title: Spin flip loss in magnetic storage of ultracold neutrons

abstract:
  We analyze the depolarization of ultracold neutrons confined in a magnetic
field configuration similar to those used in existing or proposed
magneto-gravitational storage experiments aiming at a precise measurement of
the neutron lifetime. We use an approximate quantum mechanical analysis such as
pioneered by Walstrom \emph{et al} [Nucl. Instrum. Methods Phys. Res. A 599, 82
(2009)]. Our analysis is not restricted to purely vertical modes of neutron
motion. The lateral motion is shown to cause the predominant depolarization
loss in a magnetic storage trap.


title:
Twisted reductions of integrable lattice equations, and their Lax
  representations

abstract:
  It is well known that from two-dimensional lattice equations one can derive
one-dimensional lattice equations by imposing periodicity in some direction. In
this paper we generalize the periodicity condition by adding a symmetry
transformation and apply this idea to autonomous and non-autonomous lattice
equations. As results of this approach, we obtain new reductions of the
discrete potential Korteweg-de Vries equation, discrete modified Korteweg-de
Vries equation and the discrete Schwarzian Korteweg-de Vries equation. We will
also describe a direct method for obtaining Lax representations for the reduced
equations.


title:
Constraining conformal field theory with higher spin symmetry in four
  dimensions

abstract:
  We analyze the constraints on the general form and the singularity structure
of the correlation functions of the symmetric, traceless and conserved
stress-energy tensor implied by conformal invariance and higher spin symmetry
in four dimensions. In particular, we show that all these correlation functions
will have at most double pole singularities. We then compute the 4-, 5- and
6-point functions of the stress-energy tensor and find that they are linear
combinations of the three free field expressions (scalar, fermion and Maxwell
field). This is a strong indication that all such theories are essentially
free.


title:
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief
  propagation and Decimation

abstract:
  We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method.


title: Using Quantum entanglement to study CP and CPT violations

abstract:
  We report some general phenomenological results concerning CP and CPT
violations in joint decays of entangled pseudoscalar neutral mesons.


title: Tests of Lorentz Invariance Using High Energy Astrophysics Observations

abstract:
  High-energy astrophysics observations provide the best possibilities to
detect a very small violation of Lorentz invariance, such as may be related to
the structure of space-time near the Planck scale. I discuss the possible
signatures of Lorentz invariance violation that can be manifested by observing
the spectra, polarization, and timing of gamma-rays from active galactic nuclei
and gamma-ray bursts. Other sensitive tests are provided by observations of the
spectra of ultrahigh-energy cosmic rays and very high-energy neutrinos. I also
discuss a new time-of-flight analysis of observations of GRB 090510 by the
Fermi gamma-ray Space Telescope. These results, based on high-energy
astrophysical observations, have fundamental implications for space-time
physics and quantum gravity models.


title: Notes on factorization algebras, factorization homology and applications

abstract:
  These notes are an expanded version of two series of lectures given at the
winter school in mathematical physics at les Houches and at the Vietnamese
Institute for Mathematical Sciences. They are an introduction to factorization
algebras, factorization homology and some of their applications, notably for
studying $E_n$-algebras. We give an account of homology theory for manifolds
(and spaces), which give invariant of manifolds but also invariant of
$E_n$-algebras. We particularly emphasize the point of view of factorization
algebras (a structure originating from quantum field theory) which plays, with
respect to homology theory for manifolds, the role of sheaves with respect to
singular cohomology. We mention some applications to the study of mapping
spaces and study several examples, including some over stratified spaces.


title: Elasticity effects on the stability of growing films

abstract:
  It is shown how the combination of atomic deposition and nonlinear diffusion
may lead, below a critical temperature, to the growth of nonuniform layers on a
substrate. The dynamics of such a system is of the Cahn-Hilliard type,
supplemented by reaction terms representing adsorption-desorption processes.
The instability of uniform layers leads to the formation of nanostructures
which correspond to regular spatial variations of substrate coverage. Since
coverage inhomogeneities generate internal stresses, the coupling between
coverage evolution and film elasticity fields is also considered, for film
thickness below the critical thickness for misfit dislocation nucleation. It is
shown that this coupling is destabilizing and favors nanostructure formation.
It also favors square planforms which could compete, and even dominate over the
haxagonal or stripe nanostructures induced by coverage dynamics alone


title: Pseudoscalar N-flation and axial coupling revisited

abstract:
  We revisit the dynamics of the axial coupling between many N-flatons and an
Abelian gauge field, with special attention to its statistically anisotropic
signal. The anisotropic power spectrum of curvature perturbations associated to
the large wavelength modes of the gauge vector field is generally undetectable,
since the anisotropy is confined to small scales. If the gauge field is the
electromagnetic field, provided that the number of fields participating in the
exponential expansion is large, it could be possible to generate sizable large
scale magnetic fields. However, its spectrum is blue, and appreciable power on
large scales implies an overly strong field on smaller scales, incompatibly
with observations. Furthermore, the anisotropy is also markedly enhanced, and
might be at odds with the isotropic observed sky. These aspects further demand
that the scale of inflation is kept to a minimum.


title: Expressiveness and Robustness of First-Price Position Auctions

abstract:
  Since economic mechanisms are often applied to very different instances of
the same problem, it is desirable to identify mechanisms that work well in a
wide range of circumstances. We pursue this goal for a position auction setting
and specifically seek mechanisms that guarantee good outcomes under both
complete and incomplete information. A variant of the generalized first-price
mechanism with multi-dimensional bids turns out to be the only standard
mechanism able to achieve this goal, even when types are one-dimensional. The
fact that expressiveness beyond the type space is both necessary and sufficient
for this kind of robustness provides an interesting counterpoint to previous
work on position auctions that has highlighted the benefits of simplicity. From
a technical perspective our results are interesting because they establish
equilibrium existence for a multi-dimensional bid space, where standard
techniques break down. The structure of the equilibrium bids moreover provides
an intuitive explanation for why first-price payments may be able to support
equilibria in a wider range of circumstances than second-price payments.


title:
Effective Absorption Enhancement in Small Molecule Organic Solar Cells
  by Employing Trapezoid Gratings

abstract:
  We demonstrate the optical absorption has been enhanced in the small molecule
organic solar cells by employing trapezoid grating structure. The enhanced
absorption is mainly attributed to both waveguide modes and surface plasmon
modes, which has been simulated by using finite-difference time-domain method.
The simulated results show that the surface plasmon along the semitransparent
metallic Ag anode is excited by introducing the periodical trapezoid gratings,
which induce high intensity field increment in the donor layer. Meanwhile, the
waveguide modes result a high intensity field in acceptor layer. The increment
of field improves the absorption of organic solar cells, significantly, which
has been demonstrated by simulating the electrical properties. The simulated
results exhibiting 31 % increment of the short-circuit current has been
achieved in the optimized device, which is supported by the experimental
measurement. The power conversion efficiency of the grating sample obtained in
experiment exhibits an enhancement of 7.7 %.


title: A Gaussian limit process for optimal FIND algorithms

abstract:
  We consider versions of the FIND algorithm where the pivot element used is
the median of a subset chosen uniformly at random from the data. For the median
selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$
are chosen, where $0<\alpha\le \frac{1}{2}$, $c>0$ and $n$ is the size of the
data set to be split. We consider the complexity of FIND as a process in the
rank to be selected and measured by the number of key comparisons required.
After normalization we show weak convergence of the complexity to a centered
Gaussian process as $n\to\infty$, which depends on $\alpha$. The proof relies
on a contraction argument for probability distributions on c{\`a}dl{\`a}g
functions. We also identify the covariance function of the Gaussian limit
process and discuss path and tail properties.


title:
Randomly Fluctuating Potential Controlled Multistable Resonant Tunneling
  Current through a Quantum Dot

abstract:
  We study the transport through a quantum dot subject to a randomly
fluctuating potential, generated by a sequence of pulses in the gate voltage
with the help of the autoregressive model. We find that the tunneling current
is multistable when the fluctuating potential with a finite correlation time is
applied before the non-equilibrium steady state is built up. The
non-equilibrium stationary current is heavily dependent on the history of the
fluctuating potential during the transient period if the potential has a finite
correlation time. Furthermore, the averaged current over the path of the
fluctuating potential is a function of its strength and correlation time. Our
work therefore provides a robust theoretical proposal for the controlling of
the non-equilibrium stationary current through a quantum dot in a randomly
fluctuating potential.


title:
Simulation of mirror inversion of quantum states in an XY spin chain
  using NMR

abstract:
  We report an experimental quantum simulation of unitary dynamics of an XY
spin chain with pre-engineered couplings. Using this simulation, we demonstrate
the mirror inversion of quantum states, proposed by Albanese et al. [Phys. Rev.
Lett. 93, 230502 (2004)]. The experiment is performed with a 5-qubit dipolar
coupled spin system using nuclear magnetic resonance techniques. To perform
quantum simulation we make use of the recently proposed unitary operator
decomposition algorithm of Ajoy et al. [Phys. Rev. A 85, 030303 (2012)] along
with numerical pulse optimization techniques. Further, using mirror inversion,
we demonstrate that entangled states can be transferred from one end of the
chain to the other end. The simulations are implemented with high experimental
fidelity, which implies that these kind of simulations may be possible in
larger systems.


title: The range of tree-indexed random walk

abstract:
  We provide asymptotics for the range R(n) of a random walk on the
d-dimensional lattice indexed by a random tree with n vertices. Using Kingman's
subadditive ergodic theorem, we prove under general assumptions that R(n)/n
converges to a constant, and we give conditions ensuring that the limiting
constant is strictly positive. On the other hand, in dimension 4 and in the
case of a symmetric random walk with exponential moments, we prove that R(n)
grows like n/(log n). We apply our results to asymptotics for the range of
branching random walk when the initial size of the population tends to
infinity.


title: Hybrid quantization of an inflationary model: The flat case

abstract:
  We present a complete quantization of an approximately homogeneous and
isotropic universe with small scalar perturbations. We consider the case in
which the matter content is a minimally coupled scalar field and the spatial
sections are flat and compact, with the topology of a three-torus. The
quantization is carried out along the lines that were put forward by the
authors in a previous work for spherical topology. The action of the system is
truncated at second order in perturbations. The local gauge freedom is fixed at
the classical level, although different gauges are discussed and shown to lead
to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant
quantities are considered. The reduced system is proven to admit a symplectic
structure, and its dynamical evolution is dictated by a Hamiltonian constraint.
Then, the background geometry is polymerically quantized, while a Fock
representation is adopted for the inhomogeneities. The latter is selected by
uniqueness criteria adapted from quantum field theory in curved spacetimes,
which determine a specific scaling of the perturbations. In our hybrid
quantization, we promote the Hamiltonian constraint to an operator on the
kinematical Hilbert space. If the zero mode of the scalar field is interpreted
as a relational time, a suitable ansatz for the dependence of the physical
states on the polymeric degrees of freedom leads to a quantum wave equation for
the evolution of the perturbations. Alternatively, the solutions to the quantum
constraint can be characterized by their initial data on the minimum-volume
section of each superselection sector. The physical implications of this model
will be addressed in a future work, in order to check whether they are
compatible with observations.


title: Multifractal tubes

abstract:
  Tube formulas refer to the study of volumes of $r$ neighbourhoods of sets.
For sets satisfying some (possible very weak) convexity conditions, this has a
long history. However, within the past 20 years Lapidus has initiated and
pioneered a systematic study of tube formulas for fractal sets. Following this,
it is natural to ask to what extend it is possible to develop a theory of
multifractal tube formulas for multifractal measures. In this paper we propose
and develop a framework for such a theory. Firstly, we define multifractal tube
formulas and, more generally, multifractal tube measures for general
multifractal measures. Secondly, we introduce and develop two approaches for
analysing these concepts for self-similar multifractal measures, namely:
  (1) Multifractal tubes of self-similar measures and renewal theory. Using
techniques from renewal theory we give a complete description of the asymptotic
behaviour of the multifractal tube formulas and tube measures of self-similar
measures satisfying the Open Set Condition.
  (2) Multifractal tubes of self-similar measures and zeta-functions.
Unfortunately, renewal theory techniques do not yield "explicit" expressions
for the functions describing the asymptotic behaviour of the multifractal tube
formulas and tube measures of self-similar measures. This is clearly
undesirable. For this reason, we introduce and develop a second framework for
studying multifractal tube formulas of self-similar measures. This approach is
based on multifractal zeta-functions and allow us obtain "explicit" expressions
for the multifractal tube formulas of self-similar measures, namely, using the
Mellin transform and the residue theorem, we are able to express the
multifractal tube formulas as sums involving the residues of the zeta-function.


title: Two-fluid description of two-band superconductors

abstract:
  We present a systematic study of the response properties of two-band
(multi-gap) superconductors with spin-singlet (s-wave) pairing correlations,
which are assumed to be caused by both intraband (\lambda_{ii}, i=1,2) and
interband (\lambda_{12}) pairing interactions. In this first of three planned
publications we concentrate on the properties of such superconducting systems
in global and local thermodynamic equilibrium, the latter including weak
perturbations in the stationary long-wavelength limit. The discussion of global
thermodynamic equilibrium must include the solution (analytical in the
Ginzburg-Landau and the low temperature limit) of the coupled self-consistency
equations for the two energy gaps \Delta_i(T), i=1,2. These solutions allow to
study non-universal behavior of the two relevant BCS-M\"uhlschlegel parameters,
namely the specific heat discontinuity \Delta C/C_N and the zero temperature
gaps \Delta_i(0)/\pi k_B T_c, i=1,2. The discussion of a local equilibrium
situation includes the calculation of the supercurrent density as a property of
the condensate, and the calculation of both the specific heat capacity and the
spin susceptibility as properties of the gas of thermal excitations in the
spirit of a microscopic two-fluid description. Non-monotonic behavior in the
temperature dependences of the gaps and all these local response functions is
predicted to occur particularly for very small values of the interband
pair-coupling constant \lambda_{12}.


title:
Study of young stellar objects and associated filamentary structures in
  the inner Galaxy

abstract:
  Young Stellar Objects (YSOs) in the inner Galactic region $10^0 < l < 15^0$
and $-1^0 < b < 1^0$ are studied using GLIMPSE images and GLIMPSE data
catalogue. A total number of 1107 Class I and 1566 Class II sources are
identified in this Galactic region. With the help of GLIMPSE 5.8 $\mu$m & 8
$\mu$m images, we have identified the presence of 10 major star forming sites
in the Galactic midplane, of which 8 of them are filamentary while 2 are
possible clusters of Class I $&$ II sources. The length of the identified
filaments are estimated as 8'-33' ($\sim$ 9 - 56 pc). Occurrence of
Hub-Filamentary System (HFS) is observed in many filamentary star forming
sites. Most of the Class I sources are found to be aligned along the length of
these filamentary structures, while Class II sources have a random
distribution. Mass and age distribution of 425 Class I and 241 Class II sources
associated with filaments & clusters are studied through their SED analysis.
Most of the Class I sources detected have mass $>$ 8M$_\odot$, while Class II
sources have relatively low mass regime. Class I sources have ages $\le$ 0.5
Myr, while Class II sources have ages in the range $\sim$0.1 - 3 Myr. Along
with the help of high mass star forming tracers, we demonstrate that the 10
regions studied here are forming a large number of high-mass stars.


title: Scaling Behavior of the Heisenberg Model in Three Dimensions

abstract:
  We report on extensive numerical simulations of the three-dimensional
Heisenberg model and its analysis through finite-size scaling of Lee-Yang
zeros. Besides the critical regime, we also investigate scaling in the
ferromagnetic phase. We show that, in this case of broken symmetry, the
corrections to scaling contain information on the Goldstone modes. We present a
comprehensive Lee-Yang analysis, including the density of zeros and confirm
recent numerical estimates for critical exponents.


title: Weak-noise limit of a piecewise-smooth stochastic differential equation

abstract:
  We investigate the validity and accuracy of weak-noise (saddle-point or
instanton) approximations for piecewise-smooth stochastic differential
equations (SDEs), taking as an illustrative example a piecewise-constant SDE,
which serves as a simple model of Brownian motion with solid friction. For this
model, we show that the weak-noise approximation of the path integral correctly
reproduces the known propagator of the SDE at lowest order in the noise power,
as well as the main features of the exact propagator with higher-order
corrections, provided that the singularity of the path integral associated with
the non-smooth SDE is treated with some heuristics. We also show that, as in
the case of smooth SDEs, the deterministic paths of the noiseless system
correctly describe the behaviour of the non-smooth SDE in the low-noise limit.
Finally, we consider a smooth regularisation of the piecewise-constant SDE and
study to which extent this regularisation can rectify some of the problems
encountered when dealing with discontinuous drifts and singularities in SDEs.


title:
Unified Performance Analysis of Orthogonal Transmit Beamforming Methods
  with User Selection

abstract:
  Simultaneous multiuser beamforming in multiantenna downlink channels can
entail dirty paper (DP) precoding (optimal and high complexity) or linear
precoding (suboptimal and low complexity) approaches. The system performance is
typically characterized by the sum capacity with homogenous users with perfect
channel state information at the transmitter. The sum capacity performance
analysis requires the exact probability distributions of the user
signal-to-noise ratios (SNRs) or signal-to-interference plus noise ratios
(SINRs). The standard techniques from order statistics can be sufficient to
obtain the probability distributions of SNRs for DP precoding due to the
removal of known interference at the transmitter. Derivation of such
probability distributions for linear precoding techniques on the other hand is
much more challenging. For example, orthogonal beamforming techniques do not
completely cancel the interference at the user locations, thereby requiring the
analysis with SINRs. In this paper, we derive the joint probability
distributions of the user SINRs for two orthogonal beamforming methods combined
with user scheduling: adaptive orthogonal beamforming and orthogonal linear
beamforming. We obtain compact and unified solutions for the joint probability
distributions of the scheduled users' SINRs. Our analytical results can be
applied for similar algorithms and are verified by computer simulations.


title: Units of $\mathbb{Z}C_{p^n}$

abstract:
  Let $p$ be a prime integer and $n,i$ be positive integers such that
\linebreak $S=\{-1, \ \theta, \ \mu_i=1+\theta+... + \theta^{i-1} \ \mid 1 < i
< \frac{p^n}{2}, \ gcd(p^n,i)=1 \}$ generates the group of units of
$\mathbb{Z}[\theta],$ where $\theta$ is a primitive ${p^n}$--$th$ root of
unity. Denote by $C_{p^n}$ the cyclic group of order $p^n.$ In this paper we
describe explicitly a multiplicatively independent set which generates a
complement to $\pm C_{p^n}$ in the group of units of the integral group ring of
$C_{p^n}.$


title:
Optimally Approximating the Coverage Lifetime of Wireless Sensor
  Networks

abstract:
  We consider the problem of maximizing the lifetime of coverage (MLCP) of
targets in a wireless sensor network with battery-limited sensors. We first
show that the MLCP cannot be approximated within a factor less than $\ln n$ by
any polynomial time algorithm, where $n$ is the number of targets. This
provides closure to the long-standing open problem of showing optimality of
previously known $\ln n$ approximation algorithms. We also derive a new $\ln n$
approximation to the MLCP by showing a $\ln n$ approximation to the maximum
disjoint set cover problem (DSCP), which has many advantages over previous MLCP
algorithms, including an easy extension to the $k$-coverage problem. We then
present an improvement (in certain cases) to the $\ln n$ algorithm in terms of
a newly defined quantity "expansiveness" of the network. For the special
one-dimensional case, where each sensor can monitor a contiguous region of
possibly different lengths, we show that the MLCP solution is equal to the DSCP
solution, and can be found in polynomial time. Finally, for the special
two-dimensional case, where each sensor can monitor a circular area with a
given radius around itself, we combine existing results to derive a
$1+\epsilon$ approximation algorithm for solving MLCP for any $\epsilon >0$.


title: Hierarchical sparsity priors for regression models

abstract:
  We focus on the increasingly important area of sparse regression problems
where there are many variables and the effects of a large subset of these are
negligible. This paper describes the construction of hierarchical prior
distributions when the effects are considered related. These priors allow
dependence between the regression coefficients and encourage related shrinkage
towards zero of different regression coefficients. The properties of these
priors are discussed and applications to linear models with interactions and
generalized additive models are used as illustrations. Ideas of heredity
relating different levels of interaction are encompassed.


title: The Diffuse Ultraviolet Foreground

abstract:
  Ultraviolet observations from low Earth orbit (LEO) have to deal with a
foreground comprised of airglow and zodiacal light which depend on the look
direction and on the date and time of the observation. We have used all-sky
observations from the GALEX spacecraft to find that the airglow may be divided
into a baseline dependent on the sun angle and a component dependent only on
the time from local midnight. The zodiacal light is observable only in the near
ultraviolet band (2321 \AA) of GALEX and is proportional to the zodiacal light
in the visible but with a color of 0.65 indicating that the dust grains are
less reflective in the UV.


title:
GeFRO: a New Charge Sensitive Amplifier Design with a Minimal Number of
  Front-end Components

abstract:
  A new approach was developed for the design of front-end circuits for
semiconductor radiation detectors. The readout scheme consists of a first stage
made of only a few components located close to the detector, and of a remote
second stage located far from the detector, several meters away. The second
stage amplifies the signals from the first stage and closes the feedback loop
to discharge the input node after each event. The circuit has two outputs: one
gives a "fast" signal, with a bandwidth larger than 20 MHz, allowing to
preserve the high frequency components of the detector signals, which may be
useful for timing measurements, pile-up rejection or pulse shape
discrimination. The second output gives a "slow" signal, whose gain depends
only on the value of the feedback capacitor, as happens with a classic charge
sensitive amplifier, allowing to obtain higher resolution and lower drift. The
prototype was named GeFRO for Germanium front-end, and was tested with a BEGe
detector from Canberra. The wide bandwidth of the "fast" signal gave a timing
resolution of the order of 20 ns. The noise of the circuit at the "slow" output
after a 10 us Gaussian shaping was close to 160 electrons RMS with an input
capacitance of 26 pF.


title: Characterization of 3D filament dynamics in a MAST SOL fluxtube geometry

abstract:
  Non-linear simulations of filament propagation in a realistic MAST SOL flux
tube geometry using the BOUT++ fluid modelling framework show an isolation of
the dynamics of the filament in the divertor region from the midplane region
due to three features of the magnetic geometry; the variation of magnetic
curvature along the field line, the expansion of the flux tube and strong
magnetic shear. Of the three effects, the latter two lead to a midplane
ballooning feature of the filament, whilst the former leads to a ballooning
around the X-points. In simulations containing all three effects the filament
is observed to balloon at the midplane, suggesting that the role of curvature
variation is sub-dominant to the flux expansion and magnetic shear. The
magnitudes of these effects are all strongest near the X-point which leads to
the formation of parallel density gradients. The filaments simulated, which
represent filaments in MAST, are identified as resistive ballooning, meaning
that their motion is inertially limited, not sheath limited. Parallel density
gradients can drive the filament towards a Boltzmann response when the
collisionalityof the plasma is low. The results here show that the formation of
parallel density gradients is a natural and inevitable consequence of a
realistic magnetic geometry and therefore the transition to the Boltzmann
response is a consequence of the use of realistic magnetic geometry. The
Boltzmann response causes the filament to self-organise and spin on an axis.
The transition from interchange motion to the Boltzmann response occurs with
increasing temperature through a decrease in collisionality. This is confirmed
by measuring the correlation between density and potential perturbations within
the filament, which is low in the anti-symmetric state associated with the
interchange mechanism, but high in the Boltzmann regime.


title: Extremal polynomials in stratified groups

abstract:
  We introduce a family of extremal polynomials associated with the
prolongation of a stratified nilpotent Lie algebra. These polynomials are
related to a new algebraic characterization of abnormal subriemannian geodesics
in stratified nilpotent Lie groups. They satisfy a set of remarkable structure
relations that are used to integrate the adjoint equations.


title:
A note on zero sets of fractional sobolev functions with negative power
  of integrability

abstract:
  We extend a Poincar\'{e}-type inequality for functions with large zero-sets
by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a
Hausdorff dimension estimate on the size of zero sets for fractional Sobolev
functions whose inverse is integrable. Also, for a suboptimal Hausdorff
dimension estimate, we give a completely elementary proof based on a pointwise
Poincar\'{e}-style inequality.


title: Scaling of the dynamics of flexible Lennard-Jones chains

abstract:
  The isomorph theory provides an explanation for the so-called power law
density scaling which has been observed in many molecular and polymeric glass
formers, both experimentally and in simulations. Power law density scaling
(relaxation times and transport coefficients being functions of
$\rho^{\gamma_S}/T$, where $\rho$ is density, $T$ is temperature, and
$\gamma_S$ is a material specific scaling exponent) is an approximation to a
more general scaling predicted by the isomorph theory. Furthermore, the
isomorph theory provides an explanation for Rosenfeld scaling (relaxation times
and transport coefficients being functions of excess entropy) which has been
observed in simulations of both molecular and polymeric systems. Doing
molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with
rigid bonds, we here provide the first detailed test of the isomorph theory
applied to flexible chain molecules. We confirm the existence of isomorphs,
which are curves in the phase diagram along which the dynamics is invariant in
the appropriate reduced units. This holds not only for the relaxation times but
also for the full time dependence of the dynamics, including chain specific
dynamics such as the end-to-end vector autocorrelation function and the
relaxation of the Rouse modes. As predicted by the isomorph theory, jumps
between different state points on the same isomorph happen instantaneously
without any slow relaxation. Since the LJC is a simple coarse-grained model for
alkanes and polymers, our results provide a possible explanation for why
power-law density scaling is observed experimentally in alkanes and many
polymeric systems. The theory provides an independent method of determining the
scaling exponent, which is usually treated as a empirical scaling parameter.


title:
Anomaly-free perturbations with inverse-volume and holonomy corrections
  in Loop Quantum Cosmology

abstract:
  This article addresses the issue of the closure of the algebra of constraints
for generic (cosmological) perturbations when taking into account
simultaneously the two main corrections of effective loop quantum cosmology,
namely the holonomy and the inverse-volume terms. Previous works on either the
holonomy or the inverse volume case are reviewed and generalized. In the
inverse-volume case, we point out new possibilities. An anomaly-free solution
including both corrections is found for perturbations, and the corresponding
equations of motion are derived.


title: Fresnel reflection from a cavity with net roundtrip gain

abstract:
  A planewave incident on an active etalon with net roundtrip gain may be
expected to diverge in field amplitude, yet Maxwell's equations admit only a
convergent solution. By examining a Gaussian beam obliquely incident on such a
cavity, we find that the "side-tail" of the beam leaks into the cavity and
gives rise to a field that interferes with the main portion of the beam, which
is ultimately responsible for the convergence of the field. This mechanism
offers perspective for many phenomena, and we specifically discuss the
implications for amplified total internal reflection.


title:
Performance Analysis of Optimum Zero-Forcing Beamforming with Greedy
  User Selection

abstract:
  In this letter, an exact performance analysis is presented on the sum rate of
zero-forcing beamforming with a greedy user scheduling algorithm in a downlink
system. Adopting water-filling power allocation, we derive a compact form for
the joint probability density function of the scheduled users' squared
subchannel gains when a transmitter with multiple antennas sends information to
at most two scheduled users with each having a single antenna. The analysis is
verified by numerical results.


title: High-order harmonic generation and Fano resonances

abstract:
  We present a high harmonic generation theory which generalizes the
strong-field approximation to the resonant case, when the harmonic frequency is
close to that of the transition from the ground to an autoionizing state of the
generating system. We show that the line shape of the resonant harmonic is a
product of the Fano-like factor and the harmonic line which would be emitted in
the absence of the resonance. The theory predicts rapid variation of the
harmonic phase in the vicinity of the resonance. The calculated resonant
harmonic phase is in reasonable agreement with recent measurements. Predicting
the phase-locking of a group of resonantly-enhanced harmonics, our theory
allows to study the perspectives of producing attosecond pulse train using such
harmonics.


title: The Necessity of the Hadamard Condition

abstract:
  Hadamard states are generally considered as the physical states for linear
quantized fields on curved spacetimes, for several good reasons. Here, we
provide a new motivation for the Hadamard condition: for "ultrastatic slab
spacetimes" with compact Cauchy surface, we show that the Wick squares of all
time derivatives of the quantized Klein-Gordon field have finite fluctuations
only if the Wick-ordering is defined with respect to a Hadamard state. This
provides a converse to an important result of Brunetti and Fredenhagen. The
recently proposed "S-J (Sorkin-Johnston) states" are shown, generically, to
give infinite fluctuations for the Wick square of the time derivative of the
field, further limiting their utility as reasonable states. Motivated by the
S-J construction, we also study the general question of extending states that
are pure (or given by density matrices relative to a pure state) on a
double-cone region of Minkowski space. We prove a result for general quantum
field theories showing that such states cannot be extended to any larger
double-cone without encountering singular behaviour at the spacelike boundary
of the inner region. In the context of the Klein-Gordon field this shows that
even if an S-J state is Hadamard within the double cone, this must fail at the
boundary.


title:
Bayesian models for cost-effectiveness analysis in the presence of
  structural zero costs

abstract:
  Bayesian modelling for cost-effectiveness data has received much attention in
both the health economics and the statistical literature in recent years.
Cost-effectiveness data are characterised by a relatively complex structure of
relationships linking the suitable measure of clinical benefit (\eg QALYs) and
the associated costs. Simplifying assumptions, such as (bivariate) normality of
the underlying distributions are usually not granted, particularly for the cost
variable, which is characterised by markedly skewed distributions. In addition,
individual-level datasets are often characterised by the presence of structural
zeros in the cost variable.
  Hurdle models can be used to account for the presence of excess zeros in a
distribution and have been applied in the context of cost data. We extend their
application to cost-effectiveness data, defining a full Bayesian model which
consists of a selection model for the subjects with null costs, a marginal
model for the costs and a conditional model for the measure of effectiveness
(conditionally on the observed costs). The model is presented using a working
example to describe its main features.


title:
Equation of motion and subsonic-transonic transitions of rectilinear
  edge dislocations: A collective-variable approach

abstract:
  A theoretical framework is proposed to derive a dynamic equation motion for
rectilinear dislocations within isotropic continuum elastodynamics. The theory
relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to
account for core-width generalized stacking-fault energy effects. The degrees
of freedom of the solution of the latter equation are reduced by means of the
collective-variable method, well known in soliton theory, which we reformulate
in a way suitable to the problem at hand. Through these means, two coupled
governing equations for the dislocation position and core width are obtained,
which are combined into one single complex-valued equation of motion, of
compact form. The latter equation embodies the history dependence of
dislocation inertia. It is employed to investigate the motion of an edge
dislocation under uniform time-dependent loading, with focus on the
subsonic/transonic transition. Except in the steady-state supersonic range of
velocities---which the equation does not address---our results are in good
agreement with atomistic simulations on tungsten. In particular, we provide an
explanation for the transition, showing that it is governed by a
loading-dependent dynamic critical stress. The transition has the character of
a delayed bifurcation. Moreover, various quantitative predictions are made,
that could be tested in atomistic simulations. Overall, this work demonstrates
the crucial role played by core-width variations in dynamic dislocation motion.


title:
W*-superrigidity for arbitrary actions of central quotients of braid
  groups

abstract:
  For any $n\geqslant 4$ let $\tilde B_n=B_n/Z(B_n)$ be the quotient of the
braid group $B_n$ through its center. We prove that any free ergodic
probability measure preserving (pmp) action $\tilde B_n\curvearrowright
(X,\mu)$ is W$^*$-superrigid in the following sense: if
$L^{\infty}(X)\rtimes\tilde B_n\cong L^{\infty}(Y)\rtimes\Lambda$, for an
arbitrary free ergodic pmp action $\Lambda\curvearrowright (Y,\nu)$, then the
actions $\tilde B_n\curvearrowright X,\Lambda\curvearrowright Y$ are stably
(or, virtually) conjugate. Moreover, we prove that the same holds if $\tilde
B_n$ is replaced with a finite index subgroup of the direct product $\tilde
B_{n_1}\times\cdots\times\tilde B_{n_k}$, for some $n_1,\ldots,n_k\geqslant 4$.
The proof uses the dichotomy theorem for normalizers inside crossed products by
free groups from \cite{PV11} in combination with the OE superrigidity theorem
for actions of mapping class groups from \cite{Ki06}.


title: Internal Partitions of Regular Graphs

abstract:
  An internal partition of an $n$-vertex graph $G=(V,E)$ is a partition of $V$
such that every vertex has at least as many neighbors in its own part as in the
other part. It has been conjectured that every $d$-regular graph with $n>N(d)$
vertices has an internal partition. Here we prove this for $d=6$. The case
$d=n-4$ is of particular interest and leads to interesting new open problems on
cubic graphs. We also provide new lower bounds on $N(d)$ and find new families
of graphs with no internal partitions. Weighted versions of these problems are
considered as well.


title: Critical exponents in Ising Spin Glasses

abstract:
  Extensive simulations are made of the spin glass susceptibility and
correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian
and bimodal interaction distributions. Once the transition temperature is
accurately established using a standard criterion, critical exponents and
correction terms can be readily estimated by extrapolating measurements made in
the thermodynamic limit regime. The data show that the critical exponents of
the susceptibility $\gamma$ and of the correlation length $\nu$ depend on the
form of the interaction distribution. This observation implies that quite
generally critical exponents are not universal in ISGs.


title:
Physics Case for the ILC Project: Perspective from Beyond the Standard
  Model

abstract:
  The International Linear Collider (ILC) has recently proven its technical
maturity with the publication of a Technical Design Report, and there is a
strong interest in Japan to host such a machine. We summarize key aspects of
the Beyond the Standard Model physics case for the ILC in this contribution to
the US High Energy Physics strategy process. On top of the strong guaranteed
physics case in the detailed exploration of the recently discovered Higgs
boson, the top quark and electroweak precision measurements, the ILC will offer
unique opportunities which are complementary to the LHC program of the next
decade. Many of these opportunities have connections to the Cosmic and
Intensity Frontiers, which we comment on in detail. We illustrate the general
picture with examples of how our world could turn out to be and what the ILC
would contribute in these cases, with an emphasis on value-added beyond the
LHC. These comprise examples from Supersymmetry including light Higgsinos, a
comprehensive bottom-up coverage of NLSP-LSP combinations for slepton, squark,
chargino and neutralino NLSP, a stau-coannihilation dark matter scenario and
bilinear R-parity violation as explanation for neutrino masses and mixing, as
well as generic WIMP searches and Little Higgs models as non-SUSY examples.


title: A Distinctive Disk-Jet Coupling in the Lowest-Mass Seyfert, NGC 4395

abstract:
  Simultaneous observations of X-rays and radio luminosities have been well
studied in accreting stellar-mass black holes. These observations are performed
in order to understand how mass accretion rates and jetted outflows are linked
in these individual systems. Such contemporaneous studies in supermassive black
holes (SMBH) are harder to perform, as viscous times scale linearly with mass.
However, as NGC 4395 is the lowest known mass Seyfert galaxy, we have used it
to examine the simultaneous X-ray (Swift) and radio (VLA) correlation in a SMBH
in a reasonably timed observing campaign. We find that the intrinsic X-ray
variability is stronger than the radio variability, and that the fluxes are
only weakly or tentatively coupled, similar to prior results obtained in NGC
4051. If the corona and the base of the jet are one and the same, this may
suggest that the corona in radio-quiet AGN filters disk variations, only
transferring the strongest and/or most sustained variations into the jet.
Further, when both NGC 4395 and NGC 4051 are placed on the stellar-mass L_X-L_R
plane, they appear to reside on the steeper L_X-L_R track. This suggests that
SMBHs also follow two distinct tracks just as stellar-mass black holes do, and
supports the idea that the same physical disk-jet mechanisms are at play across
the mass scale.


title:
Efficient Micro-electrode Recording Modeling using a Filtered Point
  Process

abstract:
  In this paper we present an efficient model of the neuronal potentials
recorded by a deep brain stimulation microelectrode (DBS MER) in the
subthalamic nucleus. It is shown that a computationally efficient filtered
point process consisting of 10,000 neurons, including extracellular filtering
closely matches recordings from 13 Parkinson's disease patients. The recordings
were compared using their voltage amplitude distributions, power spectral
density estimates and phase synchrony. It was found that interspike interval
times modeled using a Weibull distribution with a shape parameter of 0.8,
slightly non-Poisosnian, gave the best fit of the simulations to patient
recordings. These results indicate that part of the `background activity'
present in an DBS MER can be considered to be a very local field potential due
to the surrounding neuronal activity.Therefore, the statistics of the
interspike interval times modify the structure of the background activity.


title:
Period doubling, information entropy, and estimates for Feigenbaum's
  constants

abstract:
  The relationship between period doubling bifurcations and Feigenbaum's
constants has been studied for nearly 40 years and this relationship has helped
uncover many fundamental aspects of universal scaling across multiple nonlinear
dynamical systems. This paper will combine information entropy with symbolic
dynamics to demonstrate how period doubling can be defined using these tools
alone. In addition, the technique allows us to uncover some unexpected, simple
estimates for Feigenbaum's constants which relate them to log 2 and the golden
ratio, phi, as well as to each other.


title: Extreme cycles. The center of a Leavitt path algebra

abstract:
  In this paper we introduce new techniques in order to deepen into the
structure of a Leavitt path algebra with the aim of giving a description of the
center. Extreme cycles appear for the first time; they concentrate the purely
infinite part of a Leavitt path algebra and, jointly with the line points and
vertices in cycles without exits, are the key ingredients in order to determine
the center of a Leavitt path algebra. Our work will rely on our previous
approach to the center of a prime Leavitt path algebra \cite{CMMSS1}. We will
go further into the structure itself of the Leavitt path algebra. For example,
the ideal $I(P_{ec} \cup P_{c} \cup P_l)$ generated by vertices in extreme
cycles ($P_{ec}$), by vertices in cycles without exits ($P_c$) and by line
points ($P_l$) will be a dense ideal in some cases, for instance in the finite
one or, more generally, if every vertex connects to $P_l \cup P_c\cup P_{ec}$.
Hence its structure will contain much of the information about the Leavitt path
algebra. In the row-finite case, we will need to add a new hereditary set: the
set of vertices whose tree has infinite bifurcations ($P_{b^\infty}$).


title: Quasar Black Hole Mass Estimates in the Era of Time Domain Astronomy

abstract:
  We investigate the dependence of the normalization of the high-frequency part
of the X-ray and optical power spectral densities (PSD) on black hole mass for
a sample of 39 active galactic nuclei (AGN) with black hole masses estimated
from reverberation mapping or dynamical modeling. We obtained new Swift
observations of PG 1426+015, which has the largest estimated black hole mass of
the AGN in our sample. We develop a novel statistical method to estimate the
PSD from a lightcurve of photon counts with arbitrary sampling, eliminating the
need to bin a lightcurve to achieve Gaussian statistics, and we use this
technique to estimate the X-ray variability parameters for the faint AGN in our
sample. We find that the normalization of the high-frequency X-ray PSD is
inversely proportional to black hole mass. We discuss how to use this scaling
relationship to obtain black hole mass estimates from the short time-scale
X-ray variability amplitude with precision ~ 0.38 dex. The amplitude of optical
variability on time scales of days is also anti-correlated with black hole
mass, but with larger scatter. Instead, the optical variability amplitude
exhibits the strongest anti-correlation with luminosity. We conclude with a
discussion of the implications of our results for estimating black hole mass
from the amplitude of AGN variability.


title: Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

abstract:
  We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus
with twisted boundary conditions. Our goal is to study the interplay between
the rank of the group N, the length of the torus L and the Z_N magnetic flux.
After presenting the classical and quantum formalism, we analyze the spectrum
of the theory using perturbation theory to one-loop and using Monte Carlo
techniques on the lattice. In perturbation theory, results to all orders depend
on the combination x=\lambda NL and an angle defined in terms of the magnetic
flux (\lambda\ is 't Hooft coupling). Thus, fixing the angle, the system
exhibits a form of volume independence (NL dependence). The numerical results
interpolate between our perturbative calculations and the confinement regime.
They are consistent with x-scaling and provide interesting information about
the k-string spectrum and effective string theories. The occurrence of
tachyonic instabilities is also analysed. They seem to be avoidable in the
large N limit with a suitable scaling of the magnetic flux.


title: A Primeval Magellanic Stream and Others

abstract:
  The Magellanic Stream might have grown out of tidal interactions at high
redshift, when the young galaxies were close together, rather than from later
interactions among the Magellanic Clouds and Milky Way. This is illustrated in
solutions for the orbits of Local Group galaxies under the cosmological
condition of growing peculiar velocities at high redshift. Massless test
particles initially near and moving with the Large Magellanic Cloud in these
solutions end up with distributions in angular position and redshift similar to
the Magellanic Stream, though with the usual overly prominent leading component
that the Milky Way corona might have suppressed. Another possible example of
the effect of conditions at high redshift is a model primeval stream around the
Local Group galaxy NGC 6822. Depending on the solution for Local Group dynamics
this primeval stream can end up with position angle similar to the HI around
this galaxy, and a redshift gradient in the observed direction. The gradient is
much smaller than observed, but might have been increased by dissipative
contraction. Presented also is an even more speculative illustration of the
possible effect of initial conditions, primeval stellar streams around M31.


title: MicroBooNE light collection system

abstract:
  MicroBooNE is a neutrino experiment located on axis in the Booster Neutrino
Beamline, at Fermi National Accelerator Laboratory, scheduled to begin data
collection in 2014. The MicroBooNE detector consists of two main components: a
large liquid argon time projection chamber (LArTPC), and a light collection
system. Thirty two 8-inch diameter cryogenic photomultiplier tubes (PMTs) will
detect the scintillation light generated in the liquid argon. In this article,
we describe the basic features of the system and current status of MicroBooNE
light collection system.


title:
Interactions and charge fractionalization in an electronic
  Hong-Ou-Mandel interferometer

abstract:
  We consider an electronic analog of the Hong-Ou-Mandel (HOM) interferometer,
where two single electrons travel along opposite chiral edge states and collide
at a Quantum Point Contact. Studying the current noise, we show that because of
interactions between co-propagating edge states, the degree of
indistinguishability between the two electron wavepackets is dramatically
reduced, leading to reduced contrast for the HOM signal. This decoherence
phenomenon strongly depends on the energy resolution of the packets. Insofar as
interactions cause charge fractionalization, we show that charge and neutral
modes interfere with each other, leading to satellite dips or peaks in the
current noise. Our calculations explain recent experimental results [E.
Bocquillon, et al., Science 339, 1054(2013)] where an electronic HOM signal
with reduced contrast was observed.


title: Multi-plectoneme phase of double-stranded DNA under torsion

abstract:
  We use the worm-like chain model to study supercoiling of DNA under tension
and torque. The model reproduces experimental data for a broad range of forces,
salt concentrations and contour lengths. We find a plane of first order phase
transitions ending in a smeared out line of critical points, the
multi-plectoneme phase, which is characterized by a fast twist mediated
diffusion of plectonemes and a torque that rises after plectoneme formation
with increasing linking number. The discovery of this new phase at the same
time resolves the discrepancies between existing models and experiment.


title: Chiral and Real N=2 supersymmetric l-conformal Galilei algebras

abstract:
  Inequivalent N=2 supersymmetrizations of the l-conformal Galilei algebra in
d-spatial dimensions are constructed from the chiral (2,2) and the real (1,2,1)
basic supermultiplets of the N=2 supersymmetry. For non-negative integer and
half-integer l both superalgebras admit a consistent truncation with a
(different) finite number of generators. The real N=2 case coincides with the
superalgebra introduced by Masterov, while the chiral N=2 case is a new
superalgebra. We present D-module representations of both superalgebras. Then
we investigate the new superalgebra derived from the chiral supermultiplet. It
is shown that it admits two types of central extensions, one is found for any d
and half-integer l and the other only for d=2 and integer l. For each central
extension the centrally extended l-superconformal Galilei algebra is realized
in terms of its super-Heisenberg subalgebra generators.


title: Navigation Assistance and Web Accessibility Helper

abstract:
  Web accessibility is actually the most important aspect for providing access
to information and interaction for people with disabilities. However, it seems
that the ability of users with disabilities to navigate over the Web is not
dependent on the graphical complexity, but on the markup used to create the
structure of the website. Consequently, it is necessary to design some software
assistants to help all users to mark themselves in space during a navigation
session. In this paper, we propose an assistant for browsing on the Internet to
allow user to get one s bearings within Web navigation. We describe our
approach which puts at the disposal of the user a visited site map, thus giving
an explicit representation of virtual space. Different levels of visualization
are implemented in order to make the map more visible and less overloaded.


title:
Commutators of multilinear singular integral operators on
  non-homogeneous metric measure spaces

abstract:
  Let $(X,d,\mu)$ be a metric measure space satisfying both the geometrically
doubling and the upper doubling measure conditions, which is called
non-homogeneous metric measure space. In this paper, via a sharp maximal
operator, the boundedness of commutators generated by multilinear singular
integral with $RBMO(\mu)$ function on non-homogeneous metric measure spaces in
$m$-multiple Lebesgue spaces is obtained.


title: Presentations with negative deficiency and largeness

abstract:
  We extend the results of M. Edjvet on balanced presentations and largeness by
giving conditions under which presentations with negative deficiency define
large groups.


title:
The calculation of the muon transfer rate from protium to neon on the
  ground of a two-centre Coulomb basis

abstract:
  Results of improved calculations of the muon transfer rate from the 1S-state
of muonic protium to neon are presented in the interval of collision energies
from 10^(-4) eV to 15 eV. The calculations were made within the PSS method in
which the three-body wavefunction is expanded in eigenfunctions of a two-
centre Coulomb problem formulated in the Jacobi coordinates of the entrance
channel. This approach provides the asymptotically correct description of this
channel: the correct dissociation limit is obtained, there are no spurious
long-range interactions, the polarization attraction appears naturally, the
electron screening can be easily taken into account. The defects of the
description are removed into the muon transfer channel in which their effect is
not expected to be too significant because of large kinetic energies there. The
previous calculations carried out in this way allowed one to explain
experimentally observed features of the temperature dependence of the transfer
rate in hydrogen-neon mixtures. In the present work, a more perfect algorithm
of constructing the basis eigenfunctions has been realized and a better
agreement with experimental data has been obtained.


title:
On the importance of Internet eXchange Points for today's Internet
  ecosystem

abstract:
  Internet eXchange Points (IXPs) are generally considered to be the successors
of the four Network Access Points that were mandated as part of the
decommissioning of the NSFNET in 1994/95 to facilitate the transition from the
NSFNET to the "public Internet" as we know it today. While this popular view
does not tell the whole story behind the early beginnings of IXPs, what is true
is that since around 1994, the number of operational IXPs worldwide has grown
to more than 300 (as of May 2013), with the largest IXPs handling daily traffic
volumes comparable to those carried by the largest Tier-1 ISPs, but IXPs have
never really attracted any attention from the networking research community. At
first glance, this lack of interest seems understandable as IXPs have
apparently little to do with current "hot" topic areas such as data centers and
cloud services or software defined networking (SDN) and mobile communication.
However, we argue in this article that, in fact, IXPs are all about data
centers and cloud services and even SDN and mobile communication and should be
of great interest to networking researchers interested in understanding the
current and future Internet ecosystem. To this end, we survey the existing but
largely unknown sources of publicly available information about IXPs to
describe their basic technical and operational aspects and highlight the
critical differences among the various IXPs in the different regions of the
world, especially in Europe and North America. More importantly, we illustrate
the important role that IXPs play in today's Internet ecosystem and discuss how
IXP-driven innovation in Europe is shaping and redefining the Internet
marketplace, not only in Europe but increasingly so around the world.


title:
Estimates of the first Dirichlet eigenvalue from exit time moment
  spectra

abstract:
  We compute the first Dirichlet eigenvalue of a geodesic ball in a
rotationally symmetric model space in terms of the moment spectrum for the
Brownian motion exit times from the ball. This expression implies an estimate
as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in
these rotationally symmetric spaces, including the real space forms of constant
curvature. As an application of the model space theory we prove lower and upper
bounds for the first Dirichlet eigenvalues of extrinsic metric balls in
submanifolds of ambient Riemannian spaces which have model space controlled
curvatures. Moreover, from this general setting we thereby obtain new
generalizations of the classical and celebrated results due to McKean and
Cheung--Leung concerning the fundamental tones of Cartan-Hadamard manifolds and
the fundamental tones of submanifolds with bounded mean curvature in hyperbolic
spaces, respectively.


title: Testing Lorentz Invariance with a Double-Pass Optical Ring Cavity

abstract:
  We have developed an apparatus to test Lorentz invariance in the photon
sector by measuring the resonant frequency difference between two
counterpropagating directions of an asymmetric optical ring cavity using a
double-pass configuration. No significant evidence for the violation was found
at the level of $\delta c /c \lesssim 10^{-14}$. Details of our apparatus and
recent results are presented.


title:
Single-exposure profilometry using partitioned aperture wavefront
  imaging

abstract:
  We demonstrate a technique for instantaneous measurements of surface
topography based on the combination of a partitioned aperture wavefront imager
with a standard lamp-based reflection microscope. The technique can operate at
video rate over large fields of view, and provides nanometer axial resolution
and sub-micron lateral resolution. We discuss performance characteristics of
this technique, which we experimentally compare with scanning white light
interferometry.


title:
South African Riots: Repercussion of the Global Food Crisis and US
  Drought

abstract:
  High and volatile global food prices have led to food riots and played a
critical role in triggering the Arab Spring revolutions in recent years. The
severe drought in the US in the summer of 2012 led to a new increase in food
prices. Through the fall, they remained at a threshold above which the riots
and revolutions had predominantly occurred. Global prices at this level create
conditions where an exacerbating local circumstance can trigger unrest. Global
corn (maize) prices reached new highs, and countries that depend mostly on
maize are more likely to experience high local food prices and associated
pressures toward social unrest. Here we analyze the conditions in South Africa,
which is a heavily maize-dependent country. Coinciding with increased consumer
food indices this summer, massive labor strikes in mining and agriculture have
led to the greatest single incident of social violence since the fall of
apartheid in 1994. Worker demands for dramatic pay increases reflect that their
wages have not kept up with drastic increases in the prices of necessities,
especially food. Without attention to the global food price situation, more
incidents of food-based social instability are likely to arise. Other countries
that have manifested food-related protests and riots in 2012 include Haiti and
Argentina. Moreover, these cases of unrest are just the most visible symptom of
widespread suffering of poor populations worldwide due to elevated food prices.
Policy decisions that would directly impact food prices are decreasing the
conversion of maize to ethanol in the US, and reimposing regulations on
commodity futures markets to prevent excessive speculation, which we have shown
causes bubbles and crashes in these markets. Absent such policy actions,
governments and companies should track and mitigate the impact of high and
volatile food prices on citizens and employees.


title:
Local and global minimality results for a nonlocal isoperimetric problem
  on R^N

abstract:
  We consider a nonlocal isoperimetric problem defined in the whole space
$\R^N$, whose nonlocal part is given by a Riesz potential with exponent
$\alpha\in(0, N-1)$. We show that critical configurations with positive second
variation are local minimizers and satisfy a quantitative inequality with
respect to the $L^1$-norm. This criterion provides the existence of a
(explicitly determined) critical threshold determining the interval of volumes
for which the ball is a local minimizer, and allows to address several global
minimality issues.


title: Gluon radiation by heavy quarks at intermediate energies

abstract:
  Employing scalar QCD we study the gluon emission of heavy quarks created by
the interaction with light quarks considered as dynamical scattering centers.
We develop approximation formulas for the high energy limit and study when the
full calculation reaches this high energy limit. For zero quark masses and in
the high energy limit our model reproduces the Gunion-Bertsch results. We
justify why scalar QCD represents a good approximation to the full QCD approach
for the energy loss of heavy quarks. In the regime of accessible phenomenology
we observe that the emission at small transverse momentum (dead cone effect) is
less suppressed than originally suggested. We also investigate the influence of
a finite gluon mass on the discussed results.


title: On the diffuseness of incomplete information game

abstract:
  We introduce the "relative diffuseness" assumption to characterize the
differences between payoff-relevant and strategy-relevant diffuseness of
information. Based on this assumption, the existence of pure strategy
equilibria in games with incomplete information and general action spaces can
be obtained. Moreover, we introduce a new notion of "undistinguishable
purification" which strengthens the standard purification concept, and its
existence follows from the relative diffuseness assumption.


title:
Demonstration of white light cavity effect using stimulated Brillouin
  scattering in a fiber loop

abstract:
  A passive white light cavity (WLC) based on a fiber resonator can be used for
high-bandwidth optical data buffering. Here, we report on experimental studies
of such a WLC, employing stimulated Brillouin scattering (SBS)for producing the
negative dispersion, using two different configurations. In one configuration,
an absorption peak produced by a Brillouin pump is used. In the other
configuration, two gain peaks produced by two separate Brillouin pumps are
employed. In each case, we see evidence of the WLC effect. However, the range
of parameters accessible experimentally limits the degree of the WLC effect
significantly. We present a theoretical analysis for the optimal combinations
of parameters, such as a high Brillouin gain coefficient and a low transmission
loss, necessary for achieving the condition of a vanishing group index, as
required for creating an ideal WLC.


title: Quantum Rainbow Cosmological Model With Perfect Fluid

abstract:
  Isotropic quantum cosmological perfect fluid model is studied in the
formalism of Rainbow gravity. It is found that the only surviving matter degree
of freedom played the role of cosmic time. With the suitable choice of the
Rainbow functions it is possible to find the wave packet naturally from the
superposition of the wave functions of the Schr$\ddot{o}$dinger-Wheeler-deWitt
equation. The many-worlds interpretation of quantum mechanics is applied to
investigate the behavior of the scale factor and the behavior is found to
depend on the operator ordering. It is shown that the model in the Rainbow
framework may avoid singularity yielding a bouncing non-singular universe.


title: The Sun. A typical star in the solar neighborhood?

abstract:
  The Sun is used as the fundamental standard in chemical abundance studies,
thus it is important to know whether the solar abundance pattern is
representative of the solar neighborhood. Albeit at low precision (0.05 - 0.10
dex) the Sun seems to be a typical solar-metallicity disk star, at high
precision (0.01 dex) its abundance pattern seems abnormal when compared to
solar twins. The Sun shows a deficiency of refractory elements that could be
due to the formation of terrestrial planets. The formation of giant planets may
also introduce a signature in the chemical composition of stars. We discuss
both planet signatures and also the enhancement of neutron-capture elements in
the solar twin 18 Sco.


title: First Determination of the Weak Charge of the Proton

abstract:
  The Qweak experiment has measured the parity-violating asymmetry in polarized
e-p elastic scattering at Q^2 = 0.025(GeV/c)^2, employing 145 microamps of 89%
longitudinally polarized electrons on a 34.4cm long liquid hydrogen target at
Jefferson Lab. The results of the experiment's commissioning run are reported
here, constituting approximately 4% of the data collected in the experiment.
From these initial results the measured asymmetry is Aep = -279 +- 35
(statistics) +- 31 (systematics) ppb, which is the smallest and most precise
asymmetry ever measured in polarized e-p scattering. The small Q^2 of this
experiment has made possible the first determination of the weak charge of the
proton, QpW, by incorporating earlier parity-violating electron scattering
(PVES) data at higher Q^2 to constrain hadronic corrections. The value of QpW
obtained in this way is QpW(PVES) = 0.064 +- 0.012, in good agreement with the
Standard Model prediction of QpW(SM) = 0.0710 +- 0.0007. When this result is
further combined with the Cs atomic parity violation (APV) measurement,
significant constraints on the weak charges of the up and down quarks can also
be extracted. That PVES+APV analysis reveals the neutron's weak charge to be
QnW(PVES+APV) = -0.975 +- 0.010.


title: Parametrized modified gravity constraints after Planck

abstract:
  We constrain $f(R)$ and chameleon-type modified gravity in the framework of
the Berstchinger-Zukin parametrization using the recent released Planck data,
including both CMB temperature power spectrum and lensing potential power
spectrum. Some other external data sets are included, such as BAO measurements
from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, HST $H_0$ measurement and
supernovae from Union2.1 compilation. We also use WMAP9yr data for consistency
check and comparison. For $f(R)$ gravity, WMAP9yr results can only give quite a
loose constraint on the modified gravity parameter $B_0$, which is related to
the present value of the Compton wavelength of the extra scalar degree of
freedom, $B_0<3.37$ at $95\% {\rm C.L.}$ We demonstrate that this constraint
mainly comes from the late ISW effect. With only Planck CMB temperature
power-spectrum data, we can improve the WMAP9yr result by a factor $3.7$
($B_0<0.91$ at $95\% {\rm C.L.}$). If the Planck lensing potential
power-spectrum data are also taken into account, the constraint can be further
strenghtened by a factor $5.1$ ($B_0<0.18$ at $95\% {\rm C.L.}$). This major
improvement mainly comes from the small-scale lensing signal. Furthermore, BAO,
HST and supernovae data could slightly improve the $B_0$ bound ($B_0<0.12$ at
$95\% {\rm C.L.}$).For the chameleon-type model, we find that the data set
which we used cannot constrain the Compton wavelength $B_0$ and the potential
index $s$ of chameleon field, but can give a tight constraint on the parameter
$\beta_1=1.043^{+0.163}_{-0.104}$ at $95\% {\rm C.L.}$ ($\beta_1=1$ in general
relativity), which accounts for the non-minimal coupling between the chameleon
field and the matter component. In addition, we find that both modified gravity
models we considered favor a relatively higher Hubble parameter than the
concordance LCDM model in general relativity.


title: Formalisation of the lambda aleph Runtime

abstract:
  In previous work we describe a novel approach to dependent typing based on a
multivalued term language. In this technical report we formalise the runtime, a
kind of operational semantics, for that language. We describe a fairly
comprehensive core language, and then give a small-step operational semantics
based on an abstract machine. Errors are explicit in the semantics. We also
prove several simple properties: that every non-terminated machine state steps
to something and that reduction is deterministic once input is fixed.


title: A finite dimensional approach to Bramham's approximation theorem

abstract:
  Using pseudoholomorphic curves techniques from symplectic geometry, Barney
Bramham proved recently that every smooth irrational pseudo-rotation of the
unit disk is the limit, for the $C^0$ topology, of a sequence of smooth
periodic diffeomorphisms. We give here a finite dimensional proof of this
result that works in the case where the pseudo-rotation is smoothly conjugate
to a rotation on the boundary circle. The proof extends to $C^1$ pseudo
rotations and is based on the dynamical study of the gradient flow associated
to a generating family of functions given by Chaperon's broken geodesics
method.


title: Regular colored graphs of positive degree

abstract:
  Regular colored graphs are dual representations of pure colored D-dimensional
complexes. These graphs can be classified with respect to an integer, their
degree, much like maps are characterized by the genus. We analyse the structure
of regular colored graphs of fixed positive degree and perform their exact and
asymptotic enumeration. In particular we show that the generating function of
the family of graphs of fixed degree is an algebraic series with a positive
radius of convergence, independant of the degree. We describe the singular
behavior of this series near its dominant singularity, and use the results to
establish the double scaling limit of colored tensor models.


title: Spectrum of jet emitting disc: Application to microquasar XTE J1118+480

abstract:
  Under the framework of the magnetized accretion ejection structures, we
analyze the energy balance properties, and study the spectral energy
distributions (SEDs) of the Jet Emitting Disc (JED) model for black hole X-ray
transients. Various radiative processes are considered, i.e. synchrotron,
bremsstrahlung, and their Comptonizations, and external Comptonization of
radiation from outer thin disc. With these cooling terms taken into account, we
solve the thermal equilibrium equation self-consistently and find three
solutions, of which the cold and the hot solutions are stable. Subsequently we
investigate the theoretical SEDs for these two stable solutions.We find the hot
JED model can naturally explain the spectra of the Galactic microquasars in
their hard states. As an example, we apply this model to the case of XTE
J1118+480.


title: Double Scaling in Tensor Models with a Quartic Interaction

abstract:
  In this paper we identify and analyze in detail the subleading contributions
in the 1/N expansion of random tensors, in the simple case of a quartically
interacting model. The leading order for this 1/N expansion is made of graphs,
called melons, which are dual to particular triangulations of the D-dimensional
sphere, closely related to the "stacked" triangulations. For D<6 the subleading
behavior is governed by a larger family of graphs, hereafter called cherry
trees, which are also dual to the D-dimensional sphere. They can be resummed
explicitly through a double scaling limit. In sharp contrast with random matrix
models, this double scaling limit is stable. Apart from its unexpected upper
critical dimension 6, it displays a singularity at fixed distance from the
origin and is clearly the first step in a richer set of yet to be discovered
multi-scaling limits.


title: Analytic solution of the dynamics of quantum vortex reconnection

abstract:
  Experimental and simulational studies of the dynamics of vortex reconnections
in quantum fluids showedthat the distance $d$ between the reconnecting vortices
is close to a universal time dependence $d=D[\kappa|t_0-t|]^\alpha$ with
$\alpha$ fluctuating around 1/2 and $\kappa=h/m$ is the quantum of circulation.
Dimensional analysis, based on the assumption that the quantum of circulation
$\kappa=h/m$ is the only relevant parameter in the problem, predicts
$\alpha=1/2$. The theoretical calculation of the dimensionless coefficient $D$
in this formula remained an open problem. In this Letter we present an analytic
calculation of $D$ in terms of the given geometry of the reconnecting vortices.
We start from the numerically observed generic geometry on the way to vortex
reconnection and demonstrate that the dynamics is well described by a
self-similar analytic solution which provides the wanted information.


title:
X-ray embedded stars as driving sources of outflow-driven turbulence in
  OMC1-S

abstract:
  Outflows arising from very young stars affect their surroundings and
influence the star formation in the parental core. Multiple molecular outflows
and Herbig-Haro (HH) objects have been observed in Orion, many of them
originating from the embedded massive star-forming region known as OMC1-S. The
detection of the outflow driving sources is commonly difficult, because they
are still hidden behind large extinction, preventing their direct observation
at optical and even near and mid-IR wavelengths. With the aim of improving the
identification of the driving sources of the multiple outflows detected in
OMC1-S, we used the catalog provided by deep X-ray observations, which have
unveiled the very embedded population of pre-main sequence stars. We compared
the position of stars observed by the Chandra Orion Ultra Deep project (COUP)
in OMC1-S with the morphology of the molecular outflows and the directions of
measured proper motions of HH optical objects. We find that 6 out of 7
molecular outflows reported in OMC1-S (detection rate of 86 %) have an
extincted X-ray COUP star located at the expected position of the driving
source. In several cases, X-rays detected the possible driving sources for the
first time. This clustered embedded population revealed by Chandra is very
young, with an estimated average age of few 10^{5} yr. It is also likely
responsible for the multiple HH objects, which are the optical correspondence
of flows arising from the cloud. We show that the molecular outflows driven by
the members of the OMC1-S cluster can account for the observed turbulence at
core-scales and regulate the star formation efficiency. We discuss the effects
of outflow feedback in the formation of massive stars, concluding that the
injected turbulence in OMC1-S is compatible with a competitive accretion
scenario.


title: Large time blow up for a perturbation of the cubic Szeg\H{o} equation

abstract:
  We consider the following Hamiltonian equation on a special manifold of
rational functions, \[i\p\_tu=\Pi(|u|^2u)+\al (u|1),\ \al\in\R,\] where $\Pi $
denotes the Szeg\H{o} projector on the Hardy space of the circle $\SS^1$. The
equation with $\al=0$ was first introduced by G{\'e}rard and Grellier in
\cite{GG1} as a toy model for totally non dispersive evolution equations. We
establish the following properties for this equation. For $\al\textless{}0$,
any compact subset of initial data leads to a relatively compact subset of
trajectories. For $\al\textgreater{}0$, there exist trajectories on which high
Sobolev norms exponentially grow with time.


title:
Exact 3D solution for static and damped harmonic response of simply
  supported general laminates

abstract:
  The state-space method is adapted to obtain three dimensional exact solutions
for the static and damped dynamic behaviors of simply supported general
laminates. The state-space method is written in a general form that permits to
handle both cross-ply and antisymmetric angle-ply laminates. This general form
also permits to obtain exact solutions for general laminates, albeit with some
constraints. For the general case and for the static behavior, either an
additive term is added to the load to simulate simply supported boundary
conditions, or the plate bends in a particular way. For the dynamic behavior,
the general case leads to pairs of natural frequencies for each order, with
associated mode shapes. Finite element simulations have been performed to
validate most of the results presented in this study. As the boundary
conditions needed for the general case are not so straightforward, a specific
discussion has been added. It is shown that these boundary conditions also work
for the two aforementioned laminate classes. The damped harmonic response of a
non symmetrical isotropic sandwich is studied for different frequencies around
the fundamental frequency. The static and undamped dynamic behaviors of the
[-15/15], [0/30/0] and [-10/0/40] laminates are studied for various
length-to-thickness ratios.


title:
Comparison bewteen multi-task and single-task oracle risks in kernel
  ridge regression

abstract:
  In this paper we study multi-task kernel ridge regression and try to
understand when the multi-task procedure performs better than the single-task
one, in terms of averaged quadratic risk. In order to do so, we compare the
risks of the estimators with perfect calibration, the \emph{oracle risk}. We
are able to give explicit settings, favorable to the multi-task procedure,
where the multi-task oracle performs better than the single-task one. In
situations where the multi-task procedure is conjectured to perform badly, we
also show the oracle does so. We then complete our study with simulated
examples, where we can compare both oracle risks in more natural situations. A
consequence of our result is that the multi-task ridge estimator has a lower
risk than any single-task estimator, in favorable situations.


title: Expected topology of random real algebraic submanifolds

abstract:
  Let X be a smooth complex projective manifold of dimension n equipped with an
ample line bundle L and a rank k holomorphic vector bundle E. We assume that 0<
k <=n, that X, E and L are defined over the reals and denote by RX the real
locus of X. Then, we estimate from above and below the expected Betti numbers
of the vanishing loci in RX of holomorphic real sections of E tensored with
L^d, where d is a large enough integer. Moreover, given any closed connected
codimension k submanifold S of R^n with trivial normal bundle, we prove that a
real section of E tensored with L^d has a positive probability, independent of
d, to contain around the square root of d^n connected components diffeomorphic
to S in its vanishing locus.


title:
Physics at the CLIC e+e- Linear Collider -- Input to the Snowmass
  process 2013

abstract:
  This paper summarizes the physics potential of the CLIC high-energy e+e-
linear collider. It provides input to the Snowmass 2013 process for the
energy-frontier working groups on The Higgs Boson (HE1), Precision Study of
Electroweak Interactions (HE2), Fully Understanding the Top Quark (HE3), as
well as The Path Beyond the Standard Model -- New Particles, Forces, and
Dimensions (HE4). It is accompanied by a paper describing the CLIC accelerator
study, submitted to the Frontier Capabilities group of the Snowmass process.

categories: hep-ex hep-ph physics.acc-ph physics.ins-det


title: The KATRIN Experiment: Status and Outlook

abstract:
  The KATRIN experiment, presently under construction in Karlsruhe, Germany,
will improve on previous laboratory limits on the neutrino mass by a factor of
ten. KATRIN will use a high-activity, gaseous T2 source and a very
high-resolution spectrometer to measure the shape of the high-energy tail of
the tritium-decay beta spectrum. The shape measurement will also be sensitive
to new physics, including sterile neutrinos and Lorentz violation. This report
summarizes recent progress in the experiment.


title: Jamming-Resistant Learning in Wireless Networks

abstract:
  We consider capacity maximization in wireless networks under adversarial
interference conditions. There are n links, each consisting of a sender and a
receiver, which repeatedly try to perform a successful transmission. In each
time step, the success of attempted transmissions depends on interference
conditions, which are captured by an interference model (e.g. the SINR model).
Additionally, an adversarial jammer can render a (1-delta)-fraction of time
steps unsuccessful. For this scenario, we analyze a framework for distributed
learning algorithms to maximize the number of successful transmissions. Our
main result is an algorithm based on no-regret learning converging to an
O(1/delta)-approximation. It provides even a constant-factor approximation when
the jammer exactly blocks a (1-delta)-fraction of time steps. In addition, we
consider a stochastic jammer, for which we obtain a constant-factor
approximation after a polynomial number of time steps. We also consider more
general settings, in which links arrive and depart dynamically, and where each
sender tries to reach multiple receivers. Our algorithms perform favorably in
simulations.


title:
Spin squeezing and EPR entanglement of two bimodal condensates in
  state-dependent potentials

abstract:
  We propose and analyze a scheme to entangle the collective spin states of two
spatially separated bimodal Bose-Einstein condensates. Using a four-mode
approximation for the atomic field, we show that elastic collisions in a
state-dependent potential simultaneously create spin-squeezing in each
condensate and entangle the collective spins of the two condensates. We
investigate mostly analytically the non-local quantum correlations that arise
in this system at short times and show that Einstein-Podolsky-Rosen (EPR)
entanglement is generated between the condensates. At long times we point out
macroscopic entangled states and explain their structure. The scheme can be
implemented with condensates in state-dependent microwave potentials on an atom
chip.


title:
Impact of a body against a rigid wall. Problem involving non-smooth and
  history dependent energy dissipation mechanism

abstract:
  We study the impact of a body against a rigid wall. The body consists of a
rigid block and a viscoelastic rod described by the fractional Zener model.
Translatory motion of a body is influenced by the dry friction, described by
the set-valued Coulomb friction law. The problem is treated analytically by the
use of the Laplace transform method and solutions are obtained in a convolution
form. These solutions are compared with the ones obtained by using the
numerical method.


title: H\"older-Zygmund Estimates for Degenerate Parabolic Systems

abstract:
  We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien
system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the
case $p\geq 2$ that if the right hand side $g$ is locally in
$L^\infty(\text{BMO})$, then $u$ is locally in $L^\infty(\mathcal{C}^1)$, where
$\mathcal{C}^1$ is the 1-H\"older--Zygmund space. This is the borderline case
of the Calder\'on-Zygmund theorey. We provide local quantitative estimates. We
also show that finer properties of $g$ are conserved by $D u$, e.g.\ H\"older
continuity.
  Moreover, we prove a new decay for gradients of $p$-caloric solutions for all
$\frac{2n}{n+2}<p<\infty$.


title:
Geometry of normal graphs in Euclidean space and applications to the
  Penrose inequality in Minkowski

abstract:
  The Penrose inequality in Minkowski is a geometric inequality relating the
total outer null expansion and the area of closed, connected and spacelike
codimension-two surfaces S in the Minkowski spacetime, subject to an additional
convexity assumption. In a recent paper, Brendle and Wang find a sufficient
condition for the validity of this Penrose inequality in terms of the geometry
of the orthogonal projection of S onto a constant time hyperplane. In this
work, we study the geometry of hypersurfaces in n-dimensional euclidean space
which are normal graphs over other surfaces and relate the intrinsic and
extrinsic geometry of the graph with that of the base hypersurface. These
results are used to rewrite Brendle and Wang's condition explicitly in terms of
the time height function of S over a hyperplane and the geometry of the
projection of S along its past null cone onto this hyperplane. We also include,
in an Appendix, a self-contained summary of known and new results on the
geometry of projections along the Killing direction of codimension
two-spacelike surfaces in a strictly static spacetime.


title:
A decomposition based proof for fast mixing of a Markov chain over
  balanced realizations of a joint degree matrix

abstract:
  A joint degree matrix (JDM) specifies the number of connections between nodes
of given degrees in a graph, for all degree pairs and uniquely determines the
degree sequence of the graph. We consider the space of all balanced
realizations of an arbitrary JDM, realizations in which the links between any
two degree groups are placed as uniformly as possible. We prove that a swap
Markov Chain Monte Carlo (MCMC) algorithm in the space of all balanced
realizations of an {\em arbitrary} graphical JDM mixes rapidly, i.e., the
relaxation time of the chain is bounded from above by a polynomial in the
number of nodes $n$. To prove fast mixing, we first prove a general
factorization theorem similar to the Martin-Randall method for disjoint
decompositions (partitions). This theorem can be used to bound from below the
spectral gap with the help of fast mixing subchains within every partition and
a bound on an auxiliary Markov chain between the partitions. Our proof of the
general factorization theorem is direct and uses conductance based methods
(Cheeger inequality).


title: First-Come-First-Served for Online Slot Allocation and Huffman Coding

abstract:
  Can one choose a good Huffman code on the fly, without knowing the underlying
distribution? Online Slot Allocation (OSA) models this and similar problems:
There are n slots, each with a known cost. There are n items. Requests for
items are drawn i.i.d. from a fixed but hidden probability distribution p.
After each request, if the item, i, was not previously requested, then the
algorithm (knowing the slot costs and the requests so far, but not p) must
place the item in some vacant slot j(i). The goal is to minimize the sum, over
the items, of the probability of the item times the cost of its assigned slot.
  The optimal offline algorithm is trivial: put the most probable item in the
cheapest slot, the second most probable item in the second cheapest slot, etc.
The optimal online algorithm is First Come First Served (FCFS): put the first
requested item in the cheapest slot, the second (distinct) requested item in
the second cheapest slot, etc. The optimal competitive ratios for any online
algorithm are 1+H(n-1) ~ ln n for general costs and 2 for concave costs. For
logarithmic costs, the ratio is, asymptotically, 1: FCFS gives cost opt + O(log
opt).
  For Huffman coding, FCFS yields an online algorithm (one that allocates
codewords on demand, without knowing the underlying probability distribution)
that guarantees asymptotically optimal cost: at most opt + 2 log(1+opt) + 2.


title:
$Q$-polynomial distance-regular graphs and a double affine Hecke algebra
  of rank one

abstract:
  We study a relationship between $Q$-polynomial distance-regular graphs and
the double affine Hecke algebra of type $(C^{\vee}_1,C_1)$. Let $\Gamma$ denote
a $Q$-polynomial distance-regular graph with vertex set $X$. We assume that
$\Gamma$ has $q$-Racah type and contains a Delsarte clique $C$. Fix a vertex $x
\in C$. We partition $X$ according to the path-length distance to both $x$ and
$C$. This is an equitable partition. For each cell in this partition, consider
the corresponding characteristic vector. These characteristic vectors form a
basis for a $\mathbb{C}$-vector space ${\bf W}$.
  The universal double affine Hecke algebra of type $(C^{\vee}_1,C_1)$ is the
$\mathbb{C}$-algebra $\hat{H}_q$ defined by generators $\{t^{\pm1}_n\}^3_{n=0}$
and relations (i) $t_nt_n^{-1}=t_n^{-1}t_n=1$; (ii) $t_n+t_n^{-1}$ is central;
(iii) $t_0t_1t_2t_3 = q^{-1/2}$. In this paper, we display an
$\hat{H}_q$-module structure for ${\bf W}$. For this module and up to affine
transformation, (i) $t_0t_1+(t_0t_1)^{-1}$ acts as the adjacency matrix of
$\Gamma$; (ii) $t_3t_0+(t_3t_0)^{-1}$ acts as the dual adjacency matrix of
$\Gamma$ with respect to $C$; (iii) $t_1t_2+(t_1t_2)^{-1}$ acts as the dual
adjacency matrix of $\Gamma$ with respect to $x$. To obtain our results we use
the theory of Leonard systems.


title: Scale-invariance as the origin of dark radiation?

abstract:
  Recent cosmological data favour R^2-inflation and some amount of non-standard
dark radiation in the Universe. We show that a framework of high energy scale
invariance can explain these data. The spontaneous breaking of this symmetry
provides gravity with the Planck mass and particle physics with the electroweak
scale. We found that the corresponding massless Nambu--Goldstone bosons --
dilatons -- are produced at reheating by the inflaton decay right at the amount
needed to explain primordial abundances of light chemical elements and
anisotropy of the cosmic microwave background. Then we extended the discussion
on the interplay with Higgs-inflation and on general class of inflationary
models where dilatons are allowed and may form the dark radiation. As a result
we put a lower limit on the reheating temperature in a general scale invariant
model of inflation.


title: Polymatroid Prophet Inequalities

abstract:
  Consider a gambler and a prophet who observe a sequence of independent,
non-negative numbers. The gambler sees the numbers one-by-one whereas the
prophet sees the entire sequence at once. The goal of both is to decide on
fractions of each number they want to keep so as to maximize the weighted
fractional sum of the numbers chosen.
  The classic result of Krengel and Sucheston (1977-78) asserts that if both
the gambler and the prophet can pick one number, then the gambler can do at
least half as well as the prophet. Recently, Kleinberg and Weinberg (2012) have
generalized this result to settings where the numbers that can be chosen are
subject to a matroid constraint.
  In this note we go one step further and show that the bound carries over to
settings where the fractions that can be chosen are subject to a polymatroid
constraint. This bound is tight as it is already tight for the simple setting
where the gambler and the prophet can pick only one number. An interesting
application of our result is in mechanism design, where it leads to improved
results for various problems.


title: Detecting a trend change in cross-border epidemic transmission

abstract:
  A method for detecting a trend change in cross-border epidemic transmission
is developed for a standard epidemiological SIR compartment model and a
meta-population network model. The method is applicable to investigating the
efficacy of the implemented public health intervention in managing infectious
travelers across borders from a time series of the number of new cases reported
in multiple geographical regions. It is found that the change point of the
probability of travel movements was one week after the WHO worldwide alert on
the SARS outbreak in 2003. The alert was effective in managing infectious
travelers. On the other hand, it is found that the probability of travel
movements did not change at all for the flu pandemic in 2009. The pandemic did
not affect potential travelers despite the WHO alert.


title:
Gauge turbulence, topological defect dynamics, and condensation in Higgs
  models

abstract:
  The real-time dynamics of topological defects and turbulent configurations of
gauge fields for electric and magnetic confinement are studied numerically
within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in
such systems equilibrating after a strong initial quench such as the
overpopulation of the infrared modes. While the final equilibrium state does
not support confinement, metastable vortex defect configurations appear in the
gauge field which are found to be closely related to the appearance of
physically observable confined electric and magnetic charges. These phenomena
are seen to be intimately related to the approach of a non-thermal fixed point
of the far-from-equilibrium dynamical evolution, signalled by universal scaling
in the gauge-invariant correlation function of the Higgs field. Even when the
parameters of the Higgs action do not support condensate formation in the
vacuum, during this approach, transient Higgs condensation is observed. We
discuss implications of these results for the far-from-equilibrium dynamics of
Yang-Mills fields and potential mechanisms how confinement and condensation in
non-abelian gauge fields can be understood in terms of the dynamics of Higgs
models. These suggest that there is an interesting new class of dynamics of
strong coherent turbulent gauge fields with condensates.

categories: hep-ph cond-mat.quant-gas hep-lat nucl-th


title: Kernel Adaptive Metropolis-Hastings

abstract:
  A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the
purpose of sampling from a target distribution with strongly nonlinear support.
The algorithm embeds the trajectory of the Markov chain into a reproducing
kernel Hilbert space (RKHS), such that the feature space covariance of the
samples informs the choice of proposal. The procedure is computationally
efficient and straightforward to implement, since the RKHS moves can be
integrated out analytically: our proposal distribution in the original space is
a normal distribution whose mean and covariance depend on where the current
sample lies in the support of the target distribution, and adapts to its local
covariance structure. Furthermore, the procedure requires neither gradients nor
any other higher order information about the target, making it particularly
attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive
Metropolis-Hastings outperforms competing fixed and adaptive samplers on
multivariate, highly nonlinear target distributions, arising in both real-world
and synthetic examples. Code may be downloaded at
https://github.com/karlnapf/kameleon-mcmc.