title: Three dimensional C-, S- and E-transforms

abstract:
  Three dimensional continuous and discrete Fourier-like transforms, based on
the three simple and four semisimple compact Lie groups of rank 3, are
presented. For each simple Lie group, there are three families of special
functions ($C$-, $S$-, and $E$-functions) on which the transforms are built.
Pertinent properties of the functions are described in detail, such as their
orthogonality within each family, when integrated over a finite region $F$ of
the 3-dimensional Euclidean space (continuous orthogonality), as well as when
summed up over a lattice grid $F_M\subset F$ (discrete orthogonality). The
positive integer $M$ sets up the density of the lattice containing $F_M$. The
expansion of functions given either on $F$ or on $F_M$ is the paper's main
focus.


title: Spectral Curves for Almost-Complex Tori in $ S ^6 $

abstract:
  To each non-isotropic almost-complex immersion of a 2-torus into $ S ^ 6 $ we
associate an algebraic curve, called the spectral curve, and a linear flow in
the intersection of two Prym varieties on this spectral curve. We show that
generically the spectral curve is smooth and compute the dimension of the
moduli space of such curves and of the torus in which the eigenline bundles
lie.


title: A Region Void of Irregular Satellites Around Jupiter

abstract:
  An interesting feature of the giant planets of our solar system is the
existence of regions around these objects where no irregular satellites are
observed. Surveys have shown that, around Jupiter, such a region extends from
the outermost regular satellite Callisto, to the vicinity of Themisto, the
innermost irregular satellite. To understand the reason for the existence of
such a satellite-void region, we have studied the dynamical evolution of Jovian
irregulars by numerically integrating the orbits of several hundred test
particles, distributed in a region between 30 and 80 Jupiter-radii, for
different values of their semimajor axes, orbital eccentricities, and
inclinations. As expected, our simulations indicate that objects in or close to
the influence zones of the Galilean satellites become unstable because of
interactions with Ganymede and Callisto. However, these perturbations cannot
account for the lack of irregular satellites in the entire region between
Callisto and Themisto. It is suggested that at distances between 60 and 80
Jupiter-radii, Ganymede and Callisto may have long-term perturbative effects,
which may require the integrations to be extended to times much longer than 10
Myr. The interactions of irregular satellites with protosatellites of Jupiter
at the time of the formation of Jovian regulars may also be a destabilizing
mechanism in this region. We present the results of our numerical simulations
and discuss their applicability to similar satellite void-regions around other
giant planets.


title:
Stochastic time-dependent current-density functional theory: a
  functional theory of open quantum systems

abstract:
  The dynamics of a many-body system coupled to an external environment
represents a fundamentally important problem. To this class of open quantum
systems pertains the study of energy transport and dissipation, dephasing,
quantum measurement and quantum information theory, phase transitions driven by
dissipative effects, etc. Here, we discuss in detail an extension of
time-dependent current-density-functional theory (TDCDFT), we named stochastic
TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description
of such problems from a microscopic point of view. We discuss the assumptions
of the theory, its relation to a density matrix formalism, and the limitations
of the latter in the present context. In addition, we describe a numerically
convenient way to solve the corresponding equations of motion, and apply this
theory to the dynamics of a 1D gas of excited bosons confined in a harmonic
potential and in contact with an external bath.


title: Coupling nanomechanical cantilevers to dipolar molecules

abstract:
  We investigate the coupling of a nanomechanical oscillator in the quantum
regime with molecular (electric) dipoles. We find theoretically that the
cantilever can produce single-mode squeezing of the center-of-mass motion of an
isolated trapped molecule and two-mode squeezing of the phonons of an array of
molecules. This work opens up the possibility of manipulating dipolar crystals,
which have been recently proposed as quantum memory, and more generally, is
indicative of the promise of nanoscale cantilevers for the quantum detection
and control of atomic and molecular systems.


title: Phase diagram for quantum Hall states in graphene

abstract:
  We investigate integer and half-integer filling states (uniform and
unidimensional stripe states respectively) for graphene using the Hartree-Fock
approximation. For fixed filling factor, the ratio between the scales of the
Coulomb interaction and Landau level spacing $g=(e^2/\epsilon \ell)/(\hbar
v_F/\ell)$, with $\ell$ the magnetic length, is a field-independent constant.
However, when $B$ decreases, the number of filled negative Landau levels
increases, which surprisingly turns out to decrease the amount of Landau level
mixing. The resulting states at fixed filling factor $\nu$ (for $\nu$ not too
big) have very little Landau level mixing even at arbitrarily weak magnetic
fields. Thus in the density-field phase diagram, many different phases may
persist down to the origin, in contrast to the more standard two dimensional
electron gas, in which the origin is surrounded by Wigner crystal states. We
demonstrate that the stripe amplitudes scale roughly as $B$, so that the
density waves ``evaporate'' continuously as $B\to 0$. Tight-binding
calculations give the same scaling for stripe amplitude and demonstrate that
the effect is not an artifact of the cutoff procedure used in the continuum
calculations.


title: A route to high temperature superconductivity in composite systems

abstract:
  Apparently, some form of local superconducting pairing persists to
temperatures well above the maximum observed $T_c$ in underdoped cuprates,
\textit{i.e.} $T_c$ is suppressed due to the small phase stiffness. With this
in mind, we consider the following question -- Given a system with a high
pairing scale $\Delta_0 $ but with $T_c$ reduced by phase fluctuations, can one
design a composite system in which $T_c$ approaches its mean-field value,
$T_c\to T_{MF}\approx \Delta_0/2\$? Here, we study a simple two component model
in which a "metallic layer" with $\Delta_0=0$ is coupled by single-particle
tunneling to a "pairing layer" with $\Delta_0 >0 $ but zero phase stiffness. We
show that in the limit that the bandwidth of the metal is much larger than
$\Delta_0$, $T_c$ of the composite system can reach the upper limit $T_c
\approx\Delta_0/2$.


title: Embedded Associated Primes of Powers of Square-free Monomial Ideals

abstract:
  An ideal I in a Noetherian ring R is normally torsion-free if
Ass(R/I^t)=Ass(R/I) for all natural numbers t. We develop a technique to
inductively study normally torsion-free square-free monomial ideals. In
particular, we show that if a square-free monomial ideal I is minimally not
normally torsion-free then the least power t such that I^t has embedded primes
is bigger than beta_1, where beta_1 is the monomial grade of I, which is equal
to the matching number of the hypergraph H(I) associated to I. If in addition I
fails to have the packing property, then embedded primes of I^t do occur when
t=beta_1 +1. As an application, we investigate how these results relate to a
conjecture of Conforti and Cornu\'ejols.


title:
Infrared Passbands for Precise Photometry of Variable Stars by Amateur
  and Professional Astronomers

abstract:
  The Infrared spectral region is a rich one for variable star work, especially
of cooler stars, but it has been hard to do IR photometry because of high,
variable background, and specialized telescopic equipment that is usually
required to obtain meaningful data. Typically telescopes with IR detectors have
been at high elevations, to minimize water vapor absorption. Nearly all the
filters produced for astronomical work at observatories around the world have
not been optimized for use at anything other than the highest and driest of
observatories. This has made it difficult for amateur astronomers to contribute
to this field. Now, however, this is no longer the case. The IAU's Infrared
Working Group (IRWG) has designed and tested a set of IR filters less sensitive
to water vapor, permitting observations at any site where precise optical
photometry can be carried out. Data acquired with these filters can be
corrected easily for atmospheric (water vapor) extinction, unlike the situation
with the older IR filters. We demonstrate this with data from the University of
Calgary's Rothney Astrophysical Observatory.


title:
Multiplicative functional for reflected Brownian motion via
  deterministic ODE

abstract:
  We prove that a sequence of semi-discrete approximations converges to a
multiplicative functional for reflected Brownian motion, which intuitively
represents the Lyapunov exponent for the corresponding stochastic flow. The
method of proof is based on a study of the deterministic version of the problem
and the excursion theory.


title: Solar convection and oscillations in magnetic regions

abstract:
  The goal of this research is to investigate how magnetic field affects the
dynamics of granular convection and excitation of solar oscillations by means
of realistic numerical simulations. We have used a 3D, compressible, non-linear
radiative magnetohydrodynamics code developed at the NASA Ames Research Center.
This code takes into account several physical phenomena: compressible fluid
flow in a highly stratified medium, sub-grid scale turbulence models, radiative
energy transfer between the fluid elements, and a real-gas equation of state.
We have studied the influence of the magnetic field of various strength on the
convective cells and on the excitation mechanisms of the acoustic oscillations
by calculating spectral properties of the convective motions and oscillations.
The results reveal substantial changes of the granulation structure with
increased magnetic field, and a frequency-dependent reduction in the
oscillation power in a good agreement with solar observations. These
simulations suggest that the enhanced high-frequency acoustic emission at the
boundaries of active region ("acoustic halo" phenomenon) is caused by the
changes of the spatial-temporal spectrum of the turbulent convection in
magnetic field, resulting in turbulent motions of smaller scales and higher
frequencies than in quiet Sun regions.


title: Algorithmic problems in twisted groups of Lie type

abstract:
  This thesis contains a collection of algorithms for working with the twisted
groups of Lie type known as Suzuki groups, and small and large Ree groups. The
two main problems under consideration are constructive recognition and
constructive membership testing. We also consider problems of generating and
conjugating Sylow and maximal subgroups. The algorithms are motivated by, and
form a part of, the Matrix Group Recognition Project. Obtaining both
theoretically and practically efficient algorithms has been a central goal. The
algorithms have been developed with, and implemented in, the computer algebra
system MAGMA.


title: Bijective Proofs of Identities from Colored Binary Trees

abstract:
  This note provide bijective proofs of two combinatorial identities involving
generalized Catalan number $C_{m,5}(n)={m\over 5n+m}{5n+m\choose n}$ recently
proposed by Sun.


title:
D-brane States and Annulus Amplitudes in OSp Invariant Closed String
  Field Theory

abstract:
  In the OSp invariant closed string field theory, we construct the states
corresponding to parallel D-branes that are located at different points in the
space-time. Using these states, we evaluate annulus amplitudes. We show that
the results coincide with those of first quantized string theory.


title: Enslaved Phase-Separation Fronts in One-Dimensional Binary Mixtures

abstract:
  Phase-separation fronts leave in their wakes morphologies that are
substantially different from the morphologies formed in homogeneous
phase-separation. In this paper we focus on fronts in binary mixtures that are
enslaved phase-separation fronts, i.e. fronts that follow in the wake of a
control-parameter front. In the one-dimensional case, which is the focus of
this paper, the formed morphology is deceptively simple: alternating domains of
a regular size. However, determining the size of these domains as a function of
the front speed and other system parameters is a non-trivial problem. We
present an analytical solution for the case where no material is deposited
ahead of the front and numerical solutions and scaling arguments for more
general cases. Through these enslaved phase-separation fronts large domains can
be formed that are practically unattainable in homogeneous one-dimensional
phase-separation.


title:
Pullback Attractors for the Non-autonomous FitzHugh-Nagumo System on
  Unbounded Domains

abstract:
  The existence of a pullback attractor is established for the singularly
perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ when
external terms are unbounded in a phase space. The pullback asymptotic
compactness of the system is proved by using uniform a priori estimates for
far-field values of solutions. Although the limiting system has no global
attractor, we show that the pullback attractors for the perturbed system with
bounded external terms are uniformly bounded, and hence do not blow up as a
small parameter approaches zero.


title: Constructing Folksonomies from User-specified Relations on Flickr

abstract:
  Many social Web sites allow users to publish content and annotate with
descriptive metadata. In addition to flat tags, some social Web sites have
recently began to allow users to organize their content and metadata
hierarchically. The social photosharing site Flickr, for example, allows users
to group related photos in sets, and related sets in collections. The social
bookmarking site Del.icio.us similarly lets users group related tags into
bundles. Although the sites themselves don't impose any constraints on how
these hierarchies are used, individuals generally use them to capture
relationships between concepts, most commonly the broader/narrower relations.
Collective annotation of content with hierarchical relations may lead to an
emergent classification system, called a folksonomy. While some researchers
have explored using tags as evidence for learning folksonomies, we believe that
hierarchical relations described above offer a high-quality source of evidence
for this task.
  We propose a simple approach to aggregate shallow hierarchies created by many
distinct Flickr users into a common folksonomy. Our approach uses statistics to
determine if a particular relation should be retained or discarded. The
relations are then woven together into larger hierarchies. Although we have not
carried out a detailed quantitative evaluation of the approach, it looks very
promising since it generates very reasonable, non-trivial hierarchies.


title: Role of charge carriers for ferromagnetism in cobalt-doped rutile TiO2

abstract:
  Electric and magnetic properties of a high temperature ferromagnetic oxide
semiconductor, cobalt-doped rutile TiO2, are summarized. The cobalt-doped
rutile TiO2 epitaxial thin films with different electron densities and cobalt
contents were grown on r-sapphire substrates with laser molecular beam epitaxy.
Results of magnetization, magnetic circular dichroism, and anomalous Hall
effect measurements were examined for samples with systematically varied
electron densities and cobalt contents. The samples with high electron
densities and cobalt contents show the high temperature ferromagnetism,
suggesting that charge carriers induce the ferromagnetism.


title: Unique Phase Transition on Spin-2 Triangular Lattice of Ag2MnO2

abstract:
  Ag2MnO2 is studied as a possible candidate compound for an antiferromagnetic
XY spin model on a triangular lattice. In spite of the large Curie-Weiss
temperature of -430 K found in magnetic susceptibi-lity, Mn3+ spins with S = 2
do not undergo a conventional long-range order down to 2 K probably owing to
the geometrical frustration and two dimensionality in the system. Instead, a
unique phase transition is found at 80 K, where specific heat exhibits a clear
sign of a second-order phase transition, while magnetic susceptibility changes
smoothly without a distinct anomaly. We think that this transition is related
to the chirality degree of freedom associated with a short-range order, which
has been expected for the classical XY spin model on a triangular lattice. On
further cooling, spin-glass-like behavior is observed below 22 K, possibly
corresponding to a quasi-long-range order.


title: Direct Detection of Gravity Waves from Neutron Stars

abstract:
  In light of the discovery of the first-ever double pulsar system, PSR
J0737-3039, we re-examine an earlier proposal to directly detect gravity waves
from neutron stars, which was predicated on a hypothetical system almost
identical to the later discovered double pulsar. We re-derive the effect in
more detail, and confirm the initial estimate--sometimes doubted in the
literature--that it includes a 1/b dependence, where b is the impact parameter
of a pulsar with respect to its foreground, gravity-wave emitting, neutron star
companion. A coherent modulation in pulsar time-of-arrival measurements of 10
nano-sec/sec is possible. A one-year intermittent experiment on an instrument
comparable to the SKA could thus detect the exceedingly faint gravity waves
from individual neutron stars.


title: Constructing mean curvature 1 surfaces in $H^3$ with irregular ends

abstract:
  With the developments of the last decade on complete constant mean curvature
1 (CMC 1) surfaces in the hyperbolic 3-space $H^3$, many examples of such
surfaces are now known. However, most of the known examples have regular ends.
(An end is irregular, resp. regular, if the hyperbolic Gauss map of the surface
has an essential singularity, resp. at most a pole, there.) There are some
known surfaces with irregular ends, but they are all either reducible or of
infinite total curvature. (The surface is reducible if and only if the
monodromy of the secondary Gauss map can be simultaneously diagonalized.) Up to
now there have been no known complete irreducible CMC 1 surfaces in $H^3$ with
finite total curvature and irregular ends. The purpose of this paper is to
construct countably many 1-parameter families of genus zero CMC 1 surfaces with
irregular ends and finite total curvature, which have either dihedral or
Platonic symmetries. For all the examples we produce, we show that they have
finite total curvature and irregular ends. For the examples with dihedral
symmetry and the simplest example with tetrahedral symmetry, we show
irreducibility. Moreover, we construct a genus one CMC 1 surface with four
irregular ends, which is the first known example with positive genus whose ends
are all irregular.


title: Influence of light nuclei on neutrino-driven supernova outflows

abstract:
  We study the composition of the outer layers of a protoneutron star and show
that light nuclei are present in substantial amounts. The composition is
dominated by nucleons, deuterons, tritons and alpha particles; 3He is present
in smaller amounts. This composition can be studied in laboratory experiments
with new neutron-rich radioactive beams that can reproduce similar densities
and temperatures. After including the corresponding neutrino interactions, we
demonstrate that light nuclei have a small impact on the average energy of the
emitted electron neutrinos, but are significant for the average energy of
antineutrinos. During the early post-explosion phase, the average energy of
electron antineutrinos is slightly increased, while at later times during the
protoneutron star cooling it is reduced by about 1 MeV. The consequences of
these changes for nucleosynthesis in neutrino-driven supernova outflows are
discussed.


title: Birational geometry and localisation of categories

abstract:
  This version corrects a wrong proof of Proposition 6.3.2 and simplifies the
exposition in Section 6.


title: On q-deformed gl(l+1)-Whittaker function III

abstract:
  We identify q-deformed gl(l+1)-Whittaker functions with a specialization of
Macdonald polynomials. This provides a representation of q-deformed
gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie
algebra \hat{gl(l+1)}. We also define a system of dual Hamiltonians for
q-deformed gl(l+1)-Toda chains and give a new integral representation for
q-deformed gl(l+1)-Whittaker functions. Finally an expression of q-deformed
gl(l+1)-Whittaker function as a matrix element of a quantum torus algebra is
derived.


title: Normal forms and uniform approximations for bridge orbit bifurcations

abstract:
  We discuss various bifurcation problems in which two isolated periodic orbits
exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We
propose normal forms which locally describe the corresponding fixed point
scenarios on the Poincar\'e surface of section. Uniform approximations for the
density of states for an integrable Hamiltonian system with two degrees of
freedom are derived and successfully reproduce the numerical quantum-mechanical
results.


title: Killing-Yano tensors and multi-hermitian structures

abstract:
  We show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally
admits $2^m$ hermitian complex structures. These are derived from the existence
of a non-degenerate closed conformal Killing-Yano tensor with distinct
eigenvalues. More generally, a conformal Killing-Yano tensor, provided its
exterior derivative satisfies a certain condition, algebraically determines
$2^m$ almost complex structures that turn out to be integrable as a consequence
of the conformal Killing-Yano equations. In the complexification, these lead to
$2^m$ maximal isotropic foliations of the manifold and, in Lorentz signature,
these lead to two congruences of null geodesics. These are not shear-free, but
satisfy a weaker condition that also generalizes the shear-free condition from
4-dimensions to higher-dimensions. In odd dimensions, a conformal Killing-Yano
tensor leads to similar integrable distributions in the complexification. We
show that the recently discovered 5-dimensional solution of Lu, Mei and Pope
also admits such integrable distributions, although this does not quite fit
into the story as the obvious associated two-form is not conformal
Killing-Yano. We give conditions on the Weyl curvature tensor imposed by the
existence of a non-degenerate conformal Killing-Yano tensor; these give an
appropriate generalization of the type D condition on a Weyl tensor from four
dimensions.


title:
Drug absorption through a cell monolayer: a theoretical work on a
  non-linear three-compartment model

abstract:
  The subject of analysis is a non-linear three-compartment model, widely used
in pharmacological absorption studies. It has been transformed into a general
form, thus leading automatically to an appropriate approximation. This made the
absorption profile accessible and expressions for absorption times, apparent
permeabilities and equilibrium values were given. These findings allowed a
profound analysis of results from non-linear curve fits and delivered the
dependencies on the systems' parameters over a wide range of values. The
results were applied to an absorption experiment with multidrug
transporter-affected antibiotic CNV97100 on Caco-2 cell monolayers.


title: Contractions of low-dimensional nilpotent Jordan algebras

abstract:
  In this paper we classify the laws of three-dimensional and four-dimensional
nilpotent Jordan algebras over the field of complex numbers. We describe the
irreducible components of their algebraic varieties and extend contractions and
deformations among them. In particular, we prove that J2 and J3 are irreducible
and that J4 is the union of the Zariski closures of two rigid Jordan algebras.


title:
The Solvability and Subellipticity of Systems of Pseudodifferential
  Operators

abstract:
  The paper studies the local solvability and subellipticity for square systems
of principal type. These are the systems for which the principal symbol
vanishes of first order on its kernel. For systems of principal type having
constant characteristics, local solvability is equivalent to condition (PSI) on
the eigenvalues, see arXiv:0801.4043. This is a condition on the sign changes
of the imaginary part of the eigenvalue along the oriented bicharacteristics of
the real part.
  In the generic case when the principal symbol does not have constant
characteristics, condition (PSI) is not sufficient, not invariant and in
general not well defined. Instead we study systems which are
quasi-symmetrizable, these systems have natural invariance properties and are
of principal type. We prove that quasi-symmetrizable systems are locally
solvable. We also study the subellipticity of quasi-symmetrizable systems in
the case when principal symbol vanishes of finite order along the
bicharacteristics. In order to prove subellipticity, we assume that the
principal symbol has the approximation property, which implies that there are
no transversal bicharacteristics.


title:
Translational affine coherent states as exact solutions of the
  Wheeler-DeWitt equation

abstract:
  The Quantum Wheeler-DeWitt operator can be derived from an affine commutation
relation via the affine group representation formalism for gravity, wherein a
family of gauge-diffeomorphism invariant affine coherent states are constructed
from a fiducial state. In this article, the role of the fiducial state is
played by a regularized Gaussian peaked on densitized triad configurations
corresponding to 3-metrics of constant spatial scalar curvature. The affine
group manifold consists of points in the upper half plane, wherein each point
is labeled by two local gravitational degrees of freedom from the Yamabe
construction. From this viewpoint, here we show that the translational subgroup
of affine coherent states constitute a set of exact solutions of the
Wheeler-DeWitt equation. The affine translational parameter $b$ admits a
physical interpretation analogous to a continuous plane wave energy spectrum,
where the curvature constant $k$ plays the role of the energy. This result
shows that the affine translational subgroup generates transformations in the
curvature constant $k$ from the Yamabe problem, while $k$ is inert under the
kinematic symmetries of gravity.


title:
Period problems for mean curvature one surfaces in $H^3$ (with
  application to surfaces of low total curvature)

abstract:
  We review recent results on classifying complete constant mean curvature 1
(CMC 1) surfaces in hyperbolic 3-space with low total curvature. There are two
natural notions of "total curvature" -- one is the total absolute curvature,
which is the integral over the surface of the absolute value of the Gaussian
curvature, and the other is the dual total absolute curvature, which is the
total absolute curvature of the dual CMC 1 surface. Here we discuss results on
both notions (proven in two other papers by the authors), and we introduce new
results as well.


title: Further Development of the Tetron Model

abstract:
  After a prologue which clarifies some issues left open in my last paper, the
main features of the tetron model of elementary particles are discussed in the
light of recent developments, in particular the formation of strong and
electroweak vector bosons and a microscopic understanding of how the observed
tetrahedral symmetry of the fermion spectrum may arise.


title:
Z and W production associated with quark-antiquark pair in
  k_T-factorization at the LHC

abstract:
  We calculate and analyze Z and W production in association with
quark-antiquark pair in k_T-factorization. Numerical calculations are performed
using the Monte Carlo generator CASCADE for proton proton collisions at LHC
energy. We compare total and differential cross sections calculated in
k_T-factorization approach with total differential cross sections obtained in
LO and NLO calculations in collinear factorization approach. We provide strong
evidence that some of the effects of the NLO and even higher order collinear
calculation are already included in the LO k_T-factorization calculation.


title:
Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic
  Oscillator Under Time Quasi- Periodic Perturbations

abstract:
  We prove that the $1-d$ quantum harmonic oscillator is stable under spatially
localized, time quasi-periodic perturbations on a set of Diophantine
frequencies of positive measure. This proves a conjecture raised by
Enss-Veselic in their 1983 paper \cite{EV} in the general quasi-periodic
setting. The motivation of the present paper also comes from construction of
quasi-periodic solutions for the corresponding nonlinear equation.


title:
Some linear and nonlinear integral inequalities on time scales in two
  independent variables

abstract:
  We establish some linear and nonlinear integral inequalities of
Gronwall-Bellman-Bihari type for functions with two independent variables on
general time scales. The results are illustrated with examples, obtained by
fixing the time scales to concrete ones. An estimation result for the solution
of a partial delta dynamic equation is given as an application.


title: On the Fundamental Plane of the Galactic Globular Cluster System

abstract:
  The globular clusters (GC) of our Galaxy have been found to lie close to a
plane in the log(R_e), log(sigma), SB_e space, on the continuation of the
Fundamental Plane (FP) known to characterize the properties of early-type
galaxies. We reexamine the issue on a sample of 48 GCs selected in terms of
homogeneity criteria for the photometric data available from the literature and
perform a model-independent analysis of surface brightness profiles (SBP) and
distance moduli, estimating error bars and studying selection effects with
non-parametric statistical tests. We determine the coefficients of the FP and
their error bars. The scatter from the FP relation is likely to be intrinsic,
i.e. not due to measurement errors only. We find that in the standard FP
coordinates our sample occupies a slim, axisymmetric region of parameter space,
suggesting that the scaling relation might be around a Fundamental Line, rather
than a plane, confirming a result noted earlier. This is likely to be the
origin of the difficulties in the fit by a plane mentioned in previous
investigations. Such FL relation would imply a pure photometric scaling law,
which might be tested on wider samples and on extra-galactic GC systems. We
find a correlation of the residuals from the FP relation with the central slope
of the SBP. No other correlations are found. Finally, we reconstruct the
distribution of the values of the quantity log(K_V/(M/L)) (virial coefficient
divided by the mass-to-light ratio) through kernel density estimation and find
evidence for bimodality, which suggests that the galactic GC system may be
composed of at least two dynamically different populations. Yet, these
populations do not reflect the standard dichotomy between disk and halo
clusters. (abridged).


title:
Bounded Sobolev Norms for Linear Schr\"odinger Equations Under Resonant
  Perturbations

abstract:
  We prove that the Sobolev norm for a 1-D periodic Schroedinger equation
remain bounded under small resonant perturbations.


title:
Theoretical study of phonon-assisted singlet-singlet relaxation in
  two-electron semiconductor quantum dot molecules

abstract:
  Phonon-assisted singlet-singlet relaxation in semiconductor quantum dot
molecules is studied theoretically. Laterally coupled quantum dot structures
doped with two electrons are considered. We take into account interaction with
acoustic phonon modes via deformation potential and piezoelectric coupling. We
show that piezoelectric mechanism for the considered system is of great
importance and for some ranges of quantum dot molecule parameters is the
dominant contribution to relaxation. It is shown that the phonon-assisted
tunneling rates reach much higher values (up to 160 ns$^{-1}$ even at zero
temperature) in comparison with other decoherence processes like spin-orbit
coupling ($\sim$ 0.01 ns$^{-1}$). The influence of Coulomb interaction is
discussed and its consequences are indicated. We calculate the relaxation rates
for GaAs quantum dot molecules and study the dependence on quantum dot size,
distance and offset between the constituent quantum dots. In addition the
temperature dependence of the tunneling rates is analyzed.


title:
Superdiffusion in a class of networks with marginal long-range
  connections

abstract:
  A class of cubic networks composed of a regular one-dimensional lattice and a
set of long-range links is introduced. Networks parametrized by a positive
integer k are constructed by starting from a one-dimensional lattice and
iteratively connecting each site of degree 2 with a $k$th neighboring site of
degree 2. Specifying the way pairs of sites to be connected are selected,
various random and regular networks are defined, all of which have a power-law
edge-length distribution of the form $P_>(l)\sim l^{-s}$ with the marginal
exponent s=1. In all these networks, lengths of shortest paths grow as a power
of the distance and random walk is super-diffusive. Applying a renormalization
group method, the corresponding shortest-path dimensions and random-walk
dimensions are calculated exactly for k=1 networks and for k=2 regular
networks; in other cases, they are estimated by numerical methods. Although,
s=1 holds for all representatives of this class, the above quantities are found
to depend on the details of the structure of networks controlled by k and other
parameters.


title: Quantum work relations and response theory

abstract:
  A universal quantum work relation is proved for isolated time-dependent
Hamiltonian systems in a magnetic field as the consequence of
microreversibility. This relation involves a functional of an arbitrary
observable. The quantum Jarzynski equality is recovered in the case this
observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity
relations are deduced thereof in the linear response regime.


title:
Logarithmic bounds on Sobolev norms for time-dependent linear
  Schr\"odinger equations

abstract:
  We prove that in 1-D the growth of Sobolev norms for time-dependent linear
Schr\"odinger equations is at most logarithmic in time for any (fixed)
potential which is analytic (or Gevrey). Recently it was proven in [N] that
almost surely the Sobolev norms are unbounded, which indicates that the log is
almost surely necessary. In [W], the author showed that the Sobolev norms
remain bounded for an explicit time periodic potential. This is in the
exceptional set in the sense of [N]. The present paper together with [N, W]
give a rather complete picture of time dependent linear Schr\"odinger equations
on the circle.


title: An Intrinsic Impulse Observability Criterion for Descriptor System

abstract:
  Analyzing the order of unobservable impulse in descriptor system leads to a
new testing criterion for impulse observability, both the statement and the
proof of which use only the original system data.


title: High-Statistics Study of the tau^- -> pi^- pi^0 nu_tau Decay

abstract:
  We report a high-statistics measurement of the branching fraction for tau^-
--> pi^- pi^0 nu_tau and the invariant mass spectrum of the produced pi^- pi^0
system using 72.2 fb^-1 of data recorded with the Belle detector at the KEKB
asymmetric-energy e^+ e^- collider. The branching fraction obtained is (25.24
+/- 0.01 +/- 0.39)%, where the first error is statistical and the second is
systematic. The unfolded pi^- pi^0 mass spectrum is used to determine resonance
parameters for the rho(770), rho'(1450), and rho"(1700) mesons. We also use
this spectrum to estimate the hadronic (2pi) contribution to the anomalous
magnetic moment of the muon (a_{mu}^{pipi}). Our result for a_{mu}^{pipi}
integrated over the mass range sqrt{s} = 2m_{pi} - 1.8 GeV/c^2 is a_{mu}^{pipi}
= (523.5 +/- 1.5 (exp) +/- 2.6 (Br) +/- 2.5 (isospin))x 10^{-10}, where the
first error is due to the experimental uncertainties, the second is due to the
uncertainties in the branching fractions and the third is due to the
uncertainties in the isospin-violating corrections.


title: Consistent holographic description of boost-invariant plasma

abstract:
  Prior attempts to construct the gravity dual of boost-invariant flow of N=4
supersymmetric Yang-Mills gauge theory plasma suffered from apparent curvature
singularities in the late time expansion. This Letter shows how these problems
can be resolved by a different choice of expansion parameter. The calculations
presented correctly reproduce the plasma energy-momentum tensor within the
framework of second order viscous hydrodynamics.


title: Effect of Transparency on the D-wave Josephson Junction

abstract:
  In this paper, a dc Josephson junction between two singlet superconductors
(d-wave and s-wave) with arbitrary reflection coefficient has been investigated
theoretically following the famous paper [ Y. Tanaka and S. Kashiwaya 1996
\textit{Phys. Rev. B} {\bf 53}, R11957]. For the case of High $T_c$
superconductors, the $c$-axes are parallel to an interface with finite
transparency and their $ab$-planes have a mis-orientation. The effect of
transparency and mis-orientation on the currents is studied both analytically
and numerically. It is observed that, the current phase relations are totally
different from the case of ideal transparent Josephson junctions between d-wave
superconductors and two s-wave superconductors. This apparatus can be used to
demonstrate d-wave order parameter in High $T_c$ superconductors.


title:
Measurement of the Casimir force between a gold sphere and silicon
  surface with nanoscale trench arrays

abstract:
  We report measurements of the Casimir force between a gold sphere and a
silicon surface with an array of nanoscale, rectangular corrugations using a
micromechanical torsional oscillator. At distance between 150 nm and 500 nm,
the measured force shows significant deviations from the pairwise additive
formulism, demonstrating the strong dependence of the Casimir force on the
shape of the interacting bodies. The observed deviation, however, is smaller
than the calculated values for perfectly conducting surfaces, possibly due to
the interplay between finite conductivity and geometry effects.


title: On the generic and typical ranks of 3-tensors

abstract:
  We study the generic and typical ranks of 3-tensors of dimension l x m x n
using results from matrices and algebraic geometry. We state a conjecture about
the exact values of the generic rank of 3-tensors over the complex numbers,
which is verified numerically for l,m,n not greater than 14. We also discuss
the typical ranks over the real numbers, and give an example of an infinite
family of 3-tensors of the form l=m, n=(m-1)^2+1, m=3,4,..., which have at
least two typical ranks.


title:
Local Order and the gapped phase of the Hubbard model: a plaquette
  dynamical mean field investigation

abstract:
  The four-site DCA method of including intersite correlations in the dynamical
mean field theory is used to investigate the metal-insulator transition in the
Hubbard model. At half filling a gap-opening transition is found to occur as
the interaction strength is increased beyond a critical value. The gapped
behavior found in the 4-site DCA approximation is shown to be associated with
the onset of strong antiferromagnetic and singlet correlations and the
transition is found to be potential energy driven. It is thus more accurately
described as a Slater phenomenon (induced by strong short ranged order) than as
a Mott phenomenon. Doping the gapped phase leads to a non-Fermi-liquid state
with a Fermi surface only in the nodal regions and a pseudogap in the antinodal
regions at lower dopings $x \lesssim 0.15$ and to a Fermi liquid phase at
higher dopings.


title:
Muon Spin Rotation Measurements of Heterogeneous Field Response in
  Overdoped La2-xSrxCuO4

abstract:
  Transverse-field muon spin rotation measurements of overdoped La2-xSrxCuO4
reveal a large broadening of the local magnetic field distribution in response
to applied field, persisting to high temperatures. The field-response is
approximately Curie-Weiss like in temperature and is largest for the highest
doping investigated. Such behaviour is contrary to the canonical Fermi-liquid
picture commonly associated with the overdoped cuprates and implies extensive
heterogeneity in this region of the phase diagram. A possible explanation for
the result lies in regions of staggered magnetization about dopant cations,
analogous to what is argued to exist in underdoped systems.


title:
Tuning the effective fine structure constant in graphene: opposing
  effects of dielectric screening on short- and long-range potential scattering

abstract:
  We reduce the dimensionless interaction strength in graphene by adding a
water overlayer in ultra-high vacuum, thereby increasing dielectric screening.
The mobility limited by long-range impurity scattering is increased over 30
percent, due to the background dielectric constant enhancement leading to
reduced interaction of electrons with charged impurities. However, the
carrier-density-independent conductivity due to short range impurities is
decreased by almost 40 percent, due to reduced screening of the impurity
potential by conduction electrons. The minimum conductivity is nearly
unchanged, due to canceling contributions from the electron/hole puddle density
and long-range impurity mobility. Experimental data are compared with
theoretical predictions with excellent agreement.


title: A Tree Theorem for Inflation

abstract:
  It is shown that the generating function for tree graphs in the "in-in"
formalism may be calculated by solving the classical equations of motion
subject to certain constraints. This theorem is illustrated by application to
the evolution of a single inflaton field in a Robertson--Walker background.


title: Scalar Field as Dark Energy Accelerating Expansion of the Universe

abstract:
  The features of a homogeneous scalar field $\phi$ with classical Lagrangian
$L=\phi_{;i}\phi^{;i}/2-V(\phi)$ and tachyon field Lagrangian
$L=-V(\phi)\sqrt{1-\phi_{;i}\phi^{;i}}$ causing the observable accelerated
expansion of the Universe are analyzed. The models with constant
equation-of-state parameter $w_{de}=p_{de}/\rho_{de}<-1/3$ are studied. For
both cases the fields $\phi(a)$ and potentials $V(a)$ are reconstucted for the
parameters of cosmological model of the Universe derived from the observations.
The effect of rolling down of the potential $V(\phi)$ to minimum is shown.


title: Exciting Hard Spheres

abstract:
  We investigate the collision cascade that is generated by a single moving
incident particle on a static hard-sphere gas. We argue that the number of
moving particles at time t grows as t^{xi} and the number collisions up to time
t grows as t^{eta}, with xi=2d/(d+2) and eta=2(d+1)/(d+2) and d the spatial
dimension. These growth laws are the same as those from a hydrodynamic theory
for the shock wave emanating from an explosion. Our predictions are verified by
molecular dynamics simulations in d=1 and 2. For a particle incident on a
static gas in a half-space, the resulting backsplatter ultimately contains
almost all the initial energy.


title: Diffusion and spatial correlations in suspensions of swimming particles

abstract:
  Populations of swimming microorganisms produce fluid motions that lead to
dramatically enhanced diffusion of tracer particles. Using simulations of
suspensions of swimming particles in a periodic domain, we capture this effect
and show that it depends qualitatively on the mode of swimming: swimmers
``pushed'' from behind by their flagella show greater enhancement than swimmers
that are ``pulled'' from the front. The difference is manifested by an
increase, that only occurs for pushers, of the diffusivity of passive tracers
and the velocity correlation length with the size of the periodic domain. A
physical argument supported by a mean field theory sheds light on the origin of
these effects.


title: Entanglement in Weisskopf-Wigner theory of atomic decay in free space

abstract:
  In this paper, we use the Weisskopf-Wigner theory to study the entanglement
in the state of the free-space radiation field produced from vacuum due to
atomic decay. We show how bipartite entanglement is shared between different
partitions of the radiation modes. We investigate the role played by the size
of the partitions and their detuning with the decaying atom. The dynamics of
the atom-field entanglement during the atomic decay is also briefly discussed.
  From this dynamics, we assert that such entanglement is the physical quantity
that fix the statistical atomic decay time.


title: Fermionization and bosonization of expanding 1D anyonic fluids

abstract:
  The momentum distribution of an expanding cloud of one-dimensional hard-core
anyons is studied by an exact numerical approach, and shown to become
indistinguishable from that of a non-interacting spin-polarized Fermi gas for
large enough times (dynamical fermionization). We also consider the expansion
of one-dimensional anyons with strongly attractive short-range interactions
suddenly released from a parabolic external potential, and find that momentum
distribution approaches that of its dual system, the ideal Bose gas (dynamical
bosonization). For both processes the characteristic time scales are
identified, and the effect of the initial confinement is analyzed comparing the
dynamics associated with both harmonic and hard-wall traps.


title: Maximal solutions of equation u = uq in arbitrary domains

abstract:
  We prove bilateral capacitary estimates for the maximal solution $U_F$ of
$-\Delta u+u^q=0$ in the complement of an arbitrary closed set $F\subset\mathbb
R^N$, involving the Bessel capacity $C_{2,q'}$, for $q$ in the supercritical
range $q\geq q_{c}:=N/(N-2)$. We derive a pointwise necessary and sufficient
condition, via a Wiener type criterion, in order that $U_F(x)\to\infty$ as
$x\to y$ for given $y\in\prt F$. Finally we prove a general uniqueness result
for large solutions.


title: Semigroups of valuations on local rings, II

abstract:
  Given a noetherian local domain $R$ and a valuation $\nu$ of its field of
fractions which is non negative on $R$, we derive some very general bounds on
the growth of the number of distinct valuation ideals of $R$ corresponding to
values lying in certain parts of the value group $\Gamma$ of $\nu$. We show
that this growth condition imposes restrictions on the semigroups
$\nu(R\setminus \{0\})$ for noetherian $R$ which are stronger that those
resulting from the previous paper \cite{C2} of the first author. Given an
ordered embedding $\Gamma\subset ({\mathbf R}^h)_{\hbox{\rm lex}}$, where $h$
is the rank of $\nu$, we also study the shape in ${\mathbf R}^h$ of the parts
of $\Gamma$ which appear naturally in this study. We give examples which show
that this shape can be quite wild in a way which does not depend on the
embedding and suggest that it is a good indicator of the complexity of the
semigroup $\nu(R\setminus \{0\})$.


title:
The balance between diffusion and absorption in semilinear parabolic
  equations

abstract:
  Let $h:[0,\infty)\mapsto [0,\infty)$ be continuous and nondecreasing,
$h(t)>0$ if $t>0$, and $m,q$ be positive real numbers. We investigate the
behavior when $k\to\infty$ of the fundamental solutions $u=u_{k}$ of $\prt_{t}
u-\Delta u^m+h(t)u^q=0$ in $\Omega\ti (0,T)$ satisfying $u_{k}(x,0)=k\delta_0$.
The main question is wether the limit is still a solution of the above equation
with an isolated singularity at $(0,0)$, or a solution of the associated
ordinary differential equation $ u'+h(t)u^q=0$ which blows-up at $t=0$.


title:
The precise boundary trace of solutions of a class of supercritical
  nonlinear equations

abstract:
  We construct and study the properties of the precise boundary trace of
positive solutions of $-\Delta u+u^q=0$ in a smooth bounded domain of $\mathbb
R^N$, in the supercritical case $q\geq q_c=(N+1)/(N-1)$


title: Isonemal Prefabrics with Perpendicular Axes of Symmetry

abstract:
  This paper continues the refinement of Richard Roth's taxonomy of isonemal
weaving designs through types 11--32 of the 39 in order to solve three problems
for those designs: which designs exist in various sizes, which prefabrics can
be doubled and remain isonemal, and which can be halved and remain isonemal.


title: On the nontrivial projection problem

abstract:
  The Nontrivial Projection Problem asks whether every finite-dimensional
normed space of dimension greater than one admits a well-bounded projection of
non-trivial rank and corank or, equivalently, whether every centrally symmetric
convex body (of arbitrary dimension greater than one) is approximately affinely
equivalent to a direct product of two bodies of non-trivial dimension. We show
that this is true "up to a logarithmic factor."


title:
Coxeter group structure of cosmological billiards on compact spatial
  manifolds

abstract:
  We present a systematic study of the cosmological billiard structures of
Einstein-p-form systems in which all spatial directions are compactified on a
manifold of nontrivial topology. This is achieved for all maximally oxidised
theories associated with split real forms, for all possible compactifications
as defined by the de Rham cohomology of the internal manifold. In each case, we
study the Coxeter group that controls the dynamics for energy scales below the
Planck scale as well as the relevant billiard region. We compare and contrast
them with the Weyl group and fundamental domain that emerge from the general
BKL analysis. For generic topologies we find a variety of possibilities: (i)
The group may or may not be a simplex Coxeter group; (ii) The billiard region
may or may not be a fundamental domain. When it is not a fundamental domain, it
can be described as a sequence of pairwise adjacent chambers, known as a
gallery, and the reflections in the billiard walls provide a non-standard
presentation of the Coxeter group. We find that it is only when the Coxeter
group is a simplex Coxeter group, and the billiard region is a fundamental
domain, that there is a correspondence between billiard walls and simple roots
of a Kac-Moody algebra, as in the general BKL analysis. For each
compactification we also determine whether or not the resulting theory exhibits
chaotic dynamics.


title:
Phantom expansion with non-linear Schr\"{o}dinger-type formulation of
  scalar field cosmology

abstract:
  We describe non-flat standard Friedmann cosmology of canonical scalar field
with barotropic fluid in form of non-linear
  Schr\"{o}dinger-type (NLS) formulation in which all cosmological dynamical
quantities are expressed in term of Schr\"{o}dinger quantities as similar to
those in time-independent quantum mechanics. We assume the expansion to be
superfast, i.e. phantom expansion. We report all Schr\"{o}dinger-analogous
quantities to scalar field cosmology.
  Effective equation of state coefficient is analyzed and illustrated. We show
that in a non-flat universe, there is no fixed $w_{\rm eff}$ value for the
phantom divide. In a non-flat universe, even $w_{\rm eff} > -1$, the expansion
can be phantom. Moreover, in open universe, phantom expansion can happen even
with $w_{\rm eff} > 0$. We also report scalar field exact solutions within
frameworks of the Friedmann formulation and the NLS formulation in non-flat
universe cases.


title: Approximating with Gaussians

abstract:
  Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown
to be dense in L^2(R). Two algorithms for determining the coefficients for the
approximations are given, using orthogonal Hermite functions and least squares.
Taking the Fourier transform of this result shows low-frequency trigonometric
series are dense in L^2 with Gaussian weight function.


title:
Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type
  formulation of scalar field cosmology

abstract:
  Aspects of non-linear Schr\"{o}dinger-type (NLS) formulation of scalar
(phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big
Rip singularity are presented. Slow-roll parameters for the curvature and
barotropic density terms are introduced. We reexpress all slow-roll parameters,
slow-roll conditions and acceleration condition in NLS form. WKB approximation
in the NLS formulation is also discussed when simplifying to linear case. Most
of the Schr\"{o}dinger potentials in NLS formulation are very slowly-varying,
hence WKB approximation is valid in the ranges. In the NLS form of Big Rip
singularity, two quantities are infinity in stead of three. We also found that
approaching the Big Rip, $w_{\rm eff}\to -1 + {2}/{3q}$, $(q<0)$ which is the
same as effective phantom equation of state in the flat case.


title: Faraday spectroscopy of atoms confined in a dark optical trap

abstract:
  We demonstrate Faraday spectroscopy with high duty cycle and sampling rate
using atoms confined to a blue-detuned optical trap. Our trap consists of a
crossed pair of high-charge-number hollow laser beams, which forms a dark,
box-like potential. We have used this to measure transient magnetic fields in a
500-micron-diameter spot over a 400 ms time window with nearly unit duty cycle
at a 500 Hz sampling rate. We use these measurements to quantify and compensate
time-varying magnetic fields to ~10 nT per time sample.


title: Estimation of Large Precision Matrices Through Block Penalization

abstract:
  This paper focuses on exploring the sparsity of the inverse covariance matrix
$\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on
each off-diagonal band of the Cholesky factor from its modified Cholesky
decomposition, and penalize each block of parameters using the $L_2$-norm
instead of individual elements. We develop a one-step estimator, and prove an
oracle property which consists of a notion of block sign-consistency and
asymptotic normality. In particular, provided the initial estimator of the
Cholesky factor is good enough and the true Cholesky has finite number of
non-zero off-diagonal bands, oracle property holds for the one-step estimator
even if $p_n \gg n$, and can even be as large as $\log p_n = o(n)$, where the
data $\y$ has mean zero and tail probability $P(|y_j| > x) \leq K\exp(-Cx^d)$,
$d > 0$, and $p_n$ is the number of variables. We also prove an operator norm
convergence result, showing the cost of dimensionality is just $\log p_n$. The
advantage of this method over banding by Bickel and Levina (2008) or nested
LASSO by Levina \emph{et al.} (2007) is that it allows for elimination of
weaker signals that precede stronger ones in the Cholesky factor. A method for
obtaining an initial estimator for the Cholesky factor is discussed, and a
gradient projection algorithm is developed for calculating the one-step
estimate. Simulation results are in favor of the newly proposed method and a
set of real data is analyzed using the new procedure and the banding method.


title: The Structure of Narrative: the Case of Film Scripts

abstract:
  We analyze the style and structure of story narrative using the case of film
scripts. The practical importance of this is noted, especially the need to have
support tools for television movie writing. We use the Casablanca film script,
and scripts from six episodes of CSI (Crime Scene Investigation). For analysis
of style and structure, we quantify various central perspectives discussed in
McKee's book, "Story: Substance, Structure, Style, and the Principles of
Screenwriting". Film scripts offer a useful point of departure for exploration
of the analysis of more general narratives. Our methodology, using
Correspondence Analysis, and hierarchical clustering, is innovative in a range
of areas that we discuss. In particular this work is groundbreaking in taking
the qualitative analysis of McKee and grounding this analysis in a quantitative
and algorithmic framework.


title:
An Evolutionary-Based Approach to Learning Multiple Decision Models from
  Underrepresented Data

abstract:
  The use of multiple Decision Models (DMs) enables to enhance the accuracy in
decisions and at the same time allows users to evaluate the confidence in
decision making. In this paper we explore the ability of multiple DMs to learn
from a small amount of verified data. This becomes important when data samples
are difficult to collect and verify. We propose an evolutionary-based approach
to solving this problem. The proposed technique is examined on a few clinical
problems presented by a small amount of data.


title: Photo-detection using Bose-condensed atoms in a micro trap

abstract:
  A model of photo-detection using a Bose--Einstein condensate in an atom-chip
based micro trap is analyzed. Atoms absorb photons from the incident light
field, receive part of the photon momentum and leave the trap potential. Upon
counting of escaped atoms within predetermined time intervals, the photon
statistics of the incident light is mapped onto the atom-count statistics.
Whereas traditional photo-detection theory treats the emission centers of photo
electrons as distinguishable, here the centers of escaping atoms are condensed
and thus indistinguishable atoms. From this an enhancement of the photon-number
resolution as compared to the commonly known counting formula is derived.


title: Feature Selection for Bayesian Evaluation of Trauma Death Risk

abstract:
  In the last year more than 70,000 people have been brought to the UK
hospitals with serious injuries. Each time a clinician has to urgently take a
patient through a screening procedure to make a reliable decision on the trauma
treatment. Typically, such procedure comprises around 20 tests; however the
condition of a trauma patient remains very difficult to be tested properly.
What happens if these tests are ambiguously interpreted, and information about
the severity of the injury will come misleading? The mistake in a decision can
be fatal: using a mild treatment can put a patient at risk of dying from
posttraumatic shock, while using an overtreatment can also cause death. How can
we reduce the risk of the death caused by unreliable decisions? It has been
shown that probabilistic reasoning, based on the Bayesian methodology of
averaging over decision models, allows clinicians to evaluate the uncertainty
in decision making. Based on this methodology, in this paper we aim at
selecting the most important screening tests, keeping a high performance. We
assume that the probabilistic reasoning within the Bayesian methodology allows
us to discover new relationships between the screening tests and uncertainty in
decisions. In practice, selection of the most informative tests can also reduce
the cost of a screening procedure in trauma care centers. In our experiments we
use the UK Trauma data to compare the efficiency of the proposed technique in
terms of the performance. We also compare the uncertainty in decisions in terms
of entropy.


title: Coupling of electrons to the electromagnetic field in a localized basis

abstract:
  A simple formula is obtained for coupling electrons in a complex system to
the electromagnetic field. It includes the effect of intra-atomic excitations
and nuclear motion, and can be applied in. e.g., first-principles-based
simulations of the coupled dynamics of electrons and nuclei in materials and
molecules responding to ultrashort laser pulses. Some additional aspects of
nonadiabatic dynamical simulations are also discussed, including the potential
of "reduced Ehrenfest'" simulations for treating problems where standard
Ehrenfest simulations will fail.


title: Nonperturbative contributions to the QCD pressure

abstract:
  We summarize the most important arguments why a perturbative description of
finite-temperature QCD is unlikely to be possible and review various
well-established approaches to deal with this problem. Then, using a recently
proposed method, we investigate nonperturbative contributions to the QCD
pressure and other observables (like energy, anomaly and bulk viscosity)
obtained by imposing a functional cutoff at the Gribov horizon. Finally, we
discuss how such contributions fit into the picture of consecutive effective
theories, as proposed by Braaten and Nieto, and give an outline of the next
steps necessary to improve this type of calculation.


title: On a static charged fluid around a magnetized mass

abstract:
  We show that any magnetostatic axially symmetric solution of the
Einstein-Maxwell equations can be endowed with a specific charged fluid source
of the Polanco et al type via a simple procedure requiring the knowledge of
exclusively the magnetostatic seed spacetime. Using this procedure we construct
yet another exact solution for a massive magnetic dipole surrounded by a static
charged fluid which is different from the Polanco et al metric.


title: Hopf Algebroids

abstract: This is a preprint version of a chapter for Handbook of Algebra.


title:
Using Chandra to Unveil the High-Energy Properties of the High-Magnetic
  Field Radio Pulsar J1119-6127

abstract:
  (shortened) PSR J1119-6127 is a high magnetic field (B=4.1E13 Gauss), young
(<=1,700 year-old), and slow (P=408 ms) radio pulsar associated with the
supernova remnant (SNR) G292.2-0.5. In 2003, Chandra allowed the detection of
the X-ray counterpart of the radio pulsar, and provided the first evidence for
a compact pulsar wind nebula (PWN). We here present new Chandra observations
which allowed for the first time an imaging and spectroscopic study of the
pulsar and PWN independently of each other. The PWN is only evident in the hard
band and consists of jet-like structures extending to at least 7" from the
pulsar, with the southern `jet' being longer than the northern `jet'. The
spectrum of the PWN is described by a power law with a photon index~1.1 for the
compact PWN and ~1.4 for the southern long jet (at a fixed column density of
1.8E22/cm2), and a total luminosity of 4E32 ergs/s (0.5-7 keV), at a distance
of 8.4 kpc. The pulsar's spectrum is clearly softer than the PWN's spectrum. We
rule out a single blackbody model for the pulsar, and present the first
evidence of non-thermal (presumably magnetospheric) emission that dominates
above ~3keV. A two-component model consisting of a power law component (with
photon index ~1.5--2.0) plus a thermal component provides the best fit. The
thermal component can be fit by either a blackbody model with a temperature
kT~0.21 keV, or a neutron star atmospheric model with a temperature kT~0.14
keV. The efficiency of the pulsar in converting its rotational power, Edot,
into non-thermal X-ray emission from the pulsar and PWN is ~5E-4, comparable to
other rotation-powered pulsars with a similar Edot. We discuss our results in
the context of the X-ray manifestation of high-magnetic field radio pulsars in
comparison with rotation-powered pulsars and magnetars.


title:
Null controllability for the parabolic equation with a complex principal
  part

abstract:
  This paper is addressed to a study of the null controllability for the
semilinear parabolic equation with a complex principal part. For this purpose,
we establish a key weighted identity for partial differential operators
$(\a+i\b)\pa_t+\sum\limits_{j,k=1}^n\pa_k(a^{jk}\pa_j)$ (with real functions
$\a$ and $\b$), by which we develop a universal approach, based on global
Carleman estimate, to deduce not only the desired explicit observability
estimate for the linearized complex Ginzburg-Landau equation, but also all the
known controllability/observability results for the parabolic, hyperbolic,
Schr\"odinger and plate equations that are derived via Carleman estimates.


title: Gelfand pairs on the Heisenberg group and Schwartz functions

abstract:
  Let $\Hn$ be the $(2n+1)$-dimensional Heisenberg group and $K$ a compact
group of automorphisms of $\Hn$ such that $(K\ltimes \Hn,K)$ is a Gelfand pair.
We prove that the Gelfand transform is a topological isomorphism between the
space of $K$-invariant Schwartz functions on $\Hn$ and the space of Schwartz
function on a closed subset of $\R^s$ homeomorphic to the Gelfand spectrum of
the Banach algebra of $K$-invariant integrable functions on $\Hn$.


title: Internal Percolation Problem

abstract:
  Introduced and investigated new kind of percolation problem - so called
internal percolation problem (IP). In usual percolation problem current flows
from top to bottom of the system and here it can be called as external
percolation problem (EP) despite of the IP case when voltage is applied to the
system through bars which are inside of the hole in system. EP problem has two
major parameters: M size of system and a0 size of inclusion, lattice size etc.
IP holds one more parameter the size of hole - L. Results of computer
simulation show that critical indexes of conductance for IP problem are very
close to those in EP problem. In opposite indexes of relative spectral noise
density of 1/f noise and higher moments are really differs from EP problem. The
source of such behaviour is discussed.


title:
Convergence in the Boundary Layer for Nonhomogeneous Linear Singularly
  Perturbed Systems

abstract:
  Convergence of the solutions of nonhomogeneous linear singularly perturbed
systems to that of the corresponding reduced singular system on the half-line
[0, $\infty $) is considered. To include the situation on a neighborhood of
initial instant, a boundary layer, a distributional approach to convergence is
adopted. An explicit analytical expression for the limit as a distribution is
proved.


title: Thermodynamics and Relativity: Possible Consequences of their Close Link

abstract:
  The first part of this paper is a summary of a hypothesis previously
advanced, suggesting the existence of a close link between thermodynamics and
relativity. The second part is a preliminary comment about some possible
consequences in the fields of physics, astronomy and biology.


title: On fixed points and uniformly convex spaces

abstract:
  The purpose of this note is to present two elementary, but useful, facts
concerning actions on uniformly convex spaces. We demonstrate how each of them
can be used in an alternative proof of the triviality of the first
$L_p$-cohomology of higher rank simple Lie groups, proved in [BFGM].


title:
Stability, mobility and power currents in a two-dimensional model for
  waveguide arrays with nonlinear coupling

abstract:
  A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling,
modelling a square array of weakly coupled linear optical waveguides embedded
in a nonlinear Kerr material, is studied. We find that despite a vanishing
energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the
mobility of localized excitations is very poor. This is attributed to a large
separation in parameter space of the bifurcation points of the involved
stationary modes. At these points the stability of the fundamental modes is
changed and an asymmetric intermediate solution appears that connects the
points. The control of the power flow across the array when excited with plane
waves is also addressed and shown to exhibit great flexibility that may lead to
applications for power-coupling devices. In certain parameter regimes, the
direction of a stable propagating plane-wave current is shown to be
continuously tunable by amplitude variation (with fixed phase gradient). More
exotic effects of the nonlinear coupling terms like compact discrete breathers
and vortices, and stationary complex modes with non-trivial phase relations are
also briefly discussed. Regimes of dynamical linear stability are found for all
these types of solutions.


title:
Nuclear recoil effect on the magnetic-dipole decay rates of atomic
  levels

abstract:
  The effect of finite nuclear mass on the magnetic-dipole transition
probabilities between fine-structure levels of the same term is investigated.
Based on a rigorous QED approach a nonrelativistic formula for the recoil
correction to first order in m_e/M is derived. Numerical results for
transitions of experimental interest are presented.


title: Commissioning ATLAS and CMS with top quarks

abstract:
  The large ttbar production cross-section at the LHC suggests the use of top
quark decays to calibrate several critical parts of the detectors, such as the
trigger system, the jet energy scale and b-tagging.


title: 2XMM J083026+524133: The most X-ray luminous cluster at redshift 1

abstract:
  In the distant universe X-ray luminous clusters of galaxies are rare objects.
Large area surveys are therefore needed to probe the high luminosity end of the
cluster population at redshifts z >= 1. We correlated extended X-ray sources
from the second XMM-Newton source catalogue (2XMM) with the SDSS in order to
identify new clusters of galaxies. Distant cluster candidates in empty SDSS
fields were imaged in the R and z bands with the Large Binocular Telescope. We
extracted the X-ray spectra of the cluster candidates and fitted thermal plasma
models to the data. We determined the redshift 0.99 +-0.03 for 2XMM
J083026+524133 from its X-ray spectrum. With a bolometric luminosity of 1.8 x
10^45 erg/sec this is the most X-ray luminous cluster at redshifts z >= 1. We
measured a gas temperature of 8.2 +- 0.9 keV and and estimate a cluster mass
M(500) = 5.6 x 10^14 M(solar). The optical imaging revealed a rich cluster of
galaxies.


title: Cosmological Kaluza-Klein branes in black brane spacetimes

abstract:
  We discuss the comsological evolution of a brane in the $D(>6)$-dimensional
black brane spacetime in the context of the Kaluza-Klein (KK) braneworld
scheme, i.e., to consider KK compactification on the brane. The bulk spacetime
is composed of two copies of a patch of $D$-dimensional black three-brane
solution. The near-horizon geometry is given by $AdS_{5}\times S^{(D-5)}$ while
in the asymptotic infinity the spacetime approaches $D$-dimensional Minkowski.
We consider the brane motion from the near-horizon region toward the spatial
infinity, which induces cosmology on the brane. As is expected, in the early
times, namely when the brane is located in the near-horizon region, the
effective cosmology on the brane coincides with that in the second
Randall-Sundrum (RS II) model. Then, the brane cosmology starts to deviate from
the RS type one since the dynamics of KK compactified dimensions becomes
significant. We find that the brane Universe cannot reach the asymptotic
infinity, irrespectively of the components of matter on the brane.


title:
A Classical Analogue to the Standard Model, Chapter 3: Standard Model
  particle spectrum from scalar fields on $\mathbb{C}^{\wedge 18}$

abstract:
  The $\mathbb{C}^{\wedge 2\mathfrak{n}}$ models are analogue models which
generate Lagrangians for quasiparticles on $\mathbb{R}^{1,3}$ from
antisymmetric vector products on Grassmann manifolds. This paper introduces
$\mathbb{C}^{\wedge 18}$, the smallest member of this series which is capable
of hosting a quasiparticle spectrum analogous to the Standard Model. Once all
gaugeable degrees of freedom have been fixed, the particle spectrum of
$\mathbb{C}^{\wedge 18}$ is seen to resemble the Standard Model plus two
additional weakly interacting bosons and a ninth gluon.


title: Reasoning about quantum systems at the macroscopic level

abstract:
  In this didactical note I review in depth the rationale for using generalised
canonical distributions in quantum statistics. Particular attention is paid to
the proper definitions of quantum entropy and quantum relative entropy, as well
as to quantum state reconstruction on the basis of incomplete data. There are
two appendices in which I outline how generalised canonical distributions link
to the conventional formulation of statistical mechanics, and how classical
probability calculus emerges at the macroscopic level.


title:
Superconducting Gap and Pseudogap in Sm(O$_{1-x}$F$_x$)FeAs Layered
  Superconductor from Photoemission Spectroscopy

abstract:
  High resolution photoemission measurements have been carried out on
non-superconducting SmOFeAs parent compound and superconducting
Sm(O$_{1-x}$F$_x$)FeAs (x=0.12, and 0.15) compounds. The momentum-integrated
spectra exhibit a clear Fermi cutoff that shows little leading-edge shift in
the superconducting state which suggests the Fermi surface sheet(s) around the
$\Gamma$ point may not be gapped in this multiband superconductors. A robust
feature at 13 meV is identified in all these samples. Spectral weight
suppression near E$_F$ with decreasing temperature is observed in both undoped
and doped samples that points to a possible existence of a pseudogap in these
Fe-based compounds.


title: ${\rm Z}^{+}(4430)$ and Analogous Heavy Flavor States

abstract:
  The proximity of ${\rm Z}^+(4430)$ to the ${\rm D^{*}\bar{D}_1}$ threshold
suggests that it may be a ${\rm D^{*}\bar{D}_1}$ molecular state. The ${\rm
D^{*}\bar{D}_1}$ system has been studied dynamically from quark model, and
state mixing effect is taken into account by solving the multichannel
Schr$\ddot{\rm o}$dinger equation numerically. We suggest the most favorable
quantum number is ${\rm J^{P}=0^{-}}$, if future experiments confirm ${\rm
Z}^+(4430)$ as a loosely bound molecule state. More precise measurements of
${\rm Z}^+(4430)$ mass and width, partial wave analysis are helpful to
understand its structure. The analogous heavy flavor mesons ${\rm Z}^{+}_{bb}$
and ${\rm Z}^{++}_{bc}$ are studied as well, and the masses predicted in our
model are in agreement with the predictions from potential model and QCD sum
rule. We further apply our model to the ${\rm D\bar{D}^{*}}$ and ${\rm DD^{*}}$
system. We find the exotic ${\rm DD^{*}}$ bound molecule doesn't exist, while
the $1^{++}$ ${\rm D\bar{D}^{*}}$ bound state solution can be found only if the
screening mass $\mu$ is smaller than 0.17 GeV. The state mixing effect between
the molecular state and the conventional charmonium should be considered to
understand the nature of X(3872).


title:
Fractional Calculus: Integral and Differential Equations of Fractional
  Order

abstract:
  We introduce the linear operators of fractional integration and fractional
differentiation in the framework of the Riemann-Liouville fractional calculus.
Particular attention is devoted to the technique of Laplace transforms for
treating these operators in a way accessible to applied scientists, avoiding
unproductive generalities and excessive mathematical rigor. By applying this
technique we shall derive the analytical solutions of the most simple linear
integral and differential equations of fractional order. We show the
fundamental role of the Mittag-Leffler function, whose properties are reported
in an ad hoc Appendix. The topics discussed here will be: (a) essentials of
Riemann-Liouville fractional calculus with basic formulas of Laplace
transforms, (b) Abel type integral equations of first and second kind, (c)
relaxation and oscillation type differential equations of fractional order.

categories: math-ph cond-mat.stat-mech math.CV math.HO math.MP


title: On Metrics for Error Correction in Network Coding

abstract:
  The problem of error correction in both coherent and noncoherent network
coding is considered under an adversarial model. For coherent network coding,
where knowledge of the network topology and network code is assumed at the
source and destination nodes, the error correction capability of an (outer)
code is succinctly described by the rank metric; as a consequence, it is shown
that universal network error correcting codes achieving the Singleton bound can
be easily constructed and efficiently decoded. For noncoherent network coding,
where knowledge of the network topology and network code is not assumed, the
error correction capability of a (subspace) code is given exactly by a new
metric, called the injection metric, which is closely related to, but different
than, the subspace metric of K\"otter and Kschischang. In particular, in the
case of a non-constant-dimension code, the decoder associated with the
injection metric is shown to correct more errors then a
minimum-subspace-distance decoder. All of these results are based on a general
approach to adversarial error correction, which could be useful for other
adversarial channels beyond network coding.


title: The Origin of Semiconductor Physics in Italy: 1945 - 1965

abstract:
  The activities carried out by Italian physicists in the field of
semiconductor physics during the period spanning from 1945 to the foundation of
the National Group of Structure of the Matter (GNSM, 1965) are reviewed within
their historical context. Until the fifties, the Italian research was only
marginally involved, if at all, in the main streams of advancement in solid
state physics. Starting from the early fifties, an interest for technical
applications of the newly introduced semiconductor devices began to grow in the
electronic engineering community. In the following years, the birth of a few
experimental and theoretical groups lead by highly motivated scientists (some
of them with international experience) allowed to deal with the main topics
related to condensed matter and semiconductor phenomena. The work developed by
these "pioneers", discussed in this paper, represented an invaluable
contribution for the new generations of physicists in this research field.


title: Eigenfunction concentration for polygonal billiards

abstract:
  In this note, we extend the results on eigenfunction concentration in
billiards as proved by the third author in \cite{M1}. There, the methods
developed in Burq-Zworski \cite{BZ3} to study eigenfunctions for billiards
which have rectangular components were applied. Here we take an arbitrary
polygonal billiard $B$ and show that eigenfunction mass cannot concentrate away
from the vertices; in other words, given any neighbourhood $U$ of the vertices,
there is a lower bound $$ \int_U |u|^2 \geq c \int_B |u|^2 $$ for some $c =
c(U) > 0$ and any eigenfunction $u$.


title: BEC dark matter can explain collisions of galaxy clusters

abstract:
  We suggest that the dark matter model based on Bose Einstein condensate or
scalar field can resolve the apparently contradictory behaviors of dark matter
in the Abell 520 and the Bullet cluster. During a collision of two galaxies in
the cluster, if initial kinetic energy of the galaxies is large enough, two
dark matter halos pass each other in a soliton-like way as observed in the
Bullet cluster. If not, the halos merge due to the tiny repulsive interaction
among dark matter particles as observed in the Abell 520. This idea can also
explain the origin of the dark galaxy and the galaxy without dark matter.


title: Hydrodynamic type integrable equations on a segment and a half-line

abstract:
  The concept of integrable boundary conditions is applied to hydrodynamic type
systems. Examples of such boundary conditions for dispersionless Toda systems
are obtained. The close relation of integrable boundary conditions with
integrable reductions of multi-field systems is observed. The problem of
consistency of boundary conditions with the Hamiltonian formulation is
discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a
segment and a semi-line are presented.


title: Many-Body meets QM/MM: Application to indole in water solution

abstract:
  Spectral properties of chromophores are used to probe complex biological
processes in vitro and in vivo, yet how the environment tunes their optical
properties is far from being fully understood. Here we present a method to
calculate such properties on large scale systems, like biologically relevant
molecules in aqueous solution. Our approach is based on many body perturbation
theory combined with quantum-mechanics/molecular-mechanics (QM/MM) approach. We
show here how to include quasi-particle and excitonic effects for the
calculation of optical absorption spectra in a QM/MM scheme. We apply this
scheme, together with the well established TDDFT approach, to indole in water
solution. Our calculations show that the solvent induces a redshift in the main
spectral peak of indole, in quantitative agreement with the experiments and
point to the importance of performing averages over molecular dynamics
configurations for calculating optical properties.


title: Sharp capacitary estimates for rings in metric spaces

abstract:
  We establish sharp estimates for the $p$-capacity of metric rings with
unrelated radii in metric measure spaces equipped with a doubling measure and
supporting a Poincar\'e inequality. These estimates play an essential role in
the study of the local behavior of \p-harmonic Green's functions.


title: Missing observation analysis for matrix-variate time series data

abstract:
  Bayesian inference is developed for matrix-variate dynamic linear models
(MV-DLMs), in order to allow missing observation analysis, of any sub-vector or
sub-matrix of the observation time series matrix. We propose modifications of
the inverted Wishart and matrix $t$ distributions, replacing the scalar degrees
of freedom by a diagonal matrix of degrees of freedom. The MV-DLM is then
re-defined and modifications of the updating algorithm for missing observations
are suggested.


title: Bi-isometries and commutant lifting

abstract:
  A new functional model for pairs of commuting isometries is described.
Intertwining operators between such models are then studied in order to
approach the classification of invariant subspaces of such pairs.


title:
Note on recent measurements of the $\psi(1S)\to\ga \eta_C(1S)$ and
  $\psi(2S)\to\ga \eta_C(1S)$ branching ratios

abstract:
  Recently published measurements of the branching ratios ${\cal
B}(\psi(1S)\to\ga \eta_C(1S))$ and ${\cal B}(\psi(2S)\to\ga \eta_C(1S))$ by the
CLEO collaboration are examined in the context of a potential model that
includes both relativistic and one-loop QCD corrections to the quark-antiquark
interaction. The prediction for the width $\Gamma(\psi(1S)\to\ga \eta_C(1S))$
is in excellent agreement with the new data but the prediction for
$\Gamma(\psi(2S)\to\ga \eta_C(1S))$ is too small. In an effort to understand
this discrepancy, we derive an upper bound on $\Gamma(\psi(2S)\to\ga
\eta_C(1S))$ and point out its experimental value saturates this bound.


title: Torsion Cosmology and the Accelerating Universe

abstract:
  Investigations of the dynamic modes of the Poincare gauge theory of gravity
found only two good propagating torsion modes; they are effectively a scalar
and a pseudoscalar. Cosmology affords a natural situation where one might see
observational effects of these modes. Here we consider only the ``scalar
torsion'' mode. This mode has certain distinctive and interesting qualities. In
particular this type of torsion does not interact directly with any known
matter and it allows a critical non-zero value for the affine scalar curvature.
Via numerical evolution of the coupled nonlinear equations we show that this
mode can contribute an oscillating aspect to the expansion rate of the
Universe. From the examination of specific cases of the parameters and initial
conditions we show that for suitable ranges of the parameters the dynamic
``scalar torsion'' model can display features similar to those of the presently
observed accelerating universe.


title:
The Use of Labeled Cortical Distance Maps for Quantization and Analysis
  of Anatomical Morphometry of Brain Tissues

abstract:
  Anatomical shape differences in cortical structures in the brain can be
associated with various neuropsychiatric and neuro-developmental diseases or
disorders. Labeled Cortical Distance Map (LCDM), can be a powerful tool to
quantize such morphometric differences. In this article, we investigate various
issues regarding the analysis of LCDM distances in relation to morphometry. The
length of the LCDM distance vector provides the number of voxels (approximately
a multiple of volume (in mm^3)); median, mode, range, and variance of LCDM
distances are all suggestive of size, thickness, and shape differences. However
these measures provide a crude summary based on LCDM distances which may convey
much more information about the tissue in question. To utilize more of this
information, we pool (merge) the LCDM distances from subjects in the same group
or condition. The statistical methodology we employ require normality and
within and between sample independence. We demonstrate that the violation of
these assumptions have mild influence on the tests. We specify the types of
alternatives the parametric and nonparametric tests are more sensitive for. We
also show that the pooled LCDM distances provide powerful results for group
differences in distribution, left-right morphometric asymmetry of the tissues,
and variation of LCDM distances. As an illustrative example, we use gray matter
(GM) tissue of ventral medial prefrontal cortices (VMPFCs) from subjects with
major depressive disorder, subjects at high risk, and control subjects. We find
significant evidence that VMPFCs of subjects with depressive disorders are
different in shape compared to those of normal subjects.


title:
Impact ionization fronts in semiconductors: superfast propagation due to
  "nonlocalized" preionization

abstract:
  We discuss a new mode of ionization front passage in semiconductor
structures. The front of avalanche ionization propagates into an intrinsic
semiconductor with a constant electric field $E_{\rm m}$ in presence of a small
concentration of free nonequilibrium carriers - so called preionization. We
show that if the profile of these initial carriers decays in the direction of
the front propagation with a characteristic exponent $\lambda$, the front
velocity is determined by $v_f \approx 2 \beta_{\rm m}/\lambda$, where
$\beta_{\rm m} \equiv \beta(E_{\rm m})$ is the corresponding ionization
frequency. By a proper choice of the preionization profile one can achieve
front velocities $v_f$ that exceed the saturated drift velocity $v_s$ by
several orders of magnitude even in moderate electric fields. Our propagation
mechanism differs from the one for well-known TRAPATT fronts. Finally, we
discuss physical reasons for the appearance of preionization profiles with slow
spatial decay.


title: Can re-entrance be observed in force induced transitions?

abstract:
  A large conformational change in the reaction co-ordinate and the role of the
solvent in the formation of base-pairing are combined to settle a long standing
issue {\it i.e.} prediction of re-entrance in the force induced transition of
DNA. A direct way to observe the re-entrance, i.e a strand goes to the closed
state from the open state and again to the open state with temperature, appears
difficult to be achieved in the laboratory. An experimental protocol (in direct
way) in the constant force ensemble is being proposed for the first time that
will enable the observation of the re-entrance behavior in the
force-temperature plane. Our exact results for small oligonucleotide that forms
a hairpin structure provide the evidence that re-entrance can be observed.


title:
Cohen-Macaulay clutters with combinatorial optimization properties and
  parallelizations of normal edge ideals

abstract:
  Let C be a uniform clutter and let I=I(C) be its edge ideal. We prove that if
C satisfies the packing property (resp. max-flow min-cut property), then there
is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp.
max-flow min-cut property) such that C is a minor of C1. For arbitrary edge
ideals of clutters we prove that the normality property is closed under
parallelizations. Then we show some applications to edge ideals and clutters
which are related to a conjecture of Conforti and Cornu\'ejols and to max-flow
min-cut problems.


title: Homogeneous Polynomials with Isomorphic Milnor Algebras

abstract:
  In Theorem 3.2 we show that two homogeneous polynomials $f$ and $g$ having
isomorphic Milnor algebras are right-equivalent.


title:
Memory effects in transport through a hopping insulator: Understanding
  two-dip experiments

abstract:
  We discuss memory effects in the conductance of hopping insulators due to
slow rearrangements of many-electron clusters leading to formation of polarons
close to the electron hopping sites. An abrupt change in the gate voltage and
corresponding shift of the chemical potential change populations of the hopping
sites, which then slowly relax due to rearrangements of the clusters. As a
result, the density of hopping states becomes time dependent on a scale
relevant to rearrangement of the structural defects leading to the excess time
dependent conductivity.


title:
Diversity against adversity: How adaptive immunity evolves potent
  antibodies

abstract:
  How does immune system evolve functional proteins - potent antibodies - in
such a short time? We address this question using a microscopic, protein-level,
sequence-based model of humoral immune response with explicitly defined
interactions between Immunoglobulins, host and pathogen proteins. Potent
Immunoglobulins are discovered in this model via clonal selection and affinity
maturation. Possible outcomes of an infection (extinction of cells, survival
with complete elimination of viruses, or persistent infection) crucially depend
on mutation rates of viral and Immunoglobulin proteins. The model predicts that
there is an optimal Somatic Hypermutation (SHM) rate close to experimentally
observed 10-3 per nucleotide per replication. Further, we developed an
analytical theory which explains the physical reason for an optimal SHM program
as a compromise between deleterious effects of random mutations on nascent
maturing Immunoglobulins (adversity) and the need to generate diverse pool of
mutated antibodies from which highly potent ones can be drawn (diversity). The
theory explains such effects as dependence of B cell fate on affinity for an
incoming antigen, ceiling in affinity of mature antibodies, Germinal Center
sizes and maturation times. The theory reveals the molecular factors which
determine the efficiency of affinity maturation, providing insight into
variability of immune response to cytopathic (direct response by germline
antibodies) and poorly cytopathic viruses (crucial role of SHM in response).
These results demonstrate the feasibility and promise of microscopic
sequence-based models of immune system, where population dynamics of evolving
Immunoglobulins is explicitly tied to their molecular properties.


title:
Dynamics of meromorphic maps with small topological degree II: Energy
  and invariant measure

abstract:
  We continue our study of the dynamics of meromorphic mappings with small
topological degree on a compact K\"ahler surface $X$. Under general hypotheses
we are able to construct a canonical invariant measure which is mixing, does
not charge pluripolar sets and admits a natural geometric description.
  Our hypotheses are always satisfied when $X$ has Kodaira dimension zero, or
when the mapping is induced by a polynomial endomorphism of $\mathbf{C}^2$.
They are new even in the birational case. We also exhibit families of mappings
where our assumptions are generically satisfied and show that if
counterexamples exist, the corresponding measure must give mass to a pluripolar
set.


title: New results on solar neutrino fluxes from 192 days of Borexino data

abstract:
  We report the direct measurement of the ^7Be solar neutrino signal rate
performed with the Borexino detector at the Laboratori Nazionali del Gran
Sasso. The interaction rate of the 0.862 MeV ^7Be neutrinos is
49+-3(stat)+-4(syst) counts/(day * 100ton). The hypothesis of no oscillation
for ^7Be solar neutrinos is inconsistent with our measurement at the 4sigma
level. Our result is the first direct measurement of the survival probability
for solar nu_e in the transition region between matter-enhanced and
vacuum-driven oscillations. The measurement improves the experimental
determination of the flux of ^7Be, pp, and CNO solar nu_e, and the limit on the
magnetic moment of neutrinos.


title: The theoretical top quark cross section at the Tevatron and the LHC

abstract:
  We present results for the top quark pair cross section at the Tevatron and
the LHC. We use the resummed double differential cross section, employing the
fully kinematics-dependent soft anomalous dimension matrices, to calculate the
soft-gluon contributions at next-to-next-to-leading order (NNLO). We improve
and update our previous estimates by refining our methods, including further
subleading terms, and employing the most recent parton distribution function
sets. The NNLO soft corrections significantly enhance the NLO cross section
while considerably reducing the scale dependence. We provide a detailed
discussion of all theoretical uncertainties in our calculation, including
kinematics, scale, and parton distributions uncertainties and clarify the
differences between our work and other approaches in the literature.


title: Differentiable Rigidity under Ricci curvature lower bound

abstract:
  In this article we prove a differentiable rigidity result. Let $(Y, g)$ and
$(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$)
and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that
the metric $g_0$ is real hyperbolic and denote by $d$ the diameter of
$(X,g_0)$. We show that there exists a number $\varepsilon:=\varepsilon (n,
d)>0$ such that if the Ricci curvature of the metric $g$ is bounded below by
$-n(n-1)$ and its volume satisfies $\vol_g (Y)\leqslant (1+\varepsilon)
\vol_{g_0} (X)$ then the manifolds are diffeomorphic. The proof relies on
Cheeger-Colding's theory of limits of Riemannian manifolds under lower Ricci
curvature bound.


title:
Generalized Clausius relation and power dissipation in non equilibrium
  stochastic systems

abstract:
  We extend certain basic and general concepts of thermodynamics to discrete
Markov systems exchanging work and heat with reservoirs. In this framework we
show that the celebrated Clausius inequality can be generalized and becomes an
equality, significantly extending several recent results. We further show that
achieving zero dissipation in a system implies that detailed balance obtains,
and as a consequence there is zero power production. We obtain inequalities for
power production under more general circumstances and show that near
equilibrium obtaining maximum power production requires dissipation to be of
the same order of magnitude.


title: Stability of the Periodic Toda Lattice: Higher Order Asymptotics

abstract:
  In a recent paper we have considered the long time asymptotics of the
periodic Toda lattice under a short range perturbation and we have proved that
the perturbed lattice asymptotically approaches a modulated lattice. In the
present paper we capture the higher order asymptotics, at least away from some
resonance regions. In particular we prove that the decay rate is $O(t^{-1/2})$.
  Our proof relies on the asymptotic analysis of the associated Riemann-Hilbert
factorization problem, which is here set on a hyperelliptic curve. As in
previous studies of the free Toda lattice, the higher order asymptotics arise
from "local" Riemann-Hilbert factorization problems on small crosses centered
on the stationary phase points. We discover that the analysis of such a local
problem can be done in a chart around each stationary phase point and reduces
to a Riemann--Hilbert factorization problem on the complex plane. This result
can then be pulled back to the hyperelliptic curve.


title: Algebraic Legendrian Varieties

abstract:
  Real Legendrian subvarieties are classical objects of differential geometry
and classical mechanics and they have been studied since antiquity. However,
complex Legendrian subvarieties are much more rigid and have more exceptional
properties. The most remarkable case is the Legendrian subvarieties of
projective space and prior to the author's research only few smooth examples of
these were known.
  The first series of results of this thesis is related to the automorphism
group of any Legendrian subvariety in any projective contact manifold. The
connected component of this group (under suitable minor assumptions) is
completely determined by the sections of the distinguished line bundle on the
contact manifold vanishing on the Legendrian variety. Moreover its action
preserves the contact structure.
  The second series of results is devoted to finding new examples of smooth
Legendrian subvarieties of projective space. The contribution of this thesis is
in three steps: First we find an example of a smooth toric surface. Next we
find a smooth quasihomogeneous Fano 8-fold that admits a Legendrian embedding.
Finally, we realise that both of these are special cases of a very general
construction: a general hyperplane section of a smooth Legendrian variety,
after a suitable projection, is a smooth Legendrian variety of smaller
dimension. By applying this result to known examples and decomposable
Legendrian varieties, we construct infinitely many new examples in every
dimension, with various Picard rank, canonical degree, Kodaira dimension and
other invariants.


title: Wilson Line Integrals in the Unparticle Action

abstract:
  We consider the unparticle action that is made gauge invariant by inclusion
of an open Wilson line factor. In deriving vertexes from such an action it has
been customary to use a form of differentiating the Wilson line originally
proposed by Mandelstam. Using a simple example, we show that the Mandelstam
derivative is mathematically inconsistent. We show that there are two ways to
define differentiation of the Wilson line. The mathematically consistent method
is to differentiate the explicit dependence of the line on the endpoint. The
other method is a functional derivative and corresponds in a limiting case to
the Mandelstam derivative. We also show that the only path that can be used in
the Wilson line integral that leaves the unparticle action both Poincare and
scale invariant is the straight line.