title: Multivariate normal approximation in geometric probability

abstract:
  Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is
over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded
region in $d$-space, and $\xi_x$ is a functional determined by the Poisson
points near to $x$, i.e. satisfying an exponential stabilization condition,
along with a moments condition (examples include statistics for proximity
graphs, germ-grain models and random sequential deposition models). A known
general result says the $\mu_\lambda$-measures (suitably scaled and centred) of
disjoint sets in $R^d$ are asymptotically independent normals as $\lambda \to
\infty$; here we give an $O(\lambda^{-1/(2d + \epsilon)})$ bound on the rate of
convergence. We illustrate our result with an explicit multivariate central
limit theorem for the nearest-neighbour graph on Poisson points on a finite
collection of disjoint intervals.


title:
Particle propagation in non-trivial backgrounds: a quantum field theory
  approach

abstract:
  The basic aim of the thesis is the study of the propagation of particles and
quasiparticles in non-trivial backgrounds from the quantum field theory point
of view. By "non-trivial background" we mean either a non-vacuum state in
Minkowski spacetime or an arbitrary state in a curved spacetime. Starting with
the case of a flat spacetime, the basic properties of the particle and
quasiparticle propagation are analyzed using two different methods other than
the conventional mean-field-based techniques: on the one hand, the quantum
state corresponding to the quasiparticle excitation is explicitly constructed;
on the other hand, the spectral representation of the two-point propagators is
analyzed. Both methods lead to the same results: the energy and decay rate of
the quasiparticles are determined by the real and imaginary parts of the
retarded self-energy respectively. These general results are applied to two
particular quantum systems: first, a scalar particle immersed in a thermal
graviton bath; second, a simplified atomic model, seizing the opportunity to
connect with other statistical and first-quantized approaches. In the second
part of the thesis the results are extended to curved spacetime. Working with a
quasilocal quasiparticle concept the flat-spacetime results are recovered. In
cosmology, within the adiabatic approximation, it is possible to go beyond the
flat spacetime results and find additional effects due to the universe
expansion. The cosmologically-induced effects are analyzed, obtaining that
there might be an additional contribution to the particle decay due to the
universe expansion. In the de Sitter case, this additional contribution
coincides with the decay rate in a thermal bath in a flat spacetime at the
corresponding de Sitter temperature.


title: Schr\"odinger operators on armchair nanotubes. II

abstract:
  We consider the Schr\"odinger operator with a periodic potential on quasi-1D
models of armchair single-wall nanotubes. The spectrum of this operator
consists of an absolutely continuous part (intervals separated by gaps) plus an
infinite number of eigenvalues with infinite multiplicity. We describe the
absolutely continuous spectrum of the Schr\"odinger operator: 1) the
multiplicity, 2) endpoints of the gaps, they are given by periodic or
antiperiodic eigenvalues or resonances (branch points of the Lyapunov
function), 3) resonance gaps, where the Lyapunov function is non-real. We
determine the asymptotics of the gaps at high energy.


title: Laboratory Density Functionals

abstract:
  We compare several definitions of the density of a self-bound system, such as
a nucleus, in relation with its center-of-mass zero-point motion. A trivial
deconvolution relates the internal density to the density defined in the
laboratory frame. This result is useful for the practical definition of density
functionals.


title: Probing the nuclear EOS with fragment production

abstract:
  We discuss fragmentation mechanisms and isospin transport occurring in
central collisions between neutron rich systems at Fermi energies. In
particular, isospin effects are analyzed looking at the correlations between
fragment isotopic content and kinematical properties. Simulations are based on
an approximate solution of the Boltzmann-Langevin (BL) equation. An attempt to
solve the complete BL equation, by introducing full fluctuations in phase space
is also discussed.


title: Multidimensional cellular automata and generalization of Fekete's lemma

abstract:
  Fekete's lemma is a well known combinatorial result on number sequences: we
extend it to functions defined on $d$-tuples of integers. As an application of
the new variant, we show that nonsurjective $d$-dimensional cellular automata
are characterized by loss of arbitrarily much information on finite supports,
at a growth rate greater than that of the support's boundary determined by the
automaton's neighbourhood index.


title: Measurement of the Fermi Constant by FAST

abstract:
  An initial measurement of the lifetime of the positive muon to a precision of
16 parts per million (ppm) has been performed with the FAST detector at the
Paul Scherrer Institute. The result is tau_mu = 2.197083 (32) (15) microsec,
where the first error is statistical and the second is systematic. The muon
lifetime determines the Fermi constant, G_F = 1.166353 (9) x 10^-5 GeV^-2 (8
ppm).


title: Spectropolarimetric signatures of Earth-like extrasolar planets

abstract:
  We present results of numerical simulations of the flux (irradiance), F, and
the degree of polarization (i.e. the ratio of polarized to total flux), P, of
light that is reflected by Earth-like extrasolar planets orbiting solar-type
stars, as functions of the wavelength (from 0.3 to 1.0 micron, with 0.001
micron spectral resolution) and as functions of the planetary phase angle. We
use different surface coverages for our model planets, including vegetation and
a Fresnel reflecting ocean, and clear and cloudy atmospheres. Our
adding-doubling radiative transfer algorithm, which fully includes multiple
scattering and polarization, handles horizontally homogeneous planets only; we
simulate fluxes and polarization of horizontally inhomogeneous planets by
weighting results for homogeneous planets. Like the flux, F, the degree of
polarization, P, of the reflected starlight is shown to depend strongly on the
phase angle, on the composition and structure of the planetary atmosphere, on
the reflective properties of the underlying surface, and on the wavelength, in
particular in wavelength regions with gaseous absorption bands. The sensitivity
of P to a planet's physical properties appears to be different than that of F.
Combining flux with polarization observations thus makes for a strong tool for
characterizing extrasolar planets. The calculated total and polarized fluxes
will be made available through the CDS.


title:
Negative phase velocity in nonlinear oscillatory systems --mechanism and
  parameter distributions

abstract:
  Waves propagating inwardly to the wave source are called antiwaves which have
negative phase velocity. In this paper the phenomenon of negative phase
velocity in oscillatory systems is studied on the basis of periodically paced
complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture
on the negative phase velocity of these pacing induced waves. This picture
tells us that the competition between the frequency $\omega_{out}$ of the
pacing induced waves with the natural frequency $\omega_{0}$ of the oscillatory
medium is the key point responsible for the emergence of negative phase
velocity and the corresponding antiwaves. $\omega_{out}\omega_{0}>0$ and
$|\omega_{out}|<|\omega_{0}|$ are the criterions for the waves with negative
phase velocity. This criterion is general for one and high dimensional CGLE and
for general oscillatory models. Our understanding of antiwaves predicts that no
antispirals and waves with negative phase velocity can be observed in excitable
media.


title: Summary of the Heavy Flavor Working Group

abstract:
  During the last year many important results have been achieved in heavy
flavour physics: New measurements of charm and beauty production have been
performed at HERA and the Tevatron. A wealth of new spectroscopy data with
several new, unexpected states in the charmonium and the D_s systems has been
collected and b to d gamma transitions have been established. The oscillation
frequency in the B_s Bbar_s is now measured, and mixing in the D0 D0bar system
has been observed. Theoretical progress in the areas of open heavy flavour
production, quarkonium production and decays, and multiquark spectroscopy has
been presented at this workshop.


title: Quasiclassical approach and spin-orbit coupling

abstract:
  We discuss the quasiclassical Green function method for a two-dimensional
electron gas in the presence of spin-orbit coupling, with emphasis on the
meaning of the $\xi$-integration procedure. As an application of our approach,
we demonstrate how the spin-Hall conductivity, in the presence of spin-flip
scattering, can be easily obtained from the spin-density continuity equation.


title: Schr\"odinger operators on armchair nanotubes. I

abstract:
  We consider the Schr\"odinger operator with a periodic potential on quasi-1D
models of armchair single-wall nanotubes. The spectrum of this operator
consists of an absolutely continuous part (intervals separated by gaps) plus an
infinite number of eigenvalues with infinite multiplicity. We describe all
eigenfunctions with the same eigenvalue. We define a Lyapunov function, which
is analytic on some Riemann surface. On each sheet, the Lyapunov function has
the same properties as in the scalar case, but it has branch points, which we
call resonances. In example we show the existence of real and complex
resonances for some specific potentials.


title: Landen transformations and the integration of rational functions

abstract:
  We present a rational version of the classical Landen transformation for
elliptic integrals. This is employed to obtain explicit closed-form expressions
for a large class of integrals of even rational functions and to develop an
algorithm for the numerical integration of these functions.


title: A simple example of a new class of Landen transformation

abstract:
  The rational Landen transformation is a map on the coefficients of a rational
integrand that preserves the value of the integral. This is the rational analog
of the classical Landen transformations for elliptic integrals that leads to
the arithmetic-geometric mean of Legendre and Gauss. We present the effect of
this transformation in the simplest possible case.


title: Search for Excited Leptons at HERA

abstract:
  Searches for excited electrons and neutrinos have been performed using the
complete HERA I and II data samples collected by the H1 detector at
$\sqrt{s}=320$ GeV corresponding to an integrated luminosity of up to 435
pb$^{-1}$. In absence of a signal, the limits on the ratio of the coupling to
the compositeness scale derived extend the excluded region to higher masses
than has been possible in previous searches.


title: Deterministic Rendering of BB84 for Practical Quantum Cryptography

abstract:
  We describe how to modify the BB84 protocol for quantum cryptography in order
to make it deterministic. We study both theoretical and experimental aspects of
this issue, showing that the new scheme is as secure as the old one, more
efficient on small-scale distances, and within the range of current technology.


title: Smooth representations and sheaves

abstract:
  The paper is concerned with `geometrization' of smooth (i.e. with open
stabilizers) representations of the automorphism group of universal domains,
and with the properties of `geometric' representations of such groups. As an
application, we calculate the cohomology groups of several classes of smooth
representations of the automorphism group of an algebraically closed extension
of infinite transcendence degree of an algebraically closed field.


title: Master crossover functions for the one-component fluid "subclass"

abstract:
  Introducing three well-defined dimensionless numbers, we establish the link
between the scale dilatation method able to estimate master (i.e. unique)
singular behaviors of the one-component fluid "subclass" and the universal
crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E
74, 021113 (2006)] from the bounded results of the massive renormalization
scheme applied to the...


title: High-fidelity ion-trap quantum computing with hyperfine clock states

abstract:
  We propose the implementation of a geometric-phase gate on
magnetic-field-insensitive qubits with $\hat{\sigma}^z$-dependent forces for
trapped ion quantum computing. The force is exerted by two laser beams in a
Raman configuration. Qubit-state dependency is achieved by a small frequency
detuning from the virtually-excited state. Ion species with excited states of
long radiative lifetimes are used to reduce the chance of a spontaneous photon
emission to less than 10$^{-8}$ per gate-run. This eliminates the main source
of gate infidelity of previous implementations. With this scheme it seems
possible to reach the fault tolerant threshold.


title: Weak Values and Continuous-Variable Entanglement Concentration

abstract:
  We demonstrate a general weak measurement model which allows Gaussian
preserving entanglement concentration of the two mode squeezed vacuum. The
power of this simple and elegant protocol is through the constraints it places
on possible ancilla states and measurement strategies that will allow
entanglement concentration. In particular, it is shown how previously
discovered protocols of this kind emerge as special examples of the general
model described here. Finally, as evidence of its utility, we use it to provide
another novel example of such a protocol.


title:
Spin separation in a T ballistic nanojunction due to
  lateral-confinement-induced spin-orbit-coupling

abstract:
  We propose a new scheme of spin filtering employing ballistic nanostructures
in two dimensional electron gases (2DEGs). The proposal is essentially based on
the spin-orbit (SO) interaction arising from the lateral confining electric
field. This sets the basic difference with other works employing ballistic
crosses and T junctions with the conventional SO term arising from 2DEG
confinement. We discuss the consequences of this different approach on
magnetotransport properties of the device, showing that the filter can in
principle be used not only to generate a spin polarized current but also to
perform an electric measurement of the spin polarization of a charge current.
We focus on single-channel transport and investigate numerically the spin
polarization of the current.


title: A graviton propagator for inflation

abstract:
  We construct the scalar and graviton propagator in quasi de Sitter space up
to first order in the slow roll parameter $\epsilon\equiv -\dot{H}/H^2$. After
a rescaling, the propagators are similar to those in de Sitter space with an
$\epsilon$ correction to the effective mass. The limit $\epsilon\to 0$
corresponds to the E(3) vacuum that breaks de Sitter symmetry, but does not
break spatial isotropy and homogeneity. The new propagators allow for a
self-consistent, dynamical study of quantum back-reaction effects during
inflation.


title: Higher signal harmonics, LISA's angular resolution, and dark energy

abstract:
  It is generally believed that the angular resolution of the Laser
Interferometer Space Antenna (LISA) for binary supermassive black holes (SMBH)
will not be good enough to identify the host galaxy or galaxy cluster. This
conclusion, based on using only the dominant harmonic of the binary SMBH
signal, changes substantially when higher signal harmonics are included in
assessing the parameter estimation problem. We show that in a subset of the
source parameter space the angular resolution increases by more than a factor
of 10, thereby making it possible for LISA to identify the host galaxy/galaxy
cluster. Thus, LISA's observation of certain binary SMBH coalescence events
could constrain the dark energy equation of state to within a few percent,
comparable to the level expected from other dark energy missions.


title:
Properties of 12Be and 11Be in terms of single-particle motion in
  deformed potential

abstract:
  Inspired by the recent measurement of the B(E2;$0_{2}^{+} \to 2_{1}^+$) and
B(E0;$0_{2}^{+} \to 0_{1}^+$) values in $^{12}$Be, we give an interpretation of
available spectroscopic data on both $^{12}$Be and $^{11}$Be, using a simple
model which contains the essential feature of these two nuclei; the presence of
weakly-bound neutron(s) in deformed potentials. The agreement of the calculated
results with observed data is surprisingly good, including well-known strong E1
transitions in both nuclei.


title: BRST, anti-BRST and gerbes

abstract:
  We discuss BRST and anti--BRST transformations for an Abelian antisymmetric
gauge field in 4D and find that, in order for them to anticommute, we have to
impose a condition on the auxiliary fields. This condition is similar to the
Curci-Ferrari condition for the 4D non--Abelian 1-form gauge theories and
represents a consistency requirement. We interpret it as a signal that our
Abelian 2-form gauge field theory is based on gerbes. To support this
interpretation we discuss, in particular, the case of the 1-gerbe for our
present field theory and write the relevant equations and symmetry
transformations for 2-gerbes.


title: Filtering of spin currents based on ballistic ring

abstract:
  Quantum interference effects in rings provide suitable means for controlling
spin at mesoscopic scales. Here we apply such a control mechanism to the
spin-dependent transport in a ballistic quasi one dimensional ring patterned in
two dimensional electron gases (2DEGs). The study is essentially based on the
{\it natural} spin-orbit (SO) interactions, one arising from the laterally
confining electric field {($\beta$ term) and the other due to to the
quantum-well potential that confines electrons in the 2DEG (conventional Rashba
SO interaction or $\alpha$ term).} We focus on single-channel transport and
solve analytically the spin polarization of the current. As an important
consequence of the presence of spin splitting, we find the occurrence of spin
dependent current oscillations.
  We analyze %the effects of disorder by discussing the transport in the
presence of one non-magnetic obstacle in the ring. We demonstrate that a spin
polarized current can be induced when an unpolarized charge current is injected
in the ring, by focusing on the central role that the presence of the obstacle
plays.


title: Parking in the city

abstract:
  We show that the spacing distribution between parked cars can be obtained as
a solution of certain linear distributional fixed point equation. The results
are compared with the data measured on the streets of Hradec Kralove. We also
discuss a relation of this results to the random matrix theory.


title: Use of a $d$-Constraint During LDPC Decoding in a Bliss Scheme

abstract:
  Bliss schemes of a run length limited (RLL) codec in combination with an LDPC
codec, generate LDPC parity bits over a systematic sequence of RLL channel bits
that are inherently redundant as they satisfy e.g. a $d=1$ minimum run length
constraint. That is the subsequences consisting of runs of length $d=1$, viz.
$...010...$ and $...101...$, cannot occur. We propose to use this redundancy
during LDPC decoding in a Bliss scheme by introducing additional $d$-constraint
nodes in the factor graph used by the LDPC decoder. The messages sent from
these new nodes to the variable or codeword bit nodes exert a ``force'' on the
resulting soft-bit vector coming out of the LDPC decoding that give it a
tendency to comply with the $d$-constraints. This way, we can significantly
reduce the probability of decoding error.


title: Covering spaces and the Kakimizu complex

abstract:
  In 1992, Osamu Kakimizu defined a complex that has become known as the
Kakimizu complex of a knot. Vertices correspond to isotopy classes of minimal
genus Seifert surfaces of the knot. Higher dimensional simplices correspond to
collections of such classes of Seifert surfaces that admit disjoint
representatives. We show that this complex is simply connected.


title: Dynamic structure factor of Fermi superfluid in the BEC-BCS crossover

abstract:
  We consider cigar shaped Fermi superfluid in the BEC-BCS crossover. Using
polytropic form of equation of state, we derive low energy multibranch bosonic
excitations and the corresponding density fluctuations in three different
regimes along the crossover, namely weak-coupling BCS, unitarity and molecular
BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of
the low energy bosonic excitations by measuring dynamic structure factor.
Therefore, we calculate dynamic structure factor in those three different
regimes. In the Bragg spectroscopy, an actual observable is momentum imparted
to the superfluid due to the Bragg potential. We also present results of the
momentum imparted to the superfluid due to the Bragg pulses.


title:
Asymptotic expansions for functions of the increments of certain
  Gaussian processes

abstract:
  Let $G=\{G(x),x\ge 0\}$ be a mean zero Gaussian process with stationary
increments and set $\sigma^2(|x-y|)= E(G(x)-G(y))^2$. Let $f$ be a function
with $Ef^{2}(\eta)<\ff$, where $\eta=N(0,1)$. When $\sigma^2$ is regularly
varying at zero and \[
  \lim_{h\to 0}{h^2\over \sigma^2(h)}= 0\qquad {and}\qquad \lim_{h\to
0}{\sigma^2(h)\over h}= 0
  \quad {but} \quad ({d^{2}\over ds^2}\sigma^2(s))^{j_0} \] is locally
integrable for some integer $j_0\ge 1$, and satisfies some additional
regularity conditions, \bea && \int_a^bf(\frac{G(x+h)-G(x)}{\sigma (h)}) dx
\label{abst}\nn &&\qquad = \sum_{j=0}^{j_0} (h/\sigma(h))^{j} {E(H_{j}(\eta)
f(\eta))\over\sqrt {j!}} :(G')^{j}:(I_{[a,b]}) +o({h\over\sigma (h)})^{j_0}\nn
\eea in $L^2$. Here $H_j$ is the $j$-th Hermite polynomial. Also
$:(G')^{j}:(I_{[a,b]})$ is a $j $-th order Wick power Gaussian chaos
constructed from the Gaussian field $ G'(g) $, with covariance \[ E(G'(g)G'(\wt
g)) = \int \int \rho (x-y)g(x)\wt g(y) dx dy\label{3.7bqs}, \] where $
\rho(s)={1/2}{d^{2}\over ds^2}\sigma^2(s)$.


title:
The sum rules for the spin dependent structure functions corresponding
  to the moment at $n=0$

abstract:
  Sum rules for the spin dependent structure functions corresponding to the
moment at $n=0$ derived from the current algebra based on the canonical
quantization on the null-plane are reviewed.


title: Superfluid-Insulator and Roughening Transitions in Domain Walls

abstract:
  We have performed quantum Monte Carlo simulations to investigate the
superfluid behavior of one- and two-dimensional interfaces separating
checkerboard solid domains. The system is described by the hard-core
Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with
Ref.1, we find that (i) the interface remains superfluid in a wide range of
interaction strength before it undergoes a superfluid-insulator transition;
(ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is
accompanied by the roughening transition, driven by proliferation of charge 1/2
quasiparticles; (iii) in two dimensions, the transition belongs to the 3D U(1)
universality class and the interface remains smooth. Similar phenomena are
expected for domain walls in quantum antiferromagnets.


title: Influence of Rb, Cs and Ba on Superconductivity of Magnesium Diboride

abstract:
  Magnesium diboride has been thermally treated in the presence of Rb, Cs, and
Ba. Magnetic susceptibility shows onsets of superconductivity in the resulting
samples at 52K (Rb), 58K (Cs) and 45K (Ba). Room-temperature 11B NMR indicates
to cubic symmetry of the electric field gradient at boron site for the samples
reacted with Rb and Cs, in contrast to the axial symmetry in the initial MgB2
and in the sample treated with Ba.


title: Photon strength distributions in stable even-even molybdenum isotopes

abstract:
  Electromagnetic dipole-strength distributions up to the particle separation
energies are studied for the stable even-even nuclides $^{92,94,96,98,100}$Mo
in photon scattering experiments at the superconducting electron accelerator
ELBE of the Forschungszentrum Dresden-Rossendorf. The influence of inelastic
transitions to low-lying excited states has been corrected by a simulation of
$\gamma$ cascades using a statistical model. After corrections for branching
ratios of ground-state transitions, the photon-scattering cross-sections
smoothly connect to data obtained from $(\gamma,n)$-reactions. With the newly
determined electromagnetic dipole response of nuclei well below the particle
separation energies the parametrisation of the isovector giant-dipole resonance
is done with improved precision.


title:
Branching ratio measurement of $K_S\to \gamma \gamma$ decay using a pure
  $\ks$ beam in the KLOE detector

abstract:
  We have analyzed 1.62 fb$^{-1}$ of $e^{+}e^{-}$ collisions at a center of
mass energy $\sim M_{\phi}$ collected by the KLOE experiment at DA$\Phi$NE.
This sample corresponds to a production of $\sim$ 1.7 billion of $\ks$ $\kl$
pairs which allowed us to search for the rare $K_S\to \gamma\gamma$ decay.
$K_S$ are tagged by the $K_L$ interaction in the calorimeter and the signal is
searched for by requiring two additional prompt photons. Strong kinematic
requirements reduce the initial 0.5$\times 10^6$ events to 2300 candidates from
which we extract a signal of 600 $\pm$ 35 events. By normalizing to the $\ks
\to 2 \pi^0$ decays counted in the same sample, the measured value of BR($\ks
\to \gamma\gamma$) is (2.27 $\pm 0.13(stat.) ^{+0.03}_{-0.04} (syst.)) \times
10^{-6}$, in agreement with $O(P^4)$ Chiral Perturbation Theory predictions.


title:
The Projected Rotational Velocity Distribution of a Sample of OB stars
  from a Calibration based on Synthetic He I lines

abstract:
  We derive projected rotational velocities (vsini) for a sample of 156
Galactic OB star members of 35 clusters, HII regions, and associations. The HeI
lines at $\lambda\lambda$4026, 4388, and 4471A were analyzed in order to define
a calibration of the synthetic HeI full-widths at half maximum versus stellar
vsini. A grid of synthetic spectra of HeI line profiles was calculated in
non-LTE using an extensive helium model atom and updated atomic data. The
vsini's for all stars were derived using the He I FWHM calibrations but also,
for those target stars with relatively sharp lines, vsini values were obtained
from best fit synthetic spectra of up to 40 lines of CII, NII, OII, AlIII,
MgII, SiIII, and SIII. This calibration is a useful and efficient tool for
estimating the projected rotational velocities of O9-B5 main-sequence stars.
The distribution of vsini for an unbiased sample of early B stars in the
unbound association Cep OB2 is consistent with the distribution reported
elsewhere for other unbound associations.


title:
A Possibility of Volume Refraction of Negative Relativistic Particles in
  Bent Crystals

abstract:
  The volume coherent deflection of high-energy positive and negative particles
in uniformly bent crystals is studied. The general analysis of potential
scattering shows that the standard screening potential for a large class of
collisions can cause the volume refraction for negative particles (antiprotons,
electrons) instead of the volume reflection for positive particles (proton,
positrons).


title: Closed form solutions for symmetric water filling games

abstract:
  We study power control in optimization and game frameworks. In the
optimization framework there is a single decision maker who assigns network
resources and in the game framework users share the network resources according
to Nash equilibrium. The solution of these problems is based on so-called
water-filling technique, which in turn uses bisection method for solution of
non-linear equations for Lagrange multiplies. Here we provide a closed form
solution to the water-filling problem, which allows us to solve it in a finite
number of operations. Also, we produce a closed form solution for the Nash
equilibrium in symmetric Gaussian interference game with an arbitrary number of
users. Even though the game is symmetric, there is an intrinsic hierarchical
structure induced by the quantity of the resources available to the users. We
use this hierarchical structure to perform a successive reduction of the game.
In addition, to its mathematical beauty, the explicit solution allows one to
study limiting cases when the crosstalk coefficient is either small or large.
We provide an alternative simple proof of the convergence of the Iterative
Water Filling Algorithm. Furthermore, it turns out that the convergence of
Iterative Water Filling Algorithm slows down when the crosstalk coefficient is
large. Using the closed form solution, we can avoid this problem. Finally, we
compare the non-cooperative approach with the cooperative approach and show
that the non-cooperative approach results in a more fair resource distribution.


title: Cohomology theories for homotopy algebras and noncommutative geometry

abstract:
  This paper builds a general framework in which to study cohomology theories
of strongly homotopy algebras, namely $A_\infty, C_\infty$ and
$L_\infty$-algebras. This framework is based on noncommutative geometry as
expounded by Connes and Kontsevich. The developed machinery is then used to
establish a general form of Hodge decomposition of Hochschild and cyclic
cohomology of $C_\infty$-algebras. This generalizes and puts in a conceptual
framework previous work by Loday and Gerstenhaber-Schack.


title:
On the conundrum of deriving exact solutions from approximate master
  equations

abstract:
  We derive the exact time-evolution for a general quantum system under the
influence of pure phase-noise and demonstrate that for a Gaussian initial state
of the bath, the exact result can be obtained also within a perturbative
time-local master equation approach already in second order of the system-bath
coupling strength. We reveal that this equivalence holds if the initial state
of the bath can be mapped to a Gaussian phase-space distribution function.
Moreover, we discuss the relation to the standard Bloch-Redfield approach.


title: Star Formation in Massive Low Surface Brightness Galaxies

abstract:
  Massive low surface brightness galaxies have disk central surface
brightnesses at least one magnitude fainter than the night sky, but total
magnitudes and masses that show they are among the largest galaxies known. Like
all low surface brightness (LSB) galaxies, massive LSB galaxies are often in
the midst of star formation yet their stellar light has remained diffuse,
raising the question of how star formation is proceeding within these galaxies.
We have undertaken a multi-wavelength study to clarify the structural
parameters and stellar and gas content of these enigmatic systems. The results
of these studies, which include HI, CO, optical, near UV, and far UV images of
the galaxies will provide the most in depth study done to date of how, when,
and where star formation proceeds within this unique subset of the galaxy
population.


title: A proposal for the missing mass: it is just the outer, far one

abstract:
  The paper has benn withdrawn because the computation of the external virial
contains an error which invalidate the main result.


title:
Dynamics of the Chain of Oscillators with Long-Range Interaction: From
  Synchronization to Chaos

abstract:
  We consider a chain of nonlinear oscillators with long-range interaction of
the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha
<2. In the continues limit the system's dynamics is described by the
Ginzburg-Landau equation with complex coefficients. Such a system has a new
parameter alpha that is responsible for the complexity of the medium and that
strongly influences possible regimes of the dynamics. We study different
spatial-temporal patterns of the dynamics depending on alpha and show
transitions from synchronization of the motion to broad-spectrum oscillations
and to chaos.


title:
Mach Cones and Hydrodynamic Flow: Probing Big Bang Matter in the
  Laboratory

abstract:
  A critical discussion of the present signals for the phase transition to
quark-gluon plasma (QGP) is given. Since hadronic rescattering models predict
much larger flow than observed from 1 to 50 A GeV laboratory bombarding
energies, this observation is interpreted as potential evidence for a
first-order phase transition at high baryon density. A detailed discussion of
the collective flow as a barometer for the equation of state (EoS) of hot dense
matter at RHIC follows. Here, hadronic rescattering models can explain < 30 %
of the observed elliptic flow v_2 for $p_T > 2$ GeV/c. This is interpreted as
an evidence for the production of superdense matter at RHIC. The connection of
v_2 to jet suppression is examined. A study of Mach shocks generated by fast
partonic jets propagating through the QGP is given. The main goal is to take
into account different types of collective motion during the formation and
evolution of this matter. A significant deformation of Mach shocks in central
Au+Au collisions at RHIC and LHC energies as compared to the case of jet
propagation in a static medium is predicted. A new hydrodynamical study of jet
energy loss is presented.


title:
Simulations of turbulent convection in rotating young solar-like stars:
  Differential rotation and meridional circulation

abstract:
  We present the results of three-dimensional simulations of the deep
convective envelope of a young (10 Myr) one-solar-mass star, obtained with the
Anelastic Spherical Harmonic code. Since young stars are known to be faster
rotators than their main sequence counterparts, we have systematically studied
the impact of the stellar rotation speed, by considering stars spinning up to
five times as fast as the Sun. The aim of these nonlinear models is to
understand the complex interactions between convection and rotation. We discuss
the influence of the turbulence level and of the rotation rate on the intensity
and the topology of the mean flows. For all of the computed models, we find a
solar-type superficial differential rotation, with an equatorial acceleration,
and meridional circulation that exhibits a multicellular structure. Even if the
differential rotation contrast decreases only marginally for high rotation
rates, the meridional circulation intensity clearly weakens according to our
simulations. We have also shown that, for Taylor numbers above a certain
threshold (Ta>10^9), the convection can develop a vacillating behavior. Since
simulations with high turbulence levels and rotation rates exhibit strongly
cylindrical internal rotation profiles, we have considered the influence of
baroclinic effects at the base of the convective envelope of these young Suns,
to see whether such effect can modify the otherwise near cylindrical profiles
to produce more conical, solar-like profiles.


title: Non-Relativistic Strings in Expanding Spacetime

abstract:
  We obtain a non-relativistic diffeomorphism invariant string action as a
special limit of the Nambu-Goto action in an FLRW background. We use this
action to study non-relativistic string dynamics in an expanding universe and
construct an analytic model describing the macroscopic properties of
non-relativistic string networks. The non-relativistic constraint equations
allow arbitrarily small string velocities and thus a `frustrated' equation of
state for non-interacting strings can be obtained without the need of a
velocity damping mechanism. Assuming that colliding string segments reconnect
by exchange of partners, non-relativistic string networks exhibit scaling
behaviour, but with enhanced energy densities due to the reduced average string
velocity. Non-relativistic string networks can be relevant in several contexts
in condensed matter physics and cosmology.


title:
k-Disjunctive cuts and a finite cutting plane algorithm for general
  mixed integer linear programs

abstract:
  In this paper we give a generalization of the well known split cuts of Cook,
Kannan and Schrijver to cuts which are based on multi-term disjunctions. They
will be called k-disjunctive cuts. The starting point is the question what kind
of cuts is needed for a finite cutting plane algorithm for general mixed
integer programs. We will deal with this question in detail and derive cutting
planes based on k-disjunctions related to a given cut vector. Finally we will
show how a finite cutting plane algorithm can be established using these cuts
in combination with Gomory mixed integer cuts.


title: Implementing universal quantum gates in coupled cavities

abstract:
  We study a linear array of coupled cavities interacting with two level
systems and show how to construct individually addressable qubits in this
system from the long-lived atom-photon excitations (polaritons) at each site.
We derive the system dynamics and show that is described by an XY Hamiltonian.
We proceed by showing how to implement non-local quantum gates and show that
combined with the inherent ability for individual addressing, universal quantum
computation is possible in this system. We finally discuss the prospects for
experimental implementation using various technologies involving dopants as
atoms, quantum dots or Cooper pair boxes.


title: A computation of invariants of a rational self-map

abstract:
  I compute the dynamical degrees in C. Voisin's example of a rational self-map
of the variety of lines on a cubic fourfold.


title:
Potential density of rational points on the variety of lines of a cubic
  fourfold

abstract:
  We prove the potential density of rational points on the variety of lines of
a sufficiently general cubic fourfold defined over a number field, where
``sufficiently general'' means that a condition of Terasoma type is satisfied.
These varieties have trivial canonical bundle and have geometric Picard group
equal to $\mathbb{Z}$.


title: Nonequilibrium Renormalization Theory I

abstract:
  In the present article we consider some general class of divergent diagrams
in Keldysh diagram technique. These divergences arise for nonequilibrium matter
and closely related to the divergences in the kinetic theory of gases. We
suggest a scheme of renormalization of such divergences and illustrate it on
some examples. In the other papers of these series we develop the general
theory of renormalization of nonequilibrium diagram technique. The fact that
thermal divergences in non-equilibrium diagram technique can be renormalized
leads to the following consequence: to prove that the system tends to the
thermal equilibrium one should to take into account the behaviour of the system
on its boundary. In this paper we illustrate this fact on Bogoliubov derivation
of kinetic equations.


title:
Ramanujan's Harmonic Number Expansion into Negative Powers of a
  Triangular Number

abstract:
  An algebraic transformation of the DeTemple-Wang half-integer approximation
to the harmonic series produces the general formula and error estimate for the
Ramanujan expansion for the nth harmonic number into negative powers of the nth
triangular number. We also discuss the history of the Ramanujan expansion for
the nth harmonic number as well as sharp estimates of its accuracy, with
complete proofs, and we compare it with other approximative formulas.


title: Symplectic $C_\infty$-algebras

abstract:
  In this paper we show that a strongly homotopy commutative (or $C_\infty$-)
algebra with an invariant inner product on its cohomology can be uniquely
extended to a symplectic $C_\infty$-algebra (an $\infty$-generalisation of a
commutative Frobenius algebra introduced by Kontsevich). This result relies on
the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a
$\ci$-algebra and does not generalize to algebras over other operads.


title:
Threshold Resummation Effects in the Associated Production of Chargino
  and Neutralino at Hadron Colliders

abstract:
  We investigate the QCD effects in the associated production of the chargino
and the neutralino, $\tilde\chi^\pm_{1}$ and $\tilde\chi^0_{2}$, in the Minimal
Supersymmetric Standard Model (MSSM) at both the Fermilab Tevatron and the CERN
Large Hadron Collider (LHC). We include the next-to-leading order (NLO) QCD
corrections (including supersymmetric QCD) and the threshold resummation
effects. Our results show that, compared to the NLO predictions, the threshold
resummation effects can increase the total cross sections by 3.6% and 3.9% for
the associated production of $\tilde\chi^+_{1}\tilde\chi^0_{2}$ and
$\tilde\chi^-_{1}\tilde\chi^0_{2}$ at the LHC, respectively, and by 4.7% for
those of $\tilde\chi^\pm_{1}\tilde\chi^0_{2}$ at the Tevatron. In the invariant
mass distributions the resummation effects are significant for large invariant
mass. The threshold resummation reduces the dependence of the total cross
sections at the LHC (Tevatron) on the renormalization/factorization scales to
5% (4%) from up to 7% (11%) at NLO.


title: Stable modification of relative curves

abstract:
  We generalize theorems of Deligne-Mumford and de Jong on semi-stable
modifications of families of proper curves. The main result states that after a
generically \'etale alteration of the base any (not necessarily proper) family
of multipointed curves with semi-stable generic fiber admits a minimal
semi-stable modification. The latter can also be characterized by the property
that its geometric fibers have no certain exceptional components. The main step
of our proof is uniformization of one-dimensional extensions of valued fields.
Riemann-Zariski spaces are then used to obtain the result over any integral
base.


title:
Challenging SO(10) SUSY GUTs with family symmetries through FCNC
  processes

abstract:
  We perform a detailed analysis of the SO(10) SUSY GUT model with D3 family
symmetry of Dermisek and Raby (DR). The model is specified in terms of 24
parameters and predicts, as a function of them, the whole MSSM set of
parameters at low energy scales. Concerning the SM subset of such parameters,
the model is able to give a satisfactory description of the quark and lepton
masses, of the PMNS matrix and of the CKM matrix. We perform a global fit to
the model, including flavour changing neutral current (FCNC) processes Bs -->
mu+ mu-, B --> Xs gamma, B --> Xs l+ l- and the B(d,s) - bar B(d,s) mass
differences Delta M(d,s) as well as the flavour changing (FC) process B+ -->
tau+ nu. These observables provide at present the most sensitive probe of the
SUSY mass spectrum and couplings predicted by the model. Our analysis
demonstrates that the simultaneous description of the FC observables in
question represents a serious challenge for the DR model, unless the masses of
the scalars are moved to regions which are problematic from the point of view
of naturalness and probably beyond the reach of the LHC. We emphasize that this
problem could be a general feature of SUSY GUT models with third generation
Yukawa unification and weak-scale minimal flavour violation.


title:
Quantum breathers in capacitively coupled Josephson junctions:
  Correlations, number conservation, and entanglement

abstract:
  We consider the classical and quantum dynamics of excitations in a system of
two capacitively coupled Josephson junctions. In the classical case the
equations of motion admit discrete breather solutions, which are time periodic
and localized predominantly on one of the junctions. In the quantum case
breather states are found in the central part of the energy spectrum of the
confined nonescaping states of the system. We perform a systematic analysis of
their tunneling frequency, site correlations, fluctuations of the number of
quanta, and entanglement. Quantum breather states show strong site correlation
of quanta and are characterized by a strong excitation of quanta on one
junction which perform slow coherent tunneling motion from one junction to the
other. They suppress fluctuations of the total number of excited quanta.
Quantum breather states are the least entangled states among the group of
eigenstates in the same range of the energy spectrum. We describe how quantum
breather excitations could be experimentally observed by employing the already
developed techniques for quantum information processing using Josephson
junctions.


title: On the regularity of geodesic rays associated to test configurations

abstract:
  Geodesic rays of class C^{1,1} are constructed for any test configuration of
a positive line bundle L on X using resolution of singularities. The
construction reduces to finding a subsolution of the corresponding Monge-Ampere
equation. Geometrically, this is accomplished by the use a positive line bundle
on the resolution which is trivial outside of the exceptional divisor.


title:
Stretched-exponential decay functions from a self-consistent model of
  dielectric relaxation

abstract:
  There are many materials whose dielectric properties are described by a
stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation
function. Its physical origin and statistical-mechanical foundation have been a
matter of debate in the literature. In this paper we suggest a model of
dielectric relaxation, which naturally leads to a stretched exponential decay
function. Some essential characteristics of the underlying charge conduction
mechanisms are considered. A kinetic description of the relaxation and charge
transport processes is proposed in terms of equations with time-fractional
derivatives.


title:
Control parameters in turbulence, Self Organized Criticality and
  ecosystems

abstract:
  From the starting point of the well known Reynolds number of fluid turbulence
we propose a control parameter $R$ for a wider class of systems including
avalanche models that show Self Organized Criticality (SOC) and ecosystems. $R$
is related to the driving and dissipation rates and from similarity analysis we
obtain a relationship $R\sim N^{\beta_N}$ where $N$ is the number of degrees of
freedom. The value of the exponent $\beta_N$ is determined by detailed
phenomenology but its sign follows from our similarity analysis. For SOC,
$R=h/\epsilon$ and we show that $\beta_N<0$ hence we show independent of the
details that the transition to SOC is when $R \to 0$, in contrast to fluid
turbulence, formalizing the relationship between turbulence (since $\beta_N
>0$, $R \to \infty$) and SOC ($R=h/\epsilon\to 0$). A corollary is that SOC
phenomenology, that is, power law scaling of avalanches, can persist for finite
$R$ with unchanged exponent if the system supports a sufficiently large range
of lengthscales; necessary for SOC to be a candidate for physical systems. We
propose a conceptual model ecosystem where $R$ is an observable parameter which
depends on the rate of throughput of biomass or energy; we show this has
$\beta_N>0$, so that increasing $R$ increases the abundance of species,
pointing to a critical value for species 'explosion'.


title: Four-Group Decodable Space-Time Block Codes

abstract:
  Two new rate-one full-diversity space-time block codes (STBC) are proposed.
They are characterized by the \emph{lowest decoding complexity} among the known
rate-one STBC, arising due to the complete separability of the transmitted
symbols into four groups for maximum likelihood detection. The first and the
second codes are delay-optimal if the number of transmit antennas is a power of
2 and even, respectively. The exact pair-wise error probability is derived to
allow for the performance optimization of the two codes. Compared with existing
low-decoding complexity STBC, the two new codes offer several advantages such
as higher code rate, lower encoding/decoding delay and complexity, lower
peak-to-average power ratio, and better performance.


title:
P-V-T equation of state of epsilon iron and its densities at core
  conditions

abstract:
  The author's new p-V-T Equation of State is tested against the available
experiments of epsilon iron. The root-mean-square-deviations (RMSD) of the
molar volume, pressure, and temperature are 0.021 cm3, 2.0 GPa and 144.9 K
respectively. Separating the experiments into 200 K ranges the new EoS was
compared to the most widely used finite strain, interatomic potential, and
empirical isothermal EoSs such as the Burch-Murnaghan, the Vinet, and the
Roy-Roy respectively. Correlation coefficients, RMSDs of the residuals and
Akaike Information Criteria were used for evaluating the fittings. Based on
these fitting parameters the new p-V-T EoS is equal or better than the
conventional isothermal EoSs. The newly defined parameters were used to
calculate the density of the inner core. The calculated densities are
significantly lower than the current consensus indicating that it might be too
early excluding the possibility of a pure iron-nickel core with no light
elements.


title:
Atomistic Simulations of the Mechanical Properties of 'Super' Carbon
  Nanotubes

abstract:
  The mechanical properties of the so-called `super' carbon nanotubes (STs) are
investigated using classical molecular dynamics simulations. The STs are built
from single walled carbon nanotubes (SWCNTs) connected by Y-like junctions
forming an ordered carbon nanotube network that is then rolled into a seamless
cylinder. We observed that the ST behavior under tensile tests is similar to
the one presented by fishing nets. This interesting behavior provides a way to
vary the accessible channels to the inner parts of STs by applying external
mechanical load. The Young's modulus is dependent on the ST chirality and it
inversely varies with the ST radius. Smaller reduction of breaking strain
values due to temperature increase is predicted for zigzag STs compared to
SWCNTs. The results show that, for STs with radius ~ 5 nm, the junctions
between the constituent SWCNTs play an important role on the fracture process.
The Young's modulus and tensile strength were estimated for hierarchical
higher-order STs using scaling laws related to the ST fractal dimension. The
obtained mechanical properties suggest that STs may be used in the development
of new porous, flexible, and high-strength materials.


title: Coherent Bayesian analysis of inspiral signals

abstract:
  We present in this paper a Bayesian parameter estimation method for the
analysis of interferometric gravitational wave observations of an inspiral of
binary compact objects using data recorded simultaneously by a network of
several interferometers at different sites. We consider neutron star or black
hole inspirals that are modeled to 3.5 post-Newtonian (PN) order in phase and
2.5 PN in amplitude. Inference is facilitated using Markov chain Monte Carlo
methods that are adapted in order to efficiently explore the particular
parameter space. Examples are shown to illustrate how and what information
about the different parameters can be derived from the data. This study uses
simulated signals and data with noise characteristics that are assumed to be
defined by the LIGO and Virgo detectors operating at their design
sensitivities. Nine parameters are estimated, including those associated with
the binary system, plus its location on the sky. We explain how this technique
will be part of a detection pipeline for binary systems of compact objects with
masses up to $20 \sunmass$, including cases where the ratio of the individual
masses can be extreme.


title: On the quantization of conjugacy classes

abstract:
  Let G be a compact, simple, simply connected Lie group. A theorem of
Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the
twisted equivariant K-homology at level k+h, where h is the dual Coxeter
number. In this paper, we review this result using the language of
Dixmier-Douady bundles. We show that the additive generators of the group
R_k(G) are obtained as K-homology push-forwards of the fundamental classes of
conjugacy classes in G.


title: Universality in quantum chaos and the one parameter scaling theory

abstract:
  We adapt the one parameter scaling theory (OPT) to the context of quantum
chaos. As a result we propose a more precise characterization of the
universality classes associated to Wigner-Dyson and Poisson statistics which
takes into account Anderson localization effects. Based also on the OPT we
predict a new universality class in quantum chaos related to the
metal-insulator transition and provide several examples. In low dimensions it
is characterized by classical superdiffusion or a fractal spectrum, in higher
dimensions it can also have a purely quantum origin as in the case of
disordered systems. Our findings open the possibility of studying the metal
insulator transition experimentally in a much broader type of systems.

categories: cond-mat.dis-nn cond-mat.mes-hall nlin.CD quant-ph


title: Haar Wavelets and the Origin of Gravitational Inertia

abstract:
  Spacetime is considered to be everywhere Minkowski except at the location
where a signal wave of energy interacts with the gravitational field. The
conformal metric f[k(x-vt)]Nuv is suitably chosen to represent this
interaction, where f[k(x-vt)]is a generalized wave or signal function.
Parametrized and Taylor expanded at zero, the spacetime metric is transformed
into a Haar wavelet having parameter width tau. Applying the Haar metric to the
time component of General Relativistic wave equation reduces it from a second
ordered covariant differential equation to a first ordered partial differential
equation that allows the Einstein Tensor to be easily be expressed in the
familiar Poisson form for gravitation. By comparison with the matter density of
this equation, to the Haar-Einstein result, shows that the wavelength of a
graviton becomes the fundamental source for gravitational attraction. Since the
signal wave is unidirectional, it strongly supports Machs assumption that
inertia arises from all the matter in the universe. Furthermore, because the
Haar metric is conformal, the signal metric is solved for exactly.


title:
Bose-Einstein condensation of diquark molecules in three-flavor quark
  matter

abstract:
  We study the phase diagram of strongly interacting matter with three quark
flavors at low and intermediate densities and non-zero temperatures in the
framework of an NJL-type model with four-point interactions. At large
densities, when the interactions are weak due to asymptotic freedom, quarks
form loosely bound Cooper pairs. However, when the density decreases,
interactions become stronger and quark Cooper pairs transform smoothly into
tightly bound diquark molecules. We find that such molecules are stable at low
density and temperature and that they dissociate above a temperature $T_{\rm
diss}$ of the order of the chiral phase transition temperature $T_c \sim 170$
MeV. We also explore the conditions under which these molecules undergo
Bose-Einstein condensation (BEC). We find that BEC is only possible if we
increase the attractive interaction in the diquark channel to (probably
unrealistically) large values.


title: Curvaton reheating allows TeV Hubble scale in NO inflation

abstract:
  Curvaton reheating is studied in non-oscillatory (NO) models of inflation,
with the aim to obtain bounds on the parameters of curvaton models and find out
whether low scale inflation can be attained. Using a minimal curvaton model, it
is found that the allowed parameter space is considerably larger than in the
case of the usual oscillatory inflation models. In particular, inflation with
Hubble scale as low as 1 TeV is comfortably allowed.


title: Phenomenology for Supernova Ia Data Based on a New Cosmic Time

abstract:
  A new phenomenological theory for the expansion of our universe is presented.
Because fundamental supporting theory is still in development, its discussion
is not presented in this paper. The theory is based on a new algebraic
expression for cosmic time G Rho t^2=3/32Pi, which correctly predicts the WMAP
measured cosmological constants and the fundamental Hubble parameter H(t) for
the expansion of the universe. A replacement for dark matter, called here "dark
mass", is proposed which scales as with the expansion and incorporated. It does
not react with ordinary matter, except gravitationally, and produces flat
rotational curves for spiral galaxies. Also a new expression for the
approaching velocity of radiation in a closed 3-sphere expanding universe is
given that accounts for the early degrading negative approach of radiation for
z > 1.7. The expression is v = Hr-c. Combining these three elements produces a
luminosity distance dL that successfully predicts the apparent magnitude of
exploding supernova Ia stars and even the new gamma ray bursts with no need for
dark energy or acceleration of the expansion of the universe.


title: Inference on inspiral signals using LISA MLDC data

abstract:
  In this paper we describe a Bayesian inference framework for analysis of data
obtained by LISA. We set up a model for binary inspiral signals as defined for
the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte
Carlo (MCMC) algorithm to facilitate exploration and integration of the
posterior distribution over the 9-dimensional parameter space. Here we present
intermediate results showing how, using this method, information about the 9
parameters can be extracted from the data.


title: Minimum-error discrimination between mixed quantum states

abstract:
  We derive a general lower bound on the minimum-error probability for {\it
ambiguous discrimination} between arbitrary $m$ mixed quantum states with given
prior probabilities. When $m=2$, this bound is precisely the well-known
Helstrom limit. Also, we give a general lower bound on the minimum-error
probability for discriminating quantum operations. Then we further analyze how
this lower bound is attainable for ambiguous discrimination of mixed quantum
states by presenting necessary and sufficient conditions related to it.
Furthermore, with a restricted condition, we work out a upper bound on the
minimum-error probability for ambiguous discrimination of mixed quantum states.
Therefore, some sufficient conditions are obtained for the minimum-error
probability attaining this bound. Finally, under the condition of the
minimum-error probability attaining this bound, we compare the minimum-error
probability for {\it ambiguously} discriminating arbitrary $m$ mixed quantum
states with the optimal failure probability for {\it unambiguously}
discriminating the same states.


title: Quantum Flexoelectricity in Low Dimensional Systems

abstract:
  Symmetry breaking at surfaces and interfaces and the capability to support
large strain gradients in nanoscale systems enable new forms of
electromechanical coupling. Here we introduce the concept of quantum
flexoelectricity, a phenomenon that is manifested when the mechanical
deformation of non-polar quantum systems results in the emergence of net dipole
moments and hence linear electromechanical coupling proportional to local
curvature. The concept is illustrated in carbon systems, including
polyacetylene and nano graphitic ribbons. Using density functional theory
calculations for systems made of up to 400 atoms, we determine the
flexoelectric coefficients to be of the order of ~ 0.1 e, in agreement with the
prediction of linear theory. The implications of quantum flexoelectricity on
electromechanical device applications, and physics of carbon based materials
are discussed.


title: Learning Probabilistic Models of Word Sense Disambiguation

abstract:
  This dissertation presents several new methods of supervised and unsupervised
learning of word sense disambiguation models. The supervised methods focus on
performing model searches through a space of probabilistic models, and the
unsupervised methods rely on the use of Gibbs Sampling and the Expectation
Maximization (EM) algorithm. In both the supervised and unsupervised case, the
Naive Bayesian model is found to perform well. An explanation for this success
is presented in terms of learning rates and bias-variance decompositions.


title:
Transient current in a quantum dot asymmetrically coupled to metallic
  leads

abstract:
  The time-dependent non-crossing approximation is used to study the transient
current in a single electron transistor attached asymmetrically to two leads
following a sudden change in the energy of the dot level. We show that for
asymmetric coupling, sharp features in the density of states of the leads can
induce oscillations in the current through the dot. These oscillations persist
to much longer timescales than the timescale for charge fluctuations. The
amplitude of the oscillations increases as the temperature or source-drain bias
across the dot is reduced and saturates for values below the Kondo temperature.
We discuss the microscopic origin of these oscillations and comment on the
possibility for their experimental detection.


title: Peculiar Nature of Snake States in Graphene

abstract:
  We study the dynamics of the electrons in a non-uniform magnetic field
applied perpendicular to a graphene sheet in the low energy limit when the
excitation states can be described by a Dirac type Hamiltonian. We show that as
compared to the two-dimensional electron gas (2DEG) snake states in graphene
exibit peculiar properties related to the underlying dynamics of the Dirac
fermions. The current carried by snake states is locally uncompensated even if
the Fermi energy lies between the first non-zero energy Landau levels of the
conduction and valence bands. The nature of these states is studied by
calculating the current density distribution. It is shown that besides the
snake states in finite samples surface states also exist.


title: Peeling Bifurcations of Toroidal Chaotic Attractors

abstract:
  Chaotic attractors with toroidal topology (van der Pol attractor) have
counterparts with symmetry that exhibit unfamiliar phenomena. We investigate
double covers of toroidal attractors, discuss changes in their morphology under
correlated peeling bifurcations, describe their topological structures and the
changes undergone as a symmetry axis crosses the original attractor, and
indicate how the symbol name of a trajectory in the original lifts to one in
the cover. Covering orbits are described using a powerful synthesis of kneading
theory with refinements of the circle map. These methods are applied to a
simple version of the van der Pol oscillator.


title: Spin transport in proximity induced ferromagnetic graphene

abstract:
  Magnetic gates in close proximity to graphene can induce ferromagnetic
correlations. We study the effect of such induced magnetization dependent
Zeeman splittings on the graphene transport properties. We estimate that
induced spin splittings of the order of \Delta ~ 5 meV could be achieved with
the use of magnetic insulator gates, e.g. EuO-gates, deposited on top of
graphene. We demonstrate that such splittings in proximity induced
ferromagnetic graphene could be determined directly from the tunneling
resonances in the linear response conductance, as the top gate creates also a
tunable barrier in the graphene layer. We show how such splittings could also
be determined independently by magnetoresistance measurements in a spin-valve
geometry. Because the spin polarization of the current near the Dirac point
increases with the length of the barrier, long magnetic gates are desirable for
determining \Delta experimentally.


title: The worm-like chain model at small and large stretch

abstract:
  The relation between force and stretch in the worm-like chain model of
entropic elasticity is examined. Although no closed-form expression is valid
for all values of forcing, solutions in the form of asymptotic series can be
obtained under conditions of small and large applied force. The small and large
stretch limits correspond to regular and boundary layer perturbation problems,
respectively. The perturbation problems are solved and series solutions
obtained for force as a function of stretch. The form of the asymptotic series
suggest a uniform approximation valid for all stretch that is an improvement on
existing approximations.


title: M5-branes and Wilson Surfaces

abstract:
  We investigate the M5-brane description of the Wilson surface operators in
six-dimensional (2,0) superconformal field theory from AdS/CFT correspondence.
We consider the Wilson surface operators in high-dimensional representation,
whose description could be M5-brane string soliton solutions in $AdS_7\times
S^4$ background. We construct such string soliton solutions from the covariant
M5-brane equations of motion and discuss their properties. The supersymmetry
analysis shows that these solutions are half-BPS. We also discuss the subtle
issue on the boundary terms.


title:
Clifford Algebra of the Vector Space of Conics for decision boundary
  Hyperplanes in m-Euclidean Space

abstract:
  In this paper we embed $m$-dimensional Euclidean space in the geometric
algebra $Cl_m $ to extend the operators of incidence in ${R^m}$ to operators of
incidence in the geometric algebra to generalize the notion of separator to a
decision boundary hyperconic in the Clifford algebra of hyperconic sections
denoted as ${Cl}({Co}_{2})$. This allows us to extend the concept of a linear
perceptron or the spherical perceptron in conformal geometry and introduce the
more general conic perceptron, namely the {elliptical perceptron}. Using
Clifford duality a vector orthogonal to the decision boundary hyperplane is
determined. Experimental results are shown in 2-dimensional Euclidean space
where we separate data that are naturally separated by some typical plane conic
separators by this procedure. This procedure is more general in the sense that
it is independent of the dimension of the input data and hence we can speak of
the hyperconic elliptic perceptron.


title:
Deep Chandra and multicolor HST observations of the jets of 3C 371 and
  PKS 2201+044

abstract:
  This paper presents multiwavelength imaging and broad-band spectroscopy of
the relativistic jets in the two nearby radio galaxies 3C 371 and PKS 2201+044,
acquired with Chandra, HST, VLA, and Merlin. Radio polarization images are also
available. The two sources stand out as "intermediate'' between FRIs and FRIIs;
their cores are classified as BL Lacs, although broad and narrow optical
emission lines were detected at times. The multiwavelength images show jet
morphologies with the X-ray emission peaking closer to the nucleus than the
longer wavelengths. The jets are resolved at all wavelengths in a direction
perpendicular to the jet axis. The jets SEDs are consistent with a single
spectral component from radio to X-rays, interpreted as synchrotron emission.
The SEDs show a progressive softening from the inner to the outer regions of
the jet, indicating that the electron break energy moves to lower energies with
distance from the core. Overall, the X-ray and multiwavelength properties of
the jets of 3C 371 and PKS 2201+044 appear intermediate between those of FRIs
and FRIIs.


title: Representations of Clifford algebras with hyperbolic numbers

abstract:
  The representations of Clifford algebras and their involutions and
anti-involutions are fully investigated since decades. However, these
representations do sometimes not comply with usual conventions within physics.
A few simple examples are presented, which point out that the hyperbolic
numbers can close this gap.


title:
Interpretations for the X(4160) observed in the double charm production
  at B factories

abstract:
  Belle Collaboration has recently observed a new state, the X(4160), in the
process of double charm production $e^+e^-\to J/\psi+X(4160)$ followed by
$X(4160)\to D^*\bar{D^*}$. We discuss possible interpretations for the X(4160)
based on the NRQCD calculations and the potential model estimates for the
charmonium spectrum. We first focus on the D-wave spin-singlet $2^{-+}$
charmonium $^1D_2(2D)$, which is estimated to have a small production rate of
about 5% of that for $e^+e^-\to J/\psi+\eta_c(1S)$, and therefore is
incompatible with the observed data for X(4160). We then discuss the
possibility that the X(4160) is the known $J^{PC}=1^{--}$ charmonium state
$\psi(4160)$, which can be produced via two photon fragmentation, but the
production rate is much smaller than observed for $e^+e^-\to J/\psi+X(4160)$.
In contrast to above two possibilities, the $\eta_c(4S)$ assignment is a likely
one, which is supported by the observed relatively large production rate and
non-observation of $D\bar D$ decay of X(4160), but we have to understand why
$\eta_c(4S)$ has such a low mass, which deserves further studies. The P-wave
excited state $\chi_{c0}(3P)$ is also an interesting candidate, if the observed
broad peak around 3.8-3.9 GeV in the recoil mass of $D\bar D$ against $J/\psi$
in $e^++e^-\to J/\psi+D\bar D$ is due to the $\chi_{c0}(2P)$ state.
Measurements of production angular distributions will be helpful to distinguish
between $\eta_c(4S)$ and $\chi_{c0}(3P)$ assignments. Production mechanisms in
nonrelativistic QCD are emphasized.


title: Signatures of gravitational fixed points at the LHC

abstract:
  We study quantum-gravitational signatures at the Large Hadron Collider (LHC)
in the context of theories with extra spatial dimensions and a low fundamental
Planck scale in the TeV range. Implications of a gravitational fixed point at
high energies are worked out using Wilson's renormalisation group. We find that
relevant cross-sections involving virtual gravitons become finite. Based on
gravitational lepton pair production we conclude that the LHC is sensitive to a
fundamental Planck scale of up to 6 TeV.


title:
Coarse-Grained Finite-Temperature Theory for the Condensate in Optical
  Lattices

abstract:
  In this work, we derive a coarse-grained finite-temperature theory for a Bose
condensate in a one-dimensional optical lattice, in addition to a confining
harmonic trap potential. We start from a two-particle irreducible (2PI)
effective action on the Schwinger-Keldysh closed-time contour path. In
principle, this action involves all information of equilibrium and
non-equilibrium properties of the condensate and noncondensate atoms. By
assuming an ansatz for the variational function, i.e., the condensate order
parameter in an effective action, we derive a coarse-grained effective action,
which describes the dynamics on the length scale much longer than a lattice
constant. Using the variational principle, coarse-grained equations of motion
for the condensate variables are obtained. These equations include a
dissipative term due to collisions between condensate and noncondensate atoms,
as well as noncondensate mean-field. To illustrate the usefulness of our
formalism, we discuss a Landau instability of the condensate in optical
lattices by using the coarse-grained generalized Gross-Pitaevskii
hydrodynamics. We found that the collisional damping rate due to collisions
between the condensate and noncondensate atoms changes sign when the condensate
velocity exceeds a renormalized sound velocity, leading to a Landau instability
consistent with the Landau criterion. Our results in this work give an insight
into the microscopic origin of the Landau instability.


title: Direct Observation of Second Order Atom Tunnelling

abstract:
  Tunnelling of material particles through a classically impenetrable barrier
constitutes one of the hallmark effects of quantum physics. When interactions
between the particles compete with their mobility through a tunnel junction,
intriguing novel dynamical behaviour can arise where particles do not tunnel
independently. In single-electron or Bloch transistors, for example, the
tunnelling of an electron or Cooper pair can be enabled or suppressed by the
presence of a second charge carrier due to Coulomb blockade. Here we report on
the first direct and time-resolved observation of correlated tunnelling of two
interacting atoms through a barrier in a double well potential. We show that
for weak interactions between the atoms and dominating tunnel coupling,
individual atoms can tunnel independently, similar to the case in a normal
Josephson junction. With strong repulsive interactions present, two atoms
located on one side of the barrier cannot separate, but are observed to tunnel
together as a pair in a second order co-tunnelling process. By recording both
the atom position and phase coherence over time, we fully characterize the
tunnelling process for a single atom as well as the correlated dynamics of a
pair of atoms for weak and strong interactions. In addition, we identify a
conditional tunnelling regime, where a single atom can only tunnel in the
presence of a second particle, acting as a single atom switch. Our work
constitutes the first direct observation of second order tunnelling events with
ultracold atoms, which are the dominating dynamical effect in the strongly
interacting regime. Similar second-order processes form the basis of
superexchange interactions between atoms on neighbouring lattice sites of a
periodic potential, a central component of quantum magnetism.


title:
Mixed States Markov Random Fields with Symbolic Labels and
  Multidimensional Real Values

abstract:
  New theoretical results are presented here on the recently introduced model
called mixed states MRF. Such models were introduced in the context of image
motion analysis and are useful to represent information which can take both
discrete values accounting for symbolic states, and real values corresponding
to continuous measurements. In particular, results are given when the global
energy for the Gibbs formulation expressing the mixed states model, can be
decomposed into one term accounting for the discrete part of the model, and a
second term related to the continuous part. This decomposition theorem permits
to define conditional mixed states models in a very simple way.


title: Controlling passively-quenched single photon detectors by bright light

abstract:
  Single photon detectors based on passively-quenched avalanche photodiodes can
be temporarily blinded by relatively bright light, of intensity less than a
nanowatt. I describe a bright-light regime suitable for attacking a quantum key
distribution system containing such detectors. In this regime, all single
photon detectors in the receiver Bob are uniformly blinded by continuous
illumination coming from the eavesdropper Eve. When Eve needs a certain
detector in Bob to produce a click, she modifies polarization (or other
parameter used to encode quantum states) of the light she sends to Bob such
that the target detector stops receiving light while the other detector(s)
continue to be illuminated. The target detector regains single photon
sensitivity and, when Eve modifies the polarization again, produces a single
click. Thus, Eve has full control of Bob and can do a successful
intercept-resend attack. To check the feasibility of the attack, 3 different
models of passively-quenched detectors have been tested. In the experiment, I
have simulated the intensity diagrams the detectors would receive in a real
quantum key distribution system under attack. Control parameters and side
effects are considered. It appears that the attack could be practically
possible.


title:
Minimizing the ground state energy of an electron in a randomly deformed
  lattice

abstract:
  We provide a characterization of the spectral minimum for a random
Schr\"odinger operator of the form $H=-\Delta + \sum_{i \in
\Z^d}q(x-i-\omega_i)$ in $L^2(\R^d)$, where the single site potential $q$ is
reflection symmetric, compactly supported in the unit cube centered at 0, and
the displacement parameters $\omega_i$ are restricted so that adjacent single
site potentials do not overlap. In particular, we show that a minimizing
configuration of the displacements is given by a periodic pattern of densest
possible $2^d$-clusters of single site potentials.
  The main tool to prove this is a quite general phenomenon in the spectral
theory of Neumann problems, which we dub ``bubbles tend to the boundary.'' How
should a given compactly supported potential be placed into a bounded domain so
as to minimize or maximize the first Neumann eigenvalue of the Schr\"odinger
operator on this domain? For square or rectangular domains and reflection
symmetric potentials, we show that the first Neumann eigenvalue is minimized
when the potential sits in one of the corners of the domain and is maximized
when it sits in the center of the domain. With different methods we also show a
corresponding result for smooth strictly convex domains.


title: Regularly varying multivariate time series

abstract:
  A multivariate, stationary time series is said to be jointly regularly
varying if all its finite-dimensional distributions are multivariate regularly
varying. This property is shown to be equivalent to weak convergence of the
conditional distribution of the rescaled series given that, at a fixed time
instant, its distance to the origin exceeds a threshold tending to infinity.
The limit object, called the tail process, admits a decomposition in
independent radial and angular components. Under an appropriate mixing
condition, this tail process allows for a concise and explicit description of
the limit of a sequence of point processes recording both the times and the
positions of the time series when it is far away from the origin. The theory is
applied to multivariate moving averages of finite order with random coefficient
matrices.


title: Inflatable Dome for Moon, Mars, Asteroids and Satellites

abstract:
  On a planet without atmosphere, sustaining human life is very difficult and
dangerous, especially during short sunlit period when low temperature prevails.
To counter these environmental stresses, the author offer an innovative
artificial "Evergreen" dome, an inflated hemisphere with interiors continuously
providing a climate like that of Florida, Italy and Spain. The "Evergreen" dome
theory is developed, substantiated by computations that show it is possible for
current technology to construct and heat large enclosed volumes inexpensively.
Specifically, a satisfactory result is reached by using magnetic suspended at
high altitude sunlight reflectors and a special double thin film as a skin,
which concentrates solar energy inside the dome while, at the same time,
markedly decreasing the heat loss to exterior space. Offered design may be
employed for settlements on the Moon, Mars, asteroids and satellites.


title: Tidal Debris posing as Dark Galaxies

abstract:
  Debris sent into the intergalactic medium during tidal collisions can tell us
about several fundamental properties of galaxies, in particular their missing
mass, both in the form of cosmological Dark Matter and so-called Lost Baryons.
High velocity encounters, which are common in clusters of galaxies, are able to
produce faint tidal debris that may appear as star-less, free floating HI
clouds. These may be mistaken for Dark Galaxies, a putative class of gaseous,
dark matter dominated, objects which for some reason never managed to form
stars. VirgoHI21 is by far the most spectacular and most discussed Dark Galaxy
candidate so far detected in HI surveys. We show here that it is most likely
made out of material expelled 750 Myr ago from the nearby spiral galaxy NGC
4254 during its fly--by at about 1000 km/s by a massive intruder. Our numerical
model of the collision is able to reproduce the main characteristics of the
system: in particular the absence of stars, and its prominent velocity
gradient. Originally attributed to the gas being in rotation within a massive
dark matter halo, we find it instead to be consistent with a combination of
simple streaming motion plus projection effects (Duc & Bournaud, 2007). We
discuss several ways to identify a tidal origin in a Dark Galaxy candidate and
illustrate the method using another HI system in Virgo, VCC 2062, which is most
likely a Tidal Dwarf Galaxy (Duc et al., 2007). Now, whereas tidal debris
should not contain any dark matter from the halo of their parent galaxies, it
may exhibit missing mass in the form of dark baryons, unaccounted for by
classical observations, as recently found in the collisional ring of NGC 5291
(Bournaud et al., 2007) and probably in the TDG VCC 2062. These "Lost Baryons"
must originally have been located in the disks of their parent galaxies.


title: Quantum Signatures of Solar System Dynamics

abstract:
  Let w(i) be a period of rotation of the i-th planet around the Sun (or w(j;i)
be a period of rotation of j-th satellite around the i-th planet). From
empirical observations it is known that the sum of n(i)w(i)=0 (or the sum of
n(j)w(j;i)=0) for some integers n(i) (or n(j)), different for different
satellite systems. These conditions, known as resonance conditions, make uses
of theories such as KAM difficult to implement. The resonances in Solar System
are similar to those encountered in old quantum mechanics where applications of
methods of celestial mechanics to atomic and molecular physics were highly
sucsessful. With such a success, the birth of new quantum mechanics is
difficult to understand. In short, the rationale for its birth lies in
simplicity with which the same type of calculations are done using new methods
capable of taking care of resonances. The solution of quantization puzzle was
found by Heisenberg. In this paper new uses of Heisenberg's ideas are found.
When superimposed with the equivalence principle of general relativity, they
lead to quantum mechanical tratment of observed resonances in Solar System. To
test correctness of our theoretical predictions the number of allowed stable
orbits for planets and for equatorial stable orbits of satellites of heavy
planets is calculated resulting in good agreement with observational data. In
addition, the paper briefly discusses quantum mechanical nature of rings of
heavy planets and potential usefulness of the obtained results for cosmology.


title: On the reduction of Feynman integrals to master integrals

abstract:
  The reduction of Feynman integrals to master integrals is an algebraic
problem that requires algorithmic approaches at the modern level of
calculations. Straightforward applications of the classical Buchberger
algorithm to construct Groebner bases seem to be inefficient. An essential
modification designed especially for this problem has been worked out. It has
been already applied in two- and three-loop calculations. We are also
suggesting to combine our method with the Laporta's algorithm.


title:
Phase separation in the vicinity of "quantum critical" doping
  concentration: implications for high temperature superconductors

abstract:
  A general quantitative measure of the tendency towards phase separation is
introduced for systems exhibiting phase transitions or crossovers controlled by
charge carrier concentration. This measure is devised for the situations when
the quantitative knowledge of various contributions to free energy is
incomplete, and is applied to evaluate the chances of electronic phase
separation associated with the onset of antiferromagnetic correlations in
high-temperature cuprate superconductors. The experimental phenomenology of
lanthanum- and yittrium-based cuprates was used as input to this analysis. It
is also pointed out that Coulomb repulsion between charge carriers separated by
the distances of 1-3 lattice periods strengthens the tendency towards phase
separation by accelerating the decay of antiferromagnetic correlations with
doping. Overall, the present analysis indicates that cuprates are realistically
close to the threshold of phase separation -- nanoscale limited or even
macroscopic with charge density varying between adjacent crystal planes.


title: Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State

abstract:
  The tunneling current and shot noise of the current between two Fractional
Quantum Hall (FQH) edges in the $ \nu=12/5 $ FQH state in electronic
Mach-Zehnder interferometer are studied. It is shown that the tunneling current
and shot noise can be used to probe the existence of $k=3 $ parafermion
statistics in the $ \nu=12/5 $ FQH state. More specifically, the dependence of
the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric
under the change of the sign of the applied voltage. This property is absent in
the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron
charges in the $ \nu=12/5 $ FQH state . This number well exceeds the maximum
possible Fano factor in all Laughlin states and the $ \nu=5/2 $ Moore-Read
state which was shown previously to be $ e $ and $ 3.2 e $ respectively.


title: Stability of multiquarks in a simple string model

abstract:
  A simple string model inspired by the strong-coupling regime of Quantum
ChromoDynamics is used as a potential for studying the spectrum of multiquark
systems with two quarks and two antiquarks, with a careful treatment of the
four-body problem. It is found that the ground state is stable, lying below the
threshold for dissociation into two isolated mesons.


title: Search for Bs --> mu+ mu- at D0

abstract:
  We report results from a search for the decay Bs --> mu+ mu- using 1.3/fb of
pbar p collisions at sqrt(s)= 1.96 TeV collected by the D0 experiment at the
Fermilab Tevatron Collider. We find two candidate events, consistent with the
expected background of 1.24 +/- 0.99, and set an upper limit on the branching
fraction of B(Bs --> mu+ mu-) < 1.2e-7 at the 95% C.L.


title:
The Spitzer Survey of the Small Magellanic Cloud: Discovery of Embedded
  Protostars in the HII Region NGC 346

abstract:
  We use Spitzer Space Telescope observations from the Spitzer Survey of the
Small Magellanic Cloud (S3MC) to study the young stellar content of N66, the
largest and brightest HII region in the SMC. In addition to large numbers of
normal stars, we detect a significant population of bright, red infrared
sources that we identify as likely to be young stellar objects (YSOs). We use
spectral energy distribution (SED) fits to classify objects as ordinary (main
sequence or red giant) stars, asymptotic giant branch stars, background
galaxies, and YSOs. This represents the first large-scale attempt at blind
source classification based on Spitzer SEDs in another galaxy. We firmly
identify at least 61 YSOs, with another 50 probable YSOs; only one embedded
protostar in the SMC was reported in the literature prior to the S3MC. We
present color selection criteria that can be used to identify a relatively
clean sample of YSOs with IRAC photometry. Our fitted SEDs indicate that the
infrared-bright YSOs in N66 have stellar masses ranging from 2 Msun to 17 Msun,
and that approximately half of the objects are Stage II protostars, with the
remaining YSOs roughly evenly divided between Stage I and Stage III sources. We
find evidence for primordial mass segregation in the HII region, with the most
massive YSOs being preferentially closer to the center than lower-mass objects.
Despite the low metallicity and dust content of the SMC, the observable
properties of the YSOs appear consistent with those in the Milky Way. Although
the YSOs are heavily concentrated within the optically bright central region of
N66, there is ongoing star formation throughout the complex and we place a
lower limit on the star formation rate of 3.2 x 10^-3 Msun/yr over the last ~1
Myr.


title:
Quintessence, inflation and baryogenesis from a single
  pseudo-Nambu-Goldstone boson

abstract:
  We exhibit a model in which a single pseudo-Nambu-Goldstone boson explains
dark energy, inflation and baryogenesis. The model predicts correlated signals
in future collider experiments, WIMP searches, proton decay experiments, dark
energy probes, and the PLANCK satellite CMB measurements.


title:
The LU-LC conjecture, diagonal local operations and quadratic forms over
  GF(2)

abstract:
  We report progress on the LU-LC conjecture - an open problem in the context
of entanglement in stabilizer states (or graph states). This conjecture states
that every two stabilizer states which are related by a local unitary
operation, must also be related by a local operation within the Clifford group.
The contribution of this paper is a reduction of the LU-LC conjecture to a
simpler problem - which, however, remains to date unsolved. As our main result,
we show that, if the LU-LC conjecture could be proved for the restricted case
of diagonal local unitary operations, then the conjecture is correct in its
totality. Furthermore, the reduced version of the problem, involving such
diagonal local operations, is mapped to questions regarding quadratic forms
over the finite field GF(2). Finally, we prove that correctness of the LU-LC
conjecture for stabilizer states implies a similar result for the more general
case of stabilizer codes.


title: Different Methods of Forming Cold Fronts in Non-Merging Clusters

abstract:
  Sharp edges in X-ray surface brightness with continuous gas pressure called
cold fronts have been often found in relaxed galaxy clusters such as Abell 496.
Models that explain cold fronts as surviving cores of head-on subcluster
mergers do not work well for these clusters and competing models involving gas
sloshing have been recently proposed. Here, we test some concrete predictions
of these models in a combined analysis of density, temperature, metal
abundances and abundance ratios in a deep Chandra exposure of Abell 496. We
confirm that the chemical discontinuities found in this cluster are not
consistent with a core merger remnant scenario. However, we find chemical
gradients across a spiral "arm" discovered at 73 kpc north of the cluster
center and coincident with the sharp edge of the main cold front in the
cluster. Despite the overall SN Ia iron mass fraction dominance found within
the cooling radius of this cluster, the metal enrichment along the arm,
determined from silicon and iron abundances, is consistent with a lower SN Ia
iron mass fraction (51% +- 14%) than that measured in the surrounding regions
(85% +- 14%). The "arm" is also significantly colder than the surroundings by
0.5-1.6 keV. The arm extends from a boxy colder region surrounding the center
of the cluster, where two other cold fronts are found. This cold arm is a
prediction of current high resolution numerical simulations as a result of an
off-center encounter with a less massive pure dark matter halo and we suggest
that the cold fronts in A496 provide the first clear corroboration of such
model, where the closest encounter happened ~ 0.5 Gyr ago. We also argue for a
possible candidate dark matter halo responsible for the cold fronts in the
outskirts of A496.


title: Spitzer Observations of Powerful Radio Sources

abstract:
  We have measured the mid-infrared radiation from an orientation-unbiased
sample of powerful 3C RR galaxies and quasars using the IRS and MIPS
instruments aboard the Spitzer Space Telescope. We fit the Spitzer data as well
as other measurements from the literature with synchrotron and dust components.
At 15 microns, quasars are typically four times brighter than radio galaxies
with the same isotropic radio power. Based on our fits, half of this difference
can be attributed to the presence of non-thermal emission in the quasars but
not the radio galaxies. The other half is consistent with dust absorption in
the radio galaxies but not the quasars.


title: Symplectic $A_\infty$-algebras and string topology operations

abstract:
  In this paper we establish the existence of certain structures on the
ordinary and equivariant homology of the free loop space on a manifold or, more
generally, a formal Poincar\'e duality space. These structures; namely the loop
product, the loop bracket and the string bracket, were introduced and studied
by Chas and Sullivan under the general heading `string topology'. Our method is
based on obstruction theory for $C_\infty$-algebras and rational homotopy
theory. The resulting string topology operations are manifestly homotopy
invariant.


title: Vesicle shape, molecular tilt, and the suppression of necks

abstract:
  Can the presence of molecular-tilt order significantly affect the shapes of
lipid bilayer membranes, particularly membrane shapes with narrow necks?
Motivated by the propensity for tilt order and the common occurrence of narrow
necks in the intermediate stages of biological processes such as endocytosis
and vesicle trafficking, we examine how tilt order inhibits the formation of
necks in the equilibrium shapes of vesicles. For vesicles with a spherical
topology, point defects in the molecular order with a total strength of $+2$
are required. We study axisymmetric shapes and suppose that there is a
unit-strength defect at each pole of the vesicle. The model is further
simplified by the assumption of tilt isotropy: invariance of the energy with
respect to rotations of the molecules about the local membrane normal. This
isotropy condition leads to a minimal coupling of tilt order and curvature,
giving a high energetic cost to regions with Gaussian curvature and tilt order.
Minimizing the elastic free energy with constraints of fixed area and fixed
enclosed volume determines the allowed shapes. Using numerical calculations, we
find several branches of solutions and identify them with the branches
previously known for fluid membranes. We find that tilt order changes the
relative energy of the branches, suppressing thin necks by making them costly,
leading to elongated prolate vesicles as a generic family of tilt-ordered
membrane shapes.


title: An Observed Fundamental Plane Relation for Supermassive Black Holes

abstract:
  We study observed correlations between supermassive black hole (BHs) and the
properties of their host galaxies, and show that the observations define a BH
'fundamental plane' (BHFP), of the form M_BH sigma^(3.0+-0.3)*R_e^(0.43+-0.19),
or M_BH M_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), analogous to the FP of
elliptical galaxies. The BHFP is preferred over a simple relation between M_BH
and any of sigma, M_bulge, M_dyn, or R_e alone at >99.9% significance. The
existence of this BHFP has important implications for the formation of
supermassive BHs and the masses of the very largest black holes, and
immediately resolves several apparent conflicts between the BH masses expected
and measured for outliers in both the M_BH-sigma and M_BH-M_bulge relations.


title:
Two-loop Gell-Mann-Low function of N=1 supersymmetric Yang-Mills theory,
  regularized by higher covariant derivatives

abstract:
  Two-loop Gell-Mann-Low function is calculated for N=1 supersymmetric
Yang-Mills theory, regularized by higher covariant derivatives. The integrals,
which define it, are shown to be reduced to total derivatives and can be easily
calculated analytically.


title: Reflection Groups and Polytopes over Finite Fields, III

abstract:
  When the standard representation of a crystallographic Coxeter group is
reduced modulo an odd prime p, one obtains a finite group G^p acting on some
orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p
will often be the automorphism group of a finite abstract regular polytope. In
parts I and II we established the basics of this construction and enumerated
the polytopes associated to groups of rank at most 4, as well as all groups of
spherical or Euclidean type. Here we extend the range of our earlier criteria
for the polytopality of G^p . Building on this we investigate the class of
3-infinity groups of general rank, and then complete a survey of those locally
toroidal polytopes which can be described by our construction.


title: GRBs and Hypernova Explosions of Some Galactic Sources

abstract:
  Knowing the Kerr parameters we can make quantitative calculations of the
rotational energy of black holes. We show that Nova Sco (GRO J1655 - 40), Il
Lupi (4U 1543 - 47), XTE J1550 - 564 and GS 2023 + 338 are relics of gamma-ray
burst (GRB) and Hypernova explosions. They had more than enough rotational
energy to power themselves. In fact, they had so much energy that they would
have disrupted the accretion disk of the black hole that powered them by the
communicated rotational energy, so that the energy delivery was self limiting.
The most important feature in producing high rotational energy in the binary is
low donor (secondary star) mass.
  We suggest that V4641 Sgr (XTE J1819 - 254) and GRS 1915 + 105 underwent less
energetic explosions; because of their large donor masses. These explosions
were one or two orders of magnitude lower in energy than that of Nova Sco. Cyg
X - 1 (1956 + 350) had an even less energetic explosion, because of an even
larger donor mass.
  We find that in the evolution of the soft X-ray transient sources the donor
(secondary star) is tidally locked with the helium star, which evolved from the
giant, as the hydrogen envelope is stripped off in common envelope evolution.
The tidal locking is transferred from the helium star to the black hole into
which it falls. Depending on the mass of the donor, the black hole can be spun
up to the angular momentum necessary to power the GRB and Hypernova explosion.
The donor decouples, acting as a passive witness to the explosion which, for
the given angular momentum, then proceeds as in the Woosley Collapsar model.
  High mass donors which tend to follow from low metallicity give long GRBs
because their lower energy can be accepted by the central engine.


title: Spin ice behavior in Dy2Sn2-xSbxO7+x/2 and Dy2NbScO7

abstract:
  We report the magnetic and thermal properties of Dy2Sn2-xSbxO7+x/2, x = 0,
0.25, and 0.5, and Dy2NbScO7. We find evidence for Ising-like single ion ground
states in the Dy2Sn2-xSbxO7+x/2 materials. These materials possess nearly the
same zero point entropy as the canonical spin ices Ho2Ti2O7 and Dy2Ti2O7,
strongly suggesting that they have spin ice states at low temperatures. We also
observe a somewhat reduced zero point entropy in Dy2NbScO7, which is possibly
associated with the higher level of cation disorder. The ice-like states in
these materials with cation disorder on the B-sites of the pyrochlore lattice
provide new evidence for the robust nature of spin ice behavior in the presence
of disorder.


title: Stability of general relativistic Miyamoto-Nagai galaxies

abstract:
  The stability of a recently proposed general relativistic model of galaxies
is studied in some detail. This model is a general relativistic version of the
well known Miyamoto-Nagai model that represents well a thick galactic disk. The
stability of the disk is investigated under a general first order perturbation
keeping the spacetime metric frozen (no gravitational radiation is taken into
account). We find that the stability is associated with the thickness of the
disk. We have that flat galaxies have more not-stable modes than the thick ones
i.e., flat galaxies have a tendency to form more complex structures like rings,
bars and spiral arms.