title:
Interplay between \omega-Nucleon Interaction and Nucleon Mass in Dense
  Baryonic Matter

abstract:
  The dilaton-limit fixed point and the scaling properties of hadrons in the
close vicinity of the fixed point in dense baryonic matter uncovered in hidden
local symmetry implemented with spontaneously broken scale symmetry are shown
to reveal a surprisingly intricate interplay, hitherto unsuspected, between the
origin of the bulk of proton mass and the renormalization-group flow of the
\omega-nuclear interactions. This rends a theoretical support to the previous
(phenomenologically) observed correlation between the dropping nucleon mass and
the behavior of the \omega-nuclear interactions in dense matter described in
terms of half skyrmions that appear at a density denoted $n_{1/2}$ in skyrmion
crystals. The role of the \omega-meson degree of freedom in the source for
nucleon mass observed in this paper is highly reminiscent of its important role
in the skyrmion description of nucleon mass in hidden local symmetric theory.
One of the most notable novel results found in this paper is that the nucleon
mass in dense baryonic medium undergoes a drop roughly linear in density up to
a density (denoted $\tilde{n}$) slightly above nuclear matter density ($n_0$)
and then stays more or less constant up to the dilaton limit fixed point. The
possibility that we entertain is that $\tilde{n}$ coincides with or at least
close to $n_{1/2}$. We note that this feature can be economically captured by
the parity-doublet model for nucleons with the chiral-invariant mass $m_0\sim
(0.7-0.8) m_N$. It is found in one-loop renormalization-group analysis with the
Lagrangian adopted that while the \rho-NN coupling "runs" in density, the
\omega-NN coupling does not scale: it will scale at two-loop or higher-loop
order, but at a slower pace, so it is more appropriate to say it "walks" rather
than runs.


title: Relativistic Kinetic Theory: An Introduction

abstract:
  We present a brief introduction to the relativistic kinetic theory of gases
with emphasis on the underlying geometric and Hamiltonian structure of the
theory. Our formalism starts with a discussion on the tangent bundle of a
Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare
one-form on this bundle, from which the symplectic form and a volume form are
constructed. Then, we define an appropriate Hamiltonian on the bundle which,
together with the symplectic form yields the Liouville vector field. The
corresponding flow, when projected onto the base manifold, generates geodesic
motion. Whenever the flow is restricted to energy surfaces corresponding to a
negative value of the Hamiltonian, its projection describes a family of
future-directed timelike geodesics. A collisionless gas is described by a
distribution function on such an energy surface, satisfying the Liouville
equation. Fibre integrals of the distribution function determine the particle
current density and the stress-energy tensor. We show that the stress-energy
tensor satisfies the familiar energy conditions and that both the current and
stress-energy tensor are divergence-free.
  Our discussion also includes the generalization to charged gases, a summary
of the Einstein-Maxwell-Vlasov system in any dimensions, as well as a brief
introduction to the general relativistic Boltzmann equation for a simple gas.


title: Capture of Trojans by Jumping Jupiter

abstract:
  Jupiter Trojans are thought to be survivors of a much larger population of
planetesimals that existed in the planetary region when planets formed. They
can provide important constraints on the mass and properties of the
planetesimal disk, and its dispersal during planet migration. Here we tested a
possibility that the Trojans were captured during the early dynamical
instability among the outer planets (aka the Nice model), when the semimajor
axis of Jupiter was changing as a result of scattering encounters with an ice
giant. The capture occurs in this model when Jupiter's orbit and its Lagrange
points become radially displaced in a scattering event and fall into a region
populated by planetesimals (that previously evolved from their natal
transplanetary disk to ~5 AU during the instability). Our numerical simulations
of the new capture model, hereafter jump capture, satisfactorily reproduce the
orbital distribution of the Trojans and their total mass. The jump capture is
potentially capable of explaining the observed asymmetry in the number of
leading and trailing Trojans. We find that the capture probability is
(6-8)x10^-7 for each particle in the original transplanetary disk, implying
that the disk contained (3-4)x10^7 planetesimals with absolute magnitude H<9
(corresponding to diameter D=80 km for a 7% albedo). The disk mass inferred
from this work, M_disk=14-28 M_Earth, is consistent with the mass deduced from
recent dynamical simulations of the planetary instability.


title: Dynamics and Spatial Distribution of Global Nighttime Lights

abstract:
  Using open source data, we observe the fascinating dynamics of nighttime
light. Following a global economic regime shift, the planetary center of light
can be seen moving eastwards at a pace of about 60 km per year. Introducing
spatial light Gini coefficients, we find a universal pattern of human
settlements across different countries and see a global centralization of
light. Observing 160 different countries we document the expansion of
developing countries, the growth of new agglomerations, the regression in
countries suffering from demographic decline and the success of light pollution
abatement programs in western countries.


title:
Convergent finite differences for 1D viscous isentropic flow in Eulerian
  coordinates

abstract:
  We construct a new finite difference method for the flow of ideal viscous
isentropic gas in one spatial dimension. For the continuity equation, the
method is a standard upwind discretization. For the momentum equation, the
method is an uncommon upwind discretization, where the moment and the velocity
are solved on dual grids. Our main result is convergence of the method as
discretization parameters go to zero. Convergence is proved by adapting the
mathematical existence theory of Lions and Feireisl to the numerical setting.


title:
2D anisotropic scattering pattern fitting using a novel Monte Carlo
  method: Initial results

abstract:
  Recently, a Monte Carlo method has been presented which allows for the
form-free retrieval of size distributions from isotropic scattering patterns,
complete with uncertainty estimates linked to the data quality. Here, we
present an adaptation to this method allowing for the fitting of anisotropic 2D
scattering patterns. The model consists of a finite number of non-interacting
ellipsoids of revolution (but would work equally well for cylinders),
polydisperse in both dimensions, and takes into account disorientation in the
plane parallel to the detector plane. The method application results in three
form-free distributions, two for the ellipsoid dimensions, and one for the
orientation distribution. It is furthermore shown that a morphological
restriction is needed to obtain a unique solution.


title:
Low-Energy Electron Reflectivity of Graphene on Copper and other
  Substrates

abstract:
  The reflectivity of low energy electrons from graphene on copper substrates
is studied both experimentally and theoretically. Well-known oscillations in
the reflectivity of electrons with energies 0 - 8 eV above the vacuum level are
observed in the experiment. These oscillations are reproduced in theory, based
on a first-principles density functional description of interlayer states
forming for various thicknesses of multilayer graphene. It is demonstrated that
n layers of graphene produce a regular series of n-1 minima in the reflectance
spectra, together with a possible additional minimum associated with an
interlayer state forming between the graphene and the substrate. Both (111) and
(001) orientations of the copper substrates are studied. Similarities in their
reflectivity spectra arise from the interlayer states, whereas differences are
found because of the different Cu band structures along those orientations.
Results for graphene on other substrates, including Pt(111) and Ir(111), are
also discussed.


title:
Behavior of perturbations on spherically symmetric backgrounds in
  multi-Galileon theory

abstract:
  We consider multi-Galileon theory, the most general Galilean invariant theory
with $N$ scalar fields linearly coupled to the trace of the stress-energy
tensor. We study the behavior of perturbations on a static spherically
symmetric background with a massive point source, and show that, under the
assumptions of stability and successful Vainshtein screening, solutions cannot
be found that are free of both superluminal propagation and slowly moving,
strongly coupled fluctuations. The latter imply that the theoretical and
phenomenological issues related to a very low strong-interaction scale cannot
be avoided in this model.


title: On the Lacunarity of some eta-products

abstract:
  The lacunarity is an interesting property of a formal series. We say a series
is lacunary if "almost all" of its coefficients are zero. In this article we
considered about the lacunarity of some eta-products like \eta(z)^2\eta(bz)^2,
and proved that they are lacunary if and only if b is 1,2,3,4 or 16. Then We
write them as linear combinations of some CM forms.


title: The symmetric 1:2 resonance

abstract:
  This paper illustrates the application of Lie transform normal-form theory to
the construction of the 1:2 resonant normal form corresponding to a wide class
of natural Hamiltonian systems. We show how to compute the bifurcations of the
main periodic orbits in a potential with double reflection symmetries. The
stability analysis of the normal modes and of the periodic orbits in general
position allows us to get overall informations on the phase-space structure of
systems in which this resonance is dominating. As an example we apply these
results to a class of models useful as galactic potentials.


title: The First Fermi LAT Gamma-Ray Burst Catalog

abstract:
  In three years of observations since the beginning of nominal science
operations in August 2008, the Large Area Telescope (LAT) on board the Fermi
Gamma Ray Space Telescope has observed high-energy (>20 MeV) \gamma-ray
emission from 35 gamma-ray bursts (GRBs). Among these, 28 GRBs have been
detected above 100 MeV and 7 GRBs above ~ 20 MeV. The first Fermi-LAT catalog
of GRBs is a compilation of these detections and provides a systematic study of
high-energy emission from GRBs for the first time. To generate the catalog, we
examined 733 GRBs detected by the Gamma-Ray Burst Monitor (GBM) on Fermi and
processed each of them using the same analysis sequence. Details of the
methodology followed by the LAT collaboration for GRB analysis are provided. We
summarize the temporal and spectral properties of the LAT-detected GRBs. We
also discuss characteristics of LAT-detected emission such as its delayed onset
and longer duration compared to emission detected by the GBM, its power-law
temporal decay at late times, and the fact that it is dominated by a power-law
spectral component that appears in addition to the usual Band model.


title:
Optical signals of spin switching using the optical Stark effect in a Mn
  doped quantum dot

abstract:
  The optically induced spin dynamics of a single Mn atom embedded into a
single semiconductor quantum dot can be strongly influenced by using the
optical Stark effect. The exchange interaction gives rise to simultaneous spin
flips between the quantum dot electron and Mn. In the time domain these flips
correspond to exchange induced Rabi oscillations, which are typically
off-resonant. By applying a detuned laser pulse, the states involved in the
flipping can be brought into resonance by means of the optical Stark effect
increasing the amplitude of the Rabi oscillations to one. In this paper we
study theoretically how this spin dynamics can be monitored in time-resolved
spectroscopy. In the spectrum the exchange interaction leads to a splitting of
the exciton line into six lines, each corresponding to one of the six Mn spin
states. The dynamical behavior of the Mn spin is reflected by the strength of
the individual lines as a function of time. When an off-resonant optical pulse
is applied the spectral positions of the lines shift, but still the flipping
dynamics is visible.


title:
Understanding Operational Risk Capital Approximations: First and Second
  Orders

abstract:
  We set the context for capital approximation within the framework of the
Basel II / III regulatory capital accords. This is particularly topical as the
Basel III accord is shortly due to take effect. In this regard, we provide a
summary of the role of capital adequacy in the new accord, highlighting along
the way the significant loss events that have been attributed to the
Operational Risk class that was introduced in the Basel II and III accords.
Then we provide a semi-tutorial discussion on the modelling aspects of capital
estimation under a Loss Distributional Approach (LDA). Our emphasis is to focus
on the important loss processes with regard to those that contribute most to
capital, the so called high consequence, low frequency loss processes. This
leads us to provide a tutorial overview of heavy tailed loss process modelling
in OpRisk under Basel III, with discussion on the implications of such tail
assumptions for the severity model in an LDA structure. This provides
practitioners with a clear understanding of the features that they may wish to
consider when developing OpRisk severity models in practice. From this
discussion on heavy tailed severity models, we then develop an understanding of
the impact such models have on the right tail asymptotics of the compound loss
process and we provide detailed presentation of what are known as first and
second order tail approximations for the resulting heavy tailed loss process.
From this we develop a tutorial on three key families of risk measures and
their equivalent second order asymptotic approximations: Value-at-Risk (Basel
III industry standard); Expected Shortfall (ES) and the Spectral Risk Measure.
These then form the capital approximations.


title: Reversible limit of processes of heat transfer

abstract:
  We study a process of heat transfer between a body of heat capacity C(T) and
a sequence of N heat reservoirs, with temperatures equally spaced between an
initial temperature T_0 and a final temperature T_N. The body and the heat
reservoirs are isolated from the rest of the universe, and the body is brought
in thermal contact successively with reservoirs of increasing temperature. We
determine the change of entropy of the composite thermodynamic system in the
total process in which the temperature of the body changes from T_0 to T_N. We
find that for large values of N the total change of entropy of the composite
process is proportional to (T_N-T_0)/N, but eventually a non-monotonic behavior
is found at small values of N.


title:
Integrated Pre-Processing for Bayesian Nonlinear System Identification
  with Gaussian Processes

abstract:
  We introduce GP-FNARX: a new model for nonlinear system identification based
on a nonlinear autoregressive exogenous model (NARX) with filtered regressors
(F) where the nonlinear regression problem is tackled using sparse Gaussian
processes (GP). We integrate data pre-processing with system identification
into a fully automated procedure that goes from raw data to an identified
model. Both pre-processing parameters and GP hyper-parameters are tuned by
maximizing the marginal likelihood of the probabilistic model. We obtain a
Bayesian model of the system's dynamics which is able to report its uncertainty
in regions where the data is scarce. The automated approach, the modeling of
uncertainty and its relatively low computational cost make of GP-FNARX a good
candidate for applications in robotics and adaptive control.


title:
Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge
  Theory

abstract:
  We present a systematic method to determine BCJ numerators for one-loop
amplitudes that explores the global constraints on the loop momentum
dependence. We apply this method to amplitudes in N=4 gauge theory, working out
detailed examples up to seven points in both the MHV and the NMHV sectors. The
structure of Jacobi identities between BCJ numerators is seen to be closely
connected to that of algebraic integrand reductions. We discuss the
consequences for one-loop N=8 supergravity amplitudes obtained through the
double copy prescription. Moreover, in the MHV sector, we show how to obtain
simple BCJ box numerators using a conjectured relationship to amplitudes in
self-dual gauge theory. We also introduce simpler trace-type formulas for
integrand reductions.


title: The new Wolf-Rayet binary system WR62a

abstract:
  Context. A significant number of the Wolf-Rayet stars seem to be binary or
multiple systems, but the nature of many of them is still unknown. Dedicated
monitoring of WR stars favours the discovery of new systems.
  Aims. We explore the possibility that WR62a is a binary system.
  Methods. We analysed the spectra of WR62a, obtained between 2002 and 2010, to
look for radial-velocity and spectral variations that would suggest there is a
binary component. We searched for periodicities in the measured radial
velocities and determined orbital solutions. A period search was also performed
on the "All-Sky Automated Survey" photometry.
  Results. We find that WR62a is a double-lined spectroscopic binary with a WN5
primary star and an O 5.5-6 type secondary component in orbit with a period of
9.1447 d. The minimum masses range between 21 and 23 Mo for the WN star and
between 39 and 42 Mo for the O-type star, thus indicating that the WN star is
less massive than the O-type component. We detect a phase shift in the
radial-velocity curve of the He II 4686 emission line relative to the other
emission line curves. The equivalent width of this emission line shows a
minimum value when the WN star passes in front of the system. The analysis of
the ASAS photometry confirms the spectroscopic periodicity, presenting a
minimum at the same phase.


title: Modeling US housing prices by spatial dynamic structural equation models

abstract:
  This article proposes a spatial dynamic structural equation model for the
analysis of housing prices at the State level in the USA. The study contributes
to the existing literature by extending the use of dynamic factor models to the
econometric analysis of multivariate lattice data. One of the main advantages
of our model formulation is that by modeling the spatial variation via
spatially structured factor loadings, we entertain the possibility of
identifying similarity "regions" that share common time series components. The
factor loadings are modeled as conditionally independent multivariate Gaussian
Markov Random Fields, while the common components are modeled by latent dynamic
factors. The general model is proposed in a state-space formulation where both
stationary and nonstationary autoregressive distributed-lag processes for the
latent factors are considered. For the latent factors which exhibit a common
trend, and hence are cointegrated, an error correction specification of the
(vector) autoregressive distributed-lag process is proposed. Full probabilistic
inference for the model parameters is facilitated by adapting standard Markov
chain Monte Carlo (MCMC) algorithms for dynamic linear models to our model
formulation. The fit of the model is discussed for a data set of 48 States for
which we model the relationship between housing prices and the macroeconomy,
using State level unemployment and per capita personal income.


title: Phase space evolution of pairs created in strong electric fields

abstract:
  We study the process of energy conversion from overcritical electric field
into electron-positron-photon plasma. We solve numerically Vlasov-Boltzmann
equations for pairs and photons assuming the system to be homogeneous and
anisotropic. All the 2-particle QED interactions between pairs and photons are
described by collision terms. We evidence several epochs of this energy
conversion, each of them associated to a specific physical process. Firstly
pair creation occurs, secondly back reaction results in plasma oscillations.
Thirdly photons are produced by electron-positron annihilation. Finally
particle interactions lead to completely equilibrated thermal
electron-positron-photon plasma.


title: Observability of`Cascade Mixing' in B0 --> J/psi K0

abstract:
  In high statistics observations of B^o --> J/\psi K0, originating from the
process Upsilon(4S)--> B0 B0, it should be possible to observe `cascade
mixing', where one mixing particle, the B0, turns into another, the K0. This is
possible despite the difficulty that the length of the beam crossing region
makes a precise definition of the primary vertex impossible. This difficulty is
circumvented by using an `away side' tag to specify the initial time. We review
the formalism for describing such processes, and first apply it to simple B0
mixing, noting it gives a transparent description for CP and T asymmetries. In
particular we show that three different asymmetries of the CP and T type, with
neglect of direct CP violation, are given by the same expression.
  For "cascade mixing" we present predictions for processes of the type B_i -->
K_j via J/psi, where in the limit of no direct CP violation each state i or j
is determined by a simple tag. There are 16 such simple measureable processes,
involving 10 functions of the two time intervals involved. The coefficients of
the functions are different for each of the processes and are given in terms of
the mass splitting and the CP, T violating parameter of the B0 mass matrix m_2.
The results presented here are just consquences of the quantum mechanics of
particle mixing and do not involve any particular model of CP violation.


title: Frequency-dependent admittance of a short superconducting weak link

abstract:
  We consider the linear and non-linear electromagnetic responses of a nanowire
connecting two bulk superconductors. Andreev states appearing at a finite phase
bias substantially affect the finite-frequency admittance of such a wire
junction. Electron transitions involving Andreev levels are easily saturated,
leading to the nonlinear effects in photon absorption for the sub-gap photon
energies. We evaluate the complex admittance analytically at arbitrary
frequency and arbitrary, possibly non-equilibrium, occupation of Andreev
levels. Special care is given to the limits of a single-channel contact and a
disordered metallic weak link. We also evaluate the quasi-static fluctuations
of admittance induced by fluctuations of the occupation factors of Andreev
levels. In view of possible qubit applications, we compare properties of a weak
link with those of a tunnel Josephson junction. Compared to the latter, a weak
link has smaller low-frequency dissipation. However, because of the deeper
Andreev levels, the low-temperature quasi-static fluctuations of the inductance
of a weak link are exponentially larger than of a tunnel junction. These
fluctuations limit the applicability of nanowire junctions in superconducting
qubits.


title:
A Monte Carlo study to measure the energy spectra of the primary
  cosmic-ray components at the knee using a new Tibet AS core detector array

abstract:
  A new hybrid experiment has been started by AS{\gamma} experiment at Tibet,
China, since August 2011, which consists of a low threshold burst-detector-grid
(YAC-II, Yangbajing Air shower Core array), the Tibet air-shower array
(Tibet-III) and a large underground water Cherenkov muon detector (MD). In this
paper, the capability of the measurement of the chemical components (proton,
helium and iron) with use of the (Tibet-III+YAC-II) is investigated by means of
an extensive Monte Carlo simulation in which the secondary particles are
propagated through the (Tibet-III+YAC-II) array and an artificial neural
network (ANN) method is applied for the primary mass separation. Our simulation
shows that the new installation is powerful to study the chemical compositions,
in particular, to obtain the primary energy spectrum of the major component at
the knee.


title: Approximating 1-dimensional TSP Requires Omega(n log n) Comparisons

abstract:
  We give a short proof that any comparison-based n^(1-epsilon)-approximation
algorithm for the 1-dimensional Traveling Salesman Problem (TSP) requires
Omega(n log n) comparisons.


title: Old novae and the SW Sex phenomenon

abstract:
  From a large observing campaign, we found that nearly all non- or weakly
magnetic cataclysmic variables (CVs) in the orbital period range between 2.8
and 4 hours are of SW Sex type and as such experience very high mass transfer
rates. The exceptions seem to be some old novae that have periods around 3.5 h.
Their spectra do not show the typical SW Sex characteristics but rather
resemble those of dwarf novae with low mass transfer rates.
  The presence of old novae in this period range of SW Sex stars that do not
follow the trend but show instead rather low mass transfer rates is interpreted
as evidence for an effect of the nova eruption on the mass transfer rate of the
underlying CV similar to the hibernation scenario.


title:
Integrated Optical Dipole Trap for Cold Neutral Atoms with an Optical
  Waveguide Coupler

abstract:
  An integrated optical dipole trap uses two-color (red and blue-detuned)
traveling evanescent wave fields for trapping cold neutral atoms. To achieve
longitudinal confinement, we propose using an integrated optical waveguide
coupler, which provides a potential gradient along the beam propagation
direction sufficient to confine atoms. This integrated optical dipole trap can
support an atomic ensemble with a large optical depth due to its small mode
area. Its quasi-TE0 waveguide mode has an advantage over the HE11 mode of a
nanofiber, with little inhomogeneous Zeeman broadening at the trapping region.
The longitudinal confinement eliminates the need for a 1-D optical lattice,
reducing collisional blockaded atomic loading, potentially producing larger
ensembles. The waveguide trap allows for scalability and integrability with
nano-fabrication technology. We analyze the potential performance of such
integrated atom traps.


title: Assessing the public health relevance of a risk factor

abstract:
  In a recent series of high impact public health publications, the c-index was
used as measure of prediction to assess the public health relevance of a risk
factor. I demonstrate that the c-index is an inferior measure as compared to
the classical epidemiologic measures most commonly employed for risk prediction
and public health assessment such as disease incidence, relative risk (RR) and
population-attributable risk (PAR). I recommend using the latter measures when
assessing the public health relevance of a risk factor.


title:
Isobaric Yield Ratio Difference in Heavy-ion Collisions, and Comparison
  to Isoscaling

abstract:
  An isobaric yield ratio difference (IBD) method is proposed to study the
ratio of the difference between the chemical potential of neutron and proton to
temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$
determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of
the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the
isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are
found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni +
$^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with
a plateau in the small mass fragments plus an increasing part in the fragments
of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show
dependence on the $n/p$ ratio of the projectile. It is suggested that the
height of the plateau is decided by the difference between the neutron density
($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles,
and the width shows the overlapping volume of the projectiles in which $\rho_n$
and $\rho_p$ change very little. The difference between the IB- and
IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by
the many isotopes and isotones, while the IBD method only uses the yields of
two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than
the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys
the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the
density or the temperature, the density dependence is preferred since the low
density can result in low temperature in the peripheral reactions.


title:
Normal forms for the epicyclic approximations of the perturbed Kepler
  problem

abstract:
  We compute the normal forms for the Hamiltonian leading to the epicyclic
approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian
setting corresponds to the dynamics in the Hill synodic system where, by means
of the tidal expansion of the potential, the equations of motion take the form
of perturbed harmonic oscillators in a rotating frame. In the unperturbed,
purely Keplerian case, the post-epicyclic solutions produced with the normal
form coincide with those obtained from the expansion of the solution of the
Kepler equation. In all cases where the perturbed problem can be cast in
autonomous form, the solution is easily obtained as a perturbation series. The
generalization to the spatial problem and/or the non-autonomous case is
straightforward.


title: Reverse Mathematics and initial intervals

abstract:
  In this paper we study the reverse mathematics of two theorems by Bonnet
about partial orders. These results concern the structure and cardinality of
the collection of the initial intervals. The first theorem states that a
partial order has no infinite antichains if and only if its initial intervals
are finite unions of ideals. The second one asserts that a countable partial
order is scattered and does not contain infinite antichains if and only if it
has countably many initial intervals. We show that the left to right directions
of these theorems are equivalent to ACA_0 and ATR_0, respectively. On the other
hand, the opposite directions are both provable in WKL_0, but not in RCA_0. We
also prove the equivalence with ACA_0 of the following result of Erd\"os and
Tarski: a partial order with no infinite strong antichains has no arbitrarily
large finite strong antichains.


title:
Measurement of the proton-proton total cross section at 2, 7, 8 and 57
  TeV

abstract:
  The measurement of the total $pp$ cross section and its various
sub-components (elastic, inelastic and diffractive) is a very powerful tool to
understand the proton macro structure and fundamental QCD dynamics. In this
contribution I first provide a theoretical introduction to the topic, then a
summary of the experimental techniques and finally I review the new results
from AUGER and LHC experiments.


title: Resonant Behavior of Comet Halley and the Orionid Stream

abstract:
  Comet 1P/Halley has the unique distinction of having a very comprehensive set
of observational records for almost every perihelion passage from 240 B.C. This
has helped to constrain theoretical models pertaining to its orbital evolution.
Many previous works have shown the active role of mean motion resonances in the
evolution of various meteoroid streams. Here we look at how various resonances,
especially the 1:6 and 2:13 mean motion resonances with Jupiter, affect comet
1P/Halley and thereby enhance the chances of meteoroid particles getting
trapped in resonance, leading to meteor outbursts in some particular years.
Comet Halley itself librated in the 2:13 resonance from 240 B.C. to 1700 A.D.
and in the 1:6 resonance from 1404 B.C. to 690 B.C., while stream particles can
survive for timescales of the order of 10,000 years and 1,000 years in the 1:6
and 2:13 resonances respectively. This determines the long term dynamical
evolution and stream structure, influencing the occurrence of Orionid
outbursts. Specifically we are able to correlate the occurrence of enhanced
meteor phenomena seen between 1436-1440, 1933-1938 & 2006-2010 with the 1:6
resonance and meteor outbursts in 1916 & 1993 with the 2:13 resonance. Ancient
as well as modern observational records agree with these theoretical
simulations to a very good degree.


title: Poincar\'e polynomials of stable map spaces to Grassmannians

abstract:
  In this paper, we give generating functions for the Betti numbers of
$\bar{M}_{0,0}({G}(k,n),d)$, the moduli stack of zero pointed genus zero degree
$d$ stable maps to the Grassmannian ${G}(k,n)$ for $d=2$ and 3.


title: Active transport in dense diffusive single-file systems

abstract:
  We study a minimal model of active transport in crowded single-file
environments which generalises the emblematic model of single file diffusion to
the case when the tracer particle (TP) performs either an autonomous directed
motion or is biased by an external force, while all other particles of the
environment (bath) perform unbiased diffusions. We derive explicit expressions,
valid in the limit of high density of bath particles, of the full distribution
$P_n(X)$ of the TP position and of all its cumulants, for arbitrary values of
the bias $f$ and for any time $n$. Our analysis reveals striking features, such
as the anomalous scaling $\propto\sqrt{n}$ of all cumulants, the equality of
cumulants of the same parity characteristic of a Skellam distribution and a
convergence to a Gaussian distribution in spite of asymmetric density profiles
of bath particles. Altogether, our results provide the full statistics of the
TP position, and set the basis for a refined analysis of real trajectories of
active particles in crowded single-file environments.


title: Symmetry-surfing the moduli space of Kummer K3s

abstract:
  A maximal subgroup of the Mathieu group M24 arises as the combined
holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler
class is induced from the underlying complex torus. As a subgroup of M24, this
group is the stabilizer group of an octad in the Golay code. To meaningfully
combine the symmetry groups of distinct Kummer surfaces, we introduce the
concepts of Niemeier markings and overarching maps between pairs of Kummer
surfaces. The latter induce a prescription for symmetry-surfing the moduli
space, while the former can be seen as a first step towards constructing a
vertex algebra that governs the elliptic genus of K3 in an M24-compatible
fashion. We thus argue that a geometric approach from K3 to Mathieu Moonshine
may bear fruit.


title:
Galerkin FEM for fractional order parabolic equations with initial data
  in $H^{-s},~0 < s \le 1$

abstract:
  We investigate semi-discrete numerical schemes based on the standard Galerkin
and lumped mass Galerkin finite element methods for an initial-boundary value
problem for homogeneous fractional diffusion problems with non-smooth initial
data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex
polygonal (polyhedral) domain. We theoretically justify optimal order error
estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s
\le 1$. We confirm our theoretical findings with a number of numerical tests
that include initial data $v$ being a Dirac $\delta$-function supported on a
$(d-1)$-dimensional manifold.


title: Interference Networks: A Complex System View

abstract:
  This paper presents an unusual view of interference wireless networks based
on complex system thinking. To proceed with this analysis, a literature review
of the different applications of complex systems is firstly presented to
illustrate how such an approach can be used in a wide range of research topics,
from economics to linguistics. Then the problem of quantifying the fundamental
limits of wireless systems where the co-channel interference is the main
limiting factor is described and hence contextualized in the perspective of
complex systems. Specifically some possible internal and external pressures
that the network elements may suffer are identified as, for example, queue
stability, maximum packet loss rate and transmit power constraint. Besides,
other important external factors such as mobility and incoming traffic are also
pointed out. As a study case, a decentralized point-to-point interference
network is described and several claims about the optimal design setting for
different network states and under two mobility conditions, namely quasi-static
and highly mobile, are stated based on results found in the literature. Using
these claims as a background, the design of a robust adaptive algorithm that
each network element should run is investigated.


title: Spectrum Analysis of Bright Kepler late B- to early F- Stars

abstract:
  The Kepler satellite mission delivers single band-pass light curves of a huge
number of stars observed in the Cygnus-Lyra region opening a new window for
asteroseismology. In order to accomplish one of the preconditions for the
asteroseismic modelling of the stars, we aim to derive fundamental parameters
and individual abundances for a sample of 18 Gamma Dor (GD)/Delta Sct (DSct)
and 8 SPB/beta Cep candidate stars in the Kepler satellite field of view. We
use the spectral synthesis method to model newly obtained, high-resolution
spectra of 26 stars in order to derive their fundamental parameters and
individual abundances. The stars are then placed into the log(Teff)-log(g)
diagram and the obtained spectroscopic classification is compared to the
existing photometric one. For hot stars, the KIC temperatures appear to be
systematically underestimated, in agreement with previous findings. We also
find that the temperatures derived from our spectra agree reasonably well with
those derived from the SED fitting. According to their position in the
log(Teff)-log(g) diagram, two stars are expected GD stars, four stars are
expected DSct stars, and four stars are possibly DSct stars at the blue edge of
the instability strip. Two stars are confirmed SPB variables, and one star
falls into the SPB instability region but its parameters might be biased by
binarity. Two of the four stars that fall into the DSct instability region show
GD-type oscillation in their light curves implying that GD-like oscillations
are much more common among the DSct stars than is theoretically expected.
Moreover, one of the stars located at the hot border of the DSct instability
strip is classified as DSct-GD hybrid pulsator from its light curve analysis.
Given that these findings are fully consistent with recent investigations, we
conclude that a revision of the GD and DSct instability strips is essential.


title: On Systemic Destruction of Human Locomotor System

abstract:
  Locomotor system disorders affect a vast majority of people at some time in
their life bringing pain, functional limitations, social and economic
implications. Modern medicine cannot offer prevention and effective treatment
for most chronic musculoskeletal conditions, because their etiology and
pathogenesis are unknown. This is due to the lack of systemic understanding of
the locomotor system functioning in both healthy and unhealthy states. Here we
apply systems sciences to analyze the human locomotor system and develop a
general theory that reveals the systemic destructive process in the locomotor
system, linking together all its disorders. The systemic destruction involves
adaptation and self-organization processes in the locomotor system, whose side
effects introduce a positive feedback loop with nervous and vascular
disturbances. Most chronic musculoskeletal conditions are just manifestations
and consequences of this process. On the basis of our theoretical findings, we
developed the world's first technology that effectively counteracts the
systemic destruction and improves the locomotor system state at any age, also
preventing problems in nervous and cardiovascular systems.


title: The incompleteness of complete pseudoscalar-meson photoproduction

abstract:
  [Background] A complete set is a minimum set of observables which allows one
to determine the underlying reaction amplitudes unambiguously.
Pseudoscalar-meson photoproduction from the nucleon is characterized by four
such amplitudes and complete sets involve single- and double-polarization
observables.
  [Purpose] Identify complete sets of observables, and study how measurements
with finite error bars impact their potential to determine the reaction
amplitudes unambiguously.
  [Method] The authors provide arguments to employ the transversity
representation in order to determine the amplitudes in pseudoscalar-meson
photoproduction. It is studied whether the amplitudes in the transversity basis
for the $\gamma p \to K^+\Lambda$ reaction can be estimated without ambiguity.
To this end, data from the GRAAL collaboration and mock data from a realistic
model are analyzed.
  [Results] It is illustrated that the moduli of normalized transversity
amplitudes can be determined from precise single-polarization data. Starting
from mock data with achievable experimental resolution, it is quite likely to
obtain imaginary solutions for the relative phases of the amplitudes. Also the
real solutions face a discrete phase ambiguity which makes it impossible to
obtain a statistically significant solution for the relative phases at
realistic experimental conditions.
  [Conclusions] Single polarization observables are effective in determining
the moduli of the amplitudes in a transversity basis. Determining the relative
phases of the amplitudes from double-polarization observables is far less
evident. The availability of a complete set of observables does not allow one
to unambiguously determine the reaction amplitudes with statistical
significance.


title: Periodic modules over Gorenstein local rings

abstract:
  It is proved that the minimal free resolution of a module M over a Gorenstein
local ring R is eventually periodic if, and only if, the class of M is torsion
in a certain Z[t,t^{-1}]-module associated to R. This module, denoted J(R), is
the free Z[t,t^{-1}]-module on the isomorphism classes of finitely generated
R-modules modulo relations reminiscent of those defining the Grothendieck group
of R. The main result is a structure theorem for J(R) when R is a complete
Gorenstein local ring; the link between periodicity and torsion stated above is
a corollary.


title:
D\'emixtion et s\'egr\'egation superficielle dans les alliages
  fer-chrome

abstract:
  Ferritic steels possibly strengthened by oxide dispersion are candidates as
structural materials for generation IV and fusion nuclear reactors. Their use
is limited by incomplete knowledge of the iron-chromium phase diagram at low
temperatures and of the phenomena inducing preferential segregation of one
element at grain boundaries or at surfaces. In this context, this work
contributes to the multi-scale study of the model iron-chromium alloy and their
free surfaces by numerical simulations. This study begins with ab initio
calculations of properties related to the mixture of atoms of iron and
chromium. We highlight complex dependency of the magnetic moments of the
chromium atoms on their local chemical environment. Surface properties are also
proving sensitive to magnetism. This is the case of impurity segregation of
chromium in iron and of their interactions near the surface. In a second step,
we construct a simple energy model for high numerical efficiency. It is based
on pair interactions on a rigid lattice to which are given local chemical
environment and temperature dependencies. With this model, we reproduce the ab
initio results at zero temperature and experimental results at high
temperature. We also deduce the solubility limits at all intermediate
temperatures with mean field approximations that we compare to Monte Carlo
simulations. The last step of our work is to introduce free surfaces in our
model. We then study the effect of ab initio calculated bulk and surface
properties on surface segregation. Finally, we calculate segregation isotherms.
We therefore propose an evolution model of surface composition of iron-chromium
alloys as a function of bulk composition.


title: Uniqueness of the fractional derivative definition

abstract:
  For the Riesz fractional derivative besides the well known integral
representation two new differential representations are presented, which
emphasize the local aspects of a fractional derivative. The consequences for a
valid solution of the fractional Schroedinger equation are discussed.


title:
Robustness of Topological Order in Semiconductor-Superconductor
  Nanowires in the Coulomb Blockade Regime

abstract:
  Semiconductor-superconductor hybrid systems are promising candidates for the
realization Majorana fermions and topological order, i.e. topologically
protected degeneracies, in solid state devices. We show that the topological
order is mirrored in the excitation spectra and can be observed in nonlinear
Coulomb blockade transport through a ring-shaped nanowire. Especially, the
excitation spectrum is almost independent of magnetic flux in the topologically
trivial phase but acquires a characteristic $h/e$ magnetic flux periodicity in
the nontrivial phase. The transition between the trivial and nontrivial phase
is reflected in the closing and reopening of an excitation gap. We show that
the signatures of topological order are robust against details of the geometry,
electrostatic disorder, and the existence of additional subbands and only rely
on the topology of the nanowire and the existence of a superconducting gap.
Finally, we show that the coherence length in the nontrivial phase is much
longer than in the trivial phase. This opens the possibility to coat the
nanowire with superconducting nanograins and thereby significantly reduce the
current due to cotunneling of Cooper pairs and to enhance the Coulomb charging
energy without destroying the superconducting gap.


title:
The generalized Riemann problems for hyperbolic balance laws: A unified
  formulation towards high order

abstract:
  The Generalized Riemann Problems (GRP) for nonlinear hyperbolic systems of
balance laws in one space dimension are now well-known and can be formulated as
follows: Given initial-data which are smooth on two sides of a discontinuity,
determine the time evolution of the solution near the discontinuity. While the
classical Riemann problem serves as a primary building block in the
construction of many numerical schemes (most notably the Godunov scheme), the
analytic study of GRP will lead to an array of GRP schemes, which extend the
Godunov scheme. Currently there are extensive studies on the second-order GRP
scheme, which proves to be robust and is capable of resolving complex
multidimensional fluid dynamic problems [M. Ben-Artzi and J. Falcovitz,
"Generalized Riemann Problems in Computational Fluid Dynamics", Cambridge
University Press, 2003]. A more general formulation of the second-order GRP
solver is still confined with a class of weakly coupled systems [Numer. Math.
(2007) 106:369-425]. This paper provides a unified approach for solving the GRP
in the general context of hyperbolic balance laws, without weakly coupled
constraint, towards high order accuracy. The derivation of the second-order GRP
solver is more concise compared to those in previous works and the third-order
quadratic GRP is resolved for the first time. The latter is shown to be
necessary through numerical experiments with strong discontinuities. Our method
relies heavily on the new treatment of the rarefaction wave by deriving the
L(Q)-equations, an ODE system capturing the "evolution" of the characteristic
derivatives in x-t space for generalized Riemann invariants. The case of a
sonic point is incorporated into a general treatment. The accuracy of the
derived GRP solvers are justified and numerical examples are presented for the
performance of the resulting scheme.


title:
The Halo Occupation Distribution of X-ray-Bright Active Galactic Nuclei:
  A Comparison with Luminous Quasars

abstract:
  We perform halo occupation distribution (HOD) modeling of the projected
two-point correlation function (2PCF) of high-redshift (z~1.2) X-ray-bright
active galactic nuclei (AGN) in the XMM-COSMOS field measured by Allevato et
al. The HOD parameterization is based on low-luminosity AGN in cosmological
simulations. At the median redshift of z~1.2, we derive a median mass of
(1.02+0.21/-0.23)x10^{13} Msun/h for halos hosting central AGN and an upper
limit of ~10% on the AGN satellite fraction. Our modeling results indicate (at
the 2.5-sigma level) that X-ray AGN reside in more massive halos compared to
more bolometrically luminous, optically-selected quasars at similar redshift.
The modeling also yields constraints on the duty cycle of the X-ray AGN, and we
find that at z~1.2 the average duration of the X-ray AGN phase is two orders of
magnitude longer than that of the quasar phase. Our inferred mean occupation
function of X-ray AGN is similar to recent empirical measurements with a group
catalog and suggests that AGN halo occupancy increases with increasing halo
mass. We project the XMM-COSMOS 2PCF measurements to forecast the required
survey parameters needed in future AGN clustering studies to enable higher
precision HOD constraints and determinations of key physical parameters like
the satellite fraction and duty cycle. We find that N^{2}/A~5x10^{6} deg^{-2}
(with N the number of AGN in a survey area of A deg^{2}) is sufficient to
constrain the HOD parameters at the 10% level, which is easily achievable by
upcoming and proposed X-ray surveys.


title:
Alpha-Particle condensation in nuclear systems: present status and
  perspectives

abstract:
  Alpha clustering and alpha condensation in lighter nuclei is presently
strongly and increasingly discussed in the literature both from the
experimental side as from the theoretical one. A discussion of the present
status of the theory as well as outlooks for future developements will be
presented.


title:
Solutions of the Vlasov-Maxwell-Boltzmann system with long-range
  interactions

abstract:
  We establish the existence of renormalized solutions of the
Vlasov-Maxwell-Boltzmann system with a defect measure in the presence of
long-range interactions. We also present a control of the defect measure by the
entropy dissipation only, which turns out to be crucial in the study of
hydrodynamic limits.


title:
The effect of the Fluorescence Yield selection on the energy scales of
  Auger, HiRes and TA

abstract:
  The fluorescence yield data used for shower reconstruction in the Auger,
HiRes and TA experiments are different, not only in the overall absolute value
but also in the wavelength spectrum and the various atmospheric dependencies.
The effect on the energy reconstruction of using different fluorescence yield
parameterizations is discussed. In addition, the impact of a change in the
fluorescence spectrum depends on the optical efficiency of the telescopes. A
simple analytical procedure allows us to evaluate the combined effect of
fluorescence yield and optical efficiency showing a non-negligible deviation
between the energy scales of TA and Auger. However no relevant effect is found
in the comparison between HiRes and Auger. Finally we show that a similar
procedure could also be applied with real data.


title: Statistical and Numerical Study of Asteroid Orbital Uncertainty

abstract:
  The knowledge of the orbit or the ephemeris uncertainty of asteroid presents
a particular interest for various purposes. These quantities are for instance
useful for recovering asteroids, for identifying lost asteroids or for planning
stellar occultation campaigns. They are also needed to estimate the close
approach of Near-Earth asteroids, and subsequent risk of collision. Ephemeris
accuracy can also be used for instrument calibration purposes or for scientific
applications. Asteroid databases provide information about the uncertainty of
the orbits allowing the measure of the quality of an orbit. The aims of this
paper is to analyse these different uncertainty parameters and to estimate the
impact of the different measurements on the uncertainty of orbits. We
particularly deal with two main databases ASTORB and MPCORB providing
uncertainty parameters for asteroid orbits. Statistical methods are used in
order to estimate orbital uncertainty and compare with parameters from
databases. Simulations are also generated to deal with specific measurements
such as future Gaia or present radar measurements. Relations between the
uncertainty parameter and the characteristics of the asteroid (orbital arc,
absolute magnitude, ...) are highlighted. Moreover, a review of the different
measuments are compiled and the impact of these measures on the accuracy of the
orbit is also estimated.


title: Design of a surface acoustic wave mass sensor in the 100 GHz range

abstract:
  A design for photoacoustic mass sensors operating above 100 GHz is proposed.
The design is based on impulsive optical excitation of a pseudosurface acoustic
wave in a surface phononic crystal with nanometric periodic grating, and on
time-resolved extreme ultraviolet detection of the pseudosurface acoustic wave
frequency shift upon mass loading the device. The present design opens the path
to sensors operating in a frequency range currently unaccessible to
electro-acoustical transducers, providing enhanced sensitivity, miniaturization
and incorporating time-resolving capability while forgoing the piezoelectric
substrate requirement.


title:
Weather on Other Worlds I: Detection of Periodic Variability in the L3
  Dwarf DENIS-P J1058.7-1548 with Precise Multi-Wavelength Photometry

abstract:
  Photometric monitoring from warm Spitzer reveals that the L3 dwarf DENIS-P
J1058.7-1548 varies sinusoidally in brightness with a period of 4.25
+0.26/-0.16 hours and an amplitude of 0.388 +/- 0.043% (peak-to-valley) in the
3.6 micron band, confirming the reality of a 4.31 +/- 0.31 hour periodicity
detected in J-band photometry from the SOAR telescope. The J-band variations
are a factor of 2.17 +/- 0.35 larger in amplitude than those at 3.6 microns,
while 4.5 micron Spitzer observations yield a 4.5 micron/3.6 micron amplitude
ratio of only 0.23 +/- 0.15, consistent with zero 4.5 micron variability. This
wide range in amplitudes indicates rotationally modulated variability due to
magnetic phenomena and/or inhomogeneous cloud cover. Weak H-alpha emission
indicates some magnetic activity, but it is difficult to explain the observed
amplitudes by magnetic phenomena unless they are combined with cloud
inhomogeneities (which might have a magnetic cause). However, inhomogenous
cloudcover alone can explain all our observations, and our data align with
theory in requiring that the regions with the thickest clouds also have the
lowest effective temperature. Combined with published v sin(i) results, our
rotation period yields a 95% confidence lower limit of 0.111 solar radii on the
radius of DENIS-P J1058.7-1548, suggesting upper limits of 320 Myr and 0.055
solar masses on the age and mass. These limits should be regarded cautiously
because of 3-sigma inconsistencies with other data; however, a lower limit of
45 degrees on the inclination is more secure. DENIS-P J1058.7-1548 is only the
first of nearly two dozen low-amplitude variables discovered and analyzed by
the Weather on Other Worlds project.


title:
Mixing of partial waves near $B^* \bar B^*$ threshold in $e^+e^-$
  annihilation

abstract:
  We consider the production of $B^* \bar B^*$ meson pairs in $e^+e^-$
annihilation near the threshold. The rescattering due to pion exchange between
the mesons results in a mixing between three partial wave amplitudes: two
$P$-wave with the total spin of the meson pair S=0 and S=2 and an F-wave
amplitude. The mixing due to pion exchange with a low momentum transfer is
calculable up to c.m. energy $E \approx 15 \div 20$\,MeV above the threshold.
We find that the $P-F$ mixing is numerically quite small in this energy range,
while the mixing of the two P-wave amplitudes is rapidly changing with energy
and can reach of order one at such low energies.


title: Dynamic Credit Investment in Partially Observed Markets

abstract:
  We consider the problem of maximizing expected utility for a power investor
who can allocate his wealth in a stock, a defaultable security, and a money
market account. The dynamics of these security prices are governed by geometric
Brownian motions modulated by a hidden continuous time finite state Markov
chain. We reduce the partially observed stochastic control problem to a
complete observation risk sensitive control problem via the filtered regime
switching probabilities. We separate the latter into pre-default and
post-default dynamic optimization subproblems, and obtain two coupled
Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove
existence and uniqueness of a globally bounded classical solution to each HJB
equation, and give the corresponding verification theorem. We provide a
numerical analysis showing that the investor increases his holdings in stock as
the filter probability of being in high growth regimes increases, and decreases
his credit risk exposure when the filter probability of being in high default
risk regimes gets larger.


title: The Erd\H{o}s-Hajnal conjecture for rainbow triangles

abstract:
  We prove that every 3-coloring of the edges of the complete graph on n
vertices without a rainbow triangle contains a set of order Omega(n^{1/3}log^2
n) which uses at most two colors, and this bound is tight up to a constant
factor. This verifies a conjecture of Hajnal which is a case of the multicolor
generalization of the well-known Erd\H{o}s-Hajnal conjecture. We further
establish a generalization of this result. For fixed positive integers s and r
with s at most r, we determine a constant c_{r,s} such that the following
holds. Every r-coloring of the edges of the complete graph on n vertices
without a rainbow triangle contains a set of order Omega(n^{r(r-1)/s(s-1)}(\log
n)^{c_{r,s}}) which uses at most s colors, and this bound is tight apart from
the implied constant factor. The proof of the lower bound utilizes Gallai's
classification of rainbow-triangle free edge-colorings of the complete graph, a
new weighted extension of Ramsey's theorem, and a discrepancy inequality in
edge-weighted graphs. The proof of the upper bound uses Erd\H{o}s' lower bound
on Ramsey numbers by considering lexicographic products of 2-edge-colorings of
complete graphs without large monochromatic cliques.


title:
Traffic Congestion in Expanders, $(p,\delta)$--Hyperbolic Spaces and
  Product of Trees

abstract:
  In this paper we define the notion of $(p,\delta)$--Gromov hyperbolic space
where we relax Gromov's {\it slimness} condition to allow that not all but a
positive fraction of all triangles are $\delta$--slim. Furthermore, we study
maximum vertex congestion under geodesic routing and show that it scales as
$\Omega(p^2n^2/D_n^2)$ where $D_n$ is the diameter of the graph. We also
construct a constant degree family of expanders with congestion $\Theta(n^2)$
in contrast with random regular graphs that have congestion $O(n\log^{3}(n))$.
Finally, we study traffic congestion on graphs defined as product of trees.


title:
Collision and capture dynamics in a quantum dot: The role of doubly
  excited states

abstract:
  We investigate collision dynamics involving two electrons and a quantum dot
embedded in a quantum wire. One electron is initially at rest in the ground
state of the dot, whereas the other electron is incident on the dot with a
rather well defined velocity. Excitation, reflection and transmission
probabilities are obtained by resolving the dynamics explicitly. Also, the
probability of both electrons being unbound after collision is studied. It is
found that the dynamics is strongly influenced by the presence of doubly
excited states; reflection becomes considerably more probable in the energetic
vicinity of such states. This, in turn, contributes to an increase in the
probability of trapping also the second electron within the dot.


title: On the deformation of a Barsotti-Tate group over a curve

abstract:
  In this paper, we study deformations of pairs (C,G) where G is a height 2
BT(or BT_n) group over a complete curve on algebraically closed field k of
characteristic p. We prove that, if the curve C is a versal deformation of G,
then there exists a unique lifting of the pair to the Witt ring W. We apply
this result in the case of Shimura curves to obtain a lifting criterion.


title:
Acoustic interactions between inversion symmetric and asymmetric
  two-level systems

abstract:
  Amorphous solids, as well as many disordered lattices, display remarkable
universality in their low temperature acoustic properties. This universality is
attributed to the attenuation of phonons by tunneling two-level systems (TLSs),
facilitated by the interaction of the TLSs with the phonon field. TLS-phonon
interaction also mediates effective TLS-TLS interactions, which dictates the
existence of a glassy phase and its low energy properties. Here we consider
KBr:CN, the archetypal disordered lattice showing universality. We calculate
numerically, using conjugate gradients method, the effective TLS-TLS
interactions for inversion symmetric (CN flips) and asymmetric (CN rotations)
TLSs, in the absence and presence of disorder, in two and three dimensions. The
observed dependence of the magnitude and spatial power law of the interaction
on TLS symmetry, and its change with disorder, characterizes TLS-TLS
interactions in disordered lattices in both extreme and moderate dilutions. Our
results are in good agreement with the two-TLS model, recently introduced to
explain long-standing questions regarding the quantitative universality of
phonon attenuation and the energy scale of $\approx 1-3$ K below which
universality is observed.


title:
A note on inextensible flows of partially and pseudo null curves in
  E_1^4

abstract:
  In this paper, we study inextensible flows of partially null and pseudo null
curves in E_1^4. We give neccessary and sufficent conditions for inextensible
flows of partially null and pseudo null curves in E_1^4


title: Applying a new method to the 2-d Ising transition

abstract:
  The Ising ferromagnetic model on a square lattice is revisited using the
Galam Unifying Frame (GUF), set to investigate the dynamics of two-state
variable systems within the frame of opinion dynamics. When combined with
Metropolis dynamics, an unexpected intermediate "dis/order" phase is found with
the coexistence of two attractors associated respectively to an ordered and a
disordered phases. The basin of attraction of initial conditions for the
disordered phase attractor starts from zero size at a first critical
temperature $T_{c1}$ to embody the total landscape of initial conditions at a
second critical temperature $T_{c2}$ with $T_{c1}\approx 1.59$ and
$T_{c2}\approx 2.11$ in $J/k_B$ units. It appears that $T_{c2}$ is close to the
Onsager result $T_{c}\approx 2.27$. The transition, which is first-order like,
exhibits a vertical jump to the disorder phase at $T_{c2}$, reminiscent of the
rather abrupt vanishing of the corresponding Onsager second order transition.
However, using Glauber dynamics combined with GUF does not yield the
intermediate phase and instead the expected single transition at $T_{c}\approx
3.09$. Accordingly, although the "dis/order" phase produced by the GUF -
Metropolis combination is not physical, it is an intriguing result to be
understood. In particular the fact that Glauber and Metropolis dynamics yield
so different results using GUF needs an explanation. The possibility of
extending GUF to larger clusters is discussed.


title:
Bound States in Sharply Bent Waveguides: Analytical and Experimental
  Approach

abstract:
  Quantum wires and electromagnetic waveguides possess common features since
their physics is described by the same wave equation. We exploit this analogy
to investigate experimentally with microwave waveguides and theoretically with
the help of an effective potential approach the occurrence of bound states in
sharply bent quantum wires. In particular, we compute the bound states, study
the features of the transition from a bound to an unbound state caused by the
variation of the bending angle and determine the critical bending angles at
which such a transition takes place. The predictions are confirmed by
calculations based on a conventional numerical method as well as experimental
measurements of the spectra and electric field intensity distributions of
electromagnetic waveguides.


title:
On the equivalence of solutions for a class of stochastic evolution
  equations in a Banach space

abstract:
  We study a class of stochastic evolution equations in a Banach space $E$
driven by cylindrical Wiener process. Three different concept of solutions:
generalised strong, weak and mild are defined and the conditions under which
they are equivalent are given. We apply this result to prove existence,
uniqueness and continuity of weak solutions to stochastic delay equation with
additive noise. We also consider two examples of these equations in
non-reflexive Banach spaces: a stochastic transport equation with delay and a
stochastic McKendrick equation with delay.


title:
Anisotropic mesh refinement in polyhedral domains: error estimates with
  data in L^2(\Omega)

abstract:
  The paper is concerned with the finite element solution of the Poisson
equation with homogeneous Dirichlet boundary condition in a three-dimensional
domain. Anisotropic, graded meshes from a former paper are reused for dealing
with the singular behaviour of the solution in the vicinity of the non-smooth
parts of the boundary. The discretization error is analyzed for the piecewise
linear approximation in the H^1(\Omega)- and L^2(\Omega)-norms by using a new
quasi-interpolation operator. This new interpolant is introduced in order to
prove the estimates for L^2(\Omega)-data in the differential equation which is
not possible for the standard nodal interpolant. These new estimates allow for
the extension of certain error estimates for optimal control problems with
elliptic partial differential equation and for a simpler proof of the discrete
compactness property for edge elements of any order on this kind of finite
element meshes.


title: Change of pairing symmetry in the iron-based superconductor KFe2As2

abstract:
  The pairing mechanism in iron-based superconductors is the subject of ongoing
debate. Proximity to an antiferromagnetic phase suggests that pairing is
mediated by spin fluctuations, but orbital fluctuations have also been invoked.
The former typically favour a pairing state of extended s-wave symmetry with a
gap that changes sign between electron and hole Fermi surfaces (s+-), while the
latter yield a standard s-wave state without sign change (s++). Here we show
that applying pressure to KFe2As2 induces a change of pairing state. The
critical temperature Tc decreases with pressure initially, and then suddenly
increases, above a critical pressure Pc. The constancy of the Hall coefficient
through Pc rules out a change in the Fermi surface. There is compelling
evidence that the pairing state below Pc is d-wave, from bulk measurements at
ambient pressure. Above Pc, the high sensitivity to disorder argues for a
particular kind of s+- state. The change from d-wave to s-wave is likely to
proceed via an unusual s + id state that breaks time-reversal symmetry. The
proximity of two distinct pairing states found here experimentally is natural
given the near degeneracy of d-wave and s+- states found theoretically. These
findings make a compelling case for spin-fluctuation-mediated superconductivity
in this key iron-arsenide material.


title:
Model selection and clustering in stochastic block models with the exact
  integrated complete data likelihood

abstract:
  The stochastic block model (SBM) is a mixture model used for the clustering
of nodes in networks. It has now been employed for more than a decade to
analyze very different types of networks in many scientific fields such as
Biology and social sciences. Because of conditional dependency, there is no
analytical expression for the posterior distribution over the latent variables,
given the data and model parameters. Therefore, approximation strategies, based
on variational techniques or sampling, have been proposed for clustering.
Moreover, two SBM model selection criteria exist for the estimation of the
number K of clusters in networks but, again, both of them rely on some
approximations. In this paper, we show how an analytical expression can be
derived for the integrated complete data log likelihood. We then propose an
inference algorithm to maximize this exact quantity. This strategy enables the
clustering of nodes as well as the estimation of the number clusters to be
performed at the same time and no model selection criterion has to be computed
for various values of K. The algorithm we propose has a better computational
cost than existing inference techniques for SBM and can be employed to analyze
large networks with ten thousand nodes. Using toy and true data sets, we
compare our work with other approaches.


title:
A Competitive Ratio Approximation Scheme for the k-Server Problem in
  Fixed Finite Metrics

abstract:
  We show how to restrict the analysis of a class of online problems that
includes the $k$-server problem in finite metrics such that we only have to
consider finite sequences of request. When applying the restrictions, both the
optimal offline solutions and the best possible deterministic or randomized
online solutions only differ by at most an arbitrarily small constant factor
from the corresponding solutions without restrictions. Furthermore, we show how
to obtain an algorithm with best possible deterministic or randomized
competitive ratio for the restricted setup. Thus, for each fixed finite metrics
our result qualifies as a competitive ratio approximation scheme as defined by
G\"unther et al.


title: On the Initial Value Problem for Causal Variational Principles

abstract:
  We formulate the initial value problem for causal variational principles in
the continuous setting on a compact metric space. The existence and uniqueness
of solutions is analyzed. The results are illustrated by simple examples.


title: Fault-Tolerant Modular Reconstruction of Rational Numbers

abstract:
  In this paper we present two efficient methods for reconstructing a rational
number from several residue-modulus pairs, some of which may be incorrect. One
method is a natural generalization of that presented by Wang, Guy and Davenport
in \cite{WGD1982} (for reconstructing a rational number from \textit{correct}
modular images), and also of an algorithm presented in \cite{Abb1991} for
reconstructing an \textit{integer} value from several residue-modulus pairs,
some of which may be incorrect.


title:
Automatic instantiation of abstract tests on specific configurations for
  large critical control systems

abstract:
  Computer-based control systems have grown in size, complexity, distribution
and criticality. In this paper a methodology is presented to perform an
abstract testing of such large control systems in an efficient way: an abstract
test is specified directly from system functional requirements and has to be
instantiated in more test runs to cover a specific configuration, comprising
any number of control entities (sensors, actuators and logic processes). Such a
process is usually performed by hand for each installation of the control
system, requiring a considerable time effort and being an error prone
verification activity. To automate a safe passage from abstract tests, related
to the so called generic software application, to any specific installation, an
algorithm is provided, starting from a reference architecture and a state-based
behavioural model of the control software. The presented approach has been
applied to a railway interlocking system, demonstrating its feasibility and
effectiveness in several years of testing experience.


title:
Quantum finite automata and linear context-free languages: a decidable
  problem

abstract:
  We consider the so-called measure once finite quantum automata model
introduced by Moore and Crutchfield in 2000. We show that given a language
recognized by such a device and a linear context-free language, it is
recursively decidable whether or not they have a nonempty intersection. This
extends a result of Blondel et al. which can be interpreted as solving the
problem with the free monoid in place of the family of linear context-free
languages.


title:
1D Log Gases and the Renormalized Energy: Crystallization at Vanishing
  Temperature

abstract:
  We study the statistical mechanics of a one-dimensional log gas with general
potential and arbitrary beta, the inverse of temperature, according to the
method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles
correspond to random matrix models in some particular cases. The formal limit
beta infinite corresponds to "weighted Fekete sets" and is also treated. We
introduce a one-dimensional version of the "renormalized energy" of [SS1],
measuring the total logarithmic interaction of an infinite set of points on the
real line in a uniform neutralizing background. We show that this energy is
minimized when the points are on a lattice. By a suitable splitting of the
Hamiltonian we connect the full statistical mechanics problem to this
renormalized energy W, and this allows us to obtain new results on the
distribution of the points at the microscopic scale: in particular we show that
configurations whose W is above a certain threshhold (which tends to min W as
beta tends to infinity) have exponentially small probability. This shows that
the configurations have increasing order and crystallize as the temperature
goes to zero.


title: A Supersymmetric Theory of Vector-like Leptons

abstract:
  We study a supersymmetric extension of the vector-like lepton scenario, such
that the vacuum instability induced by large lepton Yukawa couplings is lifted
by the presence of superpartners at or below the TeV scale. In order to
preserve the unification of gauge couplings, we introduce a full 16+\bar{16} of
SO(10), and determine the maximal possible values for the Yukawa couplings
consistent with perturbativity at the GUT scale. We find that the Higgs to
diphoton decay rate can be enhanced by up to 50% while maintaining vacuum
stability and keeping the new particle masses above 100 GeV, while larger
enhancements are possible if the masses of the new particles are lowered
further.


title:
Symmetrization for Linear and Nonlinear Fractional Parabolic Equations
  of Porous Medium Type

abstract:
  We establish symmetrization results for the solutions of the linear
fractional diffusion equation $\partial_t u +(-\Delta)^{\sigma/2}u=f$ and
itselliptic counterpart $h v +(-\Delta)^{\sigma/2}v=f$, $h>0$, using the
concept of comparison of concentrations. The results extend to the nonlinear
version, $\partial_t u+(-\Delta)^{\sigma/2}A(u)=f$, but only when
$A:\re_+\to\re_+$ is a concave function. In the elliptic case, complete
symmetrization results are proved for $\,B(v)+(-\Delta)^{\sigma/2}v=f$ \ when
$B(v)$ is a convex nonnegative function for $v>0$ with $B(0)=0$, and partial
results when $B$ is concave. Remarkable counterexamples are constructed for the
parabolic equation when $A$ is convex, resp. for the elliptic equation when $B$
is concave. Such counterexamples do not exist in the standard diffusion case
$\sigma=2$.


title: Dirac operators in gauge theory

abstract:
  This paper is a mixture of expository material and current research material.
Among new results are examples of generalised harmonic spinors and their gauged
version, the generalised Seiberg-Witten equations.


title: Looking into the collapse of quantum states with entangled photons

abstract:
  We propose a scheme to investigate the time scale of the wave-function
collapse by using polarization-entangled photon pairs. The setup is similar to
those employed to investigate quantum correlations, but in the present case,
synchronization is essential at all stages. We find that it is possible to
discriminate between the scenarios of instantaneous collapse and finite-time
reduction via a large number of double measurements of polarization. The
quantities to be recorded would present distinct behaviors in each scenario,
the deviations being small but distinguishable from pure statistical
fluctuations.


title: Characterization of log del Pezzo pairs via anticanonical models

abstract:
  There are several variations of the definition of log del Pezzo pairs in the
literature. We define their suitable smooth models, and we show that they are
the same. In particular, we obtain a characterization of smooth log del Pezzo
pairs in terms of anticanonical models. As applications, we classify
non-rational weak log canonical del Pezzo pairs, and we prove that every
surface of globally F-regular type is of Fano type.


title: Complexity-Style Resources in Cryptography

abstract:
  Previously, the author has developed a framework within which to quantify and
compare the resources consumed during computational-especially unconventional
computational-processes (adding to the familiar resources of run-time and
memory space such non-standard resources as precision and energy); it is
natural and beneficial in this framework to employ various complexity-theoretic
tools and techniques. Here, we seek an analogous treatment not of computational
processes but of cryptographic protocols and similar, so as to be able to apply
the existing arsenal of complexity-theoretic methods in new ways, in the
derivation and verification of protocols in a wider, cryptographic context.
Accordingly, we advocate a framework in which one may view as resources the
costs-which may be related to computation, communication, information
(including side-channel information) or availability of primitives, for
example-incurred when executing cryptographic protocols, coin-tossing schemes,
etc. The ultimate aim is to formulate as a resource, and be able to analyse
complexity-theoretically, the security of these protocols and schemes.


title: Towards Automated Proof Strategy Generalisation

abstract:
  The ability to automatically generalise (interactive) proofs and use such
generalisations to discharge related conjectures is a very hard problem which
remains unsolved. Here, we develop a notion of goal types to capture key
properties of goals, which enables abstractions over the specific order and
number of sub-goals arising when composing tactics. We show that the goal types
form a lattice, and utilise this property in the techniques we develop to
automatically generalise proof strategies in order to reuse it for proofs of
related conjectures. We illustrate our approach with an example.


title: In-medium QCD forces at high temperature

abstract:
  We derive the quantum dynamics of heavy quark systems in quark-gluon plasma
as open quantum systems. The scatterings of a heavy quark with the hard medium
particles give rise to Debye screened QCD force and drag force and its
fluctuation. We present a unified quantum description of these in-medium QCD
forces at high temperature in the leading-order perturbation on the basis of
the influence functional formalism.


title:
Cavity optomechanics with a trapped, interacting Bose-Einstein
  condensate

abstract:
  The dispersive interaction of a Bose-Einstein condensate with a single mode
of a high-finesse optical cavity realizes the radiation pressure coupling
Hamiltonian. In this system the role of the mechanical oscillator is played by
a single condensate excitation mode that is selected by the cavity mode
function. We study the effect of atomic s-wave collisions and show that it
merely renormalizes parameters of the usual optomechanical interaction.
Moreover, we show that even in the case of strong harmonic confinement---which
invalidates the use of Bloch states---a single excitation mode of the
Bose-Einstein condensate couples significantly to the light field, that is the
simplified picture of a single "mechanical" oscillator mode remains valid.


title:
Effect of realistic finite-size impurities on Tc in Fe-based
  superconductors based on the five-orbital tight-binding model

abstract:
  We present a systematic study of the impurity effect on Tc in Fe-based
superconductors, assuming that the sign-reversal s-wave state due to
inter-pocket repulsion ($s_\pm$-wave state) is realized. For this purpose, we
introduce several realistic impurity models with non-local modifications of
potentials and hopping integrals around the impurity site. When we use the
impurity model parameters for 3d- and 4d-impurity atoms derived from the recent
first principle study by Nakamura et al., we find that the $s_\pm$-wave state
is very fragile against impurities: The superconductivity with $T_{c0}=30K$ is
destroyed by introducing small residual resistivity $\rho_0^{cr} = 5z^{-1} ~
10z^{-1} [\mu\Omega cm]$ ($z^{-1} = m^*/m$ being the mass-enhancement factor),
consistently with the previous theoretical study for the on-site impurity model
by Onari and Kontani. This result is essentially unchanged for different
non-local impurity models with realistic parameters. We also discuss the effect
of the impurity-induced non-local orbital order on the superconducting state.


title: The kernel of the radially deformed Fourier transform

abstract:
  The radially deformed Fourier transform, introduced in [S. Ben Said, T.
Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio
Math.], is an integral transform that depends on a numerical parameter $a \in
R^{+}$. So far, only for $a=1$ and $a=2$ the kernel of this integral transform
is determined explicitly.
  In the present paper, explicit formulas for the kernel of this transform are
obtained when the dimension is even and $a = 2/n$ with $n \in N$. As a
consequence, it is shown that the integral kernel is bounded in dimension 2.


title:
Fast and Furious: Shock Heated Gas as the Origin of Spatially Resolved
  Hard X-ray Emission in the Central 5 kpc of the Galaxy Merger NGC 6240

abstract:
  We have obtained a deep, sub-arcsecond resolution X-ray image of the nuclear
region of the luminous galaxy merger NGC 6240 with Chandra, which resolves the
X-ray emission from the pair of active nuclei and the diffuse hot gas in great
detail. We detect extended hard X-ray emission from kT~6 keV (~70 million K)
hot gas over a spatial scale of 5 kpc, indicating the presence of fast shocks
with velocity of ~2200 km/s. For the first time we obtain the spatial
distribution of this highly ionized gas emitting FeXXV, which shows a
remarkable correspondence to the large scale morphology of H_2(1-0) S(1) line
emission and H\alpha filaments. Propagation of fast shocks originated in the
starburst driven wind into the ambient dense gas can account for this
morphological correspondence. With an observed L(0.5-8 keV)=5.3E+41 erg/s, the
diffuse hard X-ray emission is 100 times more luminous than that observed in
the classic starburst galaxy M82. Assuming a filling factor of 1% for the 70 MK
temperature gas, we estimate its total mass (M_{hot}=1.8E+8 Msun) and thermal
energy (E_{th}=6.5E+57 ergs). The total iron mass in the highly ionized plasma
is M_{Fe}=4.6E+5 Msun. Both the energetics and the iron mass in the hot gas are
consistent with the expected injection from the supernovae explosion during the
starburst that is commensurate with its high star formation rate. No evidence
for fluorescent Fe I emission is found in the CO filament connecting the two
nuclei.


title: On the Complexity of the Orbit Problem

abstract:
  We consider higher-dimensional versions of Kannan and Lipton's Orbit
Problem---determining whether a target vector space V may be reached from a
starting point x under repeated applications of a linear transformation A.
Answering two questions posed by Kannan and Lipton in the 1980s, we show that
when V has dimension one, this problem is solvable in polynomial time, and when
V has dimension two or three, the problem is in NP^{RP}.


title:
Proposed Chiral Texture of the Magnetic Moments of Unit-Cell Loop
  Currents in the Pseudogap Phase of Cuprate Superconductors

abstract:
  We propose a novel chiral order parameter to explain the unusual polar Kerr
effect in underdoped cuprates. It is based on the loop-current model by Varma,
which is characterized by the in-plane anapole moment N and exhibits the
magnetoelectric effect. We propose a helical structure where the vector N^(n)
in the layer n is twisted by the angle pi/2 relative to N^(n-1), thus breaking
inversion symmetry. We show that coupling between magnetoelectric terms in the
neighboring layers for this structure produces optical gyrotropy, which results
in circular dichroism and the polar Kerr effect.


title: Expanding Ricci Solitons Asymptotic to Cones

abstract:
  We show that an expanding gradient Ricci solitons which is asymptotic to a
cone at infinity in a certain sense must be rotationally symmetric.


title: A Lithium-Rich Red Giant Below the Clump in the Kepler Cluster, NGC 6819

abstract:
  WIYN/HYDRA spectra in the Li 6708 Angstrom region have been obtained for 332
probable members of the old open cluster, NGC 6819. Preliminary analysis shows
a pattern of Li depletion from the top of the turnoff to the base of the giant
branch. Starting one magnitude below the level of the clump, all brighter
giants have A(Li) below 1.0, with most having upper limits below 0.5. Star
W007017, located BELOW the first-ascent red giant bump is Li-rich with A(Li) =
2.3. As a highly probable single-star astrometric and radial-velocity cluster
member, its discrepant asteroseismic membership could be a by-product of the
processes that triggered Li-enhancement. Its color-magnitude diagram location
is consistent with only one proposed enhanced mixing process among first-ascent
red giants.


title:
Search for supersymmetry in hadronic final states with missing
  transverse energy using the variables AlphaT and b-quark multiplicity in pp
  collisions at 8 TeV

abstract:
  An inclusive search for supersymmetric processes that produce final states
with jets and missing transverse energy is performed in pp collisions at a
centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated
luminosity of 11.7 inverse femtobarns collected by the CMS experiment at the
LHC. In this search, a dimensionless kinematic variable, AlphaT, is used to
discriminate between events with genuine and misreconstructed missing
transverse energy. The search is based on an examination of the number of
reconstructed jets per event, the scalar sum of transverse energies of these
jets, and the number of these jets identified as originating from bottom
quarks. No significant excess of events over the standard model expectation is
found. Exclusion limits are set in the parameter space of simplified models,
with a special emphasis on both compressed-spectrum scenarios and direct or
gluino-induced production of third-generation squarks. For the case of
gluino-mediated squark production, gluino masses up to 950-1125 GeV are
excluded depending on the assumed model. For the direct pair-production of
squarks, masses up to 450 GeV are excluded for a single light first- or
second-generation squark, increasing to 600\GeV for bottom squarks.


title: Invariants of hyperbolic 3-manifolds in relative group homology

abstract:
  Let $M$ be a complete oriented hyperbolic $3$--manifold of finite volume.
Using classifying spaces for families of subgroups we construct a class
$\beta_P(M)$ in the Adamson relative homology group
$H_3([PSL_2(\mathbb{C}):\bar{P}];\mathbb{Z})$, where $\bar{P}$ is the subgroup
of parabolic transformations which fix $\infty$ in the Riemann sphere. We also
prove that the classes $F(M)$ in the Takasu relative homology groups
$H_3(PSL_2(\mathbb{C}),\bar{P};\mathbb{Z})$ constructed by Zickert, which are
not well-defined and depend of a choice of decorations by horospheres, are all
mapped to $\beta_P(M)$ via a canonical comparison homomorphism
$H_3(PSL_2(\mathbb{C}),\bar{P};\mathbb{Z})\to
H_3([PSL_2(\mathbb{C}):\bar{P}];\mathbb{Z})$. To do this, we simplify the
construction of the classes $F(M)$ using a simpler complex which computes
$H_3(PSL_2(\mathbb{C}),\bar{P};\mathbb{Z})$, getting a simple simplicial
formula for $F(M)$, which in turn gives a simpler and more efficient formula to
compute the volume and Chern--Simons invariant than the one given by Zickert.
The constructions can be extended for any boundary-parabolic
$PSL_2(\mathbb{C})$-representation.


title:
On Periodic Reference Tracking Using Batch-Mode Reinforcement Learning
  with Application to Gene Regulatory Network Control

abstract:
  In this paper, we consider the periodic reference tracking problem in the
framework of batch-mode reinforcement learning, which studies methods for
solving optimal control problems from the sole knowledge of a set of
trajectories. In particular, we extend an existing batch-mode reinforcement
learning algorithm, known as Fitted Q Iteration, to the periodic reference
tracking problem. The presented periodic reference tracking algorithm
explicitly exploits a priori knowledge of the future values of the reference
trajectory and its periodicity. We discuss the properties of our approach and
illustrate it on the problem of reference tracking for a synthetic biology gene
regulatory network known as the generalised repressilator. This system can
produce decaying but long-lived oscillations, which makes it an interesting
system for the tracking problem. In our companion paper we also take a look at
the regulation problem of the toggle switch system, where the main goal is to
drive the system's states to a specific bounded region in the state space.


title: Unstable Galaxy Models

abstract:
  The dynamics of collisionless galaxy can be described by the Vlasov-Poisson
system. By the Jean's theorem, all the spherically symmetric steady galaxy
models are given by a distribution of {\Phi}(E,L), where E is the particle
energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann
Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is
monotonically decreasing with respect to the particle energy E. On the other
hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a
recent abstract instability criterion of Guo-Lin, we constuct examples of
unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E.


title:
Estimating Spectral Density Functions for Sturm-Liouville problems with
  two singular endpoints

abstract:
  In this paper we consider the Sturm-Liouville equation -y"+qy = lambda*y on
the half line (0,infinity) under the assumptions that x=0 is a regular singular
point and nonoscillatory for all real lambda, and that either (i) q is L_1 near
x=infinity, or (ii) q' is L_1 near infinity with q(x) --> 0 as x --> infinity,
so that there is absolutely continuous spectrum in (0,infinity).
Characterizations of the spectral density function for this doubly singular
problem, similar to those obtained in [12] and [13] (when the left endpoint is
regular) are established; corresponding approximants from the two algorithms in
[12] and [13] are then utilized, along with the Frobenius recurrence relations
and piecewise trigonometric - hyperbolic splines, to generate numerical
approximations to the spectral density function associated with the doubly
singular problem on (0,infinity). In the case of the radial part of the
separated hydrogen atom problem, the new algorithms are capable of achieving
near machine precision accuracy over the range of lambda from 0.1 to 10000,
accuracies which could not be achieved using the SLEDGE software package.


title:
Pinning model in random correlated environment: appearance of an
  infinite disorder regime

abstract:
  We study the influence of a correlated disorder on the localization phase
transition in the pinning model. When correlations are strong enough, a strong
disorder regime arises: large and frequent attractive regions appear in the
environment. We present here a pinning model in random binary ({-1,1}-valued)
environment. Defining strong disorder via the requirement that the probability
of the occurrence of a large attractive region is sub-exponential in its size,
we prove that it coincides with the fact that the critical point is equal to
its minimal possible value. We also stress that in the strong disorder regime,
the phase transition is smoother than in the homogeneous case, whatever the
critical exponent of the homogeneous model is: disorder is therefore always
relevant. We illustrate these results with the example of an environment based
on the sign of a Gaussian correlated sequence, in which we show that the phase
transition is of infinite order in presence of strong disorder. Our results
contrast with results known in the literature, in particular in the case of an
IID disorder, where the question of the influence of disorder on the critical
properties is answered via the so-called Harris criterion, and where a
conventional relevance/irrelevance picture holds.


title: Moduli of abelian covers of elliptic curves

abstract:
  For any finite abelian group G, we study the moduli space of abelian
$G$-covers of elliptic curves, in particular identifying the irreducible
components of the moduli space. We prove that, in the totally ramified case,
the moduli space has trivial rational Picard group, and it is birational to the
moduli space M_{1,n}, where n is the number of branch points. In the particular
case of moduli of bielliptic curves, we also prove that the boundary divisors
are a basis of the rational Picard group of the admissible covers
compactification of the moduli space. Our methods are entirely
algebro-geometric.


title: Steady state Ab-initio Theory of Lasers with Injected Signals

abstract:
  We present an ab-initio treatment of the steady-state of lasers with injected
signals that describes a regime, valid for micro lasers, in which the locking
transition is dominated by cross-saturation and spatial hole-burning. The
theory goes beyond standard approaches and treats multimode lasing with
injected signals and finds the possibility of partially locked states and as
well as repulsion of the free-running frequencies from the injected signal. The
theory agrees well with exact integration of the full wave and matter equations
for the system. It can also describe accurately complex modern lasers
structures and is applied to the example of deformed disk lasers. We show that
in the case of a one dimensional cavity in the locked or regenerative amplifier
regime the theory reduces to an improved version of the Adler equations in the
appropriate limit.


title: Rotating cylindrical wormholes

abstract:
  We consider stationary, cylindrically symmetric configurations in general
relativity and formulate necessary conditions for the existence of rotating
cylindrical wormholes. It is shown that in a comoving reference frame the
rotational part of the gravitational field is separated from its static part
and forms an effective stress-energy tensor with exotic properties, which
favors the existence of wormhole throats. Exact vacuum and scalar-vacuum
solutions (with a massless scalar) are considered as examples, and it turns out
that even vacuum solutions can be of wormhole nature. However, solutions
obtainable in this manner cannot have well-behaved asymptotic regions, which
excludes the existence of wormhole entrances appearing as local objects in our
Universe. To overcome this difficulty, we try to build configurations with flat
asymptotic regions by the cut-and-paste procedure: on both sides of the throat,
a wormhole solution is matched to a properly chosen region of flat space at
some surfaces $\Sigma_-$ and $\Sigma_+$. It is shown, however, that if we
describe the throat region with vacuum or scalar-vacuum solutions, one or both
thin shells appearing on $\Sigma_-$ and $\Sigma_+$ inevitably violate the null
energy condition. In other words, although rotating wormhole solutions are
easily found without exotic matter, such matter is still necessary for
obtaining asymptotic flatness.


title: Gorenstein spherical Fano varieties

abstract:
  We obtain a combinatorial description of Gorenstein spherical Fano varieties
in terms of certain polytopes, generalizing the combinatorial description of
Gorenstein toric Fano varieties by reflexive polytopes and its extension to
Gorenstein horospherical Fano varieties due to Pasquier. Using this
description, we show that the rank of the Picard group of an arbitrary
$d$-dimensional $\mathbb{Q}$-factorial Gorenstein spherical Fano variety is
bounded by $2d$. This paper also contains an overview of the description of the
natural representative of the anticanonical divisor class of a spherical
variety due to Brion.


title:
Electron tunneling through graphene-based double barriers driven by a
  periodic potential

abstract:
  Photon-assisted charge transport through a double barrier structure under a
time periodic field in graphene is studied. Within the framework of the Floquet
formalism and using the transfer matrix method, the transmission probabilities
for the central band and sidebands are calculated. A critical phase difference
between the harmonic potentials at the barriers, which cancels transmission
through the inelastic sidebands due to quantum interference is found. This
phenomenon could be of help to design graphene based filters and high-frequency
radiation detectors. Quenching of resonant tunneling by the harmonic field
applied to the barriers or the well is also discussed.


title: The finite rank theorem for Toeplitz operators in the Fock space

abstract:
  We consider Toeplitz operators in the Fock space, under rather general
conditions imposed on the symbols. It is proved that if the operator has finite
rank and the symbol is a function then the operator and the symbol should be
zero. The method of proving is different from the one used previously for
finite rank theorems, and it enables one to get rid of the compact support
condition for symbols imposed previously.