title:
Enhanced Pressure Dependence of Magnetic Exchange in A2+[V2]O4 Spinels
  Approaching the Itinerant Electron Limit

abstract:
  We report a systematic enhancement of the pressure dependence of TN in
A2+[V2]O4 spinels as the V-V separation approaches the critical separation for
a transition to itinerant-electron behavior. An intermediate phase between
localized and itinerant electron behavior is identified in Zn[V2]O4 and
Mg[V2]O4 exhibiting mobile holes as large polarons. In Zn[V2]O4, cooperative
ordering of V-V pairs below a Ts=TN does not totally suppress the V3+-ion spins
at ambient pressure, but makes TN to decrease with pressure. Our results
demonstrate that Zn[V2]O4 and Mg[V2]O4 are less localized than previously
thought.


title: N=4 Supersymmetric MICZ-Kepler systems on S3

abstract:
  Proceeding from the superfield action for $N=4, d=1$ nonlinear
supermultiplet, equipped with the most general potential term, we find the
action describing a charged particle on the sphere $S^3$ in the field of $n$
fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze
some particulary interesting potentials corresponding to the N=4 supersymmetric
extension of the integrable one- and two-center
McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on $S^3$.


title: Fast mode of rotating atoms in one-dimensional lattice rings

abstract:
  We study the rotation of atoms in one-dimensional lattice rings. In
particular, the "fast mode", where the ground state atoms rotate faster than
the stirring rotating the atoms, is studied both analytically and numerically.
The conditions for the transition to the fast mode are found to be very
different from that in continuum rings. We argue that these transition
frequencies remain unchanged for bosonic condensates described in a mean field.
We show that Fermionic interaction and filling factor have a significant effect
on the transition to the fast mode, and Pauli principle may suppress it
altogether.


title: Singular unitarity in "quantization commutes with reduction"

abstract:
  Let $M$ be a connected compact quantizable K\"ahler manifold equipped with a
Hamiltonian action of a connected compact Lie group $G$. Let
$M//G=\phi^{-1}(0)/G=M_0$ be the symplectic quotient at value 0 of the moment
map $\phi$. The space $M_0$ may in general not be smooth. It is known that, as
vector spaces, there is a natural isomorphism between the quantum Hilbert space
over $M_0$ and the $G$-invariant subspace of the quantum Hilbert space over
$M$. In this paper, without any regularity assumption on the quotient $M_0$, we
discuss the relation between the inner products of these two quantum Hilbert
spaces under the above natural isomorphism; we establish asymptotic unitarity
to leading order in Planck's constant of a modified map of the above
isomorphism under a ``metaplectic correction'' of the two quantum Hilbert
spaces.


title: On Lesieur's Measured Quantum Groupoids

abstract:
  In his thesis ([L1]), which is published in an expended and revised version
([L2]), Franck Lesieur had introduced a notion of measured quantum groupoid, in
the setting of von Neumann algebras, using intensively the notion of
pseudo-multiplicative unitary, which had been introduced in a previous article
of the author, in collaboration with Jean-Michel Vallin [EV]. In [L2], the
axioms given are very complicated and are here simplified.


title:
Generalized St\"ackel Transform and Reciprocal Transformations for
  Finite-Dimensional Integrable Systems

abstract:
  We present a multiparameter generalization of the St\"ackel transform (the
latter is also known as the coupling-constant metamorphosis) and show that
under certain conditions this generalized St\"ackel transform preserves the
Liouville integrability, noncommutative integrability and superintegrability.
The corresponding transformation for the equations of motion proves to be
nothing but a reciprocal transformation of a special form, and we investigate
the properties of this reciprocal transformation.
  Finally, we show that the Hamiltonians of the systems possessing separation
curves of apparently very different form can be related through a suitably
chosen generalized St\"ackel transform.


title: Determination of the Jet Energy Scale

abstract:
  The uncertainty in jet energy scale is one of the dominating systematic
errors for many measurements at hadron colliders - most notably for the
measurement of the top-quark-mass, inclusive jet cross section measurements and
last but not least for events with large missing transverse energy as expected
in searches beyond the standard model. This talk will review the approaches
taken at Tevatron towards controlling the jet energy scale and discuss
prospects for the LHC experiments.


title: Jacobi-Nijenhuis algebroids and their modular classes

abstract:
  Jacobi-Nijenhuis algebroids are defined as a natural generalization of
Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis
operator on a Jacobi algebroid which is compatible with it. We study modular
classes of Jacobi and Jacobi-Nijenhuis algebroids.


title:
Entanglement signatures of the quantum phase transition induced by a
  magnetic impurity in a superconductor

abstract:
  The insertion of a magnetic impurity in a superconductor induces a first
order quantum phase transition as the coupling to the electronic spin density
increases. As the transition is crossed, a discontinuity is exhibited by
various quantities, like the total spin density, the total gap function and the
gap function at the impurity location. The location of other quantum phase
transitions have been detected by singularities in entanglement measures of the
system. In this work we show that the single-site and two-site von Neumann
entropies, the mutual information and the Meyer-Wallach measure show
discontinuities at the quantum phase transition. The negativity is less
sensitive to the transition. We study in detail these quantities as a function
of spin coupling and distance from the impurity center.


title: VPSPACE and a transfer theorem over the complex field

abstract:
  We extend the transfer theorem of [KP2007] to the complex field. That is, we
investigate the links between the class VPSPACE of families of polynomials and
the Blum-Shub-Smale model of computation over C. Roughly speaking, a family of
polynomials is in VPSPACE if its coefficients can be computed in polynomial
space. Our main result is that if (uniform, constant-free) VPSPACE families can
be evaluated efficiently then the class PAR of decision problems that can be
solved in parallel polynomial time over the complex field collapses to P. As a
result, one must first be able to show that there are VPSPACE families which
are hard to evaluate in order to separate P from NP over C, or even from PAR.


title: Coherent population transfer in a chain of tunnel coupled quantum dots

abstract:
  We consider the dynamics of a single electron in a chain of tunnel coupled
quantum dots, exploring the formal analogies of this system with some of the
laser-driven multilevel atomic or molecular systems studied by Bruce W. Shore
and collaborators over the last 30 years. In particular, we describe two
regimes for achieving complete coherent transfer of population in such a
multistate system. In the first regime, by carefully arranging the coupling
strengths, the flow of population between the states of the system can be made
periodic in time. In the second regime, by employing a "counterintuitive"
sequence of couplings, the coherent population trapping eigenstate of the
system can be rotated from the initial to the final desired state, which is an
equivalent of the STIRAP technique for atoms or molecules. Our results may be
useful in future quantum computation schemes.


title: SU(N) gauge theories in the presence of a topological term

abstract:
  We review recent results on the theta dependence of the ground-state energy
and spectrum of four-dimensional SU(N) gauge theories, where theta is the
coefficient of the CP-violating topological term F-Fdual in the Lagrangian. In
particular, we discuss the results obtained by Monte Carlo simulations of the
lattice formulation of QCD, which allow the investigation of theta dependence
around theta=0 by determining the moments of the topological charge
distribution, and their correlations with other observables. The results for
N=3 and larger values of N support the scenario obtained by general large-N
scaling arguments.


title:
Some necessary and sufficient conditions for parastrophic invariance of
  the associative law in quasigroups

abstract:
  Every quasigroup $(S,\cdot)$ belongs to a set of 6 quasigroups, called
parastrophes denoted by $(S,\pi_i)$, $i\in \{1,2,3,4,5,6\}$. It is shown that
isotopy-isomorphy is a necessary and sufficient condition for any two distinct
quasigroups $(S,\pi_i)$ and $(S,\pi_j)$, $i,j\in \{1,2,3,4,5,6\}$ to be
parastrophic invariant relative to the associative law. In addition, a
necessary and sufficient condition for any two distinct quasigroups $(S,\pi_i)$
and $(S,\pi_j)$, $i,j\in \{1,2,3,4,5,6\}$ to be parastrophic invariance under
the associative law is either if the $\pi_i$-parastrophe of $H$ is equivalent
to the $\pi_i$-parastrophe of the holomorph of the $\pi_i$-parastrophe of $S$
or if the $\pi_i$-parastrophe of $H$ is equivalent to the $\pi_k$-parastrophe
of the $\pi_i$-parastrophe of the holomorph of the $\pi_i$-parastrophe of $S$,
for a particular $k\in \{1,2,3,4,5,6\}$.


title: Weak Inverse Property Loops and Some Isotopy-Isomorphy Properties

abstract:
  Two distinct isotopy-isomorphy conditions, different from those of J. M.
Osborn and Wilson's condition, for a weak inverse property loop(WIPL) are
shown. Only one of them characterizes isotopy-isomorphy in WIPLs while the
other is just a sufficient condition for isotopy-isomorphy. Under the
sufficient condition called the ${\cal T}$ condition, Artzy's result that
isotopic cross inverse property loops(CIPL) are isomorphic is proved for WIP
loops.


title: On a Pair of Universal Weak Inverse Property Loops

abstract:
  A new condition called ${\cal T}$ condition is introduced for the first time
and used to study a pair of isotopic loops. Under this condition, a loop in the
pair is a WIPL if and only if the other loop is a WIPL. Furthermore, such WIPLs
are isomorphic. The translation elements $f$ and $g$ of a CIPL with the ${\cal
T}$ condition(such that its $f,g$-isotope is an automorphic inverse property
loop) are found to be alternative, flexible, centrum and equal elements. A
necessary and sufficient condition for a pair WIPLs with a weak ${\cal T}$
condition to be isomorphic is shown. A CIPL and an isomorph are observed to
have this weak ${\cal T}$ condition.


title:
Unitary Representations of Wavelet Groups and Encoding of Iterated
  Function Systems in Solenoids

abstract:
  For points in $d$ real dimensions, we introduce a geometry for general digit
sets. We introduce a positional number system where the basis for our
representation is a fixed $d$ by $d$ matrix over $\bz$. Our starting point is a
given pair $(A, \mathcal D)$ with the matrix $A$ assumed expansive, and
$\mathcal D$ a chosen complete digit set, i.e., in bijective correspondence
with the points in $\bz^d/A^T\bz^d$. We give an explicit geometric
representation and encoding with infinite words in letters from $\mathcal D$.
We show that the attractor $X(A^T,\mathcal D)$ for an affine Iterated Function
System (IFS) based on $(A,\mathcal D)$ is a set of fractions for our digital
representation of points in $\br^d$. Moreover our positional "number
representation" is spelled out in the form of an explicit IFS-encoding of a
compact solenoid $\sa$ associated with the pair $(A,\mathcal D)$. The intricate
part (Theorem \ref{thenccycl}) is played by the cycles in $\bz^d$ for the
initial $(A,\mathcal D)$-IFS. Using these cycles we are able to write down
formulas for the two maps which do the encoding as well as the decoding in our
positional $\mathcal D$-representation.
  We show how some wavelet representations can be realized on the solenoid, and
on symbolic spaces.


title: Frames of subspaces and operators

abstract:
  We study the relationship between operators, orthonormal basis of subspaces
and frames of subspaces (also called fusion frames) for a separable Hilbert
space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of
subspaces $\mathcal{E} = \{E_i \}_{i\in I}$ of a Hilbert space $\mathcal{K}$
and a surjective $T\in L(\mathcal{K}, \mathcal{H})$ in order that
$\{T(E_i)\}_{i\in I}$ is a frame of subspaces with respect to a computable
sequence of weights. We also obtain generalizations of results in [J. A.
Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames.
Proc. Amer. Math. Soc. 134 (2006), 1031-1037], which related frames of
subspaces (including the computation of their weights) and oblique projections.
The notion of refinament of a fusion frame is defined and used to obtain
results about the excess of such frames. We study the set of admissible weights
for a generating sequence of subspaces. Several examples are given.


title: Bootstrapping confidence intervals for the change-point of time series

abstract:
  We study an AMOC time series model with an abrupt change in the mean and
dependent errors that fulfill certain mixing conditions. We obtain confidence
intervals for the unknown change-point via bootstrapping methods.
  Precisely we use a block bootstrap of the estimated centered error sequence.
Then we reconstruct a sequence with a change in the mean using the same
estimators as before. The difference between the change-point estimator of the
resampled sequence and the one for the original sequence can be use as an
approximation of the difference between the real change-point and its
estimator. This enables us to construct confidence intervals using the
empirical distribution of the resampled time series.
  A simulation study shows that the resampled confidence intervals are usually
closer to their target levels and at the same time smaller than the asymptotic
intervals.


title:
A Minimization Method for Relativistic Electrons in a Mean-Field
  Approximation of Quantum Electrodynamics

abstract:
  We study a mean-field relativistic model which is able to describe both the
behavior of finitely many spin-1/2 particles like electrons and of the Dirac
sea which is self-consistently polarized in the presence of the real particles.
The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the
photon field. All our results are non-perturbative and mathematically rigorous.


title:
Semiclassical theory of the Ehrenfest-time dependence of quantum
  transport

abstract:
  In ballistic conductors, there is a low-time threshold for the appearance of
quantum effects in transport coefficients. This low-time threshold is the
Ehrenfest time. Most previous studies of the Ehrenfest-time dependence of
quantum transport assumed ergodic electron dynamics, so that they could be
applied to ballistic quantum dots only. In this article we present a theory of
the Ehrenfest-time dependence of three signatures of quantum transport - the
Fano factor for the shot noise power, the weak localization correction to the
conductance, and the conductance fluctuations - for arbitrary ballistic
conductors.


title: Dynamical matrix of two-dimensional electron crystals

abstract:
  In a quantizing magnetic field, the two-dimensional electron (2DEG) gas has a
rich phase diagram with broken translational symmetry phases such as Wigner,
bubble, and stripe crystals. In this paper, we derive a method to get the
dynamical matrix of these crystals from a calculation of the density response
function performed in the Generalized Random Phase Approximation (GRPA). We
discuss the validity of our method by comparing the dynamical matrix calculated
from the GRPA with that obtained from standard elasticity theory with the
elastic coefficients obtained from a calculation of the deformation energy of
the crystal.


title:
New Asymptotic Profiles of Nonstationnary Solutions of the Navier-Stokes
  System

abstract:
  We show that solutions $u(x,t)$ of the non-stationnary incompressible
Navier--Stokes system in $\R^d$ ($d\geq2$) starting from mild decaying data $a$
behave as $|x|\to\infty$ as a potential field: u(x,t) = e^{t\Delta}a(x) +
\gamma_d\nabla_x(\sum_{h,k} \frac{\delta_{h,k}|x|^2 - d x_h x_k}{d|x|^{d+2}}
K_{h,k}(t))+\mathfrak{o}(\frac{1}{|x|^{d+1}}) where $\gamma_d$ is a constant
and $K_{h,k}=\int_0^t(u_h| u_k)_{L^2}$ is the energy matrix of the flow. We
deduce that, for well localized data, and for small $t$ and large enough $|x|$,
c t |x|^{-(d+1)} \le |u(x,t)|\le c' t |x|^{-(d+1)}, where the lower bound holds
on the complementary of a set of directions, of arbitrary small measure on
$\mathbb{S}^{d-1}$. We also obtain new lower bounds for the large time decay of
the weighted-$L^p$ norms, extending previous results of Schonbek, Miyakawa, Bae
and Jin.


title: Radiative Fermion Mass Hierarchy in a Non-supersymmetric Unified Theory

abstract:
  In non-supersymmetric grand unified models a ``radiative fermion mass
hierarchy" can be achieved in which the spectrum of quark and lepton masses is
determined entirely by physics at the unification scale, with many relations
following from the unified gauge symmetry, and with the masses of the lightest
family arising from loops. A simple, realistic, and predictive model of this
kind is presented. A "doubly lopsided" structure, known to lead to bilarge
neutrino mixing, plays a crucial role in the radiative hierarchy.


title:
Weather induced effects on extensive air showers observed with the
  surface detector of the Pierre Auger Observatory

abstract:
  The rate of events measured with the surface detector of the Pierre Auger
Observatory is found to be modulated by the weather conditions. This effect is
due to the increasing amount of matter traversed by the shower as the ground
pressure increases and to the inverse proportionality of the Moliere radius to
the air density near ground. Air-shower simulations with different realistic
profiles of the atmosphere support this interpretation of the observed effects.


title:
How do trehalose, maltose and sucrose influence some structural and
  dynamical properties of lysozyme ? An insight from Molecular Dynamics
  simulations

abstract:
  The influence of three well-known disaccharides, namely trehalose, maltose
and sucrose, on some structural and dynamical properties of lysozyme has been
investigated by means of molecular dynamics computer simulations in the 37-60
wt % concentration range. The effects of sugars on the protein conformation are
found relatively weak, in agreement with the preferential hydration of
lysozyme. Conversely, sugars seem to increase significantly the relaxation
times of the protein. These effects are shown to be correlated to the
fractional solvent accessibilities of lysozyme residues and further support the
slaving of protein dynamics. Moreover, a significant increase in the relaxation
times of lysozyme, sugars and water molecules is observed within the studied
concentration range and may result from the percolation of the hydrogen-bond
network of sugar molecules. This percolation appears to be of primary
importance to explain the influence of sugars on the dynamical properties of
lysozyme and water.


title: Dynamical Screening of Atom Confined by Finite-Width Fullerene

abstract:
  This is an investigation on the dynamical screening of an atom confined
within a fullerene of finite width. The two surfaces of the fullerene lead to
the presence of two surface plasmon eigenmodes. It is shown that, in the
vicinity of these two eigenfrequencies, there is a large enhancement of the
confined atom's photoabsorption rate.


title:
Fluctuations of finite-time stability exponents in the standard map and
  the detection of small islands

abstract:
  Some statistical properties of finite-time stability exponents in the
standard map can be estimated analytically. The mean exponent averaged over the
entire phase space behaves quite differently from all the other cumulants.
Whereas the mean carries information about the strength of the interaction, and
only indirect information about dynamical correlations, the higher cumulants
carry information about dynamical correlations and essentially no information
about the interaction strength. In particular, the variance and higher
cumulants of the exponent are very sensitive to dynamical correlations and
easily detect the presence of very small islands of regular motion via their
anomalous time-scalings. The average of the stability matrix' inverse trace is
even more sensitive to the presence of small islands and has a seemingly
fractal behavior in the standard map parameter. The usual accelerator modes and
the small islands created through double saddle node bifurcations, which come
halfway between the positions in interaction strength of the usual accelerator
modes, are clearly visible in the variance, whose time scaling is capable of
detecting the presence of islands as small as 0.01% of the phase space. We
study these quantities with a local approximation to the trace of the stability
matrix which significantly simplifies the numerical calculations as well as
allows for generalization of these methods to higher dimensions. We also
discuss the nature of this local approximation in some detail.


title:
Study of the Cosmic Ray Composition above 0.4 EeV using the Longitudinal
  Profiles of Showers observed at the Pierre Auger Observatory

abstract:
  The Pierre Auger Observatory has been collecting data in a stable manner
since January 2004. We present here a study of the cosmic ray composition using
events recorded in hybrid mode during the first years of data taking. These are
air showers observed by the fluorescence detector as well as the surface
detector, so the depth of shower maximum, Xmax, is measured directly. The
cosmic ray composition is studied in different energy ranges by comparing the
observed average Xmax with predictions from air shower simulations for
different nuclei. The change of <Xmax> with energy (elongation rate) is used to
derive estimates of the change in primary composition.


title: Time-Delayed Feedback control of a flashing ratchet

abstract:
  Closed-loop or feedback control ratchets use information about the state of
the system to operate with the aim of maximizing the performance of the system.
In this paper we investigate the effects of a time delay in the feedback for a
protocol that performs an instantaneous maximization of the center-of-mass
velocity. For the one and the few particle cases the flux decreases with
increasing delay, as an effect of the decorrelation of the present state of the
system with the information that the controller uses, but the delayed
closed-loop protocol succeeds to perform better than its open-loop counterpart
provided the delays are smaller than the characteristic times of the Brownian
ratchet. For the many particle case, we also show that for small delays the
center-of-mass velocity decreases for increasing delays. However, for large
delays we find the surprising result that the presence of the delay can improve
the performance of the nondelayed feedback ratchet and the flux can attain the
maximum value obtained with the optimal periodic protocol. This phenomenon is
the result of the emergence of a dynamical regime where the presence of the
delayed feedback stabilizes one quasiperiodic solution or several
(multistability), which resemble the solutions obtained in the so-called
threshold protocol. Our analytical and numerical results point towards the
feasibility of an experimental implementation of a feedback controlled ratchet
that performs equal or better than its optimal open-loop version.


title:
Power-free values, repulsion between points, differing beliefs and the
  existence of error

abstract:
  Let f be a cubic polynomial. Then there are infinitely many primes p such
that f(p) is square-free.


title: On the derived category of 1-motives, I

abstract:
  We consider the category of Deligne 1-motives over a perfect field k of
exponential characteristic p and its derived category for a suitable exact
structure after inverting p. As a first result, we provide a fully faithful
embedding into an etale version of Voevodsky's triangulated category of
geometric motives. Our second main result is that this full embedding "almost"
has a left adjoint, that we call \LAlb. Applied to the motive of a variety we
thus get a bounded complex of 1-motives, that we compute fully for smooth
varieties and partly for singular varieties. As an application we give motivic
proofs of Roitman type theorems (in characteristic 0).


title: Elementary Maps on Triangular Algebras

abstract:
  In this note we prove that elementary maps on triangular algebras are
automically additive.


title: X-ray Flares in Orion Low Mass Stars

abstract:
  Context. X-ray flares are common phenomena in pre-main sequence stars. Their
analysis gives insights into the physics at work in young stellar coronae. The
Orion Nebula Cluster offers a unique opportunity to study large samples of
young low mass stars. This work is part of the Chandra Orion Ultradeep project
(COUP), an ~10 day long X-ray observation of the Orion Nebula Cluster (ONC).
Aims. Our main goal is to statistically characterize the flare-like variability
of 165 low mass (0.1-0.3 M_sun) ONC members in order to test and constrain the
physical scenario in which flares explain all the observed emission. Methods.
We adopt a maximum likelihood piece-wise representation of the observed X-ray
light curves and detect flares by taking into account both the amplitude and
time derivative of the count-rate. We then derive the frequency and energy
distribution of the flares. Results. The high energy tail of the energy
distribution of flares is well described by a power-law with index 2.2. We test
the hypothesis that light curves are built entirely by overlapping flares with
a single power law energy distribution. We constrain the parameters of this
simple model for every single light curve. The analysis of synthetic light
curves obtained from the model indicates a good agreement with the observed
data. Comparing low mass stars with stars in the mass interval (0.9-1.2M_sun),
we establish that, at ~1 Myr, low mass and solar mass stars of similar X-ray
luminosity have very similar flare frequencies. Conclusions. Our observational
results are consistent with the following model/scenario: the light curves are
entirely built by over- lapping flares with a power-law intensity distribution;
the intense flares are individually detected, while the weak ones merge and
form a pseudo-quiescent level, which we indicate as the characteristic level.


title:
Longitudinal Shower Profile Reconstruction from Fluorescence and
  Cherenkov Light

abstract:
  Traditionally, longitudinal shower profiles are reconstructed in fluorescence
light experiments by treating the Cherenkov light contribution as background.
Here we will argue that, due to universality of the energy spectra of electrons
and positrons, both fluorescence and Cherenkov light can be used simultaneously
as signal to infer the longitudinal shower development. We present a new
profile reconstruction method that is based on the analytic least-square
solution for the estimation of the shower profile from the observed light
signal and discuss the extrapolation of the profile with a Gaisser-Hillas
function.


title: Additivity of Maps on Triangular Algebras

abstract:
  We prove that every multiplicative bijective map, Jordan bijective map, and
Jordan triple bijective map from a triangular algebra onto any ring is
automatically additive.


title:
The law of the supremum of a stable L\'{e}vy process with no negative
  jumps

abstract:
  Let $X=(X_t)_{t\ge0}$ be a stable L\'{e}vy process of index $\alpha \in(1,2)$
with no negative jumps and let $S_t=\sup_{0\le s\le t}X_s$ denote its running
supremum for $t>0$. We show that the density function $f_t$ of $S_t$ can be
characterized as the unique solution to a weakly singular Volterra integral
equation of the first kind or, equivalently, as the unique solution to a
first-order Riemann--Liouville fractional differential equation satisfying a
boundary condition at zero. This yields an explicit series representation for
$f_t$. Recalling the familiar relation between $S_t$ and the first entry time
$\tau_x$ of $X$ into $[x,\infty)$, this further translates into an explicit
series representation for the density function of $\tau_x$.


title: Free Energy of Activation for the Comorosan Effect

abstract:
  Initial reaction rate data for lactic dehydrogenase / pyruvate, lactic
dehydrogenase / lactate and malic dehydrogenase / malate enzyme reactions were
analyzed to obtain activation free energy changes of -329, -195 and -221
cal/mole, respectively, for rate increases associated with time-specific
irradiation of the crystalline substrates prior to dissolution and
incorporation in the reaction solutions. These energies, presumably, correspond
to conformational or vibrational changes in the reactants or the activated
complex. For the lactic dehydrogenase / pyruvate reaction, it is estimated that
on the order of 10% of the irradiation energy (546 nm, 400 footcandles for 5
seconds) would be required to produce the observed reaction rate increase if a
presumed photoproduct is consumed stoichiometrically with the pyruvate
substrate. These findings are consistent with the proposition that the observed
reaction rate enhancement involves photoproducts derived from oscillatory
atmospheric gas reactions at the crystalline enzyme substrate surfaces rather
than photo-excitations of the substrate molecules, per se.


title:
Very High Energy Gamma-ray Radiation from the Stellar-mass Black Hole
  Cygnus X-1

abstract:
  We report on the results from the observations in very high energy band (VHE,
E_gamma > 100 GeV) of the black hole X-ray binary (BHXB) Cygnus X-1. The
observations were performed with the MAGIC telescope, for a total of 40 hours
during 26 nights, spanning the period between June and November 2006. Searches
for steady gamma-ray signals yielded no positive result and upper limits to the
integral flux ranging between 1 and 2% of the Crab nebula flux, depending on
the energy, have been established. We also analyzed each observation night
independently, obtaining evidence of gamma-ray signals at the 4.0 standard
deviations (sigma) significance level (3.2 sigma after trial correction) for
154 minutes effective on-time (EOT) on September 24 between 20h58 and 23h41
UTC, coinciding with an X-ray flare seen by RXTE, Swift and INTEGRAL. A search
for faster-varying signals within a night resulted in an excess with a
significance of 4.9 sigma (4.1 sigma after trial correction) for 79 minutes EOT
between 22h17 and 23h41 UTC. The measured excess is compatible with a
point-like source at the position of Cygnus X-1, and excludes the nearby radio
nebula powered by its relativistic jet. The differential energy spectrum is
well fitted by an unbroken power-law described by dN/(dA dt dE) = (2.3+- 0.6) x
10^{-12} (E/1 TeV)^{-3.2 +- 0.6}. This is the first experimental evidence of
VHE emission from a stellar-mass black hole, and therefore from a confirmed
accreting X-ray binary.


title:
Electronic transport in normal-conductor/graphene/normal-conductor
  junctions and conditions for insulating behavior at a finite charge-carrier
  density

abstract:
  We investigate the conductance of normal-conductor/graphene/normal-conductor
(NGN) junctions for arbitrary on-site potentials in the normal and graphitic
parts of the system. We find that a ballistic NGN junction can display
insulating behavior even when the charge-carrier density in the graphene part
is finite. This effect originates in the different k intervals supporting
propagating modes in graphene and a normal conductor, and persists for moderate
levels of bulk, edge, or interface disorder. The ensuing conductance thresholds
could be used as an electronic tool to map out details of the graphene band
structure in absolute k space.


title:
Scaling laws for soliton pulse compression by cascaded quadratic
  nonlinearities

abstract:
  We present a detailed study of soliton compression of ultra-short pulses
based on phase-mismatched second-harmonic generation (\textit{i.e.}, the
cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The
single-cycle propagation equations in the temporal domain including
higher-order nonlinear terms are presented. The balance between the quadratic
(SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an
effective soliton number -- related to the difference between the SHG and the
Kerr soliton numbers -- and show that it has to be larger than unity for
successful pulse compression to take place. This requires that the phase
mismatch be below a critical level, which is high in a material where the
quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through
extensive numerical simulations we find dimensionless scaling laws, expressed
through the effective soliton number, which control the behaviour of the
compressed pulses. These laws hold in the stationary regime, in which
group-velocity mismatch effects are small, and they are similar to the ones
observed for fiber soliton compressors. The numerical simulations indicate that
clean compressed pulses below two optical cycles can be achieved in a
$\beta$-barium borate crystal at appropriate wavelengths, even for picosecond
input pulses.


title: Sequential weak measurement

abstract:
  The notion of weak measurement provides a formalism for extracting
information from a quantum system in the limit of vanishing disturbance to its
state. Here we extend this formalism to the measurement of sequences of
observables. When these observables do not commute, we may obtain information
about joint properties of a quantum system that would be forbidden in the usual
strong measurement scenario. As an application, we provide a physically
compelling characterisation of the notion of counterfactual quantum
computation.


title: Grassmann Integral Representation for Spanning Hyperforests

abstract:
  Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.

categories: math-ph cond-mat.stat-mech hep-lat math.CO math.MP


title: Aromatic emission from the ionised mane of the Horsehead nebula

abstract:
  We study the evolution of the Aromatic Infrared Bands (AIBs) emitters across
the illuminated edge of the Horsehead nebula and especially their survival and
properties in the HII region. We present spectral mapping observations taken
with the Infrared Spectrograph (IRS) at wavelengths 5.2-38 microns. A strong
AIB at 11.3 microns is detected in the HII region, relative to the other AIBs
at 6.2, 7.7 and 8.6 microns. The intensity of this band appears to be
correlated with the intensity of the [NeII] at 12.8 microns and of Halpha,
which shows that the emitters of the 11.3 microns band are located in the
ionised gas. The survival of PAHs in the HII region could be due to the
moderate intensity of the radiation field (G0 about 100) and the lack of
photons with energy above about 25eV. The enhancement of the intensity of the
11.3 microns band in the HII region, relative to the other AIBs can be
explained by the presence of neutral PAHs. Our observations highlight a
transition region between ionised and neutral PAHs observed with ideal
conditions in our Galaxy. A scenario where PAHs can survive in HII regions and
be significantly neutral could explain the detection of a prominent 11.3
microns band in other Spitzer observations.


title: Pulsar Kicks With Modified URCA and Electrons in Landau Levels

abstract:
  We derive the energy asymmetry given the proto-neutron star during the time
when the neutrino sphere is near the surface of the proto-neutron star, using
the modified URCA process. The electrons produced with the anti-neutrinos are
in Landau levels due to the strong magnetic field, and this leads to asymmetry
in the neutrino momentum, and a pulsar kick. The magnetic field must be strong
enough for a large fraction of the eletrons to be in the lowest Landau level,
however, there is no direct dependence of our pulsar velocity on the strength
of the magnetic field. Our main prediction is that the large pulsar kicks start
at about 10 s and last for about 10 s, with the corresponding neutrinos
correlated in the direction of the magnetic field. We predict a pulsar velocity
of 1.03 $\times 10^{-4} (T/10^{10}K)^7$ km/s, which reaches 1000 km/s if T
$\simeq 9.96 \times 10^{10}$ K.


title: Local stability of ergodic averages

abstract:
  The mean ergodic theorem is equivalent to the assertion that for every
function K and every epsilon, there is an n with the property that the ergodic
averages A_m f are stable to within epsilon on the interval [n,K(n)]. We show
that even though it is not generally possible to compute a bound on the rate of
convergence of a sequence of ergodic averages, one can give explicit bounds on
n in terms of K and || f || / epsilon. This tells us how far one has to search
to find an n so that the ergodic averages are "locally stable" on a large
interval. We use these bounds to obtain a similarly explicit version of the
pointwise ergodic theorem, and show that our bounds are qualitatively different
from ones that can be obtained using upcrossing inequalities due to Bishop and
Ivanov. Finally, we explain how our positive results can be viewed as an
application of a body of general proof-theoretic methods falling under the
heading of "proof mining."


title: How to tell a gravastar from a black hole

abstract:
  Gravastars have been recently proposed as potential alternatives to explain
the astrophysical phenomenology traditionally associated to black holes,
raising the question of whether the two objects can be distinguished at all.
Leaving aside the debate about the processes that would lead to the formation
of a gravastar and the astronomical evidence in their support, we here address
two basic questions: Is a gravastar stable against generic perturbations? If
stable, can an observer distinguish it from a black hole of the same mass? To
answer these questions we construct a general class of gravastars and determine
the conditions they must satisfy in order to exist as equilibrium solutions of
the Einstein equations. For such models we perform a systematic stability
analysis against axial-perturbations, computing the real and imaginary parts of
the eigenfrequencies. Overall, we find that gravastars are stable to axial
perturbations, but also that their quasi-normal modes differ from those of a
black hole of the same mass and thus can be used to discern, beyond dispute, a
gravastar from a black hole.


title: Electron and hole spin dynamics and decoherence in quantum dots

abstract:
  In this article we review our work on the dynamics and decoherence of
electron and hole spins in single and double quantum dots. The first part, on
electron spins, focuses on decoherence induced via the hyperfine interaction
while the second part covers decoherence and relaxation of heavy-hole spins due
to spin-orbit interaction as well as the manipulation of heavy-hole spin using
electric dipole spin resonance.


title: The generalized non-linear Schrodinger model on the interval

abstract:
  The generalized (1+1)-D non-linear Schrodinger (NLS) theory with particular
integrable boundary conditions is considered. More precisely, two distinct
types of boundary conditions, known as soliton preserving (SP) and soliton
non-preserving (SNP), are implemented into the classical $gl_N$ NLS model.
Based on this choice of boundaries the relevant conserved quantities are
computed and the corresponding equations of motion are derived. A suitable
quantum lattice version of the boundary generalized NLS model is also
investigated. The first non-trivial local integral of motion is explicitly
computed, and the spectrum and Bethe Ansatz equations are derived for the
soliton non-preserving boundary conditions.


title:
Creating pseudo Kondo-resonances by field-induced diffusion of atomic
  hydrogen

abstract:
  In low temperature scanning tunneling microscopy (STM) experiments a cerium
adatom on Ag(100) possesses two discrete states with significantly different
apparent heights. These atomic switches also exhibit a Kondo-like feature in
spectroscopy experiments. By extensive theoretical simulations we find that
this behavior is due to diffusion of hydrogen from the surface onto the Ce
adatom in the presence of the STM tip field. The cerium adatom possesses
vibrational modes of very low energy (3-4meV) and very high efficiency (> 20%),
which are due to the large changes of Ce-states in the presence of hydrogen.
The atomic vibrations lead to a Kondo-like feature at very low bias voltages.
We predict that the same low-frequency/high-efficiency modes can also be
observed at lanthanum adatoms.


title:
Supersolid phase induced by correlated hopping in spin-1/2 frustrated
  quantum magnets

abstract:
  We show that correlated hopping of triplets, which is often the dominant
source of kinetic energy in dimer-based frustrated quantum magnets, produces a
remarkably strong tendency to form supersolid phases in a magnetic field. These
phases are characterized by simultaneous modulation and ordering of the
longitudinal and transverse magnetization respectively. Using Quantum Monte
Carlo and a semiclassical approach for an effective hard-core boson model with
nearest-neighbor repulsion on a square lattice, we prove in particular that a
supersolid phase can exist even if the repulsion is not strong enough to
stabilize an insulating phase at half-filling. Experimental implications for
frustrated quantum antiferromagnets in a magnetic field at zero and finite
temperature are discussed.


title: GRB051022: physical parameters and extinction of a prototype dark burst

abstract:
  GRB051022 was undetected to deep limits in early optical observations, but
precise astrometry from radio and X-ray showed that it most likely originated
in a galaxy at z~0.8. We report radio, optical, near infra-red and X-ray
observations of GRB051022. Using the available X-ray and radio data, we model
the afterglow and calculate the energetics of the afterglow, finding it to be
an order of magnitude lower than that of the prompt emission. The broad-band
modeling also allows us to precisely define various other physical parameters
and the minimum required amount of extinction, to explain the absence of an
optical afterglow. Our observations suggest a high extinction, at least 2.3
magnitudes in the infrared (J) and at least 5.4 magnitudes in the optical (U)
in the host-galaxy restframe. Such high extinctions are unusual for GRBs, and
likely indicate a geometry where our line of sight to the burst passes through
a dusty region in the host that is not directly co-located with the burst
itself.


title:
A novel method for evaluating the critical nucleus and the surface
  tension in systems with first order phase transition

abstract:
  We introduce a novel method for calculating the size of the critical nucleus
and the value of the surface tension in systems with first order phase
transition. The method is based on classical nucleation theory, and it consists
in studying the thermodynamics of a sphere of given radius embedded in a frozen
metastable surrounding. The frozen configuration creates a pinning field on the
surface of the free sphere. The pinning field forces the sphere to stay in the
metastable phase as long as its size is smaller than the critical nucleus. We
test our method in two first-order systems, both on a two-dimensional lattice:
a system where the parameter tuning the transition is the magnetic field, and a
second system where the tuning parameter is the temperature. In both cases the
results are satisfying. Unlike previous techniques, our method does not require
an infinite volume limit to compute the surface tension, and it therefore gives
reliable estimates even by using relatively small systems. However, our method
cannot be used at, or close to, the critical point, i.e. at coexistence, where
the critical nucleus becomes infinitely large.


title: On dynamical bit sequences

abstract:
  Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random
variables, each taking the values 1 or 0 with respective probabilities p and
1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is
constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that
it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We
derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for
some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in
two very different settings:
  (i) Where \ell is a constant; and
  (ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is
described by the Kolmogorov capacitance of F for case (i) and Howroyd's
1/2-dimensional box-dimension profiles for case (ii). We also present
sample-path consequences, and a connection to capacities that answers a
question of Benjamini et. al. (2003)


title: $\nu$ masses in a SUSY SO(10) theory with spontaneous CP violation

abstract:
  We propose a possibility of spontaneous CP-violation (SCPV) at high scale in
a SUSY SO(10) theory. The model is L-R symmetric SUSY SO(10) with
\textbf{\noun{10}} and \textbf{126} dimensional Higgs generating fermion
masses, and the CP phase is generated through complex VEV of B-L breaking
\textbf{126} Higgs . The model can have potential application in explaining
$\nu$ masses and leptogenesis as well.


title:
Viscosity Information from Relativistic Nuclear Collisions: How Perfect
  is the Fluid Observed at RHIC?

abstract:
  Relativistic viscous hydrodynamic fits to RHIC data on the centrality
dependence of multiplicity, transverse and elliptic flow for sqrt{s}=200 GeV
Au+Au collisions are presented. For Glauber-type initial conditions, while data
on integrated v_2 is consistent with a ratio of viscosity over entropy density
up to eta/s=0.16, data on minimum bias v_2 seems to favor a much smaller
viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some
caveats on this result are discussed.


title: Thom polynomials for maps of curves with isolated singularities

abstract:
  Thom (residual) polynomials in characteristic classes are used in the
analysis of geometry of functional spaces. They serve as a tool in description
of classes Poincar\'e dual to subvarieties of functions of prescribed types. We
give explicit universal expressions for residual polynomials in spaces of
functions on complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These expressions
lead to a partial explicit description of a stratification of Hurwitz spaces.


title: Helix, shadow boundary and minimal submanifolds

abstract:
  Inspired by a Blaschke's work about analytic convex surfaces, we study {\em
shadow boundaries} of Riemannian submanifolds $M$, which are defined by a
parallel vector field along $M$. Since a shadow boundary is just a closed
subset of $M$, first, we will give a condition that guarantee its smoothness.
It depends on the second fundamental form of the submanifold. It is natural to
search for what kind of properties might have such submanifolds of $M$? Could
they be totally geodesic or minimal? Answers to these and related questions are
given in this work.


title:
Perturbative study of the transfer matrix on the string worldsheet in
  AdS(5)xS(5)

abstract:
  Quantum non-local charges are central to the quantum integrability of a
sigma-model. In this paper we study the quantum consistency and UV finiteness
of non-local charges of string theory in AdS(5)xS(5). We use the pure spinor
formalism. We develop the near-flat space expansion of the transfer matrix and
calculate the one-loop divergences. We find that the logarithmic divergences
cancel at the level of one loop. This gives strong support to the quantum
integrability of the full string theory. We develop a calculational setup for
the renormalization group analysis of Wilson line type of operators on the
string worldsheet.


title: On Colorings of Squares of Outerplanar Graphs

abstract:
  We study vertex colorings of the square $G^2$ of an outerplanar graph $G$. We
find the optimal bound of the inductiveness, chromatic number and the clique
number of $G^2$ as a function of the maximum degree $\Delta$ of $G$ for all
$\Delta\in \nats$. As a bonus, we obtain the optimal bound of the choosability
(or the list-chromatic number) of $G^2$ when $\Delta \geq 7$. In the case of
chordal outerplanar graphs, we classify exactly which graphs have parameters
exceeding the absolute minimum.


title: Surface waves in defocusing thermal nonlinear optical media

abstract:
  We predict that the interface of materials with defocusing thermal
nonlinearities support stable fundamental and higher-order surface waves when
the opposite edges of the medium are maintained at different temperatures. Such
surface waves exist due to the interplay between repulsion from the interface
and the defocusing thermal nonlinearity that deflect light beams from the bulk
of the medium toward its edges.


title: $H_D$-Quantum Vertex Algebras and Bicharacters

abstract:
  We define a new class of quantum vertex algebras, based on the Hopf algebra
$H_D=\mathbb{C}[D]$ of "infinitesimal translations" generated by $D$. Besides
the braiding map describing the obstruction to commutativity of products of
vertex operators, $H_D$-quantum vertex algebras have as main new ingredient a
"translation map" that describes the obstruction of vertex operators to
satisfying translation covariance. The translation map also appears as
obstruction to the state-field correspondence being a homomorphism. We use a
bicharacter construction of Borcherds to construct a large class of
$H_D$-quantum vertex algebras. One particular example of this construction
yields a quantum vertex algebra that contains the quantum vertex operators
introduced by Jing in the theory of Hall-Littlewood polynomials.


title: On multipartite posets

abstract:
  A poset $\mathbf{P} = (X,\preceq)$ is {\em $m$-partite} if $X$ has a
partition $X = X_1 \cup ... \cup X_m$ such that (1) each $X_i$ forms an
antichain in $\mathbf{P}$, and (2) $x\prec y$ implies $x\in X_i$ and $y\in X_j$
where $i<j$. In this article we derive a tight asymptotic upper bound on the
order dimension of $m$-partite posets in terms of $m$ and their bipartite
sub-posets in a constructive and elementary way.


title:
Randomly coloring planar graphs with fewer colors than the maximum
  degree

abstract:
  We study Markov chains for randomly sampling $k$-colorings of a graph with
maximum degree $\Delta$. Our main result is a polynomial upper bound on the
mixing time of the single-site update chain known as the Glauber dynamics for
planar graphs when $k=\Omega(\Delta/\log{\Delta})$. Our results can be
partially extended to the more general case where the maximum eigenvalue of the
adjacency matrix of the graph is at most $\Delta^{1-\eps}$, for fixed $\eps >
0$.
  The main challenge when $k \le \Delta + 1$ is the possibility of "frozen"
vertices, that is, vertices for which only one color is possible, conditioned
on the colors of its neighbors. Indeed, when $\Delta = O(1)$, even a typical
coloring can have a constant fraction of the vertices frozen. Our proofs rely
on recent advances in techniques for bounding mixing time using "local
uniformity" properties.


title:
Critical scaling and heterogeneous superdiffusion across the
  jamming/rigidity transition of a granular glass

abstract:
  The dynamical properties of a dense horizontally vibrated bidisperse granular
monolayer are experimentally investigated. The quench protocol produces states
with a frozen structure of the assembly, but the remaining degrees of freedom
associated with contact dynamics control the appearance of macroscopic
rigidity. We provide decisive experimental evidence that this transition is a
critical phenomenon, with increasingly collective and heterogeneous
rearrangements occurring at length scales much smaller than the grains'
diameter, presumably reflecting the contact force network fluctuations.
Dynamical correlation time and length scales soar on both sides of the
transition, as the volume fraction varies over a remarkably tiny range ($\delta
\phi/\phi \sim 10^{-3}$). We characterize the motion of individual grains,
which becomes super-diffusive at the jamming transition $\phi_J$, signaling
long-ranged temporal correlations. Correspondingly, the system exhibits
long-ranged four-point dynamical correlations in space that obey critical
scaling at the transition density.


title: Vector meson production in ultra-peripheral collisions at LHC

abstract:
  Vector meson production in ultra-peripheral collisions of heavy ions at LHC
is calculated in VDM and color dipole approaches.


title: Renormalisation and the Batalin-Vilkovisky formalism

abstract:
  This paper gives a way to renormalise certain quantum field theories on
compact manifolds. Examples include Yang-Mills theory (in dimension 4 only),
Chern-Simons theory and holomorphic Chern-Simons theory. The method is within
the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is
renormalised in a way respecting all symmetries (up to homotopy). This yields
an invariant of smooth manifolds: a certain algebraic structure on the
cohomology of the manifold tensored with a Lie algebra, which is a "higher
loop" enrichment of the natural Lie-infinity structure.


title: Coupling gauge theory to spinfoam 3d quantum gravity

abstract:
  We construct a spinfoam model for Yang-Mills theory coupled to quantum
gravity in three dimensional riemannian spacetime. We define the partition
function of the coupled system as a power series in g_0^2 G that can be
evaluated order by order using grasping rules and the recoupling theory. With
respect to previous attempts in the literature, this model assigns the
dynamical variables of gravity and Yang-Mills theory to the same simplices of
the spinfoam, and it thus provides transition amplitudes for the spin network
states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly
that the partition function has a semiclassical limit given by the Regge
discretization of the classical Yang-Mills action.


title:
The initial conditions of star formation in the Ophiuchus main cloud:
  Kinematics of the protocluster condensations

abstract:
  The earliest phases of clustered star formation and the origin of the stellar
initial mass function (IMF) are currently much debated. In order to constrain
the origin of the IMF, we investigated the internal and relative motions of
starless condensations and protostars previously detected by us in the dust
continuum at 1.2mm in the L1688 protocluster of the Ophiuchus molecular cloud
complex. The starless condensations have a mass spectrum resembling the IMF and
are therefore likely representative of the initial stages of star formation in
the protocluster. We carried out detailed molecular line observations,
including some N2H+(1-0) mapping, of the Ophiuchus protocluster condensations
using the IRAM 30m telescope. We measured subsonic or at most transonic levels
of internal turbulence within the condensations, implying virial masses which
generally agree within a factor of ~ 2 with the masses derived from the 1.2mm
dust continuum. This supports the notion that most of the L1688 starless
condensations are gravitationally bound and prestellar in nature. We measured a
global one-dimensional velocity dispersion of less than 0.4 km/s between
condensations. This small relative velocity dispersion implies that, in
general, the condensations do not have time to interact with one another before
evolving into pre-main sequence objects. Our observations support the view that
the IMF is partly determined by cloud fragmentation at the prestellar stage.
Competitive accretion is unlikely to be the dominant mechanism at the
protostellar stage in the Ophiuchus protocluster, but it may possibly govern
the growth of starless, self-gravitating condensations initially produced by
gravoturbulent fragmentation toward an IMF, Salpeter-like mass spectrum.


title:
Canonical forms, higher rank numerical range, convexity, totally
  isotropic subspace, matrix equations

abstract:
  Results on matrix canonical forms are used to give a complete description of
the higher rank numerical range of matrices arising from the study of quantum
error correction. It is shown that the set can be obtained as the intersection
of closed half planes (of complex numbers). As a result, it is always a convex
set in $\mathcal C$. Moreover, the higher rank numerical range of a normal
matrix is a convex polygon determined by the eigenvalues. These two
consequences confirm the conjectures of Choi et al. on the subject. In
addition, the results are used to derive a formula for the optimal upper bound
for the dimension of a totally isotropic subspace of a square matrix, and
verify the solvability of certain matrix equations.


title: Semi-Empirical Cepheid Period-Luminosity Relations in Sloan Magnitudes

abstract:
  In this paper we derive semi-empirical Cepheid period-luminosity (P-L)
relations in the Sloan ugriz magnitudes by combining the observed BVI mean
magnitudes from the Large Magellanic Cloud Cepheids (LMC) and theoretical
bolometric corrections. We also constructed empirical gr band P-L relations,
using the publicly available Johnson-Sloan photometric transformations, to be
compared with our semi-empirical P-L relations. These two sets of P-L relations
are consistent with each other.


title: Superluminal motion and closed signal curves

abstract:
  We discuss some properties of Lorentz invariant theories which allow for
superluminal motion. We show that, if signals are always sent forward in time,
closed curves along which signals propagate can be formed. This leads to
problems with causality and with the second law of thermodynamics. Only if one
singles out one frame with respect to which all signals travel forward in time,
the formation of 'closed signal curves' can be prevented. However, the price to
pay is that in some reference frames perturbations propagate towards the past
or towards the future, depending on the direction of emission.


title: Vertex coloring acyclic digraphs and their corresponding hypergraphs

abstract:
  We consider vertex coloring of an acyclic digraph $\Gdag$ in such a way that
two vertices which have a common ancestor in $\Gdag$ receive distinct colors.
Such colorings arise in a natural way when bounding space for various genetic
data for efficient analysis. We discuss the corresponding {\em down-chromatic
number} and derive an upper bound as a function of $D(\Gdag)$, the maximum
number of descendants of a given vertex, and the degeneracy of the
corresponding hypergraph. Finally we determine an asymptotically tight upper
bound of the down-chromatic number in terms of the number of vertices of
$\Gdag$ and $D(\Gdag)$.


title: Condition for the higher rank numerical range to be non-empty

abstract:
  It is shown that the rank-$k$ numerical range of every $n$-by-$n$ complex
matrix is non-empty if $n \ge 3k - 2$. The proof is based on a recent
characterization of the rank-$k$ numerical range by Li and Sze, the Helly's
theorem on compact convex sets, and some eigenvalue inequalities. In
particular, the result implies that $\Lambda_2(A)$ is non-empty if $n \ge 4$.
This confirms a conjecture of Choi et al. If $3k-2>n>0$, an $n$-by-$n$ complex
matrix is given for which the rank-$k$ numerical range is empty. Extension of
the result to bounded linear operators acting on an infinite dimensional
Hilbert space is also discussed.


title:
Noise induced forced synchronization of global variables in coupled
  bistable systems

abstract:
  We analyze the noise induced synchronization between a collective variable
characterizing a complex system with a finite number of interacting bistable
units and time periodic driving forces. A random phase process associated to
the collective stochastic variable is defined. Its average phase frequency and
average phase diffusion are used to characterize the phenomenon. Our analysis
is based on numerical solutions of the corresponding set of Langevin equations.


title: Pulsar Physics and GLAST

abstract:
  Rotation-powered pulsars are excellent laboratories for study of particle
acceleration as well as fundamental physics of strong gravity, strong magnetic
fields, high densities and relativity. I will review the outstanding questions
in pulsar physics and the prospects for finding answers with GLAST LAT
observations. LAT observations should significantly increase the number of
detected radio-loud and radio-quiet gamma-ray pulsars, including millisecond
pulsars, giving much better statistics for elucidating population
characteristics, will measure the high-energy spectrum and the shape of
spectral cutoffs and determine pulse profiles for a variety of pulsars of
different age. Further, measurement of phase-resolved spectra and energy
dependent pulse profiles of the brighter pulsars should allow detailed tests of
magnetospheric particle acceleration and radiation mechanisms, by comparing
data with theoretical models that have been developed.


title: Structure of Vector Mesons in Holographic Model with Linear Confinement

abstract:
  Wave functions and form factors of vector mesons are investigated in the
holographic dual model of QCD with a smooth oscillator-like wall. We introduce
wave functions conjugate to solutions of the 5D equation of motion and develop
a formalism based on these wave functions, which are very similar to those of a
quantum-mechanical oscillator. For the lowest bound state (rho-meson), we show
that, in this model, the basic elastic form factor exhibits the perfect vector
meson dominance, i.e., it is given by the rho-pole contribution alone. The
electric radius of the rho-meson is calculated, <r^2_rho>_C = 0.655 fm^2, which
is larger than in case of the hard-wall cutoff. The squared radii of higher
excited states are found to increase logarithmically rather than linearly with
the radial excitation number. We calculate the coupling constant f_rho and find
that the experimental value is closer to that calculated in the hard-wall
model.


title:
Novel technique for monitoring the performance of the LAT instrument on
  board the GLAST satellite

abstract:
  The Gamma-ray Large Area Space Telescope (GLAST) is an observatory designed
to perform gamma-ray astronomy in the energy range 20 MeV to 300 GeV, with
supporting measurements for gamma-ray bursts from 10 keV to 25 MeV. GLAST will
be launched at the end of 2007, opening a new and important window on a wide
variety of high energy astrophysical phenomena . The main instrument of GLAST
is the Large Area Telescope (LAT), which provides break-through high-energy
measurements using techniques typically used in particle detectors for collider
experiments. The LAT consists of 16 identical towers in a four-by-four grid,
each one containing a pair conversion tracker and a hodoscopic crystal
calorimeter, all covered by a segmented plastic scintillator anti-coincidence
shield. The scientific return of the instrument depends very much on how
accurately we know its performance, and how well we can monitor it and correct
potential problems promptly. We report on a novel technique that we are
developing to help in the characterization and monitoring of LAT by using the
power of classification trees to pinpoint in a short time potential problems in
the recorded data. The same technique could also be used to evaluate the effect
on the overall LAT performance produced by potential instrumental problems.


title: Base-controlled mechanical systems and geometric phases

abstract:
  In this paper, we carry a detailed study of mechanical systems with
configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables
are being controlled. The overall system's motion is considered to be induced
from the base one due to the presence of general non-holonomic constraints. It
is shown that the solution can be factorized into dynamical and geometrical
parts. Moreover, under favorable kinematical circumstances, the dynamical part
admits a further factorization since it can be reconstructed from an
intermediate (body) momentum solution, yielding a reconstruction phase formula.
Finally, we apply this results to the study of concrete mechanical systems.


title:
On the dynamics of codimension one holomorphic foliations with ample
  normal bundle

abstract:
  We investigate the accumulation to singular points of leaves of codimension
one foliations whose normal bundle is ample, with emphasis on the nonexistence
of Levi-flat hypersurfaces.


title:
Two-loop Corrections for Nuclear Matter in a Covariant Effective Field
  Theory

abstract:
  Although one-loop calculations provide a realistic description of bulk and
single-particle nuclear properties, it is necessary to examine loop corrections
to develop a systematic finite-density power-counting scheme for the nuclear
many-body problem when loops are included. Moreover, it is imperative to study
exchange and correlation corrections systematically to make reliable
predictions for other nuclear observables. One must also verify that the
natural sizes of the one-loop parameters are not destroyed by explicit
inclusion of many-body corrections. The loop expansion is applied to a chiral
effective hadronic lagrangian; with the techniques of Infrared Regularization,
it is possible to separate out the short-range contributions and to write them
as local products of fields that are already present in our lagrangian. (The
appropriate field variables must be re-defined at each order in loops.) The
corresponding parameters implicitly include short-range effects to all orders
in the interaction, so these effects need not be calculated explicitly. The
remaining (long-range) contributions that must be calculated are nonlocal and
resemble those in conventional nuclear-structure calculations. Calculations at
the two-loop level are carried out to illustrate these techniques at finite
densities and to verify that the coupling parameters remain natural when fitted
to the empirical properties of equilibrium nuclear matter.


title: Retaining Black Holes with Very Large Recoil Velocities

abstract:
  Recent numerical simulations of binary black hole mergers show the
possibility of producing very large recoil velocities (> 3000 km/s). Kicks of
this magnitude should be sufficient to eject the final black hole from
virtually any galactic potential. This result has been seen as a potential
contradiction with observations of supermassive black holes residing in the
centers of most galaxies in the local universe. Using an extremely simplified
merger tree model, we show that, even in the limit of very large ejection
probability, after a small number of merger generations there should still be
an appreciable fraction (>50%) of galaxies with supermassive black holes today.
We go on to argue that the inclusion of more realistic physics ingredients in
the merger model should systematically increase this retention fraction,
helping to resolve a potential conflict between theory and observation. Lastly,
we develop a more realistic Monte Carlo model to confirm the qualitative
arguments and estimate occupation fractions as a function of the central
galactic velocity dispersion.


title:
A Chain-Boson Model for the Decoherence and Relaxation of a Few Coupled
  SQUIDs in a Phonon Bath

abstract:
  We develop a "chain-boson model" master equation, within the Born-Markov
approximation, for a few superconducting quantum interference devices (SQUIDs)
coupled into a chain and exchanging their angular momenta with a low
temperature phonon bath. Our master equation has four generators; we
concentrate on the damping and diffusion and use them to study the relaxation
and decoherence of a Heisenberg SQUID chain whose spectrum exhibits critical
point energy-level crossings, entangled states, and pairs of resonant
transitions. We note that at an energy-level crossing the relevant bath
wavelengths are so long that even well-spaced large SQUIDs can partially
exhibit collective coupling to the bath, dramatically reducing certain
relaxation and decoherence rates. Also, transitions into entangled states can
occur even in the case of an independent coupling of each SQUID to the bath.
Finally, the pairs of resonant transitions can cause decaying oscillations to
emerge in a lower energy subspace.


title: Galactic disc warps due to intergalactic accretion flows onto the disc

abstract:
  The accretion of the intergalactic medium onto the gaseous disc is used to
explain the generation of galactic warps. A cup-shaped distortion is expected,
due to the transmission of the linear momentum; but, this effect is small for
most incident inflow angles and the predominant effect turns out to be the
transmission of angular momentum, i.e. a torque giving an integral-sign shaped
warp. The torque produced by a flow of velocity ~100 km/s and baryon density
~10^{-25} kg/m^3, which is within the possible values for the intergalactic
medium, is enough to generate the observed warps and this mechanism offers
quite a plausible explanation. The inferred rate of infall of matter, ~1
M_sun/yr, to the Galactic disc that this theory predicts agrees with the
quantitative predictions of chemical evolution resolving key issues, notably
the G-dwarf problem.
  Sanchez-Salcedo (2006) suggests that this mechanism is not plausible because
it would produce a dependence of the scaleheight of the disc with the
Galactocentric azimuth in the outer disc, but rather than being an objection
this is another argument in favour of the mechanism because this dependence is
actually observed in our Galaxy.


title:
Study of the Flux and Spectral Variations in the VHE Emission from the
  Blazar Markarian 501, with the MAGIC Telescope

abstract:
  The blazar Markarian 501 (Mrk 501) was observed above 100 GeV with the MAGIC
Telescope during May, June and July 2005. The high sensitivity of the
instrument made possible the detection of the source with high significance in
each of the observing nights. During this observational campaign, the emitted
gamma-ray flux from Mkn 501 was found to vary by one order of magnitude, and
showed a high correlation with spectral changes. Intra-night flux variability
was also observed, with flux-doubling times of ~2 minutes. The data showed a
clear evidence of a spectral peak (in the nuFnu representation) during the
nights when the gamma-ray activity was highest. The location of this spectral
feature was found to be correlated with the emitted gamma-ray flux. In these
proceedings we discuss some of the results of this unprecedented spectral and
temporal analysis of Mrk 501 observations in the very high energy range.


title:
Fourier resolved spectroscopy of 4U 1728-34: New Insights into Spectral
  and Temporal Properties of Low-Mass X-ray Binaries

abstract:
  Using archival RXTE data we derive the 2-16 keV Fourier-resolved spectra of
the Atoll source 4U 1728-34 in a sequence of its timing states as its low QPO
frequency spans the range between 6 and 94 Hz. The increase in the QPO
frequency accompanies a spectral transition of the source from its island to
its banana states. The banana-states' Fourier-resolved spectra are well fitted
by a single blackbody component with $kT \sim 2-3$ keV depending on the source
position in the color -- color diagram and the Fourier frequency, thus
indicating that this spectral component is responsible for the source
variability on these timescales. This result is in approximate agreement with
similar behavior exhibited by the Z sources, suggesting that, as in that case,
the boundary layer -- the likely source of the thermal component -- is
supported by radiation pressure. Furthermore, it is found that the iron line at
$\sim$6.6 keV, clearly present in the averaged spectra, not apparent within the
limitations of our measurements in the frequency-resolved spectra irrespective
of the frequency range. This would indicate that this spectral component
exhibits little variability on time scales comprising the interval
$10^{-2}-10^2$ seconds. In the island state the single blackbody model proved
inadequate, particularly notable in our lowest frequency band ($0.008-0.8$ Hz).
An absorbed powerlaw or an additive blackbody plus hard powerlaw model was
required to obtain a satisfactory fit. Statistics do not allow unambiguous
discrimination between these possible scenarios.


title:
Absorption spectrum in the wings of the potassium second resonance
  doublet broadened by helium

abstract:
  We have measured the reduced absorption coefficients occurring in the wings
of the potassium 4S-5P doublet lines at 404.414 nm and at 404.720 nm broadened
by helium gas at pressures of several hundred Torr. At the experimental
temperature of 900 K, we have detected a shoulder-like broadening feature on
the blue wing of the doublet which is relatively flat between 401.8 nm and
402.8 nm and which drops off rapidly for shorter wavelengths, corresponding to
absorption from the X doublet Sigma+ state to the C doublet Sigma+ state of the
K-He quasimolecule. The accurate measurements of the line profiles in the
present work will sharply constrain future calculations of potential energy
surfaces and transition dipole moments correlating to the asymptotes He-K(5p),
He-K(5s), and He-K(3d).


title: Continuous Damage Fiber Bundle Model for Strongly Disordered Materials

abstract:
  We present an extension of the continuous damage fiber bundle model to
describe the gradual degradation of highly heterogeneous materials under an
increasing external load. Breaking of a fiber in the model is preceded by a
sequence of partial failure events occurring at random threshold values. In
order to capture the subsequent propagation and arrest of cracks, furthermore,
the disorder of the number of degradation steps of material constituents, the
failure thresholds of single fibers are sorted into ascending order and their
total number is a Poissonian distributed random variable over the fibers.
Analytical and numerical calculations showed that the failure process of the
system is governed by extreme value statistics, which has a substantial effect
on the macroscopic constitutive behaviour and on the microscopic bursting
activity as well.


title: High and Low Dimensions in The Black Hole Negative Mode

abstract:
  The negative mode of the Schwarzschild black hole is central to Euclidean
quantum gravity around hot flat space and for the Gregory-Laflamme black string
instability. We analyze the eigenvalue as a function of space-time dimension by
constructing two perturbative expansions: one for large d and the other for
small d-3, and determining as many coefficients as we are able to compute
analytically. Joining the two expansions we obtain an interpolating rational
function accurate to better than 2% through the whole range of dimensions
including d=4.


title:
Poisson Nernst-Planck Model of Ion Current Rectification through a
  Nanofluidic Diode

abstract:
  We have investigated ion current rectification properties of a recently
prepared bipolar nanofluidic diode. This device is based on a single conically
shaped nanopore in a polymer film whose pore walls contain a sharp boundary
between positively and negatively charged regions. A semi-quantitative model
that employs Poisson and Nernst-Plank equations predicts current-voltage curves
as well as ionic concentrations and electric potential distributions in this
system. We show that under certain conditions the rectification degree, defined
as a ratio of currents recorded at the same voltage but opposite polarities,
can reach values of over a 1000 at a voltage range <-2 V, +2 V>. The role of
thickness and position of the transition zone on the ion current rectification
is discussed as well. We also show that rectification degree scales with the
applied voltage.


title: The cosmological constant and dark energy in braneworlds

abstract:
  We review recent attempts to address the cosmological constant problem and
the late-time acceleration of the Universe based on braneworld models. In
braneworld models, the way in which the vacuum energy gravitates in the 4D
spacetime is radically different from conventional 4D physics. It is possible
that the vacuum energy on a brane does not curve the 4D spacetime and only
affects the geometry of the extra-dimensions, offering a solution to the
cosmological constant problem. We review the idea of supersymmetric large extra
dimensions that could achieve this and also provide a natural candidate for a
quintessence field. We also review the attempts to explain the late-time
accelerated expansion of the universe from the large-distance modification of
gravity based on the braneworld. We use the Dvali-Gabadadze-Porrati model to
demonstrate how one can distinguish this model from dark energy models in 4D
general relativity. Theoretical difficulties in this approach are also
addressed.


title:
Dynamical conductance in the two-channel Kondo regime of a double dot
  system

abstract:
  We study finite-frequency transport properties of the double-dot system
recently constructed to observe the two-channel Kondo effect [R. M. Potok et
al., Nature 446, 167 (2007)]. We derive an analytical expression for the
frequency-dependent linear conductance of this device in the Kondo regime. We
show how the features characteristic of the 2-channel Kondo quantum critical
point emerge in this quantity, which we compute using the results of conformal
field theory as well as numerical renormalization group methods. We determine
the universal cross-over functions describing non-Fermi liquid vs. Fermi liquid
cross-overs and also investigate the effects of a finite magnetic field.


title: Fractionalization in a square-lattice model with time-reversal symmetry

abstract:
  We propose a two-dimensional time-reversal invariant system of essentially
non-interacting electrons on a square lattice that exhibits configurations with
fractional charges e/2. These are vortex-like topological defects in the
dimerization order parameter describing spatial modulation in the electron
hopping amplitudes. Charge fractionalization is established by a simple
counting argument, analytical calculation within the effective low-energy
theory, and by an exact numerical diagonalization of the lattice Hamiltonian.
We comment on the exchange statistics of fractional charges and possible
realizations of the system.


title: Two gravitational shock waves on the AdS_3 brane

abstract:
  A gravitational shock wave is a solution to Einstein equations describing the
gravitational field of a massless particle. We obtain such a geometry for a
particle moving on a AdS_3 brane embedded in a AdS_4 bulk (the lower
dimensional version of the "locally localized gravity" model of Karch and
Randall). In order to do this, we use two different techniques. First, we solve
directly Einstein equations sourced by a massless particle. Then we boost to
the speed of light the AdS_3 brane black hole solution of Emparan et al while
sending its mass parameter to zero. Surprisingly, we obtain two different
results. We discuss the origin of these two different solutions both in the
bulk and in the CFT picture. As a by-product, we derive the expression for the
shock wave associated to a transversally accelerating particle in AdS_4.


title:
Characterization of separability and entanglement in $(2\times{D})$- and
  $(3\times{D})$-dimensional systems by single-qubit and single-qutrit unitary
  transformations

abstract:
  We investigate the geometric characterization of pure state bipartite
entanglement of $(2\times{D})$- and $(3\times{D})$-dimensional composite
quantum systems. To this aim, we analyze the relationship between states and
their images under the action of particular classes of local unitary
operations. We find that invariance of states under the action of single-qubit
and single-qutrit transformations is a necessary and sufficient condition for
separability. We demonstrate that in the $(2\times{D})$-dimensional case the
von Neumann entropy of entanglement is a monotonic function of the minimum
squared Euclidean distance between states and their images over the set of
single qubit unitary transformations. Moreover, both in the $(2\times{D})$- and
in the $(3\times{D})$-dimensional cases the minimum squared Euclidean distance
exactly coincides with the linear entropy (and thus as well with the tangle
measure of entanglement in the $(2\times{D})$-dimensional case). These results
provide a geometric characterization of entanglement measures originally
established in informational frameworks. Consequences and applications of the
formalism to quantum critical phenomena in spin systems are discussed.

categories: quant-ph cond-mat.other hep-th math-ph math.MP


title:
Rapid Formation of Supermassive Black Hole Binaries in Galaxy Mergers
  with Gas

abstract:
  Supermassive black holes (SMBHs) are a ubiquitous component of the nuclei of
galaxies. It is normally assumed that, following the merger of two massive
galaxies, a SMBH binary will form, shrink due to stellar or gas dynamical
processes and ultimately coalesce by emitting a burst of gravitational waves.
However, so far it has not been possible to show how two SMBHs bind during a
galaxy merger with gas due to the difficulty of modeling a wide range of
spatial scales. Here we report hydrodynamical simulations that track the
formation of a SMBH binary down to scales of a few light years following the
collision between two spiral galaxies. A massive, turbulent nuclear gaseous
disk arises as a result of the galaxy merger. The black holes form an eccentric
binary in the disk in less than a million years as a result of the
gravitational drag from the gas rather than from the stars.


title: Optimal Choice of Threshold in Two Level Processor Sharing

abstract:
  We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with
the hyper-exponential job size distribution and with the Poisson arrival
process. TLPS is a convenient model to study the benefit of the file size based
differentiation in TCP/IP networks. In the case of the hyper-exponential job
size distribution with two phases, we find a closed form analytic expression
for the expected sojourn time and an approximation for the optimal value of the
threshold that minimizes the expected sojourn time. In the case of the
hyper-exponential job size distribution with more than two phases, we derive a
tight upper bound for the expected sojourn time conditioned on the job size. We
show that when the variance of the job size distribution increases, the gain in
system performance increases and the sensitivity to the choice of the threshold
near its optimal value decreases.


title:
The First Survey of X-ray Flares from Gamma Ray Bursts Observed by
  Swift: Spectral Properties and Energetics

abstract:
  Observations of gamma ray bursts (GRBs) with Swift produced the initially
surprising result that many bursts have large X-ray flares superimposed on the
underlying afterglow. The flares were sometimes intense, had rapid rise and
decay phases, and occurred late relative to the ``prompt'' phase. Some
remarkable flares are observed with fluence comparable to the prompt GRB
fluence. Many GRBs have several flares, which are sometimes overlapping. Short,
intense, repetitive, and late flaring can be most easily understood within the
context of the standard fireball model with the internal engine that powers the
prompt GRB emission in an active state at late times. However, other models for
flares have been proposed. Flare origin can be investigated by comparing the
flare spectra to that of the afterglow and the initial prompt emission. In this
work, we have analyzed all significant X-ray flares from the first 110 GRBs
observed by Swift. From this sample 33 GRBs were found to have significant
X-ray flares, with 77 flares that were detected above the 3$\sigma$ level. In
addition to temporal analysis presented in a companion paper, a variety of
spectral models have been fit to each flare. In some cases, we find that the
spectral fits favor a Band function model, which is more akin to the prompt
emission than to that of an afterglow. We find that the average fluence of the
flares is 2.4e-7 erg/cm^2/s in the 0.2-10 keV energy band, which is
approximately a factor of ten below the average prompt GRB fluence. These
results, when combined with those presented in the companion paper on temporal
properties of flares, supports the hypothesis that most X-ray flares are
late-time activity of the internal engine that spawned the initial GRB; not an
afterglow related effect.


title: The Beginning and Evolution of the Universe

abstract:
  We review the current standard model for the evolution of the Universe from
an early inflationary epoch to the complex hierarchy of structure seen today.
We summarize and provide key references for the following topics: observations
of the expanding Universe; the hot early Universe and nucleosynthesis; theory
and observations of the cosmic microwave background; Big Bang cosmology;
inflation; dark matter and dark energy; theory of structure formation; the cold
dark matter model; galaxy formation; cosmological simulations; observations of
galaxies, clusters, and quasars; statistical measures of large-scale structure;
and measurement of cosmological parameters. We conclude with discussion of some
open questions in cosmology. This review is designed to provide a graduate
student or other new worker in the field an introduction to the cosmological
literature.

categories: astro-ph gr-qc hep-ph hep-th physics.hist-ph


title:
Murre's conjectures and explicit Chow--Kuenneth projectors for some
  varieties

abstract:
  In this paper, we investigate Murre's conjectures on the structure of
rational Chow groups and exhibit explicit Chow--Kuenneth projectors for some
examples. More precisely, the examples we study are the varieties which have a
nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle
explicit Chow--Kuenneth projectors are obtained which satisfy Murre's
conjectures and the motivic Hard Lefschetz theorem is verified.


title: Equivalence of sparse circulants: the bipartite \'Ad\'am problem

abstract:
  We consider n-by-n circulant matrices having entries 0 and 1. Such matrices
can be identified with sets of residues mod n, corresponding to the columns in
which the top row contains an entry 1. Let A and B be two such matrices, and
suppose that the corresponding residue sets S_A and S_B have size at most 3. We
prove that the following are equivalent: (1) there are integers u,v mod n, with
u a unit, such that S_A = uS_B + v; (2) there are permutation matrices P,Q such
that A=PBQ. Our proof relies on some new results about vanishing sums of roots
of unity. We give examples showing this result is not always true for denser
circulants, as well as results showing it continues to hold in some situations.
We also explain how our problem relates to the Adam problem on isomorphisms of
circulant directed graphs.


title:
Simulating non-small cell lung cancer with a multiscale agent-based
  model

abstract:
  Background The epidermal growth factor receptor (EGFR) is frequently
overexpressed in many cancers, including non-small cell lung cancer (NSCLC). In
silcio modeling is considered to be an increasingly promising tool to add
useful insights into the dynamics of the EGFR signal transduction pathway.
However, most of the previous modeling work focused on the molecular or the
cellular level only, neglecting the crucial feedback between these scales as
well as the interaction with the heterogeneous biochemical microenvironment.
  Results We developed a multiscale model for investigating expansion dynamics
of NSCLC within a two-dimensional in silico microenvironment. At the molecular
level, a specific EGFR-ERK intracellular signal transduction pathway was
implemented. Dynamical alterations of these molecules were used to trigger
phenotypic changes at the cellular level. Examining the relationship between
extrinsic ligand concentrations, intrinsic molecular profiles and microscopic
patterns, the results confirmed that increasing the amount of available growth
factor leads to a spatially more aggressive cancer system. Moreover, for the
cell closest to nutrient abundance, a phase-transition emerges where a minimal
increase in extrinsic ligand abolishes the proliferative phenotype altogether.
  Conclusions Our in silico results indicate that, in NSCLC, in the presence of
a strong extrinsic chemotactic stimulus, and depending on the cell's location,
downstream EGFR-ERK signaling may be processed more efficiently, thereby
yielding a migration-dominant cell phenotype and overall, an accelerated
spatio-temporal expansion rate.


title:
Composition-sensitive parameters measured with the surface detector of
  the Pierre Auger Observatory

abstract:
  A key step towards the understanding of the origin of ultra-high energy
cosmic rays is their mass composition. Primary photons and neutrinos produce
markedly different showers from nuclei, while showers of different nuclear
species are not easy to distinguish. To maximise the discrimination with the
Pierre Auger Observatory ideally all mass-sensitive observables should be
combined, but the 10% duty cycle of the fluorescence detector limits the use of
direct measurements of shower maximum at the highest energies. Therefore, we
investigate mass-sensitive observables accessible with the surface detectors
alone. These are the signal risetime in the Cherenkov stations, the curvature
of the shower front, the muon-to-electromagnetic ratio, and the azimuthal
signal asymmetry. Risetime and curvature depend mainly on the depth of the
shower development in the atmosphere, and thus on primary energy and mass. The
muon content of a shower depends on the primary energy and the number of
nucleons, while asymmetry about the shower core is due to geometric effects and
attenuation, which are dependent on the primary mass. The mass sensitivity of
these variables is demonstrated and their application for composition studies
is discussed.


title: Lorentz spacetimes of constant curvature

abstract:
  This paper was first written in 1990, but was never published. In it, the
author presents a novel approach to the study of constant curvature spacetimes
in 2+1 dimensions. A parameterization of flat 2+1-dimensional domains of
dependence is given in terms of measured geodesic laminations. There is also an
interesting reinterpretation of Thurston's Earthquake Theorem involving anti-de
Sitter spacetimes.
  With the permission of the author, it will be published for the first time in
a forthcoming issue of Geometriae Dedicata, together with detailed "notes"
outlining the developments in the field in the intervening years. The version
posted here is nearly identical to the original; we merely corrected
typographical errors and occasional notational mistakes, and also updated the
references in the bibliography.


title: Connecting String/M Theory to the Electroweak Scale and to LHC Data

abstract:
  The Standard Model of particle physics explains (almost) all observed
non-gravitational microscopic phenomena but has many open theoretical
questions. We are on the threshold of unraveling the mysteries of the Standard
Model and discovering its extension. This could be achieved in the near future
with the help of many experiments in particle physics and cosmology, the LHC in
particular. Assuming that data confirming the existence of new physics beyond
the Standard Model is obtained, one is left with the very important and
challenging task of solving the "Inverse Problem", \emph{viz.} "How can one
deduce the nature of the underlying (perhaps microscopic) theory from data?"
This thesis explores this question in detail, and also proposes an approach to
address the problem in a meaningful way which could prove crucial to the
possible solution to this problem in the future. The proposed approach has
three aspects - a) To systematically study classes of microscopic (string/$M$
theory) constructions to the extent that they could be connected to low energy
physics (electroweak scale), b) To find patterns of experimental observables
which are sensitive to the properties of the underlying theoretical
constructions thereby allowing us to distinguish among different constructions,
and c) To try to get insights about the qualitative features of the theoretical
model from data in a bottom-up approach which complements the top-down approach
and strengthens it as well. This thesis studies all the above aspects in
detail. The methods used and results obtained in this thesis will hopefully be
of great importance in solving the Inverse Problem.


title: On Minkowskian Branching Structures

abstract:
  Contrary to its initial idea, Belnap's (1992) theory of Branching Space-Times
(BST) has models in which histories do not resemble relativistic space-times or
any other physical space-times. The aim of this paper is to define a certain
class of BST models, called "Minkowskian Branching Structures" (MBS), in which
histories are isomorphic to Minkowski space-time. By focusing on these models
rather than on general BST models, we hope that one may be able to improve on
earlier BST analyzes of physical phenomena. Also, introducing MBS' sets the
stage for recent discussions about whether or not `branching is a bad idea',
physically speaking.


title: Thermal derivation of the Coleman-De Luccia tunneling prescription

abstract:
  We derive the rate for transitions between de Sitter vacua by treating the
field theory on the static patch as a thermal system. This reproduces the
Coleman-De Luccia formalism for calculating the rate, but leads to a modified
interpretation of the bounce solution and a different prediction for the
evolution of the system after tunneling. The bounce is seen to correspond to a
sequence of configurations interpolating between initial and final
configurations on either side of the tunneling barrier, all of which are
restricted to the static patch. The final configuration, which gives the
initial data on the static patch for evolution after tunneling, is obtained
from one half of a slice through the center of the bounce, while the other half
gives the configuration before tunneling. The formalism makes no statement
about the fields beyond the horizon.
  This approach resolves several puzzling aspects and interpretational issues
concerning the Coleman-De Luccia and Hawking-Moss bounces. We work in the limit
where the back reaction of matter on metric can be ignored, but argue that the
qualitative aspects remain in the more general case. The extension to tunneling
between anti-de Sitter vacua is discussed.


title: Wavelet transforms in a critical interface model for Barkhausen noise

abstract:
  We discuss the application of wavelet transforms to a critical interface
model, which is known to provide a good description of Barkhausen noise in soft
ferromagnets. The two-dimensional version of the model (one-dimensional
interface) is considered, mainly in the adiabatic limit of very slow driving.
On length scales shorter than a crossover length (which grows with the strength
of surface tension), the effective interface roughness exponent $\zeta$ is
$\simeq 1.20$, close to the expected value for the universality class of the
quenched Edwards-Wilkinson model. We find that the waiting times between
avalanches are fully uncorrelated, as the wavelet transform of their
autocorrelations scales as white noise. Similarly, detrended size-size
correlations give a white-noise wavelet transform. Consideration of finite
driving rates, still deep within the intermittent regime, shows the wavelet
transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies.
This behavior is ascribed to intra-avalanche correlations.


title:
Nilpotent normal form for divergence-free vector fields and
  volume-preserving maps

abstract:
  We study the normal forms for incompressible flows and maps in the
neighborhood of an equilibrium or fixed point with a triple eigenvalue. We
prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent
linearization with maximal Jordan block then, to arbitrary degree, coordinates
can be chosen so that the nonlinear terms occur as a single function of two
variables in the third component. The analogue for volume-preserving
diffeomorphisms gives an optimal normal form in which the truncation of the
normal form at any degree gives an exactly volume-preserving map whose inverse
is also polynomial inverse with the same degree.


title: A time frequency analysis of wave packet fractional revivals

abstract:
  We show that the time frequency analysis of the autocorrelation function is,
in many ways, a more appropriate tool to resolve fractional revivals of a wave
packet than the usual time domain analysis. This advantage is crucial in
reconstructing the initial state of the wave packet when its coherent structure
is short-lived and decays before it is fully revived. Our calculations are
based on the model example of fractional revivals in a Rydberg wave packet of
circular states. We end by providing an analytical investigation which fully
agrees with our numerical observations on the utility of time-frequency
analysis in the study of wave packet fractional revivals.