integers then there exist algebraic automorphisms that send
P(x,y) to the polynomial x or to x^2-dy^2. Moreover for such curves (and
others) we give a sharp bound for the number of integral points (x,y) with x
and y bounded.


title: Two graph isomorphism polytopes

abstract:
  The convex hull $\psi_{n,n}$ of certain $(n!)^2$ tensors was considered
recently in connection with graph isomorphism. We consider the convex hull
$\psi_n$ of the $n!$ diagonals among these tensors. We show: 1. The polytope
$\psi_n$ is a face of $\psi_{n,n}$. 2. Deciding if a graph $G$ has a subgraph
isomorphic to $H$ reduces to optimization over $\psi_n$. 3. Optimization over
$\psi_n$ reduces to optimization over $\psi_{n,n}$. In particular, this implies
that the subgraph isomorphism problem reduces to optimization over
$\psi_{n,n}$.


title:
Exact solution of Effective mass Schrodinger Equation for the Hulthen
  potential

abstract:
  A general form of the effective mass Schrodinger equation is solved exactly
for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy
eigenvalues and the corresponding wave functions. A free parameter is used in
the transformation of the wave function.


title:
Geometric approach towards stable homotopy groups of spheres. The
  Steenrod-Hopf invariant I

abstract:
  In this paper a geometric approach toward stable homotopy groups of spheres,
based on the Pontrjagin-Thom construction is proposed. From this approach a new
proof of Hopf Invariant One Theorem by J.F.Adams for all dimensions except
$15,31,63,127$ is obtained.
  It is proved that for $n>127$ in the stable homotopy group of spheres $\Pi_n$
there is no elements with Hopf invariant one. The new proof is based on
geometric topology methods. The Pontrjagin-Thom Theorem (in the form proposed
by R.Wells) about the representation of stable homotopy groups of the real
projective infinite-dimensional space (this groups is mapped onto 2-components
of stable homotopy groups of spheres by the Khan-Priddy Theorem) by cobordism
classes of immersions of codimension 1 of closed manifolds (generally speaking,
non-orientable) is considered. The Hopf Invariant is expressed as a
characteristic number of the dihedral group for the self-intersection manifold
of an immersed codimension 1 manifold that represents the given element in the
stable homotopy group. In the new proof the Geometric Control Principle (by
M.Gromov) for immersions in a given regular homotopy classes based on
Smale-Hirsch Immersion Theorem is required.


title: Fractional statistics and finite bosonic system: A one-dimensional case

abstract:
  The equivalence is established between the one-dimensional (1D) Bose-system
with a finite number of particles and the system obeying the fractional
(intermediate) Gentile statistics, in which the maximum occupation of
single-particle energy levels is limited. The system of 1D harmonic oscillators
is considered providing the model of harmonically trapped Bose-gas. The results
are generalized for the system with power energy spectrum.


title:
Entanglement dynamics and relaxation in a few qubit system interacting
  with random collisions

abstract:
  The dynamics of a single qubit interacting by a sequence of pairwise
collisions with an environment consisting of just two more qubits is analyzed.
Each collision is modeled in terms of a random unitary operator with a uniform
probability distribution described by the uniform Haar measure. We show that
the purity of the system qubit as well as the bipartite and the tripartite
entanglement reach time averaged equilibrium values characterized by large
instantaneous fluctuations.These equilibrium values are independent of the
order of collision among the qubits. The relaxation to equilibrium is analyzed
also in terms of an ensemble average of random collision histories. Such
average allows for a quantitative evaluation and interpretation of the decay
constants. Furthermore a dependence of the transient dynamics on the initial
degree of entanglement between the environment qubits is shown to exist.
Finally the statistical properties of bipartite and tripartite entanglement are
analyzed.


title: The emerging field of language dynamics

abstract:
  A simple review by a linguist, citing many articles by physicists:
Quantitative methods, agent-based computer simulations, language dynamics,
language typology, historical linguistics


title: Fast Integer Multiplication using Modular Arithmetic

abstract:
  We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying
two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$
algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular
arithmetic. Recently, F\"{u}rer gave an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$
algorithm which however uses arithmetic over complex numbers as opposed to
modular arithmetic. In this paper, we use multivariate polynomial
multiplication along with ideas from F\"{u}rer's algorithm to achieve this
improvement in the modular setting. Our algorithm can also be viewed as a
$p$-adic version of F\"{u}rer's algorithm. Thus, we show that the two seemingly
different approaches to integer multiplication, modular and complex arithmetic,
are similar.


title:
Geometric approach towards stable homotopy groups of spheres. The
  Kervaire invariant II

abstract:
  The notion of the geometrical $\Z/2 \oplus \Z/2$--control of
self-intersection of a skew-framed immersion and the notion of the $\Z/2 \oplus
\Z/4$-structure (the cyclic structure) on the self-intersection manifold of a
$\D_4$-framed immersion are introduced. It is shown that a skew-framed
immersion $f:M^{\frac{3n+q}{4}} \looparrowright \R^n$, $0 < q <<n$ (in the
$\frac{3n}{4}+\epsilon$-range) admits a geometrical $\Z/2 \oplus \Z/2$--control
if the characteristic class of the skew-framing of this immersion admits a
retraction of the order $q$, i.e. there exists a mapping $\kappa_0:
M^{\frac{3n+q}{4}} \to \RP^{\frac{3(n-q)}{4}}$, such that this composition $I
\circ \kappa_0: M^{\frac{3n+q}{4}} \to \RP^{\frac{3(n-q)}{4}} \to \RP^{\infty}$
is the characteristic class of the skew-framing of $f$. Using the notion of
$\Z/2 \oplus \Z/2$-control we prove that for a sufficiently great $n$,
$n=2^l-2$, an arbitrary immersed $\D_4$-framed manifold admits in the regular
cobordism class (modulo odd torsion) an immersion with a $\Z/2 \oplus
\Z/4$-structure. In the last section we present an approach toward the Kervaire
Invariant One Problem.


title: Deformation data, Belyi maps, and the local lifting problem

abstract:
  We prove existence and nonexistence results for certain differential forms in
positive characteristic, called {\em good deformation data}. Some of these
results are obtained by reduction modulo $p$ of Belyi maps. As an application,
we solve the local lifting problem for groups with Sylow $p$-subgroup of order
$p$.


title: Core Persistence in Peer-to-Peer Systems: Relating Size to Lifetime

abstract:
  Distributed systems are now both very large and highly dynamic. Peer to peer
overlay networks have been proved efficient to cope with this new deal that
traditional approaches can no longer accommodate. While the challenge of
organizing peers in an overlay network has generated a lot of interest leading
to a large number of solutions, maintaining critical data in such a network
remains an open issue. In this paper, we are interested in defining the portion
of nodes and frequency one has to probe, given the churn observed in the
system, in order to achieve a given probability of maintaining the persistence
of some critical data. More specifically, we provide a clear result relating
the size and the frequency of the probing set along with its proof as well as
an analysis of the way of leveraging such an information in a large scale
dynamic distributed system.


title: Order parameters in the Verwey phase transition

abstract:
  The Verwey phase transition in magnetite is analyzed on the basis of the
Landau theory. The free energy functional is expanded in a series of components
belonging to the primary and secondary order parameters. A low-temperature
phase with the monoclinic P2/c symmetry is a result of condensation of two
order parameters X_3 and \Delta_5 . The temperature dependence of the shear
elastic constant C_44 is derived and the mechanism of its softening is
discussed.


title: Soft gamma repeaters activity in time

abstract:
  In this short note I discuss the hypothesis that bursting activity of
magnetars evolves in time analogously to the glitching activity of normal radio
pulsars (i.e. sources are more active at smaller ages), and that the increase
of the burst rate follows one of the laws established for glitching radio
pulsars. If the activity of soft gamma repeaters decreases in time in the way
similar to the evolution of core-quake glitches ($\propto t^{5/2}$), then it is
more probable to find the youngest soft gamma repeaters, but the energy of
giant flares from these sources should be smaller than observed $10^{44}$
--$10^{46}$ ergs as the total energy stored in a magnetar's magnetic field is
not enough to support thousands of bursts similar to the prototype 5 March 1979
flare.


title: Submillimeter Structure of the Disk of the Butterfly Star

abstract:
  We present a spatially resolved 894 micron map of the circumstellar disk of
the Butterfly star in Taurus (IRAS 04302+2247), obtained with the Submillimeter
Array (SMA). The predicted and observed radial brightness profile agree well in
the outer disk region, but differ in the inner region with an outer radius of
~80-120 AU. In particular, we find a local minimum of the radial brightness
distribution at the center, which can be explained by an increasing density /
optical depth combined with the decreasing vertical extent of the disk towards
the center. Our finding indicates that young circumstellar disks can be
optically thick at wavelengths as long as 894 micron. While earlier modeling
lead to general conclusions about the global disk structure and, most
importantly, evidence for grain growth in the disk (Wolf, Padgett, &
Stapelfeldt 2003), the presented SMA observations provide more detailed
constraints for the disk structure and dust grain properties in the inner,
potentially planet-forming region (inside ~80-120 AU) vs. the outer disk region
(~120-300 AU).


title:
Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole
  Physics

abstract:
  This paper gives a survey of wave dynamics in the Kerr space-time geometry,
the mathematical model of a rotating black hole in equilibrium. After a brief
introduction to the Kerr metric, we review the separability properties of
linear wave equations for fields of general spin $s=0, 1/2, 1, 2$,
corresponding to scalar, Dirac, electromagnetic fields and linearized
gravitational waves. We give results on the long-time dynamics of Dirac and
scalar waves, including decay rates for massive Dirac fields. For scalar waves,
we give a rigorous treatment of superradiance and describe rigorously a
mechanism of energy extraction from a rotating black hole. Finally, we discuss
the open problem of linear stability of the Kerr metric and present partial
results.


title:
Comparison of van der Waals coefficient C$_{6}$ of sodium clusters
  obtained via spherical jellium background model and all-electron ab-initio
  method

abstract:
  In this paper we employ two distinct approaches - all-electron \textit{ab
initio} method and the spherical jellium background model- within time
dependent density functional theory to calculate the long range dipole-dipole
dispersion coefficient (van der Waals coefficient) $C_{6}$ of sodium atom
clusters containing even number of atoms ranging from 2 to 20 atoms. The
dispersion coefficients are obtained via Casimir-Polder relation. All the
calculations are carried out with local density approximation for
exchange-correlation energy functional. These two sets of results are compared
to assess the accuracy of jellium based results and to ascertain the effect of
detail ionic structure of the clusters on the van der Waals coefficient.


title: Direct Photons in Nuclear Collisions at FAIR Energies

abstract:
  Using the extrapolation of existing data estimations of prompt photon
production at FAIR energies have been made. At $y=y_{c.m.}$ the rapidity
density of prompt photons with $p_{t}>$ 1.5 GeV/c per central Au+Au event at 25
AGeV is estimated as $\sim 10^{-4}$ . With the planed beam intensity $10^{9}$
per second and 1% interaction probability, for 10% of most central events one
can expect the prompt photon rate $\sim 10^{2}$ photons per second.
  Direct photons from the hadron scenario of ion collisions generated by the
Hadron-String-Dynamics (HSD) transport approach with implemented meson
scatterings $\pi\rho\to\pi\gamma, \pi\pi\to\rho\gamma$ have been analyzed.
Photons from short-living resonances (e.g. $\omega \to \pi^{0} \gamma$)
decaying during the dense phase of the collision should be considered as direct
photons. They contribute significantly in the direct photon spectrum at
$p_{t}=0.5 - 1$ GeV/c. At the FAIR energy 25 AGeV in Au+Au central collisions
the HSD generator predicts, as a lower estimate,
$\gamma_{direct}/\gamma_{\pi^{0}} \simeq$ 0.5% in the region $p_{t}=0.5 - 1$
GeV/c. At $p_{t}=1.5 - 2$ GeV/c $\gamma_{prompt}/\gamma_{\pi^{0}} \simeq$ 2%.
  Thermal direct photons have been evaluated with the Bjorken Hydro-Dynamics
(BHD) model. The BHD spectra differ strongly from the HSD predictions. The
direct photon spectrum is very sensitive to the initial temperature parameter
$T_{0}$ of the model. The 10 MeV increase in the $T_{0}$ value leads to $\sim$
2 times higher photon yield.


title:
Statistically optimal analysis of samples from multiple equilibrium
  states

abstract:
  We present a new estimator for computing free energy differences and
thermodynamic expectations as well as their uncertainties from samples obtained
from multiple equilibrium states via either simulation or experiment. The
estimator, which we term the multistate Bennett acceptance ratio (MBAR)
estimator because it reduces to the Bennett acceptance ratio when only two
states are considered, has significant advantages over multiple histogram
reweighting methods for combining data from multiple states. It does not
require the sampled energy range to be discretized to produce histograms,
eliminating bias due to energy binning and significantly reducing the time
complexity of computing a solution to the estimating equations in many cases.
Additionally, an estimate of the statistical uncertainty is provided for all
estimated quantities. In the large sample limit, MBAR is unbiased and has the
lowest variance of any known estimator for making use of equilibrium data
collected from multiple states. We illustrate this method by producing a highly
precise estimate of the potential of mean force for a DNA hairpin system,
combining data from multiple optical tweezer measurements under constant force
bias.


title:
Effect of the surface-stimulated mode on the kinetics of homogeneous
  crystal nucleation in droplets

abstract:
  A kinetic theory of homogeneous crystal nucleation in unary droplets is
presented taking into account that a crystal nucleus can form not only in the
volume-based mode (with all its facets within the droplet) but also in the
surface-stimulated one (with one of its facets at the droplet surface). The
previously developed thermodynamics of surface-stimulated crystal nucleation
rigorously showed that if at least one of the facets of the crystal is only
partially wettable by its melt, then it is thermodynamically more favorable for
the nucleus to form with that facet at the droplet surface rather than within
the droplet. So far, however, the kinetic aspects of this phenomenon had not
been studied at all. The theory proposed in the present paper advocates that
even in the surface-stimulated mode crystal nuclei initially emerge (as
sub-critical clusters) homogeneously in the sub-surface layer, not
"pseudo-heterogeneously" at the surface. A homogeneously emerged sub-critical
crystal can become a surface-stimulated nucleus due to density and structure
fluctuations. This effect contributes to the total rate of crystal nucleation
(as the volume-based mode does). An explicit expression for the total
per-particle rate of crystal nucleation is derived. Numerical evaluations for
water droplets suggest that the surface-stimulated mode can significantly
enhance the per-particle rate of crystal nucleation in droplets as large as 10
microns in radius. Possible experimental verification of the proposed theory is
discussed.


title: Pure Spinors and D=6 Super-Yang-Mills

abstract:
  Pure spinor cohomology has been used to describe maximally supersymmetric
theories, like D=10 super-Yang-Mills and D=11 supergravity. Supersymmetry
closes on-shell in such theories, and the fields in the cohomology
automatically satisfy the equations of motion. In this paper, we investigate
the corresponding structure in a model with off-shell supersymmetry, N=1
super-Yang-Mills theory in D=6. Here, fields and antifields are obtained as
cohomologies in different complexes with respect to the BRST operator Q. It
turns out to be natural to enlarge the pure spinor space with additional
bosonic variables, subject to some constraints generalising the pure spinor
condition, in order to accommodate the different supermultiplets in the same
generalised pure spinor wave-function. We construct another BRST operator, s,
acting in the cohomology of Q, whose cohomology implies the equations of
motion. We comment on the possible use of similar approaches in other models.


title:
The dynamical state of RX J1347.5-1145 from a combined strong lensing
  and X-ray analysis

abstract:
  We perform a combined X-ray and strong lensing analysis of RX J1347.5-1145,
one of the most luminous galaxy clusters at X-ray wavelengths. We show that
evidence from strong lensing alone, based on published VLT and new HST data,
strongly argues in favor of a complex structure. The analysis takes into
account arc positions, shapes and orientations and is done thoroughly in the
image plane. The cluster inner regions are well fitted by a bimodal mass
distribution, with a total projected mass of $M_{tot} = (9.9 \pm 0.3)\times
10^{14} M_\odot/h$ within a radius of $360 \mathrm{kpc}/h$ ($1.5'$). Such a
complex structure could be a signature of a recent major merger as further
supported by X-ray data. A temperature map of the cluster, based on deep
Chandra observations, reveals a hot front located between the first main
component and an X-ray emitting South Eastern sub-clump. The map also unveils a
filament of cold gas in the innermost regions of the cluster, most probably a
cooling wake caused by the motion of the cD inside the cool core region. A
merger scenario in the plane of the sky between two dark matter sub-clumps is
consistent with both our lensing and X-ray analyses, and can explain previous
discrepancies with mass estimates based on the virial theorem.


title:
Discretisation of heterogeneous and anisotropic diffusion problems on
  general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid
  interfaces

abstract:
  A discretisation scheme for heterogeneous anisotropic diffusion problems on
general meshes is developed and studied. The unknowns of this scheme are the
values at the centre of the control volumes and at some internal interfaces
which may for instance be chosen at the diffusion tensor discontinuities. The
scheme is therefore completely cell centred if no edge unknown is kept. It is
shown to be accurate on several numerical examples. Mathematical convergence of
the approximate solution to the continuous solution is obtained for general
(possibly discontinuous) tensors, general (possibly non-conforming) meshes, and
with no regularity assumption on the solution. An error estimate is then drawn
under sufficient regularity assumptions on the solution.


title:
A devil in the detail: parameter cross-talk from the solar cycle and
  estimation of solar p-mode frequencies

abstract:
  Frequencies, powers and damping rates of the solar p modes are all observed
to vary over the 11-yr solar activity cycle. Here, we show that simultaneous
variations of these parameters give rise to a subtle cross-talk effect, which
we call the ``devil in the detail'', that biases p-mode frequencies estimated
from analysis of long power frequency spectra. We also show that the resonant
peaks observed in the power frequency spectra show small distortions due to the
effect. Most of our paper is devoted to a study of the effect for Sun-as-a-star
observations of the low-l p modes. We show that for these data the significance
of the effect is marginal. We also touch briefly on the likely l dependence of
the effect, and discuss the implications of these results for solar structure
inversions.


title: The Noise Susceptibility of a Photo-excited Coherent Conductor

abstract:
  We report the theory of the \emph{dynamical response of current fluctuations}
of a photo-excited conductor. We have performed the calculation for a coherent
conductor described by arbitrary energy-dependent transmissions and for
arbitrary frequencies. We consider two experimental setups that correspond to
different ways of symmetrizing the current operators, leading to different
predictions. Our results are in very good, quantitative agreement with a recent
measurement. We demonstrate that the dynamical response of noise that we have
calculated is the key concept that relates Dynamical Coulomb Blockade, i.e. the
electron-electron correction to the conductance due to the presence of an
external impedance, to quantum noise.


title: GHZ versus W : Quantum Teleportation through Noisy Channels

abstract:
  Which state does lose less quantum information between GHZ and W states when
they are prepared for two-party quantum teleportation through noisy channel? We
address this issue by solving analytically a master equation in the Lindbald
form with introducing the noisy channels which makes the quantum channels to be
mixed states. It is found that the answer of the question is dependent on the
type of the noisy channel. If, for example, the noisy channel is ($L_{2,x}$,
$L_{3,x}$, $L_{4,x}$)-type where $L's$ denote the Lindbald operators, GHZ state
is always more robust than W state, i.e. GHZ state preserves more quantum
information. In, however, ($L_{2,y}$, $L_{3,y}$, $L_{4,y}$)-type channel the
situation becomes completely reversed. In ($L_{2,z}$, $L_{3,z}$,
$L_{4,z}$)-type channel W state is more robust than GHZ state when the noisy
paramter ($\kappa$) is comparatively small while GHZ state becomes more robust
when $\kappa$ is large. In isotropic noisy channel we found that both states
preserve equal amount of quantum information. A relation between the average
fidelity and entanglement for the mixed state quantum channels are discussed.


title: Frustrated spin-1/2 square lattice in the layered perovskite PbVO(3)

abstract:
  We report on the magnetic properties of the layered perovskite PbVO(3). The
results of magnetic susceptibility and specific heat measurements as well as
band structure calculations consistently suggest that the S=1/2 square lattice
of vanadium atoms in PbVO(3) is strongly frustrated due to
next-nearest-neighbor antiferromagnetic interactions. The ratio of
next-nearest-neighbor (J(2)) to nearest-neighbor (J(1)) exchange integrals is
estimated to be J(2)/J(1)\approx 0.2-0.4. Thus, PbVO(3) is within or close to
the critical region of the J(1)-J(2) frustrated square lattice. Supporting
this, no sign of long-range magnetic ordering was found down to 1.8 K.


title: Indices for Superconformal Field Theories in 3,5 and 6 Dimensions

abstract:
  We present a trace formula for a Witten type Index for superconformal field
theories in d=3,5 and 6 dimensions, generalizing a similar recent construction
in d=4. We perform a detailed study of the decomposition of long
representations into sums of short representations at the unitarity bound to
demonstrate that our trace formula yields the most general index (i.e. quantity
that is guaranteed to be protected by superconformal symmetry alone) for the
corresponding superalgebras. Using the dual gravitational description, we
compute our index for the theory on the world volume of N M2 and M5 branes in
the large N limit. We also compute our index for recently constructed Chern
Simons theories in three dimensions in the large N limit, and find that, in
certain cases, this index undergoes a large N phase transition as a function of
chemical potentials.


title: Bulk Properties of QCD-matter at Highest Collider Energies

abstract:
  The Large Hadron Collider at CERN will provide Pb-Pb collisions at energies
up to $\sqrt{s_{NN}}$ = 5.5 TeV. We speculate on global observables, i.e. the
charged particle density at mid-rapidity, chemical freeze-out conditions and
collective parameters for transverse radial an elliptic flow. Finally, we
present an idea how to address the important issue of thermalization by
measuring the correlated production of heavy-quark hadrons.


title:
Lie Symmetries, qualitative analysis and exact solutions of nonlinear
  Schr\"odinger equations with inhomogeneous nonlinearities

abstract:
  Using Lie group theory and canonical transformations, we construct explicit
solutions of nonlinear Schrodinger equations with spatially inhomogeneous
nonlinearities. We present the general theory, use it to study different
examples and use the qualitative theory of dynamical systems to obtain some
properties of these solutions.


title: Fullerene graphs have exponentially many perfect matchings

abstract:
  A fullerene graph is a planar cubic 3-connected graph with only pentagonal
and hexagonal faces. We show that fullerene graphs have exponentially many
perfect matchings.


title:
Thermodynamics of (2+1)-dimensional acoustic black hole based on the
  generalized uncertainty principle

abstract:
  We study thermodynamic quantities of an acoustic black hole and its
thermodynamic stability in a cavity based on the generalized uncertainty
principle. It can be shown that there is a minimal black hole which can be a
stable remnant after black hole evaporation. Moreover, the behavior of the free
energy shows that the large black hole is stable too. Therefore, the acoustic
black hole can decay into the remnant or the large black hole.


title:
Parameterizations and fitting of bi-directed graph models to categorical
  data

abstract:
  We discuss two parameterizations of models for marginal independencies for
discrete distributions which are representable by bi-directed graph models,
under the global Markov property. Such models are useful data analytic tools
especially if used in combination with other graphical models. The first
parameterization, in the saturated case, is also known as the multivariate
logistic transformation, the second is a variant that allows, in some (but not
all) cases, variation independent parameters. An algorithm for maximum
likelihood fitting is proposed, based on an extension of the Aitchison and
Silvey method.


title: The distribution of prime numbers on the square root spiral

abstract:
  Prime Numbers clearly accumulate on defined spiral graphs,which run through
the Square Root Spiral. These spiral graphs can be assigned to different
spiral-systems, in which all spiral-graphs have the same direction of rotation
and the same -- second difference -- between the numbers, which lie on these
spiral-graphs. A mathematical analysis shows, that these spiral graphs are
caused exclusively by quadratic polynomials. For example the well known Euler
Polynomial x2+x+41 appears on the Square Root Spiral in the form of three
spiral-graphs, which are defined by three different quadratic polynomials. All
natural numbers,divisible by a certain prime factor, also lie on defined spiral
graphs on the Square Root Spiral (or Spiral of Theodorus, or Wurzelspirale).
And the Square Numbers 4, 9, 16, 25, 36 even form a highly three-symmetrical
system of three spiral graphs, which divides the square root spiral into three
equal areas. Fibonacci number sequences also play a part in the structure of
the Square Root Spiral. With the help of the Number-Spiral, described by Mr.
Robert Sachs, a comparison can be drawn between the Square Root Spiral and the
Ulam Spiral. The shown sections of his study of the number spiral contain
diagrams, which are related to my analysis results, especially in regards to
the distribution of prime numbers.


title: Is dark matter a BEC or scalar field?

abstract:
  This is a brief review on the history of the Bose-Einstein condensate (BEC)
or boson star model of galactic dark matter halos, where ultra-light scalar
dark matter particles condense in a single BEC quantum state. The halos can be
described as a self-gravitating, possibly self-interacting, coherent scalar
field.
  On a scale larger than galaxies, dark matter behaves like cold dark matter
while below that scale the quantum mechanical nature suppresses the dark matter
structure formation due to the minimum length scale determined by the mass
$m\st{>}{\sim}10^{-24} eV$ and the self-interaction of the particles. This
property could alleviate the cusp problem and missing satellite problems of the
$\Lambda$CDM model. Furthermore, this model well reproduces the observed
rotation curves of spiral and dwarf galaxies, which makes the model promising.


title:
Large Deviations for Stochastic Evolution Equations with Small
  Multiplicative Noise

abstract:
  The Freidlin-Wentzell large deviation principle is established for the
distributions of stochastic evolution equations with general monotone drift and
small multiplicative noise. As examples, the main results are applied to derive
the large deviation principle for different types of SPDE such as stochastic
reaction-diffusion equations, stochastic porous media equations and fast
diffusion equations, and the stochastic p-Laplace equation in Hilbert space.
The weak convergence approach is employed in the proof to establish the Laplace
principle, which is equivalent to the large deviation principle in our
framework.


title: Boundedness of Fourier Integral Operators on $\mathcal{F} L^p$ spaces

abstract:
  We study the action of Fourier Integral Operators (FIOs) of H{\"o}rmander's
type on ${\mathcal{F}} L^p({\mathbb {R}}^d_{comp}$, $1\leq p\leq\infty$. We
see, from the Beurling-Helson theorem, that generally FIOs of order zero fail
to be bounded on these spaces when $p\not=2$, the counterexample being given by
any smooth non-linear change of variable. Here we show that FIOs of order
$m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is
proved to be sharp in every dimension $d\geq1$, even for phases which are
linear in the dual variables. The proofs make use of tools from time-frequency
analysis such as the theory of modulation spaces.


title: Deligne-Beilinson cohomology and abelian links invariants

abstract:
  For the abelian Chern-Simons field theory, we consider the quantum functional
integration over the Deligne-Beilinson cohomology classes and we derive the
main properties of the observables in a generic closed orientable 3-manifold.
We present an explicit path-integral non-perturbative computation of the
Chern-Simons links invariants in the case of the torsion-free 3-manifolds
$S^3$, $S^1 \times S^2$ and $S^1 \times \Sigma_g$.


title: The study of dense matter through jet modification

abstract:
  The use of jet modification to study the properties of dense matter is
reviewed. Different sets of jet correlations measurements which may be used to
obtain both the space-time and momentum space structure of the produced matter
are outlined.


title: Generalized geometrical structures of odd dimensional manifolds

abstract:
  We define an almost--cosymplectic--contact structure which generalizes
cosymplectic and contact structures of an odd dimensional manifold.
Analogously, we define an almost--coPoisson--Jacobi structure which generalizes
a Jacobi structure. Moreover, we study relations between these structures and
analyse the associated algebras of functions. As examples of the above
structures, we present geometrical dynamical structures of the phase space of a
general relativistic particle, regarded as the 1st jet space of motions in a
spacetime. We describe geometric conditions by which a metric and a connection
of the phase space yield cosymplectic and dual coPoisson structures, in case of
a spacetime with absolute time (a Galilei spacetime), or
almost--cosymplectic--contact and dual almost--coPoisson--Jacobi structures, in
case of a spacetime without absolute time (an Einstein spacetime).


title: Slip flow over structured surfaces with entrapped microbubbles

abstract:
  On hydrophobic surfaces, roughness may lead to a transition to a
superhydrophobic state, where gas bubbles at the surface can have a strong
impact on a detected slip. We present two-phase lattice Boltzmann simulations
of a Couette flow over structured surfaces with attached gas bubbles. Even
though the bubbles add slippery surfaces to the channel, they can cause
negative slip to appear due to the increased roughness. The simulation method
used allows the bubbles to deform due to viscous stresses. We find a decrease
of the detected slip with increasing shear rate which is in contrast to some
recent experimental results implicating that bubble deformation cannot account
for these experiments. Possible applications of bubble surfaces in microfluidic
devices are discussed.


title: The hidden X-ray breaks in afterglow light curves

abstract:
  Gamma-Ray Burst (GRB) afterglow observations in the Swift era have a
perceived lack of achromatic jet breaks compared to the BeppoSAX, or pre-Swift
era. Specifically, relatively few breaks, consistent with jet breaks, are
observed in the X-ray light curves of these bursts. If these breaks are truly
missing, it has serious consequences for the interpretation of GRB jet
collimation and energy requirements, and the use of GRBs as standard candles.
  Here we address the issue of X-ray breaks which are possibly 'hidden' and
hence the light curves are misinterpreted as being single power-laws. We show
how a number of precedents, including GRB 990510 & GRB 060206, exist for such
hidden breaks and how, even with the well sampled light curves of the Swift
era, these breaks may be left misidentified. We do so by synthesising X-ray
light curves and finding general trends via Monte Carlo analysis. Furthermore,
in light of these simulations, we discuss how to best identify achromatic
breaks in afterglow light curves via multi-wavelength analysis.


title:
The optical depth of the Universe to ultrahigh energy cosmic ray
  scattering in the magnetized large scale structure

abstract:
  This paper provides an analytical description of the transport of ultrahigh
energy cosmic rays in an inhomogeneously magnetized intergalactic medium. This
latter is modeled as a collection of magnetized scattering centers such as
radio cocoons, magnetized galactic winds, clusters or magnetized filaments of
large scale structure, with negligible magnetic fields in between. Magnetic
deflection is no longer a continuous process, it is rather dominated by
scattering events. We study the interaction between high energy cosmic rays and
the scattering agents. We then compute the optical depth of the Universe to
cosmic ray scattering and discuss the phenomological consequences for various
source scenarios. For typical parameters of the scattering centers, the optical
depth is greater than unity at 5x10^{19}eV, but the total angular deflection is
smaller than unity. One important consequence of this scenario is the
possibility that the last scattering center encountered by a cosmic ray be
mistaken with the source of this cosmic ray. In particular, we suggest that
part of the correlation recently reported by the Pierre Auger Observatory may
be affected by such delusion: this experiment may be observing in part the last
scattering surface of ultrahigh energy cosmic rays rather than their source
population. Since the optical depth falls rapidly with increasing energy, one
should probe the arrival directions of the highest energy events beyond
10^{20}eV on an event by event basis to circumvent this effect.


title: Counting RSA-integers

abstract:
  In the RSA cryptosystem integers of the form n=p.q with p and q primes of
comparable size (`RSA-integers') play an important role. It is a folklore
result of cryptographers that C_r(x), the number of integers n<=x that are of
the form n=pq with p and q primes such that p<q<rp, is for fixed r>1
asymptotically equal to c_r*x*log^{-2}x for some constant c_r>0. Here we prove
this and show that c_r=2log r.


title:
A prime-to-p version of the Grothendieck anabelian conjecture for
  hyperbolic curves over finite fields of characteristic p>0

abstract:
  In this paper, we prove a prime-to-p version of Grothendieck's anabelian
conjecture for hyperbolic curves over finite fields of characteristic p>0,
whose original (full profinite) version was proved by Tamagawa in the affine
case and by Mochizuki in the proper case.


title: Binary crystals in two-dimensional two-component Yukawa mixtures

abstract:
  The zero-temperature phase diagram of binary mixtures of particles
interacting via a screened Coulomb pair potential is calculated as a function
of composition and charge ratio. The potential energy obtained by a Lekner
summation is minimized among a variety of candidate two-dimensional crystals. A
wealth of different stable crystal structures is identified including
$A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large
(small) charge.] Their elementary cells consist of triangular, square or
rhombic lattices of the $A$ particles with a basis comprising various
structures of $A$ and $B$ particles. For small charge asymmetry there are no
intermediate crystals besides the pure $A$ and $B$ triangular crystals.


title:
Derivation of the spatio-temporal model equations for the thermoacoustic
  resonator

abstract:
  We derive the model equations describing the thermoacoustic resonator, that
is, an acoustical resonator containing a viscous medium inside. Previous
studies on this system have addressed this sytem in the frame of the plane-wave
approximation, we extend the previous model to by considering spatial effects
in a large aperture resonator. This model exhibits pattern formation and
localized structures scenario.


title: A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations

abstract:
  With the example of the spherically symmetric scalar wave equation on
Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e.
spectral with respect to both spatial and time directions) can be applied for
solving hyperbolic equations. The calculations are carried out within the
framework of conformally compactified space-times. In our formulation, the
equation becomes singular at null infinity and yields regular boundary
conditions there. In this manner it becomes possible to avoid "artificial"
conditions at some numerical outer boundary at a finite distance. We obtain
highly accurate numerical solutions possessing exponential spectral
convergence, a feature known from solving elliptic PDEs with spectral methods.
Our investigations are meant as a first step towards the goal of treating time
evolution problems in General Relativity with spectral methods in space and
time.


title: A Diffractive Study of Parametric Process in Nonlinear Photonic Crystals

abstract:
  We report a general description of quasi-phase-matched parametric process in
nonlinear photonic crystals (NLPC) by extending the conventional X-ray
diffraction theory in solids. Under the virtual wave approximation,
phase-matching resonance is equivalent to the diffraction of the scattered
virtual wave. Hence a modified NLPC Ewald construction can be built up, which
illustrates the nature of the accident for the diffraction of the virtual wave
in NLPC and further reveals the complete set of diffractions of the virtual
wave for both of the air-dielectric and dielectric-dielectric contacts. We show
the two basic linear sequences, the anti-stacking and para-stacking linear
sequences, in one-dimension (1D) NLPC and present a general rule for multiple
phase-matching resonances in 1D NLPC. The parameters affecting the NLPC
structure factor are investigated, which indicate that not only the Ewald
construction but also the relative NLPC atom size together determine whether a
diffraction of the virtual wave can occur in 2D NLPC. The results also show
that 1D NLPC is a better choice than 2D NLPC for a single parametric process.


title:
Inversion of the spin polarization of localized electrons driven by dark
  excitons

abstract:
  The creation of free excitons by absorption of circularly polarized photons,
and their subsequent fast capture by donors, is at the origin of the spin
polarization of donor-bound electrons. The sign of the electronic spin
polarization at low density of excitation is, as expected, fixed by the
helicity of the exciting light; but at high density of excitation we show that
the spin polarization is of the opposite sign. This striking inversion is
explained, here, by the contribution of dark excitons to mechanisms of spin
polarization of localized electrons.


title: Decoherence versus disentanglement for two qubits in a squeezed bath

abstract:
  We study the relation between the sudden death and revival of the
entanglement of two qubits in a common squeezed reservoir, and the normal
decoherence, by getting closer to the Decoherence Free Subspace and calculating
the effect on the death and revival times.


title: A Method for Deriving Transverse Masses Using Lagrange Multipliers

abstract:
  We use Lagrange multipliers to extend the traditional definition of
Transverse Mass used in experimental high energy physics. We demonstrate the
method by implementing it to derive a new Transverse Mass that can be used as a
discriminator to distinguish between top decays via a charged W or a charged
Higgs Boson.


title:
Tight-binding electronic spectra on graphs with spherical topology. I.
  The effect of a magnetic charge

abstract:
  This is the first of two papers devoted to tight-binding electronic spectra
on graphs with the topology of the sphere. In this work the one-electron
spectrum is investigated as a function of the radial magnetic field produced by
a magnetic charge sitting at the center of the sphere. The latter is an integer
multiple of the quantized magnetic charge of the Dirac monopole, that integer
defining the gauge sector. An analysis of the spectrum is carried out for the
five Platonic solids (tetrahedron, cube, octahedron, dodecahedron and
icosahedron), the C$_{60}$ fullerene, and two families of polyhedra, the
diamonds and the prisms. Except for the fullerene, all the spectra are obtained
in closed form. They exhibit a rich pattern of degeneracies. The total energy
at half filling is also evaluated in all the examples as a function of the
magnetic charge.


title: The Quiver of Projectives in Hereditary Categories with Serre Duality

abstract:
  Let k be an algebraically closed field and A a k-linear hereditary category
satisfying Serre duality with no infinite radicals between the preprojective
objects. If A is generated by the preprojective objects, then we show that A is
derived equivalent to rep_k Q for a so called strongly locally finite quiver Q.
To this end, we introduce light cone distances and round trip distances on
quivers which will be used to investigate sections in stable translation
quivers of the form \mathbb{Z} Q.


title: On classes defining a homological dimension

abstract:
  A class $\mathcal F$ of objects of an abelian category $\mathcal A$ is said
to define a \emph{homological dimension} if for any object in $\mathcal A$ the
length of any $\mathcal F$-resolution is uniquely determined. In the present
paper we investigate classes satisfying this property.


title:
Chemical and thermal structure of protoplanetary disks as observed with
  ALMA

abstract:
  We predict how protoplanetary disks around low-mass young stars would appear
in molecular lines observed with the ALMA interferometer. Our goal is to
identify those molecules and transitions that can be used to probe and
distinguish between chemical and physical disk structure and to define
necessary requirements for ALMA observations. Disk models with and without
vertical temperature gradient as well as with uniform abundances and those from
a chemical network are considered. As an example, we show the channel maps of
HCO$^+$(4-3) synthesized with a non-LTE line radiative transfer code and used
as an input to the GILDAS ALMA simulator to produce noise-added realistic
images. The channel maps reveal complex asymmetric patterns even for the model
with uniform abundances and no vertical thermal gradient. We find that a
spatial resolution of $0.2-0.5\arcsec$ and 0.5--10 hours of integration time
will be needed to disentangle large-scale temperature gradients and the
chemical stratification in disks in lines of abundant molecules.


title: Nanoscale spin-polarization in dilute magnetic semiconductor (In,Mn)Sb

abstract:
  Results of point contact Andreev reflection (PCAR) experiments on (In,Mn)Sb
are presented and analyzed in terms of current models of charge conversion at a
superconductor-ferromagnet interface. We investigate the influence of surface
transparency, and study the crossover from ballistic to diffusive transport
regime as contact size is varied. Application of a Nb tip to a (In,Mn)Sb sample
with Curie temperature Tc of 5.4 K allowed the determination of
spin-polarization when the ferromagnetic phase transition temperature is
crossed. We find a striking difference between the temperature dependence of
the local spin polarization and of the macroscopic magnetization, and
demonstrate that nanoscale clusters with magnetization close to the saturated
value are present even well above the magnetic phase transition temperature.