title: The geodesic X-ray transform with matrix weights

abstract:
  Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly
convex boundary, such that the manifold admits a strictly convex function. We
show that the attenuated ray transform in the presence of an arbitrary
connection and Higgs field is injective modulo the natural obstruction for
functions and one-forms. We also show that the connection and the Higgs field
are uniquely determined by the scattering relation modulo gauge
transformations. The proofs involve a reduction to a local result showing that
the geodesic X-ray transform with a matrix weight can be inverted locally near
a point of strict convexity at the boundary, and a detailed analysis of layer
stripping arguments based on strictly convex exhaustion functions. As a
somewhat striking corollary, we show that these integral geometry problems can
be solved on strictly convex manifolds of dimension $\geq 3$ having
non-negative sectional curvature (similar results were known earlier in
negative sectional curvature). We also apply our methods to solve some inverse
problems in quantum state tomography and polarization tomography.


title:
Automatic Extraction of Causal Relations from Natural Language Texts: A
  Comprehensive Survey

abstract:
  Automatic extraction of cause-effect relationships from natural language
texts is a challenging open problem in Artificial Intelligence. Most of the
early attempts at its solution used manually constructed linguistic and
syntactic rules on small and domain-specific data sets. However, with the
advent of big data, the availability of affordable computing power and the
recent popularization of machine learning, the paradigm to tackle this problem
has slowly shifted. Machines are now expected to learn generic causal
extraction rules from labelled data with minimal supervision, in a domain
independent-manner. In this paper, we provide a comprehensive survey of causal
relation extraction techniques from both paradigms, and analyse their relative
strengths and weaknesses, with recommendations for future work.


title:
Belief-Invariant and Quantum Equilibria in Games of Incomplete
  Information

abstract:
  Drawing on ideas from game theory and quantum physics, we investigate
nonlocal correlations from the point of view of equilibria in games of
incomplete information. These equilibria can be classified in decreasing power
as communication equilibria, belief-invariant equilibria, and correlated
equilibria, all of which contain the familiar Nash equilibria. The notion of
belief-invariant equilibrium appeared in game theory in the 90s. However, the
class of non-signalling correlations associated to belief-invariance arose
naturally already in the 80s in the foundations of quantum mechanics. In the
present work, we explain and unify these two origins of the idea and study the
above classes of equilibria, together with quantum correlated equilibria, using
tools from quantum information but the language of (algorithmic) game theory.
We present a general framework of belief-invariant communication equilibria,
which contains correlated equilibria and quantum correlated equilibria as
special cases. Our framework also contains the theory of Bell inequalities and
their violations due to non-locality, which is a question of intense interest
in the foundations of quantum mechanics, and it was indeed the original
motivation for the aforementioned studies. Moreover, in our framework we can
also model quantum games where players have conflicting interests, a recent
developing topic in physics. We then use our framework to show new results
related to the social welfare of equilibria. Namely, we exhibit a game where
belief-invariance is socially better than any correlated equilibrium, and a
game where all non-belief-invariant communication equilibria have a suboptimal
social welfare. We also show that optimal social welfare can sometimes be
achieved by quantum mechanical correlations, which do not need an informed
mediator to be implemented, and go beyond the classical shared randomness
approach.


title: The Legendre Transform in Modern Optimization

abstract:
  The Legendre transform (LET) is a product of a general duality principle: any
smooth curve is, on the one hand, a locus of pairs, which satisfy the given
equation and, on the other hand, an envelope of a family of its tangent lines.
An application of the LET to a strictly convex and smooth function leads to the
Legendre identity (LEID). For strictly convex and three times differentiable
function the LET leads to the Legendre invariant (LEINV). Although the LET has
been known for more then 200 years both the LEID and the LEINV are critical in
modern optimization theory and methods. The purpose of the paper (survey) is to
show the role of the LEID and the LEINV play in both constrained and
unconstrained optimization.


title:
Layer- and Frequency-Dependent Second Harmonic Generation in Reflection
  from GaSe Atomic Crystals

abstract:
  We report optical second-harmonic generation (SHG) in reflection from GaSe
crystals of 1 to more than 100 layers using a fundamental picosecond pulsed
pump at 1.58 eV and a supercontinuum white light pulsed laser with energies
ranging from 0.85 to 1.4 eV. The measured reflected SHG signal is maximal in
samples of $\sim$20 layers, decreasing in thicker samples as a result of
interference. The thickness- and frequency-dependence of the SHG response of
samples thicker than $\sim$7 layers can be reproduced by a second-order optical
susceptibility that is the same as in bulk samples. For samples $\lesssim$7
layers, the second-order optical susceptibility is reduced compared to that in
thicker samples, which is attributed to the expected bandgap increase in mono-
and few-layer GaSe.


title: Radiative coupling of A and B excitons in ZnO

abstract:
  Radiation-induced coupling between A and B excitons in ZnO is theoretically
studied. Considering the center-of-mass motion of excitons in bulk and thin
film structures, we reveal the eigenmodes of an exciton--radiation coupled
system and the ratio of each excitonic component, which is determined from
diagonalization of the self-consistent equation between the polarization and
the Maxwell electric field. In particular, in a nano-to-bulk crossover size
regime, the large interaction volume between multipole-type excitonic waves and
radiation waves causes radiative coupling between excitons from different
valence bands, which leads to an enhancement of the radiative correction. The
results presented in this study are in striking contrast with the conventional
view of the optical response of excitons in ZnO, where A and B excitons are
independently assigned to their respective spectral structures. It is also
clarified that the density of each excitonic component is of a significant
value for attribution of nonlinear optical signals.


title: The Red Supergiant Content of M31

abstract:
  We investigate the red supergiant (RSG) population of M31, obtaining radial
velocities of 255 stars. These data substantiate membership of our
photometrically-selected sample, demonstrating that Galactic foreground stars
and extragalactic RSGs can be distinguished on the basis of B-V, V-R two-color
diagrams. In addition, we use these spectra to measure effective temperatures
and assign spectral types, deriving physical properties for 192 RSGs.
Comparison with the solar-metallicity Geneva evolutionary tracks indicates
astonishingly good agreement. The most luminous RSGs in M31 are likely evolved
from 25-30 Mo stars, while the vast majority evolved from stars with initial
masses of 20 Mo or less. There is an interesting bifurcation in the
distribution of RSGs with effective temperatures that increases with higher
luminosities, with one sequence consisting of early K-type supergiants, and
with the other consisting of M-type supergiants that become later (cooler) with
increasing luminosities. This separation is only partially reflected in the
evolutionary tracks, although that might be due to the mis-match in
metallicities between the solar Geneva models and the higher-than-solar
metallicity of M31. As the luminosities increase the median spectral type also
increases; i.e., the higher mass RSGs spend more time at cooler temperatures
than do those of lower luminosities, a result which is new to this study.
Finally we discuss what would be needed observationally to successfully build a
luminosity function that could be used to constrain the mass-loss rates of RSGs
as our Geneva colleagues have suggested.


title:
Towards an analytical theory of the third-body problem for highly
  elliptical orbits

abstract:
  When dealing with satellites orbiting a central body on a highly elliptical
orbit, it is necessary to consider the effect of gravitational perturbations
due to external bodies. Indeed, these perturbations can become very important
as soon as the altitude of the satellite becomes high, which is the case around
the apocentre of this type of orbit. For several reasons, the traditional tools
of celestial mechanics are not well adapted to the particular dynamic of highly
elliptical orbits. On the one hand, analytical solutions are quite generally
expanded into power series of the eccentricity and therefore limited to
quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to
the motion of the third-body is often neglected. We propose several tools to
overcome these limitations. Firstly, we have expanded the disturbing function
into a finite polynomial using Fourier expansions of elliptic motion functions
in multiple of the satellite's eccentric anomaly (instead of the mean anomaly)
and involving Hansen-like coefficients. Next, we show how to perform a
normalization of the expanded Hamiltonian by means of a time-dependent Lie
transformation which aims to eliminate periodic terms. The difficulty lies in
the fact that the generator of the transformation must be computed by solving a
partial differential equation involving variables which are linear with time
and the eccentric anomaly which is not time linear. We propose to solve this
equation by means of an iterative process.

categories: astro-ph.EP math-ph math.MP physics.space-ph


title: Real wave propagation in the isotropic relaxed micromorphic model

abstract:
  For the recently introduced isotropic relaxed micromorphic generalized
continuum model, we show that under the assumption of positive definite energy,
planar harmonic waves have real velocity. We also obtain a necessary and
sufficient condition for real wave velocity which is weaker than
positive-definiteness of the energy. Connections to isotropic linear elasticity
and micropolar elasticity are established. Notably, we show that strong
ellipticity does not imply real wave velocity in micropolar elasticity, while
it does in isotropic linear elasticity.


title: Theoretical determination of the hadronic (g-2) of the muon

abstract:
  An approach is discussed on the determination of the leading order hadronic
contribution to the muon anomaly, $a_\mu^{HAD}$, based entirely on theory. This
method makes no use of $e^+ e^-$ annihilation data, a likely source of the
current discrepancy between theory and experiment beyond the $3\, \sigma$
level. What this method requires is essentially knowledge of the first
derivative of the vector current correlator at zero-momentum. In the
heavy-quark sector this is obtained from the well known heavy quark expansion
in perturbative QCD, leading to values of $a_\mu^{HAD}$ in the charm- and
bottom-quark region which were fully confirmed by later lattice QCD (LQCD)
results. In the light-quark sector, using recent preliminary LQCD results for
the first derivative of the vector current correlator at zero-momentum leads to
the value $a_\mu^{HAD} = (729 - 871)\, \times\,10^{-10}$, which is
significantly larger than values obtained from using $e^+ e^-$ data. A separate
approach based on the operator product expansion (OPE), and designed to quench
the contribution of these data, reduces the discrepancy by at least 40\%. In
addition, it exposes a tension between the OPE and $e^+ e^-$ data, thus
suggesting the blame for the discrepancy on the latter.


title:
Homotopy theory of $C_\infty$-algebras and characteristic classes of
  fiber bundles

abstract:
  In this paper we give a Chern-Weil-type construction of characteristic
classes of fiber bundles, based on homotopy theory of C-infinity algebras. Our
idea is to replace a family of closed manifolds to a family of C-infinity
morphisms with family of metrics.


title: Timing Channel: Achievable Rate in the Finite Block-Length Regime

abstract:
  The exponential server timing channel is known to be the simplest, and in
some sense canonical, queuing timing channel. The capacity of this
infinite-memory channel is known. Here, we discuss practical finite-length
restrictions on the codewords and attempt to understand the maximal rate that
can be achieved for a target error probability. By using Markov chain analysis,
we prove a lower bound on the maximal channel coding rate achievable at
blocklength $n$ and error probability $\epsilon$. The bound is approximated by
$C- n^{-1/2} \sigma Q^{-1}(\epsilon)$ where $Q$ denotes the Q-function and
$\sigma^2$ is the asymptotic variance of the underlying Markov chain. A closed
form expression for $\sigma^2$ is given.


title:
How priors of initial hyperparameters affect Gaussian process regression
  models

abstract:
  The hyperparameters in Gaussian process regression (GPR) model with a
specified kernel are often estimated from the data via the maximum marginal
likelihood. Due to the non-convexity of marginal likelihood with respect to the
hyperparameters, the optimization may not converge to the global maxima. A
common approach to tackle this issue is to use multiple starting points
randomly selected from a specific prior distribution. As a result the choice of
prior distribution may play a vital role in the predictability of this
approach. However, there exists little research in the literature to study the
impact of the prior distributions on the hyperparameter estimation and the
performance of GPR. In this paper, we provide the first empirical study on this
problem using simulated and real data experiments. We consider different types
of priors for the initial values of hyperparameters for some commonly used
kernels and investigate the influence of the priors on the predictability of
GPR models. The results reveal that, once a kernel is chosen, different priors
for the initial hyperparameters have no significant impact on the performance
of GPR prediction, despite that the estimates of the hyperparameters are very
different to the true values in some cases.


title:
Differential operators on domains with conical points: precise uniform
  regularity estimates

abstract:
  We study families of strongly elliptic, second order differential operators
with singular coefficients on domains with conical points. We obtain uniform
estimates on their inverses and on the regularity of the solutions to the
associated Poisson problem with mixed boundary conditions. The coefficients and
the solutions belong to (suitable) weighted Sobolev spaces. The space of
coefficients is a Banach space that contains, in particular, the space of
smooth functions. Hence, our results extend classical well-posedness results
for strongly elliptic equations in domains with conical points to problems with
singular coefficients. We furthermore provide precise uniform estimates on the
norms of the solution operators.


title:
New stability results for sequences of metric measure spaces with
  uniform Ricci bounds from below

abstract:
  The aim of this paper is to provide new stability results for sequences of
metric measure spaces $(X_i,d_i,m_i)$ convergent in the measured
Gromov-Hausdorff sense. By adopting the so-called extrinsic approach of
embedding all metric spaces into a common one $(X,d)$, we extend the results of
Gigli-Mondino-Savar\'e by providing Mosco convergence of Cheeger's energies and
compactness theorems in the whole range of Sobolev spaces $H^{1,p}$, including
the space $BV$, and even with a variable exponent $p_i\in [1,\infty]$. In
addition, building on the results of Ambrosio-Stra-Trevisan, we provide local
convergence results for gradient derivations. We use these tools to improve the
spectral stability results, previously known for $p>1$ and for Ricci limit
spaces, getting continuity of Cheeger's constant. In the dimensional case
$N<\infty$, we improve some rigidity and almost rigidity results by Ketterer
and Cavaletti-Mondino. On the basis of the second-order calculus by Gigli, in
the class of $RCD(K,\infty)$ spaces we provide stability results for Hessians
and $W^{2,2}$ functions and we treat the stability of the Bakry-\'Emery
condition $BE(K,N)$ and of ${\bf Ric}\geq KI$, with $K$ and $N$ not necessarily
constant.


title: Momentum space imaging of the FFLO state

abstract:
  In a magnetic field superconductors (SC) with small orbital effect exhibit
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase above the Pauli limiting
field. It is characterized by Cooper pairs with finite center of mass momentum
and is stabilized by the gain in Zeeman energy of depaired electrons in the
imbalanced Fermi gas. The ground state is a coherent superposition of paired
and depaired states. This concept, although central to the FFLO state lacks a
direct experimental confirmation. We propose that STM quasiparticle
interference (QPI) can give a direct momentum space image of the depaired
states in the FFLO wave function. For a proof of principle we investigate a 2D
single orbital tight binding model with a SC s-wave order parameter. Using the
equilibrium values of pair momentum and SC gap we calculate the spectral
function of quasiparticles and associated QPI spectrum as function of magnetic
field. We show that the characteristic depaired Fermi surface parts appear as a
fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its
evolution with field strength. Its observation in STM experiments would
constitute a direct proof for FFLO ground state wave function.


title:
Distributed optimization decomposition for joint economic dispatch and
  frequency regulation

abstract:
  Economic dispatch and frequency regulation are typically viewed as
fundamentally different problems in power systems and, hence, are typically
studied separately. In this paper, we frame and study a joint problem that co-
optimizes both slow timescale economic dispatch resources and fast timescale
frequency regulation resources. We show how the joint problem can be decomposed
without loss of optimality into slow and fast timescale sub-problems that have
appealing interpretations as the economic dispatch and frequency regulation
problems respectively. We solve the fast timescale sub-problem using a
distributed frequency control algorithm that preserves the stability of the
network during transients. We solve the slow timescale sub-problem using an
efficient market mechanism that coordinates with the fast timescale
sub-problem. We investigate the performance of the decomposition on the IEEE
24-bus reliability test system.


title: Affine Rigidity and Conics at Infinity

abstract:
  We prove that if a framework of a graph is neighborhood affine rigid in
$d$-dimensions (or has the stronger property of having an equilibrium stress
matrix of rank $n-d-1$) then it has an affine flex (an affine, but non
Euclidean, transform of space that preserves all of the edge lengths) if and
only if the framework is ruled on a single quadric. This strengthens and also
simplifies a related result by Alfakih. It also allows us to prove that the
property of super stability is invariant with respect to projective transforms
and also to the coning and slicing operations. Finally this allows us to unify
some previous results on the Strong Arnold Property of matrices.


title: Review Networks for Caption Generation

abstract:
  We propose a novel extension of the encoder-decoder framework, called a
review network. The review network is generic and can enhance any existing
encoder- decoder model: in this paper, we consider RNN decoders with both CNN
and RNN encoders. The review network performs a number of review steps with
attention mechanism on the encoder hidden states, and outputs a thought vector
after each review step; the thought vectors are used as the input of the
attention mechanism in the decoder. We show that conventional encoder-decoders
are a special case of our framework. Empirically, we show that our framework
improves over state-of- the-art encoder-decoder systems on the tasks of image
captioning and source code captioning.


title: Solution of linear ill-posed problems using random dictionaries

abstract:
  In the present paper we consider application of overcomplete dictionaries to
solution of general ill-posed linear inverse problems. In the context of
regression problems, there has been enormous amount of effort to recover an
unknown function using such dictionaries. One of the most popular methods,
lasso and its versions, is based on minimizing empirical likelihood and
unfortunately, requires stringent assumptions on the dictionary, the, so
called, compatibility conditions. Though compatibility conditions are hard to
satisfy, it is well known that this can be accomplished by using random
dictionaries. In the present paper, we show how one can apply random
dictionaries to solution of ill-posed linear inverse problems. We put a
theoretical foundation under the suggested methodology and study its
performance via simulations.


title:
Study on flexible and organizable time-resolved measurement system and
  technology for multi-pulsed electron beam parameter

abstract:
  The proof test and debugging of the multi-pulsed electron accelerator,
Dragon-2,requires a thorough comprehension of the quality of the beams. This
puts forward a rigid requirement on the measurement system that it should have
the ability that not only differentiates the three pulses on the whole but also
tells the details of each pulse.In the measurements, beam energy is converted
by a target to the Optical Transition Radiation (OTR) light, the information
carried by which provides a good approach to measure beam profile and
divergence simultaneously. Combining with this characteristic of OTR light, the
concept of dual-imaging method is adopted in the design of optical imaging
system. To avoid interference of the system optical parameters with one
another, the original system is separated into two parts by functions, one for
beam profile measurements and the other for divergence measurements.
Correspondingly a splitter is interposed immediately after the OTR target which
splits the light into two parts in perpendicular directions, one part forming a
beam spot, and the remaining becoming polarized through a polarizer and imaged
by an OTR lens and forming a beam divergence pattern. Again the use of
splitters helps the light beam enter different framing camera for different
use.With a time resolution of 2ns, the system can provide 8 frames of beam
details within any one of the three pulses,at the same time as acquiring the
quality of the three pulses on the whole.


title: Cross-validation estimate of the number of clusters in a network

abstract:
  Network science investigates methodologies that summarise relational data to
obtain better interpretability. Identifying modular structures is a fundamental
task, and assessment of the coarse-grain level is its crucial step. Here, we
propose principled, scalable, and widely applicable assessment criteria to
determine the number of clusters in modular networks based on the leave-one-out
cross-validation estimate of the edge prediction error.


title:
Design of nonlinear optical response of multipole-type excitons by film
  thickness and incident pulse width

abstract:
  We theoretically investigate the nonlinear optical pulse responses of
excitons in a thin film where the excitonic center-of-mass motion is confined.
A large interaction volume between excitons and radiation yields particular
coupled states with radiative decay times reaching several femto-seconds. By
considering two polarization directions of light, we reveal that these
fast-decay modes dominantly survive in an optical Kerr spectra even under a
massive nonradiative damping $\Gamma=30$ meV. The results clearly show that
there is an optimal combination of the incident pulse width and the film
thickness for maximizing the integrated intensity of nonlinear signals.


title:
A Candidate Young Massive Planet in Orbit around the Classical T Tauri
  Star CI Tau

abstract:
  The ~2 Myr old classical T Tauri star CI Tau shows periodic variability in
its radial velocity (RV) variations measured at infrared (IR) and optical
wavelengths. We find that these observations are consistent with a massive
planet in a ~9-day period orbit. These results are based on 71 IR RV
measurements of this system obtained over 5 years, and on 26 optical RV
measurements obtained over 9 years. CI Tau was also observed photometrically in
the optical on 34 nights over ~one month in 2012. The optical RV data alone are
inadequate to identify an orbital period, likely the result of star spot and
activity induced noise for this relatively small dataset. The infrared RV
measurements reveal significant periodicity at ~9 days. In addition, the full
set of optical and IR RV measurements taken together phase coherently and with
equal amplitudes to the ~9 day period. Periodic radial velocity signals can in
principle be produced by cool spots, hot spots, and reflection of the stellar
spectrum off the inner disk, in addition to resulting from a planetary
companion. We have considered each of these and find the planet hypothesis most
consistent with the data. The radial velocity amplitude yields an Msin(i) of
~8.1 M_Jup; in conjunction with a 1.3 mm continuum emission measurement of the
circumstellar disk inclination from the literature, we find a planet mass of
~11.3 M_Jup, assuming alignment of the planetary orbit with the disk.


title:
Automatic Open Knowledge Acquisition via Long Short-Term Memory Networks
  with Feedback Negative Sampling

abstract:
  Previous studies in Open Information Extraction (Open IE) are mainly based on
extraction patterns. They manually define patterns or automatically learn them
from a large corpus. However, these approaches are limited when grasping the
context of a sentence, and they fail to capture implicit relations. In this
paper, we address this problem with the following methods. First, we exploit
long short-term memory (LSTM) networks to extract higher-level features along
the shortest dependency paths, connecting headwords of relations and arguments.
The path-level features from LSTM networks provide useful clues regarding
contextual information and the validity of arguments. Second, we constructed
samples to train LSTM networks without the need for manual labeling. In
particular, feedback negative sampling picks highly negative samples among
non-positive samples through a model trained with positive samples. The
experimental results show that our approach produces more precise and abundant
extractions than state-of-the-art open IE systems. To the best of our
knowledge, this is the first work to apply deep learning to Open IE.


title: Compression and Conditional Emulation of Climate Model Output

abstract:
  Numerical climate model simulations run at high spatial and temporal
resolutions generate massive quantities of data. As our computing capabilities
continue to increase, storing all of the data is not sustainable, and thus it
is important to develop methods for representing the full datasets by smaller
compressed versions. We propose a statistical compression and decompression
algorithm based on storing a set of summary statistics as well as a statistical
model describing the conditional distribution of the full dataset given the
summary statistics. The statistical model can be used to generate realizations
representing the full dataset, along with characterizations of the
uncertainties in the generated data. Thus, the methods are capable of both
compression and conditional emulation of the climate models. Considerable
attention is paid to accurately modeling the original dataset--one year of
daily mean temperature data--particularly with regard to the inherent spatial
nonstationarity in global fields, and to determining the statistics to be
stored, so that the variation in the original data can be closely captured,
while allowing for fast decompression and conditional emulation on modest
computers.


title:
Effect of planet ingestion on low-mass stars evolution: the case of
  2MASS J08095427--4721419 star in the Gamma Velorum cluster

abstract:
  We analysed the effects of planet ingestion on the characteristics of a
pre-MS star similar to the Gamma Velorum cluster member 2MASS
J08095427--4721419 (#52). We discussed the effects of changing the age $t_0$ at
which the accretion episode occurs, the mass of the ingested planet and its
chemical composition. We showed that the mass of the ingested planet required
to explain the current [Fe/H]^#52 increases by decreasing the age $t_0$ and/or
by decreasing the Iron content of the accreted matter.
  We compared the predictions of a simplified accretion method -- where only
the variation of the surface chemical composition is considered -- with that of
a full accretion model that properly accounts for the modification of the
stellar structure. We showed that the two approaches result in different
convective envelope extension which can vary up to 10 percent. We discussed the
impact of the planet ingestion on a stellar model in the colour-magnitude
diagram, showing that a maximum shift of about 0.06 dex in the colour and 0.07
dex in magnitude are expected and that such variations persist even much later
the accretion episode. We also analysed the systematic bias in the stellar mass
and age inferred by using a grid of standard non accreting models to recover
the characteristics of an accreting star. We found that standard non accreting
models can safely be adopted for mass estimate, as the bias is <= 6 percent,
while much more caution should be used for age estimate where the differences
can reach about 60 percent.


title: Divisor braids

abstract:
  We study a novel type of braid groups on a closed orientable surface
$\Sigma$. These are fundamental groups of certain manifolds that are hybrids
between symmetric products and configuration spaces of points on $\Sigma$; a
class of examples arises naturally in gauge theory, as moduli spaces of
vortices in toric fibre bundles over $\Sigma$. The elements of these braid
groups, which we call divisor braids, have coloured strands that are allowed to
intersect according to rules specified by a graph $\Gamma$. In situations where
there is more than one strand of each colour, we show that the corresponding
braid group admits a metabelian presentation as a central extension of the free
Abelian group $H_1(\Sigma;\mathbb{Z})^{\oplus r}$, where $r$ is the number of
colours, and describe its Abelian commutator. This computation relies crucially
on producing a link invariant (of closed divisor braids) in the three-manifold
$S^1 \times \Sigma $ for each graph $\Gamma$. We also describe the von Neumann
algebras associated to these groups in terms of rings that are familiar from
noncommutative geometry.


title: Multiscale methods for wave problems in heterogeneous media

abstract:
  In this paper we give a survey on various multiscale methods for the
numerical solution of second order hyperbolic equations in highly heterogeneous
media. We concentrate on the wave equation and distinguish between two classes
of applications. First we discuss numerical methods for the wave equation in
heterogeneous media without scale separation. Such a setting is for instance
encountered in the geosciences, where natural structures often exhibit a
continuum of different scales, that all need to be resolved numerically to get
meaningful approximations. Approaches tailored for these settings typically
involve the construction of generalized finite element spaces, where the basis
functions incorporate information about the data variations. In the second part
of the paper, we discuss numerical methods for the case of structured media
with scale separation. This setting is for instance encountered in engineering
sciences, where materials are often artificially designed. If this is the case,
the structure and the scale separation can be explicitly exploited to compute
appropriate homogenized/upscaled wave models that only exhibit a single coarse
scale and that can be hence solved at significantly reduced computational
costs.


title: Non-thermal line-broadening in solar prominence

abstract:
  We show that the line broadening in quiescent solar prominences is mainly due
to non-thermal velocities. We have simultaneously observed a wide range of
optically thin lines in quiescent prominences, selected for bright and narrow
Mg\,b emission without line satellites from macro-shifts. We find a ratio of
reduced widths of H-gamma and H-delta of 1.05 +-0.03 which can hardly be
attributed to saturation, since both are optically thin for the prominences
observed: tau(gamma)<0.3 ; tau(delta)<0.15. We confirm the ratio of reduced
widths of He4772(triplet) and He5015(singlet of 1.1 +-0.05 at higher
significance and detect a width ratio of Mgb2 and Mg4571 (both from the triplet
system) of 1.3 +-0.1. The discrepant widths of lines from different atoms, and
even from the same atom, cannot be represented by a unique pair [T_kin ;
V_nth]. Values of T_kin deduced from observed line radiance using models,
indicate low temperatures down to T_kin~5000K. Non-thermal velocities, related
to different physical states of the respective emitting prominence region, seem
to be the most important line broadening mechanism.


title: Modelling and Bayesian analysis of the Abakaliki Smallpox Data

abstract:
  The celebrated Abakaliki smallpox data have appeared numerous times in the
epidemic modelling literature, but in almost all cases only a specific subset
of the data is considered. There is one previous analysis of the full data set,
but this relies on approximation methods to derive a likelihood. The data
themselves continue to be of interest due to concerns about the possible
re-emergence of smallpox as a bioterrorism weapon. We present the first full
Bayesian analysis using data-augmentation Markov chain Monte Carlo methods
which avoid the need for likelihood approximations. Results include estimates
of basic model parameters as well as reproduction numbers and the likely path
of infection. Model assessment is carried out using simulation-based methods.


title: Topologically Protected Loop Flows in High Voltage AC Power Grids

abstract:
  Geographical features such as mountain ranges or big lakes and inland seas
often result in large closed loops in high voltage AC power grids. Sizable
circulating power flows have been recorded around such loops, which take up
transmission line capacity and dissipate but do not deliver electric power.
Power flows in high voltage AC transmission grids are dominantly governed by
voltage angle differences between connected buses, much in the same way as
Josephson currents depend on phase differences between tunnel-coupled
superconductors. From this previously overlooked similarity we argue here that
circulating power flows in AC power grids are analogous to supercurrents
flowing in superconducting rings and in rings of Josephson junctions. We
investigate how circulating power flows can be created and how they behave in
the presence of ohmic dissipation. We show how changing operating conditions
may generate them, how significantly more power is ohmically dissipated in
their presence and how they are topologically protected, even in the presence
of dissipation, so that they persist when operating conditions are returned to
their original values. We identify three mechanisms for creating circulating
power flows, (i) by loss of stability of the equilibrium state carrying no
circulating loop flow, (ii) by tripping of a line traversing a large loop in
the network and (iii) by reclosing a loop that tripped or was open earlier.
Because voltage angles are uniquely defined, circulating power flows can take
on only discrete values, much in the same way as circulation around vortices is
quantized in superfluids.


title: Eshelby inclusions in granular matter: theory and simulations

abstract:
  We present a numerical implementation of an active inclusion in a granular
material submitted to a biaxial test. We discuss the dependence of the response
to this perturbation on two parameters: the intra-granular friction coefficient
on one hand, the degree of the loading on the other hand. We compare the
numerical results to theoretical predictions taking into account the change of
volume of the inclusion as well as the anisotropy of the elastic matrix.


title: Population Properties of Brown Dwarf Analogs to Exoplanets

abstract:
  We present a kinematic analysis of 152 low surface gravity M7-L8 dwarfs by
adding 8 parallaxes, 38 radial velocities, and 19 proper motions. We find 39
objects to be high-likelihood or bona fide members of nearby moving groups, 92
objects to be ambiguous members and 21 objects that are non-members. We find
that gravity classification and photometric color separate 5-150 Myr sources
from > 3 Gyr field objects, but they do not correlate one-to-one with the
narrower 5 -150 Myr age range. The absolute magnitudes of low-gravity sources
from J band through W3 show a flux redistribution when compared to equivalent
field sources that is correlated with spectral subtype. Clouds, which are a far
more dominant opacity source for L dwarfs, are the likely cause. On CMDs, the
latest-type low-gravity L dwarfs drive the elbow of the L/T transition up to 1
mag redder and 1 mag fainter than field dwarfs at M_J but are consistent with
or brighter than the elbow at M_W1 and M_W2. Furthermore, there is an
indication on CMD's (such as M_J versus (J-W2) of increasingly redder sequences
separated by gravity classification. Examining bolometric luminosities for
planets and low-gravity objects, we confirm that young M dwarfs are
overluminous while young L dwarfs are normal compared to the field. This
translates into warmer M dwarf temperatures compared to the field sequence
while lower temperatures for L dwarfs.


title: The semi-classical energy of open Nambu-Goto strings

abstract:
  We compute semi-classical corrections to the energy of rotating open
Nambu-Goto strings with and without masses at the ends, using methods from
quantum field theory on curved space-times.


title:
Identifying non-k-separability of a class of N-qubit complete graph
  states using correlation tensors

abstract:
  We derive a general expression for standard tensor norm of $N$-body
correlation tensors for $N$-qubit complete graph states. With the help of this
expression, we formulate a separability criterion that identifies
non-$k$-separability of a class of $N$-qubit complete graph states, including
GHZ state. We illustrate the performance of our criterion by considering the
$N$-qubit complete graph states added with colored product noise. We also
demonstrate that few local measurement settings are sufficient to evaluate our
criterion.


title: Note sur les inegalites isoperimetriques en dimension 2

abstract:
  This text talk about the isoperimetric inequalities of Nehari, Huber and
Alexandrov in dimension 2.


title: High fidelity bi-directional nuclear qubit initialization in SiC

abstract:
  Dynamic nuclear polarization (DNP) is an attractive method for initializing
nuclear spins that are strongly coupled to optically active electron spins
because it functions at room temperature and does not require strong magnetic
fields. In this Letter, we demonstrate that DNP, with near-unity polarization
efficiency, can be generally realized in weakly coupled hybrid registers, and
furthermore that the nuclear spin polarization can be completely reversed with
only sub-Gauss magnetic field variations. This mechanism offers new avenues for
DNP-based sensors and radio-frequency free control of nuclear qubits.


title:
Quadratic band touching with long range interactions in and out of
  equilibrium

abstract:
  Motivated by recent advances in cold atomic systems, we study the equilibrium
and quench properties of two dimensional fermions with quadratic band touching
at the Fermi level, in the presence of infinitely long range interactions.
Unlike when only short range interactions are present, both nematic and quantum
anomalous Hall (QAH) states state appear at weak interactions, separated by a
narrow coexistence region, whose boundaries mark second and third order quantum
phase transitions. After an interaction quench, the QAH order exhibits three
distinct regions: persistent or damped oscillations and exponential decay to
zero. In contrast, the nematic order always reaches a non-zero stationary value
through power law damped oscillations, due to the interplay of the symmetry of
the interaction and the specific topology of the quadratic band touching.


title:
Correlated disorder in the Kuramoto model: Effects on phase coherence,
  finite-size scaling, and dynamic fluctuations

abstract:
  We consider a mean-field model of coupled phase oscillators with quenched
disorder in the natural frequencies and coupling strengths. A fraction $p$ of
oscillators are positively coupled, attracting all others, while the remaining
fraction $1-p$ are negatively coupled, repelling all others. The frequencies
and couplings are deterministically chosen in a manner which correlates them,
thereby correlating the two types of disorder in the model. We first explore
the effect of this correlation on the system's phase coherence. We find that
there is a a critical width $\gamma_c$ in the frequency distribution below
which the system spontaneously synchronizes. Moreover, this $\gamma_c$ is
independent of $p$. Hence, our model and the traditional Kuramoto model
(recovered when $p=1$) have the same critical width $\gamma_c$. We next explore
the critical behavior of the system by examining the finite-size scaling and
the dynamic fluctuation of the traditional order parameter. We find that the
model belongs to the same universality class as the Kuramoto model with
deterministically (not randomly) chosen natural frequencies for the case of
$p<1$.

categories: cond-mat.stat-mech math-ph math.DS math.MP nlin.CD


title: Asymmetries in Heavy Quark Pair and Dijet Production at an EIC

abstract:
  Asymmetries in heavy quark pair and dijet production in electron-proton
collisions allow studies of gluon TMDs in close analogy to studies of quark
TMDs in semi-inclusive DIS. Here we present expressions for azimuthal
asymmetries for both unpolarized and transversely polarized proton cases and
consider the maximal asymmetries allowed. The latter are found to be rather
sizeable, except in certain kinematic limits which are pointed out. In
addition, we consider the small-x limit and expectations from a
McLerran-Venugopalan model for unpolarized and linearly polarized gluons and
from a perturbative, large transverse momentum calculation for the T-odd gluon
TMDs. Comparison to related observables at RHIC and LHC is expected to provide
valuable information about the process dependence of the gluon TMDs. In
particular this will offer the possibility of a sign change test of the gluon
Sivers TMD and two other T-odd gluon TMDs. This provides additional motivation
for studies of azimuthal asymmetries in heavy quark pair and dijet production
at a future Electron-Ion Collider.


title: Optimizing Teleportation Cost in Distributed Quantum Circuits

abstract:
  The presented work provides a procedure for optimizing the communication cost
of a distributed quantum circuit (DQC) in terms of the number of qubit
teleportations. Because of technology limitations which do not allow large
quantum computers to work as a single processing element, distributed quantum
computation is an appropriate solution to overcome this difficulty. Previous
studies have applied ad-hoc solutions to distribute a quantum system for
special cases and applications. In this study, a general approach is proposed
to optimize the number of teleportations for a DQC consisting of two spatially
separated and long-distance quantum subsystems. To this end, different
configurations of locations for executing gates whose qubits are in distinct
subsystems are considered and for each of these configurations, the proposed
algorithm is run to find the minimum number of required teleportations.
Finally, the configuration which leads to the minimum number of teleportations
is reported. The proposed method can be used as an automated procedure to find
the configuration with the optimal communication cost for the DQC.


title:
Spectral Properties of the Ruelle Operator for Product Type Potentials
  on Shift Spaces

abstract:
  We study a class of potentials $f$ on one sided full shift spaces over finite
or countable alphabets, called potentials of product type. We obtain explicit
formulae for the leading eigenvalue, the eigenfunction (which may be
discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness
property of these quantities is also discussed and it is shown that there
always exists a Bernoulli equilibrium state even if $f$ does not satisfy
Bowen's condition. We apply these results to potentials $f:\{-1,1\}^\mathbb{N}
\to \mathbb{R}$ of the form $$
  f(x_1,x_2,\ldots)
  =
  x_1 + 2^{-\gamma} \, x_2 + 3^{-\gamma} \, x_3 + ...+n^{-\gamma} \, x_n +
\ldots
  $$ with $\gamma >1$. For $3/2 < \gamma \leq 2$, we obtain the existence of
two different eigenfunctions. Both functions are (locally) unbounded and exist
a.s. (but not everywhere) with respect to the eigenmeasure and the measure of
maximal entropy, respectively.

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


title: On diagonal entries of Cartan matrices of p-blocks

abstract:
  In this short note, we show some inequalities on Cartan matrices, centers and
socles of blocks of group algebras. Our main theorems are generalizations of
the facts on dimension of Reynolds ideals.


title:
Determining the mid-plane conditions of circumstellar discs using gas
  and dust modelling: a study of HD 163296

abstract:
  The mass of gas in protoplanetary discs is a quantity of great interest for
assessing their planet formation potential. Disc gas masses are, however,
traditionally inferred from measured dust masses by applying an assumed
standard gas-to-dust ratio of $g/d=100$. Furthermore, measuring gas masses
based on CO observations has been hindered by the effects of CO freeze-out.
Here we present a novel approach to study the mid-plane gas by combining
C$^{18}$O line modelling, CO snowline observations and the spectral energy
distribution (SED) and selectively study the inner tens of au where freeze-out
is not relevant. We apply the modelling technique to the disc around the Herbig
Ae star HD 163296 with particular focus on the regions within the CO snowline
radius, measured to be at 90 au in this disc. Our models yield the mass of
C$^{18}$O in this inner disc region of
$M_{\text{C}^{18}\text{O}}(<90\,\text{au})\sim 2\times10^{-8}$ M$_\odot$. We
find that most of our models yield a notably low $g/d<20$, especially in the
disc mid-plane ($g/d<1$). Our only models with a more interstellar medium
(ISM)-like $g/d$ require C$^{18}$O to be underabundant with respect to the ISM
abundances and a significant depletion of sub-micron grains, which is not
supported by scattered light observations. Our technique can be applied to a
range of discs and opens up a possibility of measuring gas and dust masses in
discs within the CO snowline location without making assumptions about the
gas-to-dust ratio.


title: Convex integral functionals of processes of bounded variation

abstract:
  This article characterizes conjugates and subdifferentials of convex integral
functionals over the linear space $\mathcal N^\infty$ of stochastic processes
of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified
with the Banach dual of the space of regular processes. Our proofs are based on
new results on the interchange of integration and minimization of integral
functionals over BV processes. Under mild conditions, the domain of the
conjugate is shown to be contained in the space of semimartingales which leads
to several applications in the duality theory in stochastic control and
mathematical finance.


title:
Constraints on Z' models from LHC dijet searches and implications for
  dark matter

abstract:
  We analyse a combination of ATLAS and CMS searches for dijet resonances at
run I and run II, presenting the results in a way that can be easily applied to
a generic Z' model. As an illustrative example, we consider a simple model of a
Z' coupling to quarks and dark matter. We first study a benchmark case with
fixed couplings and then focus on the assumption that the Z' is responsible for
setting the dark matter relic abundance. Dijet constraints place significant
bounds on this scenario, allowing us to narrow down the allowed range of dark
matter masses for given Z' mass and width.


title: Non semi-simple TQFTs from unrolled quantum $sl(2)$

abstract:
  Invariants of 3-manifolds from a non semi-simple category of modules over a
version of quantum $sl(2)$ were obtained by the last three authors in
arXiv:1202.3553 . They are invariants of $3$-manifolds together with a
cohomology class which can be interpreted as a line bundle with flat
connection. In arXiv:1404.7289 we have extended those invariants to graded
TQFTs on suitable cobordism categories. Here we give an overview of
constructions and results, and describe the TQFT vector spaces. Then we provide
a new, algebraic, approach to the computation of these vector spaces.


title: Self-tallying Quantum Anonymous Voting

abstract:
  Anonymous voting is a voting method of hiding the link between a vote and a
voter, the context of which ranges from governmental elections to decision
making in small groups like councils or companies. In this paper, we propose a
quantum anonymous voting protocol assisted by two kinds of entangled quantum
states. Particularly, we provide a mechanism of opening and permuting the
ordered votes of all the voters in an anonymous manner; any party, who is
interested in the voting results, can acquire a permutation copy, and then
obtains the voting result through simple calculation. Unlike all previous
quantum works on anonymous voting, our quantum anonymous protocol firstly
possesses the properties of privacy, self-tallying, non-reusability,
verifiability and fairness at the same time. Besides, we demonstrate that the
entanglement of the novel quantum states used in our protocol makes the attack
from outside eavesdropper and inside dishonest voters impossible. We also
generalize our protocol to execute tasks of anonymous multi-party computation,
such as anonymous broadcast and anonymous ranking.


title:
Design of MLSD-Based Receivers for Short-Range Optical Communications
  Using the Volterra Expansion

abstract:
  Maximum Likelihood Sequence Detectors (MLSD) have been largely used to
mitigate the Chromatic Dispersion (CD) in Intensity Modulation/Direct Detection
(IM/DD) optical communication systems. For practical applications, the high
complexity of the receivers remains an important issue. In this paper, we
analyze the design of MLSD-based receivers using the Orthogonal Volterra Kernel
Model for IM/DD optical communication systems in Metro Optical applications. We
discuss the impact in complexity and performance of the main parameters of the
model and provide three design options for the MLSDbased receiver. Finally we
provide numerical simulations showing the Bit Error Rate (BER) performances of
the three considered designs for both On-Off Keying (OOK) and higher order
Pulse Amplitude Modulation (PAM).


title:
Metastable inhomogeneous vortex configuration with non-uniform filling
  fraction inside a blind hole array patterned in a BSCCO single crystal and
  concentrating magnetic flux inside it

abstract:
  Using magneto-optical imaging technique, we map local magnetic field
distribution inside a hexagonally ordered array of blind holes patterned in
BSCCO single crystals. The nature of the spatial distribution of local magnetic
field and shielding currents across the array reveals the presence of a
non-uniform vortex configuration partially matched with the blind holes at
sub-matching fields. We observe that the filling fraction is different in two
different regions of the array. The mean vortex configuration within the array
is described as a patchy vortex configuration with the patches having different
mean filling fraction. The patchy nature of the vortex configuration is more
pronounced at partial filling of the array at low fields while the
configuration becomes more uniform with a unique filling fraction at higher
fields. The metastable nature of this patchy vortex configuration is revealed
by the application of magnetic field pulses of fixed height or individual
pulses of varying height to the array. The metastability of the vortex
configuration allows for a relatively easy way of producing flux reorganization
and flux focusing effects within the blind hole array. Effect of the magnetic
field pulses modifies the vortex configuration within the array and produces a
uniform enhancement in the shielding current around the patterned array edges.
The enhanced shielding current concentrates magnetic flux within the array by
driving vortices away from the edges and towards the center of the array. The
enhanced shielding current also prevents the uninhibited entry of vortices into
the array. We propose that the metastable patchy vortex configuration within
the blind hole array is due to a non-uniform pinning landscape leading to
non-uniform filling of individual blind holes.


title: Trading VIX Futures under Mean Reversion with Regime Switching

abstract:
  This paper studies the optimal VIX futures trading problems under a
regime-switching model. We consider the VIX as mean reversion dynamics with
dependence on the regime that switches among a finite number of states. For the
trading strategies, we analyze the timings and sequences of the investor's
market participation, which leads to several corresponding coupled system of
variational inequalities. The numerical approach is developed to solve these
optimal double stopping problems by using projected-successive-over-relaxation
(PSOR) method with Crank-Nicolson scheme. We illustrate the optimal boundaries
via numerical examples of two-state Markov chain model. In particular, we
examine the impacts of transaction costs and regime-switching timings on the
VIX futures trading strategies.


title:
Steganalysis via a Convolutional Neural Network using Large Convolution
  Filters for Embedding Process with Same Stego Key

abstract:
  For the past few years, in the race between image steganography and
steganalysis, deep learning has emerged as a very promising alternative to
steganalyzer approaches based on rich image models combined with ensemble
classifiers. A key knowledge of image steganalyzer, which combines relevant
image features and innovative classification procedures, can be deduced by a
deep learning approach called Convolutional Neural Networks (CNN). These kind
of deep learning networks is so well-suited for classification tasks based on
the detection of variations in 2D shapes that it is the state-of-the-art in
many image recognition problems. In this article, we design a CNN-based
steganalyzer for images obtained by applying steganography with a unique
embedding key. This one is quite different from the previous study of {\em Qian
et al.} and its successor, namely {\em Pibre et al.} The proposed architecture
embeds less convolutions, with much larger filters in the final convolutional
layer, and is more general: it is able to deal with larger images and lower
payloads. For the "same embedding key" scenario, our proposal outperforms all
other steganalyzers, in particular the existing CNN-based ones, and defeats
many state-of-the-art image steganography schemes.


title: On the Lp-quantiles for the Student t distribution

abstract:
  L_p-quantiles represent an important class of generalised quantiles and are
defined as the minimisers of an expected asymmetric power function, see Chen
(1996). For p=1 and p=2 they correspond respectively to the quantiles and the
expectiles. In his paper Koenker (1993) showed that the tau quantile and the
tau expectile coincide for every tau in (0,1) for a class of rescaled Student t
distributions with two degrees of freedom. Here, we extend this result proving
that for the Student t distribution with p degrees of freedom, the tau quantile
and the tau L_p-quantile coincide for every tau in (0,1) and the same holds for
any affine transformation. Furthermore, we investigate the properties of
L_p-quantiles and provide recursive equations for the truncated moments of the
Student t distribution.


title: Clean quantum and classical communication protocols

abstract:
  By how much must the communication complexity of a function increase if we
demand that the parties not only correctly compute the function but also return
all registers (other than the one containing the answer) to their initial
states at the end of the communication protocol? Protocols that achieve this
are referred to as clean and the associated cost as the clean communication
complexity. Here we present clean protocols for calculating the Inner Product
of two $n$-bit strings, showing that (in the absence of pre-shared
entanglement) at most $n+3$ qubits or $n+O(\sqrt{n})$ bits of communication are
required. The quantum protocol provides inspiration for obtaining the optimal
method to implement distributed CNOT gates in parallel whilst minimizing the
amount of quantum communication. For more general functions, we show that
nearly all Boolean functions require close to $2n$ bits of classical
communication to compute and close to $n$ qubits if the parties have access to
pre-shared entanglement. Both of these values are maximal for their respective
paradigms.


title: Some studies on Loewy lengths of centers of p-blocks

abstract:
  In this paper, we investigate some relations between the Loewy lengths of the
centers of blocks of group algebras and its defect groups. In particular, we
give a new upper bound of the Loewy length and determine the structure of
blocks with large Loewy length.


title:
On Fast Convergence of Proximal Algorithms for SQRT-Lasso Optimization:
  Don't Worry About Its Nonsmooth Loss Function

abstract:
  Many machine learning techniques sacrifice convenient computational
structures to gain estimation robustness and modeling flexibility. However, by
exploring the modeling structures, we find these "sacrifices" do not always
require more computational efforts. To shed light on such a "free-lunch"
phenomenon, we study the square-root-Lasso (SQRT-Lasso) type regression
problem. Specifically, we show that the nonsmooth loss functions of SQRT-Lasso
type regression ease tuning effort and gain adaptivity to inhomogeneous noise,
but is not necessarily more challenging than Lasso in computation. We can
directly apply proximal algorithms (e.g. proximal gradient descent, proximal
Newton, and proximal Quasi-Newton algorithms) without worrying the
nonsmoothness of the loss function. Theoretically, we prove that the proximal
algorithms combined with the pathwise optimization scheme enjoy fast
convergence guarantees with high probability. Numerical results are provided to
support our theory.


title:
Solving large-scale nonlinear eigenvalue problems by rational
  interpolation approach and resolvent sampling based Rayleigh-Ritz method

abstract:
  Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently
encountered in computational science and engineering. The applicability of most
existing methods is limited by matrix structures, property of eigen-solutions,
size of the problem, etc. This paper aims to break those limitations and to
develop robust and universal NEP solvers for large-scale engineering
applications. The novelty lies in two aspects. First, a rational interpolation
approach (RIA) is proposed based on the Keldysh theorem for holomorphic matrix
functions. Comparing with the existing contour integral approach (CIA), the RIA
provides the possibility to select sampling points in more general regions and
has advantages in improving accuracy and reducing computational cost. Second, a
resolvent sampling scheme using the RIA is proposed for constructing reliable
search spaces for the Rayleigh-Ritz procedure, based on which a robust
eigen-solver, denoted by RSRR, is developed for solving general NEPs. RSRR can
be easily implemented and parallelized. The advantages of the RIA and the
performance of RSRR are demonstrated by a variety of benchmark and practical
problems.


title:
A multicaloric material as a link between electrocaloric and
  magnetocaloric refrigeration

abstract:
  The existence and feasibility of the multicaloric, polycrystalline material
0.8Pb(Fe1/2Nb1/2)O3-0.2Pb(Mg1/2W1/2)O3, exhibiting magnetocaloric and
electrocaloric properties, are demonstrated. Both the electrocaloric and
magnetocaloric effects are observed over a broad temperature range below room
temperature. The maximum magnetocaloric temperature change of ~0.26 K is
obtained with a magnetic-field amplitude of 70 kOe at a temperature of 5 K,
while the maximum electrocaloric temperature change of ~0.25 K is obtained with
an electric-field amplitude of 60 kV/cm at a temperature of 180 K. The material
allows a multicaloric cooling mode or a separate caloric-modes operation
depending on the origin of the external field and the temperature at which the
field is applied.


title:
Uniformly de Bruijn sequences and symbolic Diophantine approximation on
  fractals

abstract:
  Intrinsic Diophantine approximation on fractals, such as the Cantor ternary
set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of
the main goals of this paper is to develop and utilize the theory of infinite
de Bruijn sequences in order to answer closely related questions. In
particular, we prove that the set of infinite de Bruijn sequences in $k\geq 2$
letters, thought of as a set of real numbers via a decimal expansion, has
positive Hausdorff dimension. For a given $k$, these sequences bear a strong
connection to Diophantine approximation on certain fractals. In particular, the
optimality of an intrinsic Dirichlet function on these fractals with respect to
the height function defined by symbolic representations of rationals follows
from these results.


title: Black hole Skyrmion in a generalized Skyrme model

abstract:
  We study a Skyrme-like model with the Skyrme term and a sixth-order
derivative term as higher-order terms, coupled to gravity and we construct
Schwarzschild black hole Skyrme hair. We find, surprisingly, that the
sixth-order derivative term alone cannot stabilize the black hole hair
solutions; the Skyrme term with a large enough coefficient is a necessity.


title: Hidden flavor symmetries of SO(10) GUT

abstract:
  The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well
as with singlets) have certain intrinsic ("built-in") symmetries which do not
depend on the model parameters. Thus, the symmetric Yukawa interactions of the
10 and 126 dimensional Higgses have intrinsic discrete $Z_2\times Z_2$
symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional
Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet
fermions with fermionic 16-plets have $U(1)^3$ symmetry. We consider a
possibility that some elements of these intrinsic symmetries are the residual
symmetries, which originate from the (spontaneous) breaking of a larger
symmetry group $G_f$. Such an embedding leads to the determination of certain
elements of the relative mixing matrix $U$ between the matrices of Yukawa
couplings $Y_{10}$, $Y_{126}$, $Y_{120}$, and consequently, to restrictions of
masses and mixings of quarks and leptons. We explore the consequences of such
embedding using the symmetry group conditions. We show how unitarity emerges
from group properties and obtain the conditions it imposes on the parameters of
embedding. We find that in some cases the predicted values of elements of $U$
are compatible with the existing data fits. In the supersymmetric version of
SO(10) such results are renormalization group invariant.


title:
Towards Extending Noiseless Privacy -- Dependent Data and More Practical
  Approach

abstract:
  In 2011 Bhaskar et al. pointed out that in many cases one can ensure
sufficient level of privacy without adding noise by utilizing adversarial
uncertainty. Informally speaking, this observation comes from the fact that if
at least a part of the data is randomized from the adversary's point of view,
it can be effectively used for hiding other values. So far the approach to that
idea in the literature was mostly purely asymptotic, which greatly limited its
adaptation in real-life scenarios. In this paper we aim to make the concept of
utilizing adversarial uncertainty not only an interesting theoretical idea, but
rather a practically useful technique, complementary to differential privacy,
which is the state-of-the-art definition of privacy. This requires
non-asymptotic privacy guarantees, more realistic approach to the randomness
inherently present in the data and to the adversary's knowledge. In our paper
we extend the concept proposed by Bhaskar et al. and present some results for
wider class of data. In particular we cover the data sets that are dependent.
We also introduce rigorous adversarial model. Moreover, in contrast to most of
previous papers in this field, we give detailed (non-asymptotic) results which
is motivated by practical reasons. Note that it required a modified approach
and more subtle mathematical tools, including Stein method which, to the best
of our knowledge, was not used in privacy research before. Apart from that, we
show how to combine adversarial uncertainty with differential privacy approach
and explore synergy between them to enhance the privacy parameters already
present in the data itself by adding small amount of noise.


title:
Attosecond delay of xenon $4d$ photoionization at the giant resonance
  and Cooper minimum

abstract:
  A Kohn-Sham time-dependent local-density-functional scheme is utilized to
predict attosecond time delays of xenon 4d photoionization that involves the 4d
giant dipole resonance and Cooper minimum. The fundamental effect of electron
correlations to uniquely determine the delay at both regions is demonstrated.
In particular, for the giant dipole resonance, the delay underpins strong
collective effect, emulating the recent prediction at C60 giant plasmon
resonance [T. Barillot et al, Phys. Rev. A 91, 033413 (2015)]. For the Cooper
minimum, a qualitative similarity with a photorecombination experiment near
argon 3p minimum [S. B. Schoun et al, Phys. Rev. Lett. 112, 153001 (2014)] is
found. The result should encourage attosecond measurements of Xe 4d
photoemission.


title:
Asteroseismic modelling of the two F-type hybrid pulsators KIC10080943A
  and KIC10080943B

abstract:
  Pulsating binary stars are ideal targets for testing the theory of stellar
structure and evolution. Fundamental parameters can be derived to high
precision from binary modelling and provide crucial constraints for seismic
modelling. High-order gravity modes are sensitive to the conditions near the
convective core and therefore allow for a determination of parameters
describing interior physics, especially the convective-core overshooting
parameter. KIC\,10080943 is a binary system that contains two gravity- and
pressure-mode hybrid pulsators. A detailed observational study has provided
fundamental and seismic parameters for both components. We aim to find a model
that is able to predict the observed g-mode period spacings and stellar
parameters of both components of KIC 10080943. By calculating model grids with
the stellar evolution code MESA and the seismic code GYRE, we can compare
theoretical properties to the observed mean period spacing and position in the
Hertzsprung-Russell diagram. The masses of our best models are somewhat below
the values estimated from binarity, which is a consequence of the low observed
mean g-mode period spacing. We find that the amount of core overshooting and
diffusive mixing can be well constrained by the equal-age requirement for the
two stars, however, we find no significant difference for different shapes of
core overshooting. The measured rotation rates are within the limit of validity
for the first-order perturbation approximation. We can find a good fit by using
the traditional approximation for the pulsations, when taking slightly younger
models with a higher asymptotic period spacing. This is because the zonal modes
experience a slight shift due to the Coriolis force, which the first-order
perturbation approximation ignores.


title: Parameterized complexity of fair deletion problems

abstract:
  Deletion problems are those where given a graph $G$ and a graph property
$\pi$, the goal is to find a subset of edges such that after its removal the
graph $G$ will satisfy the property $\pi$. Typically, we want to minimize the
number of elements removed. In fair deletion problems we change the objective:
we minimize the maximum number of deletions in a neighborhood of a single
vertex.
  We study the parameterized complexity of fair deletion problems with respect
to the structural parameters of the tree-width, the path-width, the size of a
minimum feedback vertex set, the neighborhood diversity, and the size of
minimum vertex cover of graph $G$. We prove the W[1]-hardness of the fair FO
vertex-deletion problem with respect to the first three parameters combined.
Moreover, we show that there is no algorithm for fair FO vertex-deletion
problem running in time $n^{o(k^{1/3})}$, where $n$ is the size of the graph
and $k$ is the sum of the first three mentioned parameters, provided that the
Exponential Time Hypothesis holds.
  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion
problem parameterized by the size of minimum vertex cover and an FPT algorithm
for the fair MSO vertex-deletion problem parameterized by the neighborhood
diversity


title: Multi-Object Tracking and Identification over Sets

abstract:
  The ability for an autonomous agent or robot to track and identify
potentially multiple objects in a dynamic environment is essential for many
applications, such as automated surveillance, traffic monitoring, human-robot
interaction, etc. The main challenge is due to the noisy and incomplete
perception including inevitable false negative and false positive errors from a
low-level detector. In this paper, we propose a novel multi-object tracking and
identification over sets approach to address this challenge. We define joint
states and observations both as finite sets, and develop motion and observation
functions accordingly. The object identification problem is then formulated and
solved by using expectation-maximization methods. The set formulation enables
us to avoid directly performing observation-to-object association. We
empirically confirm that the overall algorithm outperforms the state-of-the-art
in a popular PETS dataset.


title: Symplectic analysis of three dimensional Abelian topological gravity

abstract:
  A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is
performed; we show that this formalism is equivalent and more economical than
Dirac's method. In particular, we identify the complete set of constraints of
the theory, from which the number of physical degrees of freedom is explicitly
computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac
ones coincide to each other. Moreover, we perform the Faddeev-Jackiw analysis
of the theory at the chiral point, and the full set of constraints and the
generalized Faddeev-Jackiw brackets are constructed. Finally we compare our
results with those found in the literature and we discuss some remarks and
prospects.


title: Cornering diphoton resonance models at the LHC

abstract:
  We explore the ability of the high luminosity LHC to test models which can
explain the 750 GeV diphoton excess. We focus on a wide class of models where a
750 GeV singlet scalar couples to Standard Model gauge bosons and quarks, as
well as dark matter. Including both gluon and photon fusion production
mechanisms, we show that LHC searches in channels correlated with the diphoton
signal will be able to probe wide classes of diphoton models with $\mathcal{L}
\sim 3000\, \text{fb}^{-1}$ of data. Furthermore, models in which the scalar is
a portal to the dark sector can be cornered with as little as $\mathcal{L} \sim
30\, \text{fb}^{-1}$.


title:
Mean curvature flow of arbitrary codimension in complex projective
  spaces

abstract:
  In this paper, we investigate the mean curvature flow of submanifolds of
arbitrary codimension in $\mathbb{C}\mathbb{P}^m$. We prove that if the initial
submanifold satisfies a pinching condition, then the mean curvature flow
converges to a round point in finite time, or converges to a totally geodesic
submanifold as $t \rightarrow \infty$. Consequently, we obtain a new
differentiable sphere theorem for submanifolds in $\mathbb{C}\mathbb{P}^m$. Our
work improves the convergence theorem for mean curvature flow due to Pipoli and
Sinestrari {\cite{PiSi2015}}.


title:
First Measurement of the Muon Neutrino Charged Current Single Pion
  Production Cross Section on Water with the T2K Near Detector

abstract:
  The T2K off-axis near detector, ND280, is used to make the first differential
cross section measurements of muon neutrino charged current single positive
pion production on a water target at energies ${\sim}0.8$ GeV. The differential
measurements are presented as a function of muon and pion kinematics, in the
restricted phase-space defined by $p_{\pi^+}>200$MeV/c, $p_{\mu^-}>200$MeV/c,
$\cos \theta_{\pi^+}>0.3$ and $\cos \theta_{\mu^-}>0.3$. The total flux
integrated $\nu_\mu$ charged current single positive pion production cross
section on water in the restricted phase-space is measured to be
$\langle\sigma\rangle_\phi=4.25\pm0.48 (\mathrm{stat})\pm1.56
(\mathrm{syst})\times10^{-40} \mathrm{cm}^{2}/\mathrm{nucleon}$. The total
cross section is consistent with the NEUT prediction ($5.03\times10^{-40}
\mathrm{cm}^{2}/\mathrm{nucleon}$) and 2$\sigma$ lower than the GENIE
prediction ($7.68\times10^{-40} \mathrm{cm}^{2}/\mathrm{nucleon}$). The
differential cross sections are in good agreement with the NEUT generator. The
GENIE simulation reproduces well the shapes of the distributions, but
over-estimates the overall cross section normalization.


title:
Active transport improves the precision of linear long distance
  molecular signalling

abstract:
  Molecular signalling in living cells occurs at low copy numbers and is
thereby inherently limited by the noise imposed by thermal diffusion. The
precision at which biochemical receptors can count signalling molecules is
intimately related to the noise correlation time. In addition to passive
thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can
transiently bind to molecular motors and are actively transported across
biological cells. Active transport is most beneficial when trafficking occurs
over large distances, for instance up to the order of 1 metre in neurons. Here
we explain how intermittent active transport allows for faster equilibration
upon a change in concentration triggered by biochemical stimuli. Moreover, we
show how intermittent active excursions induce qualitative changes in the noise
in effectively one-dimensional systems such as dendrites. Thereby they allow
for significantly improved signalling precision in the sense of a smaller
relative deviation in the concentration read-out by the receptor. On the basis
of linear response theory we derive the exact mean field precision limit for
counting actively transported molecules. We explain how intermittent active
excursions disrupt the recurrence in the molecular motion, thereby facilitating
improved signalling accuracy. Our results provide a deeper understanding of how
recurrence affects molecular signalling precision in biological cells and novel
diagnostic devices.


title:
Projective product coverings and sequential motion planning algorithms
  in real projective spaces

abstract:
  For positive integers $m$ and $s$, let $\mathbf{m}_s$ stand for the $s$-th
tuple $(m,\ldots,m)$. We show that, for large enough $s$, the higher
topological complexity $TC_s$ of an even dimensional real projective space
$RP^m$ is characterized as the smallest positive integer $k=k(m,s)$ for which
there is a $(\mathbb{Z}_2)^{s-1}$-equivariant map from Davis' projective
product space $P_{\mathbf{m}_s}$ to the $(k+1)$-th join-power
$((\mathbb{Z}_2)^{s-1})^{\ast(k+1)}$. This is a (partial) generalization of
Farber-Tabachnikov-Yuzvinsky's work relating $TC_2$ to the immersion dimension
of real projective spaces. In addition, we compute the exact value of
$TC_s(RP^m)$ for $m$ even and $s$ large enough.


title: Computing Correct Truncated Excited State Wavefunctions

abstract:
  We demonstrate that, if a truncated expansion of a wave function is small,
then the standard excited states computational method, of optimizing one root
of a secular equation, may lead to an incorrect wave function - despite the
correct energy according to the theorem of Hylleraas, Undheim and McDonald -
whereas our proposed method [J. Comput. Meth. Sci. Eng. 8, 277 (2008)]
(independent of orthogonality to lower lying approximants) leads to correct
reliable small truncated wave functions. The demonstration is done in He
excited states, using truncated series expansions in Hylleraas coordinates, as
well as standard configuration-interaction truncated expansions.

categories: physics.atom-ph physics.chem-ph physics.comp-ph quant-ph


title:
Thermal form factor approach to the ground-state correlation functions
  of the XXZ chain in the antiferromagnetic massive regime

abstract:
  We use the form factors of the quantum transfer matrix in the
zero-temperature limit in order to study the two-point ground-state correlation
functions of the XXZ chain in the antiferromagnetic massive regime. We obtain
novel form factor series representations of the correlation functions which
differ from those derived either from the q-vertex-operator approach or from
the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate
that our novel representations are numerically more efficient and allow for a
straightforward calculation of the large-distance asymptotic behaviour of the
two-point functions. Keeping control over the temperature corrections to the
two-point functions we see that these are of order $T^\infty$ in the whole
antiferromagnetic massive regime. The isotropic limit of our result yields a
novel form factor series representation for the two-point correlation functions
of the XXX chain at zero magnetic field.


title: Adaptive Neural Compilation

abstract:
  This paper proposes an adaptive neural-compilation framework to address the
problem of efficient program learning. Traditional code optimisation strategies
used in compilers are based on applying pre-specified set of transformations
that make the code faster to execute without changing its semantics. In
contrast, our work involves adapting programs to make them more efficient while
considering correctness only on a target input distribution. Our approach is
inspired by the recent works on differentiable representations of programs. We
show that it is possible to compile programs written in a low-level language to
a differentiable representation. We also show how programs in this
representation can be optimised to make them efficient on a target distribution
of inputs. Experimental results demonstrate that our approach enables learning
specifically-tuned algorithms for given data distributions with a high success
rate.


title: Single-hit resolution measurement with MEG II drift chamber prototypes

abstract:
  Drift chambers operated with helium-based gas mixtures represent a common
solution for tracking charged particles keeping the material budget in the
sensitive volume to a minimum. The drawback of this solution is the worsening
of the spatial resolution due to primary ionisation fluctuations, which is a
limiting factor for high granularity drift chambers like the MEG II tracker. We
report on the measurements performed on three different prototypes of the MEG
II drift chamber aimed at determining the achievable single-hit resolution. The
prototypes were operated with helium/isobutane gas mixtures and exposed to
cosmic rays, electron beams and radioactive sources. Direct measurements of the
single hit resolution performed with an external tracker returned a value of
110 $\mu$m, consistent with the values obtained with indirect measurements
performed with the other prototypes.


title:
Chirality-induced magnon transport in AA-stacked bilayer honeycomb
  chiral magnets

abstract:
  In this Letter, we study the magnetic transport in AA-stacked bilayer
honeycomb chiral magnets coupled either ferromagnetically or
antiferromagnetically. For both couplings, we observe chirality-induced gaps,
chiral protected edge states, magnon Hall and magnon spin Nernst effects of
magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall
and spin Nernst conductivities do not change sign as function of magnetic field
or temperature similar to single-layer honeycomb ferromagnetic insulator. In
contrast, for antiferromagnetically coupled layers, we observe a sign change in
the thermal Hall and spin Nernst conductivities as the magnetic field is
reversed. We discuss possible experimental accessible honeycomb bilayer quantum
materials in which these effects can be observed.


title: Nonlinear and Quantum Optics with Whispering Gallery Resonators

abstract:
  Optical Whispering Gallery Modes (WGMs) derive their name from a famous
acoustic phenomenon of guiding a wave by a curved boundary observed nearly a
century ago. This phenomenon has a rather general nature, equally applicable to
sound and all other waves. It enables resonators of unique properties
attractive both in science and engineering. Very high quality factors of
optical WGM resonators persisting in a wide wavelength range spanning from
radio frequencies to ultraviolet light, their small mode volume, and tunable
in- and out- coupling make them exceptionally efficient for nonlinear optical
applications. Nonlinear optics facilitates interaction of photons with each
other and with other physical systems, and is of prime importance in quantum
optics. In this paper we review numerous applications of WGM resonators in
nonlinear and quantum optics. We outline the current areas of interest,
summarize progress, highlight difficulties, and discuss possible future
development trends in these areas.


title:
An evaporating planet in the wind: stellar wind interactions with the
  radiatively braked exosphere of GJ436 b

abstract:
  The warm Neptune GJ436b was observed with HST/STIS at three different epochs
in the stellar Ly-alpha line, showing deep, repeated transits caused by a giant
exosphere of neutral hydrogen. The low radiation pressure from the M-dwarf host
star was shown to play a major role in the dynamics of the escaping gas. Yet by
itself it cannot explain the time-variable spectral features detected in each
transit. Here we investigate the combined role of radiative braking and stellar
wind interactions using numerical simulations with the EVaporating Exoplanet
code (EVE) and we derive atmospheric and stellar properties through the direct
comparison of simulated and observed spectra. Our simulations match the last
two epochs well. The observed sharp early ingresses come from the abrasion of
the planetary coma by the stellar wind. Spectra observed during the transit can
be produced by a dual exosphere of planetary neutrals (escaped from the upper
atmosphere of the planet) and neutralized protons (created by charge-exchange
with the stellar wind). We find similar properties at both epochs for the
planetary escape rate (2.5x10$^{8}$ g/s), the stellar photoionization rate
(2x10$^{-5}$ /s), the stellar wind bulk velocity (85 km/s), and its kinetic
dispersion velocity (10 km/s). We find high velocities for the escaping gas
(50-60 km/s) that may indicate MHD waves that dissipate in the upper atmosphere
and drive the planetary outflow. In the last epoch the high density of the
stellar wind (3x10$^{3}$ /cm3) led to the formation of an exospheric tail
mainly composed of neutralized protons. The observations of GJ436 b allow for
the first time to clearly separate the contributions of radiation pressure and
stellar wind and to probe the regions of the exosphere shaped by each
mechanism.


title: Many physical laws are ridge functions

abstract:
  A ridge function is a function of several variables that is constant along
certain directions in its domain. Using classical dimensional analysis, we show
that many physical laws are ridge functions; this fact yields insight into the
structure of physical laws and motivates further study into ridge functions and
their properties. We also connect dimensional analysis to modern subspace-based
techniques for dimension reduction, including active subspaces in deterministic
approximation and sufficient dimension reduction in statistical regression.


title: Exotic Discoveries in Familiar Places: Theory of the Onia and Exotics

abstract:
  This brief overview presents an introduction to the heavy-quark exotic hadron
candidates, $X$, $Y$, $Z$, $P_c$, believed to be tetraquark and pentaquark
states. After an abridged account of their discovery, we outline the various
theoretical pictures employed to describe their structure, with special focus
on the new dynamical diquark picture.


title:
The C*-algebra of a minimal homeomorphism with finite mean dimension has
  finite radius of comparison

abstract:
  Let $X$ be an infinite compact metric space and let $h$ be a minimal
homeomorphism of $X$. We prove that the radius of comparison of the
transformation group C*-algebra of $h$ is at most $1$ plus $36$ times the mean
dimension of $h$.


title:
Instability to a heterogeneous oscillatory state in randomly connected
  recurrent networks with delayed interactions

abstract:
  Oscillatory dynamics are ubiquitous in biological networks. Possible sources
of oscillations are well understood in low-dimensional systems, but have not
been fully explored in high-dimensional networks. Here we study large networks
consisting of randomly coupled rate units. We identify a novel type of
bifurcation in which a continuous part of the eigenvalue spectrum of the linear
stability matrix crosses the instability line at non-zero-frequency. This
bifurcation occurs when the interactions are delayed and partially
anti-symmetric, and leads to a heterogeneous oscillatory state in which
oscillations are apparent in the activity of individual units, but not on the
population-average level.


title:
Boundary Element Procedure for 3D Electromagnetic Transmission Problems
  with Large Conductivity

abstract:
  We consider the scattering of time periodic electro-magnetic fields by
metallic obstacles, the eddy current problem. In this interface problem
different sets of Maxwell equations must be solved in the obstacle and outside,
while the tangential components of both electric and magnetic fields are
continuous across the interface. We describe an asymptotic procedure, which
applies for large conductivity and reflects the skin effect in metals. The key
to our method is to introduce a special integral equation procedure for the
exterior boundary value problem corresponding to perfect conductors. The
asymptotic procedure leads to a great reduction in complexity for the numerical
solution since it involves solving only the exterior boundary value problem.
Furthermore we introduce a new fem/bem coupling procedure for the transmission
problem and consider the implementation of the Galerkin elements for the
perfect conductor problem and present numerical experiments.


title: Radial motions in disk stars: ellipticity or secular flows?

abstract:
  Average stellar orbits of the Galactic disk may have some small intrinsic
ellipticity which breaks the exact axisymmetry and there may also be some
migration of stars inwards or outwards. Both phenomena can be detected through
kinematic analyses. We use the red clump stars selected spectroscopically from
APOGEE (APO Galactic Evolution Experiment), with known distances and radial
velocities, to measure the radial component of the Galactocentric velocities
within 5 kpc$<R<$16 kpc, $|b|<5^\circ$ and within 20 degrees from the
Sun-Galactic center line. The average Galactocentric radial velocity is
$V_R=(1.48\pm 0.35)[R({\rm kpc})-(8.8\pm 2.7)]$ km/s outwards in the explored
range, with a higher contribution from stars below the Galactic plane. Two
possible explanations can be given for this result: i) the mean orbit of the
disk stars is intrinsically elliptical with a Galactocentric radial gradient of
eccentricity around 0.01 kpc$^{-1}$; or ii) there is a net secular expansion of
the disk, in which stars within $R\approx 9-11$ kpc are migrating to the region
$R\gtrsim 11$ kpc at the rate of $\sim 2$ M$_\odot $/yr, and stars with
$R\lesssim 9$ kpc are falling toward the center of the Galaxy. This migration
ratio would be unattainable for a long time and it should decelerate, otherwise
the Galaxy would fade away in around 1 Gyr. At present, both hypotheses are
speculative and one would need data on the Galactocentric radial velocities for
other azimuths different to the center or anticenter in order to confirm one of
the scenarios.


title: Structural Analysis of User Choices for Mobile App Recommendation

abstract:
  Advances in smartphone technology have promoted the rapid development of
mobile apps. However, the availability of a huge number of mobile apps in
application stores has imposed the challenge of finding the right apps to meet
the user needs. Indeed, there is a critical demand for personalized app
recommendations. Along this line, there are opportunities and challenges posed
by two unique characteristics of mobile apps. First, app markets have organized
apps in a hierarchical taxonomy. Second, apps with similar functionalities are
competing with each other. While there are a variety of approaches for mobile
app recommendations, these approaches do not have a focus on dealing with these
opportunities and challenges. To this end, in this paper, we provide a
systematic study for addressing these challenges. Specifically, we develop a
Structural User Choice Model (SUCM) to learn fine-grained user preferences by
exploiting the hierarchical taxonomy of apps as well as the competitive
relationships among apps. Moreover, we design an efficient learning algorithm
to estimate the parameters for the SUCM model. Finally, we perform extensive
experiments on a large app adoption data set collected from Google Play. The
results show that SUCM consistently outperforms state-of-the-art top-N
recommendation methods by a significant margin.


title:
Bayesian Variable Selection and Estimation Based on Global-Local
  Shrinkage Priors

abstract:
  In this paper, we consider Bayesian variable selection problem of linear
regression model with global-local shrinkage priors on the regression
coefficients. We propose a variable selection procedure that select a variable
if the ratio of the posterior mean to the ordinary least square estimate of the
corresponding coefficient is greater than $1/2$. Under the assumption of
orthogonal designs, we show that if the local parameters have polynomial-tailed
priors, our proposed method enjoys the oracle property in the sense that it can
achieve variable selection consistency and optimal estimation rate at the same
time. However, if, instead, an exponential-tailed prior is used for the local
parameters, the proposed method does not have the oracle property.


title: A Smooth Distributed Feedback for Global Rendezvous of Unicycles

abstract:
  This paper presents a solution to the rendezvous control problem for a
network of kinematic unicycles in the plane, each equipped with an onboard
camera measuring its relative displacement with respect to its neighbors in
body frame coordinates. A smooth, time-independent control law is presented
that drives the unicycles to a common position from arbitrary initial
conditions, under the assumption that the sensing digraph contains a
reverse-directed spanning tree. The proposed feedback is very simple, and
relies only on the onboard measurements. No global positioning system is
required, nor any information about the unicycles' orientations.


title: Generalized equivariant model structures on $\mathbf{Cat}^I$

abstract:
  Let $I$ be a small category, $\mathcal{C}$ be the category $\mathbf{Cat}$,
$\mathbf{Ac}$ or $\mathbf{Pos}$ of small categories, acyclic categories, or
posets, respectively. Let $\mathcal{O}$ be a locally small class of objects in
$\mathbf{Set}^I$ such that $\mathrm{colim}_I O=*$ for every $O\in \mathcal{O}$.
We prove that $\mathcal{C}^I$ admits the $\mathcal{O}$-equivariant model
structure in the sense of Farjoun, and that it is Quillen equivalent to the
$\mathcal{O}$-equivariant model structure on $\mathbf{sSet}^I$. This
generalizes previous results of Bohmann-Mazur-Osorno-Ozornova-Ponto-Yarnall and
of May-Stephan-Zakharevich when $I=G$ is a discrete group and $\mathcal{O}$ is
the set of orbits of $G$.


title: A Power Law Approach to Estimating Fake Social Network Accounts

abstract:
  This paper presents a method to validate the true patrons of a brand, group,
artist or any other entity on the social networking site Twitter. We analyze
the trend of total number of tweets, average retweets and total number of
followers for various nodes for different social and political backgrounds. We
argue that average retweets to follower ratio reveals the overall value of the
individual accounts and helps estimate the true to fake account ratio.


title: Compressed sensing for real measurements of quaternion signals

abstract:
  The article concerns compressed sensing methods in the quaternion algebra. We
prove that it is possible to uniquely reconstruct - by $\ell_1$ norm
minimization - a sparse quaternion signal from a limited number of its real
linear measurements, provided the measurement matrix satisfies so-called
restricted isometry property with a sufficiently small constant. We also
provide error estimates for the reconstruction of a non-sparse quaternion
signal in the noisy and noiseless cases.


title: Continuity of the renormalized volume under geometric limits

abstract:
  We extend the concept of renormalized volume for geometrically finite
hyperbolic $3$-manifolds, and show that is continuous for geometrically
convergent sequences of hyperbolic structures over an acylindrical 3-manifold
$M$ with geometrically finite limit. This allows us to show that the
renormalized volume attains its minimum (in terms of the conformal class at
$\partial M = S$) at the geodesic class, the conformal class for which the
boundary of the convex core is totally geodesic.


title:
Reconstructing the high energy irradiation of the evaporating hot
  Jupiter HD 209458b

abstract:
  The atmosphere of the exoplanet HD 209458b is undergoing sustained mass loss,
believed to be caused by X-ray and extreme-ultraviolet (XUV) irradiation from
its star. The majority of this flux is not directly observable due to
interstellar absorption, but is required in order to correctly model the
photo-evaporation of the planet and photo-ionisation of the outflow. We present
a recovered high energy spectrum for HD\,209458 using a Differential Emission
Measure (DEM) retrieval technique. We construct a model of the stellar corona
and transition region for temperatures between 10$^{4.1}$ and 10$^{8}$ K which
is constrained jointly by ultraviolet line strengths measured with the Cosmic
Origins Spectrograph (COS) on the Hubble Space Telescope (HST) and X-ray flux
measurements from XMM-Newton. The total hydrogen ionising luminosity ($\lambda
< 912$ \AA) is found to be 10$^{28.26}$ erg s$^{-1}$, which is similar to the
value for the mean activity level of the Sun. This luminosity is incompatible
with energy limited mass loss rates estimated from the same COS dataset, even
the lower bound requires an uncomfortably high energetic efficiency of >40%.
However, our luminosity is compatible with early estimates of the mass loss
rate of HD 209458b based on results from the HST Space Telescope Imaging
Spectrograph (STIS). Precisely reconstructed XUV irradiation is a key input to
determining mass loss rates and efficiencies for exoplanet atmospheres.


title:
Multilevel Threshold Secret and Function Sharing based on the Chinese
  Remainder Theorem

abstract:
  A recent work of Harn and Fuyou presents the first multilevel (disjunctive)
threshold secret sharing scheme based on the Chinese Remainder Theorem. In this
work, we first show that the proposed method is not secure and also fails to
work with a certain natural setting of the threshold values on compartments. We
then propose a secure scheme that works for all threshold settings. In this
scheme, we employ a refined version of Asmuth-Bloom secret sharing with a
special and generic Asmuth-Bloom sequence called the {\it anchor sequence}.
Based on this idea, we also propose the first multilevel conjunctive threshold
secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we
discuss how the proposed schemes can be used for multilevel threshold function
sharing by employing it in a threshold RSA cryptosystem as an example.


title:
Compliant Conditions for Polynomial Time Approximation of Operator
  Counts

abstract:
  In this paper, we develop a computationally simpler version of the operator
count heuristic for a particular class of domains. The contribution of this
abstract is threefold, we (1) propose an efficient closed form approximation to
the operator count heuristic using the Lagrangian dual; (2) leverage compressed
sensing techniques to obtain an integer approximation for operator counts in
polynomial time; and (3) discuss the relationship of the proposed formulation
to existing heuristics and investigate properties of domains where such
approaches appear to be useful.