title: Nonsymmetric Dynamical Thin-Shell Wormhole in Robinson--Trautman Class

abstract:
  The thin-shell wormhole created using the Darmois-Israel formalism applied to
Robinson-Trautman family of spacetimes is presented. The stress energy tensor
created on the throat is interpreted in terms of two dust streams and it is
shown that asymptotically this wormhole settles to the Schwarzschild wormhole
with a throat located at the horizon position. This behavior shows a nonlinear
stability (within the Robinson-Trautman class) of this spherically symmetric
wormhole. The gravitational radiation emitted by the Robinson-Trautman wormhole
during the transition to spherical symmetry is indistinguishable from that of
the corresponding black hole Robinson-Trautman spacetime. Subsequently, we show
that the higher-dimensional generalization of Robinson-Trautman geometry offers
a possibility of constructing wormholes without the need to violate the energy
conditions for matter induced on the throat.


title:
An Erd\"os--R\'ev\'esz type law of the iterated logarithm for order
  statistics of a stationary Gaussian process

abstract:
  Let $\{X(t):t\in\mathbb R_+\}$ be a stationary Gaussian process with almost
surely (a.s.) continuous sample paths, $\mathbb E X(t) = 0$, $\mathbb E X^2(t)
= 1$ and correlation function satisfying (i) $r(t) = 1 - C|t|^{\alpha} +
o(|t|^{\alpha})$ as $t\to 0$ for some $0\le\alpha\le 2, C>0$, (ii) $\sup_{t\ge
s}|r(t)|<1$ for each $s>0$ and (iii) $r(t) = O(t^{-\lambda})$ as $t\to\infty$
for some $\lambda>0$. For any $n\ge 1$, consider $n$ mutually independent
copies of $X$ and denote by $\{X_{r:n}(t):t\ge 0\}$ the $r$th smallest order
statistics process, $1\le r\le n$. We provide a tractable criterion for
assessing whether, for any positive, non-decreasing function $f$, $\mathbb
P(\mathscr E_f)=\mathbb P(X_{r:n}(t) > f(t)\, \text{i.o.})$ equals 0 or 1.
Using this criterion we find that, for a family of functions $f_p(t)$, such
that $z_p(t)=\mathbb P(\sup_{s\in[0,1]}X_{r:n}(s)>f_p(t))=\mathscr
C(t\log^{1-p} t)^{-1}$, $\mathscr C>0$, $\mathbb P(\mathscr E_{f_p})= 1_{\{p\ge
0\}}$. Consequently, with $\xi_p (t) = \sup\{s:0\le s\le t, X_{r:n}(s)\ge
f_p(s)\}$, for $p\ge 0$, $\lim_{t\to\infty}\xi_p(t)=\infty$ and
$\limsup_{t\to\infty}(\xi_p(t)-t)=0$ a.s.. Complementary, we prove an
Erd\"os-R\'ev\'esz type law of the iterated logarithm lower bound on
$\xi_p(t)$, i.e., $\liminf_{t\to\infty}(\xi_p(t)-t)/h_p(t) = -1$ a.s., $p>1$,
$\liminf_{t\to\infty}\log(\xi_p(t)/t)/(h_p(t)/t) = -1$ a.s., $p\in(0,1]$, where
$h_p(t)=(1/z_p(t))p\log\log t$.


title:
Probing polaron excitation spectra in organic semiconductors by
  photoinduced-absorption-detected two-dimensional coherent spectroscopy

abstract:
  We report a theoretical description and experimental implementation of a
novel two-dimensional coherent excitation spectroscopy based on
quasi-steady-state photoinduced absorption measurement of a long-lived
nonlinear population. We have studied a
semiconductor-polymer:fullerene-derivative distributed heterostructure by
measuring the 2D excitation spectrum by means of photoluminescence,
photocurrent and photoinduced absorption from metastable polaronic products. We
conclude that the photoinduced absorption probe is a viable and valuable probe
in this family of 2D coherent spectroscopies.


title:
Deformation theory of bialgebras, higher Hochschild cohomology and
  formality

abstract:
  A first goal of this paper is to precisely relate the homotopy theories of
bialgebras and $E_2$-algebras. For this, we construct a conservative and fully
faithful $\infty$-functor from pointed conilpotent homotopy bialgebras to
augmented $E_2$-algebras which consists in an appropriate "cobar" construction.
Then we prove that the (derived) formal moduli problem of homotopy bialgebras
structures on a bialgebra is equivalent to the (derived) formal moduli problem
of $E_2$-algebra structures on this "cobar" construction. We show consequently
that the $E_3$-algebra structure on the higher Hochschild complex of this cobar
construction, given by the solution to the higher Deligne conjecture, controls
the deformation theory of this bialgebra. This implies the existence of an
$E_3$-structure on the deformation complex of a dg bialgebra, solving a
long-standing conjecture of Gerstenhaber-Schack. On this basis we solve a
long-standing conjecture of Kontsevich, by proving the $E_3$-formality of the
deformation complex of the symmetric bialgebra. This provides as a corollary a
new proof of Etingof-Kazdhan deformation quantization of Lie bialgebras which
extends to homotopy dg Lie bialgebras and is independent from the choice of an
associator. Along the way, we establish new general results of independent
interest about the deformation theory of algebraic structures, which shed a new
light on various deformation complexes and cohomology theories studied in the
literature.


title: Basis entropy: A useful physical quantity about projective measurement

abstract:
  Projective measurement can increase the entropy of a state $\rho$, the
increased entropy is not only up to the basis of projective measurement, but
also has something to do with the properties of the state itself. In this paper
we define this increased entropy as basis entropy. And then we discuss the
usefulness of this new concept by showing its application in deciding whether a
state is pure or not and detecting the existence of quantum discord. And as
shown in the paper, this new concept can also be used to describe decoherence.


title:
On the Prime Graph Question for Integral Group Rings of 4-primary groups
  II

abstract:
  In this article the study of the Prime Graph Question for the integral group
ring of almost simple groups which have an order divisible by exactly $4$
different primes is continued. We provide more details on the recently
developed "lattice method" which involves the calculation of
Littlewood-Richardson coefficients. We apply the method obtaining results
complementary to those previously obtained using the HeLP-method. In particular
the "lattice method" is applied to infinite series of groups for the first
time. We also prove the Zassenhaus Conjecture for four more simple groups.
Furthermore we show that the Prime Graph Question has a positive answer around
the vertex $3$ provided the Sylow $3$-subgroup is of order $3$.


title: Optical model potential of deuteron with $1p$-shell nuclei

abstract:
  A set of global optical potential parameters, DA1p, for deuterons with the
$1p$-shell nuclei is obtained by simultaneously fitting 67 sets of experimental
data of deuteron elastic scattering from \nuc{6}{Li}, \nuc{9}{Be}, \nuc{10}{B},
\nuc{11}{B}, \nuc{12}{C}, \nuc{13}{C}, \nuc{14}{N}, \nuc{16}{O} and \nuc{18}{O}
with incident energies between 5.25 and 170 MeV. DA1p improves the description
of the deuteron elastic scattering from the $1p$-shell nuclei with respect to
the existing systematic deuteron potentials and can give satisfactory
reproduction to the experimental data with radiative nuclei such as
\nuc{9}{Li}, \nuc{10}{Be}, \nuc{14}{C} and \nuc{14}{O}.


title: The higher-order black-body radiation shift of atomic energy-levels

abstract:
  The one-loop correction and two-loop contribution to black-body radiation
(BBR) shift are restudied. The S-matrix approach and nonrelativistic quantum
electrodynamics (NRQED) are adopted in finite temperature case. The
relativistic correction to one-loop BBR-shift has a $(Z\alpha)^{2}\alpha
T^2/m$-order contribution. In the two-loop case, the pure thermal (real) photon
part is too tiny to be detected; while the corrections induced by the thermal
and virtual mixing diagram are at $(Z\alpha)^{2}\alpha^2 T^2/m$ order. We
calculate the relativistic correction to one-loop BBR-shift in the ground state
of hydrogen and ionized helium, which is larger than the leading term. As the
leading term is proportional to $T^4/Z^4$. We estimate these higher-order
corrections may be larger than the leading term, when the system is a highly
ionized (large $Z$) or a cold (small $T$) one.


title:
An Integral Spectral Representation of the Massive Dirac Propagator in
  the Kerr Geometry in Eddington-Finkelstein-type Coordinates

abstract:
  We consider the massive Dirac equation in the non-extreme Kerr geometry in
horizon-penetrating advanced Eddington-Finkelstein-type coordinates and derive
a functional analytic integral representation of the associated propagator
using the spectral theorem for unbounded self-adjoint operators, Stone's
formula, and quantities arising in the analysis of Chandrasekhar's separation
of variables. This integral representation describes the dynamics of Dirac
particles outside and across the event horizon, up to the Cauchy horizon. In
the derivation, we first write the Dirac equation in Hamiltonian form and show
the essential self-adjointness of the Hamiltonian. For the latter purpose, as
the Dirac Hamiltonian fails to be elliptic at the event and the Cauchy horizon,
we cannot use standard elliptic methods of proof. Instead, we employ a new,
general method for mixed initial-boundary value problems that combines results
from the theory of symmetric hyperbolic systems with near-boundary elliptic
methods. In this regard and since the time evolution may not be unitary because
of Dirac particles impinging on the ring singularity, we also impose a suitable
Dirichlet-type boundary condition on a time-like inner hypersurface placed
inside the Cauchy horizon, which has no effect on the dynamics outside the
Cauchy horizon. We then compute the resolvent of the Dirac Hamiltonian via the
projector onto a finite-dimensional, invariant spectral eigenspace of the
angular operator and the radial Green's matrix stemming from Chandrasekhar's
separation of variables. Applying Stone's formula to the spectral measure of
the Hamiltonian in the spectral decomposition of the Dirac propagator, that is,
by expressing the spectral measure in terms of this resolvent, we obtain an
explicit integral representation of the propagator.


title:
Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS
  Equation via Multi-symplectic Scheme

abstract:
  We consider a finite dimensional approximation of the stochastic nonlinear
Schr\"odinger equation driven by multiplicative noise, which is derived by
applying a symplectic method to the original equation in spatial direction.
Both the unique ergodicity and the charge conservation law for this finite
dimensional approximation are obtained on the unit sphere. To simulate the
ergodic limit over long time for the finite dimensional approximation, we
discretize it further in temporal direction to obtain a fully discrete scheme,
which inherits not only the stochastic multi-symplecticity and charge
conservation law of the original equation but also the unique ergodicity of the
finite dimensional approximation. The temporal average of the fully discrete
numerical solution is proved to converge to the ergodic limit with order one
with respect to the time step for a fixed spatial step. Numerical experiments
verify our theoretical results on charge conservation, ergodicity and weak
convergence.


title:
Filtering of Continuous Time Periodically Correlated Isotropic Random
  Fields

abstract:
  The problem of optimal linear estimation of functionals depending on the
unknown values of a random field $\zeta(t,x)$, which is mean-square continuous
periodically correlated with respect to time argument $t\in\mathbb R$ and
isotropic on the unit sphere ${S_n}$ with respect to spatial argument
$x\in{S_n}$. Estimates are based on observations of the field
$\zeta(t,x)+\theta(t,x)$ at points $(t,x):t\leq 0,x\in S_{n}$, where
$\theta(t,x)$ is an uncorrelated with $\zeta(t,x)$ random field, which is
mean-square continuous periodically correlated with respect to time argument
$t\in\mathbb R$ and isotropic on the sphere ${S_n}$ with respect to spatial
argument $x\in{S_n}$. Formulas for calculating the mean square errors and the
spectral characteristics of the optimal linear estimate of functionals are
derived in the case of spectral certainty where the spectral densities of the
fields are exactly known. Formulas that determine the least favourable spectral
densities and the minimax (robust) spectral characteristics are proposed in the
case where the spectral densities are not exactly known while a class of
admissible spectral densities is given.


title:
Large data mass-subcritical NLS: critical weighted bounds imply
  scattering

abstract:
  We consider the mass-subcritical nonlinear Schr\"odinger equation in all
space dimensions with focusing or defocusing nonlinearity. For such equations
with critical regularity $s_c\in(\max\{-1,-\frac{d}{2}\},0)$, we prove that any
solution satisfying $\|\, |x|^{|s_c|}e^{-it\Delta} u\|_{L_t^\infty L_x^2}
<\infty$ on its maximal interval of existence must be global and scatter.


title: C*-envelopes and the Hao-Ng isomorphism for discrete groups

abstract:
  Using non-selfadjoint techniques, we establish the Hao-Ng isomorphism for the
reduced crossed product and all discrete groups. For the full crossed product
an analogous result holds for all discrete groups but the C*-correspondences
involved have to be hyperrigid. These results are obtained by calculating the
C*-envelope of the reduced crossed product of an operator algebra by a discrete
group.


title: The abundance and environment of dark matter haloes

abstract:
  An open question in cosmology and the theory of structure formation is to
what extent does environment affect the properties of galaxies and haloes. The
present paper aims at shedding light on this problem. The paper focuses on the
analysis of a dark matter only simulation and it addresses the issue of how the
environment affects the abundance of haloes, which are are assigned four
attributes: their virial mass, an ambient density calculated with an aperture
that scales with $R_{vir}$ ($\Delta_M$), a fixed-aperture ($\Delta_R$) ambient
density, and a cosmic web classification (i.e. voids, sheets, filaments, and
knots, as defined by the V--web algorithm). $\Delta_M$ is the mean density
around a halo evaluated within a sphere of a radius of $5$\rvir, where \rvir\
is the virial radius. $\Delta_R$ is the density field Gaussian smoothed with
$R=4h^{-1}$Mpc, evaluated at the center of the halo.
  The main result of the paper is that the difference between haloes in
different web elements stems from the difference in their mass functions, and
does not depend on their adaptive-aperture ambient density. A dependence on the
fixed-aperture ambient density is induced by the cross correlation between the
mass of a halo and its fixed-aperture ambient density.


title: Coordination in Categorical Compositional Distributional Semantics

abstract:
  An open problem with categorical compositional distributional semantics is
the representation of words that are considered semantically vacuous from a
distributional perspective, such as determiners, prepositions, relative
pronouns or coordinators. This paper deals with the topic of coordination
between identical syntactic types, which accounts for the majority of
coordination cases in language. By exploiting the compact closed structure of
the underlying category and Frobenius operators canonically induced over the
fixed basis of finite-dimensional vector spaces, we provide a morphism as
representation of a coordinator tensor, and we show how it lifts from atomic
types to compound types. Linguistic intuitions are provided, and the importance
of the Frobenius operators as an addition to the compact closed setting with
regard to language is discussed.


title: The lopsided distribution of satellite galaxies

abstract:
  The distribution of smaller satellite galaxies around large central galaxies
has attracted attention because peculiar spatial and kinematic configurations
have been detected in some systems. A particularly striking example of such
behavior is seen in the satellite system of the Andromeda galaxy, where around
80\% are on the nearside of that galaxy, facing the Milky Way. Motivated by
this departure from anisotropy, we examined the spatial distribution of
satellites around pairs of galaxies in the SDSS. By stacking tens of thousands
of satellites around galaxy pairs we found that satellites tend to bulge
towards the other central galaxy, preferably occupying the space between the
pair, rather than being spherically or axis-symmetrically distributed around
each host. The bulging is a function of the opening angle examined and is
fairly strong -- there are up to $\sim$10\% more satellites in the space
between the pair, than expected from uniform. Consequently, it is a
statistically very strong signal, being inconsistent with a uniform
distribution at the 5$\sigma$ level. The possibility that the observed signal
is the result of the overlap of two haloes with extended satellite
distributions, is ruled out by testing this hypothesis by performing the same
tests on isolated galaxies (and their satellites) artificially placed at
similar separations. These findings highlight the unrelaxed and interacting
nature of galaxies in pairs.


title: Differential geometry of moduli spaces of quiver bundles

abstract:
  Let P be a parabolic subgroup of a simple affine algebraic group G defined
over C and X a compact connected K\"ahler manifold. L. \'Alvarez-C\'onsul and
O. Garc\'ia-Prada associated to these a quiver Q and representations of Q into
holomorphic vector bundles on X. Our aim here is to investigate the
differential geometric properties of the moduli spaces representations of Q
into vector bundles on X. In particular, we construct a Hermitian form on these
moduli spaces. A fiber integral formula is proved for this Hermitian form; this
fiber integral formula implies that the Hermitian form is K\"ahler. We compute
the curvature of this K\"ahler form. Under an assumption which says that X is a
complex projective manifold, this K\"ahler form is realized as the curvature of
a certain determinant line bundle equipped with a Quillen metric.


title:
A resolution of singularities for Drinfeld's compactification by stable
  maps

abstract:
  Drinfeld's relative compactification plays a basic role in the theory of
automorphic sheaves, and its singularities encode representation-theoretic
information in the form of intersection cohomology. We introduce a resolution
of singularities consisting of stable maps from nodal deformations of the curve
into twisted flag varieties. As an application, we prove that the twisted
intersection cohomology sheaf on Drinfeld's compactification is universally
locally acyclic over the moduli stack of $G$-bundles at points sufficiently
antidominant relative to their defect.


title: A Deep Learning Approach to Block-based Compressed Sensing of Images

abstract:
  Compressed sensing (CS) is a signal processing framework for efficiently
reconstructing a signal from a small number of measurements, obtained by linear
projections of the signal. Block-based CS is a lightweight CS approach that is
mostly suitable for processing very high-dimensional images and videos: it
operates on local patches, employs a low-complexity reconstruction operator and
requires significantly less memory to store the sensing matrix. In this paper
we present a deep learning approach for block-based CS, in which a
fully-connected network performs both the block-based linear sensing and
non-linear reconstruction stages. During the training phase, the sensing matrix
and the non-linear reconstruction operator are \emph{jointly} optimized, and
the proposed approach outperforms state-of-the-art both in terms of
reconstruction quality and computation time. For example, at a 25% sensing rate
the average PSNR advantage is 0.77dB and computation time is over 200-times
faster.


title:
Circular polarizations of gravitational waves from core-collapse
  supernovae: a clear indication of rapid rotation

abstract:
  We propose to employ the circular polarization of gravitational waves emitted
by core-collapse supernovae as an unequivocal indication of rapid rotation deep
in their cores. It has been demonstrated by three dimensional simulations that
non-axisymmetric accretion flows may develop spontaneously via hydrodynamical
instabilities in the post-bounce cores. It is not surprising then that the
gravitational waves emitted by such fluid motions are circularly polarized. We
show in this letter that a network of the second generation detectors of
gravitational waves worldwide may be able to detect such polarizations up to
the opposite side of Galaxy as long as the rotation period is shorter than a
few seconds prior to collapse.


title:
Weakly mixing, topologically weakly mixing, and sensitivity for
  non-autonomous discrete systems

abstract:
  This paper is concerned with relationships of weakly mixing, topologically
weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown
that weakly mixing implies topologically weakly mixing and sensitivity for
measurable systems with a fully supported measure; and topological weakly
mixing implies sensitivity for general dynamical systems. However, the inverse
conclusions are not true and some counterexamples are given. The related
existing results for autonomous discrete systems are generalized to
non-autonomous discrete systems and their conditions are weaken.


title:
Measurement of the transverse momentum spectrum of the Higgs boson
  produced in pp collisions at sqrt(s) = 8 TeV using H to WW decays

abstract:
  The cross section for Higgs boson production in pp collisions is studied
using the H to WW decay mode, followed by leptonic decays of the W bosons to an
oppositely charged electron-muon pair in the final state. The measurements are
performed using data collected by the CMS experiment at the LHC at a
centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of
19.4 inverse femtobarns. The Higgs boson transverse momentum (pT) is
reconstructed using the lepton pair pT and missing pT. The differential cross
section times branching fraction is measured as a function of the Higgs boson
pT in a fiducial phase space defined to match the experimental acceptance in
terms of the lepton kinematics and event topology. The production cross section
times branching fraction in the fiducial phase space is measured to be 39 +/- 8
(stat) +/- 9 (syst) fb. The measurements are found to agree, within
experimental uncertainties, with theoretical calculations based on the standard
model.


title:
Thermodynamics of a one-dimensional system of point bosons: comparison
  of the traditional approach with a new one

abstract:
  We compare two approaches to the construction of the thermodynamics of a
one-dimensional periodic system of spinless point bosons: the Yang--Yang
approach and a new approach proposed by the author. In the latter, the
elementary excitations are introduced so that there is only one type of
excitations (as opposed to Lieb's approach with two types of excitations:
particle-like and hole-like). At the weak coupling, these are the excitations
of the Bogolyubov type. The equations for the thermodynamic quantities in these
approaches are different, but their solutions coincide (this is shown below and
is the main result). In this case, the new approach is simpler. An important
point is that the thermodynamic formulae in the new approach for any values of
parameters are formulae for an ensemble of quasiparticles with the Bose
statistics, whereas a formulae in the traditional Yang--Yang approach have the
Fermi-like one-particle form.


title: Universal Schlesinger system and Birkhoff factorization

abstract:
  The aim of this paper is to establish an infinite dimensional generalization
of the Schlesinger system -- a system of PDE's describing isomonodromic
deformations of Fuchsian systems. This universal Schlesinger system first
appeared in a paper by Korotkin and Samtleben in the finite dimensional case
(i.e. when it reduces to the finite dimensional Schlesinger system). We intend
here to establish it in its full generality, and to give its geometrical
meaning in terms of deformations of Birkhoff factorizations.
  The Birkhoff factorization we are considering consists in finding a piecewise
holomorphic matrix-valued function $Y$ on $\mathbb P^1\smallsetminus\mathbb
S^1$ which admits a prescribed multiplicative jump $G : \mathbb S^1\to
\text{GL}_N(\mathbb C)$ across the unit circle $\mathbb S^1$.
  We explain how this factorization can be deformed by the action of the group
of diffeomorphisms of the circle, which acts by composition on the
multiplicative jump $G$. The integrability equations of this "isomonodromic"
deformation is given by the universal Schlesinger system, which is then
naturally expressed by means of Virasoro generators.


title: The Cryogenic Storage Ring CSR

abstract:
  An electrostatic cryogenic storage ring, CSR, for beams of anions and cations
with up to 300 keV kinetic energy per unit charge has been designed,
constructed and put into operation. With a circumference of 35 m, the ion-beam
vacuum chambers and all beam optics are in a cryostat and cooled by a
closed-cycle liquid helium system. At temperatures as low as (5.5 $\pm$ 1) K
inside the ring, storage time constants of several minutes up to almost an hour
were observed for atomic and molecular, anion and cation beams at an energy of
60 keV. The ion-beam intensity, energy-dependent closed-orbit shifts
(dispersion) and the focusing properties of the machine were studied by a
system of capacitive pickups. The Schottky-noise spectrum of the stored ions
revealed a broadening of the momentum distribution on a time scale of 1000 s.
Photodetachment of stored anions was used in the beam lifetime measurements.
The detachment rate by anion collisions with residual-gas molecules was found
to be extremely low. A residual-gas density below 140 cm$^{-3}$ is derived,
equivalent to a room-temperature pressure below 10$^{-14}$ mbar. Fast atomic,
molecular and cluster ion beams stored for long periods of time in a cryogenic
environment will allow experiments on collision- and radiation-induced
fragmentation processes of ions in known internal quantum states with merged
and crossed photon and particle beams.

categories: physics.atom-ph physics.acc-ph physics.atm-clus physics.chem-ph


title: Distances between classes in $W^{1,1}(\Omega;{\mathbb S}^1)$

abstract:
  We introduce an equivalence relation on the space $W^{1,1}(\Omega;{\mathbb
S}^1)$ which classifies maps according to their "topological singularities". We
establish sharp bounds for the distances (in the usual sense and in the
Hausdorff sense) between the equivalence classes. Similar questions are
examined for the space $W^{1,p}(\Omega;{\mathbb S}^1)$ when $p>1$.


title: On the singularity type of full mass currents in big cohomology classes

abstract:
  Let $X$ be a compact K\"ahler manifold and $\{\theta\}$ be a big cohomology
class. We prove several results about the singularity type of full mass
currents, answering a number of open questions in the field. First, we show
that the Lelong numbers and multiplier ideal sheaves of
$\theta$-plurisubharmonic functions with full mass are the same as those of the
current with minimal singularities. Second, given another big and nef class
$\{\eta\}$, we show the inclusion $\mathcal{E}(X,\eta) \cap {PSH}(X,\theta)
\subset \mathcal{E}(X,\theta).$ Third, we characterize big classes whose full
mass currents are "additive". Our techniques make use of a characterization of
full mass currents in terms of the envelope of their singularity type. As an
essential ingredient we also develop the theory of weak geodesics in big
cohomology classes. Numerous applications of our results to complex geometry
are also given.


title: A Dirichlet Form approach to MCMC Optimal Scaling

abstract:
  This paper develops the use of Dirichlet forms to deliver proofs of optimal
scaling results for Markov chain Monte Carlo algorithms (specifically,
Metropolis-Hastings random walk samplers) under regularity conditions which are
substantially weaker than those required by the original approach (based on the
use of infinitesimal generators). The Dirichlet form methods have the added
advantage of providing an explicit construction of the underlying
infinite-dimensional context. In particular, this enables us directly to
establish weak convergence to the relevant infinite-dimensional distributions.


title:
Accretion disks around neutron and strange stars in $\mathcal{R}^2$
  gravity

abstract:
  We study the electromagnetic spectrum of accretion disks around neutron and
strange stars in $\mathcal{R}^2$ gravity. Both static and rapidly rotating
models are investigated. The results are compared with the General Relativistic
results. We found difference between the results in both theories of about 50\%
for the electromagnetic flux and about 20\% in the luminosity for models with
equal mass and angular velocity in both theories. The observed differences are
much lower for models rotating with Kelperian velocity and with equal masses.


title: Adaptive Submodular Ranking and Routing

abstract:
  We study a general stochastic ranking problem where an algorithm needs to
adaptively select a sequence of elements so as to "cover" a random scenario
(drawn from a known distribution) at minimum expected cost. The coverage of
each scenario is captured by an individual submodular function, where the
scenario is said to be covered when its function value goes above a given
threshold. We obtain a logarithmic factor approximation algorithm for this
adaptive ranking problem, which is the best possible (unless P=NP). This
problem unifies and generalizes many previously studied problems with
applications in search ranking and active learning. The approximation ratio of
our algorithm either matches or improves the best result known in each of these
special cases. Furthermore, we extend our results to an adaptive vehicle
routing problem, where costs are determined by an underlying metric. This
routing problem is a significant generalization of the previously-studied
adaptive traveling salesman and traveling repairman problems. Our approximation
ratio nearly matches the best bound known for these special cases. Finally, we
present experimental results for some applications of adaptive ranking.


title: Bound States via Higgs Exchanging and Resonant Di-Higgs

abstract:
  The standard model (SM)-like Higgs boson $h$ has spin zero and light mass
around weak scale, so it has the potential to mediate a new and relatively
strong force for the particle $\phi$ in the new physics (NP) sector; then
$\phi$ may form bound state $B_h$ via exchanging $h$. This phenomena may arise
in a wide context, for instance composite Higgs, supersymmetry (SUSY) and
radiative neutrino (or more widely in the models with a strong Higgs portal for
triggering classical scale symmetry breaking or strong first-order phase
transition). For illustration we focus on two typical examples, the
stop/sbottom sector and an inert Higgs doublet. Furthermore, we point out that
$B_h$ must give rise to a clear resonant di-Higgs signature, which recently has
been extensively searched for at the large hadron collider (LHC). Moreover,
Higgs radiative decay such as to di-photon probably will be significantly
modified provided that $\phi$ is charged or/and colored.


title:
Distinguishing Thermal Fluctuations from Instrumental Error for High
  Pressure Charged Gas

abstract:
  Thermodynamic parameters such as temperature and pressure can be defined from
the statistical behavior of a system. Therefore, thermal fluctuation is an
inseparable characteristic of these parameters which eventually finds its way
into experimental data. Analyzing these fluctuations is very useful in studying
the phase transitions of a physical system or its behavior around critical
points. However, this approach is not straightforward as most of the times it
is impossible to distinguish meaningful thermal fluctuations from those due to
the instrumental errors. In this article, we have offered a method by which an
experimenter can separate this multi-sourced fluctuation into its constitutive
parts according to their sources. Although the article is only focused on a
specific system, which is a high pressure charged gas, we have used a
computational method which could be used for various other systems. Our
proposed idea is very efficient and reduces the required computation time by a
remarkable fraction. We have used Euler algorithm, which generally does not
hold the internal energy conserved; But we have used this fact as a tool which
allows us to surf in the phase space of the system and reach different energy
levels in significantly less time. Although system does not spend enough time
in a single energy level to equilibrate, but we have been able to extract the
details of the equilibrium state out of our data. Using numerical computations
combined with theoretical modelings we have given a final expression for the
amount of the overall fluctuations existing in the measured pressure values.
This expression is given in terms of the characteristics of both the gas and
the barometer so that it can be experimentally verified.


title: Sum uncertainty relations based on Wigner-Yanase skew information

abstract:
  We study sum uncertainty relations for arbitrary finite $N$ quantum
mechanical observables. Some uncertainty inequalities are presented by using
skew information introduced by Wigner and Yanase. These uncertainty
inequalities are nontrivial as long as the observables are mutually
noncommutative. The relations among these new and existing uncertainty
inequalities have been investigated. Detailed examples are presented.


title: Spatial Gibbs random graphs

abstract:
  Many real-world networks of interest are embedded in physical space. We
present a new random graph model aiming to reflect the interplay between the
geometries of the graph and of the underlying space. The model favors
configurations with small average graph distance between vertices, but adding
an edge comes at a cost measured according to the geometry of the ambient
physical space. In most cases, we identify the order of magnitude of the
average graph distance as a function of the parameters of the model. As the
proofs reveal, hierarchical structures naturally emerge from our simple
modeling assumptions. Moreover, a critical regime exhibits an infinite number
of discontinuous phase transitions.


title:
What is the Best Feature Learning Procedure in Hierarchical Recognition
  Architectures?

abstract:
  (This paper was written in November 2011 and never published. It is posted on
arXiv.org in its original form in June 2016). Many recent object recognition
systems have proposed using a two phase training procedure to learn sparse
convolutional feature hierarchies: unsupervised pre-training followed by
supervised fine-tuning. Recent results suggest that these methods provide
little improvement over purely supervised systems when the appropriate
nonlinearities are included. This paper presents an empirical exploration of
the space of learning procedures for sparse convolutional networks to assess
which method produces the best performance. In our study, we introduce an
augmentation of the Predictive Sparse Decomposition method that includes a
discriminative term (DPSD). We also introduce a new single phase supervised
learning procedure that places an L1 penalty on the output state of each layer
of the network. This forces the network to produce sparse codes without the
expensive pre-training phase. Using DPSD with a new, complex predictor that
incorporates lateral inhibition, combined with multi-scale feature pooling, and
supervised refinement, the system achieves a 70.6\% recognition rate on
Caltech-101. With the addition of convolutional training, a 77\% recognition
was obtained on the CIfAR-10 dataset.


title:
Leveraging energy storage to optimize data center electricity cost in
  emerging power markets

abstract:
  Energy storage in data centers has mainly been used as devices to backup
generators during power outages. Recently, there has been a growing interest in
using energy storage devices to actively shape power consumption in data
centers to reduce their skyrocketing electricity bills. In this paper, we
consider using energy storage in data centers for two applications in a joint
fashion: reducing peak demand charges and enabling data centers to participate
in regulation markets. We develop an optimization framework that captures the
cost of electricity, degradation of energy storage devices, as well as the
benefit from regulation markets. Under this frame- work, using real data
Microsoft data center traces and PJM regulation signals, we show the
electricity bill of a data center can be reduced by up to 20%. Furthermore, we
demonstrate that the saving from joint optimization can be even larger than the
sum of individually optimizing each component. We quantify the particular
aspects of data center load profiles that lead to this superlinear gain.
Compared to prior works that consider using energy storage devices for each
single application alone, our results suggest that energy storage in data
centers can have much larger impacts than previously thought possible.


title: Bousfield Localization and Eilenberg-Moore Categories

abstract:
  We prove the equivalence of several hypotheses that have appeared recently in
the literature for studying left Bousfield localization and algebras over a
monad. We find conditions so that there is a model structure for local
algebras, so that localization preserves algebras, and so that localization
lifts to the level of algebras. We include examples coming from the theory of
colored operads, and applications to spaces, spectra, and chain complexes.


title:
Exacerbating the cosmological constant problem with interacting dark
  energy

abstract:
  Future cosmological surveys will probe the expansion history of the universe
and constrain phenomenological models of dark energy. Such models do not
address the fine-tuning problem of the vacuum energy, i.e. the cosmological
constant problem (c.c.p.), but can make it spectacularly worse. We show that
this is the case for 'interacting dark energy' models in which the masses of
the dark matter states depend on the dark energy sector. If realised in nature,
these models have far-reaching implications for proposed solutions to the
c.c.p. that require the number of vacua to exceed the fine-tuning of the vacuum
energy density. We show that current estimates of the number of flux vacua in
string theory, $N_{\rm vac} \sim {\cal O}(10^{272,000})$, is far too small to
realise certain simple models of interacting dark energy \emph{and} solve the
cosmological constant problem anthropically. These models admit distinctive
observational signatures that can be targeted by future gamma-ray
observatories, hence making it possible to observationally rule out the
anthropic solution to the cosmological constant problem in theories with a
finite number of vacua.


title: Understanding the Thermoelectric Properties of LaCoO$_{3}$ Compound

abstract:
  We present the thermoelectric (TE) properties of LaCoO$_{3}$ compound in the
temperature range 300-600 K. The experimental value of Seebeck coefficient
($\alpha$) at 300 K is found to be $\sim$635 $\mu$V/K. The value of $\alpha$
decreases continuously with increase in temperature and reaches to $\sim$46
$\mu$V/K at $\sim$600 K. The electronic and TE properties of the compound have
also been investigated by combining the \textit{ab-initio} electronic
structures and Boltzmann transport calculations. LSDA plus Hubbard U (U= 2.75
eV) calculation on low spin configuration of the compound gives an energy gap
of $\sim$0.5 eV, which is close to the experimentally reported energy gap. The
effective mass of holes (\textit{m$^{*}_h$}) at $\Gamma$ point is nearly two
times larger than the value of effective mass of electrons (\textit{m$^{*}_e$})
at FB point along the L and T directions, whereas the \textit{m$^{*}_e$} at FB
point along the $\Gamma$ direction is nearly eight times larger than the value
of \textit{m$^{*}_h$} at $\Gamma$ point along the FB direction. The large
effective mass at FB point along the $\Gamma$ direction suggests that the TE
property of this compound is mainly decided by the effective mass of the charge
carriers in this direction. The calculated temperature dependent values of
$\alpha$ are in fairly good agreement with experimental data in the temperature
range 300-360 K, and above this temperature slight deviation is observed. The
value of power factor (PF) for \textit{n}-type is $\sim$1.3 times larger the
value of \textit{p}-type doped compound at 1100 K. The value of
\textit{figure-of-merit} (\textit{ZT}) for \textit{n}-type doped compound is
obtained $\sim$0.35 in the temperature range 600-1100 K, which suggests that
with appropriate \textit{n}-type doping this compound can be used as a good TE
material in the high temperature region.


title: OpenAI Gym

abstract:
  OpenAI Gym is a toolkit for reinforcement learning research. It includes a
growing collection of benchmark problems that expose a common interface, and a
website where people can share their results and compare the performance of
algorithms. This whitepaper discusses the components of OpenAI Gym and the
design decisions that went into the software.


title: Deep Reinforcement Learning for Dialogue Generation

abstract:
  Recent neural models of dialogue generation offer great promise for
generating responses for conversational agents, but tend to be shortsighted,
predicting utterances one at a time while ignoring their influence on future
outcomes. Modeling the future direction of a dialogue is crucial to generating
coherent, interesting dialogues, a need which led traditional NLP models of
dialogue to draw on reinforcement learning. In this paper, we show how to
integrate these goals, applying deep reinforcement learning to model future
reward in chatbot dialogue. The model simulates dialogues between two virtual
agents, using policy gradient methods to reward sequences that display three
useful conversational properties: informativity (non-repetitive turns),
coherence, and ease of answering (related to forward-looking function). We
evaluate our model on diversity, length as well as with human judges, showing
that the proposed algorithm generates more interactive responses and manages to
foster a more sustained conversation in dialogue simulation. This work marks a
first step towards learning a neural conversational model based on the
long-term success of dialogues.


title: Scattered locally C*-algebras

abstract:
  In this paper, we introduce the notion of a scattered locally $C^{\ast }$
-algebra and we give conditions for a locally $C^{\ast }$-algebra to be
scattered. Given an action $\alpha $ of a locally compact group $G$ on a
scattered locally $C^{\ast }$-algebra $A[\tau_{\Gamma }]$, it is natural to ask
under what conditions the crossed product $A[\tau_{\Gamma }]\times_{\alpha }G$
is also scattered. We obtain some results concerning this question.


title: Permanence and Community Structure in Complex Networks

abstract:
  The goal of community detection algorithms is to identify densely-connected
units within large networks. An implicit assumption is that all the constituent
nodes belong equally to their associated community. However, some nodes are
more important in the community than others. To date, efforts have been
primarily driven to identify communities as a whole, rather than understanding
to what extent an individual node belongs to its community. Therefore, most
metrics for evaluating communities, for example modularity, are global. These
metrics produce a score for each community, not for each individual node. In
this paper, we argue that the belongingness of nodes in a community is not
uniform.
  The central idea of permanence is based on the observation that the strength
of membership of a vertex to a community depends upon two factors: (i) the the
extent of connections of the vertex within its community versus outside its
community, and (ii) how tightly the vertex is connected internally. We discuss
how permanence can help us understand and utilize the structure and evolution
of communities by demonstrating that it can be used to -- (i) measure the
persistence of a vertex in a community, (ii) design strategies to strengthen
the community structure, (iii) explore the core-periphery structure within a
community, and (iv) select suitable initiators for message spreading.
  We demonstrate that the process of maximizing permanence produces meaningful
communities that concur with the ground-truth community structure of the
networks more accurately than eight other popular community detection
algorithms. Finally, we show that the communities obtained by this method are
(i) less affected by the changes in vertex-ordering, and (ii) more resilient to
resolution limit, degeneracy of solutions and asymptotic growth of values.


title:
Continuum dynamics of the formation, migration and dissociation of
  self-locked dislocation structures on parallel slip planes

abstract:
  In continuum models of dislocations, proper formulations of short-range
elastic interactions of dislocations are crucial for capturing various types of
dislocation patterns formed in crystalline materials. In this article, the
continuum dynamics of straight dislocations distributed on two parallel slip
planes is modelled through upscaling the underlying discrete dislocation
dynamics. Two continuum velocity field quantities are introduced to facilitate
the discrete-to-continuum transition. The first one is the local migration
velocity of dislocation ensembles which is found fully independent of the
short-range dislocation correlations. The second one is the decoupling velocity
of dislocation pairs controlled by a threshold stress value, which is proposed
to be the effective flow stress for single slip systems. Compared to the almost
ubiquitously adopted Taylor relationship, the derived flow stress formula
exhibits two features that are more consistent with the underlying discrete
dislocation dynamics: i) the flow stress increases with the in-plane component
of the dislocation density only up to a certain value, hence the derived
formula admits a minimum inter-dislocation distance within slip planes; ii) the
flow stress smoothly transits to zero when all dislocations become
geometrically necessary dislocations. A regime under which inhomogeneities in
dislocation density grow is identified, and is further validated through
comparison with discrete dislocation dynamical simulation results. Based on the
findings in this article and in our previous works, a general strategy for
incorporating short-range dislocation correlations in continuum models of
dislocations is proposed.


title: Neural Net Models for Open-Domain Discourse Coherence

abstract:
  Discourse coherence is strongly associated with text quality, making it
important to natural language generation and understanding. Yet existing models
of coherence focus on measuring individual aspects of coherence (lexical
overlap, rhetorical structure, entity centering) in narrow domains.
  In this paper, we describe domain-independent neural models of discourse
coherence that are capable of measuring multiple aspects of coherence in
existing sentences and can maintain coherence while generating new sentences.
We study both discriminative models that learn to distinguish coherent from
incoherent discourse, and generative models that produce coherent text,
including a novel neural latent-variable Markovian generative model that
captures the latent discourse dependencies between sentences in a text.
  Our work achieves state-of-the-art performance on multiple coherence
evaluations, and marks an initial step in generating coherent texts given
discourse contexts.


title:
Some homological properties of skew PBW extensions arising in
  non-commutative algebraic geometry

abstract:
  In this short paper we study for the skew PBW (Poincar\'e-Birkhoff-Witt)
extensions some homological properties arising in non-commutative algebraic
geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and
strongly noetherianity. Skew PBW extensions include a considerable number of
non-commutative rings of polynomial type such that classical PBW extensions,
quantum polynomial rings, multiplicative analogue of the Weyl algebra, some
Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in
3 variables, among many others. For some key examples we present the
parametrization of its point modules.


title:
The influence of elastic strain gradient on the upper limit of
  flexocoupling strength, spatially-modulated phases and soft phonon dispersion
  in ferroics

abstract:
  Within the framework of Landau-Ginzburg-Devonshire (LGD) theory we studied
the role of the flexocoupling between the order parameter and elastic strain
gradients in the stability of a spatially-modulated phase (SMP) in ferroics
with commensurate and incommensurate long-range ordered phases under the
presence of squired elastic strain gradient. The squired elastic strain
gradient is required for the free energy stability to arbitrary strain
gradients. Obtained analytical expressions showed that the fundamental upper
limit for the magnitude of the static bulk flexoelectric effect strength,
established by Yudin and Tagantsev under the absence of squired elastic strain
gradient and higher order gradients terms, should be substituted by the
temperature-dependent condition on the flexoelectric coupling strength under
the presence of the gradient terms. Moreover, we established that the SMP
appears and becomes stable in commensurate ferroics if the flexocoupling
constant exceeds the critical value, defined by the reduced temperature, strain
and order parameter gradients constants, striction and expansion coefficients
in the LGD functional. We calculated the soft phonon dispersion in ferroics
with commensurate and incommensurate long-range ordered phases allowing for the
squired elastic strain gradient, as well as static and dynamic flexocoupling.
Appeared that the dispersion for the optic mode is slightly sensitive to the
flexocoupling, while the dispersion of acoustic mode strongly depends on the
coupling strength. Obtained results demonstrate that the non-trivial
differences in the dispersion of optic and acoustic modes appear under the
change of flexocoupling constant.


title: Exact Recovery with Symmetries for Procrustes Matching

abstract:
  The Procrustes matching (PM) problem is the problem of finding the optimal
rigid motion and labeling of two point sets so that they are as close as
possible. Both rigid and non-rigid shape matching problems can be formulated as
PM problems. Recently [Maron et al.] presented a novel convex semi-definite
programming relaxation (PM-SDP) for PM which achieves state of the art results
on common shape matching benchmarks.
  In this paper we analyze the successfulness of PM-SDP in solving PM problems
without noise (Exact PM problems). We begin by showing Exact PM to be
computationally equivalent to the graph isomorphism problem. We demonstrate
some natural theoretical properties of the relaxation, and use these properties
together with the moment interpretation of [Lasserre] to show that for exact PM
problems and for (generic) input shapes which are asymmetric or bilaterally
symmetric, the relaxation returns a correct solution of PM.
  For symmetric shapes, PM has multiple solutions. The non-convex set of
optimal solutions of PM is strictly contained in the convex set of optimal
solutions of PM-SDP, so that `most' solutions of PM-SDP will not be solutions
of PM. We deal with this by showing the solution set of PM to be the extreme
points of the solution set of PM-SDP, and suggesting a random algorithm which
returns a solution of PM with probability one, and returns all solutions of PM
with equal probability. We also show these results can be extended to the
almost-exact case.
  To the best of our knowledge, our work is the first to achieve exact recovery
in the presence of multiple solutions.


title: Gated-Attention Readers for Text Comprehension

abstract:
  In this paper we study the problem of answering cloze-style questions over
documents. Our model, the Gated-Attention (GA) Reader, integrates a multi-hop
architecture with a novel attention mechanism, which is based on multiplicative
interactions between the query embedding and the intermediate states of a
recurrent neural network document reader. This enables the reader to build
query-specific representations of tokens in the document for accurate answer
selection. The GA Reader obtains state-of-the-art results on three benchmarks
for this task--the CNN \& Daily Mail news stories and the Who Did What dataset.
The effectiveness of multiplicative interaction is demonstrated by an ablation
study, and by comparing to alternative compositional operators for implementing
the gated-attention. The code is available at
https://github.com/bdhingra/ga-reader.


title: Pairwise Quantization

abstract:
  We consider the task of lossy compression of high-dimensional vectors through
quantization. We propose the approach that learns quantization parameters by
minimizing the distortion of scalar products and squared distances between
pairs of points. This is in contrast to previous works that obtain these
parameters through the minimization of the reconstruction error of individual
points. The proposed approach proceeds by finding a linear transformation of
the data that effectively reduces the minimization of the pairwise distortions
to the minimization of individual reconstruction errors. After such
transformation, any of the previously-proposed quantization approaches can be
used. Despite the simplicity of this transformation, the experiments
demonstrate that it achieves considerable reduction of the pairwise distortions
compared to applying quantization directly to the untransformed data.


title:
Enhancement of hopping conductivity by spontaneous fractal ordering of
  low-energy sites

abstract:
  Variable-range hopping conductivity has long been understood in terms of a
canonical prescription for relating the single-particle density of states to
the temperature-dependent conductivity. Here we demonstrate that this
prescription breaks down in situations where a large and long-ranged random
potential develops. In particular, we examine a canonical model of a completely
compensated semiconductor, and we show that at low temperatures hopping
proceeds along self-organized, low-dimensional subspaces having fractal
dimension $d = 2$. We derive and study numerically the spatial structure of
these subspaces, as well as the conductivity and density of states that result
from them. One of our prominent findings is that fractal ordering of low energy
sites greatly enhances the hopping conductivity, and allows Efros-Shklovskii
type conductivity to persist up to unexpectedly high temperatures.


title:
View-tolerant face recognition and Hebbian learning imply
  mirror-symmetric neural tuning to head orientation

abstract:
  The primate brain contains a hierarchy of visual areas, dubbed the ventral
stream, which rapidly computes object representations that are both specific
for object identity and relatively robust against identity-preserving
transformations like depth-rotations. Current computational models of object
recognition, including recent deep learning networks, generate these properties
through a hierarchy of alternating selectivity-increasing filtering and
tolerance-increasing pooling operations, similar to simple-complex cells
operations. While simulations of these models recapitulate the ventral stream's
progression from early view-specific to late view-tolerant representations,
they fail to generate the most salient property of the intermediate
representation for faces found in the brain: mirror-symmetric tuning of the
neural population to head orientation. Here we prove that a class of
hierarchical architectures and a broad set of biologically plausible learning
rules can provide approximate invariance at the top level of the network. While
most of the learning rules do not yield mirror-symmetry in the mid-level
representations, we characterize a specific biologically-plausible Hebb-type
learning rule that is guaranteed to generate mirror-symmetric tuning to faces
tuning at intermediate levels of the architecture.


title: Computing Heegaard genus is NP-hard

abstract:
  We show that {\sc Heegaard Genus $\leq g$}, the problem of deciding whether a
triangulated 3-manifold admits a Heegaard splitting of genus less than or equal
to $g$, is NP-hard. The result follows from a quadratic time reduction of the
NP-complete problem {\sc CNF-SAT} to {\sc Heegaard Genus $\leq g$}.


title:
Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional
  Estimators

abstract:
  We provide finite-sample analysis of a general framework for using k-nearest
neighbor statistics to estimate functionals of a nonparametric continuous
probability density, including entropies and divergences. Rather than plugging
a consistent density estimate (which requires $k \to \infty$ as the sample size
$n \to \infty$) into the functional of interest, the estimators we consider fix
k and perform a bias correction. This is more efficient computationally, and,
as we show in certain cases, statistically, leading to faster convergence
rates. Our framework unifies several previous estimators, for most of which
ours are the first finite sample guarantees.


title: Spontaneous breaking of time-reversal symmetry in topological insulators

abstract:
  The system of spinless fermions on a hexagonal lattice is studied . We have
considered tight-binding model with the hopping integrals between the
nearest-neighbor and next-nearest-neighbor lattice sites, that depend on the
direction of the link. The links are divided on three types depending on the
direction, the hopping integrals are defined by different phases along the
links. The energy of the system depends on the phase differences, the solutions
for the phases, that correspond to the minimums of the energy, lead to a
topological insulator state with the nontrivial Chern numbers. We have analyzed
distinct topological states and phase transitions, the behavior of the chiral
gapless edge modes, have defined the Chern numbers. The band structure of
topological insulator (TI) is calculated, the ground-state phase diagram in the
parameter space is obtained. We propose a novel mechanism of realization of TI,
when the TI state is result of spontaneous breaking of time-reversal symmetry
due to nontrivial stable solutions for the phases that determine the hopping
integrals along the links and show that the Haldane model can be implemented in
real compounds of the condensed matter physics.


title: Arrays of coupled chemical oscillators

abstract:
  Oscillating chemical reactions result from complex periodic changes in the
concentration of the reactants. In spatially ordered ensembles of candle flame
oscillators the fluctuations in the ratio of oxygen atoms with respect to that
of carbon, hydrogen and nitrogen produces an oscillation in the visible part of
the flame related to the energy released per unit mass of oxygen. Thus, the
products of the reaction vary in concentration as a function of time, giving
rise to an oscillation in the amount of soot and radiative emission.
Synchronisation of interacting dynamical sub-systems occurs as arrays of flames
that act as master and slave oscillators, with groups of candles numbering
greater than two, creating a synchronised motion in three-dimensions. In a ring
of candles the visible parts of each flame move together, up and down and back
and forth, in a manner that appears like a "worship". Here this effect is shown
for rings of flames which collectively empower a central flame to pulse to
greater heights. In contrast, situations where the central flames are
suppressed are also found. The phenomena leads to in-phase synchronised states
emerging between periods of anti-phase synchronisation for arrays with
different columnar sizes of candle and positioning.


title:
An Energy-Efficient Compressive Sensing Framework Incorporating Online
  Dictionary Learning for Long-term Wireless Health Monitoring

abstract:
  Wireless body area network (WBAN) is emerging in the mobile healthcare area
to replace the traditional wire-connected monitoring devices. As wireless data
transmission dominates power cost of sensor nodes, it is beneficial to reduce
the data size without much information loss. Compressive sensing (CS) is a
perfect candidate to achieve this goal compared to existing compression
techniques. In this paper, we proposed a general framework that utilize CS and
online dictionary learning (ODL) together. The learned dictionary carries
individual characteristics of the original signal, under which the signal has
an even sparser representation compared to pre-determined dictionaries. As a
consequence, the compression ratio is effectively improved by 2-4x comparing to
prior works. Besides, the proposed framework offloads pre-processing from
sensor nodes to the server node prior to dictionary learning, providing further
reduction in hardware costs. As it is data driven, the proposed framework has
the potential to be used with a wide range of physiological signals.


title:
The Evolution and Internal Structure of Jupiter and Saturn with
  Compositional Gradients

abstract:
  The internal structure of gas giant planets may be more complex than the
commonly assumed core-envelope structure with an adiabatic temperature profile.
Different primordial internal structures as well as various physical processes
can lead to non-homogenous compositional distributions. A non-homogenous
internal structure has a significant impact on the thermal evolution and final
structure of the planets. In this paper, we present alternative structure and
evolution models for Jupiter and Saturn allowing for non-adiabatic primordial
structures and the mixing of heavy elements by convection as these planets
evolve. We present the evolution of the planets accounting for various initial
composition gradients, and in the case of Saturn, include the formation of a
helium-rich region as a result of helium rain. We investigate the stability of
regions with composition gradients against convection, and find that the helium
shell in Saturn remains stable and does not mix with the rest of the envelope.
In other cases, convection mixes the planetary interior despite the existence
of compositional gradients, leading to the enrichment of the envelope with
heavy elements. We show that non-adiabatic structures (and cooling histories)
for both Jupiter and Saturn are feasible. The interior temperatures in that
case are much higher that for standard adiabatic models. We conclude that the
internal structure is directly linked to the formation and evolution history of
the planet. These alternative internal structures of Jupiter and Saturn should
be considered when interpreting the upcoming Juno and Cassini data.


title: A note on the tolerated Tverberg theorem

abstract:
  In this paper we give an asymptotically tight bound for the tolerated
Tverberg Theorem when the dimension and the size of the partition are fixed. To
achieve this we study certain partitions of order-type homogeneous sets and use
a generalization of the Erd\H{o}s-Szekeres theorem.


title:
The distribution of first hitting times of random walks on
  Erd\H{o}s-R\'enyi networks

abstract:
  Analytical results for the distribution of first hitting times of random
walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random
initial node, a random walker hops between adjacent nodes until it hits a node
which it has already visited before. At this point, the path terminates. The
path length, namely the number of steps, $d$, pursued by the random walker from
the initial node up to its termination is called the first hitting time or the
first intersection length. Using recursion equations, we obtain analytical
results for the tail distribution of the path lengths, $P(d > \ell)$. The
results are found to be in excellent agreement with numerical simulations. It
is found %turns out that the distribution $P(d > \ell)$ follows a product of an
exponential distribution and a Rayleigh distribution. The mean, median and
standard deviation of this distribution are also calculated, in terms of the
network size and its mean degree. The termination of an RW path may take place
either by backtracking to the previous node or by retracing of its path, namely
stepping into a node which has been visited two or more time steps earlier. We
obtain analytical results for the probabilities, $p_b$ and $p_r$, that the
cause of termination will be backtracking or retracing, respectively. It is
shown that in dilute networks the dominant termination scenario is backtracking
while in dense networks most paths terminate by retracing. We also obtain
expressions for the conditional distributions $P(d=\ell | b)$ and $P(d=\ell |
r)$, for those paths which are terminated by backtracking or by retracing,
respectively. These results provide useful insight into the general problem of
survival analysis and the statistics of mortality rates when two or more
termination scenarios coexist.


title: Shallow Networks for High-Accuracy Road Object-Detection

abstract:
  The ability to automatically detect other vehicles on the road is vital to
the safety of partially-autonomous and fully-autonomous vehicles. Most of the
high-accuracy techniques for this task are based on R-CNN or one of its faster
variants. In the research community, much emphasis has been applied to using 3D
vision or complex R-CNN variants to achieve higher accuracy. However, are there
more straightforward modifications that could deliver higher accuracy? Yes. We
show that increasing input image resolution (i.e. upsampling) offers up to 12
percentage-points higher accuracy compared to an off-the-shelf baseline. We
also find situations where earlier/shallower layers of CNN provide higher
accuracy than later/deeper layers. We further show that shallow models and
upsampled images yield competitive accuracy. Our findings contrast with the
current trend towards deeper and larger models to achieve high accuracy in
domain specific detection tasks.


title:
Spin current contribution in the spectrum of collective excitations of
  degenerate partially polarized spin-1/2 fermions at separate dynamics of
  spin-up and spin-down fermions

abstract:
  The spectrum of collective excitations of degenerate partially polarized
spin-1/2 fermions is considered. The spin-up fermions and the spin-down
fermions are considered as different fluids. Corresponding two-fluid
hydrodynamics consistent with a non-linear Pauli equation is suggested. An
equation of state for the spin current caused by the distribution of particles
on different energy levels is suggested for the degenerate regime, where the
spin current is caused by the Pauli blocking. Spectrum of three waves is found
as a solution of the hydrodynamic equations: two sound waves and one spin wave.
Their spectrums are calculated for two regimes: propagation parallel and
perpendicular to the direction of the equilibrium spin polarization.


title: Spectral analysis for differential systems with a singularity

abstract:
  We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with
$n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal,
$A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some
distinguished fundamental system of solutions is constructed. Also, we discuss
the inverse scattering problem and obtain the uniqueness result.


title:
Quasi-symmetries and rigidity for determinantal point processes
  associated with de Branges spaces

abstract:
  In this note, we show that determinantal point processes on the real line
corresponding to de Branges spaces of entire functions are rigid in the sense
of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under
the group of diffeomorphisms of the line with compact support.


title:
Breaking of Galilean invariance in the hydrodynamic formulation of
  ferromagnetic thin films

abstract:
  Microwave magnetodynamics in ferromagnets are often studied in the
small-amplitude or weakly nonlinear regime corresponding to modulations of a
well-defined magnetic state. However, strongly nonlinear regimes, where the
aforementioned approximations are not applicable, have become experimentally
accessible. By re-interpreting the governing Landau-Lifshitz equation of
motion, we derive an exact set of equations of dispersive hydrodynamic form
that are amenable to analytical study even when full nonlinearity and exchange
dispersion are included. The resulting equations are shown to, in general,
break Galilean invariance. A magnetic Mach number is obtained as a function of
static and moving reference frames. The simplest class of solutions are termed
uniform hydrodynamic states (UHSs), which exhibit fluid-like behavior including
laminar flow at subsonic speeds and the formation of a Mach cone and
wave-fronts at supersonic speeds. A regime of modulational instability is also
possible, where the UHS is violently unstable. The hydrodynamic interpr


title:
Finite Gr\"obner basis algebra with unsolvable nilpotency problem and
  zero divisors problem

abstract:
  This work presents a sample constructions of two algebras both with the ideal
of relations defined by a finite Gr\"obner basis. For the first algebra the
question whether a given element is nilpotent is algorithmically unsolvable,
for the second one the question whether a given element is a zero divisor is
algorithmically unsolvable. This gives a negative answer to questions raised by
Latyshev.


title:
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction
  via Low-Rank Hankel Matrix Completion

abstract:
  A spectrally sparse signal of order $r$ is a mixture of $r$ damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of $n$ regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that $O(r^2\log^2(n))$ number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on $3$D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data.


title: Active Regression with Adaptive Huber Loss

abstract:
  This paper addresses the scalar regression problem through a novel solution
to exactly optimize the Huber loss in a general semi-supervised setting, which
combines multi-view learning and manifold regularization. We propose a
principled algorithm to 1) avoid computationally expensive iterative schemes
while 2) adapting the Huber loss threshold in a data-driven fashion and 3)
actively balancing the use of labelled data to remove noisy or inconsistent
annotations at the training stage. In a wide experimental evaluation, dealing
with diverse applications, we assess the superiority of our paradigm which is
able to combine robustness towards noise with both strong performance and low
computational cost.


title: Generalized elastica problems under area constraint

abstract:
  It was recently proved that the elastic energy
$E(\gamma)=\tfrac{1}{2}\int_\gamma\kappa^2 ds$ of a closed curve $\gamma$ with
curvature $\kappa$ has a minimizer among all plane, simple, regular and closed
curves of given enclosed area $A(\gamma)$, and that the minimum is attained
only for circles. Here we show under which hypothesis the result can be
extended to other functionals involving the curvature. As an example we show
that the optimal shape remains a circle for the $p$-elastic energy
$\int_\gamma|\kappa|^p ds$, whenever $p>1$.


title:
SDEs with uniform distributions: Peacocks, Conic martingales and ergodic
  uniform diffusions

abstract:
  It is known since Kellerer (1972) that for any process that is increasing for
the convex order, or "peacock" as in Hirsch et al. 2011, there exist
martingales with the same marginals laws. Nevertheless, there is no general
constructive method for finding such martingales that yields diffusions. We
consider the uniform peacock, namely the peacock with uniform law at all times
on a generic time-varying support [a(t); b(t)]. We derive explicitly the
corresponding SDEs and prove that, under certain "conic" conditions on a(t) and
b(t), they admit a unique strong diffusive solution. To guess the candidate SDE
we resort to the approach of inverting the Fokker Planck equation. Dupire
(1994) did this for volatility modeling. Here we tackle the inversion with the
caveats needed when dealing with uniform margins with conic boundaries. This
was done originally in the unpublished preprint by Brigo (1999). Independently,
Madan and Yor (2002) obtained the result as a simple application of Dupire.
Once the SDE is guessed, we analyze it rigorously, discussing the cases where
our approach adds strong uniqueness of the solution of the SDE and cases where
only a weak solution is obtained. We further study the local time and activity
of the solution. We then study the peacock with uniform law at all times on a
constant support [-1; 1] and derive the SDE of an associated mean-reverting
diffusion process with uniform margins that is not a martingale. For the
related SDE we prove existence of a solution. We derive the exact transition
densities for both the mean reverting and the original conic martingale cases.
We prove limit-laws and ergodic results: the SDE solution transition law tends
to be uniform after a long time. Finally, we provide a numerical study
confirming the desired uniform behaviour. These results may be used to model
random probabilities, recovery rates or correlations.


title: Fake Conformal Symmetry in Unimodular Gravity

abstract:
  We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It
is shown that the Noether currents for both Weyl symmetry and global scale
symmetry, identically vanish as in the conformally invariant scalar-tensor
gravity. We clearly explain why in the class of conformally invariant
gravitational theories, the Noether currents vanish by starting with the
conformally invariant scalar-tensor gravity. Moreover, we comment on both
classical and quantum-mechanical equivalences among Einstein's general
relativity, the conformally invariant scalar-tensor gravity and the
Weyl-transverse (WTDiff) gravity. Finally, we discuss the Weyl current in the
conformally invariant scalar action and see that it is also vanishing.


title: A MAD Model for Gamma-Ray Burst Variability

abstract:
  We present a model for the temporal variability of long gamma-ray bursts
during the prompt phase (the highly variable first 100 seconds or so), in the
context of a magnetically arrested disk (MAD) around a black hole. In this
state, sufficient magnetic flux is held on to the black hole such that it
stalls the accretion near the inner region of the disk. The system transitions
in and out of the MAD state, which we relate to the variable luminosity of the
GRB during the prompt phase, with a characteristic timescale defined by the
free fall time in the region over which the accretion is arrested. We present
simple analytic estimates of the relevant energetics and timescales, and
compare them to gamma-ray burst observations. In particular, we show how this
model can reproduce the characteristic one second time scale that emerges from
various analyses of the prompt emission light curve. We also discuss how our
model can accommodate the potentially physically important correlation between
a burst quiescent time and the duration of its subsequent pulse (Ramirez-Ruiz &
Merloni 2001).


title:
A nonlinear structural subgrid-scale closure for compressible MHD Part
  II: a priori comparison on turbulence simulation data

abstract:
  Even though compressible plasma turbulence is encountered in many
astrophysical phenomena, its effect is often not well understood. Furthermore,
direct numerical simulations are typically not able to reach the extreme
parameters of these processes. For this reason, large-eddy simulations (LES),
which only simulate large and intermediate scales directly, are employed. The
smallest, unresolved scales and the interactions between small and large scales
are introduced by means of a subgrid-scale (SGS) model. We propose and verify a
new set of nonlinear SGS closures for future application as an SGS model in LES
of compressible magnetohydrodynamics (MHD). We use 15 simulations (without
explicit SGS model) of forced, isotropic, homogeneous turbulence with varying
sonic Mach number $\mathrm{M_s} = 0.2$ to $20$ as reference data for the most
extensive \textit{a priori} tests performed so far in literature. In these
tests we explicitly filter the reference data and compare the performance of
the new closures against the most widely tested closures. These include
eddy-viscosity and scale-similarity type closures with different
normalizations. Performance indicators are correlations with the turbulent
energy and cross-helicty flux, the average SGS dissipation, the topological
structure and the ability to reproduce the correct magnitude and direction of
the SGS vectors. We find that only the new nonlinear closures exhibit
consistently high correlations (median value \textgreater$0.8$) with the data
over the entire parameter space and outperform the other closures in all tests.
Moreover, we show that these results are independent of resolution and chosen
filter scale. Additionally, the new closures are effectively coefficient-free
with a deviation of less than $20\%$.

categories: physics.flu-dyn astro-ph.GA astro-ph.SR physics.comp-ph physics.plasm-ph


title:
Transport coefficients for a confined Brownian ratchet operating between
  two heat reservoirs

abstract:
  We discuss two-dimensional diffusion of a Brownian particle confined to a
periodic asymmetric channel with soft walls modeled by a parabolic potential.
In the channel, the particle experiences different noise intensities, or
temperatures, in the transversal and longitudinal directions. The model is
inspired by the famous Feynman's ratchet and pawl. Using ideas of the
Fick-Jacobs approximation we derive the mean velocity of the particle, the
effective diffusion coefficient, and the stationary probability density in the
potential unit cell. The derived results are exact for small channel width.
Yet, we check by exact numerical calculation that they qualitatively describe
the ratchet effect observed for an arbitrary width of the channel.


title: Properties of sets of isometries of Gromov hyperbolic spaces

abstract:
  We prove an inequality concerning isometries of a Gromov hyperbolic metric
space, which does not require the space to be proper or geodesic. It involves
the joint stable length, a hyperbolic version of the joint spectral radius, and
shows that sets of isometries behave like sets of $2 \times 2$ real matrices.
Among the consequences of the inequality, we obtain the continuity of the joint
stable length and an analogue of Berger-Wang theorem.


title:
Computing Hypergeometric Solutions of Second Order Linear Differential
  Equations using Quotients of Formal Solutions and Integral Bases

abstract:
  We present two algorithms for computing hypergeometric solutions of second
order linear differential operators with rational function coefficients. Our
first algorithm searches for solutions of the form \[ \exp(\int r \,
dx)\cdot{_{2}F_1}(a_1,a_2;b_1;f) \] where $r,f \in \overline{\mathbb{Q}(x)}$,
and $a_1,a_2,b_1 \in \mathbb{Q}$. It uses modular reduction and Hensel lifting.
Our second algorithm tries to find solutions in the form \[ \exp(\int r \,
dx)\cdot \left( r_0 \cdot{_{2}F_1}(a_1,a_2;b_1;f) + r_1
\cdot{_{2}F_1}'(a_1,a_2;b_1;f) \right) \] where $r_0, r_1 \in
\overline{\mathbb{Q}(x)}$, as follows: It tries to transform the input equation
to another equation with solutions of the first type, and then uses the first
algorithm.


title: The moving particle lemma for the exclusion process on a weighted graph

abstract:
  We prove a version of the moving particle lemma for the exclusion process on
any finite weighted graph, based on the octopus inequality of Caputo, Liggett,
and Richthammer. In light of their proof of Aldous' spectral gap conjecture, we
conjecture that our moving particle lemma is optimal in general. Our result can
be applied to graphs which lack translational invariance, including, but not
limited to, fractal graphs. An application of our result is the proof of local
ergodicity for the exclusion process on a class of weighted graphs, the details
of which are reported in a follow-up paper [arXiv:1705.10290].

categories: math.PR cond-mat.stat-mech math-ph math.MP


title:
Unitary Representations of the Translational Group Acting as Local
  Diffeomorphisms of Space-Time

abstract:
  We develop a new mathematical approach to diffeomorphism invariant quantum
states for the quantisation of general field theories such as general
relativity and modified gravity. Treating quantum fields as fibre bundles, we
discuss operators acting on the fibre algebra that defines a Hilbert space. The
algebras of two types of operators are considered in detail, namely the
observables as generic physical variables and the quantum operators suitable
for describing symmetries and transformations. We then introduce generalised
quantum states of these operators and examine their properties. By establishing
a link between the commutativity and group cohomology of the translational
group as a subgroup of the Poincare group, we show that this leads to the
construction of quantum states invariant under the action of the translational
group, as the local gauge group of diffeomorphisms, with unitary
representations.


title:
A bound on the averaged spectral shift function and a lower bound on the
  density of states for random Schr\"odinger operators on $\mathbb{R}^d$

abstract:
  We obtain a bound on the expectation of the spectral shift function for
alloy-type random Schr\"odinger operators on $\mathbb{R}^d$ in the region of
localisation, corresponding to a change from Dirichlet to Neumann boundary
conditions along the boundary of a finite volume. The bound scales with the
area of the surface where the boundary conditions are changed. As an
application of our bound on the spectral shift function, we prove a reverse
Wegner inequality for finite-volume Schr\"odinger operators in the region of
localisation with a constant locally uniform in the energy. The application
requires that the single-site distribution of the independent and identically
distributed random variables has a Lebesgue density that is also bounded away
from zero. The reverse Wegner inequality implies a strictly positive, locally
uniform lower bound on the density of states for these continuum random
Schr\"odinger operators.


title:
Neumann boundary value problem for gernera curvature flow with forcing
  term

abstract:
  In this paper, we prove long time existence and convergence results for a
class of general curvature flows with Neumann boundary condition. This is the
first result for the Neumann boundary problem of non Monge-Ampere type
curvature equations. Our method also works for the corresponding elliptic
setting.


title: Big Data Caching for Networking: Moving from Cloud to Edge

abstract:
  In order to cope with the relentless data tsunami in $5G$ wireless networks,
current approaches such as acquiring new spectrum, deploying more base stations
(BSs) and increasing nodes in mobile packet core networks are becoming
ineffective in terms of scalability, cost and flexibility. In this regard,
context-aware $5$G networks with edge/cloud computing and exploitation of
\emph{big data} analytics can yield significant gains to mobile operators. In
this article, proactive content caching in $5$G wireless networks is
investigated in which a big data-enabled architecture is proposed. In this
practical architecture, vast amount of data is harnessed for content popularity
estimation and strategic contents are cached at the BSs to achieve higher
users' satisfaction and backhaul offloading. To validate the proposed solution,
we consider a real-world case study where several hours of mobile data traffic
is collected from a major telecom operator in Turkey and a big data-enabled
analysis is carried out leveraging tools from machine learning. Based on the
available information and storage capacity, numerical studies show that several
gains are achieved both in terms of users' satisfaction and backhaul
offloading. For example, in the case of $16$ BSs with $30\%$ of content ratings
and $13$ Gbyte of storage size ($78\%$ of total library size), proactive
caching yields $100\%$ of users' satisfaction and offloads $98\%$ of the
backhaul.


title:
Quantum frequency conversion and strong coupling of photonic modes using
  four-wave mixing in integrated microresonators

abstract:
  Single photon-level quantum frequency conversion has recently been
demonstrated using silicon nitride microring resonators. The resonance
enhancement offered by such systems enables high-efficiency translation of
quantum states of light across wide frequency ranges at sub-watt pump powers.
Using a quantum-mechanical Hamiltonian formalism, we present a detailed
theoretical analysis of the conversion dynamics in these systems, and show that
they are capable of converting single- and multi-photon quantum states.
Analytic formulas for the conversion efficiency, spectral conversion
probability density, and pump power requirements are derived which are in good
agreement with previous theoretical and experimental results. We show that with
only modest improvement to the state of the art, efficiencies exceeding 95% are
achievable using less than 100 mW of pump power. At the critical driving
strength that yields maximum conversion efficiency, the spectral conversion
probability density is shown to exhibit a flat-topped peak, indicating a range
of insensitivity to the spectrum of a single photon input. Two alternate
theoretical approaches are presented to study the conversion dynamics: a
dressed mode approach that yields a better intuitive picture of the conversion
process, and a study of the temporal dynamics of the participating modes in the
resonator, which uncovers a regime of Rabi-like coherent oscillations of single
photons between two different frequency modes. This oscillatory regime arises
from the strong coupling of distinct frequency modes mediated by coherent
pumps.


title: Semi-Supervised Learning with Generative Adversarial Networks

abstract:
  We extend Generative Adversarial Networks (GANs) to the semi-supervised
context by forcing the discriminator network to output class labels. We train a
generative model G and a discriminator D on a dataset with inputs belonging to
one of N classes. At training time, D is made to predict which of N+1 classes
the input belongs to, where an extra class is added to correspond to the
outputs of G. We show that this method can be used to create a more
data-efficient classifier and that it allows for generating higher quality
samples than a regular GAN.


title: Curie: A method for protecting SVM Classifier from Poisoning Attack

abstract:
  Machine learning is used in a number of security related applications such as
biometric user authentication, speaker identification etc. A type of causative
integrity attack against machine learning called Poisoning attack works by
injecting specially crafted data points in the training data so as to increase
the false positive rate of the classifier. In the context of the biometric
authentication, this means that more intruders will be classified as valid
user, and in case of speaker identification system, user A will be classified
user B. In this paper, we examine poisoning attack against SVM and introduce -
Curie - a method to protect the SVM classifier from the poisoning attack. The
basic idea of our method is to identify the poisoned data points injected by
the adversary and filter them out. Our method is light weight and can be easily
integrated into existing systems. Experimental results show that it works very
well in filtering out the poisoned data.


title: Barycentric coordinate neighbourhoods in Riemannian manifolds

abstract:
  We quantify conditions that ensure that a signed measure on a Riemannian
manifold has a well defined centre of mass. We then use this result to quantify
the extent of a neighbourhood on which the Riemannian barycentric coordinates
of a set of $n+1$ points on an $n$-manifold provide a true coordinate chart,
i.e., the barycentric coordinates provide a diffeomorphism between a
neighbourhood of a Euclidean simplex, and a neighbourhood containing the points
on the manifold.


title: The average number of spanning trees in sparse graphs with given degrees

abstract:
  We give an asymptotic expression for the expected number of spanning trees in
a random graph with a given degree sequence $\boldsymbol{d}=(d_1,\ldots, d_n)$,
provided that the number of edges is at least $n + \textstyle{\frac{1}{2}}
d_{\max}^4$, where $d_{\max}$ is the maximum degree. A key part of our argument
involves establishing a concentration result for a certain family of functions
over random trees with given degrees, using Pr\"ufer codes.


title:
A Deep-Learning Approach for Operation of an Automated Realtime Flare
  Forecast

abstract:
  Automated forecasts serve important role in space weather science, by
providing statistical insights to flare-trigger mechanisms, and by enabling
tailor-made forecasts and high-frequency forecasts. Only by realtime forecast
we can experimentally measure the performance of flare-forecasting methods
while confidently avoiding overlearning.
  We have been operating unmanned flare forecast service since August, 2015
that provides 24-hour-ahead forecast of solar flares, every 12 minutes. We
report the method and prediction results of the system.


title: HopsFS: Scaling Hierarchical File System Metadata Using NewSQL Databases

abstract:
  Recent improvements in both the performance and scalability of
shared-nothing, transactional, in-memory NewSQL databases have reopened the
research question of whether distributed metadata for hierarchical file systems
can be managed using commodity databases. In this paper, we introduce HopsFS, a
next generation distribution of the Hadoop Distributed File System (HDFS) that
replaces HDFS' single node in-memory metadata service, with a distributed
metadata service built on a NewSQL database. By removing the metadata
bottleneck, HopsFS enables an order of magnitude larger and higher throughput
clusters compared to HDFS. Metadata capacity has been increased to at least 37
times HDFS' capacity, and in experiments based on a workload trace from
Spotify, we show that HopsFS supports 16 to 37 times the throughput of Apache
HDFS. HopsFS also has lower latency for many concurrent clients, and no
downtime during failover. Finally, as metadata is now stored in a commodity
database, it can be safely extended and easily exported to external systems for
online analysis and free-text search.


title: Matter wave speckle observed in an out-of-equilibrium quantum fluid

abstract:
  We report the results of a direct comparison of a freely expanding turbulent
Bose-Einstein condensate and the propagation of an optical speckle pattern. We
found remarkably similar statistical properties underlying the spatial
propagation of both phenomena. The calculated second-order correlation together
with the typical correlation length of each system is used to compare and
substantiate our observations. We believe that the close analogy existing in
between an expanding turbulent quantum gas and a traveling optical speckle,
might burgeon into an exciting new research field investigating disordered
quantum matter.

categories: cond-mat.quant-gas cond-mat.dis-nn physics.atom-ph physics.flu-dyn quant-ph


title: Periodic solutions of the sinh-Gordon equation and integrable systems

abstract:
  We study the space of periodic solutions of the elliptic $\sinh$-Gordon
equation by means of spectral data consisting of a Riemann surface $Y$ and a
divisor $D$. We show that the space $M_g^{\mathbf{p}}$ of real periodic finite
type solutions with fixed period $\mathbf{p}$ can be considered as a completely
integrable system $(M_g^{\mathbf{p}},\Omega,H_2)$ with a symplectic form
$\Omega$ and a series of commuting Hamiltonians $(H_n)_{n \in \mathbb{N}}$. In
particular we relate the gradients of these Hamiltonians to the Jacobi fields
$(\omega_n)_{n\in \mathbb{N}_0}$ from the Pinkall-Sterling iteration. Moreover,
a connection between the symplectic form $\Omega$ and Serre duality is
established.


title:
On the asymptotic behavior of solutions to Einstein's vacuum equations
  in wave coordinates

abstract:
  We give asymptotics for Einstein vacuum equations in wave coordinates with
small asymptotically flat data. We show that the behavior is wave like at null
infinity and homogeneous towards time like infinity. We use the asymptotics to
show that the outgoing null hypersurfaces approach the Schwarzschild ones for
the same mass and that the radiated energy is equal to the initial mass.


title: Proof of tightness of Varshamov - Gilbert bound for binary codes

abstract:
  We prove tightness of right logarithmic asymptotic of Varshamov- Gilbert
bound for linear binary codes We find general asymptotic coding bound for
linear codes


title:
Generalized Suffix Tree based Multiple Sequence Alignment for Service
  Virtualization

abstract:
  Assuring quality of contemporary software systems is a very challenging task
due to the often large complexity of the deployment environments in which they
will operate. Service virtualization is an approach to this challenge where
services within the deployment environment are emulated by synthesising service
response messages from models or by recording and then replaying service
interaction messages with the system. Record-and-replay techniques require an
approach where (i) message prototypes can be derived from recorded system
interactions (i.e. request-response sequences), (ii) a scheme to match incoming
request messages against message prototypes, and (iii) the synthesis of
response messages based on similarities between incoming messages and the
recorded system interactions. Previous approaches in service virtualization
have required a multiple sequence alignment (MSA) algorithm as a means of
finding common patterns of similarities and differences between messages
required by all three steps.
  In this paper, we present a novel MSA algorithm based on Generalized Suffix
Trees (GSTs). We evaluated the accuracy and efficiency of the proposed
algorithm against six enterprise service message trace datasets, with the
proposed algorithm performing up to 50 times faster than standard MSA
approaches. Furthermore, the algorithm has applicability to other domains
beyond service virtualization.


title: Suites r\'ecurrentes lin\'eaires d'ordre 2 \`a divisibilit\'e forte

abstract:
  We reprove twice, in a simpler but as elementary way, a result by Hor\'ak and
Skula (1985) who determined, among all sequences of integers defined by
$$u_1=1,\quad u_2=R,\quad u_{n+2}=Pu_{n+1}-Qu_n$$ for some integers $P,Q,R$,
those which satisfy the strong divisibility condition $$\forall i,j\in\mathbb
N^*\quad u_i\land u_j=\left|u_{i\land j}\right|,$$ where $\land$ denotes the
greatest common divisor.


title:
Deep Linear Discriminant Analysis on Fisher Networks: A Hybrid
  Architecture for Person Re-identification

abstract:
  Person re-identification is to seek a correct match for a person of interest
across views among a large number of imposters. It typically involves two
procedures of non-linear feature extractions against dramatic appearance
changes, and subsequent discriminative analysis in order to reduce intra-
personal variations while enlarging inter-personal differences. In this paper,
we introduce a hybrid architecture which combines Fisher vectors and deep
neural networks to learn non-linear representations of person images to a space
where data can be linearly separable. We reinforce a Linear Discriminant
Analysis (LDA) on top of the deep neural network such that linearly separable
latent representations can be learnt in an end-to-end fashion. By optimizing an
objective function modified from LDA, the network is enforced to produce
feature distributions which have a low variance within the same class and high
variance between classes. The objective is essentially derived from the general
LDA eigenvalue problem and allows to train the network with stochastic gradient
descent and back-propagate LDA gradients to compute the gradients involved in
Fisher vector encoding. For evaluation we test our approach on four benchmark
data sets in person re-identification (VIPeR [1], CUHK03 [2], CUHK01 [3], and
Market1501 [4]). Extensive experiments on these benchmarks show that our model
can achieve state-of-the-art results.


title:
A time splitting approach to quasilinear Degenerate Parabolic Partial
  Differential Equations

abstract:
  In this paper, we discuss the Cauchy problem for a degenerate parabolic
hyperbolic equation with a multiplicative noise. We focus on the existence of a
solution. Using nondegenerate smooth approximations, Debussche, Hofmanov\'a and
Vovelle [8] proved the existence of a kinetic solution. On the other hand, we
propose to construct a sequence of approximations by applying a time splitting
method and prove that this converges strongly in $L^1$ to a kinetic solution.
This method will somewhat give us not only a simpler and more direct argument
but an improvement over the existence result.