title: Photometry of Star Clusters in the M31 Galaxy. Aperture Size Effects

abstract:
  A study of aperture size effects on star cluster photometry in crowded fields
is presented. Tests were performed on a sample of 285 star cluster candidates
in the South-West field of the M31 galaxy disk, measured in the Local Group
Galaxy Survey mosaic images (Massey et al. 2006). In the majority of cases the
derived UBVRI photometry errors represent the accuracy of cluster colors well,
however, for faint objects, residing in crowded environments, uncertainties of
colors could be underestimated. Therefore, prior to deriving cluster parameters
via a comparison of measured colors with SSP models, biases of colors, arising
due to background crowding, must be taken into account. A comparison of our
photometry data with Hubble Space Telescope observations of the clusters by
Krienke and Hodge (2007) is provided.


title: Accuracy of Star Cluster Parameters from Integrated UBVRI Photometry

abstract:
  We study the capability of the UBVRI photometric system to quantify star
clusters in terms of age, metallicity, and color excess by their integrated
photometry. The well known age-metallicity-extinction degeneracy was analyzed
for various parameter combinations, assuming different levels of photometric
accuracy. We conclude that the UBVRI photometric system enables us to estimate
star cluster parameters over a wide range, if the overall photometric accuracy
is better than ~0.03 mag.


title: Sudden modulation theory of hole spin-3/2 relaxation

abstract:
  We investigate the hole spin-3/2 relaxation process induced by nonadiabatic
stochastic modulations of the instantaneous Luttinger Hamiltonian. The theory
allows to consider fluctuations of both the direction and the magnitude of a
hole wave vector in all regimes of momentum scattering: from
collision-dominated to ballistic.


title: Self-Dual Vortices in the Fractional Quantum Hall System

abstract:
  Based on the $\phi$-mapping theory, we obtain an exact Bogomol'nyi self-dual
equation with a topological term, which is ignored in traditional self-dual
equation, in the fractional quantum Hall system. It is revealed that there
exist self-dual vortices in the system. We investigate the inner topological
structure of the self-dual vortices and show that the topological charges of
the vortices are quantized by Hopf indices and Brouwer degrees. Furthermore, we
study the branch processes in detail. The vortices are found generating or
annihilating at the limit points and encountering, splitting or merging at the
bifurcation points of the vector field $\vec\phi$.


title: Twisted Quantum Deformations of Lorentz and Poincar\'{e} algebras

abstract:
  We discussed twisted quantum deformations of D=4 Lorentz and Poincare
algebras. In the case of Poincare algebra it is shown that almost all classical
r-matrices of S.Zakrzewski classification can be presented as a sum of
subordinated r-matrices of Abelian and Jordanian types. Corresponding twists
describing quantum deformations are obtained in explicit form. This work is an
extended version of the paper \url{arXiv:0704.0081v1 [math.QA]}.


title: Casimir force for a scalar field in warped brane worlds

abstract:
  In looking for imprints of extra dimensions in brane world models one usually
builts these so that they are compatible with known low energy physics and thus
focuses on high energy effects. Nevertheless, just as submillimeter Newton's
law tests probe the mode structure of gravity other low energy tests might
apply to matter. As a model example, in this work we determine the 4D Casimir
force corresponding to a scalar field subject to Dirichlet boundary conditions
on two parallel planes lying within the single brane of a Randall-Sundrum
scenario extended by one compact extra dimension. Using the Green's function
method such a force picks the contribution of each field mode as if it acted
individually but with a weight given by the square of the mode wave functions
on the brane. In the low energy regime one regains the standard 4D Casimir
force that is associated to a zero mode in the massless case or to a
quasilocalized or resonant mode in the massive one whilst the effect of the
extra dimensions gets encoded as an additional term.


title:
Cryptanalysis of an Image Encryption Scheme Based on a Compound Chaotic
  Sequence

abstract:
  Recently, an image encryption scheme based on a compound chaotic sequence was
proposed. In this paper, the security of the scheme is studied and the
following problems are found: (1) a differential chosen-plaintext attack can
break the scheme with only three chosen plain-images; (2) there is a number of
weak keys and some equivalent keys for encryption; (3) the scheme is not
sensitive to the changes of plain-images; and (4) the compound chaotic sequence
does not work as a good random number resource.


title:
Data Assimilation for Wildland Fires: Ensemble Kalman filters in coupled
  atmosphere-surface models

abstract:
  Two wildland fire models are described, one based on
reaction-diffusion-convection partial differential equations, and one based on
semi-empirical fire spread by the level let method. The level set method model
is coupled with the Weather Research and Forecasting (WRF) atmospheric model.
The regularized and the morphing ensemble Kalman filter are used for data
assimilation.


title:
Influence of the hexadecapole deformation on the two neutrino
  double-$\be ta $ decay

abstract:
  The two neutrino double beta $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of $
^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and
$^{150}$Nd nuclei for the $0^{+}\to 0^{+}$ transition is studied in the PHFB
model in conjunction with the pairing plus quadrupole-quadrupole plus
hexadecapole-hexadecapole effective two-body interaction and the effect of the
latter is investigated on the calculation of nuclear transition matrix elements
$M_{2\nu}$. The reliability of the intrinsic wave functions of parent and
daughter nuclei involved in the $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of above
mentioned nuclei is established by obtaining an overall agreement between a
number of theoretically calculated spectroscopic properties, namely the yrast
spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, static
quadrupole moments $Q(2^{+})$ and $g$-factors $g(2^{+})$ and the available
experimental data. The effect of deformation on $M_{2\nu}$ is also investigated
to inveterate its inverse relation with nuclear deformation.


title: Shear viscosity of liquid helium 4 above the lambda point

abstract:
  In liquid helium 4, many features associated to Bose statistics have been
masked by the strongly interacting nature of the liquid. As an example of these
features, we examine the shear viscosity of liquid helium 4 above the lambda
point. Applying the linear-response theory to Poiseuille's formula for the
capillary flow, the reciprocal of the shear viscosity coefficient is considered
as a transport coefficient.
  Using the Kramers-Kronig relation, we relate a superfluid flow in a capillary
with that in a rotating bucket, and express the reciprocal of the shear
viscosity coefficient in terms of the susceptibility of the system. A formula
for the kinematic shear viscosity is obtained which describes the influence of
Bose statistics. Using this formula, we study the gradual fall of the kinematic
shear viscosity from 3.7K to the lambda point in liquid helium 4 at 1 atm.


title: Electroproduction of Light Vector Mesons

abstract:
  An analysis of light vector meson photoproduction at small Bjorken $x \leq
0.2$ is done on the basis of the generalized parton distributions (GPDs). Our
results on the cross section and spin density matrix elements (SDME) are in
good agreement with experiments.


title: Some Observational Aspects of R Coronae Borealis Stars

abstract:
  Some of the observational aspects related to the evolutionary status and dust
production in R Cor Bor stars are discussed. Recent work regarding the surface
abundances, stellar winds and evidence for dust production in these high
luminosty hydrogen deficient stars are also reviewed. Possibility of the
stellar winds being maintained by surface magnetic fields is also considered.


title: Strong tunable coupling between a superconducting charge and phase qubit

abstract:
  We have realized a tunable coupling over a large frequency range between an
asymmetric Cooper pair transistor (charge qubit) and a dc SQUID (phase qubit).
Our circuit enables the independent manipulation of the quantum states of each
qubit as well as their entanglement. The measurements of the charge qubit's
quantum states is performed by resonant read-out via the measurement of the
quantum states of the SQUID. The measured coupling strength is in agreement
with an analytic theory including a capacitive and a tunable Josephson coupling
between the two qubits.


title: Fluorine in R Coronae Borealis and Extreme Helium Stars

abstract:
  Neutral fluorine lines are identified in the optical spectra of several R
Coronae Borealis stars (RCBs) at maximum light. These lines provide the first
measurement of the fluorine abundance in these stars. Fluorine is enriched in
some RCBs by factors of 800 to 8000 relative to its likely initial abundance.
The overabundances of fluorine are evidence for the synthesis of fluorine.
These results are discussed in the light of the scenario that RCBs are formed
by accretion of an He white dwarf by a C-O white dwarf. Sakurai's object (V4334
Sgr), a final He-shell flash product, shows no detectable neutral fluorine
lines.


title:
Characterization of the critical magnetic field in the Dirac-Coulomb
  equation

abstract:
  We consider a relativistic hydrogenic atom in a strong magnetic field. The
ground state level depends on the strength of the magnetic field and reaches
the lower end of the spectral gap of the Dirac-Coulomb operator for a certain
critical value, the critical magnetic field. We also define a critical magnetic
field in a Landau level ansatz. In both cases, when the charge Z of the nucleus
is not too small, these critical magnetic fields are huge when measured in
Tesla, but not so big when the equation is written in dimensionless form. When
computed in the Landau level ansatz, orders of magnitude of the critical field
are correct, as well as the dependence in Z. The computed value is however
significantly too big for a large Z, and the wave function is not well
approximated. Hence, accurate numerical computations involving the Dirac
equation cannot systematically rely on the Landau level ansatz. Our approach is
based on a scaling property. The critical magnetic field is characterized in
terms of an equivalent eigenvalue problem. This is our main analytical result,
and also the starting point of our numerical scheme.


title: GUIDE: Unifying Evolutionary Engines through a Graphical User Interface

abstract:
  Many kinds of Evolutionary Algorithms (EAs) have been described in the
literature since the last 30 years. However, though most of them share a common
structure, no existing software package allows the user to actually shift from
one model to another by simply changing a few parameters, e.g. in a single
window of a Graphical User Interface. This paper presents GUIDE, a Graphical
User Interface for DREAM Experiments that, among other user-friendly features,
unifies all kinds of EAs into a single panel, as far as evolution parameters
are concerned. Such a window can be used either to ask for one of the well
known ready-to-use algorithms, or to very easily explore new combinations that
have not yet been studied. Another advantage of grouping all necessary elements
to describe virtually all kinds of EAs is that it creates a fantastic pedagogic
tool to teach EAs to students and newcomers to the field.


title: Static global monopoles in higher dimensional space time

abstract:
  We present an exact solution around global monopole resulting from the
breaking of a global S0(3) symmetry in a five dimensional space time. We have
shown that the global monopole in higher dimensional space time exerts
gravitational force which is attractive in nature. It is also shown that the
space around global monopole has a deficit solid angle. Finally, we study
monopole in higher dimensional space time within the framework of Lyra
geometry.


title:
Effect of muon-nuclear inelastic scattering on high-energy atmospheric
  muon spectrum at large depth underwater

abstract:
  The energy spectra of hadron cascade showers produced by the cosmic ray muons
travelling through water as well as the muon energy spectra underwater at the
depth up to 4 km are calculated with two models of muon inelastic scattering on
nuclei, the recent hybrid model (two-component, 2C) and the well-known
generalized ector-meson-dominance model for the comparison. The 2C model
involves photonuclear interactions at low and moderate virtualities as well as
the hard scattering including the weak neutral current processes. For the muon
scattering off nuclei substantial uclear effects, shadowing, nuclear binding
and Fermi motion of nucleons are taken into account. It is shown that deep
nderwater muon energy spectrum calculated with the 2C model are noticeably
distorted at energies above 100 TeV as compared to that obtained with the GVMD
model.


title: Skutterudite Results Shed Light on Heavy Fermion Physics

abstract:
  Only few selected examples among the great diversity of anomalous rare earth
skutterudite are reviewed. Focus is first given on PrFe4P12 in comparison with
URu2Si2. For PrFe4P12, great progress has been made on determining the nature
of the order parameter (OP). A non magnetic order parameter with a multipolar
component emerges here while for URu2Si2 the nature of the so-called hidden
order remains mysterious. The two systems have several similarities in their
temperature--pressure (T, P) and magnetic field--temperature (H, T) phase
diagrams, in their spin dynamics, in their nesting character and in their high
sensitivity to impurities. Advances on one side must stimulate new views on the
other. Besides general considerations on the choice of the OP, a simple basic
problem is the treatment of the Kondo coupling in a system with low charge
carrier number for the cases of uncompensated and compensated semi-metal. An
interesting problem is also the possible decoupling between exciton modes and
itinerant carriers.


title: Multispace and Multilevel BDDC

abstract:
  BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.


title:
A Simple Theoretical Prediction of the Data Corresponding to
  Observationally Estimated Value of Cosmological Constant

abstract:
  In this work a satisfactory, simple theoretical prediction of the data
corresponding to observationally (by fine tuning condition) estimated value of
the cosmological constant is given. It is supposed (in conceptually analogy
with holographic principle) that cosmological constant, like classical surface
tension coefficient by a liquid drop, does not correspond to a volume (bulk)
vacuum mass (energy) density distribution but that it corresponds to a surface
vacuum mass (energy) density distribution. Then form of given surface mass
distribution and fine tuning condition imply observed growing (for $\sim$ 61
magnitude order) of the scale factor (from initial, corresponding to Planck
length, to recent, at the beginning of the cosmic acceleration, corresponding
to 10 Glyr length).


title: On Dynamics of $\ell$- Volterra Quadratic Stochastic Operators

abstract:
  We introduce a notion of $\ell$-Volterra quadratic stochastic operator
defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. The
$\ell$-Volterra operator is a Volterra operator iff $\ell=m$. We study
structure of the set of all $\ell$-Volterra operators and describe their
several fixed and periodic points. For $m=2$ and 3 we describe behavior of
trajectories of $(m-1)$-Volterra operators. The paper also contains many
remarks with comparisons of $\ell$-Volterra operators and Volterra ones.


title: Distributed Slicing in Dynamic Systems

abstract:
  Peer to peer (P2P) systems are moving from application specific architectures
to a generic service oriented design philosophy. This raises interesting
problems in connection with providing useful P2P middleware services capable of
dealing with resource assignment and management in a large-scale, heterogeneous
and unreliable environment. The slicing service, has been proposed to allow for
an automatic partitioning of P2P networks into groups (slices) that represent a
controllable amount of some resource and that are also relatively homogeneous
with respect to that resource. In this paper we propose two gossip-based
algorithms to solve the distributed slicing problem. The first algorithm speeds
up an existing algorithm sorting a set of uniform random numbers. The second
algorithm statistically approximates the rank of nodes in the ordering. The
scalability, efficiency and resilience to dynamics of both algorithms rely on
their gossip-based models. These algorithms are proved viable theoretically and
experimentally.


title:
The Nature of the Superconducting phase Transitions in Strongly type-II
  Superconductors in the Pauli Paramagnetic limit

abstract:
  Superconducting phase transitions in strongly type-II superconductors in the
Pauli paramagnetic limit are considered within the framework of the
Gorkov-Ginzburg-Landau approach in the lowest Landau level approximation for
both s and d-wave electron pairing. Simple analytical expressions for the
quadratic and quartic coefficients in the order parameter expansion of the
superconducting free energy are derived without relying on gradient or
wavenumber expansions. The existence of a changeover from continuos to
discontinuos superconducting phase transitions predicted to occur in the clean
limit is shown to depend only on the dimensionality of the underlying
electronic band structure. Such a changeover can take place in the quasi 2D
regime below a critical value of a 3D-2D crossover parameter.


title: Gravitational energy and cosmic acceleration

abstract:
  Cosmic acceleration is explained quantitatively, as an apparent effect due to
gravitational energy differences that arise in the decoupling of bound systems
from the global expansion of the universe. "Dark energy" is a misidentification
of those aspects of gravitational energy which by virtue of the equivalence
principle cannot be localised, namely gradients in the energy due to the
expansion of space and spatial curvature variations in an inhomogeneous
universe. A new scheme for cosmological averaging is proposed which solves the
Sandage-de Vaucouleurs paradox. Concordance parameters fit supernovae
luminosity distances, the angular scale of the sound horizon in the CMB
anisotropies, and the effective comoving baryon acoustic oscillation scale seen
in galaxy clustering statistics. Key observational anomalies are potentially
resolved, and unique predictions made, including a quantifiable variance in the
Hubble flow below the scale of apparent homogeneity.


title:
Unexpectedly small empirical vector strangeness of nucleons realized in
  a baryon model

abstract:
  Most of model considerations of the hidden nucleon strangeness, as well as
some preliminary experimental evidence, led to the expectations of relatively
sizeable strange vector form factors of the proton. For example, it seemed that
the contribution of the fluctuating strange quark-antiquark pairs accounts for
as much as one tenth of the proton's magnetic moment. By the same token, baryon
models which failed to produce the "vector strangeness" of the nucleon seemed
disfavored. Recently, however, more accurate measurements and more
sophisticated data analysis, as well as lattice simulations, revealed that the
form factors associated with the vector strangeness of the nucleon are much
smaller than thought previously; in fact, due to the experimental
uncertainties, the measured strange vector-current proton form factors may be
consistent with zero. In the light of that, we re-asses the merit of the baryon
models leading to little or no vector strangeness of the nucleon. It is done on
the concrete example of the baryon model which essentially amounts to the MIT
bag enriched by the diluted instanton liquid.


title: Dark energy without dark energy

abstract:
  An overview is presented of a recently proposed "radically conservative"
solution to the problem of dark energy in cosmology. The proposal yields a
model universe which appears to be quantitatively viable, in terms of its fit
to supernovae luminosity distances, the angular scale of the sound horizon in
the cosmic microwave background (CMB) anisotropy spectrum, and the baryon
acoustic oscillation scale. It may simultaneously resolve key anomalies
relating to primordial lithium abundances, CMB ellipticity, the expansion age
of the universe and the Hubble bubble feature. The model uses only general
relativity, and matter obeying the strong energy condition, but revisits
operational issues in interpreting average measurements in our presently
inhomogeneous universe, from first principles. The present overview examines
both the foundational issues concerning the definition of gravitational energy
in a dynamically expanding space, the quantitative predictions of the new model
and its best-fit cosmological parameters, and the prospects for an era of new
observational tests in cosmology.


title:
Time delays and energy transport velocities in three dimensional ideal
  cloaking

abstract:
  We obtained the energy transport velocity distribution for a three
dimensional ideal cloak explicitly. Near the operation frequency, the energy
transport velocity has rather peculiar distribution. The velocity along a line
joining the origin of the cloak is a constant, while the velocity approaches
zero at the inner boundary of the cloak. A ray pointing right into the origin
of the cloak will experience abrupt changes of velocities when it impinges on
the inner surface of the cloak. This peculiar distribution causes infinite time
delays for the ideal cloak within a geometric optics description.


title:
All-optical switching and multistability in photonic structures with
  liquid crystal defects

abstract:
  We demonstrate that one-dimensional photonic crystals with pure nematic
liquid-crystal defects can operate as all-optical switching devices based on
optical orientational nonlinearities of liquid crystals. We show that such a
periodic structure is responsible for a modulated threshold of the optical
Fr\'eedericksz transition in the spectral domain, and this leads to all-optical
switching and light-induced multistability. This effect has no quasi-statics
electric field analogue, and it results from nonlinear coupling between light
and a defect mode.


title: Functional equations of the dilogarithm in motivic cohomology

abstract:
  We prove relations between fractional linear cycles in Bloch's integral
cubical higher Chow complex in codimension two of number fields, which
correspond to functional equations of the dilogarithm.
  These relations suffice, as we shall demonstrate with a few examples, to
write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for
certain number fields F to detect torsion cycles.
  Using the regulator map to Deligne cohomology, one can check the
non-triviality of the torsion cycles thus obtained. Using this combination of
methods, we obtain explicit higher Chow cycles generating the integral motivic
cohomology groups of some number fields.


title:
The Hemispheric Asymmetry of Solar Activity During the Twentieth Century
  and the Solar Dynamo

abstract:
  We believe the Babcock--Leighton process of poloidal field generation to be
the main source of irregularity in the solar cycle. The random nature of this
process may make the poloidal field in one hemisphere stronger than that in the
other hemisphere at the end of a cycle. We expect this to induce an asymmetry
in the next sunspot cycle. We look for evidence of this in the observational
data and then model it theoretically with our dynamo code. Since actual polar
field measurements exist only from 1970s, we use the polar faculae number data
recorded by Sheeley (1991) as a proxy of the polar field and estimate the
hemispheric asymmetry of the polar field in different solar minima during the
major part of the twentieth century. This asymmetry is found to have a
reasonable correlation with the asymmetry of the next cycle. We then run our
dynamo code by feeding information about this asymmetry at the successive
minima and compare with observational data. We find that the theoretically
computed asymmetries of different cycles compare favourably with the
observational data, the correlation coefficient being 0.73. Due to the coupling
between the two hemispheres, any hemispheric asymmetry tends to get attenuated
with time. The hemispheric asymmetry of a cycle either from observational data
or from theoretical calculation statistically tends to be less than the
asymmetry in the polar field (as inferred from the faculae data) in the
preceding minimum. This reduction factor turns out to be 0.38 and 0.60
respectively in observational data and theoretical simulation.


title:
Shot noise in a quantum dot coupled to non-magnetic leads: Effects of
  Coulomb interaction

abstract:
  We study electron transport through a quantum dot, connected to non-magnetic
leads, in a magnetic field. A super-Poissonian electron noise due to the
effects of both interacting localized states and dynamic channel blockade is
found when the Coulomb blockade is partially lifted. This is sharp contrast to
the sub-Poissonian shot noise found in the previous studies for a large bias
voltage, where the Coulomb blockade is completely lifted. Moreover, we show
that the super-Poissonian shot noise can be suppressed by applying an electron
spin resonance (ESR) driving field. For a sufficiently strong ESR driving field
strength, the super-Poissonian shot noise will change to be sub-Poissonian.


title: Supercooling and the Metal-Insulator Phase Transition of NdNiO$_{3}$

abstract:
  We report the temperature and time dependence of electrical resistivity on
high temperature, high oxygen pressure prepared polycrystalline samples of
NdNiO_3. NdNiO_3 is metallic above 195 K and below that temperature it
undergoes a transition to an insulating state. We find that on cooling NdNiO_3
below 195 K it goes into a state which is not in thermodynamic equilibrium and
slowly relaxes over several hours. As we cool it further and go below about 110
K it goes into a stable insulating state. On heating the system from the
insulating state towards 200 K we find that it remains stable and insulating
and undergoes a rather sharp insulator to metal transition in the temperature
range 185 K to 195 K. We try to make sense of these and a few other interesting
observations on the basis of our current understanding of first order phase
transitions, supercooling, and metal-insulator transitions.


title: Field-dependent thermal transport in the Haldane chain compound NENP

abstract:
  We present a study of the magnetic field-dependent thermal transport in the
spin S=1 chain material Ni(C2H8N2)2NO2(ClO4) (NENP). The measured thermal
conductivity is found to be very sensitive to the field-induced changes in the
spin excitation spectrum. The magnetic contribution to the total heat
conductivity is analyzed in terms of a quasiparticle model, and we obtain a
temperature and momentum independent mean free path. This implies that the
motion of quasiparticles is effectively three dimensional despite the tiny
interchain coupling.


title: Two Fractal Overlap Time Series: Earthquakes and Market Crashes

abstract:
  We find prominent similarities in the features of the time series for the
(model earthquakes or) overlap of two Cantor sets when one set moves with
uniform relative velocity over the other and time series of stock prices. An
anticipation method for some of the crashes have been proposed here, based on
these observations.


title: Finite-size scaling in extreme statistics

abstract:
  We study the convergence and shape correction to the limit distributions of
extreme values due to the finite size (FS) of data sets. A renormalization
method is introduced for the case of independent, identically distributed (iid)
variables, showing that the iid universality classes are subdivided according
to the exponent of the FS convergence, which determines the leading order FS
shape correction function as well. We find that, for the correlated systems of
subcritical percolation and 1/f^alpha stationary (alpha<1) noise, the iid shape
correction compares favorably to simulations. Furthermore, for the strongly
correlated regime (alpha>1) of 1/f^alpha noise, the shape correction is
obtained in terms of the limit distribution itself.


title: Computational study of the vibrating disturbances to the lung function

abstract:
  Frequently during its lifetime a human organism is subjected to the
acoustical and similar to them vibrating impacts. Under the certain conditions
such influence may cause physiological changes in the organs functioning. Thus
the study of the oscillatory mechanical impacts to the organism is very
important task of the numerical physiology. It allows to investigate the
endurance limits of the organism and to develop protective measures in order to
extend them. The noise nuisances affects to the most parts of the organism
disrupting their functions. The vibrating disturbances caused to the lung
function as one of the most sensitive to the acoustical impacts is considered
in this work. The model proposed to describe the air motion in
trachea-bronchial tree is based on the one dimensional no-linear theory
including mass and momentum conservation for the air flow in flexible tubes.


title: BRST charge for nonlinear algebras

abstract:
  We study the construction of the classical nilpotent canonical BRST charge
for the nonlinear gauge algebras where a commutator (in terms of Poisson
brackets) of the constraints is a finite order polynomial of the constraints.


title: On bases of tropical Pl\"ucker functions

abstract:
  We consider functions $f:B\to\Rset$ that obey tropical analogs of classical
Pl\"ucker relations on minors of a matrix. The most general set $B$ that we
deal with in this paper is of the form $\{x\in \Zset^n\colon 0\le x\le a, m\le
x_1+...+x_n\le m'\}$ (a rectangular integer box ``truncated from below and
above''). We construct a basis for the set $\Tscr$ of tropical Pl\"ucker
functions on $B$, a subset $\Bscr\subseteq B$ such that the restriction map
$\Tscr\to\Rset^\Bscr$ is bijective. Also we characterize, in terms of the
restriction to the basis, the classes of submodular, so-called skew-submodular,
and discrete concave functions in $\Tscr$, discuss a tropical analogue of the
Laurentness property, and present other results.


title: A simple model for describing a lattice with a double occupancy

abstract:
  A simple model is presented to investigate an impact of the double occupied
sites on the ground state energy of a lattice. The model is seen as a useful
tool to introduce undergraduate or graduate physics students to an array of a
relatively simple mathematical apparatus and physical ideas which they can
choose later for a deeper study. Instead of analyzing a system of electrons in
a periodic potential, a system of sites having different energy states related
to a number of extra electrons at a site is considered. The simplification is
achieved by introducing operators for one-electron sites and two-electron sites
as independent entities. A simple modeling function for the ground state of the
system is constructed. Linear and quadratic lattices are considered. For a
quadratic lattice the existence of a critical temperature is shown.


title: About Torsional Weyl-Dirac Electrodynamics

abstract:
  A classical general relativistic theory possessing magnetic currents, as well
electric ones and admitting massive photons was built up. As the geometric
basis serves a space with Weylian non-metricity and torsion. The theory is
coordinate covariant as well Weyl-gauge covariant. In the limit one obtains the
ordinary Einstein-Maxwell theory.


title: On quantum cryptography with bipartite bound entangled states

abstract:
  Recently the explicit applicability of bound entanglement in quantum
cryptography has been shown. In this paper some of recent results respecting
this topic are reviewed. In particular relevant notions and definitions are
reminded. The new construction of bound entangled states containing secure
correlations is presented. It provides low dimensional 6\otimes6 bound
entangled states with nonzero distillable key.


title:
$\Lambda$-adic modular symbols and several variable $p$-adic L-functions
  over totally real fields

abstract:
  We interpolate cohomology classes attached to families of Hilbert modular
forms. Using this we construct a two variable $p$-adic L-function which
interpolates one variable $p$-adic L-functions.


title: A ptototype compartmental model of blood pressure distribution

abstract:
  We consider a system of differential equations the behavior of which
solutions possesses several properties characteristic of the blood pressure
distribution. The system can be used for a compartmental modeling of the
cardiovascular system. It admits a unique bounded solution such that all
coordinates of the solution are separated from zero by positive numbers, and
which is periodic, eventually periodic or almost periodic depending on the
moments of heart contraction. Appropriate numerical simulations are provided.


title:
On the irrationality of Ramanujan's mock theta functions and other
  q-series at an infinite number of points

abstract:
  We show that all of Ramanujan's mock theta functions of order 3, Watson's
three additional mock theta functions of order 3, the Rogers-Ramanujan
q-series, and 6 mock theta functions of order 5 take on irrational values at
the points q=\pm 1/2,\pm 1/3,\pm 1/4,...


title: Topos theory and `neo-realist' quantum theory

abstract:
  Topos theory, a branch of category theory, has been proposed as mathematical
basis for the formulation of physical theories. In this article, we give a
brief introduction to this approach, emphasising the logical aspects. Each
topos serves as a `mathematical universe' with an internal logic, which is used
to assign truth-values to all propositions about a physical system. We show in
detail how this works for (algebraic) quantum theory.


title: Holographic Chaplygin DGP cosmologies

abstract:
  In the present paper, we present an extra dimensions inspired model that is
built on the DGP brane-world scenario, then we take the dark energy component
on the brane to be a Chaplygin gas. After that we consider a holographic model
of Chaplygin gas in the framework of DGP cosmology. We show that the
holographic Chaplygin gas can mimic a phantom fluid and cross the phantom
divide in a DGP brane-world setup.


title: On growth and torsion of groups

abstract:
  We give a subexponential upper bound and a superpolynomial lower bound on the
growth function of the Fabrykowski-Gupta group.
  As a consequence, we answer negatively a question by Longobardi, Maj and
Rhemtulla about characterizing groups containing no free subsemigroups on two
generators.


title: Small permutation classes

abstract:
  We establish a phase transition for permutation classes (downsets of
permutations under the permutation containment order): there is an algebraic
number $\kappa$, approximately 2.20557, for which there are only countably many
permutation classes of growth rate (Stanley-Wilf limit) less than $\kappa$ but
uncountably many permutation classes of growth rate $\kappa$, answering a
question of Klazar. We go on to completely characterize the possible
sub-$\kappa$ growth rates of permutation classes, answering a question of
Kaiser and Klazar. Central to our proofs are the concepts of generalized grid
classes (introduced herein), partial well-order, and atomicity (also known as
the joint embedding property).


title: Study DDO 68: new evidences for galaxy youth

abstract:
  DDO 68 is the second most metal-poor star-forming galaxy (12+log(O/H)=7.14).
Its peculiar optical morphology and the data on its HI distribution and
kinematics indicate the merger origin. We use the photometry of the SDSS
u,g,r,i images of DDO 68 to estimate its stellar population ages. The available
H-alpha-images of DDO 68 were used to select several representative regions
without nebular emission. The analysis of obtained colours was performed via
comparison with the PEGASE2 evolutionary tracks for various star formation (SF)
laws, including the two extremes: instantaneous SF and continuous SF with
constant SF rate. The (u-g), (g-r) colours derived for all selected regions,
are consistent with a few `instantaneous' SF episodes with ages from ~0.05 to
~1Gyr. Combining the fluxes and colours of visible stellar subsystems with
PEGASE2 models, we have estimated the total mass of visible stars in DDO 68 of
~2.4x10^7 Mo. This comprises only ~6% of the total galaxy baryonic mass. All
available data do not contradict to the option that DDO 68 is a kind of very
rare candidate `young' galaxy, whose dominant stellar build-up took place in
course of the recent (with the first encounter ~1 Gyr ago) merger of two very
gas-rich disks. DDO 68 best approximates on its properties cosmologically young
low-mass galaxies.


title: Graphene on metal surface: gap opening and n-doping

abstract:
  Graphene grown on metal surface, Cu(111), with a boron nitride(BN) buffer
layer is studied for the first time. Our first-principles calculations reveal
that charge is transferred from the copper substrate to graphene through the BN
buffer layer which results in a n-doped graphene in the absence of a gate
voltage. More importantly, a gap of 0.2 eV which is comparable to that of a
typical narrow gap semicondutor opens just 0.5 eV below the Fermi-level at the
Dirac point. The Fermi-level can be easily shifted inside this gap to make
graphene a semiconductor which is crucial for graphene-based electronic
devices. A graphene based p-n junction can be realized with graphene eptaxially
grown on metal surface.


title: A two-page disproof of the Borsuk partition conjecture

abstract:
  It is presented the simplest known disproof of the Borsuk conjecture stating
that if a bounded subset of n-dimensional Euclidean space contains more than n
points, then the subset can be partitioned into n+1 nonempty parts of smaller
diameter.
  The argument is due to N. Alon and is a remarkable application of
combinatorics and algebra to geometry. This note is purely expository and is
accessible for students.


title:
A Method for the Precision Mass Measurement of the Stop Quark at the
  International Linear Collider

abstract:
  Many supersymmetric models predict new particles within the reach of the next
generation of colliders. For an understanding of the model structure and the
mechanism(s) of symmetry breaking, it is important to know the masses of the
new particles precisely. In this article the measurement of the mass of the
scalar partner of the top quark (stop) at an e+e- collider is studied. A
relatively light stop is motivated by attempts to explain electroweak
baryogenesis and can play an important role in dark matter relic density. A
method is presented which makes use of cross-section measurements near the
pair-production threshold as well as at higher center-of-mass energies. It is
shown that this method not only increases the statistical precision, but also
greatly reduces the systematic uncertainties, which can be important. Numerical
results are presented, based on a realistic event simulation, for two signal
selection strategies: using conventional selection cuts, and using an Iterative
Discriminant Analysis (IDA). Our studies indicate that a precision of
$\Delta\mstop = 0.42$ GeV can be achieved, representing a major improvement
over previous studies. While the analysis of stops is particularly challenging
due to the possibility of stop hadronization, the general procedure could be
applied to the mass measurement of other particles as well. We also comment on
the potential of the IDA to discover a stop quark in this scenario, and we
revisit the accuracy of the theoretical predictions for the neutralino relic
density


title:
Asymptotic Mutual Information Statistics of Separately-Correlated Rician
  Fading MIMO Channels

abstract:
  Precise characterization of the mutual information of MIMO systems is
required to assess the throughput of wireless communication channels in the
presence of Rician fading and spatial correlation. Here, we present an
asymptotic approach allowing to approximate the distribution of the mutual
information as a Gaussian distribution in order to provide both the average
achievable rate and the outage probability. More precisely, the mean and
variance of the mutual information of the separatelycorrelated Rician fading
MIMO channel are derived when the number of transmit and receive antennas grows
asymptotically large and their ratio approaches a finite constant. The
derivation is based on the replica method, an asymptotic technique widely used
in theoretical physics and, more recently, in the performance analysis of
communication (CDMA and MIMO) systems. The replica method allows to analyze
very difficult system cases in a comparatively simple way though some authors
pointed out that its assumptions are not always rigorous. Being aware of this,
we underline the key assumptions made in this setting, quite similar to the
assumptions made in the technical literature using the replica method in their
asymptotic analyses. As far as concerns the convergence of the mutual
information to the Gaussian distribution, it is shown that it holds under some
mild technical conditions, which are tantamount to assuming that the spatial
correlation structure has no asymptotically dominant eigenmodes. The accuracy
of the asymptotic approach is assessed by providing a sizeable number of
numerical results. It is shown that the approximation is very accurate in a
wide variety of system settings even when the number of transmit and receive
antennas is as small as a few units.


title: Topological Defects in Spherical Nematics

abstract:
  We study the organization of topological defects in a system of nematogens
confined to the two-dimensional sphere (S^2). We first perform Monte Carlo
simulations of a fluid system of hard rods (spherocylinders) living in the
tangent plane of S^2. The sphere is adiabatically compressed until we reach a
jammed nematic state with maximum packing density. The nematic state exhibits
four +1/2 disclinations arrayed on a great circle rather than at the vertices
of a regular tetrahedron. This arises from the high elastic anisotropy of the
system in which splay (K_1) is far softer than bending (K_3). We also introduce
and study a lattice nematic model on S^2 with tunable elastic constants and map
out the preferred defect locations as a function of elastic anisotropy. We
establish the existence of a one-parameter family of degenerate ground states
in the extreme splay-dominated limit K_1/K_3 -> 0. Thus the global defect
geometry is controllable by tuning the relative splay to bend modulus.


title: How the Pauli principle governs the decay of three-cluster systems

abstract:
  New approach to the problem of multichannel continuum spectrum of
three-cluster systems composed of an s-cluster and two neutrons is suggested
based on the discrete representation of a complete basis of allowed states of
the multiparticle harmonic oscillator. The structure of the eigenfunctions and
behavior of the eigenvalues of the three-cluster norm kernel are analyzed.
Classification of the eigenvalues of the three-cluster systems with the help of
eigenvalues of the two-body subsystem is suggested. Asymptotic boundary
conditions for a three-cluster wave function in the continuum consistent with
the requirements of the Pauli principle are established. Such asymptotic
behavior corresponds rather to subsequent decay of the three-cluster system
than to the so-called "democratic decay" associated with the hyperspherical
harmonics. The 3H+n+n configuration of the 5H nucleus is considered in detail.


title:
Variability of Disk Emission in Pre-Main Sequence and Related Stars. I.
  HD 31648 and HD 163296 - Isolated Herbig Ae Stars Driving Herbig-Haro Flows

abstract:
  Infrared photometry and spectroscopy covering a time span of a quarter
century are presented for HD 31648 (MWC 480) and HD 163296 (MWC 275). Both are
isolated Herbig Ae stars that exhibit signs of active accretion, including
driving bipolar flows with embedded Herbig-Haro (HH) objects. HD 163296 was
found to be relatively quiescent photometrically in its inner disk region, with
the exception of a major increase in emitted flux in a broad wavelength region
centered near 3 microns in 2002. In contrast, HD 31648 has exhibited sporadic
changes in the entire 3-13 micron region throughout this span of time. In both
stars the changes in the 1-5 micron flux indicate structural changes in the
region of the disk near the dust sublimation zone, possibly causing its
distance from the star to vary with time. Repeated thermal cycling through this
region will result in the preferential survival of large grains, and an
increase in the degree of crystallinity. The variability observed in these
objects has important consequences for the interpretation of other types of
observations. For example, source variability will compromise models based on
interferometry measurements unless the interferometry observations are
accompanied by nearly-simultaneous photometric data.


title:
A Fast Hierarchical Multilevel Image Segmentation Method using Unbiased
  Estimators

abstract:
  This paper proposes a novel method for segmentation of images by hierarchical
multilevel thresholding. The method is global, agglomerative in nature and
disregards pixel locations. It involves the optimization of the ratio of the
unbiased estimators of within class to between class variances. We obtain a
recursive relation at each step for the variances which expedites the process.
The efficacy of the method is shown in a comparison with some well-known
methods.


title: Theta-functions on the Kodaira-Thurston manifold

abstract:
  The Kodaira--Thurston M manifold is a compact, 4-dimensional nilmanifold
which is symplectic and complex but not Kaehler. We describe a construction of
theta-functions associated to M which parallels the classical theory of
theta-functions associated to the torus (from the point of view of
representation theory and geometry), and yields pseudoperiodic complex-valued
functions on R^4.
  There exists a three-step nilpotent Lie group G which acts transitively on
the Kodaira--Thurston manifold M in a Hamiltonian fashion. The theta-functions
discussed in this paper are intimately related to the representation theory of
G in much the same way the classical theta-functions are related to the
Heisenberg group. One aspect of our results which has not appeared in the
classical theory is a connection between the representation theory of G and the
existence of Lagrangian and special Lagrangian foliations and torus fibrations
in M.


title:
Class of viable modified $f(R)$ gravities describing inflation and the
  onset of accelerated expansion

abstract:
  A general approach to viable modified $f(R)$ gravity is developed in both the
Jordan and the Einstein frames. A class of exponential, realistic modified
gravities is introduced and investigated with care. Special focus is made on
step-class models, most promising from the phenomenological viewpoint and which
provide a natural way to classify all viable modified gravities. One- and
two-steps models are explicitly considered, but the analysis is extensible to
$N$-step models. Both inflation in the early universe and the onset of recent
accelerated expansion arise in these models in a natural, unified way.
Moreover, it is demonstrated that models in this category easily pass all local
tests, including stability of spherical body solution, non-violation of
Newton's law, and generation of a very heavy positive mass for the additional
scalar degree of freedom.


title: State determination: an iterative algorithm

abstract:
  An iterative algorithm for state determination is presented that uses as
physical input the probability distributions for the eigenvalues of two or more
observables in an unknown state $\Phi$. Starting form an arbitrary state
$\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to
$\Phi$ or to a Pauli partner. This algorithm for state reconstruction is
efficient and robust as is seen in the numerical tests presented and is a
useful tool not only for state determination but also for the study of Pauli
partners. Its main ingredient is the Physical Imposition Operator that changes
any state to have the same physical properties, with respect to an observable,
of another state.


title:
Probing Majorana Phases and Neutrino Mass Spectrum in the Higgs Triplet
  Model at the LHC

abstract:
  Doubly charged Higgs bosons (H^++) are a distinctive signature of the Higgs
Triplet Model of neutrino mass generation. If H^++ is relatively light
(m_{H^++} < 400GeV) it will be produced copiously at the LHC, which could
enable precise measurements of the branching ratios of the decay channels H^++
to l_i l_j. Such branching ratios are determined solely by the neutrino mass
matrix which allows the model to be tested at the LHC. We quantify the
dependence of the leptonic branching ratios on the absolute neutrino mass and
Majorana phases, and present the permitted values for the channels ee, emu and
mumu. It is shown that precise measurements of these three branching ratios are
sufficient to extract information on the neutrino mass spectrum and probe the
presence of CP violation from Majorana phases.


title: Graphene Physics in Graphite

abstract:
  Single layers of carbon dubbed "graphenes", from which graphite is built,
have attracted broad interest in the scientific community because of recent
exciting experimental results. Graphene is interesting from a fundamental
research perspective, as well as for potential technological applications.
Here, we provide a brief overview of recent developments in this field,
focusing especially on the electronic properties of graphite. Experimental
evidence indicates that high-quality graphite is a multi-layer system with
nearly decoupled 2D graphene planes. Based on experimental observations, we
anticipate that thin graphite samples and not single layers will be the most
promising candidates for graphene-based electronics.


title: The Witten equation, mirror symmetry and quantum singularity theory

abstract:
  For any non-degenerate, quasi-homogeneous hypersurface singularity, we
describe a family of moduli spaces, a virtual cycle, and a corresponding
cohomological field theory associated to the singularity. This theory is
analogous to Gromov-Witten theory and generalizes the theory of r-spin curves,
which corresponds to the simple singularity A_{r-1}.
  We also resolve two outstanding conjectures of Witten. The first conjecture
is that ADE-singularities are self-dual; and the second conjecture is that the
total potential functions of ADE-singularities satisfy corresponding
ADE-integrable hierarchies. Other cases of integrable hierarchies are also
discussed.


title: Rabi oscillations in semiconductor multi-wave mixing response

abstract:
  We studied the semiconductor response with respect to high intensity resonant
excitation on short time scale when the contribution of the Fermi statistics of
the electrons and holes prevails. We studied both the single and double pulse
excitations. For the latter case we considered the time evolution of the
multi-wave mixing exciton polarization. The main difference between the
excitation by a single pulse or by two non-collinear pulses is that the Rabi
oscillations of the multi-wave mixing response are characterized by two
harmonics. Analyzing the operator dynamics governed by the external excitation
we found that there are three invariant spin classes, which do not mix with the
evolution of the system. Two classes correspond to the bright exciton states
and one contains all dark states. We found that the dynamics of the classes is
described by six frequencies and the Rabi frequencies are only two of them (one
for each bright class). We discuss the effect of the dispersion of the
electrons and holes and the Coulomb interaction describing the semiconductor by
the semiconductor Bloch equation (SBE). We show that if initially the system is
in the ground state then the SBE preserves the invariant spin classes thus
proving absence of the dark excitons in the framework of this description. We
found that due to the mass difference between holes of different kind
additional Rabi frequencies, two of those present in the operator dynamics,
should appear in the evolution of the exciton polarization.


title:
On the Origin of Bimodal Horizontal-Branches in Massive Globular
  Clusters: The Case of NGC 6388 and NGC 6441

abstract:
  Despite the efforts of the past decade, the origin of the bimodal
horizontal-branch (HB) found in some globular clusters (GCs) remains a
conundrum. Inspired by the discovery of multiple stellar populations in the
{\it most massive} Galactic GC, $\omega$ Centauri, we investigate the
possibility that two distinct populations may coexist and are responsible for
the bimodal HBs in the {\it third} and {\it fifth} brightest GCs, NGC 6388 and
NGC 6441. Using the population synthesis technique, we examine two different
chemical ``self-enrichment'' hypotheses in which a primordial GC was
sufficiently massive to contain two or more distinct populations as suggested
by the populations found in $\omega$ Cen: (1) the age-metallicity relation
scenario in which two populations with different metallicity and age coexist,
following an internal age-metallicity relation, and (2) the super-helium-rich
scenario in which GCs contain a certain fraction of helium-enhanced stars, for
instance, the second generation stars formed from the helium-enriched ejecta of
the first. The comparative study indicates that the detailed color-magnitude
diagram morphologies and the properties of the RR Lyrae variables in NGC 6388
and NGC 6441 support the latter scenario; i.e., the model which assumes a minor
fraction ($\sim$ 15 %) of helium-excess (Y $\simeq$ 0.3) stars. The results
suggest that helium content is the main driver behind the HB bimodality found
most often in massive GCs. If confirmed, the GC-to-GC variation of helium
abundance should be considered a {\it local} effect, further supporting the
argument that age is the {\it global} second parameter of HB morphology.


title: WKB Approximation in Noncommutative Gravity

abstract:
  We consider the quasi-commutative approximation to a noncommutative geometry
defined as a generalization of the moving frame formalism. The relation which
exists between noncommutativity and geometry is used to study the properties of
the high-frequency waves on the flat background.


title: The Witten equation and its virtual fundamental cycle

abstract:
  We study a system of nonlinear elliptic PDEs associated with a
quasi-homogeneous polynomial. These equations were proposed by Witten as the
replacement for the Cauchy-Riemann equation in the singularity
(Landau-Ginzburg) setting. We introduce a perturbation to the equation and
construct a virtual cycle for the moduli space of its solutions. Then, we study
the wall-crossing of the deformation of the virtual cycle under perturbation
and match it to classical Picard-Lefschetz theory. An extended virtual cycle is
obtained for the original equation. Finally, we prove that the extended virtual
cycle satisfies a set of axioms similar to those of Gromov-Witten theory and
r-spin theory.

categories: math.AG hep-th math-ph math.AP math.MP math.SG


title:
Chaos in Partial Differential Equations, Navier-Stokes Equations and
  Turbulence

abstract:
  I will briefly survey the most important results obtained so far on chaos in
partial differential equations. I will also survey progresses and make some
comments on Navier-Stokes equations and turbulence.

categories: math.AP math-ph math.DS math.MP nlin.CD physics.flu-dyn


title: Accurate and Efficient Expression Evaluation and Linear Algebra

abstract:
  We survey and unify recent results on the existence of accurate algorithms
for evaluating multivariate polynomials, and more generally for accurate
numerical linear algebra with structured matrices. By "accurate" we mean that
the computed answer has relative error less than 1, i.e., has some correct
leading digits. We also address efficiency, by which we mean algorithms that
run in polynomial time in the size of the input. Our results will depend
strongly on the model of arithmetic: Most of our results will use the so-called
Traditional Model (TM). We give a set of necessary and sufficient conditions to
decide whether a high accuracy algorithm exists in the TM, and describe
progress toward a decision procedure that will take any problem and provide
either a high accuracy algorithm or a proof that none exists. When no accurate
algorithm exists in the TM, it is natural to extend the set of available
accurate operations by a library of additional operations, such as $x+y+z$, dot
products, or indeed any enumerable set which could then be used to build
further accurate algorithms. We show how our accurate algorithms and decision
procedure for finding them extend to this case. Finally, we address other
models of arithmetic, and the relationship between (im)possibility in the TM
and (in)efficient algorithms operating on numbers represented as bit strings.


title:
The mean free path of protons and neutrons in isospin-asymmetric nuclear
  matter

abstract:
  We calculate the mean free path of protons and neutrons in symmetric and
asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross
sections. Those are obtained from calculations of the G-matrix including
relativistic "Dirac" effects. The dependence of the mean free path on energy
and isospin asymmetry is discussed. We conclude by suggesting possible ways our
microscopic predictions may be helpful in conjunction with studies of rare
isotopes.


title: Elements of Radio Waves

abstract:
  We present a summary of the basic properties of the radio wave generation,
propagation and reception, with a special attention to the gigahertz bandwidth
region which is of interest for wireless sensor networks. We also present some
measurement results which use the so-called RSSI indicator in order to track
how the field strength varies with position and distance of the transceivers.
We hope the paper may be useful to anyone who looks for a quick review of the
fundamentals of electromagnetic theory with application to antennas.


title: Bregman distances and Chebyshev sets

abstract:
  A closed set of a Euclidean space is said to be Chebyshev if every point in
the space has one and only one closest point in the set. Although the situation
is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that
in Euclidean spaces a closed set is Chebyshev if and only if the set is convex.
In this paper, from the more general perspective of Bregman distances, we show
that if every point in the space has a unique nearest point in a closed set,
then the set is convex. We provide two approaches: one is by nonsmooth
analysis; the other by maximal monotone operator theory. Subdifferentiability
properties of Bregman nearest distance functions are also given.


title: The Dynamics of a Mobile Phone Network

abstract:
  The empirical study of network dynamics has been limited by the lack of
longitudinal data. Here we introduce a quantitative indicator of link
persistence to explore the correlations between the structure of a mobile phone
network and the persistence of its links. We show that persistent links tend to
be reciprocal and are more common for people with low degree and high
clustering. We study the redundancy of the associations between persistence,
degree, clustering and reciprocity and show that reciprocity is the strongest
predictor of tie persistence. The method presented can be easily adapted to
characterize the dynamics of other networks and can be used to identify the
links that are most likely to survive in the future.


title: Counting Labelled Trees with Given Indegree Sequence

abstract:
  For a labelled tree on the vertex set $[n]:=\{1,2,..., n\}$, define the
direction of each edge $ij$ to be $i\to j$ if $i<j$. The indegree sequence of
$T$ can be considered as a partition $\lambda \vdash n-1$. The enumeration of
trees with a given indegree sequence arises in counting secant planes of curves
in projective spaces. Recently Ethan Cotterill conjectured a formula for the
number of trees on $[n]$ with indegree sequence corresponding to a partition
$\lambda$. In this paper we give two proofs of Cotterill's conjecture: one is
`semi-combinatorial" based on induction, the other is a bijective proof.


title:
Measurement of Temporal Correlations of the Overhauser Field in a Double
  Quantum Dot

abstract:
  In quantum dots made from materials with nonzero nuclear spins, hyperfine
coupling creates a fluctuating effective Zeeman field (Overhauser field) felt
by electrons, which can be a dominant source of spin qubit decoherence. We
characterize the spectral properties of the fluctuating Overhauser field in a
GaAs double quantum dot by measuring correlation functions and power spectra of
the rate of singlet-triplet mixing of two separated electrons. Away from zero
field, spectral weight is concentrated below 10 Hz, with 1/f^2 dependence on
frequency, f. This is consistent with a model of nuclear spin diffusion, and
indicates that decoherence can be largely suppressed by echo techniques.


title: Massive Neutrino in Non-commutative Space-time

abstract:
  We consider the noncommutative standard model based on $SU(3)\times
SU(2)\times U(1)$. We study the gauge transformation of right handed neutrino
and its direct interaction with photon in the noncommutative space-time. We
show that the massive Dirac neutrinos, through the Higgs mechanism, can not
accommodate this extension of the standard model; while the massive Majorana
neutrinos are consistent with the gauge symmetry of the model. The
electromagnetic properties and the dispersion relations for the neutrino in the
noncommutative standard model is examined. We also compare the results with the
noncommutative standard model based on $U(3)\times U(2)\times U(1) $.


title: A Supernova Riddle

abstract:
  Analysis of the polarization of light from supernovae can reveal the shape
and distribution of matter ejected from exploding stars. Here we review the
young field of Type Ia supernova spectropolarimetry and critically evaluate,
and place in context, the recent work of Wang et al. (2007, Science, 315, 212)
in which a suggestive trend is found in data from 17 Type Ia events.


title: Plurisubharmonic functions in calibrated geometry and q-convexity

abstract:
  Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called
$\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex
subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is
q-convex. A continuous $\omega^q$-plurisubharmonic function admits a local
approximation by smooth, $\omega^q$-plurisubharmonic functions. For any closed
subvariety $Z\subset M$, $\dim Z < q$, there exists a strictly
$\omega^q$-plurisubharmonic function in a neighbourhood of $Z$ (this result is
known for q-convex functions). This theorem is used to give a new proof of
Sibony's lemma on integrability of positive closed (p,p)-forms which are
integrable outside of a complex subvariety of codimension >p.


title: Valuation bases for generalized algebraic series fields

abstract:
  We investigate valued fields which admit a valuation basis. Given a countable
ordered abelian group G and a real closed, or algebraically closed field F, we
give a sufficient condition for a valued subfield of the field of generalized
power series F((G)) to admit a K-valuation basis. We show that the field of
rational functions F(G) and the field F(G) of power series in F((G)) algebraic
over F(G) satisfy this condition. It follows that for archimedean F and
divisible G the real closed field F(G) admits a restricted exponential
function.


title:
Diffuse $\gamma$-rays and $\bar{p}$ flux from dark matter annihilation
  -- a model for consistent results with EGRET and cosmic ray data

abstract:
  In this work we develop a new propagation model for the Galactic cosmic rays
based on the GALPROP code, including contributions from dark matter
annihilation. The model predicts compatible Galactic diffuse $\gamma$ ray
spectra with EGRET data in all sky regions. It also gives consistent results of
the diffuse $\gamma$ ray longitude and latitude distributions. Further the
results for B/C, $^{10}$Be/$^9$Be, proton, electron and antiproton spectra are
also consistent with cosmic ray measurements. In the model we have taken a
universal proton spectrum throughout the Galaxy without introducing large
fluctuation for the proton energy loss is negligible. The dark matter
annihilation signals are `boosted' after taking the contribution from subhalos
into account. Another interesting feature of the model is that it gives better
description of the diffuse $\gamma$ rays when taking the source distribution
compatible with supernova remnants data, which is different from previous
studies.


title:
The electronic structure of La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_4$
  probed by high- and low-energy angle-resolved photoelectron spectroscopy:
  evolution with probing depth

abstract:
  We present angle-resolved photoelectron spectroscopy data probing the
electronic structure of the Nd-substituted high-$T_c$ cuprate
La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_4$ (Nd-LSCO). Data have been acquired at
low and high photon energies, $h\nu$ = 55 and 500 eV, respectively. Earlier
comparable low-energy studies of La$_{1.4-x}$Nd$_{0.6}$Sr$_{x}$CuO$_4$ ($x =
0.10, 0.12, 0.15$) have shown strongly suppressed photoemission intensity, or
absence thereof, in large parts of the Brillouin zone. Contrary to these
findings we observe spectral weight at all points along the entire Fermi
surface contour at low and high photon energies. No signs of strong charge
modulations are found. At high photon energy, the Fermi surface shows obvious
differences in shape as compared to the low-energy results presented here and
in similar studies. The observed difference in shape and the high
bulk-sensitivity at this photon energy suggest intrinsic electronic structure
differences between the surface and bulk regions.


title: One-magnon (electromagnon) light scattering in BiFeO3 single crystals

abstract:
  We observed Raman scattering from magnon in frequency range from 10 to 65
cm-1 in BiFeO3 single crystals at cryogenic temperatures; the temperature
dependence of the magnon frequency at 18.2 cm-1 approximates an S=5/2 Brillouin
function up to the temperature (280 K) at which the magnon becomes overdamped.
The diverging cross-section and the frequency-shift at 140K and 200 K implies a
magnon-reorientation transition as in orthoferrites. Magnons in polar materials
such as BiFeO3 are often termed electromagnons meaning that they possess an
electric dipole moment due to magnetoelectric coupling.


title:
Magnetic Fields in Blazar Pc-scale Jets - Possible connection to Spin
  Rates of Black holes ?

abstract:
  We re-examine the differences observed in the pc-scale magnetic field
geometry of high and low optical polarization Quasars (HPQs, LPRQs) using the
MOJAVE sample. We find that, as previously reported, HPQ jets exhibit
predominantly transverse B fields while LPRQ jets tend to display longitudinal
B fields. We attempt to understand these results along with the different B
field geometry observed in the low and high energy peaked BL Lacs (LBLs, HBLs)
using a simple picture wherein the spinning central black holes in these AGNs
influence the speed and strength of the jet components (spine, sheath). Higher
spin rates in HPQs compared to LPRQs and LBLs compared to HBLs could explain
the different total radio powers, VLBI jet speeds, and the observed B field
geometry in these AGN classes.


title:
Applying Bayesian Neural Networks to Event Reconstruction in Reactor
  Neutrino Experiments

abstract:
  A toy detector has been designed to simulate central detectors in reactor
neutrino experiments in the paper. The electron samples from the Monte-Carlo
simulation of the toy detector have been reconstructed by the method of
Bayesian neural networks (BNN) and the standard algorithm, a maximum likelihood
method (MLD), respectively. The result of the event reconstruction using BNN
has been compared with the one using MLD. Compared to MLD, the uncertainties of
the electron vertex are not improved, but the energy resolutions are
significantly improved using BNN. And the improvement is more obvious for the
high energy electrons than the low energy ones.


title:
Casimir and Vacuum Energy of 5D Warped System and Sphere Lattice
  Regularization

abstract:
  We examine the Casimir energy of 5D electro-magnetism in the recent
standpoint. Z$_2$ symmetry is taken into account. After confirming the
consistency with the past result, we do new things based on a new
regularization. The regularization is based on the minimal area principle and
the regularized configuration is the {\it sphere lattice}. We do it not in the
Kaluza-Klein expanded form but in the closed form. The formalism is based on
the heat-kernel approach using the position/momentum propagator. A useful
expression of the Casimir energy, in terms of the P/M propagator, is obtained.
Renormalization flow is realized as the change along the extra-axis.


title: Torsional Weyl-Dirac Electrodinamics

abstract:
  Issuing from a geometry with nonmetricity and torsion we build up a classical
theory of gravitation and electromagnetism. The theory is coordinate covariant
as well Weyl-gauge covariant. Massless and massive photons, intrinsic electr.
and magn. currents exist in this framework. The field EQ-s and EQ-s of motion
are derived from a geometrically based action. It is shown that the magn.-magn.
interaction is transmitted by massive photons. A magn. charge (monopole) cannot
be located together with an electr. one. In absence of torsion and in the
Einstein gauge one obtains the Einstein-Maxwell theory.


title:
On two approaches to the building of local models for electron density
  based on Irkutsk digizond data

abstract:
  In the paper the step-by-step principles for making local model of electron
density are described. They are based on modulation principle - electron
density dependence on time is a product of a number of temporal variations
caused by solar radiation, magnetic activity, Earth orientation and unknown
additional periodical processes (not a sum, as they suppose sometimes when
making such models). A multiranges modulation principle is also suggested, that
allows automatically extend the set of parameters by using new ones, obtained
by filtration (or averaging) of basic set of parameters over the time. In the
paper we describe two approaches to the model creation - descriptional and
predictional ones.
  To test the approach three different models were created for daily electron
density logarithm using the described principles. We have used the data of
Irkutsk digisonde over the period 2003-2007 years for testing. It becomes clear
that a non-optimal choice of the number of model parameters could increase
prediction error, inspite the error over the set, used for analysis, will
decrease. It is shown that one year prediction has accuracy about 9-23%
depending on the height, and the highest error corresponds to the height about
200km. From the modelling we could also see that with increasing of the height
the number of parameters increases, and this could be caused by inaccuracy of
the model or by not taking additional physical mechanisms into consideration.

categories: physics.geo-ph physics.ao-ph physics.data-an physics.plasm-ph


title: Faster polynomial multiplication via multipoint Kronecker substitution

abstract:
  We give several new algorithms for dense polynomial multiplication based on
the Kronecker substitution method. For moderately sized input polynomials, the
new algorithms improve on the performance of the standard Kronecker
substitution by a sizeable constant, both in theory and in empirical tests.


title:
Asymptotic behavior of the conductance in disordered wires with
  perfectly conducting channels

abstract:
  We study the conductance of disordered wires with unitary symmetry focusing
on the case in which $m$ perfectly conducting channels are present due to the
channel-number imbalance between two-propagating directions. Using the exact
solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission
eigenvalues, we obtain the average and second moment of the conductance in the
long-wire regime. For comparison, we employ the three-edge Chalker-Coddington
model as the simplest example of channel-number-imbalanced systems with $m =
1$, and obtain the average and second moment of the conductance by using a
supersymmetry approach. We show that the result for the Chalker-Coddington
model is identical to that obtained from the DMPK equation.


title: Unstable periodic orbits in a chaotic meandering jet flow

abstract:
  We study the origin and bifurcations of typical classes of unstable periodic
orbits in a jet flow that was introduced before as a kinematic model of chaotic
advection, transport and mixing of passive scalars in meandering oceanic and
atmospheric currents. A method to detect and locate the unstable periodic
orbits and classify them by the origin and bifurcations is developed. We
consider in detail period-1 and period-4 orbits playing an important role in
chaotic advection. We introduce five classes of period-4 orbits: western and
eastern ballistic ones, whose origin is associated with ballistic resonances of
the fourth order, rotational ones, associated with rotational resonances of the
second and fourth orders, and rotational-ballistic ones associated with a
rotational-ballistic resonance. It is a new kind of nonlinear resonances that
may occur in chaotic flow with jets and/or circulation cells. Varying the
perturbation amplitude, we track out the origin and bifurcations of the orbits
for each class.


title: On one polynomial $p$-adic dynamical system

abstract:
  In the paper we describe basin of attraction and the Siegel discs of the
$p$-adic dynamical system $f(x)=x^{2n+1}+ax^{n+1}$ over complex $p$-adic field.


title:
Perceptron capacity revisited: classification ability for correlated
  patterns

abstract:
  In this paper, we address the problem of how many randomly labeled patterns
can be correctly classified by a single-layer perceptron when the patterns are
correlated with each other. In order to solve this problem, two analytical
schemes are developed based on the replica method and Thouless-Anderson-Palmer
(TAP) approach by utilizing an integral formula concerning random rectangular
matrices. The validity and relevance of the developed methodologies are shown
for one known result and two example problems. A message-passing algorithm to
perform the TAP scheme is also presented.


title:
Representations of $GL_2(\Fq)$ and $SL_2(\Fq)$, and some remarks about
  $GL_n(\Fq)$

abstract:
  The goal of these notes is to give a self-contained account of the
representation theory of $GL_2$ and $SL_2$ over a finite field, and to give
some indication of how the theory works for $GL_n$ over a finite field.


title: Closed String with Masses in Models of Baryons and Glueballs

abstract:
  The closed string carrying $n$ point-like masses is considered as the model
of a baryon ($n=3$), a glueball ($n=2$ or 3) or another exotic hadron. For this
system the rotational states are obtained and classified. They correspond to
exact solutions of dynamical equations, describing an uniform rotation of the
string with massive points. These rotational states result in a set of
quasilinear Regge trajectories with different behavior. The stability problem
for the so called central rotational states (with a mass at the rotational
center) is solved with using the analysis of small disturbances. These states
turned out to be unstable, if the central mass is less than some critical
value.


title:
Unitarity bounds in the Higgs model including triplet fields with
  custodial symmetry

abstract:
  We study bounds on Higgs boson masses from perturbative unitarity in the
Georgi-Machacek model, whose Higgs sector is composed of a scalar isospin
doublet, a real and a complex isospin triplet fields. This model can be
compatible with the electroweak precision data without fine tuning because of
the imposed global SU(2)_R symmetry in the Higgs potential, by which the
electroweak rho parameter is unity at the tree level. All possible two-body
elastic-scattering channels are taken into account to evaluate the S-wave
amplitude matrix, and then the condition of perturbative unitarity is imposed
on the eigenvalues to obtain constraint on the Higgs parameters. Masses of all
scalar bosons turn out to be bounded from above, some of which receive more
strict upper bounds as compared to that in the standard model (712 GeV). In
particular, the upper bound of the lightest scalar boson, whatever it would be,
is about 270 GeV.


title:
Iterative Solution for Generalized Sombrero-shaped Potential in
  $N$-dimensional Space

abstract:
  An explicit convergent iterative solution for the lowest energy state of the
Schroedinger equation with generalized $N$-dimensional Sombrero-shaped
potential is presented. The condition for the convergence of the iteration
procedure and the dependence of the shape of the groundstate wave function on
the parameters are discussed.


title: Induced Gravity in Deconstructed Space at Finite Temperature

abstract:
  We study self-consistent cosmological solutions for an Einstein universe in a
graph-based induced gravity model. Especially, we demonstrate specific results
for cycle graphs.


title:
Oscillatory instability in super-diffusive reaction -- diffusion
  systems: fractional amplitude and phase diffusion equations

abstract:
  Nonlinear evolution of a reaction--super-diffusion system near a Hopf
bifurcation is studied. Fractional analogues of complex Ginzburg-Landau
equation and Kuramoto-Sivashinsky equation are derived, and some of their
analytical and numerical solutions are studied.


title: On Compression of Cryptographic Keys

abstract:
  Any secured system can be modeled as a capability-based access control system
in which each user is given a set of secret keys of the resources he is granted
access to. In some large systems with resource-constrained devices, such as
sensor networks and RFID systems, the design is sensitive to memory or key
storage cost. With a goal to minimize the maximum users' key storage, key
compression based on key linking, that is, deriving one key from another
without compromising security, is studied. A lower bound on key storage needed
for a general access structure with key derivation is derived. This bound
demonstrates the theoretic limit of any systems which do not trade off security
and can be treated as a negative result to provide ground for designs with
security tradeoff. A concrete, provably secure key linking scheme based on
pseudorandom functions is given. Using the key linking framework, a number of
key pre-distribution schemes in the literature are analyzed.


title:
Weakly non-linear dynamics in reaction -- diffusion systems with
  L\'{e}vy flights

abstract:
  Reaction--diffusion equations with a fractional Laplacian are reduced near a
long wave Hopf bifurcation. The obtained amplitude equation is shown to be the
complex Ginzburg-Landau equation with a fractional Laplacian. Some of the
properties of the normal complex Ginzburg-Landau equation are generalised for
the fractional analogue. In particular, an analogue of Kuramoto-Sivashinsky
equation is derived.


title: On Distributed Computation in Noisy Random Planar Networks

abstract:
  We consider distributed computation of functions of distributed data in
random planar networks with noisy wireless links. We present a new algorithm
for computation of the maximum value which is order optimal in the number of
transmissions and computation time.We also adapt the histogram computation
algorithm of Ying et al to make the histogram computation time optimal.


title:
A class function on the mapping class group of an orientable surface and
  the Meyer cocycle

abstract:
  In this paper we define a $\mathbf{QP}^1$-valued class function on the
mapping class group $\mathcal{M}_{g,2}$ of a surface $\Sigma_{g,2}$ of genus
$g$ with two boundary components. Let $E$ be a $\Sigma_{g,2}$ bundle over a
pair of pants $P$. Gluing to $E$ the product of an annulus and $P$ along the
boundaries of each fiber, we obtain a closed surface bundle over $P$. We have
another closed surface bundle by gluing to $E$ the product of $P$ and two
disks.
  The sign of our class function cobounds the 2-cocycle on $\mathcal{M}_{g,2}$
defined by the difference of the signature of these two surface bundles over
$P$.


title: Algebraic tori - thirty years after

abstract:
  This is an expanded version of my talk given at the International Conference
``Algebra and Number Theory'' dedicated to the 80th anniversary of V. E.
Voskresenskii, which was held at the Samara State University in May 2007. The
goal is to give an overview of results of V. E. Voskresenskii on arithmetic and
birational properties of algebraic tori which culminated in his monograph
"Algebraic Tori" published in Russian 30 years ago. I shall try to put these
results and ideas into somehow broader context and also to give a brief digest
of the relevant activity related to the period after the English version of the
monograph "Algebraic Groups and Their Birational Invariants" appeared.


title: Production cross section of rotating string

abstract:
  We calculate production cross sections of a single rotating string from a
collision of two light states in bosonic string theory. We find that the cross
sections are written in terms of the modified Bessel function of the first kind
with the degree given by the angular momentum in the high energy regime. We
also obtain a similar formula from the partial wave expansion of four point
amplitudes. Asymptotic behavior of the cross sections is consistent with a well
known form factor of a string.


title:
Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm
  J$ model of spin glasses

abstract:
  We investigate the distribution of zeros of the partition function of the
two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex
field plane. We use the method to analytically implement the idea of numerical
transfer matrix which provides us with the exact expression of the partition
function as a polynomial of fugacity. The results show that zeros are
distributed in a wide region in the complex field plane. Nevertheless we
observe that zeros on the imaginary axis play dominant roles in the critical
behaviour since zeros on the imaginary axis are in closer proximity to the real
axis. We estimate the density of zeros on the imaginary axis by an
importance-sampling Monte Carlo algorithm, which enables us to sample very rare
events. Our result suggests that the density has an essential singularity at
the origin. This observation is consistent with the existence of Griffiths
singularities in the present systems. This is the first evidence for Griffiths
singularities in spin glass systems in equilibrium.


title:
Mass and angular-momentum inequalities for axi-symmetric initial data
  sets. II. Angular-momentum

abstract:
  We extend the validity of Dain's angular-momentum inequality to maximal,
asymptotically flat, initial data sets on a simply connected manifold with
several asymptotically flat ends which are invariant under a U(1) action and
which admit a twist potential.


title:
Nonrelativistic, Quasirelativistic and Relativistic Sets of Wave
  Functions, and Slater Orbitals of Particles with Arbitrary Spin

abstract:
  Using the complete orthonormal basis sets of nonrelativistic and
quasirelativistic orbitals introduced by the author in previous papers for
particles with arbitrary spin the new analytical relations for the -component
relativistic tensor wave functions and tensor Slater orbitals in coordinate,
momentum and four-dimensional spaces are derived, where. The relativistic
tensor function sets are expressed through the corresponding nonrelativistic
and quasirelativistic orbitals. The analytical formulas for overlap integrals
over relativistic tensor Slater orbitals with the same screening constants in
coordinate space are also derived.


title:
Non-minimal coupling for the gravitational and electromagnetic fields:
  black hole solutions and solitons

abstract:
  Using a Lagrangian formalism, a three-parameter non-minimal Einstein-Maxwell
theory is established. The three parameters, $q_1$, $q_2$ and $q_3$,
characterize the cross-terms in the Lagrangian, between the Maxwell field and
terms linear in the Ricci scalar, Ricci tensor, and Riemann tensor,
respectively. Static spherically symmetric equations are set up, and the three
parameters are interrelated and chosen so that effectively the system reduces
to a one parameter only, $q$. Specific black hole and other type of
one-parameter solutions are studied. First, as a preparation, the
Reissner-Nordstr\"om solution, with $q_1=q_2=q_3=0$, is displayed. Then, we
seek for solutions in which the electric field is regular everywhere as well as
asymptotically Coulombian, and the metric potentials are regular at the center
as well as asymptotically flat. In this context, the one-parameter model with
$q_1\equiv -q$, $q_2=2q$, $q_3=-q$, called the Gauss-Bonnet model, is analyzed
in detail. The study is done through the solution of the Abel equation (the key
equation), and the dynamical system associated with the model. There is extra
focus on an exact solution of the model and its critical properties. Finally,
an exactly integrable one-parameter model, with $q_1\equiv -q$, $q_2=q$,
$q_3=0$, is considered also in detail. A special sub-model, in which the
Fibonacci number appears naturally, of this one-parameter model is shown, and
the corresponding exact solution is presented. Interestingly enough, it is a
soliton of the theory, the Fibonacci soliton, without horizons and with a mild
conical singularity at the center.


title: Plasmonic nature of van der Waals forces between nanoparticles

abstract:
  We propose a new approach to calculate van der Waals forces between
nanoparticles where the van der Waals energy can be reduced to the energy of
elementary surface plasmon oscillations in nanoparticles. The general theory is
applied to describe the interaction between 2 metallic nanoparticles and
between a nanoparticle and a perfectly conducting plane. Our results could be
used to prove experimentally the existence of plasmonic molecules and to
elaborate new control mechanisms for the adherence of nanoparticles between
each other or onto surfaces.


title: Singularities of the Magnon Boundstate S-Matrix

abstract:
  We study the conjectured exact S-matrix for the scattering of BPS magnon
boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. The
conjectured S-matrix exhibits both simple and double poles at complex momenta.
Some of these poles lie parametrically close to the real axis in momentum space
on the branch where particle energies are positive. We show that all such poles
are precisely accounted for by physical processes involving one or more
on-shell intermediate particles belonging to the known BPS spectrum.


title: The Bogomolov multiplier of finite simple groups

abstract:
  The subgroup of the Schur multiplier of a finite group G consisting of all
cohomology classes whose restriction to any abelian subgroup of G is zero is
called the Bogomolov multiplier of G. We prove that if G is quasisimple or
almost simple, its Bogomolov multiplier is trivial.


title: On 5D Small Black Holes

abstract:
  Using higher order corrections we argue that five dimensional N=2 and N=4
small black holes exhibit supersymmetry enhancement in near horizon geometry
leading to eight and sixteen supercharges, respectively. Using this enhancement
at supergravity level we can identify the global supergroup of the near horizon
geometry. In particular we show how this supergroup distinguishes between small
and large black holes in N=2 case.


title: Order one invariants of planar curves

abstract: We give a complete description of all order 1 invariants of planar curves.


title: Physics with Beta-Beam

abstract:
  A Beta-beam would be a high intensity source of pure $\nu_e$ and/or
$\bar\nu_e$ flux with known spectrum, ideal for precision measurements. Myriad
of possible set-ups with suitable choices of baselines, detectors and the
beta-beam neutrino source with desired energies have been put forth in the
literature. In this talk we present a comparitive discussion of the physics
reach of a few such experimental set-ups.


title: Quantum Phases of Trapped Ions in an Optical Lattice

abstract:
  We propose loading trapped ions into microtraps formed by an optical lattice.
For harmonic microtraps, the Coulomb coupling of the spatial motions of
neighboring ions can be used to construct a broad class of effective
short-range Hamiltonians acting on an internal degree of freedom of the ions.
For large anharmonicities, on the other hand, the spatial motion of the ions
itself represents a spin-1/2 model with frustrated dipolar XY interactions. We
illustrate the latter setup with three systems: the linear chain, the zig-zag
ladder, and the triangular lattice. In the frustrated zig-zag ladder with
dipolar interactions we find chiral ordering beyond what was predicted
previously for a next-nearest-neighbor model. In the frustrated anisotropic
triangular lattice with nearest-neighbor interactions we find that the
transition from the one-dimensional gapless spin-liquid phase to the
two-dimensional spiraling ordered phase passes through a gapped spin-liquid
phase, similar to what has been predicted for the same model with Heisenberg
interactions. Further, a second gapped spin-liquid phase marks the transition
to the two-dimensional Neel-ordered phase.


title: Bursting oscillations induced by small noise

abstract:
  We consider a model of a square-wave bursting neuron residing in the regime
of tonic spiking. Upon introduction of small stochastic forcing, the model
generates irregular bursting. The statistical properties of the emergent
bursting patterns are studied in the present work. In particular, we identify
two principal statistical regimes associated with the noise-induced bursting.
In the first case, (type I) bursting oscillations are created mainly due to the
fluctuations in the fast subsystem. In the alternative scenario, type II
bursting, the random perturbations in the slow dynamics play a dominant role.
We propose two classes of randomly perturbed slow-fast systems that realize
type I and type II scenarios. For these models, we derive the Poincare maps.
The analysis of the linearized Poincare maps of the randomly perturbed systems
explains the distributions of the number of spikes within one burst and reveals
their dependence on the small and control parameters present in the models. The
mathematical analysis of the model problems is complemented by the numerical
experiments with a generic Hodgkin-Huxley type model of a bursting neuron.


title:
Polytope Representations for Linear-Programming Decoding of Non-Binary
  Linear Codes

abstract:
  In previous work, we demonstrated how decoding of a non-binary linear code
could be formulated as a linear-programming problem. In this paper, we study
different polytopes for use with linear-programming decoding, and show that for
many classes of codes these polytopes yield a complexity advantage for
decoding. These representations lead to polynomial-time decoders for a wide
variety of classical non-binary linear codes.


title: Bilinear virial identities and applications

abstract:
  We prove bilinear virial identities for the nonlinear Schrodinger equation,
which are extensions of the Morawetz interaction inequalities. We recover and
extend known bilinear improvements to Strichartz inequalities and provide
applications to various nonlinear problems, most notably on domains with
boundaries.


title: Threefold onset of vortex loops in superconductors with a magnetic core

abstract:
  A magnetic inclusion inside a superconductor gives rise to a fascinating
complex of {\it vortex loops}. Our calculations, done in the framework of the
Ginzburg-Landau theory, reveal that {\it loops always nucleate in triplets}
around the magnetic core. In a mesoscopic superconducting sphere, the final
superconducting state is characterized by those confined vortex loops and the
ones that eventually spring to the surface of the sphere, evolving into {\it
vortex pairs} piercing through the sample surface.


title:
Transverse magnetization and torque in asymmetrical mesoscopic
  superconductors

abstract:
  We show that asymmetrical mesoscopic superconductors bring new insight into
vortex physics where we found the remarkable coexistence of long and short
vortices. We study an asymmetrical mesoscopic sphere, that lacks one of its
quadrants, and obtain its three-dimensional vortex patterns by solving the
Ginzburg-Landau theory. We find that the vortex patterns are asymmetric whose
effects are clearly visible and detectable in the transverse magnetization and
torque.


title:
Effect of the boundary condition on the vortex patterns in mesoscopic
  three-dimensional superconductors - disk and sphere

abstract:
  The vortex state of mesoscopic three-dimensional superconductors is
determined using a minimization procedure of the Ginzburg-Landau free energy.
We obtain the vortex pattern for a mesoscopic superconducting sphere and find
that vortex lines are naturally bent and are closest to each other at the
equatorial plane. For a superconducting disk with finite height, and under an
applied magnetic field perpendicular to its major surface, we find that our
method gives results consistent with previous calculations. The matching
fields, the magnetization and $H_{c3}$, are obtained for models that differ
according to their boundary properties. A change of the Ginzburg-Landau
parameters near the surface can substantially enhance $H_{c3}$ as shown here.


title:
Hysteretic behavior in weakly coupled double-dot transport in the spin
  blockade regime

abstract:
  Double quantum dot systems in the spin blockade regime exhibit leakage
currents that have been attributed to the Hyperfine interaction. We model
weakly coupled double-dot transport using a rate equation approach which
accounts for Hyperfine flip-flop transitions. The rate equations allow us to
obtain self-consistently the time evolution for electronic charge occupations
and for the nuclei polarizations in each dot. We analyze the current in the
spin blockade region as a function of magnetic field and observe hysteretic
behavior for fields corresponding to the crossing between triplet and singlet
states.


title:
Isospin excitations of a trapped 1D gas of attractively interacting
  fermions

abstract:
  We consider a gas of fermions with a short-range attractive intercomponent
interaction in a parabolic external potential and derive the conditions of the
local density approximation. The obtained spectrum of quasiparticle (isospin)
excitations shows equidistant low-energy levels, which is equivalent to a
linear momentum dependence and is fundamentally different from the ordinary
Dirac spectrum in the spatially uniform case.


title:
From Equivalence Principles to Cosmology: Cosmic Polarization Rotation,
  CMB Observation, Neutrino Number Asymmetry, Lorentz Invariance and CPT

abstract:
  In this paper, we review the approach leading to cosmic polarization rotation
observation and present the current status with an outlook. In the study of the
relations among equivalence principles, we found that long-range
pseudoscalar-photon interaction is allowed. Pseudoscalar-photon interaction
would induce a rotation of linear polarization of electromagnetic wave
propagating with cosmological/astrophysical distance. In 2002, DASI
successfully observed the polarization of the cosmological microwave background
radiation. In 2003, WMAP observed the correlation of polarization with
temperature anisotropy at more than 10 sigma in the cosmological microwave
background. From this high polarization-temperature correlation in WMAP
observation, we put a limit of 0.1 rad on the rotation of linear polarization
of cosmological microwave background (CMB) propagation. Pseudoscalar-photon
interaction is proportional to the gradient of the pseudoscalar field. From
phenomenological point of view, this gradient could be neutrino number
asymmetry current, other density current, or a constant vector. In these
situations, Lorentz invariance or CPT may or may not effectively be violated.
In this paper, we review and compile various results. Better accuracy in CMB
polarization observation is expected from PLANCK mission to be launched next
year. A dedicated CMB polarization observer in the future would probe this
fundamental issue more deeply.