title: On the Reproducibility of TCGA Ovarian Cancer MicroRNA Profiles

abstract:
  Dysregulated microRNA (miRNA) expression is a well-established feature of
human cancer. However, the role of specific miRNAs in determining cancer
outcomes remains unclear. Using Level 3 expression data from the Cancer Genome
Atlas (TCGA), we identified 61 miRNAs that are associated with overall survival
in 469 ovarian cancers profiled by microarray (p<0.01). We also identified 12
miRNAs that are associated with survival when miRNAs were profiled in the same
specimens using Next Generation Sequencing (miRNA-Seq) (p<0.01). Surprisingly,
only 1 miRNA transcript is associated with ovarian cancer survival in both
datasets. Our analyses indicate that this discrepancy is due to the fact that
miRNA levels reported by the two platforms correlate poorly, even after
correcting for potential issues inherent to signal detection algorithms.
Further investigation is warranted.


title: Tunnelling current through fractional quantum Hall interferometers

abstract:
  We calculate the tunnelling current through a Fabry-P\'{e}rot interferometer
in the fractional quantum Hall regime. Within linear response theory (weak
tunnelling but arbitrary source-drain voltage) we find a general expression for
the current due to tunnelling of quasiparticles in terms of Carlson's $R$
function. Our result is valid for fractional quantum Hall states with an edge
theory consisting of a charged channel and any number of neutral channels, with
possibly different edge velocities and different chiralities. We analyse the
case with a single neutral channel in detail, which applies for instance to the
edge of the Moore-Read state. In addition we consider an asymmetric
interferometer with different edge lengths between the point contacts on
opposite edges, and we study the behaviour of the current as a function of
varying edge length. Recent experiments attempted to measure the Aharanov-Bohm
effect by changing the area inside the interferometer using a plunger gate.
Theoretical analyses of these experiments have so far not taken into account
the accompanying change in the edge lengths. We show that the tunnelling
current exhibits multiple osculations as a function of this edge length, with
frequencies proportional to the injected edge current and inversely
proportional to the edge velocities. In particular the edge velocities can be
measured by looking at the Fourier spectrum of the edge current. We provide a
numerical scheme to calculate and plot the $R$ function, and include sample
plots for a variety of edge states with parameter values which are
experimentally relevant.


title:
Coherent topological defect dynamics and collective modes in
  superconductors and electronic crystals

abstract:
  The control of condensed matter systems out of equilibrium by laser pulses
allows us to investigate the system trajectories through symmetry-breaking
phase transitions. Thus the evolution of both collective modes and single
particle excitations can be followed through diverse phase transitions with
femtosecond resolution. Here we present experimental observations of the order
parameter trajectory in the normal-superconductor transition and charge-density
wave ordering transitions. Of particular interest is the coherent evolution of
topological defects forming during the transition via the Kibble-Zurek
mechanism, which appears to be measurable in optical pump probe experiments.
Experiments on CDW systems reveal some new phenomena, such as coherent
oscillations of the order parameter, the creation and emission of dispersive
amplitudon modes upon the annihilation of topological defects, and mixing with
weakly coupled finite-frequency (massive) bosons.


title:
A Deterministic Annealing Approach to Optimization of Zero-delay
  Source-Channel Codes

abstract:
  This paper studies optimization of zero-delay source-channel codes, and
specifically the problem of obtaining globally optimal transformations that map
between the source space and the channel space, under a given transmission
power constraint and for the mean square error distortion. Particularly, we
focus on the setting where the decoder has access to side information, whose
cost surface is known to be riddled with local minima. Prior work derived the
necessary conditions for optimality of the encoder and decoder mappings, along
with a greedy optimization algorithm that imposes these conditions iteratively,
in conjunction with the heuristic "noisy channel relaxation" method to mitigate
poor local minima. While noisy channel relaxation is arguably effective in
simple settings, it fails to provide accurate global optimization results in
more complicated settings including the decoder with side information as
considered in this paper. We propose a global optimization algorithm based on
the ideas of "deterministic annealing"- a non-convex optimization method,
derived from information theoretic principles with analogies to statistical
physics, and successfully employed in several problems including clustering,
vector quantization and regression. We present comparative numerical results
that show strict superiority of the proposed algorithm over greedy optimization
methods as well as over the noisy channel relaxation.


title:
Bialgebra structure on Bridgeland's Hall algebra of two-periodic
  complexes

abstract:
  We study the bialgebra structure of the Hall algebra of two-periodic
complexes recently introduced by Bridgeland. We introduce coproduct on
Bridgeland's Hall algebra, and show that in the hereditary case the resulting
bialgebra structure coincides with that on Drinfeld double of the ordinary Hall
algebra


title:
\Lambda-enhanced Sub-Doppler Cooling of Lithium Atoms in D1 Gray
  Molasses

abstract:
  Following the bichromatic sub-Doppler cooling scheme on the D1 line of 40K
recently demonstrated in (Fernandes et al. 2012), we introduce a similar
technique for 7Li atoms and obtain temperatures of 60 uK while capturing all of
the 5x10^8 atoms present from the previous stage. We investigate the influence
of the detuning between the the two cooling frequencies and observe a threefold
decrease of the temperature when the Raman condition is fulfilled. We interpret
this effect as arising from extra cooling due to long-lived coherences between
hyperfine states. Solving the optical Bloch equations for a simplified,
\Lambda-type three-level system we identify the presence of an efficient
cooling force near the Raman condition. After transfer into a quadrupole
magnetic trap, we measure a phase space density of ~10^-5. This laser cooling
offers a promising route for fast evaporation of lithium atoms to quantum
degeneracy in optical or magnetic traps.


title:
Fermi bubble $\gamma$-rays as a result of diffusive injection of
  Galactic cosmic rays

abstract:
  Recently, the {\it{Fermi}} space telescope has discovered two large
$\gamma$-ray emission regions, the so-called "Fermi bubbles", that extend up to
$\sim 50^\circ$ above and below the Galactic center. The $\gamma$-ray emission
from the bubbles are found to follow a hard spectrum with no significant
spatial variation in intensity and spectral shape. The origin of the emission
is still not clearly understood. Suggested explanations include injection of
cosmic-ray nuclei from the Galactic center by high-speed Galactic winds,
electron acceleration by multiple shocks and stochastic electron acceleration
inside the bubbles. In this letter, it is proposed that the $\gamma$-rays can
be the result of diffusive injection of Galactic cosmic-ray protons during
their propagation through the Galaxy. Considering that the bubbles are slowly
expanding, and cosmic rays undergo much slower diffusion inside the bubbles
than in the averaged Galaxy and at the same time suffer losses due to adiabatic
expansion and inelastic collisions with the bubble plasma, this model can
explain the observed intensity profile, the emission spectrum and the measured
luminosity without invoking any additional particle production processes unlike
other existing models.


title: The ubiquity of Psi-matroids

abstract:
  Solving (for tame matroids) a problem of Aigner-Horev, Diestel and Postle, we
prove that every tame matroid M can be reconstructed from its canonical tree
decomposition into 3-connected pieces, circuits and cocircuits together with
information about which ends of the decomposition tree are used by M .
  For every locally finite graph G, we show that every tame matroid whose
circuits are topological circles of G and whose cocircuits are bonds of G is
determined by the set Psi of ends it uses, that is, it is a Psi-matroid.


title: On a fat small object argument

abstract:
  Good colimits introduced by J. Lurie generalize transfinite composites and
provide an important tool for understanding cofibrant generation in locally
presentable categories. We will explore the relation of good colimits to
transfinite composites further and show, in particular, how they eliminate the
use of large objects in the usual small object argument.


title: Solar Superabsorption of Semiconductor Materials

abstract:
  We theoretically demonstrate the fundamental limit in volume for given
materials (e.g. Si, a-Si, CdTe) to fully absorb the solar radiation above
bandgap, which we refer as solar superabsorption limit. We also point out the
general principles for experimentally designing light trapping structures to
approach the superabsorption. This study builds upon an intuitive model,
coupled leaky mode theory (CLMT), for the analysis of light absorption in
nanostructures. The CLMT provides a useful variable transformation. Unlike the
existing methods that rely on information of physical features (e.g.
morphology, dimensionality) to analyze light absorption, the CLMT can evaluate
light absorption in given materials with only two variables, the radiative loss
and the resonant wavelength, of leaky modes, regardless the physical features
of the materials. This transformation allows for surveying the entire variable
space to find out the solar superabsorption and provides physical insights to
guide the design of solar superabsorbing structures.


title:
Constraints on anomalous color dipole operators from Higgs boson
  production at the LHC

abstract:
  Physics beyond the standard model (SM) can be parameterized with an effective
Lagrangian that respects the symmetries of the standard model and contains many
operators of dimension six. We consider the subset of these operators that is
responsible for flavor diagonal anomalous color magnetic (CMDM) and electric
(CEDM) dipole couplings between quarks and gluons. Invariance of these
operators under the SM implies that they contribute to Higgs boson production
at the LHC and we study the corresponding constraints that can be placed on
them. For the case of the top-quark we first review constraints from top-quark
pair production and decay, and then compare them to what can be achieved by
studying $t\bar{t}h$ production. We also constrain the corresponding couplings
for $b$-quarks and light quarks by studying $pp \to b\bar{b}h$ and $pp \to hX$
respectively.


title:
Production of J/psi and Upsilon mesons in pp collisions at sqrt(s) = 8
  TeV

abstract:
  The production of J/psi and Upsilon mesons in pp collisions at sqrt(s) = 8
TeV is studied with the LHCb detector. The J/psi and Upsilon mesons are
reconstructed in the mu+mu- decay mode and the signal yields are determined
with a fit to the mu+mu- invariant mass distributions. The analysis is
performed in the rapidity range 2.0<y<4.5 and transverse momentum range
0<p_T<14(15) GeV/c of the J/psi(Upsilon) mesons. The J/psi and Upsilon
production cross-sections and the fraction of J/psi mesons from b-hadron decays
are measured as a function of the meson p_T and y.


title: A local-global principle for the telescope conjecture

abstract:
  We prove an etale local-global principle for the telescope conjecture and use
it to show that the telescope conjecture holds for derived categories of
Azumaya algebras on noetherian schemes as well as for many classifying stacks
and gerbes. This specializes to give another proof of the fact that the
telescope conjecture holds for noetherian schemes.


title: Rank of divisors on hyperelliptic curves and graphs under specialization

abstract:
  Let $(G, \omega)$ be a hyperelliptic vertex-weighted graph of genus $g \geq
2$. We give a characterization of $(G, \omega)$ for which there exists a smooth
projective curve $X$ of genus $g$ over a complete discrete valuation field with
reduction graph $(G, \omega)$ such that the ranks of any divisors are preserved
under specialization. We explain, for a given vertex-weighted graph $(G,
\omega)$ in general, how the existence of such $X$ relates the Riemann--Roch
formulae for $X$ and $(G, \omega)$, and also how the existence of such $X$ is
related to a conjecture of Caporaso.


title: Berezinskii-Kosterlitz-Thouless transition in a photonic lattice

abstract:
  Phase transitions give crucial insight into many-body systems, as crossovers
between different regimes of order are determined by the underlying dynamics.
These dynamics, in turn, are often constrained by dimensionality and geometry.
For example, in one- and two-dimensional systems with continuous symmetry,
thermal fluctuations prevent the formation of long-range order[1,2].
Two-dimensional systems are particularly significant, as vortices can form in
the plane but cannot tilt out of it. At high temperatures, random motion of
these vortices destroys large-scale coherence. At low temperatures, vortices
with opposite spin can pair together, cancelling their circulation and allowing
quasi-long-range order to appear. This Berezenskii-Kosterlitz-Thouless (BKT)
transition[3,4] is essentially classical, arising for example in the
traditional XY model for spins, but to date experimental evidence has been
obtained only in cold quantum systems. Measurements of superfluid sound
speed[5] and critical velocity[6] have been consistent with scaling
predictions, and vortices have been observed directly in cold atom
experiments[7,8]. However, the presence of trapping potentials restricts
measurement to vortex density, rather than number, and obscures the process of
vortex unbinding. Further, atom and fluid experiments suffer from parasitic
heating and difficulties in phase recording, leading to results that differ
from theory in many quantitative aspects. Here, we use a nonlinear optical
system to directly observe the ideal BKT transition, including vortex pair
dynamics and the correlation properties of the wavefunction, for both repulsive
and attractiveinteractions (the photonic equivalent of ferromagnetic and
antiferromagnetic conditions[9]). The results confirm the thermodynamics of the
BKT transition and expose outstanding issues in the crossovers to superfluidity
and Bose-Einstein condensation.


title: Magnetohydrodynamic Modeling of the Solar Eruption on 2010 April 8

abstract:
  The structure of the coronal magnetic field prior to eruptive processes and
the conditions for the onset of eruption are important issues that can be
addressed through studying the magnetohydrodynamic stability and evolution of
nonlinear force-free field (NLFFF) models. This paper uses data-constrained
NLFFF models of a solar active region that erupted on 2010 April 8 as initial
condition in MHD simulations. These models, constructed with the techniques of
flux rope insertion and magnetofrictional relaxation, include a stable, an
approximately marginally stable, and an unstable configuration. The simulations
confirm previous related results of magnetofrictional relaxation runs, in
particular that stable flux rope equilibria represent key features of the
observed pre-eruption coronal structure very well and that there is a limiting
value of the axial flux in the rope for the existence of stable NLFFF
equilibria. The specific limiting value is located within a tighter range, due
to the sharper discrimination between stability and instability by the MHD
description. The MHD treatment of the eruptive configuration yields very good
agreement with a number of observed features like the strongly inclined initial
rise path and the close temporal association between the coronal mass ejection
and the onset of flare reconnection. Minor differences occur in the velocity of
flare ribbon expansion and in the further evolution of the inclination; these
can be eliminated through refined simulations. We suggest that the slingshot
effect of horizontally bent flux in the source region of eruptions can
contribute significantly to the inclination of the rise direction. Finally, we
demonstrate that the onset criterion formulated in terms of a threshold value
for the axial flux in the rope corresponds very well to the threshold of the
torus instability in the considered active region.


title:
Scalar fluctuations of the scalar metric during inflation from a
  non-perturbative 5D large-scale repulsive gravity model

abstract:
  We develop a non-perturbative formalism for scalar metric fluctuations from a
5D extended version of general relativity in vacuum. In this work we
concentrate our efforts on calculations valid on large cosmological scales,
which are the dominant during the inflationary phase of the universe. The
resulting metric in this limit is obtained after implementing a planar
coordinate transformation on a 5D Ricci-flat metric solution. We calculate the
spectrum of these fluctuations with an effective 4D Schwarzschild-de Sitter
spacetime on cosmological scales, which is obtained after we make a static
foliation on the non-compact extra coordinate. Our results show how the squared
metric fluctuations of the primordial universe become scale invariant with the
inflationary expansion.


title: Algebraic semantics for a modal logic close to S1

abstract:
  The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict
implication. While there are Kripke semantics for S2 and S3, there is no known
natural semantics for S1. We extend S1 by a Substitution Principle SP which
generalizes a reference rule of S1. In system S1+SP, the relation of strict
equivalence $\varphi\equiv\psi$ satisfies the identity axioms of R. Suszko's
non-Fregean logic adapted to the language of modal logic (we call these axioms
the axioms of propositional identity). This enables us to develop a framework
of algebraic semantics which captures S1+SP as well as the Lewis systems
S3--S5. So from the viewpoint of algebraic semantics, S1+SP turns out to be an
interesting modal logic. We show that S1+SP is strictly contained between S1
and S3 and differs from S2. It is the weakest modal logic containing S1 such
that strict equivalence is axiomatized by propositional identity.


title:
Cosmological constraints from baryon acoustic oscillations and
  clustering of large-scale structure

abstract:
  We constrain cosmological parameters using combined measurements of the
baryon acoustic oscillation (BAO) feature in the correlation function of
galaxies and Ly-\alpha absorbers that together cover 0.1 < z < 2.4. The BAO
position measurements alone -- without fixing the absolute sound horizon
`standard ruler' length with cosmic microwave background (CMB) data --
constrain \Omega_m = 0.303 +/- 0.040 (68 per cent confidence) for a flat
\Lambda CDM model, and w = -1.06^{+0.33}_{-0.32}, \Omega_m =
0.292^{+0.045}_{-0.040} for a flat wCDM model. Adding other large-scale
structure (LSS) clustering constraints -- correlation function shape, the
Alcock-Paczynski test and growth rate information -- to the BAO considerably
tightens constraints (\Omega_m = 0.290 +/- 0.019, H_0 = 67.5 +/- 2.8 km s^{-1}
Mpc^{-1}, \sigma_8 = 0.80 +/- 0.05 for \Lambda CDM, and w = -1.14 +/- 0.19 for
wCDM). The LSS data mildly prefer a lower value of H_0, and a higher value of
\Omega_m, than local distance ladder and type IA supernovae (SNe) measurements,
respectively. While tension in the combined CMB, SNe and distance ladder data
appears to be relieved by allowing w < -1, this freedom introduces tension with
the LSS \sigma_8 constraint from the growth rate of matter fluctuations. The
combined constraint on w from CMB, BAO and LSS clustering for a flat wCDM model
is w = -1.03 +/- 0.06.


title:
On an Inversion Theorem for Stratonovich's Signatures of
  Multidimensional Diffusion Paths

abstract:
  In the present paper, we prove that with probability one, the Stratonovich
signatures of a multidimensional diffusion process (possibly degenerate) over
[0,1], which is the collection of all iterated Stratonovich's integrals of the
diffusion process over [0,1], determine the diffusion sample paths.


title: On the Masami Yasuda stopping game

abstract:
  The sero-sum stopping game for the stochastic sequences has been formulated
in late sixties of the twenty century by Dynkin (1969). The formulation had the
assumption about separability of decision moment of the players which
simplified the construction of the solution. Further research by Neveu (1975)
extended the model by admitting more general behaviour of the players and their
pay--offs. In new formulation there is the problem with existence of the
equilibrium. The proper approach to solution of the problem without restriction
of former models was developed by Yasuda (1975). The results was crucial in
these research. The author made often reference to the Yasuda's (1985) result
in his works (see the author's papers (1993,1995)) as well as see results of
others stimulated by this paper. Withal, in this note another stopping game
model, developed by Yasuda with coauthors (see e.g. Kurano at al. (1980) and
the author and Yasuda (1995)) is recalled. The application of the model to an
analysis of system of detectors shows the power of the game theory methods.
  In the last part of the paper I would like to express my personal relation to
the Masami Yasuda game.


title:
Interaction between viscous varying modified cosmic Chaplygin gas and
  Tachyonic fluid

abstract:
  In this paper we study the interaction between the general form of viscous
varying modified cosmic Chaplygin gas and the Tachyon fluid in the framework of
Einstein gravity. We want to reconstruct the Tachyon potential and total
equation of state parameter graphically by using numerical methods. In the
presence of deceleration parameter, the interaction between components becomes
sign changeable to explain different evolutionary eras in the universe. We
review the potential and total equation of state parameter in Emergent,
Intermediate and Logamediate scenarios of scale factor numerically. Analysis of
total equation of state parameter show that, $\omega_{tot}<-1$ and
$\omega_{tot}>-1$ imply the phantom-like and quintessence-like behaviors
respectively. we have checked the effects of cosmic and viscosity elements on
the interaction process. Stability is checked in all the models by the squared
velocity of sound.


title: Lyapunov-type Inequalities for Partial Differential Equations

abstract:
  In this work we present a Lyapunov inequality for linear and quasilinear
elliptic differential operators in $N-$dimensional domains $\Omega$. We also
consider singular and degenerate elliptic problems with $A_p$ coefficients
involving the $p-$Laplace operator with zero Dirichlet boundary condition.
  As an application of the inequalities obtained, we derive lower bounds for
the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones
in the literature.


title: Tests of universal three-body physics in an ultracold Bose-Fermi mixture

abstract:
  Recent measurements of Efimov resonances in a number of ultracold atom
species have revealed an unexpected universality, in which three-body
scattering properties are determined by the van der Waals length of the
two-body interaction potential. To investigate whether this universality
extends to heteronuclear mixtures, we measure loss rate coefficients in an
ultracold trapped gas of $^{40}$K and $^{87}$Rb atoms. We find an Efimov-like
resonance in the rate of inelastic collisions between $^{40}$K$^{87}$Rb
Feshbach molecules and $^{87}$Rb atoms. However, we do not observe any
Efimov-related resonances in the rates of inelastic collisions between three
atoms. These observations are compared to previous measurements by the LENS
group of Efimov resonances in a $^{41}$K and $^{87}$Rb mixture as well as to
recent predictions.


title: Euclidean Upgrade from a Minimal Number of Segments

abstract:
  In this paper, we propose an algebraic approach to upgrade a projective
reconstruction to a Euclidean one, and aim at computing the rectifying
homography from a minimal number of 9 segments of known length. Constraints are
derived from these segments which yield a set of polynomial equations that we
solve by means of Gr\"obner bases. We explain how a solver for such a system of
equations can be constructed from simplified template data. Moreover, we
present experiments that demonstrate that the given problem can be solved in
this way.


title: A Geometric Approach Towards Momentum Conservation

abstract:
  In this work, a geometric discretization of the Navier-Stokes equations is
sought by treating momentum as a covector-valued volume-form. The novelty of
this approach is that we treat conservation of momentum as a tensor equation
and describe a higher order approximation to this tensor equation. The
resulting scheme satisfies mass and momentum conservation laws exactly, and
resembles a staggered-mesh finite-volume method. Numerical test-cases to which
the discretization scheme is applied are the Kovasznay flow, and lid-driven
cavity flow.


title:
Spin blocker made of semiconductor double quantum well using the Rashba
  effect

abstract:
  We propose a lateral spin-blockade device that uses an InGaAs/InAlAs double
quantum well (DQW), where the values of the Rashba spin-orbit parameter
$\alpha_{\rm R}$ are opposite in sign but equal in magnitude between the
constituent quantum wells (QW). By tuning the channel length of DQW and the
magnitude of the externally applied in-plane magnetic field, one can block the
transmission of one spin (e.g., spin-down) component, leading to a
spin-polarized current. Such a spin-blocking effect, brought about by wave
vector matching of the spin-split Fermi surfaces between the two QWs, paves the
way for a new scheme of spin-polarized electric current generation for future
spintronics applications based on semiconductor band engineering.


title:
Multi-site photometric campaign on the high amplitude {\delta} Scuti
  star KIC 6382916

abstract:
  We present results of a multi-site photometric campaign on the high-amplitude
$\delta$\,Scuti star KIC\,6382916 in the {\it Kepler} field. The star was
observed over a 85-d interval at five different sites in North America and
Europe during 2011. {\it Kepler} photometry and ground-based multicolour light
curves of KIC\,6382916 are used to investigate the pulsational content and to
identify the principal modes. High-dispersion spectroscopy was also obtained in
order to derive the stellar parameters and projected rotational velocity. From
an analysis of the {\it Kepler} time series, three independent frequencies and
a few hundred combination frequencies are found. The light curve is dominated
by two modes with frequencies $f_{1}$= 4.9107 and $f_{2}$= 6.4314\,d$^{-1}$.
The third mode with $f_{3}$= 8.0350\,d$^{-1}$ has a much lower amplitude. We
attempt mode identification by examining the amplitude ratios and phase
differences in different wavebands from multicolour photometry and comparing
them to calculations for different spherical harmonic degree, $l$. We find that
the theoretical models for $f_1$ and $f_2$ are in a best agreement with the
observations and lead to value of l = 1 modes, but the mode identification of
$f_3$ is uncertain due to its low amplitude. Non-adiabatic pulsation models
show that frequencies below 6\,d$^{-1}$ are stable, which means that the low
frequency of $f_1$ cannot be reproduced. This is further confirmation that
current models predict a narrower pulsation frequency range than actually
observed.


title: Sp\'eculation et auto-stabilisation

abstract:
  Self-stabilization ensures that, after any transient fault, the system
recovers in a finite time and eventually exhibits a correct behaviour.
Speculation consists in guaranteeing that the system satisfies its requirements
for any execution but exhibits significantly better performances for a subset
of executions that are more probable. A speculative protocol is in this sense
supposed to be both robust and efficient in practice. We introduce the notion
of speculative stabilization which we illustrate through the mutual exclusion
problem. We then present a novel speculatively stabilizing mutual exclusion
protocol. Our protocol is self-stabilizing for any asynchronous execution. We
prove that its stabilization time for synchronous executions is diam(g)/2 steps
(where diam(g) denotes the diameter of the system). This complexity result is
of independent interest. The celebrated mutual exclusion protocol of Dijkstra
stabilizes in n steps (where n is the number of processes) in synchronous
executions and the question whether the stabilization time could be strictly
smaller than the diameter has been open since then (almost 40 years). We show
that this is indeed possible for any underlying topology. We also provide a
lower bound proof that shows that our new stabilization time of diam(g)/2 steps
is optimal for synchronous executions, even if asynchronous stabilization is
not required.


title: Spectral Analysis of hypoelliptic random walks

abstract:
  We study the spectral theory of a reversible Markov chain associated to a
hypoelliptic random walk on a manifold M. This random walk depends on a
parameter h which is roughly the size of each step of the walk. We prove
uniform bounds with respect to h on the rate of convergence to equilibrium, and
the convergence when h goes to zero to the associated hypoelliptic diffusion.


title:
Virtual Delamination Testing through Non-Linear Multi-Scale
  Computational Methods: Some Recent Progress

abstract:
  This paper deals with the parallel simulation of delamination problems at the
meso-scale by means of multi-scale methods, the aim being the Virtual
Delamination Testing of Composite parts. In the non-linear context, Domain
Decomposition Methods are mainly used as a solver for the tangent problem to be
solved at each iteration of a Newton-Raphson algorithm. In case of strongly
nonlinear and heterogeneous problems, this procedure may lead to severe
difficulties. The paper focuses on methods to circumvent these problems, which
can now be expressed using a relatively general framework, even though the
different ingredients of the strategy have emerged separately. We rely here on
the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix,
2001). The method proposed in this paper introduces three additional features:
(i) the adaptation of the macro-basis to situations where classical
homogenization does not provide a good preconditioner, (ii) the use of
non-linear relocalization to decrease the number of global problems to be
solved in the case of unevenly distributed non-linearities, (iii) the
adaptation of the approximation of the local Schur complement which governs the
convergence of the proposed iterative technique. Computations of delamination
and delamination-buckling interaction with contact on potentially large
delaminated areas are used to illustrate those aspects.


title: Weak error expansion of the implicit Euler scheme

abstract:
  In this paper, we extend the Talay Tubaro theorem to the implicit Euler
scheme.


title: Sharpness of Rickman's Picard theorem in all dimensions

abstract:
  We show that given $n\ge 3$, $q\ge 1$, and a finite set $\{y_1,\ldots, y_q\}$
in $\mathbb R^n$ there exists a quasiregular mapping $\mathbb R^n \to \mathbb
R^n$ omitting exactly points $y_1,\ldots, y_q$.


title: Weak error in negative Sobolev spaces for the stochastic heat equation

abstract:
  In this paper, we make another step in the study of weak error of the
stochastic heat equation by considering norms as functional.


title:
On the redshift evolution (0 < z < 4) of dust attenuation and of the
  total (UV+IR) star formation rate density

abstract:
  Using new homogeneous LFs in the FUV and in the FIR Herschel/PEP and
Herschel/HerMES, we study the evolution of the dust attenuation with redshift.
With this information in hand, we are able to estimate the redshift evolution
of the total (FUV + FIR) star formation rate density SFRD_TOT. By integrating
SFRD_TOT, we follow the mass building and analyze the redshift evolution of the
stellar mass density (SMD). This letter aims at providing a complete view of
star formation from the local universe to z = 4 and, using assumptions on
earlier star formation history, compares this evolution to what was known
before in an attempt to draw a homogeneous picture of the global evolution of
star formation in galaxies.
  The main conclusions of this letter are: 1) the dust attenuation A_FUV is
found to increase from z = 0 to z \sim 1.2 and then starts to decrease up to
our last data point at z = 3.6; 2) the estimated SFRD confirms published
results up to z = 2. At z > 2, we observe either a plateau or a small increase
up to z = 3 and then a likely decrease up to z = 3.6; 3) the peak of A_FUV is
delayed with respect to the plateau of SFRD_TOT and a likely origin might be
found in the evolution of the bright ends of the FUV and FIR LFs; 4) using
assumptions (namely exponential rise and linear rise with time) for the
evolution of the star formation density from z = 3.6 to z_form = 10, we
integrate SFRD_TOT and find a good agreement with the published SMDs.


title: Network Control Systems RTAI framework A Review

abstract:
  With the advancement in the automation industry, to perform complex remote
operations is required. Advancements in the networking technology has led to
the development of different architectures to implement control from a large
distance. In various control applications of the modern industry, the agents,
such as sensors, actuators, and controllers are basically geographically
distributed. For efficient working of a control application, all of the agents
have to exchange information through a communication media. At present, an
increasing number of distributed control systems are based on platforms made up
of conventional PCs running open-source real-time operating systems. Often,
these systems needed to have networked devices supporting synchronized
operations with respect to each node. A framework is studied that relies on
standard software and protocol as RTAI, EtherCAT, RTnet and IEEE 1588. RTAI and
its various protocols are studied in network control systems environment.


title: The First Hard X-Ray Power Spectral Density Functions of AGN

abstract:
  We present results of our Power Spectral Density (PSD) analysis of 30 AGN
using the 58 month light curves from Swift's Burst Alert Telescope (BAT) in the
14-150 keV band. PSDs were fit using a Monte Carlo based algorithm to take into
account windowing effects and measurement error. All but one source were found
to be fit very well using an unbroken power law with a slope of ~-1, consistent
at low frequencies with previous studies in the 2-10 keV band, with no evidence
of a break in the PSD. For 5 of the highest S/N sources we tested the energy
dependence of the PSD and found no significant difference in the PSD at
different energies. Unlike previous studies of X-ray variability in AGN, we do
not find any significant correlations between the hard X-ray variability and
different properties of the AGN including luminosity and black hole mass. The
lack of break frequencies and correlations seem to indicate that AGN are
similar to the high state of Galactic Black Holes.


title:
Molecular Hydrogen in the Damped Lyman-alpha System towards GRB 120815A
  at z=2.36

abstract:
  We present the discovery of molecular hydrogen (H_2), including the presence
of vibrationally-excited H_2^* in the optical spectrum of the afterglow of GRB
120815A at z=2.36 obtained with X-shooter at the VLT. Simultaneous photometric
broad-band data from GROND and X-ray observations by Swift/XRT place further
constraints on the amount and nature of dust along the sightline. The galactic
environment of GRB 120815A is characterized by a strong DLA with
log(N(H)/cm^-2) = 21.95 +/- 0.10, prominent H_2 absorption in the Lyman-Werner
bands (log(N(H_2)/cm^-2) = 20.53 +/- 0.13) and thus a molecular gas fraction
log f(H_2)=-1.14 +/- 0.15. The distance d between the absorbing neutral gas and
GRB 120815A is constrained via photo-excitation modeling of fine-structure and
meta-stable transitions of FeII and NiII to d = 0.5 +/- 0.1 kpc. The DLA
metallicity ([Zn/H] = -1.15 +/- 0.12), visual extinction (A_V < 0.15 mag) and
dust depletion ([Zn/Fe] = 1.01 +/- 0.10) are intermediate between the values of
well-studied, H_2-deficient GRB-DLAs observed at high spectral resolution, and
the approximately solar metallicity, highly-obscured and H_2-rich GRB 080607
sightline. With respect to N(H), metallicity, as well as dust-extinction and
depletion, GRB 120815A is fairly representative of the average properties of
GRB-DLAs. This demonstrates that molecular hydrogen is present in at least a
fraction of the more typical GRB-DLAs, and H_2 and H_2^* are probably more
wide-spread among GRB-selected systems than the few examples of previous
detections would suggest.


title: Soft RPV Through the Baryon Portal

abstract:
  Supersymmetric (SUSY) models with R-parity generically predict sparticle
decays with invisible neutralinos, which yield distinctive missing energy
events at colliders. Since most LHC searches are designed with this
expectation, the putative bounds on sparticle masses become considerably weaker
if R-parity is violated so that squarks and gluinos decay to jets with large
QCD backgrounds. Here we introduce a scenario in which baryonic R-parity
violation (RPV) arises effectively from soft SUSY-breaking interactions, but
leptonic RPV remains accidentally forbidden to evade constraints from proton
decay and FCNCs. The model features a global R-symmetry that initially forbids
RPV interactions, a hidden R-breaking sector, and a heavy mediator that
communicates this breaking to the visible sector. After R-symmetry breaking,
the mediator is integrated out and an effective RPV A-term arises at tree
level; RPV couplings between quarks and squarks arise only at loop level and
receive additional suppression. Although this mediator must be heavy compared
to soft masses, the model introduces no new hierarchy since viable RPV can
arise when the mediator mass is near the SUSY breaking scale. In generic
regions of parameter space, a light thermally-produced gravitino is stable and
can be a viable dark matter candidate.


title: Ultraviolet Extinction at High Galactic Latitudes

abstract:
  In order to study the properties and effects of high Galactic latitude dust
we present an analysis of 373,303 galaxies selected from the Galaxy Evolution
Explorer (GALEX) All-Sky Survey and Wide-Field Infrared Explorer (WISE) All-Sky
Data Release. By examining the variation in aggregate ultraviolet colors and
number density of these galaxies we measure the extinction curve at high
latitude. We additionally consider a population of spectroscopically selected
galaxies from the Sloan Digital Sky Survey (SDSS) to measure extinction in the
optical. We find that dust at high latitude is neither quantitatively nor
qualitatively consistent with standard reddening laws. Extinction in the FUV
and NUV is ~10% and ~35% higher than expected, with significant variation
across the sky. We find that no single R_V parameter fits both the optical and
ultraviolet extinction at high latitude, and that while both show detectable
variation across the sky, these variations are not related. We propose that the
overall trends we detect likely stem from an increase in very small silicate
grains in the ISM.


title:
Physical Naturalness and Dynamical Breaking of Classical Scale
  Invariance

abstract:
  We propose a model of a confining dark sector, dark technicolor, that
communicates with the Standard Model through the Higgs portal. In this model
electroweak symmetry breaking and dark matter share a common origin, and the
electroweak scale is generated dynamically. Our motivation to suggest this
model is the absense of evidence for new physics from recent LHC data. Although
the conclusion is far from certain at this point, this lack of evidence may
suggest that no mechanism exists at the electroweak scale to stabilise the
Higgs mass against radiative corrections from UV physics. The usual reaction to
this puzzling situation is to conclude that the stabilising new physics is
either hidden from us by accident, or that it appears at energies that are
currently inaccessible, such that nature is indeed fine-tuned. In order to
re-examine the arguments that have lead to this dichotomy, we review the
concept of naturalness in effective field theories, discussing in particular
the role of quadratic divergences in relation to different energy scales. This
leads us to suggest classical scale invariance as a guidline for model
building, implying that explicit mass scales are absent in the underlying
theory.


title:
Modeling the Atomic-to-Molecular Transition and Chemical Distributions
  of Turbulent Star-Forming Clouds

abstract:
  We use 3D-PDR, a three-dimensional astrochemistry code for modeling
photodissociation regions (PDRs), to post-process hydrodynamic simulations of
turbulent, star-forming clouds. We focus on the transition from atomic to
molecular gas, with specific attention to the formation and distribution of H,
C+, C, H2 and CO. First, we demonstrate that the details of the cloud chemistry
and our conclusions are insensitive to the simulation spatial resolution, to
the resolution at the cloud edge, and to the ray angular resolution. We then
investigate the effect of geometry and simulation parameters on chemical
abundances and find weak dependence on cloud morphology as dictated by gravity
and turbulent Mach number. For a uniform external radiation field, we find
similar distributions to those derived using a one-dimensional PDR code.
However, we demonstrate that a three-dimensional treatment is necessary for a
spatially varying external field, and we caution against using one-dimensional
treatments for non-symmetric problems. We compare our results with the work of
Glover et al. (2010), who self-consistently followed the time evolution of
molecule formation in hydrodynamic simulations using a reduced chemical
network. In general, we find good agreement with this in situ approach for C
and CO abundances. However, the temperature and H2 abundances are discrepant in
the boundary regions (Av < 5), which is due to the different number of rays
used by the two approaches.


title: Using memory to identify phase transitions on a Cayley Tree

abstract:
  We provide a concrete and systematic connection between the statistical
physics of the Ising ferromagnet on a Cayley tree, and the study of memory in
exponentially expanding spaces. Memory turns out to be a clear signal of the
`Bethe-Peierls' phase transition, and the average of memory divided by its
standard deviation provides a clear signal of the `spin-glass' transition
temperature. Numerical Monte Carlo simulations are used to make transparent the
existence of the two different transition temperatures. The quantities used to
spot the phase transitions with Monte Carlo could be useful when studying other
systems where analytical methods don't work.


title:
On the internal pollution mechanisms in the globular cluster NGC 6121
  (M4): heavy-element abundances and AGB models

abstract:
  Globular clusters display significant variations in their light-element
content, pointing to the existence of a second stellar generation formed from
the ejecta of an earlier generation. The nature of these internal polluters is
still a matter of debate: the two most popular scenarios indicate
intermediate-mass AGB stars and fast rotating massive stars. Abundances
determination for some key elements can help distinguish between these
competitor candidates. We present in this paper Y abundances for a sample of
103 red giant branch stars in NGC 6121. Within measurement errors, we find that
the [Y/Fe] is constant in this cluster contrary to a recent suggestion. For a
subsample of six stars we also find [Rb/Fe] to be constant, consistent with
previous studies showing no variation in other s-process elements. We also
present a new set of stellar yields for intermediate-mass AGB stellar models of
5 and 6 solar masses, including heavy element s-process abundances. The
uncertainties on the mass-loss rate, the mixing-length parameter, and the
nuclear reaction rates have a major impact on the stellar abundances. Within
the IM-AGB pollution scenario, the constant abundance of heavy elements inside
the cluster requires a marginal s-process efficiency in IM-AGB stars. Such a
constrain could still be satisfied by the present models assuming a stronger
mass-loss rate. The uncertainties mentioned above are limiting the predictive
power of intermediate-mass AGB models. For these reasons, at the moment we are
not able to clearly rule out their role as main polluters of the second
population stars in globular clusters.


title: Self-sustained Clusters and Ergodicity Breaking in Spin Models

abstract:
  The emergence of self-sustained clusters and their role in ergodicity
breaking is investigated in fully connected Ising and Sherrington-Kirkpatick
(SK) models. The analysis reveals a clustering behavior at various parameter
regimes, as well as yet unobserved phenomena such as the absence of non-trivial
clusters in the Ising ferromagnetic and paramagnetic regimes, the formation of
restricted spin clusters in SK spin glass and a first order phase transition in
cluster sizes in the SK ferromagnet. The method could be adapted to investigate
other spin models.


title: Casting Light on BSM Physics with SM Standard Candles

abstract:
  The Standard Model (SM) has had resounding success in describing almost every
measurement performed by the ATLAS and CMS experiments. In particular, these
experiments have put many beyond the SM models of natural Electroweak Symmetry
Breaking into tension with the data. It is therefore remarkable that it is
still the LEP experiment, and not the LHC, which often sets the gold standard
for understanding the possibility of new color-neutral states at the
electroweak (EW) scale. Recently, ATLAS and CMS have started to push beyond LEP
in bounding heavy new EW states, but a gap between the exclusions of LEP and
the LHC typically remains. In this paper we show that measurements of SM
Standard Candles can be repurposed to set entirely complementary constraints on
new physics. To demonstrate this, we use WW cross section measurements to set
bounds on a set of slepton-based simplified models which fill in the gaps left
by LEP and dedicated LHC searches. Having demonstrated the sensitivity of the
WW measurement to light sleptons, we also find regions where sleptons can
improve the fit of the data compared to the NLO SM WW prediction alone.
Remarkably, in those regions the sleptons also provide for the right
relic-density of Bino-like Dark Matter and provide an explanation for the
longstanding 3 sigma discrepancy in the measurement of (g-2)_\mu.


title: Singularities with the highest Mather minimal log discrepancy

abstract:
  This paper characterizes singularities with Mather minimal log discrepancies
in the highest unit interval, i.e., the interval between $d-1$ and $d$, where
$d$ is the dimension of the scheme. The class of these singularities coincides
with one of the classes of (1) compound Du Val singularities, (2) normal
crossing double singularities, (3) pinch points, and (4) pairs of non-singular
varieties and boundaries with multiplicities less than or equal to 1 at the
point. As a corollary, we also obtain one implication of an equivalence
conjectured by Shokurov for the usual minimal log discrepancies.


title: Array of Fabry-P\'erot waveguide resonators with tunable coupling

abstract:
  We demonstrate the elements of a coupled-resonator optical waveguide in a
side-coupled Fabry-P\'erot configuration, and show that the coupling rate
between adjacent waveguides can be widely tuned through the thermo-optic
effect. The device is linearly scalable and can be combined with other
integrated devices, with applications as an optical delay line or as a key
element in a cavity-QED based quantum simulator.


title: On properties of the Generalized Wasserstein distance

abstract:
  The Wasserstein distances $W_p$ ($p\geq 1$), defined in terms of solution to
the Monge-Kantorovich problem, are known to be a useful tool to investigate
transport equations. In particular, the Benamou-Brenier formula characterizes
the square of the Wasserstein distance $W_2$ as the infimum of the kinetic
energy, or action functional, of all vector fields moving one measure to the
other.
  Another important property of the Wasserstein distances is the
Kantorovich-Rubinstein duality stating the equality between the distance $W_1$
and the supremum of the integrals of Lipschitz continuous functions with
Lipschitz constant bounded by one.
  An intrinsic limitation of Wasserstein distances is the fact that they are
defined only between measures having the same mass. To overcome such
limitation, we recently introduced the generalized Wasserstein distances
$W_p^{a,b}$, defined in terms of both the classical Wasserstein distance $W_p$
and the total variation (or $L^1$) distance. Here $p$ plays the same role as
for the classic Wasserstein distance, while $a$ and $b$ are weights for the
transport and the total variation term.
  In this paper we prove two important properties of the generalized
Wasserstein distances:
  1) a generalized Benamou-Brenier formula providing the equality between
$W_2^{a,b}$ and the supremum of an action functional, which includes a
transport term (kinetic energy) and a source term.
  2) a duality \`{a} la Kantorovich-Rubinstein establishing the equality
between $W_1^{1,1}$ and the flat metric.


title:
Keck Spectroscopy of Gravitationally Lensed z=4 Galaxies: Improved
  Constraints on the Escape Fraction of Ionizing Photons

abstract:
  The fraction of ionizing photons that escape from young star-forming galaxies
is one of the largest uncertainties in determining the role of galaxies in
cosmic reionization. Yet traditional techniques for measuring this fraction are
inapplicable at the redshifts of interest due to foreground screening by the
Lyman alpha forest. In an earlier study, we demonstrated a reduction in the
equivalent width of low-ionization absorption lines in composite spectra of
Lyman break galaxies at z=4 compared to similar measures at z=3. This might
imply a lower covering fraction of neutral gas and hence an increase with
redshift in the escape fraction of ionizing photons. However, our spectral
resolution was inadequate to differentiate between several alternative
explanations, including changes with redshift in the outflow kinematics. Here
we present higher quality spectra of 3 gravitationally lensed Lyman break
galaxies at z=4 with a spectral resolution sufficient to break this degeneracy
of interpretation. We present a method for deriving the covering fraction of
low-ionization gas as a function of outflow velocity and compare the results
with similar quality data taken for galaxies at lower redshift. We find a
significant trend of lower covering fractions of low-ionization gas for
galaxies with strong \Lya emission. In combination with the demographic trends
of \Lya emission with redshift from our earlier work, our results provide new
evidence for a reduction in the average H I covering fraction, and hence an
increase in the escape fraction of ionizing radiation from Lyman break
galaxies, with redshift.


title:
Lie groups and numerical solutions of differential equations: Invariant
  discretization versus differential approximation

abstract:
  We briefly review two different methods of applying Lie group theory in the
numerical solution of ordinary differential equations. On specific examples we
show how the symmetry preserving discretization provides difference schemes for
which the "first differential approximation" is invariant under the same Lie
group as the original ordinary differential equation.


title:
Statistical and systematic errors for gravitational-wave inspiral
  signals: A principal component analysis

abstract:
  Identifying the source parameters from a gravitational-wave measurement alone
is limited by our ability to discriminate signals from different sources and
the accuracy of the waveform family employed in the search. Here we address
both issues in the framework of an adapted coordinate system that allows for
linear Fisher-matrix type calculations of waveform differences that are both
accurate and computationally very efficient. We investigate statistical errors
by using principal component analysis of the post-Newtonian (PN) expansion
coefficients, which is well conditioned despite the Fisher matrix becoming ill
conditioned for larger numbers of parameters. We identify which combinations of
physical parameters are most effectively measured by gravitational-wave
detectors for systems of neutron stars and black holes with aligned spin. We
confirm the expectation that the dominant parameter of the inspiral waveform is
the chirp mass. The next dominant parameter depends on a combination of the
spin and the symmetric mass ratio. In addition, we can study the systematic
effect of various spin contributions to the PN phasing within the same
parametrization, showing that the inclusion of spin-orbit corrections up to
next-to-leading order, but not necessarily of spin-spin contributions, is
crucial for an accurate inspiral waveform model. This understanding of the
waveform structure throughout the parameter space is important to set up an
efficient search strategy and correctly interpret future gravitational-wave
observations.


title: Higher-order compatible discretization on hexahedrals

abstract:
  We derive a compatible discretization method that relies heavily on the
underlying geometric structure, and obeys the topological sequences and
commuting properties that are constructed. As a sample problem we consider the
vorticity-velocity-pressure formulation of the Stokes problem. We motivate the
choice for a mixed variational formulation based on both geometric as well as
physical arguments. Numerical tests confirm the theoretical results that we
obtain a pointwise divergence-free solution for the Stokes problem and that the
method obtains optimal convergence rates.


title:
Local Quantum Uncertainty and Bounds on Quantumness for Orthogonally
  invariant class of states

abstract:
  Local quantum uncertainty (in short LQU) was introduced by Girolami et.
al.(Phy. Rev. Lett. \textbf{110}, 240402) as a measure of quantum uncertainty
in a quantum state as achievable on single local measurement. However, such
quantity do satisfy all necessary criteria to serve as measure of discord like
quantum correlation and it has no closed formula except only for $2\otimes n$
system. Here, we consider orthogonal invariant class of states which includes
both the Werner and Isotropic class of states and explore the possibility of
closed form formula. Further, we extend our quest to the possibility of closed
form of geometric discord and measurement induced nonlocality for this class.
We also provide a comparative study of the bounds of general quantum
correlations with entanglement, as measured by negativity, for an interesting
subclass of states.


title: Charged black holes on Kaluza-Klein bubbles

abstract:
  We construct exact solutions of the Einstein-Maxwell-Dilaton field equations
in five dimensions, which describe general configurations of charged and static
black holes sitting on a Kaluza-Klein bubble. More specifically we discuss the
configurations describing two black holes sitting on a Kaluza-Klein bubble and
also the general charged static black Saturn balanced by a Kaluza-Klein bubble.
A straightforward extension of the solution generating technique leads to a new
solution describing the charged static black Saturn on the Taub-bolt instanton.
We compute the conserved charges and investigate some of the thermodynamic
properties of these systems.


title:
Quantum Corrections to Bekenstein-Hawking Black Hole Entropy and Gravity
  Partition Functions

abstract:
  Algebraic aspects of the computation of partition functions for quantum
gravity and black holes in $AdS_3$ are discussed. We compute the sub-leading
quantum corrections to the Bekenstein-Hawking entropy. It is shown that the
quantum corrections to the classical result can be included systematically by
making use of the comparison with conformal field theory partition functions,
via the $AdS_3/CFT_2$ correspondence. This leads to a better understanding of
the role of modular and spectral functions, from the point of view of the
representation theory of infinite-dimensional Lie algebras. Besides, the sum of
known quantum contributions to the partition function can be presented in a
closed form, involving the Patterson-Selberg spectral function. These
contributions can be reproduced in a holomorphically factorized theory whose
partition functions are associated with the formal characters of the Virasoro
modules. We propose a spectral function formulation for quantum corrections to
the elliptic genus from supergravity states.


title:
Geometric Stability Spectra of Dipolar Bose Gases in Tunable Optical
  Lattices

abstract:
  We examine the stability of quasi-two-dimensional dipolar Bose-Einstein
condensates in the presence of weak optical lattices of various geometries. We
find that when the condensate possesses a roton-maxon quasiparticle dispersion,
the conditions for stability exhibit a strong dependence both on the lattice
geometry and the polarization tilt. This results in rich structures in the
system's stability diagram akin to spectroscopic signatures. We show how these
structures originate from the mode matching of rotons to the perturbing
lattice. In the case of a one-dimensional lattice, some of the features emerge
only when the polarization axis is tilted into the plane of the condensate. Our
results suggest that the stability diagram may be used as a novel means to
spectroscopically measure rotons in dipolar condensates.


title: The inverse problem for the local ray transform

abstract:
  In this paper we consider the local X-ray transform for general flows. We
extend the results on the local and global invertibility of the geodesic ray
transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a
general flow. The key improvement is that our argument for the ellipticity of
the conjugated operator $A_F$ (which is defined in Section 2) can be applied to
flows other than the geodesic flow.


title:
Preventing Calibration Attacks on the Local Oscillator in
  Continuous-Variable Quantum Key Distribution

abstract:
  Establishing an information-theoretic secret key between two parties using a
quantum key distribution (QKD) system is only possible when an accurate
characterization of the quantum channel and proper device calibration routines
are combined. Indeed, security loopholes due to inappropriate calibration
routines have been shown for discrete-variable QKD. Here, we propose and
provide experimental evidence of an attack targeting the local oscillator
calibration routine of a continuous-variable QKD system. The attack consists in
manipulating the classical local oscillator pulses during the QKD run in order
to modify the clock pulses used at the detection stage. This allows the
eavesdropper to bias the shot noise estimation usually performed using a
calibrated relationship. This loophole can be used to perform successfully an
intercept-resend attack. We characterize the loophole and suggest possible
countermeasures.


title:
Recovery of bilevel causal signals with finite rate of innovation using
  positive sampling kernels

abstract:
  Bilevel signal $x$ with maximal local rate of innovation $R$ is a
continuous-time signal that takes only two values 0 and 1 and that there is at
most one transition position in any time period of 1/R.In this note, we
introduce a recovery method for bilevel causal signals $x$ with maximal local
rate of innovation $R$ from their uniform samples $x*h(nT), n\ge 1$, where the
sampling kernel $h$ is causal and positive on $(0, T)$, and the sampling rate
$\tau:=1/T$ is at (or above) the maximal local rate of innovation $R$. We also
discuss stability of the bilevel signal recovery procedure in the presence of
bounded noises.


title:
A refinement of the Shuffle Conjecture with cars of two sizes and
  $t=1/q$

abstract:
  The original Shuffle Conjecture of Haglund et al. has a symmetric function
side and a combinatorial side. The symmetric function side may be simply
expressed as $<\nabla e_n, h_{\mu}>$ where \nabla is the Macdonald polynomial
eigen-operator of Bergeron and Garsia and $h_\mu$ is the homogeneous basis
indexed by $\mu=(\mu_1,\mu_2,...,\mu_k)$ partitions of n. The combinatorial
side q,t-enumerates a family of Parking Functions whose reading word is a
shuffle of k successive segments of 1,2,3,...,n of respective lengths
$\mu_1,\mu_2,...,\mu_k$. It can be shown that for t=1/q the symmetric function
side reduces to a product of q-binomial coefficients and powers of q. This
reduction suggests a surprising combinatorial refinement of the general Shuffle
Conjecture. Here we prove this refinement for k=2 and t=1/q. The resulting
formula gives a q-analogue of the well studied Narayana numbers.


title:
Creation of a homogeneous plasma column by means of hohlraum radiation
  for ion-stopping measurements

abstract:
  In this work, we present the results of two-dimensional
radiation-hydrodynamics simulations of a hohlraum target whose outgoing
radiation is used to produce a homogeneously ionized carbon plasma for ion-beam
stopping measurements. The cylindrical hohlraum with gold walls is heated by a
frequency-doubled ($\lambda_l = 526.5$ $\mu m$) $1.4$ $ns$ long laser pulse
with the total energy of $E_l = 180$ $J$. At the laser spot, the peak matter
and radiation temperatures of, respectively, $T \approx 380$ $eV$ and $T_r
\approx 120$ $eV$ are observed. X-rays from the hohlraum heat the attached
carbon foam with a mean density of $\rho_C = 2$ $mg/cm^3$ to a temperature of
$T \approx 25$ $eV$. The simulation shows that the carbon ionization degree ($Z
\approx 3.75$) and its column density stay relatively stable (within variations
of about $\pm7\%$) long enough to conduct the ion-stopping measurements. Also,
it is found that a special attention should be paid to the shock wave, emerging
from the X-ray heated copper support plate, which at later times may
significantly distort the carbon column density traversed by the fast ions.


title: The 1882 Conjugacy Classes of the First Basic Renner Monoid of Type E_6

abstract:
  In this paper we find all conjugacy classes of the first basic Renner monoid
of type E_6. They are listed in the tables of the paper.


title: Decision Problems for Additive Regular Functions

abstract:
  Additive Cost Register Automata (ACRA) map strings to integers using a finite
set of registers that are updated using assignments of the form "x := y + c" at
every step. The corresponding class of additive regular functions has multiple
equivalent characterizations, appealing closure properties, and a decidable
equivalence problem. In this paper, we solve two decision problems for this
model. First, we define the register complexity of an additive regular function
to be the minimum number of registers that an ACRA needs to compute it. We
characterize the register complexity by a necessary and sufficient condition
regarding the largest subset of registers whose values can be made far apart
from one another. We then use this condition to design a PSPACE algorithm to
compute the register complexity of a given ACRA, and establish a matching lower
bound. Our results also lead to a machine-independent characterization of the
register complexity of additive regular functions. Second, we consider
two-player games over ACRAs, where the objective of one of the players is to
reach a target set while minimizing the cost. We show the corresponding
decision problem to be EXPTIME-complete when costs are non-negative integers,
but undecidable when costs are integers.


title:
Photon elliptic flow in relativistic heavy-ion collisions: hadronic
  versus partonic sources

abstract:
  We study the transverse momentum spectrum and the elliptic flow v2 of photons
produced in Au+Au collisions at sqrt(s)=200 GeV using the Parton-Hadron-String
Dynamics (PHSD) transport approach. As sources for photon production, we
incorporate the interactions of off-shell quarks and gluons in the strongly
interacting quark-gluon plasma (q+qbar->g+gamma and q/qbar+g->q/qbar+gamma),
the decays of hadrons (pi->gamma+gamma, eta->gamma+gamma, omega->pi+gamma,
eta'->rho+gamma, phi->eta+gamma, a_1->pi+gamma) as well as their interactions
(pi+pi->rho+gamma, rho+pi->pi+gamma, bremsstrahlung m+m->m+m+gamma). The PHSD
calculations reproduce the transverse momentum spectrum, the effective
temperature T_eff and the elliptic flow v2 of both inclusive and direct photons
as measured by the PHENIX Collaboration. The photons produced in the QGP
contribute slightly less then 50% to the observed spectrum, but have small v2.
We find that the large direct photon v2 - comparable to that of hadrons - can
be attributed to the intermediate hadronic scattering channels not subtracted
from the data when following the same extraction procedure for v2 as in the
PHENIX experiment. On the other hand the v2 of direct photons - as evaluated by
the weighted average of direct photon channels - gives a lower signal. The
difference between the two extraction procedures for the direct photon v2 can
be attributed to different definitions for the yield ratio of direct photons to
the background photons. The QGP phase causes the strong elliptic flow of
photons indirectly, by enhancing the v2 of final hadrons due to the partonic
interaction in terms of explicit parton collisions and the mean-field
potentials. We also show that the presence of the QGP radiation is manifest in
the slope of the direct photon spectrum, leading to a slope parameter T_eff far
above the critical temperature for the deconfinement phase transition.


title: The conditional entropy power inequality for Gaussian quantum states

abstract:
  We propose a generalization of the quantum entropy power inequality involving
conditional entropies. For the special case of Gaussian states, we give a proof
based on perturbation theory for symplectic spectra. We discuss some
implications for entanglement-assisted classical communication over additive
bosonic noise channels.


title: Transient growth in linearly stable Taylor-Couette flows

abstract:
  Non-normal transient growth of disturbances is considered as an essential
prerequisite for subcritical transition in shear flows, i.e. transition to
turbulence despite linear stability of the laminar flow. In this work we
present numerical and analytical computations of linear transient growth
covering all linearly stable regimes of Taylor--Couette flow. Our numerical
experiments reveal comparable energy amplifications in the different regimes.
For high shear Reynolds numbers Re the optimal transient energy growth always
follows a 2/3-scaling with Re, which allows for large amplifications even in
regimes where the presence of turbulence remains debated. In co-rotating
Rayleigh-stable flows the optimal perturbations become increasingly columnar in
their structure, as the optimal axial wavenumber goes to zero. In this limit of
axially invariant perturbations we show that linear stability and transient
growth are independent of the cylinders' rotation-ratio and we derive a
universal 2/3-scaling of optimal energy growth with Re using WKB-theory. Based
on this, a semi-empirical formula for the estimation of linear transient growth
valid in all regimes is obtained.


title: Equilateral sets and a Sch\"utte Theorem for the 4-norm

abstract:
  A well-known theorem of Sch\"utte (1963) gives a sharp lower bound for the
ratio between the maximum distance and minimum distance between n+2 points in
n-dimensional Euclidean space. In this brief note we adapt B\'ar\'any's elegant
proof of this theorem to the space $\ell_4^n$. This gives a new proof that the
largest cardinality of an equilateral set in $\ell_4^n$ is n+1, and gives a
constructive bound for an interval $(4-\epsilon_n,4+\epsilon_n)$ of values of p
close to 4 for which it is guaranteed that the largest cardinality of an
equilateral set in $\ell_p^n$ is n+1.


title: Threshold-limited spreading in social networks with multiple initiators

abstract:
  A classical model for social-influence-driven opinion change is the threshold
model. Here we study cascades of opinion change driven by threshold model
dynamics in the case where multiple {\it initiators} trigger the cascade, and
where all nodes possess the same adoption threshold $\phi$. Specifically, using
empirical and stylized models of social networks, we study cascade size as a
function of the initiator fraction $p$. We find that even for arbitrarily high
value of $\phi$, there exists a critical initiator fraction $p_c(\phi)$ beyond
which the cascade becomes global. Network structure, in particular clustering,
plays a significant role in this scenario. Similarly to the case of single-node
or single-clique initiators studied previously, we observe that community
structure within the network facilitates opinion spread to a larger extent than
a homogeneous random network. Finally, we study the efficacy of different
initiator selection strategies on the size of the cascade and the cascade
window.


title: Synchronization in fiber lasers arrays

abstract:
  We consider an array of fiber lasers coupled through the nearest neighbors.
The model is a generalized nonlinear Schroedinger equation where the usual
Laplacian is replaced by the graph Laplacian. For a graph with no symmetries,
we show that there is no resonant transfer of energy between the different
eigenmodes. We illustrate this and confirm our result on a simple graph. This
shows that arrays of fiber ring lasers can be made temporally coherent.


title: Excitations of a trapped two component Bose Einstein Condensate

abstract:
  We present analysis of the excitation spectrum for a 2 component quasi2D Bose
Einstein Condensate. We study how the character of the excitations change
across the miscible to immiscible phase transition. We find that the bulk
excitations are typical of a single-component BEC with the addition of
interface bending excitations. We study how these excitations change as a
function of the interaction strength.


title:
On the large-scale geometry of the L^p-metric on the symplectomorphism
  group of the two-sphere

abstract:
  We prove that the vector space R^d of any finite dimension d with the
standard metric embeds in a bi-Lipschitz way into the group of area-preserving
diffeomorphisms G of the two-sphere endowed with the L^p-metric for p>2. Along
the way we show that the L^p-metric on the group G is unbounded for p>2 by
elementary methods.


title: Staged Self-Assembly and Polyomino Context-Free Grammars

abstract:
  Previous work by Demaine et al. (2012) developed a strong connection between
smallest context-free grammars and staged self-assembly systems for
one-dimensional strings and assemblies. We extend this work to two-dimensional
polyominoes and assemblies, comparing staged self-assembly systems to a natural
generalization of context-free grammars we call polyomino context-free grammars
(PCFGs). We achieve nearly optimal bounds on the largest ratios of the smallest
PCFG and staged self-assembly system for a given polyomino with n cells. For
the ratio of PCFGs over assembly systems, we show the smallest PCFG can be an
Omega(n/(log(n))^3)-factor larger than the smallest staged assembly system,
even when restricted to square polyominoes. For the ratio of assembly systems
over PCFGs, we show that the smallest staged assembly system is never more than
a O(log(n))-factor larger than the smallest PCFG and is sometimes an
Omega(log(n)/loglog(n))-factor larger.


title: Ideals generated by superstandard tableaux

abstract:
  We investigate products J of ideals of "row initial" minors in the polynomial
ring K[X] defined by a generic m-by-n matrix. Such ideals are shown to be
generated by a certain set of standard bitableaux that we call superstandard.
These bitableaux form a Gr\"obner basis of J, and J has a linear minimal free
resolution. These results are used to derive a new generating set for the
Grothendieck group of finitely generated (T_m x GL_n(K))-equivariant modules
over K[X]. We employ the Knuth--Robinson--Schensted correspondence and a toric
deformation of the multi-Rees algebra that parameterizes the ideals J.


title: The Non-Abelian Exponentiation theorem for multiple Wilson lines

abstract:
  We study the structure of soft gluon corrections to multi-leg scattering
amplitudes in a non-Abelian gauge theory by analysing the corresponding product
of semi-infinite Wilson lines. We prove that diagrams exponentiate such that
the colour factors in the exponent are fully connected. This completes the
generalisation of the non-Abelian exponentiation theorem, previously proven in
the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary
representations of the colour group. Our proof is based on the replica trick in
conjunction with a new formalism where multiple emissions from a Wilson line
are described by effective vertices, each having a connected colour factor. The
exponent consists of connected graphs made out of these vertices. We show that
this readily provides a general colour basis for webs. We further discuss the
kinematic combinations that accompany each connected colour factor, and
explicitly catalogue all three-loop examples, as necessary for a direct
computation of the soft anomalous dimension at this order.


title:
On well-posedness of the Cauchy problem for the wave equation in static
  spherically symmetric spacetimes

abstract:
  We give simple conditions implying the well-posedness of the Cauchy problem
for the propagation of classical scalar fields in general (n+2)-dimensional
static and spherically symmetric spacetimes. They are related to properties of
the underlying spatial part of the wave operator, one of which being the
standard essentially self-adjointness. However, in many examples the spatial
part of the wave operator turns out to be not essentially selfadjoint, but it
does satisfy a weaker property that we call here quasi essentially
self-adjointness, which is enough to ensure the desired well-posedness. This is
why we also characterize this second property.
  We state abstract results, then general results for a class of operators
encompassing many examples in the literature, and we finish with the explicit
analysis of some of them.


title: Non-Gaussianities and Curvature Perturbations from Hybrid Inflation

abstract:
  For the original hybrid inflation as well as the supersymmetric F-term and
D-term hybrid models, we calculate the level of non-gaussianities and the power
spectrum of curvature perturbations generated during the waterfall, taking into
account the contribution of entropic modes. We focus on the regime of mild
waterfall, in which inflation continues for more than about 60 e-folds N during
the waterfall. We find that the associated f_nl parameter goes typically from
f_nl \simeq -1 / N_exit in the regime with N >> 60, where N_exit is the number
of e-folds between the time of Hubble exit of a pivot scale and the end of
inflation, down to f_nl ~-0.3 when N \gtrsim 60, i.e. much smaller in magnitude
than the current bound from Planck. Considering only the adiabatic
perturbations, the power spectrum is red, with a spectral index n_s = 1 - 4 /
N_exit, in the case N >> 60, whereas in the case N \gtrsim 60, it increases up
to unity. Including the contribution of entropic modes does not change the
observable predictions in the first case. However, in the second case, they are
a relevant source for the power spectrum of curvature perturbations, of which
the amplitude increases by several orders of magnitudes and can lead to black
hole formation. We conclude that due to the important contribution of entropic
modes, the parameter space leading to a mild waterfall phase is excluded by CMB
observations for all the considered models.


title:
Homogenisation and spectral convergence of a periodic elastic composite
  with weakly compressible inclusions

abstract:
  A two phase elastic composite with weakly compressible elastic inclusions is
considered. The homogenised two-scale limit problem is found, via a version of
the method of two-scale convergence, and analysed. The microscopic part of the
two-scale limit is found to solve a Stokes type problem and shown to have no
microscopic oscillations when the composite is subjected to body forces that
are microscopically irrotational. The composites spectrum is analysed and shown
to converge, in an appropriate sense, to the spectrum of the two-scale limit
problem. A characterisation of the two-scale limit spectrum is given in terms
of the limit macroscopic and microscopic behaviours.


title: New pseudo-planar binomials in characteristic two and related schemes

abstract:
  Planar functions in odd characteristic were introduced by Dembowski and
Ostrom in order to construct finite projective planes in 1968. They were also
used in the constructions of DES-like iterated ciphers, error-correcting codes,
and signal sets. Recently, a new notion of pseudo-planar functions in even
characteristic was proposed by Zhou. These new pseudo-planar functions, as an
analogue of planar functions in odd characteristic, also bring about finite
projective planes. There are three known infinite families of pseudo-planar
monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In
this paper, three new classes of pseudo-planar binomials are provided.
Moreover, we find that each pseudo-planar function gives an association scheme
which is defined on a Galois ring.


title: An Algorithm for Training Polynomial Networks

abstract:
  We consider deep neural networks, in which the output of each node is a
quadratic function of its inputs. Similar to other deep architectures, these
networks can compactly represent any function on a finite training set. The
main goal of this paper is the derivation of an efficient layer-by-layer
algorithm for training such networks, which we denote as the \emph{Basis
Learner}. The algorithm is a universal learner in the sense that the training
error is guaranteed to decrease at every iteration, and can eventually reach
zero under mild conditions. We present practical implementations of this
algorithm, as well as preliminary experimental results. We also compare our
deep architecture to other shallow architectures for learning polynomials, in
particular kernel learning.


title: Brittleness of Bayesian inference and new Selberg formulas

abstract:
  The incorporation of priors in the Optimal Uncertainty Quantification (OUQ)
framework \cite{OSSMO:2011} reveals brittleness in Bayesian inference; a model
may share an arbitrarily large number of finite-dimensional marginals with, or
be arbitrarily close (in Prokhorov or total variation metrics) to, the
data-generating distribution and still make the largest possible prediction
error after conditioning on an arbitrarily large number of samples. The initial
purpose of this paper is to unwrap this brittleness mechanism by providing (i)
a quantitative version of the Brittleness Theorem of \cite{BayesOUQ} and (ii) a
detailed and comprehensive analysis of its application to the revealing example
of estimating the mean of a random variable on the unit interval $[0,1]$ using
priors that exactly capture the distribution of an arbitrarily large number of
Hausdorff moments.
  However, in doing so, we discovered that the free parameter associated with
Markov and Kre\u{\i}n's canonical representations of truncated Hausdorff
moments generates reproducing kernel identities corresponding to reproducing
kernel Hilbert spaces of polynomials.
  Furthermore, these reproducing identities lead to biorthogonal systems of
Selberg integral formulas.
  This process of discovery appears to be generic: whereas Karlin and Shapley
used Selberg's integral formula to first compute the volume of the Hausdorff
moment space (the polytope defined by the first $n$ moments of a probability
measure on the interval $[0,1]$), we observe that the computation of that
volume along with higher order moments of the uniform measure on the moment
space, using different finite-dimensional representations of subsets of the
infinite-dimensional set of probability measures on $[0,1]$ representing the
first $n$ moments, leads to families of equalities corresponding to classical
and new Selberg identities.


title: Finding Hidden Cliques of Size \sqrt{N/e} in Nearly Linear Time

abstract:
  Consider an Erd\"os-Renyi random graph in which each edge is present
independently with probability 1/2, except for a subset $\sC_N$ of the vertices
that form a clique (a completely connected subgraph). We consider the problem
of identifying the clique, given a realization of such a random graph.
  The best known algorithm provably finds the clique in linear time with high
probability, provided $|\sC_N|\ge 1.261\sqrt{N}$ \cite{dekel2011finding}.
Spectral methods can be shown to fail on cliques smaller than $\sqrt{N}$. In
this paper we describe a nearly linear time algorithm that succeeds with high
probability for $|\sC_N|\ge (1+\eps)\sqrt{N/e}$ for any $\eps>0$. This is the
first algorithm that provably improves over spectral methods.
  We further generalize the hidden clique problem to other background graphs
(the standard case corresponding to the complete graph on $N$ vertices). For
large girth regular graphs of degree $(\Delta+1)$ we prove that `local'
algorithms succeed if $|\sC_N|\ge (1+\eps)N/\sqrt{e\Delta}$ and fail if
$|\sC_N|\le(1-\eps)N/\sqrt{e\Delta}$.


title: Efficiency Guarantees in Auctions with Budgets

abstract:
  In settings where players have a limited access to liquidity, represented in
the form of budget constraints, efficiency maximization has proven to be a
challenging goal. In particular, the social welfare cannot be approximated by a
better factor then the number of players. Therefore, the literature has mainly
resorted to Pareto-efficiency as a way to achieve efficiency in such settings.
While successful in some important scenarios, in many settings it is known that
either exactly one incentive-compatible auction that always outputs a
Pareto-efficient solution, or that no truthful mechanism can always guarantee a
Pareto-efficient outcome. Traditionally, impossibility results can be avoided
by considering approximations. However, Pareto-efficiency is a binary property
(is either satisfied or not), which does not allow for approximations.
  In this paper we propose a new notion of efficiency, called \emph{liquid
welfare}. This is the maximum amount of revenue an omniscient seller would be
able to extract from a certain instance. We explain the intuition behind this
objective function and show that it can be 2-approximated by two different
auctions. Moreover, we show that no truthful algorithm can guarantee an
approximation factor better than 4/3 with respect to the liquid welfare, and
provide a truthful auction that attains this bound in a special case.
  Importantly, the liquid welfare benchmark also overcomes impossibilities for
some settings. While it is impossible to design Pareto-efficient auctions for
multi-unit auctions where players have decreasing marginal values, we give a
deterministic $O(\log n)$-approximation for the liquid welfare in this setting.


title:
Subspace-preserving sparsification of matrices with minimal perturbation
  to the near null-space. Part I: Basics

abstract:
  This is the first of two papers to describe a matrix sparsification algorithm
that takes a general real or complex matrix as input and produces a sparse
output matrix of the same size. The non-zero entries in the output are chosen
to minimize changes to the singular values and singular vectors corresponding
to the near null-space of the input. The output matrix is constrained to
preserve left and right null-spaces exactly. The sparsity pattern of the output
matrix is automatically determined or can be given as input.
  If the input matrix belongs to a common matrix subspace, we prove that the
computed sparse matrix belongs to the same subspace. This works without
imposing explicit constraints pertaining to the subspace. This property holds
for the subspaces of Hermitian, complex-symmetric, Hamiltonian, circulant,
centrosymmetric, and persymmetric matrices, and for each of the skew
counterparts.
  Applications of our method include computation of reusable sparse
preconditioning matrices for reliable and efficient solution of high-order
finite element systems. The second paper in this series describes our
open-source implementation, and presents further technical details.


title:
Subspace-preserving sparsification of matrices with minimal perturbation
  to the near null-space. Part II: Approximation and Implementation

abstract:
  This is the second of two papers to describe a matrix sparsification
algorithm that takes a general real or complex matrix as input and produces a
sparse output matrix of the same size. The first paper presented the original
algorithm, its features, and theoretical results.
  Since the output of this sparsification algorithm is a matrix rather than a
vector, it can be costly in memory and run-time if an implementation does not
exploit the structural properties of the algorithm and the matrix. Here we show
how to modify the original algorithm to increase its efficiency. This is
possible by computing an approximation to the exact result. We introduce extra
constraints that are automatically determined based on the input matrix. This
addition reduces the number of unknown degrees of freedom but still preserves
many matrix subspaces. We also describe our open-source library that implements
this sparsification algorithm and has interfaces in C++, C, and MATLAB.


title: Spectral gap actions and invariant states

abstract:
  We define spectral gap actions of discrete groups on von Neumann algebras and
study their relations with invariant states. We will show that a finitely
generated ICC group $\Gamma$ is inner amenable if and only if there exist more
than one inner invariant states on the group von Neumann algebra $L(\Gamma)$.
Moreover, a countable discrete group $\Gamma$ has property $(T)$ if and only if
for any action $\alpha$ of $\Gamma$ on a von Neumann algebra $N$, every
$\alpha$-invariant state on $N$ is a weak-$^*$-limit of a net of normal
$\alpha$-invariant states.


title:
Periodic Landau gauge and Quantum Hall effect in twisted bilayer
  graphene

abstract:
  Energy versus magnetic field (Hofstadter butterfly diagram) in twisted
bilayer graphene is studied theoretically. If we take the usual Landau gauge,
we cannot take a finite periodicity even when the magnetic flux through a
supercell is a rational number. We show that the \textit{periodic} Landau
gauge, which has the periodicity in one direction, makes it possible to obtain
the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux
through a supercell normalized by the flux quantum can be a fractional number
with a small denominator, even when a magnetic field is not extremely strong.
As a result, quantized Hall conductance can be a solution of nontrivial
Diophantine equation.


title:
A GEMM interface and implementation on NVIDIA GPUs for multiple small
  matrices

abstract:
  We present an interface and an implementation of the General Matrix Multiply
(GEMM) routine for multiple small matrices processed simultaneously on NVIDIA
graphics processing units (GPUs). We focus on matrix sizes under 16. The
implementation can be easily extended to larger sizes. For single precision
matrices, our implementation is 30% to 600% faster than the batched cuBLAS
implementation distributed in the CUDA Toolkit 5.0 on NVIDIA Tesla K20c. For
example, we obtain 104 GFlop/s and 216 GFlop/s when multiplying 100,000
independent matrix pairs of size 10 and 16, respectively. Similar improvement
in performance is obtained for other sizes, in single and double precision for
real and complex types, and when the number of matrices is smaller. Apart from
our implementation, our different function interface also plays an important
role in the improved performance. Applications of this software include Finite
Element computation on GPUs.


title: Batched Kronecker product for 2-D matrices and 3-D arrays on NVIDIA GPUs

abstract:
  We describe an interface and an implementation for performing Kronecker
product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays
processed in parallel as a batch. This method is suited to cases where the
Kronecker product component matrices are identical but the operands in a
matrix-free application vary in the batch. Any batched GEMM (General Matrix
Multiply) implementation, for example ours [1] or the one in cuBLAS, can also
be used for performing batched Kronecker products on GPUs. However, the
specialized implementation presented here is faster and uses less memory.
Partly this is because a simple GEMM based approach would require extra copies
to and from main memory. We focus on matrix sizes less than or equal to 16,
since these are the typical polynomial degrees in Finite Elements, but the
implementation can be easily extended for other sizes. We obtain 143 and 285
GFlop/s for single precision real when processing matrices of size 10 and 16,
respectively on NVIDIA Tesla K20c using CUDA 5.0. The corresponding speeds for
3-D array Kronecker products are 126 and 268 GFlop/s, respectively. Double
precision is easily supported using the C++ template mechanism.


title: An LP-based 3/2-approximation algorithm for the graphic s-t path TSP

abstract:
  We design a new LP-based algorithm for the graphic $s$-$t$ path Traveling
Salesman Problem (TSP), which achieves the best approximation factor of 1.5.
The algorithm is based on the idea of narrow cuts due to An, Kleinberg, and
Shmoys. It partly answers an open question of Seb\H{o}.


title: Wall-crossing in genus zero quasimap theory and mirror maps

abstract:
  For each positive rational number epsilon, the theory of epsilon-stable
quasimaps to certain GIT quotients W//G developed in arXiv:1106.3724[math.AG]
gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic
theory corresponding to epsilon --> 0. For epsilon >1 one obtains the usual
Gromov-Witten theory of W//G, while the other theories are new. However, they
are all expected to contain the same information and in particular the
numerical invariants should be related by wall-crossing formulas. In this paper
we analyze the genus zero picture and find that the wall-crossing in this case
significantly generalizes toric mirror symmetry (the toric cases correspond to
abelian groups G). In particular, we give a geometric interpretation of the
mirror map as a generating series of quasimap invariants. We prove our
wall-crossing formulas for all targets W//G which admit a torus action with
isolated fixed points, as well as for zero loci of sections of homogeneous
vector bundles on such W//G.


title:
Unidirectional Amplification and Shaping of Optical Pulses by Three-Wave
  Mixing with Negative Phonons

abstract:
  A possibility to greatly enhance frequency-conversion efficiency of
stimulated Raman scattering is shown by making use of extraordinary properties
of three-wave mixing of ordinary and backward waves. Such processes are
commonly attributed to negative-index plasmonic metamaterials. This work
demonstrates the possibility to replace such metamaterials that are very
challenging to engineer by readily available crystals which support elastic
waves with contra-directed phase and group velocities. The main goal of this
work is to investigate specific properties of indicated nonlinear optical
process in short pulse regime and to show that it enables elimination of
fundamental detrimental effect of fast damping of optical phonons on the
process concerned. Among the applications is the possibility of creation of a
family of unique photonic devices such as unidirectional Raman amplifiers and
femtosecond pulse shapers with greatly improved operational properties.


title:
Quantifying entanglement of arbitrary-dimensional multipartite pure
  states in terms of the singular values of coefficient matrices

abstract:
  The entanglement quantification and classification of multipartite quantum
states are two important research fields in quantum information. In this work,
we study the entanglement of arbitrary-dimensional multipartite pure states by
looking at the averaged partial entropies of various bipartite partitions of
the system, namely, the so-called Manhattan distance ($l_1$ norm) of averaged
partial entropies (MAPE), and it is proved to be an entanglement measure for
pure states. We connected the MAPE with the coefficient matrices, which are
important tools in entanglement classification and reexpressed the MAPE for
arbitrary-dimensional multipartite pure states by the nonzero singular values
of the coefficient matrices. The entanglement properties of the $n$-qubit Dicke
states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and $D_3^n$
states are investigated in terms of the MAPE, and the relation between the rank
of the coefficient matrix and the degree of entanglement is demonstrated for
symmetric states by two examples.


title:
Quartic Poisson algebras and quartic associative algebras and
  realizations as deformed oscillator algebras

abstract:
  We introduce the most general quartic Poisson algebra generated by a second
and a fourth order integral of motion of a 2D superintegrable classical system.
We obtain the corresponding quartic (associative) algebra for the quantum
analog and we extend Daskaloyannis' construction in obtained in context of
quadratic algebras and we obtain the realizations as deformed oscillator
algebras for this quartic algebra. We obtain the Casimir operator and discuss
how these realizations allow to obtain the finite dimensional unitary
irreductible representations of quartic algebras and obtain algebraically the
degenerate energy spectrum of superintegrable systems. We apply the
construction and the formula obtained for the structure function on a
superintegrable system related to type I Laguerre exceptionnal orthogonal
polynomials introduced recently.


title: High-dimensional quantum state transfer through a quantum spin chain

abstract:
  In this paper, we investigate a high-dimensional quantum state transfer
protocol. An arbitrary unknown high-dimensional state can be transferred with
high fidelity between two remote registers through a XX coupling spin chain of
arbitrary length. The evolution of the state transfer is determined by the
natural dynamics of the chain without external modulation and coupling strength
engineering. As a consequence, entanglement distribution with high efficiency
can be achieved. Also the strong field and high spin quantum number can
counteract partly the effect of finite temperature to ensure high fidelity of
the protocol when the quantum data bus is in the thermal equilibrium state
under an external magnetic field.


title: Efficient Lyndon factorization of grammar compressed text

abstract:
  We present an algorithm for computing the Lyndon factorization of a string
that is given in grammar compressed form, namely, a Straight Line Program
(SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where
$m$ is the size of the Lyndon factorization, $n$ is the size of the SLP, and
$h$ is the height of the derivation tree of the SLP. Since the length of the
decompressed string can be exponentially large w.r.t. $n, m$ and $h$, our
result is the first polynomial time solution when the string is given as SLP.


title: Global $C^2$ estimates for convex solutions of curvature equations

abstract:
  We establish $C^2$ a priori estimate for convex hypersurfaces whose principal
curvatures $\kappa=(\kappa_1,..., \kappa_n)$ satisfying Weingarten curvature
equation $\sigma_k(\kappa(X))=f(X,\nu(X))$. We also obtain such estimate for
admissible 2-convex hypersurfaces in the case $k=2$. Our estimates resolve a
longstanding problem in geometric fully nonlinear elliptic equations.


title:
Classification of Darboux transformations for operators of the form
  $\partial_x\partial_y +a \partial_x + b\partial_y +c$

abstract:
  Darboux transformations are non-group type symmetries of linear differential
operators. One can define Darboux transformations algebraically by the
intertwining relation $ML=L_1M$ or the intertwining relation $ML=L_1N$ in the
cases when the first one is too restrictive.
  Here we show that Darboux transformations for operators of the form
$\partial_x\partial_y +a \partial_x + b\partial_y +c$ (often referred to as 2D
Schr\"odinger operators) are always compositions of atomic Darboux
transformations of two different types. This is in contrast with the case of 1D
Schr\"odinger operators and other 1D operators, where there is only one atomic
kind of Darboux transformations.


title:
A simple, reliable, and no-destructive method for the measurement of
  vacuum pressure

abstract:
  We present a simple, reliable, and no-destructive method for the measurement
of vacuum pressure in a magneto-optical trap. The vacuum pressure is verified
to be proportional to collision rate constant between cold atoms and background
gas with a coefficient k, which can be calculated by simple ideal gas law. The
rate constant for loss due to collisions with all background gases can be
derived from the total collision loss rate by a series of loading curve of cold
atoms under different trapping laser intensities. The presented method is also
applicable for other cold atom systems and meets the miniaturization
requirement of commercial applications.


title:
Ramification of the Gauss Map of Complete Minimal Surfaces in R^3 and
  R^4 on Annular Ends

abstract:
  In this article, we study the ramification of the Gauss map of complete
minimal surfaces in R^3 and R^4 on annular ends. We obtain results which are
similar to the ones obtained by Fujimoto and Ru for (the whole) complete
minimal surfaces, thus we show that the restriction of the Gauss map to an
annular end of such a complete minimal surface cannot have more branching (and
in particular not avoid more values) than on the whole complete minimal
surface. We thus give an improvement of the results on annular ends of complete
minimal surfaces of Kao.