title: Local vertical measurements and violation of Bell inequality

abstract:
  For two qubits belonging to Alice and Bob, we derive an approach to setup the
bound of Bell operator in the condition that Alice and Bob continue to perform
local vertical measurements. For pure states we find that if the entanglement
of the two qubits is less than 0.2644 (measured with von Neumann entropy) the
violation of the Bell inequality will never be realized, and only when the
entanglement is equal to 1 the maximal violation ($2\sqrt{2}$) can occur. For
specific form of mixed states, we prove that the bound of the Bell inequality
depends on the concurrence. Only when the concurrence is greater than 0.6 the
violation of the Bell inequality can occur, and the maximal violation can never
be achieved. We suggest that the bound of the Bell operator in the condition of
local vertical measurements may be used as a measure of the entanglement.


title: Dynamical Properties of a Rotating Bose-Einstein Condensate

abstract:
  Within a variational approach to solve the Gross-Pitaevskii equation we
investigate dynamical properties of a rotating Bose-Einstein condensate which
is confined in an anharmonic trap. In particular, we calculate the
eigenfrequencies of low-energy excitations out of the equilibrium state and the
aspect ratio of the condensate widths during the free expansion.


title: The spectral flow, the Fredholm index, and the spectral shift function

abstract:
  We discuss the well known ``Fredholm index=spectral flow'' theorem and show
that it can be interpreted as a limit case of an identity involving two
spectral shift functions.


title: On deformations of Ashtekar's constraint algebra

abstract:
  We show that the constraint algebra of Ashtekar's Hamiltonian formulation of
general relativity can be non-trivially deformed by allowing the cosmological
constant to become an arbitrary function of the (Weyl) curvature. Our result
implies that there is not one but infinitely many (parameterized by an
arbitrary function) four-dimensional gravity theories propagating two degrees
of freedom.


title:
Uniqueness of roots up to conjugacy for some affine and finite type
  Artin groups

abstract:
  Let $G$ be one of the Artin groups of finite type ${\mathbf B}_n={\mathbf
C}_n$, and affine type $\tilde{\mathbf A}_{n-1}$ and $\tilde{\mathbf C}_{n-1}$.
In this paper, we show that if $\alpha$ and $\beta$ are elements of $G$ such
that $\alpha^k=\beta^k$ for some nonzero integer $k$, then $\alpha$ and $\beta$
are conjugate in $G$. For the Artin group of type $\mathbf A_n$, this was
recently proved by J. Gonz\'alez-Meneses.
  In fact, we prove a stronger theorem, from which the above result follows
easily by using descriptions of those Artin groups as subgroups of the braid
group on $n+1$ strands. Let $P$ be a subset of $\{1,...,n\}$. An $n$-braid is
said to be \emph{$P$-pure} if its induced permutation fixes each $i\in P$, and
\emph{$P$-straight} if it is $P$-pure and it becomes trivial when we delete all
the $i$-th strands for $i\not\in P$. Exploiting the Nielsen-Thurston
classification of braids, we show that if $\alpha$ and $\beta$ are $P$-pure
$n$-braids such that $\alpha^k=\beta^k$ for some nonzero integer $k$, then
there exists a $P$-straight $n$-braid $\gamma$ with
$\beta=\gamma\alpha\gamma^{-1}$. Moreover, if $1\in P$, the conjugating element
$\gamma$ can be chosen to have the first strand algebraically unlinked with the
other strands. Especially in case of $P=\{1,...,n\}$, our result implies the
uniqueness of root of pure braids, which was known by V. G. Bardakov and by D.
Kim and D. Rolfsen.


title: On the role of Lifshitz invariants in liquid crystals

abstract:
  The interaction between an external action and the order parameter, via a
dependence described by a so-called Lifshitz invariant, is very important to
determine the final configuration of the liquid crystal cells. The external
action can be an electric field applied to the bulk or the confinement due to
free surfaces or cell walls. The Lifshitz invariant includes the order
parameter in the form of an elastic strain. This coupling between elastic
strains and fields, inserted in a Landau-Ginzburg formalism, is well known and
give rise to striction effects causing undulations in the director
configuration. We want to discuss here the role of Lifshitz coupling terms,
following an approach similar to that introduced by Dzyaloshinskii for magnetic
materials. Case studies on nematics in planar and cylindrical cells are also
proposed.


title:
Theory of quantum magneto-oscillations in underdoped cuprate
  superconductors

abstract:
  Magneto-oscillations in kinetic and magnetic response functions of a few
underdoped cuprates are perhaps one of the most striking observations since
many probes of underdoped cuprates clearly point to a non Fermi-liquid normal
state. Their observation in the vortex state well below the upper critical
field raises a doubt concerning their normal state origin. Here I propose an
explanation of the magneto-oscillations as emerging from the quantum
interference of the vortex lattice and checkerboard modulations of the electron
density of states revealed by STM with atomic resolution in some cuprate
superconductors. The checkerboard effectively pins the vortex lattice, when the
period of the latter is commensurate with the period of the checkerboard. This
condition yields 1/\sqrt{B} periodicity of the response functions versus
magnetic field B, rather than 1/B periodicity of conventional normal state
oscillations. Our solution of the Gross-Pitaevskii-type equation for composed
charged bosons accounting for the d-wave symmetry of the order-parameter and
its checkerboard modulations describes well changes in resonant frequency of
the tunnel-diode oscillator circuit with YBa2Cu4O8 and the oscillatory part of
the Hall resistance and magnetic susceptibility in the mixed state of
YBa2Cu3O6.5.


title: Geometry of A_g and Its Compactifications

abstract:
  In this survey we give a brief introduction to, and review the progress made
in the last decade in understanding the geometry of the moduli spaces A_g of
principally polarized abelian varieties and its compactifications. Topics
surveyed include: compactifications; birational geometry: nef and effective
cones, canonical models; homology, Chow rings and intersection theory; and
subvarieties of moduli spaces. We also discuss some open problems and possible
further directions. This is an expanded and updated version of the talk given
at the 2005 Summer Institute for Algebraic Geometry


title:
A new analysis method to determine beta-decay half-lives in experiments
  with complex background

abstract:
  This paper reports the first application of a new technique to measure the
beta-decay half -lives of exotic nuclei in complex background conditions. Since
standard tools were not adapted to extract the relevant information, a new
analysis method was developed. The time distribution of background events is
established by recording time correlations in backward time. The beta half
lives of the nuclides and the detection efficiency of the set-up are determined
simultaneously from a least-squares fit of the ratio of the time-correlation
spectra recorded in forward and in backward time, using numerical functions.
The necessary numerical functions are calculated in a Monte-Carlo code using
the known operation parameters of the experiment and different values for the
two free parameters, half-life and detection efficiency, as input parameters.


title: Symmetric units in modular group algebras

abstract:
  Let p be a prime, G a locally finite p-group, K a commutative ring of
characteristic p. The anti-automorphism g\mapsto g\m1 of G extends linearly to
an anti-automorphism a\mapsto a^* of KG. An element a of KG is called symmetric
if a^*=a. In this paper we answer the question: for which G and K do the
symmetric units of KG form a multiplicative group.


title: Unitary units in modular group algebras

abstract:
  Let p be a prime, K a field of characteristic p, G a locally finite p-group,
KG the group algebra, and V the group of the units of KG with augmentation 1.
The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this
extension leaves V setwise invariant, and its restriction to V followed by
v\mapsto v^{-1} lives an automorphism of V. The elements of V fixed by this
automorphism are called unitary; they form a subgroup. Our first theorem
describes the K and G for which this subgroup is normal in V.
  For each element g in G, let \bar{g} denote the sum (in KG) of the distinct
powers of g. The elements 1+(g-1)h\bar{g} with g,h\in G are the bicyclic units
of KG. Our second theorem describes the K and G for which all bicyclic units
are unitary.


title: Structure of metastable 2D liquid helium

abstract:
  We present diffusion Monte Carlo (DMC) results on a new metastable,
superfluid phase above the crystal ground state in two-dimensional 4He at
densities > 0.065 1/A^2. The state is anisotropic with hexatic orbital order.
This implies that the liquid--solid phase transition has two stages: A second
order phase transition from the isotropic superfluid to the hexatic superfluid,
followed by a first order transition that localizes atoms into the triangular
crystal order. This metastable hexatic phase has finite condensate fraction and
it provides a natural explanation for the superflow in the supersolid grain
boundaries.


title: Detection of faint companions through stochastic speckle discrimination

abstract:
  We propose a new post-processing technique for the detection of faint
companions from a sequence of adaptive optics corrected short exposures. The
algorithm exploits the difference in shape between the on-axis and off-axis
irradiance distributions and it does not require the signal to be above the
noise level. We show that the method is particularly useful in dealing with
static speckles. Its application to real and simulated data gives excellent
results in the low-signal regime where it outperforms the standard approach of
computing signal-to-noise ratio on one long exposure. We also show that
accurate noise estimation in adaptive optics images of close companions is
rendered impossible due to the presence of static speckles. This new method
provides means of reliable estimation of the confidence intervals for the
detection hypothesis.


title:
Relationship between ferroelectricity and Dzyaloshinskii-Moriya
  interaction in multiferroics and the effect of bond-bending

abstract:
  We studied the microscopic mechanism of multiferroics, in particular with the
"spin current" model (Hosho Katsura, Naoto Nagaosa and Aleander V. Balatsky,
Phys. Rev. Lett. 95, 057205 (2005)). Starting from a system with helical spin
configuration, we solved for the forms of the electron wave functions and
analyzed their characteristics. The relation between ferroelectricity and
Dzyaloshinskii-Moriya interaction (I. Dzyaloshinskii, J. Phys. Chem. Solids 4,
241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)) is clearly established.
There is also a simple relation between the electric polarization and the wave
vector of magnetic orders. Finally, we show that the bond-bending exists in
transition metal oxides can enhance ferroelectricity.


title:
First access to beta half-lives approaching the r-process path near
  N=126

abstract:
  Heavy neutron-rich nuclei close to N=126 were produced by fragmentation of a
1 A GeV 208Pb beam at the FRS at GSI. The beta-decay half-lives of 8 nuclides
have been determined. The comparison of the data with model calculations
including an approach based on the self-consistent ground-state description and
continuum QRPA considering the Gamow-Teller and first-forbidden decays provide
a first indication on the importance of first-forbidden transitions around
A=195. The measured data indicate that the matter flow in the r-process to
heavier fissioning nuclei is faster than previously expected.


title: Perturbed Defects and T-Systems in Conformal Field Theory

abstract:
  Defect lines in conformal field theory can be perturbed by chiral defect
fields. If the unperturbed defects satisfy su(2)-type fusion rules, the
operators associated to the perturbed defects are shown to obey functional
relations known from the study of integrable models as T-systems. The procedure
is illustrated for Virasoro minimal models and for Liouville theory.


title:
Homology of coloured posets: a generalisation of Khovanov's cube
  construction

abstract:
  We define a homology theory for a certain class of posets equipped with a
representation. We show that when restricted to Boolean lattices this homology
is isomorphic to the homology of the "cube" complex defined by Khovanov.


title:
Semiclassical approach to the description of the basic properties of
  nanoobjects

abstract:
  Present paper is a review of results, obtained in the framework of
semiclassical approach in nanophysics. Semiclassical description, based on
Electrostatics and Thomas-Fermi model was applied to calculate dimensions of
the electronic shell of a fullerene molecule and a carbon nanotube. This
simplified approach yields surprisingly accurate results in some cases.
Semiclassical approach provides rather good description of the dimensions of
the electronic shell of a fullerene molecule. Two types of dipole oscillations
in a fullerene molecule were considered and their frequencies were calculated.
Similar calculations were performed for a carbon nanotube also. These results
look rather reasonable. Three types of dipole oscillations in carbon nanotube
were considered and their frequencies were calculated. Frequencies of the
longitudinal collective oscillations of delocalized electrons in carbon peapod
were calculated as well. Metallic cluster was modeled as a spherical ball. It
was shown that metallic cluster is stable; its bulk modulus and the frequency
of the dipole oscillation of the electronic shell relative to the ions were
calculated.


title:
Erratum to Star formation triggered by SN explosions: an application to
  the stellar association of $\beta$Pictoris

abstract:
  In the present study, considering the physical conditions that are relevant
interactions between supernova remnants (SNRs) and dense molecular clouds for
triggering star formation we have built a diagram of SNR radius versus cloud
density in which the constraints above delineate a shaded zone where star
formation is allowed. We have also performed fully 3-D radiatively cooling
numerical simulations of the impact between SNRs and clouds under different
initial conditions in order to follow the initial steps of these interactions.
We determine the conditions that may lead either to cloud collapse and star
formation or to complete cloud destruction and find that the numerical results
are consistent with those of the SNR-cloud density diagram. Finally, we have
applied the results above to the $\beta-$ Pictoris stellar association which is
composed of low mass Post-T Tauri stars with an age of 11 Myr. It has been
recently suggested that its formation could have been triggered by the shock
wave produced by a SN explosion localized at a distance of about 62 pc that may
have occurred either in the Lower Centaurus Crux (LCC) or in the Upper
Centaurus Lupus (UCL) which are both nearby older subgroups of that association
(Ortega and co-workers).Using the results of the analysis above we have shown
that the suggested origin for the young association at the proposed distance is
plausible only for a very restricted range of initial conditions for the parent
molecular cloud, i.e., a cloud with a radius of the order of 10 pc, a density
of the order of 10$-$20 cm$^{-3}$, and a temperature of the order of 10$-$100 K
}.


title:
Equation of state in the inner crust of neutron stars: discusion of the
  unbound neutron states

abstract:
  In this paper, we calculate the stable Wigner-Seitz (W-S) cells in the inner
crust of neutron stars and we discuss the nuclear shell effects. A distinction
is done between the shell effects due to the bound states and those induced by
the unbound states, which are shown to be spurious. We then estimate the
effects of the spurious shells on the total energy and decompose it into a
smooth and a residual part. We propose a correction to the Hartree-Fock binding
energy in Wigner-Seitz cell (HF-WS).


title: Search method for coincident events from LIGO and IceCube detectors

abstract:
  We present a coincidence search method for astronomical events using
gravitational wave detectors in conjunction with other astronomical
observations. We illustrate our method for the specific case of the LIGO
gravitational wave detector and the IceCube neutrino detector. LIGO
trigger-events and IceCube events which occur within a given time window are
selected as time-coincident events. Then the spatial overlap of the
reconstructed event directions is evaluated using an unbinned maximum
likelihood method. Our method was tested with Monte Carlo simulations based on
realistic LIGO and IceCube event distributions. We estimated a typical false
alarm rate for the analysis to be 1 event per 435 years. This is significantly
smaller than the false alarm rates of the ndividual detectors.


title:
On the Exact Matrix Representation for Transverse Magnetic Multiple
  Scattering by an Infinite Grating of Insulating Dielectric Circular Cylinders
  at Oblique Incidence

abstract:
  A computational algorithm for the exact equations representing the scattering
coefficients of an infinite grating of insulating dielectric circular cylinders
associated with obliquely incident vertically polarized plane electromagnetic
waves is generated by matrix methods, and the solution for the scattering
coefficients is acquired by a matrix inversion procedure.


title:
Genetic simulation of quantum dynamics by the principle of quantum state
  selection

abstract:
  The simple genetic algorithm is proposed for the simulation of quantum many
body dynamics. It uses the selection of entangled quantum states and has the
inbuilt absolute decoherence that comes from the limitation of classical
memory. It utilizes the "pre-quantum field" in the form of interacting between
the different "quantum worlds". It is shown how this selection model can be
applied to the problem of molecular association in chemical reactions.


title:
Phase Transitions and Computational Difficulty in Random Constraint
  Satisfaction Problems

abstract:
  We review the understanding of the random constraint satisfaction problems,
focusing on the q-coloring of large random graphs, that has been achieved using
the cavity method of the physicists. We also discuss the properties of the
phase diagram in temperature, the connections with the glass transition
phenomenology in physics, and the related algorithmic issues.


title: Continuity of CP-semigroups in the point-strong operator topology

abstract:
  We prove that if $\{\phi_t\}_{t \geq 0}$ is a CP-semigroup acting on a von
Neumann algebra $M \subseteq B(H)$, then for every $A\in M$ and $\xi \in H$,
the map $t \mapsto \phi_t(A)\xi$ is norm-continuous. We discuss the
implications of this fact to the existence of dilations of CP-semigroups to
semigroups of endomorphisms.


title: Photon position eigenvectors lead to complete photon wave mechanics

abstract:
  We have recently constructed a photon position operator with commuting
components. This was long thought to be impossible, but our position
eigenvectors have a vortex structure like twisted light. Thus they are not
spherically symmetric and the position operator does not transform as a vector,
so that previous non-existence arguments do not apply. We find two classes of
position eigenvectors and obtain photon wave functions by projection onto the
bases of position eigenkets that they define, following the usual rules of
quantum mechanics. The hermitian position operator, r0, leads to a
Landau-Peierls wave function, while field-like eigenvectors of the nonhermitian
position operator and its adjoint lead to a biorthonormal basis. These two
bases are equivalent in the sense that they are related by a similarity
transformation. The eigenvectors of the nonhermitian position operators lead to
a field-potential wave function pair. These field-like positive frequency wave
functions satisfy Maxwell's equations, and thus justify the supposition that
MEs describe single photon wave mechanics. The expectation value of the number
operator is photon density with undetected photons integrated over, consistent
with Feynman's conclusion that the density of non-interacting particles can be
interpreted as probability density.


title: VLT observations of Compact Central Objects

abstract:
  We present the first results of our VLT observation campaign of the Central
Compact Objects (CCOs) in SNRs RX J085201.4-461753 (Vela Jr), 1E 1648-5051 (RCW
103) and RX J171328.4-394955 (G347.3-0.5). For Vela Jr., we found that the
source is embedded in a compact optical nebulosity, possibly a bow-shock or a
photo-ionization nebula, and we identified a candidate IR counterpart to the
CCO. For RCW 103, we found no convincing evidence neither for 6 hrs IR
modulation nor for variability on any time scale from the proposed counterpart,
as well as for the other candidates close to the revised Chandra position. For
G347.3-0.5, we identified few possible IR counterparts but none of them is
apparently associated with the CCO.


title: Geometric Spanners With Small Chromatic Number

abstract:
  Given an integer $k \geq 2$, we consider the problem of computing the
smallest real number $t(k)$ such that for each set $P$ of points in the plane,
there exists a $t(k)$-spanner for $P$ that has chromatic number at most $k$. We
prove that $t(2) = 3$, $t(3) = 2$, $t(4) = \sqrt{2}$, and give upper and lower
bounds on $t(k)$ for $k>4$. We also show that for any $\epsilon >0$, there
exists a $(1+\epsilon)t(k)$-spanner for $P$ that has $O(|P|)$ edges and
chromatic number at most $k$. Finally, we consider an on-line variant of the
problem where the points of $P$ are given one after another, and the color of a
point must be assigned at the moment the point is given. In this setting, we
prove that $t(2) = 3$, $t(3) = 1+ \sqrt{3}$, $t(4) = 1+ \sqrt{2}$, and give
upper and lower bounds on $t(k)$ for $k>4$.


title:
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I.
  Foundations

abstract:
  Linear cosmological perturbation theory is pivotal to a theoretical
understanding of current cosmological experimental data provided e.g. by cosmic
microwave anisotropy probes. A key issue in that theory is to extract the gauge
invariant degrees of freedom which allow unambiguous comparison between theory
and experiment. When one goes beyond first (linear) order, the task of writing
the Einstein equations expanded to n'th order in terms of quantities that are
gauge invariant up to terms of higher orders becomes highly non-trivial and
cumbersome. This fact has prevented progress for instance on the issue of the
stability of linear perturbation theory and is a subject of current debate in
the literature. In this series of papers we circumvent these difficulties by
passing to a manifestly gauge invariant framework. In other words, we only
perturb gauge invariant, i.e. measurable quantities, rather than gauge variant
ones. Thus, gauge invariance is preserved non perturbatively while we construct
the perturbation theory for the equations of motion for the gauge invariant
observables to all orders. In this first paper we develop the general framework
which is based on a seminal paper due to Brown and Kuchar as well as the
realtional formalism due to Rovelli. In the second, companion, paper we apply
our general theory to FRW cosmologies and derive the deviations from the
standard treatment in linear order. As it turns out, these deviations are
negligible in the late universe, thus our theory is in agreement with the
standard treatment. However, the real strength of our formalism is that it
admits a straightforward and unambiguous, gauge invariant generalisation to
higher orders. This will also allow us to settle the stability issue in a
future publication.


title: Static Interactions of non-Abelian Vortices

abstract:
  Interactions between non-BPS non-Abelian vortices are studied in non-Abelian
U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The
distinctive feature of a non-Abelian vortex is the presence of an internal
CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of
the couplings, the vortices are BPS and there is no net force between two
static parallel vortices at arbitrary distance. On the other hand, for generic
values of the couplings the interactions between two vortices depend
non-trivially on their relative internal orientations. We discuss the problem
both with a numerical approach (valid for small deviations from the BPS limit)
and in a semi-analytical way (valid at large vortex separations). The
interactions can be classified with respect to their asymptotic property at
large vortex separation. In a simpler fine-tuned model, we find two regimes
which are quite similar to the usual type I/II Abelian superconductors. In the
generic model we find other two new regimes: type I*/II*. Unlike the type I
(type II) case, where the interaction is always attractive (repulsive), the
type I* and II* have both attractive and repulsive interactions depending on
the relative orientation. We have found a rich variety of interactions at small
vortex separations. For some values of the couplings, a bound state of two
static vortices at a non-zero distance exists.


title:
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II.
  FRW Background and First Order

abstract:
  In our companion paper we identified a complete set of manifestly
gauge-invariant observables for general relativity. This was possible by
coupling the system of gravity and matter to pressureless dust which plays the
role of a dynamically coupled observer. The evolution of those observables is
governed by a physical Hamiltonian and we derived the corresponding equations
of motion. Linear perturbation theory of those equations of motion around a
general exact solution in terms of manifestly gauge invariant perturbations was
then developed. In this paper we specialise our previous results to an FRW
background which is also a solution of our modified equations of motion. We
then compare the resulting equations with those derived in standard
cosmological perturbation theory (SCPT). We exhibit the precise relation
between our manifestly gauge-invariant perturbations and the linearly
gauge-invariant variables in SCPT. We find that our equations of motion can be
cast into SCPT form plus corrections. These corrections are the trace that the
dust leaves on the system in terms of a conserved energy momentum current
density. It turns out that these corrections decay, in fact, in the late
universe they are negligible whatever the value of the conserved current. We
conclude that the addition of dust which serves as a test observer medium,
while implying modifications of Einstein's equations without dust, leads to
acceptable agreement with known results, while having the advantage that one
now talks about manifestly gauge-invariant, that is measurable, quantities,
which can be used even in perturbation theory at higher orders.


title: Density dependence of the "symmetry energy" in the lattice gas model

abstract:
  Isoscaling behavior of the statistical emission fragments from the
equilibrated sources with $Z$ = 30 and $N$ = 30, 33, 36 and 39, resepectively,
is investigated in the framework of isospin dependent lattice gas model. The
dependences of isoscaling parameters $\alpha$ on source isospin asymmetry,
temperature and freeze-out density are studied and the "symmetry energy" is
deduced from isoscaling parameters. Results show that "symmetry energy"
$C_{sym}$ is insensitive to the change of temperature but follows the power-law
dependence on the freeze-out density $\rho$. The later gives $C_{sym}$ =
30$(\rho/\rho_0)^{0.62}$ if the suitable asymmetric nucleon-nucleon potential
is taken. The effect of strength of asymmetry of nucleon-nucleon interaction
potential on the density dependence of the "symmetry energy" is dicussed.


title:
Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of
  Loop Quantum Gravity

abstract:
  We perform a canonical, reduced phase space quantisation of General
Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of
the reduced phase space is made possible by the combination of 1. the Brown --
Kuchar mechanism in the presence of pressure free dust fields which allows to
deparametrise the theory and 2. Rovelli's relational formalism in the extended
version developed by Dittrich to construct the algebra of gauge invariant
observables. Since the resulting algebra of observables is very simple, one can
quantise it using the methods of LQG. Basically, the kinematical Hilbert space
of non reduced LQG now becomes a physical Hilbert space and the kinematical
results of LQG such as discreteness of spectra of geometrical operators now
have physical meaning. The constraints have disappeared, however, the dynamics
of the observables is driven by a physical Hamiltonian which is related to the
Hamiltonian of the standard model (without dust) and which we quantise in this
paper.


title:
Theoretical study of interacting electrons in one dimension - ground
  states and experimental signatures

abstract:
  This dissertation focuses on a theoretical study of interacting electrons in
one dimension. The research elucidates the ground state (zero temperature)
electronic phase diagram of an aluminum arsenide quantum wire which is an
example of an interacting one dimensional electron liquid. Using one
dimensional field theoretic methods involving abelian bosonization and the
renormalization group we show the existence of a spin gapped quantum wire with
electronic ground states such as charge density wave and singlet
superconductivity. The superconducting state arises due to the unique umklapp
interaction present in the aluminum arsenide quantum wire bandstructure
discussed in this dissertation. It is characterized by Cooper pairs carrying a
finite pairing momentum. This is a realization of the Fulde-Ferrell-Larkin-
Ovchinnikov state which is known to lead to inhomogeneous superconductivity.
The dissertation also presents a theoretical analysis of the finite temperature
single hole spectral function of the one dimensional electron liquid with
gapless spin and charge modes (Luttinger liquid). The hole spectral function is
measured in angle resolved photoemission spectroscopy experiments. The results
predict a kink in the effective electronic dispersion of the Luttinger liquid.
A systematic study of the temperature and interaction dependence of the kink
provides an alternative way to detect spincharge separation in one dimensional
systems where the peak due to the spin part of the spectral function is
suppressed.


title: Interaction effects in mixed-valent Kondo insulators

abstract:
  We study theoretically the class of mixed-valent Kondo insulators, employing
a recently developed local moment approach to heavy Fermion systems using the
asymmetric periodic Anderson model (PAM). Novel features in spectra and
transport, observable experimentally but lying outside the scope of the
symmetric PAM or the Kondo lattice model, emerge naturally within the present
theory. We argue in particular that a shoulder-like feature in the optical
conductivity, that is distinct from the usual mid-infrared or direct gap peak
and has been observed experimentally in mixed-valent compounds such as
CeOs4Sb12 and YbAl3, is of intrinsic origin. Detailed comparison is made
between the resultant theory and transport/optical experiments on the
filled-skutterudite compound CeOs4Sb12, and good agreement is obtained.


title: Minimal types in super-dependent theories

abstract:
  We give necessary and sufficient geometric conditions for a theory definable
in an o-minimal structure to interpret a real closed field. The proof goes
through an analysis of thorn-minimal types in super-rosy dependent theories of
finite rank. We prove that such theories are coordinatised by thorn-minimal
types and that such a type is unstable if an only if every non-algebraic
extension thereof is. We conclude that a type is stable if and only if it
admits a coordinatisation in thorn-minimal stable types. We also show that
non-trivial thorn-minimal stable types extend stable sets.


title:
On the regularity criterion of weak solution for the 3D viscous
  Magneto-hydrodynamics equations

abstract:
  We improve and extend some known regularity criterion of weak solution for
the 3D viscous Magneto-hydrodynamics equations by means of the Fourier
localization technique and Bony's para-product decomposition.


title:
The nonequilibrium statistical operator with finite duration of the
  present time moment

abstract:
  The method of the nonequilibrium statistical operator accounts for the
history of a system, influence of its past history to its present state. It is
suggested to take into account the finite duration of the present time moment,
which according to I.Prigogine's results, is equal to the average Lyapunov
time.


title:
Influence of the atomic scale inhomogeneity of the pair interaction on
  the local pair formation and density of states in high-T_c superconductors

abstract:
  The influence of the atomic-scale inhomogeneities of the pairing interaction
on the superconducting order parameter distribution and the LDOS is studied in
the framework of mean-field BCS theory for two-dimensional lattice model. It is
found that the ratio of the local low-temperature gap in differential
conductance to the local temperature of vanishing the gap $2\Delta_g/T_p$ can
take large enough values compared to the homogeneous case. This ratio
practically does not depend on the location in the sample and is independent on
the concentration of local pair interaction perturbations in wide range of
concentrations. The obtained results could bear a relation to the recent
measurements by Gomes {\it et. al} Nature, 447, 569 (2007).


title: WASP-3b: a strongly-irradiated transiting gas-giant planet

abstract:
  We report the discovery of WASP-3b, the third transiting exoplanet to be
discovered by the WASP and SOPHIE collaboration. WASP-3b transits its host star
USNO-B1.0 1256-0285133 every 1.846834+-0.000002 days. Our high precision
radial-velocity measurements present a variation with amplitude characteristic
of a planetary-mass companion and in-phase with the light-curve. Adaptive
optics imaging shows no evidence for nearby stellar companions, and
line-bisector analysis excludes faint, unresolved binarity and stellar activity
as the cause of the radial-velocity variations. We make a preliminary
spectroscopic analysis of the host star finding it to have Teff = 6400+-100 K
and log g = 4.25+-0.05 which suggests it is most likely an unevolved main
sequence star of spectral type F7-8V. Our simultaneous modelling of the transit
photometry and reflex motion of the host leads us to derive a mass of 1.76
+0.08 -0.14 M_J and radius 1.31 +0.07-0.14 R_J for WASP-3b. The proximity and
relative temperature of the host star suggests that WASP-3b is one of the
hottest exoplanets known, and thus has the potential to place stringent
constraints on exoplanet atmospheric models.


title:
Phenomenological Scaling of Rapidity Dependence for Anisotropic Flows in
  25 MeV/nucleon Ca + Ca by Quantum Molecular Dynamics Model

abstract:
  Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till
the mass number 4 as a function of rapidity have been studied for 25
MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum
Molecular Dynamics model. A phenomenological scaling behavior of rapidity
dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a
function of mass number plus a constant term, which may arise from the
interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps
almost independent of rapidity and remains a rough constant of 1/2 for all
light fragments.


title:
Security Analysis of a Remote User Authentication Scheme with Smart
  Cards

abstract:
  Yoon et al. proposed a new efficient remote user authentication scheme using
smart cards to solve the security problems of W. C. Ku and S. M. Chen scheme.
This paper reviews Yoon et al. scheme and then proves that the password change
phase of Yoon et al. scheme is still insecure. This paper also proves that the
Yoon et al. is still vulnerable to parallel session attack.


title: Fuzzy Geometry of Phase Space and Quantization of Massive Fields

abstract:
  The quantum space-time and the phase space with fuzzy structure is
investigated as the possible quantization formalism. In this theory the state
of nonrelativistic particle corresponds to the element of fuzzy ordered set
(Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space
coordinate x acquires principal uncertainty dx. It's shown that Shroedinger
formalism of Quantum Mechanics can be completely derived from consideration of
particle evolution in fuzzy phase space with minimal number of axioms.


title: The Shubnikov-de Haas effect in multiband quasi-two dimensional metals

abstract:
  We analyze the behavior of the longitudinal conductivity $\sigma_{zz}$ in a
field perpendicular to the highly conducting plane of a quasi-2D {\em
multiband} metal in the case of closed system and open systems where $\tau$ is
fixed, $\tau$ oscillates due to intra-band scattering and $\tau$ oscillates due
to inter-band scattering. In all but one case, we find that there are also
mixing frequencies present -- however they exhibit different qualitative
behaviors, as befits their different origins, and in the case of inter-band
scattering in an opensystem, may in fact be absent in the dHvA oscillations of
that system.


title: Tensor products of maximal abelian subalgebras of C*-algebras

abstract:
  It is shown that if $C_1$ and $C_2$ are maximal abelian self-adjoint
subalgebras (masas) of C*-algebras $A_1$ and $A_2$, respectively, then the
completion $C_1\otimes C_2$ of the algebraic tensor product $C_1\odot C_2$ of
$C_1$ and $C_2$ in any C*-tensor product $A_1\otimes_{\beta} A_2$ is maximal
abelian provided that $C_1$ has the extension property of Kadison and Singer
and $C_2$ contains an approximate identity for $A_2$. An example is given to
show that $C_1\otimes C_2$ can fail to be a masa in $A_1\otimes_{\beta} A_2$
with $A_1$ and $A_2$ unital if neither $C_1$ nor $C_2$ has the extension
property. This gives an answer to a long-standing question, but leaves open
some other interesting problems, one of which turns out to have a potentially
intriguing implication for the Kadison-Singer extension problem.


title: Kernel Convergence Estimates for Diffusions with Continuous Coefficients

abstract:
  We are interested in the kernel of one-dimensional diffusion equations with
continuous coefficients as evaluated by means of explicit discretization
schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both
semidiscrete triangulations with continuous time and explicit Euler schemes
with time step small enough for the method to be stable. We find sharp uniform
bounds for the convergence rate as a function of the degree of smoothness which
we conjecture. The bounds also apply to the time derivative of the kernel and
its first two space derivatives. Our proof is constructive and is based on a
new technique of path conditioning for Markov chains and a renormalization
group argument. Convergence rates depend on the degree of smoothness and
H\"older differentiability of the coefficients. We find that the fastest
convergence rate is of order $O(h^2)$ and is achieved if the coefficients have
a bounded second derivative. Otherwise, explicit schemes still converge for any
degree of H\"older differentiability except that the convergence rate is
slower. H\"older continuity itself is not strictly necessary and can be relaxed
by an hypothesis of uniform continuity.


title: Free Fermions and Thermal AdS/CFT

abstract:
  The dynamics of finite temperature U(N) gauge theories on $S^3$ can be
described, at weak coupling, by an effective unitary matrix model. Here we
present an exact solution to these models, for any value of $N$, in terms of a
sum over representations. Taking the large $N$ limit of this solution provides
a new perspective on the deconfinement transition which is supposed to be dual
to the Hawking-Page transition. The large $N$ phase transition manifests itself
here in a manner similar to the Douglas-Kazakov phase transition in 2d
Yang-Mills theory. We carry out a complete analysis of the saddle
representation in the simplest case involving only the order parameter ${\rm
Tr}U$. We find that the saddle points corresponding to thermal $AdS$, the small
black hole and the large black hole can all be described in terms of free
fermions. They all admit a simple phase space description {\it a la} the BPS
geometries of Lin, Lunin and Maldacena.


title: Calorimeter Assisted Tracking Algorithm for SiD

abstract:
  Calorimeter-assisted track finding algorithm takes advantage of the finely
segmented electromagnetic calorimeter proposed for the SiD detector concept by
looking for "MIP stubs" produced by charged particles in the calorimeter, and
using them as seeds for pattern recognition in the tracker. The algorithm
allows for efficient reconstruction of tracks that cannot be found using seeds
provided by the vertex detector, even if standalone pattern recognition in the
outer tracker is difficult. The algorithm has been implemented as a package in
the org.lcsim framework. Current status of the package and its performance in
non-prompt tracks reconstruction are described.


title:
Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite
  $W^\ast$-algebras

abstract:
  It is shown that the bona fide generalization of the Vitali-Hahn-Saks Theorem
to von Neumann algebras is possible if, and only if, the algebra is finite.
This settles the problem on the noncommutative Vitali-Hahn-Saks Theorem
completely and provides new means of characterizing finite von Neumann
algebras.


title: Critical Current Calculations For Long $0$-$\pi$ Josephson Junctions

abstract:
  A zigzag boundary between a $d_{x^2-y^2}$ and an $s$-wave superconductor is
believed to behave like a long Josephson junction with alternating sections of
$0$ and $\pi$ symmetry. We calculate the field-dependent critical current of
such a junction, using a simple model. The calculation involves discretizing
the partial differential equation for the phase difference across a long
$0$-$\pi$ junction. In this form, the equations describe a hybrid ladder of
inductively coupled small $0$ and $\pi$ resistively and capacitively shunted
Josephson junctions (RCSJ's). The calculated critical critical current density
$J_c(H_a)$ is maximum at non-zero applied magnetic field $H_a$, and depends
strongly on the ratio of Josephson penetration depth $\lambda_J$ to facet
length $L_f$. If $\lambda_J/L_f \gg 1$ and the number of facets is large, there
is a broad range of $H_a$ where $J_c(H_a)$ is less than $2\%$ of the maximum
critical current density of a long $0$ junction. All of these features are in
qualitative agreement with recent experiments. In the limit $\lambda_J/L_f \to
\infty$, our model reduces to a previously-obtained analytical superposition
result for $J_c(H_a)$. In the same limit, we also obtain an analytical
expression for the effective field-dependent quality factor $Q_J(H_a)$, finding
that $Q_J(H_a) \propto \sqrt{J_c(H_a)}$. We suggest that measuring the
field-dependence of $Q_J(H_a)$ would provide further evidence that this RCSJ
model applies to a long $0$-$\pi$ junction between a d-wave and an s-wave
superconductor.


title:
Comment on ``Time-dependent quasi-Hermitian Hamiltonians and the unitary
  quantum evolution''

abstract:
  In arXiv:0710.5653v1 M. Znojil claims that he has found and corrected an
error in my paper: [Phys. Lett. B \textbf{650}, 208 (2007), arXiv:0706.1872v2]
and that it is possible to escape its main conclusion, namely that the
unitarity of the time-evolution and observability of the Hamiltonian imply
time-independence of the metric operator. In this note I give a very short
calculation showing that the analysis given by M. Znojil also leads to the same
conclusion as of my above-mentioned paper. This is actually a reconfirmation of
the validity of the results of the latter paper.


title:
Analogues of the Smale and Hirsch Theorems for Cooperative Boolean and
  Other Discrete Systems

abstract:
  Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have
been used in multiple applications, most recently for the modeling of gene and
protein networks. In this paper we study to what extent well-known theorems by
Smale and Hirsch, which form part of the theory of (continuous) monotone
dynamical systems, generalize or fail to do so in the discrete case.
  We show that that arbitrary m-dimensional systems cannot necessarily be
embedded into n-dimensional cooperative systems for n=m+1, as in the Smale
theorem for the continuous case, but we show that this is possible for n=m+2 as
long as p is sufficiently large.
  We also prove that a natural discrete analogue of strong cooperativity
implies nontrivial bounds on the lengths of periodic orbits and imposes a
condition akin to Lyapunov stability on all attractors. Finally, we explore
several natural candidates for definitions of irreducibility of a discrete
system. While some of these notions imply the strong cooperativity of a given
cooperative system and impose even tighter bounds on the lengths of periodic
orbits than strong cooperativity alone, other plausible definitions allow the
existence of exponentially long periodic orbits.


title:
Nonlocal SU(3) chiral quark models at finite temperature: the role of
  the Polyakov loop

abstract:
  We analyze the role played by the Polyakov loop in the description of the
chiral phase transition within the framework of nonlocal SU(3) chiral models
with flavor mixing. We show that its presence provides a substantial
enhancement of the predicted critical temperature, bringing it to a better
agreement with the most recent results of lattice calculations.


title:
Modeling He-rich subdwarfs through the Hot-Flasher scenario: First
  Results

abstract:
  We present first results from evolutionary simulations aimed at exploring the
Hot-Flasher scenario for the formation of H-deficient subdwarf stars. The two
types of late hot flashers that lead to He-enriched surfaces, "deep" and
"shallow" mixing cases, are investigated for different metallicities.


title: The quenched critical point of a diluted disordered polymer model

abstract:
  We consider a model for a polymer interacting with an attractive wall through
a random sequence of charges. We focus on the so-called diluted limit, when the
charges are very rare but have strong intensity. In this regime, we determine
the quenched critical point of the model, showing that it is different from the
annealed one. The proof is based on a rigorous renormalization procedure.
Applications of our results to the problem of a copolymer near a selective
interface are discussed.


title: Collinear and soft gluon corrections to Higgs production at NNNLO

abstract:
  I present analytical expressions for the collinear and soft gluon corrections
to Higgs production via the process b bbar -> H as well as gg -> H through
next-to-next-to-next-to-leading order (NNNLO). The soft corrections are
complete while the collinear corrections include leading and some subleading
logarithms. Numerical results at the Tevatron and the LHC are presented,
primarily for b bbar -> H. It is shown that the collinear terms greatly improve
the soft and virtual approximation at next-to-leading order (NLO) and
next-to-next-to-leading order (NNLO), especially when subleading terms are
included. The NNNLO collinear and soft corrections provide significant
enhancements to the total cross section. I also provide expressions for the
collinear and soft corrections through NNNLO for the related Drell-Yan process.


title: Effect of two-boson exchange on parity-violating e-p scattering

abstract:
  We compute the corrections from two-photon and photon-Z exchange in
parity-violating elastic electron-proton scattering, used to extract the
strange form factors of the proton. We use a hadronic formalism that
successfully reconciled the earlier discrepancy in the proton's electron to
magnetic form factor ratio, suitably extended to the weak sector. Implementing
realistic electroweak form factors, we find effects of the order 2-3% at Q^2 <
0.1 GeV^2, which are largest at backward angles, and have a strong Q^2
dependence at low Q^2. Two-boson contributions to the weak axial current are
found to be enhanced at low Q^2 and for forward angles. We provide corrections
at kinematics relevant for recent and upcoming parity-violating experiments.


title:
Comment on ``Quasienergy anholonomy and its application to adiabatic
  quantum state manipulation''

abstract:
  In their Letter [A. Tanaka and M. Miyamoto, Phys. Rev. Lett. 98, 160407
(2007)], Tanaka and Miyamoto introduce a kicked spin model, for which they
point out the generic existence of exotic eigenvalue anholonomy. They proceed
to show the potential utility of the model for quantum state manipulation and
quantum information processing. While we believe their model to be vary useful
and their argument to be revealing, In our view, there are three missing
elements in the article, without which their discussion seems to be incomplete
and the prospect of the application limited. They are on dynamical phase, gauge
potential, and on adiabaticity.


title: Symmetry preserving discretization of SL(2,R) invariant equations

abstract:
  Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We
show that solution methods incorporating the Lie point symmetries provide
better results than standard methods.


title: LQG vertex with finite Immirzi parameter

abstract:
  We extend the definition of the "flipped" loop-quantum-gravity vertex to the
case of a finite Immirzi parameter. We cover the Euclidean as well as the
Lorentzian case. We show that the resulting dynamics is defined on a Hilbert
space isomorphic to the one of loop quantum gravity, and that the area operator
has the same discrete spectrum as in loop quantum gravity. This includes the
correct dependence on the Immirzi parameter, and, remarkably, holds in the
Lorentzian case as well. The ad hoc flip of the symplectic structure that was
initially required to derive the flipped vertex is not anymore needed for
finite Immirzi parameter. These results establish a bridge between canonical
loop quantum gravity and the spinfoam formalism in four dimensions.


title:
Large-$N_c$ relations for the electromagnetic N to Delta(1232)
  transition

abstract:
  We examine the large-$N_c$ relations which express the electromagnetic
$N$-to-$\Delta$ transition quantities in terms of the electromagnetic
properties of the nucleon. These relations are based on the known large-$N_c$
relation between the $N\to \Delta$ electric quadrupole moment and the neutron
charge radius, and a newly derived large-$N_c$ relation between the electric
quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Extending these
relations to finite, but small, momentum transfer we find that the description
of the electromagnetic $N\to\Delta$ ratios ($R_{EM}$ and $R_{SM}$) in terms of
the nucleon form factors predicts a structure which may be ascribed to the
effect of the ``pion cloud''. These relations also provide useful constraints
for the $N \to \Delta$ generalized parton distributions.


title:
Isospin breaking in $K\pi$ vector form-factors for the weak and rare
  decays $K_{\ell3}$, $K\to\pi\nu\bar\nu$ and $K\to\pi\ell^+\ell^-$

abstract:
  We calculate the two form-factors for the four Kaon to pion transitions via a
vector current to order $p^6$ in Chiral Perturbation Theory to first order in
isospin breaking via the quark masses. In addition we derive relations between
these form-factors valid to first order in the up-down quark-mass difference
but to all orders in Chiral Perturbation Theory.
  We present numerical results for all eight form-factors at $t=0$ and for
varying $t$ and for the scalar form-factors at the Callan-Treiman point.


title: Leibniz rules for enveloping algebras in symmetric ordering

abstract:
  Given a finite-dimensional Lie algebra, and a representation by derivations
on the completed symmetric algebra of its dual, a number of interesting twisted
constructions appear: certain twisted Weyl algebras, deformed Leibniz rules,
quantized ``star'' product. We first illuminate a number of interrelations
between these constructions and then proceed to study a special case in certain
precise sense corresponding to the symmetric or Weyl ordering. This case has
been known earlier to be related to computations with Hausdorff series, for
example the expression for the star product is in such terms. For the deformed
Leibniz rule, hence a coproduct, we present here a new nonsymmetric expression,
which is then expanded into a sum of expressions labelled by a class of planar
trees, and for a given tree evaluated by Feynman-like rules. These expressions
are filtered by a bidegree and we show recursion formulas for the sums of
expressions of a given bidegree, and compare the recursions to recursions for
Hausdorff series, including the comparison of initial conditions. This way we
show a direct corespondence between the Hausdorff series and the expression for
twisted coproduct.


title: Space-based research in fundamental physics and quantum technologies

abstract:
  Space-based experiments today can uniquely address important questions
related to the fundamental laws of Nature. In particular, high-accuracy physics
experiments in space can test relativistic gravity and probe the physics beyond
the Standard Model; they can perform direct detection of gravitational waves
and are naturally suited for precision investigations in cosmology and
astroparticle physics. In addition, atomic physics has recently shown
substantial progress in the development of optical clocks and atom
interferometers. If placed in space, these instruments could turn into powerful
high-resolution quantum sensors greatly benefiting fundamental physics.
  We discuss the current status of space-based research in fundamental physics,
its discovery potential, and its importance for modern science. We offer a set
of recommendations to be considered by the upcoming National Academy of
Sciences' Decadal Survey in Astronomy and Astrophysics. In our opinion, the
Decadal Survey should include space-based research in fundamental physics as
one of its focus areas. We recommend establishing an Astronomy and Astrophysics
Advisory Committee's interagency ``Fundamental Physics Task Force'' to assess
the status of both ground- and space-based efforts in the field, to identify
the most important objectives, and to suggest the best ways to organize the
work of several federal agencies involved. We also recommend establishing a new
NASA-led interagency program in fundamental physics that will consolidate new
technologies, prepare key instruments for future space missions, and build a
strong scientific and engineering community. Our goal is to expand NASA's
science objectives in space by including ``laboratory research in fundamental
physics'' as an element in agency's ongoing space research efforts.


title: Selection rules and quark correlations in the $N^*$ resonance spectrum

abstract:
  A "$\Lambda$ selection rule" for $N^*$ resonances in the presence of QCD
mixing effects is identified. Due to the QCD mixing, excitations of {\bf
20}-plets are possible in SU(6). We show that this selection rule is useful for
classifying PDG states at N=2, and for clarifying whether strongly correlated
diquarks survive for $L > 0$.


title:
Disentangling neutrino-nucleon cross section and high energy neutrino
  flux with a km^3 neutrino telescope

abstract:
  The energy--zenith angular event distribution in a neutrino telescope
provides a unique tool to determine at the same time the neutrino-nucleon cross
section at extreme kinematical regions, and the high energy neutrino flux. By
using a simple parametrization for fluxes and cross sections, we present a
sensitivity analysis for the case of a km^3 neutrino telescope. In particular,
we consider the specific case of an under-water Mediterranean telescope placed
at the NEMO site, although most of our results also apply to an under-ice
detector such as IceCube. We determine the sensitivity to departures from
standard values of the cross sections above 1 PeV which can be probed
independently from an a-priori knowledge of the normalization and energy
dependence of the flux. We also stress that the capability to tag downgoing
neutrino showers in the PeV range against the cosmic ray induced background of
penetrating muons appears to be a crucial requirement to derive meaningful
constraints on the cross section.


title: Matter-wave vortices in cigar-shaped and toroidal waveguides

abstract:
  We study vortical states in a Bose-Einstein condensate (BEC) filling a
cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger
equation (NPSE) is derived in this setting, for the models with both repulsive
and attractive inter-atomic interactions. Analytical formulas for the density
profiles are obtained from the NPSE in the case of self-repulsion within the
Thomas-Fermi approximation, and in the case of the self-attraction as exact
solutions (bright solitons). A crucially important ingredient of the analysis
is the comparison of these predictions with direct numerical solutions for the
vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The
comparison demonstrates that the NPSE provides for a very accurate
approximation, in all the cases, including the prediction of the stability of
the bright solitons and collapse threshold for them. In addition to the
straight cigar-shaped trap, we also consider a torus-shaped configuration. In
that case, we find a threshold for the transition from the axially uniform
state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern,
due to the instability in the self-attractive BEC filling the circular trap.


title:
2+1 Flavor Polyakov--Nambu--Jona-Lasinio Model at Finite Temperature and
  Nonzero Chemical Potential

abstract:
  We extend the Polyakov-loop improved Nambu--Jona-Lasinio (PNJL) model to 2+1
flavor case to study the chiral and deconfinement transitions of strongly
interacting matter at finite temperature and nonzero chemical potential. The
Polyakov-loop, the chiral susceptibility of light quarks (u and d) and the
strange quark number susceptibility as functions of temperature at zero
chemical potential are determined and compared with the recent results of
Lattice QCD simulations. We find that there is always an inflection point in
the curve of strange quark number susceptibility accompanying the appearance of
the deconfinement phase, which is consistent with the result of Lattice QCD
simulations. Predictions for the case at nonzero chemical potential and finite
temperature are made as well. We give the phase diagram in terms of the
chemical potential and temperature and find that the critical endpoint (CEP)
moves down to low temperature and finally disappears with the decrease of the
strength of the 't Hooft flavor-mixing interaction.


title: Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model

abstract:
  Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of
the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of
freedom we construct the Pohlmeyer-reduced version of the corresponding sigma
model. The Pohlmeyer reduction procedure involves several steps. Starting with
a coset space string sigma model in the conformal gauge and writing the
classical equations in terms of currents one can fix the residual conformal
diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables
(related locally to currents but non-locally to the original string coordinate
fields) so that the Virasoro constraints are automatically satisfied. The
resulting gauge-fixed equations can be obtained from a Lagrangian of a
non-abelian Toda type: a gauged WZW model with an integrable potential coupled
also to a set of 2d fermionic fields. A gauge-fixed form of the
Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of
the gauged WZW model. Its small-fluctuation spectrum contains 8 bosonic and 8
fermionic degrees of freedom with equal masses. We conjecture that the reduced
model has world-sheet supersymmetry and is ultraviolet-finite. We show that in
the special case of the AdS_2 x S^2 superstring model the reduced theory is
indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of
the sine-Gordon model.


title:
Restoring the density-gradient expansion for exchange in solids and
  surfaces

abstract:
  Successful modern generalized gradient approximations (GGA's) are biased
toward atomic energies. Restoration of the first-principles gradient expansion
for exchange over a wide range of density gradients eliminates this bias. We
introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves
equilibrium properties of densely-packed solids and their surfaces.


title:
The Divine Clockwork: Bohr's correspondence principle and Nelson's
  stochastic mechanics for the atomic elliptic state

abstract:
  We consider the Bohr correspondence limit of the Schrodinger wave function
for an atomic elliptic state. We analyse this limit in the context of Nelson's
stochastic mechanics, exposing an underlying deterministic dynamical system in
which trajectories converge to Keplerian motion on an ellipse. This solves the
long standing problem of obtaining Kepler's laws of planetary motion in a
quantum mechanical setting. In this quantum mechanical setting, local mild
instabilities occur in the Kelperian orbit for eccentricities greater than
1/\sqrt{2} which do not occur classically.


title:
Localized cohomology and some applications of Popa's cocycle
  super-rigidity theorem

abstract:
  We prove that orbit equivalence of measure preserving ergodic a.e. free
actions of a countable group with the relative property (T) is a complete
analytic equivalence relation.


title:
Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron
  Resonance Region Transverse Cross Sections

abstract:
  An empirical fit is described to measurements of inclusive inelastic
electron-deuteron cross sections in the kinematic r ange of four-momentum
transfer $0 \le Q^2<10$ GeV$^2$ and final state invariant mass $1.1<W<3.2$ GeV.
The deuteron fit relies on a fit of the ratio $R_p$ of longitudinal to
transverse cross sections for the proton, and the assumption $R_p=R_n$. The
underlying fit parameters describe the average cross section for proton and
neutron, with a plane-wave impulse approximation used to fit to the deuteron
data. An additional term is used to fill in the dip between the quasi-elastic
peak and the $\Delta(1232)$ resonance. The mean deviation of data from the fit
is 3%, with less than 4% of the data points deviating from the fit by more than
10%.


title: Color Variability of the Blazar AO 0235+16

abstract:
  Multicolor (UBVRIJHK) observations of the blazar AO 0235+16 are analyzed. The
light curves were compiled at the Turin Observatory from literature data and
the results of observations obtained in the framework of the WEBT program
(http://www.to.astro/blazars/webt/). The color variability of the blazar was
studied in eight time intervals with a sufficient number of multicolor optical
observations; JHK data are available for only one of these. The spectral energy
distribution (SED) of the variable component remained constant within each
interval, but varied strongly from one interval to another. After correction
for dust absorption, the SED can be represented by a power law in all cases,
providing evidence for a synchrotron nature of the variable component. We show
that the variability at both optical and IR wavelengths is associated with the
same variable source.


title: Lectures on Models of Neutrino Masses and Mixings

abstract:
  We present a concise review of models for neutrino masses and mixings with
particular emphasis on recent developments and current problems. We discuss in
detail attempts at reproducing approximate tri-bimaximal mixing starting from
discrete symmetry groups, notably A4. We discuss the problems encountered when
trying to extend the symmetry to the quark sector and to construct Grand
Unified versions.


title: Definable Davies' Theorem

abstract:
  We prove the following analogue of a Theorem of R.O. Davies: Every
$\Sigma^1_2$ function $f:\R\times\R\to\R$ can be represented as a sum of
rectangular $\Sigma^1_2$ functions if and only if all reals are constructible.


title: Isoperimetry and Rough Path Regularity

abstract:
  Optimal sample path properties of stochastic processes often involve
generalized H\"{o}lder- or variation norms. Following a classical result of
Taylor, the exact variation of Brownian motion is measured in terms of $\psi
(x) \equiv $ $x^{2}/\log \log (1/x) $ near $0+$. Such $\psi $-variation results
extend to classes of processes with values in abstract metric spaces. (No
Gaussian or Markovian properties are assumed.) To establish integrability
properties of the $\psi $-variation we turn to a large class of Gaussian rough
paths (e.g. Brownian motion and L\'{e}vy's area viewed as a process in a Lie
group) and prove Gaussian integrability properties using Borell's inequality on
abstract Wiener spaces. The interest in such results is that they are
compatible with rough path theory and yield certain sharp regularity and
integrability properties (for iterated Stratonovich integrals, for example)
which would be difficult to obtain otherwise. At last, $\psi $-variation is
identified as robust regularity property of solutions to (random) rough
differential equations beyond semimartingales.


title: A note on convergence of the equi-energy sampler

abstract:
  In a recent paper `The equi-energy sampler with applications statistical
inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou,
Zhou & Wong have presented a new stochastic simulation method called the
equi-energy (EE) sampler. This technique is designed to simulate from a
probability measure $\pi$, perhaps only known up to a normalizing constant. The
authors demonstrate that the sampler performs well in quite challenging
problems but their convergence results (Theorem 2) appear incomplete. This was
pointed out, in the discussion of the paper, by Atchad\'e & Liu (2006) who
proposed an alternative convergence proof. However, this alternative proof,
whilst theoretically correct, does not correspond to the algorithm that is
implemented. In this note we provide a new proof of convergence of the
equi-energy sampler based on the Poisson equation and on the theory developed
in Andrieu et al. (2007) for \emph{Non-Linear} Markov chain Monte Carlo (MCMC).
The objective of this note is to provide a proof of correctness of the EE
sampler when there is only one feeding chain; the general case requires a much
more technical approach than is suitable for a short note. In addition, we also
seek to highlight the difficulties associated with the analysis of this type of
algorithm and present the main techniques that may be adopted to prove the
convergence of it.


title: A slice theorem for quivers with an involution

abstract:
  We study the Luna slice theorem in the case of quivers with an involution or
supermixed quivers as introduced by Zubkov. We construct an analogue to the
notion of a local quiver setting. We use this technique to determine dimension
vectors of simple supermixed representations.


title:
Optical spectroscopy of Arp220: the star formation history of the
  closest ULIRG

abstract:
  We present optical spectra of the merging system Arp 220,taken with the
William Herschel Telescope(WHT) on La Palma. These data were taken with the aim
of investigating the evolution and star formation history of this object.
Spectral synthesis modelling has been used to estimate the ages of the stellar
populations found in the diffuse light sampled by the spectra. The data show a
remarkable uniformity in the stellar populations across the full 65 arcsec
covered by our slit positions, sampling the measurable extent of the galaxy.
The results are consistent with a dominant intermediate-age stellar population
(ISP) with age 0.5 < t_{ISP} $\leq$ 0.9 Gyr that is present at all locations,
with varying contributions from a young ($\leq$ 0.1 Gyr) stellar population
(YSP) component. However, it is notable that while the flux contribution of the
YSP component in the extended regions is relatively small ($\leq$ 40%),
adequate fits in the nuclear region are only found for combinations with a
significant contribution of a YSP component (22 - 63%). Moreover, while a low
intrinsic reddening (E(B - V)$\lsim$ 0.3) is found for the ISPs in the extended
regions, intrinsic reddening values as high as E(B - V) ~ 1.0 are required in
the galactic center. This clearly reflects the presence of a reddening
gradient, with higher concentrations of gas and dust towards the nuclear
regions, coinciding with dust lanes in the HST images. Overall, our results are
consistent with models that predict an epoch of enhanced star formation
coinciding with the first pass of the merging nuclei (represented by the ISP),
with a further episode of star formation occurring as the nuclei finally merge
together (represented by the YSP and ULIRG).


title:
Finite-volume Correction to the Pion Decay Constant in the
  Epsilon-Regime

abstract:
  In the chiral limit of QCD, the pion decay constant F can be extracted from
lattice gauge theory by means of a coupling to isospin chemical potential. Here
we compute the leading correction due to finite volume in the epsilon-expansion
of chiral perturbation theory. A comparison is made to recent Monte Carlo data.


title:
Magnetic resonance in iron oxide nanoparticles: quantum features and
  effect of size

abstract:
  In order to better understand the transition from quantum to classical
behavior in spin system, electron magnetic resonance (EMR) is studied in
suspensions of superparamagnetic magnetite nanoparticles with an average
diameter of ~ 9 nm and analyzed in comparison with the results obtained in the
maghemite particles of smaller size (~ 5 nm). It is shown that both types of
particles demonstrate common EMR behavior, including special features such as
the temperature-dependent narrow spectral component and multiple-quantum
transitions. These features are common for small quantum systems and not
expected in classical case. The relative intensity of these signals rapidly
decreases with cooling or increase of particle size, marking gradual transition
to the classical FMR behavior.


title:
Relative population size, co-operation pressure and strategy correlation
  in two-population evolutionary dynamics

abstract:
  We study the coupled dynamics of two populations of random replicators by
means of statistical mechanics methods, and focus on the effects of relative
population size, strategy correlations and heterogeneities in the respective
co-operation pressures. To this end we generalise existing path-integral
approaches to replicator systems with random asymmetric couplings. This
technique allows one to formulate an effective dynamical theory, which is exact
in the thermodynamic limit and which can be solve for persistent order
parameters in a fixed-point regime regardless of the symmetry of the
interactions. The onset of instability can be determined self-consistently. We
calculate quantities such as the diversity of the respective populations and
their fitnesses in the stationary state, and compare results with data from a
numerical integration of the replicator equations


title: Spherical and hyperbolic lengths of images of arcs

abstract:
  Let $f$ be an analytic function on the unit disc which is in the Dirichlet
class, so the Euclidean area of the image, counting multiplicity, is finite.
The Euclidean length of a radial arc of hyperbolic length $\rho$ is then
$o(\rho^1/2)$. In this note we consider the corresponding results when $f$ maps
into the unit disc with the hyperbolic metric or the Riemann sphere with the
spherical metric. Similar but not identical results hold.


title:
On the distribution of \alpha p modulo one for primes p of a special
  form

abstract:
  A classical problem in analytic number theory is to study the distribution of
$\alpha p$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set of
primes. We consider the subsequence generated by the primes $p$ such that $p+2$
is an almost-prime (the existence of infinitely many such $p$ is another
topical result in prime number theory) and prove that its distribution has a
similar property.


title:
Two magnetic regimes in doped ZnO corresponding to a dilute magnetic
  semiconductor and a dilute magnetic insulator

abstract:
  Films of ZnO doped with magnetic ions, Mn and Co and, in some cases, with Al
have been fabricated with a very wide range of carrier densities. Ferromagnetic
behaviour is observed in both insulating and metallic films, but not when the
carrier density is intermediate. Insulating films exhibit variable range
hopping at low temperatures and are ferromagnetic at room temperature due to
the interaction of the localised spins with static localised states. The
magnetism is quenched when carriers in the localised states become mobile. In
the metallic (degenerate semiconductor) range, robust ferromagnetism reappears
together with very strong magneto-optic signals and room temperature anomalous
Hall data. This demonstrates the polarisation of the conduction bands and
indicates that, when ZnO is doped into the metallic regime, it behaves as a
genuine magnetic semiconductor.


title: Tube formulas for self-similar fractals

abstract:
  Tube formulas (by which we mean an explicit formula for the volume of an
$\epsilon$-neighbourhood of a subset of a suitable metric space) have been used
in many situations to study properties of the subset. For smooth submanifolds
of Euclidean space, this includes Weyl's celebrated results on spectral
asymptotics, and the subsequent relation between curvature and spectrum.
Additionally, a tube formula contains information about the dimension and
measurability of rough sets. In convex geometry, the tube formula of a convex
subset of Euclidean space allows for the definition of certain curvature
measures. These measures describe the curvature of sets which are not too
irregular to support derivatives. In this survey paper, we describe some recent
advances in the development of tube formulas for self-similar fractals, and
their applications and connections to the other topics mentioned here.


title:
Vibrational Recognition of Adsorption Sites for Carbon Monoxide on
  Platinum and Platinum-Ruthenium Surfaces

abstract:
  We have studied the vibrational properties of CO adsorbed on platinum and
platinum-ruthenium surfaces using density-functional perturbation theory within
the Perdew-Burke-Ernzerhof generalized-gradient approximation. The calculated
C-O stretching frequencies are found to be in excellent agreement with
spectroscopic measurements. The frequency shifts that take place when the
surface is covered with ruthenium monolayers are also correctly predicted. This
agreement for both shifts and absolute vibrational frequencies is made more
remarkable by the frequent failure of local and semilocal exchange-correlation
functionals in predicting the stability of the different adsorption sites for
CO on transition metal surfaces. We have investigated the chemical origin of
the C-O frequency shifts introducing an orbital-resolved analysis of the force
and frequency density of states, and assessed the effect of donation and
backdonation on the CO vibrational frequency using a GGA + molecular U
approach. These findings rationalize and establish the accuracy of
density-functional calculations in predicting absolute vibrational frequencies,
notwithstanding the failure in determining relative adsorption energies, in the
strong chemisorption regime.


title: The insulin-RB synapse in health and disease: cellular rocket science

abstract:
  Time has come for a survey of our knowledge on the physical interaction
between the growth-promoting insulin molecule and retinoblastoma tumor
suppressor protein (RB). Theoretical and experimental observations over the
past 15 years reviewed here indicate that the insulin-RB dimer may represent an
essential molecular crossroads involved in major physiological and pathological
conditions. Within this system, the putative tumor suppressor insulin-degrading
enzyme (IDE) should be an important modulator. Perhaps most remarkably, the
abstraction of this encounter between insulin and RB, two growth-regulatory
giants acting either in concert or against each other depending on the
respective cellular requirements, reveals that Nature may compute in
controlling cell fate and we could follow in its footsteps towards developing
more efficient therapeutics as well as novel technical devices.


title: Diagonal multi-matrix correlators and BPS operators in N=4 SYM

abstract:
  We present a complete basis of multi-trace multi-matrix operators that has a
diagonal two point function for the free matrix field theory at finite N. This
generalises to multiple matrices the single matrix diagonalisation by Schur
polynomials. Crucially, it involves intertwining the gauge group U(N) and the
global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups
S_n. When applied to N=4 super Yang-Mills we consider the U(3) subgroup of the
full symmetry group. The diagonalisation allows the description of a dual basis
to multi-traces, which permits the characterisation of the metric on operators
transforming in short representations at weak coupling. This gives a framework
for the comparison of quarter and eighth-BPS giant gravitons of AdS_5 x S^5
spacetime to gauge invariant operators of the dual N=4 SYM.


title:
Maximum Likelihood Method for Cross Correlations with Astrophysical
  Sources

abstract:
  We generalize the Maximum Likelihood-type method used to study cross
correlations between a catalog of candidate astrophysical sources and Ultrahigh
Energy Cosmic Rays (UHECRs), to allow for differing source luminosities. The
new method is applicable to any sparse data set such as UHE gamma rays or
astrophysical neutrinos. Performance of the original and generalized techniques
is evaluated in simulations of various scenarios. Applying the new technique to
data, we find an excess correlation of about 9 events between HiRes UHECRs and
known BLLacs, with a 6*10^-5 probability of such a correlation arising by
chance.


title:
Slip boundary conditions for shear flow of polymer melts past atomically
  flat surfaces

abstract:
  Molecular dynamics simulations are carried out to investigate the dynamic
behavior of the slip length in thin polymer films confined between atomically
smooth thermal surfaces. For weak wall-fluid interactions, the shear rate
dependence of the slip length acquires a distinct local minimum followed by a
rapid growth at higher shear rates. With increasing fluid density, the position
of the local minimum is shifted to lower shear rates. We found that the ratio
of the shear viscosity to the slip length, which defines the friction
coefficient at the liquid/solid interface, undergoes a transition from a nearly
constant value to the power law decay as a function of the slip velocity. In a
wide range of shear rates and fluid densities, the friction coefficient is
determined by the product of the value of surface induced peak in the structure
factor and the contact density of the first fluid layer near the solid wall.


title: Noncommutative Tangent Cones and Calabi Yau Algebras

abstract:
  We study the generalization of the idea of a local quiver of a representation
of a formally smooth algebra, to broader classes of finitely generated
algebras. In this new setting we can construct for every semisimple
representation $M$ a local model and a non-commutative tangent cone. The
representation schemes of these new algebras model the local structure and the
tangent cone of the representation scheme of the original algebra at $M$. In
this way one can try to classify algebras according to their local behavior. As
an application we will show that the tangent cones of Calabi Yau 2 Algebras are
always preprojective algebras. For Calabi Yau 3 Algebras the corresponding
statement would be that the local model and the tangent cones derive from
superpotentials. Although we do not have a proof in all cases, we will show
that this will indeed hold in many cases.


title: Recalibration of Data in the VDFS Science Archives

abstract:
  The VDFS comprises the system to pipeline process and archive the data from
infrared observations taken by both the WFCAM instrument on UKIRT and the
forthcoming VISTA telescope. These include the largest near-IR surveys to date,
such as UKIDSS, which produce terabyte sized catalogues of over 10^9 rows. Such
large data volumes present a performance challenge when the catalogue data,
stored in a relational database, require many iterations of astrometric and
photometric recalibration. Here we present the VDFS recalibration solution that
will be employed in the WSA from the forthcoming UKIDSS Data Release 4 and VSA
from its inception.


title: Einstein-Weyl from Kaluza-Klein

abstract:
  We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl
tensor and point out the emergence of the Einstein-Weyl equations for the
reduction from four to three dimensions. As a byproduct we get a simple
expression for the gravitational instanton density in terms of the Kaluza-Klein
functions.


title: Generic features of the spectrum of trapped polarized fermions

abstract:
  We show that bimodal radio frequency spectra universally arise at
intermediate temperatures in models of strongly interacting trapped Fermi
gases. The bimodality is independent of superfluidity or pseudogap physics,
depending only on the functional form of the equation of state -- which is
constrained by dimensional analysis at low temperatures and the virial
expansion at high temperatures. In addition to these model independent results,
we present a simple calculation of the radio frequency line-shape of a highly
polarized Fermi gas which uses energetic considerations to include final state
interactions. While this model only qualitatively captures the line-shapes
observed in the experiments, it provides a conceptually clean and powerful
technique for estimating the energy scales and how they vary with experimental
parameters.


title: Engineering Space for Light via Transformation Optics

abstract:
  Conceptual studies and numerical simulations are performed for imaging
devices that transform a near-field pattern into magnified far-zone images and
are based on high-order spatial transformation in cylindrical domains. A lens
translating a near-field pattern from an almost circular input boundary onto a
magnified far-field image at a flat output boundary is considered. The lens is
made of a metamaterial with anisotropic permittivity and permeability both
depending on a single 'scaling' parameter of the transformation. Open designs
of the lens with a truncated body ('3/4-body' and '1/4-body' lenses) are
suggested and analyzed. It is shown that the ideal full-lens and the '3/4-body'
lens produce identical images. Numerical simulations of '1/4-body' designs
indicate that further truncation of the lens could limit its per-formance. A
light concentrator, "focusing" far-zone fields into a nanometer-scale area, is
also considered.


title: An algebraic index theorem for Poisson manifolds

abstract:
  The formality theorem for Hochschild chains of the algebra of functions on a
smooth manifold gives us a version of the trace density map from the zeroth
Hochschild homology of a deformation quantization algebra to the zeroth Poisson
homology. We propose a version of the algebraic index theorem for a Poisson
manifold which is based on this trace density map.


title: The true complexity of a system of linear equations

abstract:
  It is well-known that if a subset A of a finite Abelian group G satisfies a
quasirandomness property called uniformity of degree k, then it contains
roughly the expected number of arithmetic progressions of length k, that is,
the number of progressions one would expect in a random subset of G of the same
density as A. One is naturally led to ask which degree of uniformity is
required of A in order to control the number of solutions to a general system
of linear equations. Using so-called "quadratic Fourier analysis", we show that
certain linear systems that were previously thought to require quadratic
uniformity are in fact governed by linear uniformity. More generally, we
conjecture a necessary and sufficient condition on a linear system L which
guarantees that any subset A of F_p^n which is uniform of degree k contains the
expected number of solutions to L.


title: Population-Based Reversible Jump Markov Chain Monte Carlo

abstract:
  In this paper we present an extension of population-based Markov chain Monte
Carlo (MCMC) to the trans-dimensional case. One of the main challenges in
MCMC-based inference is that of simulating from high and trans-dimensional
target measures. In such cases, MCMC methods may not adequately traverse the
support of the target; the simulation results will be unreliable. We develop
population methods to deal with such problems, and give a result proving the
uniform ergodicity of these population algorithms, under mild assumptions. This
result is used to demonstrate the superiority, in terms of convergence rate, of
a population transition kernel over a reversible jump sampler for a Bayesian
variable selection problem. We also give an example of a population algorithm
for a Bayesian multivariate mixture model with an unknown number of components.
This is applied to gene expression data of 1000 data points in six dimensions
and it is demonstrated that our algorithm out performs some competing Markov
chain samplers.


title:
Ground state heavy baryon production in a relativistic quark-diquark
  model

abstract:
  We use current-current interaction to calculate the fragmentation functions
to describe the production of spin-1/2, spin-1/2$'$ and spin-3/2 baryons with
massive constituents in a relativistic quark-diquark model. Our results are in
their analytic forms and are applicable for singly, doubly and triply heavy
baryons. We discuss the production of $\Omega_{bbc}$, $\Omega_{bcc}$ and
$\Omega_{ccc}$ baryons in some detail. The results are satisfactorily compared
with those obtained for triply heavy baryons calculated in a perturbative
regime within reasonable values of the parameters involved.


title: LISA sources and science

abstract:
  LISA is a planned space-based gravitational-wave (GW) detector that would be
sensitive to waves from low-frequency sources, in the band of roughly (0.03 -
0.1) mHz < f < 0.1 Hz. This is expected to be an extremely rich chunk of the GW
spectrum -- observing these waves will provide a unique view of dynamical
processes in astrophysics. Here we give a quick survey of some key LISA sources
and what GWs can uniquely teach us about these sources. Particularly noteworthy
science which is highlighted here is the potential for LISA to track the
moderate to high redshift evolution of black hole masses and spins through the
measurement of GWs generated from massive black hole binaries (which in turn
form by the merger of galaxies and protogalaxies). Measurement of these binary
black hole waves has the potential to determine the masses and spins of the
constituent black holes with percent-level accuracy or better, providing a
unique high-precision probe of an aspect of early structure growth. This
article is based on the "Astrophysics and Relativity using LISA" talk given by
the author at the Seventh Edoardo Amaldi Conference on Gravitational Waves; it
is largely an updating of the author's writeup of a talk given at the Sixth
International LISA Symposium.


title: A Tutorial on Spectral Clustering

abstract:
  In recent years, spectral clustering has become one of the most popular
modern clustering algorithms. It is simple to implement, can be solved
efficiently by standard linear algebra software, and very often outperforms
traditional clustering algorithms such as the k-means algorithm. On the first
glance spectral clustering appears slightly mysterious, and it is not obvious
to see why it works at all and what it really does. The goal of this tutorial
is to give some intuition on those questions. We describe different graph
Laplacians and their basic properties, present the most common spectral
clustering algorithms, and derive those algorithms from scratch by several
different approaches. Advantages and disadvantages of the different spectral
clustering algorithms are discussed.


title:
Search for Mid-IR Flux Variations from The Anomalous X-ray Pulsar 4U
  0142+61

abstract:
  We report on our Spitzer observations of the anomalous X-ray pulsar 4U
0142+61, made following a large X-ray burst that occurred on 2007 February 7.
To search for mid-infrared flux variations, four imaging observations were
carried out at 4.5 and 8.0 $\mu$m with the Infrared Array Camera from February
14 to 21. No significant flux variations were detected, and the average fluxes
were 32.1$\pm$2.0 $\mu$Jy at 4.5 $\mu$m and 59.8$\pm8.5$ $\mu$Jy at 8.0 $\mu$m,
consistent with those obtained in 2005. The non-detection of variability is
interesting in light of reported rapid variability from this source in the
near-infrared, but consistent with the fact that the source already went back
to its quiescent state before our observations began, as indicated by
contemporaneous X-ray observations. In order to understand the origin of the
near-infrared variability, frequent, simultaneous multi-wavelength observations
are needed.


title: Thick triangulations of hyperbolic n-manifolds

abstract:
  We show that a complete hyperbolic n-manifold has a geodesic triangulation
such that the tetrahedra contained in the thick part are L-bilipschitz
diffeomorphic to the standard Euclidean n-simplex, for some constant L
depending only on the dimension and the constant used to define the thick-thin
decomposition of M.


title: Some properties of the Alday-Maldacena minimum

abstract:
  The Alday-Maldacena solution, relevant to the n=4 gluon amplitude in N=4 SYM
at strong coupling, was recently identified as a minimum of the regularized
action in the moduli space of solutions of the AdS_5 sigma-model equations of
motion. Analogous solutions of the Nambu-Goto equations for the n=4 case are
presented and shown to form (modulo the reparametrization group) an equally
large but different moduli space, with the Alday-Maldacena solution at the
intersection of the sigma-model and Nambu-Goto moduli spaces. We comment upon
the possible form of the regularized action for n=5. A function of moduli
parameters z_a is written, whose minimum reproduces the BDDK one-loop
five-gluon amplitude. This function may thus be considered as some kind of
Legendre transform of the BDDK formula and has its own value independently of
the Alday-Maldacena approach.


title: Upper and Lower Bounds on Gravitational Entropy

abstract:
  The entropy in the interior of the Universe has many contributions including
well understood ones from radiation and relic neutrinos. The gravitational
entropy is larger and more subtle. One contribution which provides our lower
bound is from supermassive black holes at the centers of galaxies. The
remainder is harder to pin down. We suggest an upper bound which is many orders
of magnitude below the holographic bound yet above that of the supermassive
black holes. We propose that gravitational entropy in dark matter halos is the
largest contributor to the present entropy of the universe.


title: Coinductive Proof Principles for Stochastic Processes

abstract:
  We give an explicit coinduction principle for recursively-defined stochastic
processes. The principle applies to any closed property, not just equality, and
works even when solutions are not unique. The rule encapsulates low-level
analytic arguments, allowing reasoning about such processes at a higher
algebraic level. We illustrate the use of the rule in deriving properties of a
simple coin-flip process.


title: Sine-Gordon-like action for the Superstring in AdS(5) x S(5)

abstract:
  We propose an action for a sine-Gordon-like theory, which reproduces the
classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring
on AdS(5) x S(5). The action is relativistically invariant. It is a
mass-deformed gauged WZW model for SO(4,1) x SO(5) / SO(4) x SO(4) interacting
with fermions.


title: Charging and Growth of Fractal Dust Grains

abstract:
  The structure and evolution of aggregate grains formed within a plasma
environment are dependent upon the charge acquired by the micron-sized dust
grains during the coagulation process. The manner in which the charge is
arranged on developing irregular structures can affect the fractal dimension of
aggregates formed during collisions, which in turn influences the coagulation
rate and size evolution of the dust within the plasma cloud. This paper
presents preliminary models for the charge and size evolution of fractal
aggregates immersed in a plasma environment calculated using a modification to
the orbital-motion-limited (OML) theory. Primary electron and ion currents
incident on points on the aggregate surface are determined using a
line-of-sight (LOS) approximation: only those electron or ion trajectories
which are not blocked by another grain within the aggregate contribute to the
charging current. Using a self-consistent iterative approach, the equilibrium
charge and dipole moment are calculated for the dust aggregate. The charges are
then used to develop a heuristic charging scheme which can be implemented in
coagulation models. While most coagulation theories assume that it is difficult
for like-charged grains to coagulate, the OML_LOS approximation indicates that
the electric potentials of aggregate structures are often reduced enough to
allow significant coagulation to occur.


title: Searches at LHC Beyond the Standard Model

abstract:
  The discovery potentials of ATLAS and CMS experiments at the Large Hadron
Collider (LHC) for Supersimmetry (SUSY), Extra Dimensions (ED), new Gauge
Bosons and R-Hadrons are discussed. Beyond Standard-Model (BSM) searches at LHC
require a detailed understanding of the detector performance, reconstruction
algorithms and triggering. Precision measurements of Standard Model (SM)
processes are also mandatory to acquire the necessary knowledge of SM
background. Both ATLAS and CMS efforts are hence addressed to determine the
best calibration candles and to design a realistic plan for the initial period
of data taking.


title:
A Geometric Approach to Confidence Sets for Ratios: Fieller's Theorem,
  Generalizations, and Bootstrap

abstract:
  We present a geometric method to determine confidence sets for the ratio
E(Y)/E(X) of the means of random variables X and Y. This method reduces the
problem of constructing confidence sets for the ratio of two random variables
to the problem of constructing confidence sets for the means of one-dimensional
random variables. It is valid in a large variety of circumstances. In the case
of normally distributed random variables, the so constructed confidence sets
coincide with the standard Fieller confidence sets. Generalizations of our
construction lead to definitions of exact and conservative confidence sets for
very general classes of distributions, provided the joint expectation of (X,Y)
exists and the linear combinations of the form aX + bY are well-behaved.
Finally, our geometric method allows to derive a very simple bootstrap approach
for constructing conservative confidence sets for ratios which perform
favorably in certain situations, in particular in the asymmetric heavy-tailed
regime.


title: Simulation of charge reversal in salty environments: Giant overcharging?

abstract:
  We have performed MD simulations of a highly charged colloid in a solution of
3:1 and additional 1:1 salt. The dependency of the colloid's inverted charge on
the concentration of the additional 1:1 salt has been studied. Most theories
predict, that the inverted charge increases when the concentration of
monovalent salt grows, up to what is called "giant overcharging", while
experiments and simulational studies observe the opposite. Our simulations
agree with the experimental findings and shed light onto the weaknesses of the
theories.


title: SUSY in the Light of B Physics and Electroweak Precision Observables

abstract:
  Indirect information about the possible scale of supersymmetry (SUSY)
breaking can be obtained from the comparison of precisely measured observables
(and also of exclusion limits) with accurate theory predictions incorporating
SUSY loop corrections. Recent results are reviewed obtained from a combined
analysis of the most sensitive electroweak precision observables (EWPO), M_W,
sin^2_theta^eff, Gamma_Z, (g-2)_\mu and M_h, and B-physics observables (BPO),
BR(b -> s \gamma), BR(B_s -> \mu^+\mu^-), BR(B_u -> \tau \nu_\tau) and \Delta
M_{B_s}. Assuming that the lightest supersymmetric particle (LSP) provides the
cold dark matter density preferred by WMAP and other cosmological data, \chi^2
fits are performed to the parameters of the constrained minimal supersymmetric
extension of the Standard Model (CMSSM), in which the SUSY-breaking parameters
are universal at the GUT scale, and the non-universal Higgs model (NUHM), in
which this constraint is relaxed for the soft SUSY-breaking contributions to
the Higgs masses. Within the CMSSM indirect bounds on the mass of the lightest
CP-even Higgs boson are derived.


title: Decomposing p-groups via Jordan algebras

abstract:
  For finite p-groups P of class 2 and exponent p the following are invariants
of fully refined central decompositions of P: the number of members in the
decomposition, the multiset of orders of the members, and the multiset of
orders of their centers. Unlike for direct product decompositions, Aut P is not
always transitive on the set of fully refined central decompositions, and the
number of orbits can in fact be any positive integer. The proofs use the
standard semi-simple and radical structure of Jordan algebras. These algebras
also produce useful criteria for a p-group to be centrally indecomposable.