title: Non Perturbative Renormalization Group and Bose-Einstein Condensation

abstract:
  These lectures are centered around a specific problem, the effect of weak
repulsive interactions on the transition temperature $T_c$ of a Bose gas. This
problem provides indeed a beautiful illustration of many of the techniques
which have been discussed at this school on effective theories and
renormalization group. Effective theories are used first in order to obtain a
simple hamiltonian describing the atomic interactions: because the typical
atomic interaction potentials are short range, and the systems that we consider
are dilute, these potentials can be replaced by a contact interaction whose
strength is determined by the s-wave scattering length. Effective theories are
used next in order to obtain a simple formula for the shift in $T_c$: one
exploits there the fact that near $T_c$ the physics is dominated by low
momentum modes whose dynamics is most economically described in terms of
classical fields; the ingredients needed to calculate the shift of $T_c$ can be
obtained from this classical field theory. Finally the renormalization group is
used both to obtain a qualitative understanding, and also as a non perturbative
tool to evaluate quantitatively the shift in $T_c$.


title: 2-filteredness and the point of every Galois topos

abstract:
  A locally connected topos is a Galois topos if the Galois objects generate
the topos. We show that the full subcategory of Galois objects in any connected
locally connected topos is an inversely 2-filtered 2-category, and as an
application of the construction of 2-filtered bi-limits of topoi, we show that
every Galois topos has a point.


title: How synchronization protects from noise

abstract:
  Synchronization phenomena are pervasive in biology. In neuronal networks, the
mechanisms of synchronization have been extensively studied from both
physiological and computational viewpoints. The functional role of
synchronization has also attracted much interest and debate. In particular,
synchronization may allow distant sites in the brain to communicate and
cooperate with each other, and therefore it may play a role in temporal binding
and in attention and sensory-motor integration mechanisms.
  In this article, we study another role for synchronization: the so-called
"collective enhancement of precision." We argue, in a full nonlinear dynamical
context, that synchronization may help protect interconnected neurons from the
influence of random perturbations -- intrinsic neuronal noise -- which affect
all neurons in the nervous system. This property may allow reliable
computations to be carried out even in the presence of significant noise (as
experimentally found e.g., in retinal ganglion cells in primates), as
mathematically it is key to obtaining meaningful downstream signals, whether in
terms of precisely-timed interaction (temporal coding), population coding, or
frequency coding. Using stochastic contraction theory, we show how
synchronization of nonlinear dynamical systems helps protect these systems from
random perturbations.
  Our main contribution is a mathematical proof that, under specific quantified
conditions, the impact of noise on each individual system and on the spatial
mean can essentially be cancelled through synchronization. Similar concepts may
be applicable to questions in systems biology.


title: Semiclassical Coulomb field

abstract:
  The contribution of different modes of the Coulomb field to decoherence and
to the dynamical breakdown of the time reversal invariance is calculated in the
one-loop approximation for non-relativistic electron gas. The dominant
contribution was found to come from the usual collective modes in the plasma,
namely the zero-sound and the plasmon oscillations. The length scale of the
quantum-classical transition is found to be close to the Thomas-Fermi screening
length. It is argued that the extension of these modes to the whole Fock-space
yield optimal pointer states.


title: SOLIS Vector Spectromagnetograph: status and science

abstract:
  The Vector Spectromagnetograph (VSM) instrument has been recording
photospheric and chromospheric magnetograms daily since August 2003. Full-disk
photospheric vector magnetograms are observed at least weekly and, since
November 2006, area-scans of active regions daily. Quick-look vector magnetic
images, plus X3D and FITS formated files, are now publicly available daily. In
the near future, Milne-Eddington inversion parameter data will also be
available and a typical observing day will include three full-disk photospheric
vector magnetograms. Besides full-disk observations, the VSM is capable of high
temporal cadence area-scans of both the photosphere and chromosphere.
Carrington rotation and daily synoptic maps are also available from the
photospheric magnetograms and coronal hole estimate images.


title: Time reparametrization symmetry in spin glass models

abstract:
  We study the long-time aging dynamics of spin-glass models with two-spin
interactions by performing a Renormalization Group transformation on the time
variable in the non-equilibrium dynamical generating functional. We obtain the
RG equations and find that the flow converges to an exact fixed point. We show
that this fixed point is invariant under reparametrizations of the time
variable. This continuous symmetry is broken, as evidenced by the fact that the
observed correlations and responses are not invariant under it. We argue that
this gives rise to the presence of Goldstone modes, and that those Goldstone
modes shape the behavior of fluctuations in the nonequilibrium dynamics.


title:
Hitchin integrable systems, deformations of spectral curves, and KP-type
  equations

abstract:
  An effective family of spectral curves appearing in Hitchin fibrations is
determined. Using this family the moduli spaces of stable Higgs bundles on an
algebraic curve are embedded into the Sato Grassmannian. We show that the
Hitchin integrable system, the natural algebraically completely integrable
Hamiltonian system defined on the Higgs moduli space, coincides with the KP
equations. It is shown that the Serre duality on these moduli spaces
corresponds to the formal adjoint of pseudo-differential operators acting on
the Grassmannian. From this fact we then identify the Hitchin integrable system
on the moduli space of Sp(2m)-Higgs bundles in terms of a reduction of the KP
equations. We also show that the dual Abelian fibration (the SYZ mirror dual)
to the Sp(2m)-Higgs moduli space is constructed by taking the symplectic
quotient of a Lie algebra action on the moduli space of GL-Higgs bundles.


title: Ruppeiner Geometry of Black Hole Thermodynamics

abstract:
  The Hessian of the entropy function can be thought of as a metric tensor on
state space. In the context of thermodynamical fluctuation theory Ruppeiner has
argued that the Riemannian geometry of this metric gives insight into the
underlying statistical mechanical system; the claim is supported by numerous
examples. We study these geometries for some families of black holes and find
that the Ruppeiner geometry is flat for Reissner--Nordstr\"om black holes in
any dimension, while curvature singularities occur for the Kerr black holes.
Kerr black holes have instead flat Weinhold curvature.


title: Excited-state OH Masers and Supernova Remnants

abstract:
  The collisionally pumped, ground-state 1720 MHz maser line of OH is widely
recognized as a tracer for shocked regions and observed in star forming regions
and supernova remnants. Whereas some lines of excited states of OH have been
detected and studied in star forming regions, the subject of excited-state OH
in supernova remnants -- where high collision rates are to be expected -- is
only recently being addressed. Modeling of collisional excitation of OH
demonstrates that 1720, 4765 and 6049 MHz masers can occur under similar
conditions in regions of shocked gas. In particular, the 6049 and 4765 MHz
masers become more significant at increased OH column densities where the 1720
MHz masers begin to be quenched. In supernova remnants, the detection of
excited-state OH line maser emission could therefore serve as a probe of
regions of higher column densities. Using the Very Large Array, we searched for
excited-state OH in the 4.7, 7.8, 8.2 and 23.8 GHz lines in four well studied
supernova remnants with strong 1720 MHz maser emission (SgrAEast, W28, W44 and
IC443). No detections were made, at typical detection limits of around 10
mJy/beam. The search for the 6 GHz lines were done using Effelsberg since the
VLA receivers did not cover those frequencies, and are reported on in an
accompanying letter (Fish, Sjouwerman & Pihlstrom 2007). We also
cross-correlated the positions of known supernova remnants with the positions
of 1612 MHz maser emission obtained from blind surveys. No probable
associations were found, perhaps except in the SgrAEast region. The lack of
detections of excited-state OH indicates that the OH column densities suffice
for 1720 MHz inversion but not for inversion of excited-state transitions,
consistent with the expected results for C-type shocks.


title: Unparticle physics at the photon collider

abstract:
  Recently, a conceptually new physics beyond the Standard Model (SM),
unparticle, has been proposed, where a hidden conformal sector is coupled to
the SM sector through higher dimensional operators. In this setup, we
investigate unparticle physics at the photon collider, in particular,
unparticle effects on the gamma gamma to gamma gamma process. Since this
process occurs at loop level in the SM, the unparticle effects can be
significant even if the cutoff scale is very high. In fact, we find that the
unparticle effects cause sizable deviations from the SM results. The scaling
dimension of the unparticle d_U reflects the dependence of the cross section on
the final state photon invariant mass, so that precision measurements of this
dependence may reveal the scaling dimension of the unparticle.


title:
Global well-posedness, scattering and blow-up for the energy-critical,
  focusing Hartree equation in the radial case

abstract:
  We establish global existence, scattering for radial solutions to the
energy-critical focusing Hartree equation with energy and $\dot{H}^1$ norm less
than those of the ground state in $\mathbb{R}\times \mathbb{R}^d$, $d\geq 5$.


title:
Intrinsic relation between ground-state fidelity and the
  characterization of a quantum phase transition

abstract:
  The notion of fidelity in quantum information science has been recently
applied to analyze quantum phase transitions from the viewpoint of the ground
state (GS) overlap for various many-body systems. In this work, we unveil the
intrinsic relation between the GS fidelity and the derivatives of GS energy and
find that they play equivalent role in identifying the quantum phase
transition. The general connection between the two approaches enables us to
understand the different singularity and scaling behaviors of fidelity
exhibited in various systems on general grounds. Our general conclusions are
illustrated via several quantum spin models which exhibit different kinds of
QPTs.


title: Bootstrap Approximations in Contractor Renormalization

abstract:
  We propose a bootstrap method for approximating the long-range terms in the
Contractor Renormalization (CORE) method. The idea is tested on the 2-D
Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain
renormalization group flows that directly reveal the Neel phase of the
unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model
for weak frustration. However, we find that this bootstrap method is dependent
on blocking and truncation schemes. For this reason, we discuss these
dependencies and unresolved issues that researchers who use this approach must
consider.


title: Direct CP and T Violation in Baryonic B Decays

abstract:
  We review the direct CP and T violation in the three-body baryonic B decays
in the standard model. In particular, we emphasize that the direct CP violating
asymmetry in $B^\pm\to p\bar p K^{*\pm}$ is around 22% and the direct $T$
violating asymmetry in $\bar B^0 \ra \Lambda \bar p \pi^+$ can be as large as
12%, which are accessible to the current B factories at KEK and SLAC as well as
SuperB and LHCb.


title: On a generalization of Chen's iterated integrals

abstract:
  Chen's iterated integrals may be generalized by interpolation of functions of
the positive integer number of times which particular forms are iterated in
integrals along specific paths, to certain complex values. These generalized
iterated integrals satisfy both an additive and a (non-classical)
multiplicative iterative property, in addition to a comultiplication formula.
  This theory is developed in the first part of the paper, after which various
applications are discussed, including the expression of certain zeta functions
as complex iterated integrals (from which an obstruction to the existence of a
contour integration proof of the functional equation for the Dedekind zeta
function emerges); an elegant reformulation of a result of Gel'fand and Shilov
in the theory of distributions which gives a way of thinking about complex
iterated derivatives; and a direct topological proof of the monodromy of
polylogarithms.


title: CPT conserving cosmological birefringence

abstract:
  We demonstrate that the cosmological birefringence can arise from CPT
conserving effect, originated from the CPT-even dimension-six Chern-Simons-like
term. We show that a sizable rotation polarization angle in the data of the
cosmic microwave background radiation polarization can be induced.


title:
Cosmology with dark energy decaying through its chemical-potential
  contribution

abstract:
  The consideration of dark energy's quanta, required also by thermodynamics,
introduces its chemical potential into the cosmological equations. Isolating
its main contribution, we obtain solutions with dark energy decaying to matter
or radiation. When dominant, their energy densities tend asymptotically to a
constant ratio, explaining today's dark energy-dark matter coincidence, and in
agreement with supernova redshift data.


title:
Double-spin asymmetries for small-Q_T Drell-Yan pair production in
  transversely polarized p\bar{p} collisions

abstract:
  We discuss the Drell-Yan process at a measured transverse-momentum $Q_T$ of
the produced lepton pair in collisions of transversely polarized protons and
antiprotons, to be observed at the proposed spin experiments at GSI. The large
logarithmic contributions from multiple soft gluon emission, accompanying the
Drell-Yan mechanism at small $Q_T$, are resummed to all orders in QCD
perturbation theory up to next-to-leading logarithmic (NLL) accuracy. Numerical
evaluation shows the impact of the NLL as well as LL effect on the dilepton
$Q_T$ spectra. For the corresponding $Q_T$-dependent spin asymmetry $\aqt$, the
LL effect gives significant modification while the NLL effect is marginal,
leading to QCD prediction that $\aqt$ at GSI is flat at small and moderate
$Q_T$ and almost equals the conventional asymmetry $A_{TT}$ associated with the
$Q_T$-integrated cross sections. This flat behavior in turn allows us to use
analytic saddle-point evaluation of the resummation formula in the limit
$Q_T\to 0$, not only to obtain quantitative estimate of $\aqt$, but also to
clarify mechanisms behind the relation $\aqt \simeq A_{TT}$ characteristic of
$p\bar{p}$ collisions at GSI.


title:
Anderson localization of electron states in graphene in different types
  of disorder

abstract:
  Anderson localization of electron states on graphene lattice with diagonal
and off-diagonal (OD) disorder in the absence of magnetic field is investigated
by using the standard finite-size scaling analysis. In the presence of diagonal
disorder all states are localized as predicted by the scaling theory for
two-dimensional systems. In the case of OD disorder, the states at the Dirac
point (E=0) are shown to be delocalized due to the specific chiral symmetry,
although other states ($E \neq 0$) are still localized. In OD disorder the
conductance at E=0 in an $M\times L$ rectangular system at the thermodynamical
limit is calculated with the transfer-matrix technique for various values of
ratio $M/L$ and different types of distribution functions of the OD elements
$t_{nn'}$. It is found that if all the $t_{nn'}$'s are positive the conductance
is independent of $L/M$ as restricted by 2 delocalized channels at E=0. If the
distribution function includes the sign randomness of elements $t_{nn'}$, the
conductivity, rather than the conductance, becomes $L/M$ independent. The
calculated value of the conductivity is around $\frac{4e^2}{h}$, in consistence
with the experiments.


title: CODATA Recommended Values of the Fundamental Physical Constants: 2006

abstract:
  This paper gives the 2006 self-consistent set of the basic constants and
conversion factors of physics and chemistry recommended by the Committee on
Data for Science and Technology (CODATA) for international use. Further, it
describes in detail the adjustment of the values of the constants, including
the selection of the final set of input data based on the results of
least-squares analyses. The 2006 adjustment takes into account the data
considered in the 2002 adjustment as well as the data that became available
between 31 December 2002, the closing date of that adjustment, and 31 December
2006, the closing date of the new adjustment. The new data have led to a
significant reduction in the uncertainties of many recommended values. The 2006
set replaces the previously recommended 2002 CODATA set and also may be found
on the World Wide Web at physics.nist.gov/constants.


title:
Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty
  of Fermions in Graphene

abstract:
  We investigate geometric phase of fermion states under relative vibrations of
two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation
using Floquet scheme. In a period of vibration the fermions acquire different
geometric phases depending on their momenta. There are two regions in the
momentum space: the adiabatic region where the geometric phase can be
approximated by the Berry phase and the chaotic region where the geometric
phase drastically fluctuates in changing parameters. The energy of fermions due
to vibrations shows spikes in the chaotic region. The results suggest a
possible dephasing mechanism which may cause classical-like transport
properties in graphene.


title: Small primitive roots and malleability of RSA moduli

abstract:
  In a paper of P. Paillier and J. Villar a conjecture is made about the
malleability of an RSA modulus. In this paper we present an explicit algorithm
refuting the conjecture. Concretely we can factorize an RSA modulus n using
very little information on the factorization of a concrete n' coprime to n.
However, we believe the conjecture might be true, when imposing some extra
conditions on the auxiliary n' allowed to be used. In particular, the paper
shows how subtle the notion of malleability is.


title:
Observation of an extended VHE gamma-ray emission from MSH 15-52 with
  CANGAROO-III

abstract:
  We have observed the supernova remnant MSH 15-52 (G320.4-1.2), which contains
the gamma-ray pulsar PSR B1509-58, using the CANGAROO-III imaging atmospheric
Cherenkov telescope array from April to June in 2006. We detected gamma rays
above 810 GeV at the 7 sigma level during a total effective exposure of 48.4
hours. We obtained a differential gamma-ray flux at 2.35 TeV of
(7.9+/-1.5_{stat}+/-1.7_{sys}) \times 10^{-13} cm^{-2}s^{-1}TeV^{-1} with a
photon index of 2.21+/-0.39_{stat}+/-0.40_{sys}, which is compatible with that
of the H.E.S.S. observation in 2004. The morphology shows extended emission
compared to our Point Spread Function. We consider the plausible origin of the
high energy emission based on a multi-wavelength spectral analysis and
energetics arguments.


title: Extremal dilatonic black holes in 4D Gauss-Bonnet gravity

abstract:
  This is a report of our recent investigation on the extremal dilatonic black
holes in four dimensional Gauss-Bonnet gravity. We found that a global solution
can exist only when the dilaton coupling is less than a critical value which
can be determined numerically. Moreover, the black hole horizon is stretched by
the Gauss-Bonnet correction and the entropy is twice the value given by
Bekenstein-Hawking formula.


title: Examples of para-cocyclic objects induced by BD-laws

abstract:
  In a recent paper arXiv:0705.3190, we gave a general construction of a
para-cocyclic structure on a cosimplex, associated to a so called admissible
septuple -- consisting of two categories, three functors and two natural
transformations, subject to compatibility relations. The main examples of such
admissible septuples were induced by algebra homomorphisms. In this note we
provide more general examples coming from appropriate (`locally braided')
morphisms of monads.


title: Polyakov loop extended NJL model with imaginary chemical potential

abstract:
  The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary
chemical potential is studied. The model possesses the extended ${\mathbb
Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended
${\mathbb Z}_{3}$ symmetry, such as the partition function, the chiral
condensate and the modified Polyakov loop, have the Roberge-Weiss (RW)
periodicity. The phase diagram of confinement/deconfinement transition derived
with the PNJL model is consistent with the RW prediction on it and the results
of lattice QCD. The phase diagram of chiral transition is also presented by the
PNJL model.


title:
Four-Step Evolution of Spin-Hall Conductance: Tight-Binding Electrons
  with Rashba Coupling in a Magnetic Field

abstract:
  An intriguing magneto-transport property is demonstrated by tight-binding
lattice electrons with Rashba spin-orbit coupling (SOC) in a magnetic field.
With the flux strength $\phi={2\pi/N}$ ($N$ is an integer) and the Zeeman
splitting fixed, when increasing the Rashba SOC $\lambda$, the spin-Hall and
charge-Hall conductances (SHC and CHC) undergo four-step evolutions: the SHC
shows size-dependent resonances and jumps at three critical $\lambda_{c}$'s,
and changes its sign at $\lambda_{c1}$ and $\lambda_{c3}$; while the CHC
exhibits three quantum jumps by $-Ne^2/h$, $+2Ne^2/h$ and $-Ne^2/h$. Such
four-step evolutions are also reflected in topological characters and spin
polarizations of edge states of a cylindrical system, and are robust against
weak disorder.


title:
Charged and Neutral Currents in a 3-3-1 Model with Right-Handed
  Neutrinos

abstract:
  The charged and the neutral currents are obtained by using a formal
algebraical approach (developed and applied by the author) within the exact
solution of a 3-3-1 gauge model with right-handed neutrinos. The entire
Standard Model phenomenology is recovered without imposing any supplemental
condition, but only by choosing an adecquate set of parameters from the very
beginning of the calculus. A new and rich phenomenology regarding the particles
and their currents occurs as well. The appealing feature of our results resides
in the exact expressions of the currents which need not the adjustment usually
due to the small mixing angle $\phi$ between neutral bosons $Z$ and
$Z^{\prime}$ (like in the most of the papers in the literature treating the
same issue). The required mixing was considered and aleready performed as an
intermediate step by the solving method itself, since the physical eigenstates
of those bosons were determined and then identified in the neutral currents.


title: Quasithermodynamics and a Correction to the Stefan--Boltzmann Law

abstract:
  We provide a correction to the Stefan--Boltzmann law and discuss the problem
of a phase transition from the superfluid state into the normal state.


title: Asymptotic Giant Branch Stars in the Phoenix Dwarf Galaxy

abstract:
  JHKs near-infrared photometry of stars in the Phoenix dwarf galaxy is
presented and discussed. Combining these data with the optical photometry of
Massey et al. allows a rather clean separation of field stars from Phoenix
members. The discovery of a Mira variable (P = 425 days), which is almost
certainly a carbon star, leads to an estimate of the distance modulus of
23.10+/-0.18 that is consistent with other estimates and indicates the
existence of a significant population of age ~2 Gyr. The two carbon stars of Da
Costa have M{bol} = -3.8 and are consistent with belonging to a population of
similar age; some other possible members of such a population are identified. A
Da Costa non-carbon star is Delta Ks~0.3 mag brighter than these two carbon
stars. It may be an AGB star of the dominant old population. The nature of
other stars lying close to it in the Ks,(J-Ks) diagram needs studying.


title: Suzaku Observation of AXP 1E 1841-045 in SNR Kes 73

abstract:
  Anomalous X-ray pulsars (AXPs) are thought to be magnetars, which are neutron
stars with ultra strong magnetic field of $10^{14}$-- $10^{15}$ G. Their energy
spectra below $\sim$10 keV are modeled well by two components consisting of a
blackbody (BB) ($\sim$0.4 keV) and rather steep power-law (POW) function
(photon index $\sim$2-4). Kuiper et al.(2004) discovered hard X-ray component
above $\sim$10 keV from some AXPs. Here, we present the Suzaku observation of
the AXP 1E 1841-045 at the center of supernova remnant Kes 73. By this
observation, we could analyze the spectrum from 0.4 to 50 keV at the same time.
Then, we could test whether the spectral model above was valid or not in this
wide energy range. We found that there were residual in the spectral fits when
fit by the model of BB + POW. Fits were improved by adding another BB or POW
component. But the meaning of each component became ambiguous in the
phase-resolved spectroscopy. Alternatively we found that NPEX model fit well
for both phase-averaged spectrum and phase-resolved spectra. In this case, the
photon indices were constant during all phase, and spectral variation seemed to
be very clear. This fact suggests somewhat fundamental meaning for the emission
from magnetars.


title: General Single Field Inflation with Large Positive Non-Gaussianity

abstract:
  Recent analysis of the WMAP three year data suggests
$f_{NL}^{local}\simeq86.8$ in the WMAP convention. It is necessary to make sure
whether general single field inflation can produce a large positive $f_{NL}$
before turning to other scenarios. We give some examples to generate a large
positive $f_{NL}^{equil}$ in general single field inflation. Our models are
different from ghost inflation. Due to the appearance of non-conventional
kinetic terms, $f_{NL}^{equil}\gg1$ can be realized in single field inflation.


title:
Extracting MSSM Masses From Heavy Higgs Decays to Four Leptons at the
  LHC

abstract:
  It is well known that finding and measuring the masses of particles in the
Minimal Supersymmetric Standard Model (MSSM) at the Large Hadron Collider (LHC)
may be possible using invariant mass distributions in exclusive channels
containing n_j jets and n_l leptons. We perform this analysis for the (n_j,
n_l) = (0,4) decay of heavy Higgs bosons to neutralinos, pp \to H/A \to \chi_i
\chi_j (i,j =2,3,4), which then decay to four leptons and two lightest
neutralinos \chi_1 via on-shell sleptons. When i=j and the sleptons are
degenerate, our Monte Carlo study shows that the LHC will be able to measure
the Higgs and relevant neutralino and slepton masses to roughly
  30%; however, if one of these is already known within 5%, the other three may
be found to equal or better accuracy. This would provide the first accurate
measurement of the H/A mass via invariant mass distribution techniques.


title: A Problem of Powers and the Product of Spatial Product Systems

abstract:
  In the 2002 AMS summer conference on ``Advances in Quantum Dynamics'' in
Mount Holyoke Robert Powers proposed a sum operation for spatial E0-semigroups.
Still during the conference Skeide showed that the Arveson system of that sum
is the product of spatial Arveson systems. This product may but need not
coincide with the tensor product of Arveson systems. The Powers sum of two
spatial E0-semigroups is, therefore, up to cocycle conjugacy Skeide's product
of spatial noises.


title: Dark Matter Problem in the Local Supercluster

abstract:
  The Local Supercluster is an ideal laboratory to study distribution of
luminous and dark matter in the nearby Universe. The 1100 small groups have
been selected using algorithm based on assumption that a total energy of
physical pair of galaxies must be negative. The properties of the groups have
been considered.


title: Cosmology of gravitational vacuum

abstract:
  Production of gravitational vacuum defects and their contribution to the
energy density of our Universe are discussed. These topological microstructures
(defects) could be produced in the result of creation of the Universe from
"nothing" when a gravitational vacuum condensate has appeared. They must be
isotropically distributed over the isotropic expanding Universe. After Universe
inflation these microdefects are smoothed, stretched and broken up. A part of
them could survive and now they are perceived as the structures of Lambda-term
and an unclustered dark matter. It is shown that the parametrization
noninvariance of the Wheeler-De Witt equation can be used to describe
phenomenologically vacuum topological defects of different dimensions
(worm-holes, micromembranes, microstrings and monopoles). The mathematical
illustration of these processes may be the spontaneous breaking of the local
Lorentz-invariance of the quasi-classical equations of gravity. Probably the
gravitational vacuum condensate has fixed time in our Universe. Besides,
3-dimensional topological defects renormalize Lambda-term.


title: SUSY Les Houches Accord 2

abstract:
  The Supersymmetry Les Houches Accord (SLHA) provides a universal set of
conventions for conveying spectral and decay information for supersymmetry
analysis problems in high energy physics. Here, we propose extensions of the
conventions of the first SLHA to include various generalisations: the minimal
supersymmetric standard model with violation of CP, R-parity, and flavour, as
well as the simplest next-to-minimal model.


title: A contact geometric proof of the Whitney-Graustein theorem

abstract:
  The Whitney-Graustein theorem states that regular closed curves in the
2-plane are classified, up to regular homotopy, by their rotation number. Here
we give a simple proof based on contact geometry.


title: When did vacuum energy of the Universe become cosmological constant?

abstract:
  A quark-gluon phase transition in the Universe is researched after which
vacuum (dark) energy has hardened and become cosmological constant. Before this
a vacuum component of the Universe was changing by jumps during phase
transitions since vacuum condensates of quantum fields carried a negative
contribution in its positive density energy. This quintessence period of the
Universe life took place during the first parts of a second when our Universe
was losing high symmetry. Using Zel'dovich's formula the modern value of vacuum
energy is also calculated. It is shown that a quantum chromodynamical vacuum
which is characterized by pseudogoldstone bosons existed definitely when
temperature of the Universe was T~150 MeV. Therefore there is a large
probability that dark energy is vacuum energy.


title:
A robust and reliable method for detecting signals of interest in
  multiexponential decays

abstract:
  The concept of rejecting the null hypothesis for definitively detecting a
signal was extended to relaxation spectrum space for multiexponential
reconstruction. The novel test was applied to the problem of detecting the
myelin signal, which is believed to have a time constant below 40ms, in T2
decays from MRI's of the human brain. It was demonstrated that the test allowed
the detection of a signal in a relaxation spectrum using only the information
in the data, thus avoiding any potentially unreliable prior information. The
test was implemented both explicitly and implicitly for simulated T2
measurements. For the explicit implementation, the null hypothesis was that a
relaxation spectrum existed that had no signal below 40ms and that was
consistent with the T2 decay. The confidence level by which the null hypothesis
could be rejected gave the confidence level that there was signal below the
40ms time constant. The explicit implementation assessed the test's performance
with and without prior information where the prior information was the
nonnegative relaxation spectrum assumption. The test was also implemented
implicitly with a data conserving multiexponential reconstruction algorithm
that used left invertible matrices and that has been published previously. The
implicit and explicit implementations demonstrated similar characteristics in
detecting the myelin signal in both the simulated and experimental T2 decays,
providing additional evidence to support the close link between the two tests.
[Full abstract in paper]


title: Horizontal loops in Engel space

abstract:
  A simple proof is given of the following result first observed by J. Adachi:
embedded circles tangent to the standard Engel structure on Euclidean 4-space
are classified, up to isotopy via such embeddings, by their rotation number.


title: Evolution of Alfven wave-driven solar winds to red giants

abstract:
  In this talk we introduce our recent results of global 1D MHD simulations for
the acceleration of solar and stellar winds. We impose transverse photospheric
motions corresponding to the granulations, which generate outgoing Alfven
waves. The Alfven waves effectively dissipate by 3-wave coupling and direct
mode conversion to compressive waves in density-stratified atmosphere. We show
that the coronal heating and the solar wind acceleration in the open magnetic
field regions are natural consequence of the footpoint fluctuations of the
magnetic fields at the surface (photosphere). We also discuss winds from red
giant stars driven by \Alfven waves, focusing on different aspects from the
solar wind. We show that red giants wind are highly structured with
intermittent magnetized hot bubbles embedded in cool chromospheric material.


title:
The moments of Minkowski question mark function: the dyadic period
  function

abstract:
  The Minkowski question mark function ?(x) arises as a real distribution of
rationals in the Farey tree. We examine the generating function of moments of
?(x). It appears that the generating function is a direct dyadic analogue of
period functions for Maass wave forms and it is defined in the cut plane
C(0,infinity). The exponential generating function satisfies the integral
equation with kernel being the Bessel function. The solution of this integral
equation leads to the definition of dyadic eigenfunctions, arising from a
certain Hilbert-Schmidt operator. Finally, we describe p-adic distribution of
rationals in the Stern-Brocot tree. Surprisingly, the Eisenstein series G_1(z)
does manifest in both real and p-adic cases.


title: Cosmology of Vacuum

abstract:
  Shortly the vacuum component of the Universe from the geometry point of view
and from the point of view of the standard model of physics of elementary
particles is discussed. Some arguments are given to the calculated value of the
cosmological constant (Zeldovich approximation). A new component of space
vacuum (the gravitational vacuum condensate) is involved the production of
which has fixed time in our Universe. Also the phenomenon of vacuum
selforganization must be included in physical consideration of the Universe
evolution.


title:
Non-Equilibrium Thermodynamics formalism for Marcus cross-exchange
  electron transfer reaction rates

abstract:
  The cross-exchange electron transfer expression arising from Marcus theory is
deduced using Onsager's non-equilibrium Thermodynamics formalism.


title:
Statistical properties of the Calkin--Wilf tree: real an p-adic
  distribution

abstract:
  We examine statistical properties of the Calkin--Wilf tree and give
number-theoretical applications.


title:
On connection between reducibility of an n-ary quasigroup and that of
  its retracts

abstract:
  An $n$-ary operation $Q:S^n\to S$ is called an $n$-ary quasigroup of order
$|S|$ if in the equation $x_0=Q(x_1,...,x_n)$ knowledge of any $n$ elements of
$x_0,...,x_n$ uniquely specifies the remaining one. An $n$-ary quasigroup $Q$
is (permutably) reducible if
$Q(x_1,...,x_n)=P(R(x_{s(1)},...,x_{s(k)}),x_{s(k+1)},...,x_{s(n)})$ where $P$
and $R$ are $(n-k+1)$-ary and $k$-ary quasigroups, $s$ is a permutation, and
$1<k<n$. An $m$-ary quasigroup $R$ is called a retract of $Q$ if it can be
obtained from $Q$ or one of its inverses by fixing $n-m>0$ arguments.
  We show that every irreducible $n$-ary quasigroup has an irreducible
$(n-1)$-ary or $(n-2)$-ary retract; moreover, if the order is finite and prime,
then it has an irreducible $(n-1)$-ary retract. We apply this result to show
that all $n$-ary quasigroups of order 5 or 7 whose all binary retracts are
isotopic to $Z_5$ or $Z_7$ are reducible for $n>3$.
  Keywords: $n$-ary quasigroups, retracts, reducibility, latin hypercubes


title:
Generating and zeta functions, structure, spectral and analytic
  properties of the moments of Minkowski question mark function

abstract:
  In this paper we are interested in moments of Minkowski question mark
function ?(x). It appears that, to certain extent, the results are analogous to
the results obtained for objects associated with Maass wave forms: period
functions, L-series, distributions, spectral properties. These objects can be
naturally defined for ?(x) as well. Despite the fact that there are various
nice results about the nature of ?(x), these investigations are mainly
motivated from the perspective of metric number theory, Hausdorff dimension,
singularity and generalizations. In this work it is shown that analytic and
spectral properties of various integral transforms of ?(x) do reveal
significant information about the question mark function. We prove asymptotic
and structural results about the moments, calculate certain integrals involving
?(x), define an associated zeta function, generating functions, Fourier series,
and establish intrinsic relations among these objects. At the end of the paper
it is shown that certain object associated with ?(x) establish a bridge between
realms of imaginary and real quadratic irrationals.


title: On the connection between gamma and radio radiation spectra in pulsars

abstract:
  The model of pulsar radio emission is discussed in which a coherent radio
emis-sion is excited in a vacuum gap above polar cap of neutron star. Pulsar X
and gamma radiation are considered as the result of low-frequency radio
emission inverse Comp-ton scattering on ultra relativistic electrons
accelerated in the gap. The influence of the pulsar magnetic field on Compton
scattering is taken into account. The relation of radio and gamma radiation
spectra has been found in the framework of the model.


title:
Ionic Cloud Distribution close to a Charged Surface in the Presence of
  Salt

abstract:
  Despite its importance, the understanding of ionic cloud distribution close
to a charged macroion under physiological salt conditions has remained very
limited especially for strongly coupled systems with, for instance, multivalent
counterions. Here we present a formalism that predicts both counterion and
coion distributions in the vicinity of a charged macroion for an arbitrary
amount of added salt and in both limits of mean field and strong coupling. The
distribution functions are calculated explicitly for ions next to an infinite
planar charged wall. We present a schematic phase diagram identifying different
physical regimes in terms of electrostatic coupling parameter and bulk salt
concentration.


title: The Maximal Probability that k-wise Independent Bits are All 1

abstract:
  A k-wise independent distribution on n bits is a joint distribution of the
bits such that each k of them are independent. In this paper we consider k-wise
independent distributions with identical marginals, each bit has probability p
to be 1. We address the following question: how high can the probability that
all the bits are 1 be, for such a distribution? For a wide range of the
parameters n,k and p we find an explicit lower bound for this probability which
matches an upper bound given by Benjamini et al., up to multiplicative factors
of lower order. The question we investigate can be seen as a relaxation of a
major open problem in error-correcting codes theory, namely, how large can a
linear error correcting code with given parameters be?
  The question is a type of discrete moment problem, and our approach is based
on showing that bounds obtained from the theory of the classical moment problem
provide good approximations for it. The main tool we use is a bound controlling
the change in the expectation of a polynomial after small perturbation of its
zeros.


title:
Deflection of Ultra Slow Light by Earth Gravity on Laboratory Length
  Scale

abstract:
  The high speed of light in vacuo together with the weakness of Earth gravity
rules out any experimental detection of gravitational deflection of light on
the laboratory length scale. Recent advances in coherent optics that produce
ultra slow light in highly dispersive media with the group velocities down to
~102 ms-1, or even less, however, open up this possibility. In this work, we
present a theoretical study for a possible laboratory observation of the
deflection of such an ultra slow light in the highly dispersive medium under
Earth gravity. Our general relativistic calculation is based on the Gordon
optical metric modified so as to include dispersion. The calculated linear
vertical deflection turns out to be ~0.1 mm for a horizontal traversal of 0.1
m, and a group speed vg ~ 102 ms-1. Experimental realizability and some
conceptual points involved will be briefly discussed.


title: Security for Wiretap Networks via Rank-Metric Codes

abstract:
  The problem of securing a network coding communication system against a
wiretapper adversary is considered. The network implements linear network
coding to deliver $n$ packets from source to each receiver, and the wiretapper
can eavesdrop on $\mu$ arbitrarily chosen links. A coding scheme is proposed
that can achieve the maximum possible rate of $k=n-\mu$ packets that are
information-theoretically secure from the adversary. A distinctive feature of
our scheme is that it is universal: it can be applied on top of any
communication network without requiring knowledge of or any modifications on
the underlying network code. In fact, even a randomized network code can be
used. Our approach is based on Rouayheb-Soljanin's formulation of a wiretap
network as a generalization of the Ozarow-Wyner wiretap channel of type II.
Essentially, the linear MDS code in Ozarow-Wyner's coset coding scheme is
replaced by a maximum-rank-distance code over an extension of the field in
which linear network coding operations are performed.


title:
On the Kinetic Equation and Electrical Resistivity in Systems with
  Strong Spin- Hole Interaction

abstract:
  The problem of constructing the kinetic equation with the description of
motion of a hole in systems with strong spin- hole interaction (such as high-
temperature superconductors) in terms of the spin polaron has been considered
in the framework of the regular antiferromagnetic $s-d$ model. It has been
shown by the example of the electrical resistivity that kinetics is determined
by the properties of the bands of the spin polaron (rather than "bar hole") and
their quasiparticle residues $Z_{k}$. The cases of low and optimal doping of
the $CuO_{2}$ plane have been considered. It has been shown that the
rearrangement of the spectrum of the lower polaron band, as well as the strong
doping dependence of the quasiparticle residues $Z_{k}$ is decisive in the
unified consideration of these cases.


title: Factorization, Fibration and Torsion

abstract:
  A simple definition of torsion theory is presented, as a factorization system
with both classes satisfying the 3--for--2 property. Comparisons with the
traditional notion are given, as well as connections with the notions of
fibration and of weak factorization system, as used in abstract homotopy
theory.


title:
Measuring supermassive black holes with gas kinematics - II. The LINERs
  IC 989, NGC 5077, and NGC 6500

abstract:
  We present results from a kinematical study of the gas in the nucleus of a
sample of three LINER galaxies, obtained from archival HST/STIS long-slit
spectra. We found that, while for the elliptical galaxy NGC 5077, the observed
velocity curves are consistent with gas in regular rotation around the galaxy's
center, this is not the case for the two remaining objects. By modeling the
surface brightness distribution and rotation curve from the emission lines in
NGC 5077, we found that the observed kinematics of the circumnuclear gas can be
accurately reproduced by adding to the stellar mass component a black hole mass
of M_bh = 6.8 (-2.8,+4.3) 10**8 M_sun (uncertainties at a 1 sigma level); the
radius of its sphere of influence (R_sph ~ 0".34) is well-resolved at the HST
resolution. The BH mass estimate in NGC 5077 is in fairly good agreement with
both the M_bh-M_bul (with an upward scatter of ~ 0.4 dex) and M_bh-sigma
correlations (with an upward scatter of 0.5 dex in the Tremaine et al. form and
essentially no scatter using the Ferrarese et al. form) and provides further
support for the presence of a connection between the ``residuals'' from the
M_bh-sigma correlation and the bulge effective radius. This indicates the
presence of a black hole's ``fundamental plane'' in the sense that a
combination of at least sigma and R_e drives the correlations between M_bh and
host bulge properties.


title: Krall--type Orthogonal Polynomials in several variables

abstract:
  For a bilinear form obtained by adding a Dirac mass to a positive definite
moment functional in several variables, explicit formulas of orthogonal
polynomials are derived from the orthogonal polynomials associated with the
moment functional. Explicit formula for the reproducing kernel is also derived
and used to establish certain inequalities for classical orthogonal
polynomials.


title: Random turn walk on a half line with creation of particles at the origin

abstract:
  We consider a version of random motion of hard core particles on the
semi-lattice $ 1, 2, 3,...$, where in each time instant one of three possible
events occurs, viz., (a) a randomly chosen particle hops to a free neighboring
site, (b) a particle is created at the origin (namely, at site 1) provided that
site 1 is free and (c) a particle is eliminated at the origin (provided that
the site 1 is occupied). Relations to the BKP equation are explained. Namely,
the tau functions of two different BKP hierarchies provide generating functions
respectively (I) for transition weights between different particle
configurations and (II) for an important object: a normalization function which
plays the role of the statistical sum for our non-equilibrium system. As an
example we study a model where the hopping rate depends on two parameters ($r$
and $\beta$). For time $\time\to\infty$ we obtain the asymptotic configuration
of particles obtained from the initial empty state (the state without
particles) and find an analog of the first order transition at $\beta=1$.

categories: cond-mat.dis-nn cond-mat.other math-ph math.MP math.PR nlin.SI


title: Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity

abstract:
  We consider a modification of the standard Einstein theory in four
dimensions, alternative to R. Jackiw and S.-Y. Pi, Phys. Rev. D 68, 104012
(2003), since it is based on the first-order (Einstein-Cartan) approach to
General Relativity, whose gauge structure is manifest. This is done by
introducing an additional topological term in the action which becomes a
Lorentz-violating term by virtue of the dependence of the coupling on the
space-time point. We obtain a condition on the solutions of the Einstein
equations, such that they persist in the deformed theory, and show that the
solutions remarkably correspond to the classical solutions of a collection of
independent 2+1-d (topological) Chern-Simons gravities. Finally, we study the
relation with the standard second-order approach and argue that they both
coincide to leading order in the modulus of the Lorentz-violating vector field.


title:
Time drift of cosmological redshifts as a test of the Copernican
  principle

abstract:
  We present the time drift of the cosmological redshift in a general
spherically symmetric spacetime. We demonstrate that its observation would
allow us to test the Copernican principle and so determine if our universe is
radially inhomogeneous, an important issue in our understanding of dark energy.
In particular, when combined with distance data, this extra observable allows
one to fully reconstruct the geometry of a spacetime describing a spherically
symmetric under-dense region around us, purely from background observations.


title: $q$-Analogue of the Dunkl transform on the real line

abstract:
  In this paper, we consider a $q$-analogue of the Dunkl operator on
$\mathbb{R}$, we define and study its associated Fourier transform which is a
$q$-analogue of the Dunkl transform. In addition to several properties, we
establish an inversion formula and prove a Plancherel theorem for this
$q$-Dunkl transform. Next, we study the $q$-Dunkl intertwining operator and its
dual via the $q$-analogues of the Riemann-Liouville and Weyl transforms. Using
this dual intertwining operator, we provide a relation between the $q$-Dunkl
transform and the $q^2$-analogue Fourier transform introduced and studied by R.
Rubin.


title: Recent progress in defining and understanding jets

abstract:
  This talk reviews some key developments that have taken place in
hadron-collider jet finding over the past couple of years, including: technical
advances such as the complete formulation of an infrared safe seedless cone
algorithm and fast computational approaches to sequential recombination jet
finders like the kt algorithm, together with universal methods for subtracting
pileup; progress in understanding the sensitivity of jet algorithms to the
underlying event and hadronisation; and work that exploits our knowledge of QCD
divergences to better define and predict heavy-flavour jet cross sections.


title: Dual Phase Cosmic Rays

abstract:
  A calculation based on flat spacetime symmetries shows how there can be two
quantum phases. For one, extreme phase change determines a conventional
classical trajectory and four-momentum, i.e. mass times four-velocity. The
other phase occurs in an effective particle state, with the effective energy
and momentum being the rate of change of the phase with respect to time and
distance. A cosmic ray proton moves along a classical trajectory, but exists in
an effective particle state with an effective energy that depends on the local
gravitational potential. Assumptions are made so that a cosmic ray proton in an
ultra-high energy state detected near the Earth was in a much less energetic
state in interstellar space. A 300 EeV proton incident on the Earth was a 2 PeV
proton in interstellar space. The model predicts such protons are in states
with even more energy near the Sun than when near the Earth.


title:
On the Basis Polynomials in the Theory of Permutations with Prescribed
  Up-Down Structure

abstract:
  Let $\pi=(\pi_1,\pi_2,\hdots,\pi_n)$ be permutation of the elements
$1,2,\hdots,n. $ Positive integer $k\leq2^{n-1}$ we call index of $\pi,$ if in
its binary notation as $n$-digital binary number, the 1's correspond to the
ascent points. We study behavior and properties of numbers of permutations of
$n$ elements having index $k.$


title:
Initiation to mould calculus through the example of saddle-node
  singularities

abstract:
  This article proposes an initiation to \'Ecalle's mould calculus, a powerful
combinatorial tool which yields surprisingly explicit formulas for the
normalising series attached to an analytic germ of singular vector field. This
is illustrated on the case of saddle-node singularities, generated by
two-dimensional vector fields which are formally conjugate to Euler's vector
field $x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal
normalisation proves to be resurgent in $1/x$.


title: A new approach to temperate generalized functions

abstract:
  A new approach to the algebra G_{\tau} of temperate nonlinear generalized
functions is proposed, in which G_{\tau} is based on the space O_{M} endowed
with is natural topology in contrary to previous constructions. Thus, this
construction fits perfectly in the general scheme of construction of Colombeau
type algebras and reveals better properties of G_{\tau}. This is illustrated by
the natural introduction of a regularity theory in G_{\tau}, of the Fourier
transform, with the definition of G_{O_{C prime}}, the space of rapidly
generalized distributions which is the Fourier image of G_{\tau}.


title:
Non-existence of absolutely continuous invariant probabilities for
  exponential maps

abstract:
  We show that for entire maps of the form $z \mapsto \lambda \exp(z)$ such
that the orbit of zero is bounded and such that Lebesgue almost every point is
transitive, no absolutely continuous invariant probability measure can exist.
This answers a long-standing open problem.


title: Degree complexity of a family of birational maps: II. Exceptional cases

abstract:
  We compute the degree complexity of the family of birational maps considered
in \cite{bedford-kim-tuyen-abarenkova-maillard} for all exceptional cases. Some
interesting properties of the family are also given.


title: Asymptotics of Convex sets in En and Hn

abstract:
  We study convex sets C of finite (but non-zero volume in Hn and En. We show
that the intersection of any such set with the ideal boundary of Hn has
Minkowski (and thus Hausdorff) dimension of at most (n-1)/2, and this bound is
sharp. In the hyperbolic case we show that for any k <= (n-1)/2 there is a
bounded section S of C through any prescribed point p, and we show an upper
bound on the radius of the ball centered at p containing such a section. We
show similar bounds for sections through the origin of convex body in En, and
give asymptotic estimates as 1 << k << n.


title:
Individual addressing of trapped ions and coupling of motional and spin
  states using rf radiation

abstract:
  Individual electrodynamically trapped and laser cooled ions are addressed in
frequency space using radio-frequency radiation in the presence of a static
magnetic field gradient. In addition, an interaction between motional and spin
states induced by an rf field is demonstrated employing rf-optical double
resonance spectroscopy. These are two essential experimental steps towards
realizing a novel concept for implementing quantum simulations and quantum
computing with trapped ions.


title:
An Algorithm to Estimate Monotone Normal Means and its Application to
  Identify the Minimum Effective Dose

abstract:
  In the standard setting of one-way ANOVA with normal errors, a new algorithm,
called the Step Down Maximum Mean Selection Algorithm (SDMMSA), is proposed to
estimate the treatment means under an assumption that the treatment mean is
nondecreasing in the factor level. We prove that i) the SDMMSA and the Pooled
Adjacent Violator Algorithm (PAVA), a widely used algorithm in many problems,
generate the same estimators for normal means, ii) the estimators are the
mle's, and iii) the distribution of each of the estimators is stochastically
nondecreasing in each of the treatment means. As an application of this
stochastic ordering, a sequence of null hypotheses to identify the minimum
effective dose (MED) is formulated under the assumption of monotone
treatment(dose) means. A step-up testing procedure, which controls the
experimentwise error rate in the strong sense, is constructed. When the MED=1,
the proposed test is uniformly more powerful than Hsu and Berger's (1999).


title: A new extension of the Erdos-Heilbronn conjecture

abstract:
  Let A_1,...,A_n be finite subsets of a field F, and let
f(x_1,...,x_n)=x_1^k+...+x_n^k+g(x_1,...,x_n)\in F[x_1,...,x_n] with deg g<k.
We obtain a lower bound for the cardinality of {f(x_1,...,x_n): x_1\in
A_1,...,x_n\in A_n, and x_i\not=x_j if i\not=j}. The result extends the
Erdos-Heilbronn conjecture in a new way.


title: Invariant Functions on Grassmannians

abstract:
  It is known, that every function on the unit sphere in $\bbr^n$, which is
invariant under rotations about some coordinate axis, is completely determined
by a function of one variable. Similar results, when invariance of a function
reduces dimension of its actual argument, hold for every compact symmetric
space and can be obtained in the framework of Lie-theoretic consideration. In
the present article, this phenomenon is given precise meaning for functions on
the Grassmann manifold $G_{n,i}$ of $i$-dimensional subspaces of $\bbr^n$,
which are invariant under orthogonal transformations preserving complementary
coordinate subspaces of arbitrary fixed dimension. The corresponding integral
formulas are obtained. Our method relies on bi-Stiefel decomposition and does
not invoke Lie theory.


title: Computing knock out strategies in metabolic networks

abstract:
  Given a metabolic network in terms of its metabolites and reactions, our goal
is to efficiently compute the minimal knock out sets of reactions required to
block a given behaviour. We describe an algorithm which improves the
computation of these knock out sets when the elementary modes (minimal
functional subsystems) of the network are given. We also describe an algorithm
which computes both the knock out sets and the elementary modes containing the
blocked reactions directly from the description of the network and whose
worst-case computational complexity is better than the algorithms currently in
use for these problems. Computational results are included.


title: Central Extensions of Gerbes

abstract:
  We introduce the notion of central extension of gerbes on a topological
space. We then show that there are obstruction classes to lifting objects and
isomorphisms in a central extension. We also discuss pronilpotent gerbes. These
results are used in a subsequent paper to study twisted deformation
quantization on algebraic varieties.


title:
Spectral convergence for high contrast elliptic periodic problems with a
  defect via homogenization

abstract:
  We consider an eigenvalue problem for a divergence form elliptic operator
$A_\epsilon$ with high contrast periodic coefficients with period $\epsilon$ in
each coordinate, where $\epsilon$ is a small parameter. The coefficients are
perturbed on a bounded domain of `order one' size. The local perturbation of
coefficients for such operator could result in emergence of localized waves -
eigenfunctions with corresponding eigenvalues lying in the gaps of the
Floquet-Bloch spectrum. We prove that, for the so-called double porosity type
scaling, the eigenfunctions decay exponentially at infinity, uniformly in
$\epsilon$. Then, using the tools of two-scale convergence for high contrast
homogenization, we prove the strong two-scale compactness of the eigenfunctions
of $A_\epsilon$. This implies that the eigenfunctions converge in the sense of
the strong two-scale convergence to the eigenfunctions of a two-scale limit
homogenized operator $A_0$, consequently establishing `asymptotic one-to-one
correspondence' between the eigenvalues and the eigenfunctions of these two
operators. We also prove by direct means the stability of the essential
spectrum of the homogenized operator with respect to the local perturbation of
its coefficients. That allows us to establish not only the strong two-scale
resolvent convergence of $A_\epsilon$ to $A_0$ but also the Hausdorff
convergence of the spectra of $A_\epsilon$ to the spectrum of $A_0$, preserving
the multiplicity of the isolated eigenvalues.


title: Perturbation of the Wigner equation in inner product C*-modules

abstract:
  Let $\A$ be a $C^*$-algebra and $\B$ be a von Neumann algebra that both act
on a Hilbert space $\Ha$. Let $\M$ and $\N$ be inner product modules over $\A$
and $\B$, respectively. Under certain assumptions we show that for each mapping
$f\colon{\mathcal M} \to {\mathcal N}$ satisfying
$$\||\ip{f(x)}{f(y)}|-|\ip{x}{y}| \|\leq\phi(x,y)\qquad (x,y\in{\mathcal M}),$$
where $\phi$ is a control function, there exists a solution $I\colon{\mathcal
M} \to {\mathcal N}$ of the Wigner equation
$$|\ip{I(x)}{I(y)}|=|\ip{x}{y}|\qquad (x, y \in {\mathcal M})$$ such that
$$\|f(x)-I(x)\|\leq\sqrt{\phi(x,x)} \qquad (x\in {\mathcal M}).$$


title: A zero divisor graph determined by equivalence classes of zero divisors

abstract:
  We study the zero divisor graph determined by equivalence classes of zero
divisors of a commutative Noetherian ring R. We demonstrate how to recover
information about R from this structure. In particular, we determine how to
identify associated primes from the graph.


title:
Evolution of the electronic excitation spectrum with strongly
  diminishing hole-density in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}

abstract:
  A complete knowledge of its excitation spectrum could greatly benefit efforts
to understand the unusual form of superconductivity occurring in the lightly
hole-doped copper-oxides. Here we use tunnelling spectroscopy to measure the
T\to 0 spectrum of electronic excitations N(E) over a wide range of
hole-density p in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+/delta}. We
introduce a parameterization for N(E) based upon an anisotropic energy-gap
/Delta (\vec k)=/Delta_{1}(Cos(k_{x})-Cos(k_{y}))/2 plus an effective
scattering rate which varies linearly with energy /Gamma_{2}(E) . We
demonstrate that this form of N(E) allows successful fitting of differential
tunnelling conductance spectra throughout much of the
Bi_{2}Sr_{2}CaCu_{2}O_{8+/delta} phase diagram. The resulting average
/Delta_{1} values rise with falling p along the familiar trajectory of
excitations to the 'pseudogap' energy, while the key scattering rate
/Gamma_{2}^{*}=/Gamma_{2}(E=/Delta_{1}) increases from below ~1meV to a value
approaching 25meV as the system is underdoped from p~16% to p<10%. Thus, a
single, particle-hole symmetric, anisotropic energy-gap, in combination with a
strongly energy and doping dependent effective scattering rate, can describe
the spectra without recourse to another ordered state. Nevertheless we also
observe two distinct and diverging energy scales in the system: the energy-gap
maximum /Delta_{1} and a lower energy scale /Delta_{0} separating the spatially
homogeneous and heterogeneous electronic structures.


title: Supermetrics on supermanifolds

abstract:
  By virtue of the well-known theorem, a structure Lie group K of a principal
bundle $P$ is reducible to its closed subgroup H iff there exists a global
section of the quotient bundle P/K. In gauge theory, such sections are treated
as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold of
P. Under some conditions, this theorem is extended to principal superbundles in
the category of G-supermanifolds. Given a G-supermanifold M and a graded frame
superbundle over M with a structure general linear supergroup, a reduction of
this structure supergroup to an orthgonal-symplectic supersubgroup is
associated to a supermetric on a G-supermanifold M.


title:
Analysis of electric-field-induced spin splitting in wide
  modulation-doped quantum wells

abstract:
  We analyze the proper inclusion of electric-field-induced spin splittings in
the framework of the envelope function approximation. We argue that the Rashba
effect should be included in the form of a macroscopic potential as diagonal
terms in a multiband approach rather than the commonly used Rashba term
dependent on k and electric field. It is pointed out that the expectation value
of the electric field in a subband is sometimes not unique because the
expectation values can even have opposite signs for the spin-split subband
components. Symmetric quantum wells with Dresselhaus terms and the influence of
the interfaces on the spin splitting are also discussed. We apply a well
established multiband approach to wide modulation-doped InGaSb quantum wells
with strong built-in electric fields in the interface regions. We demonstrate
an efficient mechanism for switching on and off the Rashba splitting with an
electric field being an order of magnitude smaller than the local built-in
field that determines the Rashba splitting. The implications of our findings
for spintronic devices, in particular the Datta-Das spin transistor and
proposed modifications of it, are discussed.


title:
Necessary conditions for linear noncooperative N-player delta
  differential games on time scales

abstract:
  We present necessary conditions for linear noncooperative N-player delta
dynamic games on a generic time scale. Necessary conditions for an open-loop
Nash-equilibrium and for a memoryless perfect state Nash-equilibrium are
proved.


title:
A deformation problem for Galois representations over imaginary
  quadratic fields

abstract:
  We prove the modularity of minimally ramified ordinary residually reducible
p-adic Galois representations of an imaginary quadratic field F under certain
assumptions. We first exhibit conditions under which the residual
representation is unique up to isomorphism. Then we prove the existence of
deformations arising from cuspforms on GL_2(A_F) via the Galois representations
constructed by Taylor et al. We establish a sufficient condition (in terms of
the non-existence of certain field extensions which in many cases can be
reduced to a condition on an L-value) for the universal deformation ring to be
a discrete valuation ring and in that case we prove an R=T theorem. We also
study reducible deformations and show that no minimal characteristic 0
reducible deformation exists.


title: Nash bargaining with a nondeterministic threat

abstract:
  We consider bargaining problems which involve two participants, with a
nonempty closed, bounded convex bargaining set of points in the real plane
representing all realizable bargains. We also assume that there is no definite
threat or disagreement point which will provide the default bargain if the
players cannot agree on some point in the bargaining set. However, there is a
nondeterministic threat: if the players fail to agree on a bargain, one of them
will be chosen at random with equal probability, and that chosen player will
select any realizable bargain as the solution, subject to a reasonable
restriction.


title: The Thermal State of the Intergalactic Medium at Redshift $5<z<6$

abstract: This paper has been withdrawn


title: An analytical error model for quantum computer simulation

abstract:
  Quantum computers (QCs) must implement quantum error correcting codes (QECCs)
to protect their logical qubits from errors, and modeling the effectiveness of
QECCs on QCs is an important problem for evaluating the QC architecture. The
previously developed Monte Carlo (MC) error models may take days or weeks of
execution to produce an accurate result due to their random sampling approach.
We present an alternative analytical error model that generates, over the
course of executing the quantum program, a probability tree of the QC's error
states. By calculating the fidelity of the quantum program directly, this error
model has the potential for enormous speedups over the MC model when applied to
small yet useful problem sizes. We observe a speedup on the order of 1,000X
when accuracy is required, and we evaluate the scaling properties of this new
analytical error model.


title: Mass matrices for quarks and leptons in triangular form

abstract:
  We assume that all quark and lepton mass matrices have upper triangular form.
Using all available experimental data on quark and lepton masses and mixing
angles we make a fit in which we determine mass matrices elements. There are
too many free parameters and our solutions are not uniqe. We look for solutions
with small non diagonal mixing matrix elements. In order to reduce the number
of free parameters we assume that the matrix element $(M)_{13}$ vanishes in
\underline{all} mass matrices. Such universal assumption was drown from
considering different numerical solutions. The lepton sector, due to large
mixing angles and very small errors for charged lepton masses, is more
restrictive then quark sector. We present the solution in this case. The
absolute values of neutrino masses are not fixed. The another possibility of
reducing number of free parameters was considered by us before. With the
additional assumption motivated by SU(5) symmetry which connects mixing in
right handed down quarks with left handed charged leptons we get a solution in
which observed Cabibbo-Kobayashi-Maskawa mixing for quarks comes mainly from
non diagonal terms in up quark mass matrix. From the fit we get also
predictions for neutrino masses.


title: Can Classical Noise Enhance Quantum Transmission?

abstract:
  A modified quantum teleportation protocol broadens the scope of the classical
forbidden-interval theorems for stochastic resonance. The fidelity measures
performance of quantum communication. The sender encodes the two classical bits
for quantum teleportation as weak bipolar subthreshold signals and sends them
over a noisy classical channel. Two forbidden-interval theorems provide a
necessary and sufficient condition for the occurrence of the nonmonotone
stochastic resonance effect in the fidelity of quantum teleportation. The
condition is that the noise mean must fall outside a forbidden interval related
to the detection threshold and signal value. An optimal amount of classical
noise benefits quantum communication when the sender transmits weak signals,
the receiver detects with a high threshold, and the noise mean lies outside the
forbidden interval. Theorems and simulations demonstrate that both
finite-variance and infinite-variance noise benefit the fidelity of quantum
teleportation.


title:
A SERS Investigation of Cyanide Adsorption and Reactivity during the
  Electrodeposition of Gold, Silver and Copper from Aqueous Cyanocomplexes
  Solutions

abstract:
  In this paper we report on the reactivity of adsorbed cyanide deriving from
ligand release during metal electrodeposition from cyanocomplex solutions of
Au(I), Au(III), Ag(I) and Cu(I) in H2O and D2O. When CN is adsorbed at cathodic
potentials in excess of the HER threshold, metal-dependent reactivity can be
detected by SERS. Finite surface coverages with adsorbed CN at such cathodic
potentials can be obtained only if CN is delivered directly to the cathode
surface as by decomplexing of the cyanocomplexes of the metals undergoing
cathodic reduction. In Au(I) and Au(III) baths, Au-CN reacts with Au-H and is
hydrogenated to adsorbed CH2=NH and CH3-NH2. In Ag(I) baths, Ag-CN reacts with
Ag-H giving rise to polycyanogens. No reactivity of Cu-CN was found, under
otherwise identical conditions. Our conclusions are supported also by dedicated
DFT molecular computations.


title:
An SERS study of the galvanostatic sequence employed for the
  electrochemical deposition of Copper in the fabrication of Interconnects

abstract:
  This paper reports the first study carried out by surface-enhanced Raman
spectroscopy (SERS) during the galvanostatic electrodeposition (ECD) of copper
from an acidic sulphate solution, in the presence of polyethylene glycol (PEG),
bis-(3-sulfopropyl)-disulfide Na salt (SPS), benzyl-phenyl modified
polyethyleneimine (BPPEI) and chloride ions. The analysis of SERS spectra
recorded during electrodeposition allowed to get an insight into the complex
interfacial behaviour of the organic blend, in terms of co-adsorption and
reactivity. At open-circuit (OC), the additives co-adsorb on the copper
cathode. Upon increasing the cathodic polarization, progressive SPS-scavenging
action of PEG was observed. BPPEI is adsorbed in the entire process window and
cathodic reaction products of PEG were identified. The joint action of the
organic additives yields a continuous deposit with crystallites of submicron
dimensions, as revealed by Scanning Electron Microscopy (SEM).


title:
Reply to `On a recent proposal of faster than light quantum
  communication'

abstract:
  In a recent paper the author proposed the possibility of an experiment to
perform faster-than-light communication via the collapse of the quantum
wave-function. This was analyzed by Bassi and Ghirardi, and it is believed that
this analysis itself merits a detailed examination.


title: Determinantal Correlations for Classical Projection Processes

abstract:
  Recent applications in queuing theory and statistical mechanics have isolated
the process formed by the eigenvalues of successive minors of the GUE.
Analogous eigenvalue processes, formed in general from the eigenvalues of
nested sequences of matrices resulting from random corank 1 projections of
classical random matrix ensembles, are identified for the LUE and JUE. The
correlations for all these processes can be computed in a unified way. The
resulting expressions can then be analyzed in various scaling limits. At the
soft edge, with the rank of the minors differing by an amount proportional to
$N^{2/3}$, the scaled correlations coincide with those known from the soft edge
scaling of the Dyson Brownian motion model.


title: Local quasiparticle lifetimes in a d-wave superconductor

abstract:
  Scanning tunnelling spectroscopy (STS) measurements find that the surface of
Bi-2212 is characterized by nanoscale sized regions, "gap patches," which have
different magnitudes for the d-wave energy gap. Recent studies have shown that
the tunnelling conductance can be fit using a BCS-type density of states for a
d-wave superconductor with a local quasiparticle scattering rate. The fit is
made with a scattering rate which varies linearly with energy and has a slope
that is positively correlated with the local value of the gap. We revisit a
model of quasiparticle scattering by impurities and spin fluctuations which was
previously used to describe the lifetimes of nodal quasiparticles measured by
angle-resolved photoemission (ARPES). We argue that the broadening of the local
density of states is in general determined by the imaginary part of the
self-energy of the system averaged over a small region. The size of this region
is set by a mean free path which depends upon the energy. At low energies, this
region is found to be significantly larger than a gap "patch", so that the
density of states measured by STS is homogeneous in this energy range. At
higher energies where the mean free path is comparable with the patch size, the
density of states is inhomogeneous. We show that a local self-energy in the
impurity-plus-spin fluctuation model, while not strictly linear, yields a local
density of states (LDOS) nearly identical to the full theory, and argue that it
is consistent with the STS data as well as the phenomenological linear
scattering rate extracted from experiment. We also explore the qualitative
consequences of this phenomenology for the spectral widths observed in ARPES
and predict the existence of Fermi arcs in the superconducting state.


title: Reserved-Length Prefix Coding

abstract:
  Huffman coding finds an optimal prefix code for a given probability mass
function. Consider situations in which one wishes to find an optimal code with
the restriction that all codewords have lengths that lie in a user-specified
set of lengths (or, equivalently, no codewords have lengths that lie in a
complementary set). This paper introduces a polynomial-time dynamic programming
algorithm that finds optimal codes for this reserved-length prefix coding
problem. This has applications to quickly encoding and decoding lossless codes.
In addition, one modification of the approach solves any quasiarithmetic prefix
coding problem, while another finds optimal codes restricted to the set of
codes with g codeword lengths for user-specified g (e.g., g=2).


title: Complete gradient shrinking Ricci solitons have finite topological type

abstract:
  We show that a complete Riemannian manifold has finite topological type
(i.e., homeomorphic to the interior of a compact manifold with boundary),
provided its Bakry-\'{E}mery Ricci tensor has a positive lower bound, and
either of the following conditions:
  (i) the Ricci curvature is bounded from above; (ii) the Ricci curvature is
bounded from below and injectivity radius is bounded away from zero.
  Moreover, a complete shrinking Ricci soliton has finite topological type if
its scalar curvature is bounded.


title: Congruences between modular forms and lowering the level mod l^n

abstract:
  In this article we study the behavior of inertia groups for modular Galois
mod l^n representations and in some cases we give a generalization of Ribet's
lowering the level result


title:
Wafer-Scale Assembly of Semiconductor Nanowire Arrays by Contact
  Printing

abstract:
  Controlled and uniform assembly of "bottom-up" nanowire (NW) materials with
high scalability has been one of the significant bottleneck challenges facing
the potential integration of nanowires for both nano and macro electronic
circuit applications. Many efforts have focused on tackling this challenge, and
while significant progress has been made, still most presented approaches lack
either the desired controllability in the positioning of nanowires or the
needed uniformity over large scales. Here, we demonstrate wafer-scale assembly
of highly ordered, dense, and regular arrays of NWs with high uniformity and
reproducibility through a simple contact printing process. We demonstrate
contact printing as a versatile strategy for direct transfer and controlled
positioning of various NW materials into complex structural configurations on
substrates. The assembled NW pitch is shown to be readily modulated through the
surface chemical treatment of the receiver substrate, with the highest density
approaching ~8 NW/um, ~95% directional alignment and wafer-scale uniformity.
Furthermore, we demonstrate that our printing approach enables large-scale
integration of NW arrays for various device structures on both Si and plastic
substrates, with a controlled semiconductor channel width, and therefore ON
current, ranging from a single NW (~10 nm) and up to ~250 um, consisting of a
parallel array of over 1,250 NWs.


title: Dilaton and Second-Rank Tensor Fields as Supersymmetric Compensators

abstract:
  We formulate a supersymmetric theory in which both a dilaton and a
second-rank tensor play roles of compensators. The basic off-shell multiplets
are a linear multiplet (B_{\mu\nu}, \chi, \phi) and a vector multiplet (A_\mu,
\l; C_{\mu\nu\rho}), where \phi and B_{\m\n} are respectively a dilaton and a
second-rank tensor. The third-rank tensor C_{\mu\nu\rho} in the vector
multiplet is 'dual' to the conventional D-field with 0 on-shell or 1 off-shell
degree of freedom. The dilaton \phi is absorbed into one longitudinal component
of A_\mu, making it massive. Initially, B_{\mu\nu} has 1 on-shell or 3
off-shell degrees of freedom, but it is absorbed into the longitudinal
components of C_{\mu\nu\rho}. Eventually, C_{\mu\nu\rho} with 0 on-shell or 1
off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees
of freedom, turning into a propagating massive field. These basic multiplets
are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld
action. Some of these results are also reformulated in superspace. The proposed
mechanism may well provide a solution to the long-standing puzzle of massless
dilatons and second-rank tensors in supersymmetric models inspired by string
theory.


title:
Kinetic dissipation and anisotropic heating in a turbulent collisionless
  plasma

abstract:
  The kinetic evolution of the Orszag-Tang vortex is studied using
collisionless hybrid simulations. In the magnetohydrodynamic regime this vortex
leads rapidly to broadband turbulence. Significant differences from MHD arise
at small scales, where the fluid scale energy dissipates into heat almost
exclusively through the magnetic field because the protons are decoupled from
the magnetic field. Although cyclotron resonance is absent, the protons heat
preferentially in the plane perpendicular to the mean field, as in the corona
and solar wind. Effective transport coefficients are calculated.


title: Note on two phase phenomena in financial markets

abstract:
  The two phase behavior in financial markets actually means the bifurcation
phenomenon, which represents the change of the conditional probability from an
unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon
in Hang-Seng index is carefully investigated. It is observed that the
bifurcation phenomenon in financial index is not universal, but specific under
certain conditions. The phenomenon just emerges when the power-law exponent of
absolute increment distribution is between 1 and 2 with appropriate period.
Simulations on a randomly generated time series suggest the bifurcation
phenomenon itself is subject to the statistics of absolute increment, thus it
may not be able to reflect the essential financial behaviors. However, even
under the same distribution of absolute increment, the range where bifurcation
phenomenon occurs is far different from real market to artificial data, which
may reflect certain market information.


title: Meaning and Form in a Language Computer Simulation

abstract:
  Thousands of different forms (words) are associated with thousands of
different meanings (concepts) in a language computer model. Reasonable
agreement with reality is found for the number of languages in a family and the
Hamming distances between languages.


title:
Appearance of Light Clusters in Post-bounce Evolution of Core-Collapse
  Supernovae

abstract:
  We explore the abundance of light clusters in core-collapse supernovae at
post-bounce stage in a quantum statistical approach. Adopting the profile of a
supernova core from detailed numerical simulations, we study the distribution
of light bound clusters up to alpha particles (A=2-4) as well as heavy nuclei
(A > 4) in dense matter at finite temperature. Within the frame of a
cluster-mean field approach, the abundances of light clusters are evaluated
accounting for self-energy, Pauli blocking and effects of continuum
correlations. We find that deuterons and tritons, in addition to 3He and 4He,
appear abundantly in a wide region from the surface of the proto-neutron star
to the position of the shock wave. The appearance of light clusters may modify
the neutrino emission in the cooling region and the neutrino absorption in the
heating region, and, thereby, influence the supernova mechanism.


title:
Specific heat evidence for two-gap superconductivity in ternary-iron
  silicide Lu$_{2}$Fe$_{3}$Si$_{5}$

abstract:
  We report low-temperature specific heat studies on single-crystalline
ternary-iron silicide superconductor Lu$_{2}$Fe$_{3}$Si$_{5}$ with$T_c$ = 6.1 K
down to $\sim T_c/20$. We confirm a reduced normalized jump in specific heat at
$T_c$, and find that the specific heat divided by temperature $C/T$ shows
sudden drop at $\sim T_c/5$ and goes to zero with further decreasing
temperature. These results indicate the presence of two distinct
superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$, similar to a typical two-gap
superconductor MgB$_{2}$. We also report Hall coefficients, band structure
calculation, and the anisotropy of upper critical fields for
Lu$_{2}$Fe$_{3}$Si$_{5}$, which support the anisotropic multiband nature and
reinforce the existence of two superconducting gaps in
Lu$_{2}$Fe$_{3}$Si$_{5}$.


title:
Dimensionless Measures of Turbulent Magnetohydrodynamic Dissipation
  Rates

abstract:
  The magnetic Reynolds number R_M, is defined as the product of a
characteristic scale and associated flow speed divided by the microphysical
magnetic diffusivity. For laminar flows, R_M also approximates the ratio of
advective to dissipative terms in the total magnetic energy equation, but for
turbulent flows this latter ratio depends on the energy spectra and approaches
unity in a steady state. To generalize for flows of arbitrary spectra we define
an effective magnetic dissipation number, R_{M,e}, as the ratio of the
advection to microphysical dissipation terms in the total magnetic energy
equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl
numbers, and distinct pairs of inner and outer scales for magnetic and kinetic
spectra. As expected, for a substantial parameter range R_{M,e}\sim {O}(1) <<
R_M. We also distinguish R_{M,e} from {\tilde R}_{M,e} where the latter is an
effective magnetic Reynolds number for the mean magnetic field equation when a
turbulent diffusivity is explicitly imposed as a closure. That R_{M,e} and
{\tilde R}_{M,e} approach unity even if R_M>>1 highlights that, just as in
hydrodynamic turbulence,energy dissipation of large scale structures in
turbulent flows via a cascade can be much faster than the dissipation of large
scale structures in laminar flows. This illustrates that the rate of energy
dissipation by magnetic reconnection is much faster in turbulent flows, and
much less sensitive to microphysical reconnection rates compared to laminar
flows.


title:
Spontaneously Localized Photonic Modes Due to Disorder in the Dielectric
  Constant

abstract:
  We present the first experimental evidence for the existence of strongly
localized photonic modes due to random two dimensional fluctuations in the
dielectric constant. In one direction, the modes are trapped by ordered Bragg
reflecting mirrors of a planar, one wavelength long, microcavity. In the cavity
plane, they are localized by disorder, which is due to randomness in the
position, composition and sizes of quantum dots located in the anti-node of the
cavity. We extend the theory of disorder induced strong localization of
electron states to optical modes and obtain quantitative agreement with the
main experimental observations.


title: Lindel\"of's hypothesis is true and Riemann's one is not

abstract:
  We present an elementary, short and simple proof of the validity of the
Lindel\"of hypothesis about the Riemann zeta-function. The obtained estimate
and classical results by Bohr-Landau and Littlewood disprove Riemann's
hypothesis.


title:
String-Like Electrostatic Interaction from QED with Infinite Magnetic
  Field

abstract:
  In the limit of infinite external magnetic field B the static field of an
electric charge is squeezed into a string parallel to B. Near the charge the
potential grows like |x_3|(ln |x_3| + const) with the coordinate x_3 along the
string. The energy of the string breaking is finite and very close to the
effective photon mass.


title: Primordial Black Holes

abstract:
  Primordial black holes (PBHs) are a profound signature of primordial
cosmological structures and provide a theoretical tool to study nontrivial
physics of the early Universe. The mechanisms of PBH formation are discussed
and observational constraints on the PBH spectrum, or effects of PBH
evaporation, are shown to restrict a wide range of particle physics models,
predicting an enhancement of the ultraviolet part of the spectrum of density
perturbations, early dust-like stages, first order phase transitions and stages
of superheavy metastable particle dominance in the early Universe. The
mechanism of closed wall contraction can lead, in the inflationary Universe, to
a new approach to galaxy formation, involving primordial clouds of massive BHs
created around the intermediate mass or supermassive BH and playing the role of
galactic seeds.


title:
Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial
  automorphism

abstract:
  In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of
a polynomial ring. In the present paper, we reconstruct their theory by using
the "generalized Shestakov-Umirbaev inequality", which was recently given by
the author. As a consequence, we obtain a more precise tameness criterion for
polynomial automorphisms. In particular, we show that no tame automorphism of a
polynomial ring admits a reduction of type IV.


title: Spin observables of the reaction pd-3He eta and quasi-bound 3He-eta pole

abstract:
  A formalism for spin observables of the reaction
  $pd\to ~^3He\eta$ is derived in a model independent way.
  The general case with a full set of six independent spin amplitudes is
studied. Furthermore, approximations by five and four spin amplitudes are
investigated in the near threshold region. This region is of great interest to
search for a quasi-bound $^3He-\eta$ state, in particular, by measurement of
energy dependence of relative phases of s- and p-wave amplitudes. Complete
polarization experiments, allowing determination of spin amplitudes, are
analyzed. It is shown that measurement of only analyzing powers and spin
correlation coefficients hardly allows one to separate the s- and p-wave
amplitudes, but additional measurement of polarization transfer coefficients
simplifies this problem. Specific observables, given by products of one s- and
one p-wave amplitudes, are found. Measurement of these observables will provide
new independent information on the $^3He-\eta$ pole position.


title: Spectrum of coherently backscattered light from two atoms

abstract:
  We present a detailed analytical and numerical analysis of the inelastic
coherent backscattering spectrum of laser light incident on cold atoms. We
identify frequency domains where the interference contribution can be positive
\emph{as well as} negative -- or exhibits dispersive character. These
distinctive features are explained by reciprocity arguments and dressed state
two-photon scattering amplitudes.


title: Combinatorics of the change-making problem

abstract:
  We investigate the structure of the currencies (systems of coins) for which
the greedy change-making algorithm always finds an optimal solution (that is, a
one with minimum number of coins). We present a series of necessary conditions
that must be satisfied by the values of coins in such systems. We also uncover
some relations between such currencies and their sub-currencies.


title: Applications of Physics and Mathematics to Social Science

abstract:
  This article introduces into the whole section on Social Sciences, edited by
A. Nowak for this Encyclopedia, concentrating on the applications of
mathematics and physics. Here under "mathematics" we include also all computer
simulations if they are not taken from physics, while physics applications
include simulations of models which basically existed already in physics before
they were applied to social simulations. Thus obviously there is no sharp
border between applications from physics and from mathematics in the sense of
our definition. Also social science is not defined precisely. We will include
some economics as well as some linguistics, but not social insects or fish
swarms, nor human epidemics or demography. Also, we mention not only this
section by also the section on agent-based modelling edited by F. Castiglione
as containing articles of social interest.


title: Gravitational waves from hyperbolic encounters

abstract:
  The emission of gravitational waves from a system of massive objects
interacting on hyperbolic orbits is studied in the quadrupole approximation.
Analytic expressions are derived for the gravitational radiation luminosity,
the total energy output and the gravitational radiation amplitude. An
estimation of the expected number of events towards different targets (i.e.
globular clusters and the center of the Galaxy) is also given. In particular,
for a dense stellar cluster at the galactic center, a rate up to one event per
year is obtained.


title: Simulations of Nanowire Transistors: Atomistic vs. Effective Mass Models

abstract:
  The ballistic performance of electron transport in nanowire transistors is
examined using a 10 orbital sp3d5s* atomistic tight-binding model for the
description of the electronic structure, and the top-of-the-barrier
semiclassical ballistic model for calculation of the transport properties of
the transistors. The dispersion is self consistently computed with a 2D Poisson
solution for the electrostatic potential in the cross section of the wire. The
effective mass of the nanowire changes significantly from the bulk value under
strong quantization, and effects such as valley splitting strongly lift the
degeneracies of the valleys. These effects are pronounced even further under
filling of the lattice with charge. The effective mass approximation is in good
agreement with the tight binding model in terms of current-voltage
characteristics only in certain cases. In general, for small diameter wires,
the effective mass approximation fails.


title:
Simulating Genomes and Populations in the Mutation Space: An example
  with the evolution of HIV drug resistance

abstract:
  When simulating biological populations under different evolutionary genetic
models, backward or forward strategies can be followed. Backward simulations,
also called coalescent-based simulations, are computationally very efficient.
However, this framework imposes several limitations that forward simulation
does not. In this work, a new simple and efficient model to perform forward
simulation of populations and/or genomes is proposed. The basic idea considers
an individual as the differences (mutations) between this individual and a
reference or consensus genotype. Thus, this individual is no longer represented
by its complete sequence or genotype. An example of the efficiency of the new
model with respect to a more classical forward one is demonstrated. This
example models the evolution of HIV resistance using the B_FR.HXB2 reference
sequence to study the emergence of known resistance mutants to Zidovudine and
Didanosine drugs


title: Bandstructure Effects in Silicon Nanowire Electron Transport

abstract:
  Bandstructure effects in the electronic transport of strongly quantized
silicon nanowire field-effect-transistors (FET) in various transport
orientations are examined. A 10-band sp3d5s* semi-empirical atomistic
tight-binding model coupled to a self consistent Poisson solver is used for the
dispersion calculation. A semi-classical, ballistic FET model is used to
evaluate the current-voltage characteristics. It is found that the total gate
capacitance is degraded from the oxide capacitance value by 30% for wires in
all the considered transport orientations ([100], [110], [111]). Different wire
directions primarily influence the carrier velocities, which mainly determine
the relative performance differences, while the total charge difference is
weakly affected. The velocities depend on the effective mass and degeneracy of
the dispersions. The [110] and secondly the [100] oriented 3nm thick nanowires
examined, indicate the best ON-current performance compared to [111] wires. The
dispersion features are strong functions of quantization. Effects such as
valley splitting can lift the degeneracies especially for wires with cross
section sides below 3nm. The effective masses also change significantly with
quantization, and change differently for different transport orientations. For
the cases of [100] and [111] wires the masses increase with quantization,
however, in the [110] case, the mass decreases. The mass variations can be
explained from the non-parabolicities and anisotropies that reside in the first
Brillouin zone of silicon.


title:
One-loop Corrections to Scalar and Tensor Perturbations during Inflation
  in Stochastic Gravity

abstract:
  Based on the stochastic gravity, we study the loop corrections to the scalar
and tensor perturbations during inflation. Since the loop corrections to scalar
perturbations suffer infrared (IR) divergence, we consider the IR
regularization to obtain the finite value. We find that the loop corrections to
the scalar perturbations are amplified by the e-folding; in other words there
appear the logarithmic correction, just as discussed by M.Sloth et al. On the
other hand, we find that the tensor perturbations do not suffer from infrared
divergence.


title:
A UV study of nearby luminous infrared galaxies: star formation
  histories and the role of AGN

abstract:
  We employ UV and optical photometry, from the GALEX and SDSS surveys
respectively, to study the star formation histories of 561 luminous infrared
galaxies (LIRGs) in the nearby Universe. A small fraction (~4%) of these
galaxies have spheroidal or near-spheroidal morphologies and could be
progenitors of elliptical galaxies. The remaining galaxies are morphologically
late-type or ongoing mergers. 61% of the LIRGs do not show signs of
interactions, while the remaining objects are either interacting (~18%) or show
post-merger morphologies (~19%). The (SSP-weighted) average age of the
underlying stellar populations in these objects is typically 5-9 Gyrs, with a
mean value of ~6.8 Gyrs. ~60% of the LIRG population began their recent star
formation (RSF) episode within the last Gyr, while the remaining objects began
their RSF episodes 1 to 3 Gyrs in the past. Up to 35% of the stellar mass in
the remnant forms in these episodes - the mean value is ~15%. The (decay)
timescales of the star formation are typically a few Gyrs, indicating that the
star formation rate does not decline significantly during the course of the
burst. 14% of the LIRG population host (Type 2) AGN. The AGN hosts exhibit UV
and optical colours that are redder than those of the normal (non-AGN)
population. However, there is no evidence for a systematically higher dust
content in the AGN hosts. AGN typically appear ~0.5-0.7 Gyrs after the onset of
star formation and the redder colours are a result of older RSF episodes, with
no measurable evidence of negative feedback from the AGN on the star formation
in their host galaxies. (abridged)


title:
Nonlocality in unambiguous pure-state identification without classical
  knowledge

abstract:
  For two bipartite pure states, we consider the problem of unambiguous
identification without classical knowledge on the states. The optimal success
probability by means of local operations and classical communication is shown
to be less than the maximum attainable by the global measuring scheme.