title: Percolation of overlapping squares or cubes on a lattice

abstract:
  Porous media are often modelled as systems of overlapping obstacles, which
leads to the problem of two percolation thresholds in such systems, one for the
porous matrix and the other one for the void space. Here we investigate these
percolation thresholds in the model of overlapping squares or cubes of linear
size $k>1$ randomly distributed on a regular lattice. We find that the
percolation threshold of obstacles is a nonmonotonic function of $k$, whereas
the percolation threshold of the void space is well approximated by a function
linear in $1/k$. We propose a generalization of the excluded volume
approximation to discrete systems and use it to investigate the transition
between continuous and discrete percolation, finding a remarkable agreement
between the theory and numerical results. We argue that the continuous
percolation threshold of aligned squares on a plane is the same for the solid
and void phases and estimate the continuous percolation threshold of the void
space around aligned cubes in a 3D space as 0.036(1). We also discuss the
connection of the model to the standard site percolation with complex
neighborhood.


title:
A Tucker decomposition process for probabilistic modeling of diffusion
  magnetic resonance imaging

abstract:
  Diffusion magnetic resonance imaging (dMRI) is an emerging medical technique
used for describing water diffusion in an organic tissue. Typically, rank-2
tensors quantify this diffusion. From this quantification, it is possible to
calculate relevant scalar measures (i.e. fractional anisotropy and mean
diffusivity) employed in clinical diagnosis of neurological diseases.
Nonetheless, 2nd-order tensors fail to represent complex tissue structures like
crossing fibers. To overcome this limitation, several researchers proposed a
diffusion representation with higher order tensors (HOT), specifically 4th and
6th orders. However, the current acquisition protocols of dMRI data allow
images with a spatial resolution between 1 $mm^3$ and 2 $mm^3$. This voxel size
is much smaller than tissue structures. Therefore, several clinical procedures
derived from dMRI may be inaccurate. Interpolation has been used to enhance
resolution of dMRI in a tensorial space. Most interpolation methods are valid
only for rank-2 tensors and a generalization for HOT data is missing. In this
work, we propose a novel stochastic process called Tucker decomposition process
(TDP) for performing HOT data interpolation. Our model is based on the Tucker
decomposition and Gaussian processes as parameters of the TDP. We test the TDP
in 2nd, 4th and 6th rank HOT fields. For rank-2 tensors, we compare against
direct interpolation, log-Euclidean approach and Generalized Wishart processes.
For rank-4 and rank-6 tensors we compare against direct interpolation. Results
obtained show that TDP interpolates accurately the HOT fields and generalizes
to any rank.


title: Production of D-mesons in $p$+$p$ and $p$+Pb collisions at LHC energies

abstract:
  We present theoretical model comparison with published ALICE results for
D-mesons (D$^0$, D$^+$ and D$^{*+}$) in $p$+$p$ collisions at $\sqrt{s}$ = 7
TeV and $p$+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. Event generator
HIJING, transport calculation of AMPT and calculations from NLO(MNR) and FONLL
have been used for this study. We found that HIJING and AMPT model predictions
are matching with published D-meson cross-sections in $p$+$p$ collisions, while
both under-predict the same in $p$+Pb collisions. Attempts were made to explain
the $R_{pPb}$ data using NLO-pQCD(MNR), FONLL and other above mentioned models.


title: Wi-Fi Coexistence with Duty Cycled LTE-U

abstract:
  Coexistence of Wi-Fi and LTE-Unlicensed (LTE-U) technologies has drawn
significant concern in industry. In this paper, we investigate the Wi-Fi
performance in the presence of duty cycle based LTE-U transmission on the same
channel. More specifically, one LTE-U cell and one Wi-Fi basic service set
(BSS) coexist by allowing LTE-U devices transmit their signals only in
predetermined duty cycles. Wi-Fi stations, on the other hand, simply contend
the shared channel using the distributed coordination function (DCF) protocol
without cooperation with the LTE-U system or prior knowledge about the duty
cycle period or duty cycle of LTE-U transmission. We define the fairness of the
above scheme as the difference between Wi-Fi performance loss ratio
(considering a defined reference performance) and the LTE-U duty cycle (or
function of LTE-U duty cycle). Depending on the interference to noise ratio
(INR) being above or below -62dbm, we classify the LTE-U interference as strong
or weak and establish mathematical models accordingly. The average throughput
and average service time of Wi-Fi are both formulated as functions of Wi-Fi and
LTE-U system parameters using probability theory. Lastly, we use the Monte
Carlo analysis to demonstrate the fairness of Wi-Fi and LTE-U air time sharing.


title: Picard-Lefschetz Monodromy Groups of Quadratic Hypersurfaces

abstract:
  We study the topology of the space of affine hyperplanes $L \subset \CC^n$
which are in general position with respect to a given generic quadratic
hypersurface $A$, and calculate the monodromy action of the fundamental group
of this space on the relative homology groups $H_*(\CC^n, A \cup L)$ associated
with such hyperplanes.


title: Transport mechanism through metal-cobaltite interfaces

abstract:
  The resistive switching (RS) properties as a function of temperature were
studied for Ag/La$_{1-x}$Sr$_x$CoO$_3$ (LSCO) interfaces. The LSCO is a
fully-relaxed 100 nm film grown by metal organic deposition on a LaAlO$_3$
substrate. Both low and a high resistance states were set at room temperature
and the temperature dependence of their current-voltage (IV) characteristics
was mea- sured taking care to avoid a significant change of the resistance
state. The obtained non-trivial IV curves of each state were well reproduced by
a circuit model which includes a Poole-Frenkel element and two ohmic
resistances. A microscopic description of the changes produced by the RS is
given, which enables to envision a picture of the interface as an area where
conductive and insulating phases are mixed, producing Maxwell-Wagner
contributions to the dielectric properties.


title: Now, and the Flow of Time

abstract:
  The progression of time can be understood by assuming that the Hubble
expansion takes place in 4 dimensions rather than in 3. The flow of time
consists of the continuous creation of new moments, new nows, that accompany
the creation of new space. This model suggests a modification to the metric
tensor of the vacuum that leads to testable consequences. Two cosmological
tests are proposed, but they present both experimental and theoretical
problems. A more practical and immediate test is based on a predicted lag in
the emergence of gravitational radiation when two black holes merge. In such
mergers (as recently observed by the LIGO team), a macroscopic volume (millions
of cubic kilometers) of space is created in the region in which the
gravitational wave is generated; this one-time creation of new space should be
accompanied by the creation of detectable level of new time, resulting in a
time delay that could be observed as a growing lag in the emission of the wave
as the merger takes place


title: Totally acyclic approximations

abstract:
  Let $R$ be a commutative local ring. We study the subcategory of the homotopy
category of $R$-complexes consisting of the totally acyclic $R$-complexes. In
particular, in the context where $Q\to R$ is a surjective local ring
homomorphism such that $R$ has finite projective dimension over $Q$, we define
an adjoint pair of functors between the homotopy category of totally acyclic
$R$-complexes and that of $Q$-complexes, which are analogous to the classical
adjoint pair between the module categories of $R$ and $Q$. We give detailed
proofs of the adjunction in terms of the unit and counit. As a consequence, one
obtains a precise notion of approximations of totally acyclic $R$-complexes by
totally acyclic $Q$-complexes.


title: Subspace Condition for Bernstein's Lethargy Theorem

abstract:
  In this paper, we consider a condition on subspaces in order to improve
bounds given in the Bernstein's Lethargy Theorem (BLT) for Banach spaces. Let
$d_1 \geq d_2 \geq \dots d_n \geq \dots > 0$ be an infinite sequence of numbers
converging to $0$, and let $Y_1 \subset Y_2 \subset \dots\subset Y_n \subset
\dots \subset X$ be a sequence of closed nested subspaces in a Banach space $X$
with the property that $\overline{Y}_{n}\subset Y_{n+1}$ for all $n\ge1$. We
prove that for any $c \in (0,1]$, there exists an element $x_c \in X$ such that
$$ c d_n \leq \rho(x_c, Y_n) \leq \min (4, \tilde{a}) c\, d_n. $$ Here,
$\rho(x, Y_n)= \inf \{ ||x-y||: \,\,y\in Y_n\}$, $$\tilde{a}
=\sup_{i\ge1}\sup_{\left \{ q_{i} \right \}}\left \{ a_{n_{i+1}-1}^{-3}\right
\}$$ where the sequence $\{a_n\}$ is defined as: for all $ n \geq 1 $, $$ a_n =
\inf_{l \geq n} \, \inf_{q \in \langle q_l, q_{l+1},\dots \rangle}
\frac{\rho(q,Y_l)}{||q||} $$ in which each point $q_n$ is taken from $Y_{n+1}
\setminus Y_{n}$, and satisfies $\inf\limits_{n\ge1} a_n > 0$. The sequence
$\{n_i\}_{i\ge1}$ is given by %Theorem \ref{100}, $\{n_i\}$ satisfying
(\ref{ni}) and $n_{i}\leq n<n_{i+1}$. $$ n_1=1;~n_{i+1}= \min \left \{ n\ge1 :
\frac{d_n}{{a_{n}^{2}}} \leq d_{n_{i}}\right \},~i\geq 1. $$


title: String networks with junctions in competition models

abstract:
  In this work we give specific examples of competition models, with six and
eight species, whose three-dimensional dynamics naturally leads to the
formation of string networks with junctions, associated with regions that have
a high concentration of enemy species. We study the two- and three-dimensional
evolution of such networks, both using stochastic network and mean field theory
simulations. If the predation, reproduction and mobility probabilities do not
vary in space and time, we find that the networks attain scaling regimes with a
characteristic length roughly proportional to $t^{1/2}$, where $t$ is the
physical time, thus showing that the presence of junctions, on its own, does
not have a significant impact on their scaling properties.


title:
All those Ramsey classes (Ramsey classes with closures and forbidden
  homomorphisms)

abstract:
  We prove the Ramsey property for classes of ordered structures with closures
and given local properties. This generalises earlier results: the
Ne\v{s}et\v{r}il-R\"odl Theorem, the Ramsey property of partial orders and
metric spaces as well as the authors' Ramsey lift of bowtie-free graphs. We use
this framework to solve several open problems and give new examples of Ramsey
classes. Among others, we find Ramsey lifts of convexly ordered $S$-metric
spaces and prove the Ramsey theorem for finite models (i.e. structures with
both functions and relations) thus providing the ultimate generalisation of the
structural Ramsey theorem. Both of these results are natural, and easy to
state, yet their proofs involve most of the theory developed here.
  We also characterise Ramsey lifts of classes of structures defined by
finitely many forbidden homomorphisms and extend this to special cases of
classes with closures. This has numerous applications. For example, we find
Ramsey lifts of many Cherlin-Shelah-Shi classes.


title: Is a UCM fluid flow near a stationary point always singular? - Part II

abstract:
  Oftentimes observed divergence of numerical solutions to benchmark flows of
the UCM viscoelastic fluid is a known and widely discussed issue. Some authors
consider such singularities 'invincible'. Following the previous research, the
article gives more arguments against this position, for which it considers two
typical flows with a stagnation point, often a place of the flows' singularity.
For the flow spread over a wall, as previously for the counterflows, numerical
and asymptotic analytical solutions are presented. Both kinds of flows turn out
regular in the stagnation points, in particular, for high Weissenberg numbers.
A good accordance is demonstrated between the analytical and numerical results.


title:
Gear fault diagnosis based on Gaussian correlation of vibrations signals
  and wavelet coefficients

abstract:
  The features of non-stationary multi-component signals are often difficult to
be extracted for expert systems. In this paper, a new method for feature
extraction that is based on maximization of local Gaussian correlation function
of wavelet coefficients and signal is presented. The effect of empirical mode
decomposition (EMD) to decompose multi-component signals to intrinsic mode
functions (IMFs), before using of local Gaussian correlation is discussed. The
experimental vibration signals from two gearbox systems are used to show the
efficiency of the presented method. Linear support vector machine (SVM) is
utilized to classify feature sets extracted with the presented method. The
obtained results show that the features extracted in this method have excellent
ability to classify faults without any additional feature selection; it is also
shown that EMD can improve or degrade features according to the utilized
feature reduction method.


title:
A new framework for magnetohydrodynamic simulations with anisotropic
  pressure

abstract:
  We describe a new theoretical and numerical framework of the
magnetohydrodynamic simulation incorporated with an anisotropic pressure
tensor, which can play an important role in a collisionless plasma. A classical
approach to handle the anisotropy is based on the double adiabatic
approximation assuming that a pressure tensor is well described only by the
components parallel and perpendicular to the local magnetic field. This
gyrotropic assumption, however, fails around a magnetically neutral region,
where the cyclotron period may get comparable to or even longer than a
dynamical time in a system, and causes a singularity in the mathematical
expression. In this paper, we demonstrate that this singularity can be
completely removed away by the combination of direct use of the 2nd-moment of
the Vlasov equation and an ingenious gyrotropization model. Numerical tests
also verify that the present model properly reduces to the standard MHD or the
double adiabatic formulation in an asymptotic manner under an appropriate
limit.


title:
Spin Filtering through Single-Wall Carbon Nanotubes Functionalized with
  Single-Stranded DNA

abstract:
  High spin polarization materials or spin filters are key components in
spintronics, a niche subfield of electronics where carrier spins play a
functional role. Carrier transmission through these materials is "spin
selective" i.e. these materials are able to discriminate between "up" and
"down" spins. Common spin filters include transition metal ferromagnets and
their alloys, with typical spin selectivity (or, polarization) ~50% or less.
Here we consider carrier transport in an archetypical one-dimensional molecular
hybrid in which a single wall carbon nanotube (SWCNT) is wrapped around by
single stranded deoxyribonucleic acid (ssDNA). By magnetoresistance
measurements we show that this system can act as a spin filter with maximum
spin polarization approaching ~74% at low temperatures, significantly larger
than transition metals under comparable conditions. Inversion asymmetric
helicoidal potential of the charged ssDNA backbone induces a Rashba spin-orbit
interaction in the SWCNT channel and polarizes carrier spins. Our results are
consistent with recent theoretical work that predicted spin dependent
conductance in ssDNA-SWCNT hybrid. Ability to generate highly spin polarized
carriers using molecular functionalization can lead to magnet-less and
contact-less spintronic devices in the future. This can eliminate the
conductivity mismatch problem and open new directions for research in organic
spintronics.


title: Approximate Marginal Posterior for Log Gaussian Cox Processes

abstract:
  The log Gaussian Cox process is a flexible class of Cox processes, whose
intensity surface is stochastic, for incorporating complex spatial and time
structure of point patterns. The straightforward inference based on Markov
chain Monte Carlo is computationally heavy because the computational cost of
inverse or Cholesky decomposition of high dimensional covariance matrices of
Gaussian latent variables is cubic order of their dimension. Furthermore, since
hyperparameters for Gaussian latent variables have high correlations with
sampled Gaussian latent processes themselves, standard Markov chain Monte Carlo
strategies are inefficient. In this paper, we propose an efficient and scalable
computational strategy for spatial log Gaussian Cox processes. The proposed
algorithm is based on pseudo-marginal Markov chain Monte Carlo approach. Based
on this approach, we propose estimation of approximate marginal posterior for
parameters and comprehensive model validation strategies. We provide details
for all of the above along with some simulation investigation for univariate
and multivariate settings and analysis of a point pattern of tree data
exhibiting positive and negative interaction between different species.


title:
Manipulation of the large Rashba spin splitting in polar two-dimensional
  transition metal dichalcogenides

abstract:
  Transition metal dichalcogenide (TMD) monolayers MXY (M=Mo, W, X(not equal
to)Y=S, Se, Te) are two-dimensional polar semiconductors. Setting WSeTe
monolayer as an example and using density functional theory calculations, we
investigate the manipulation of Rashba spin orbit coupling (SOC) in the MXY
monolayer. It is found that the intrinsic out-of-plane electric field due to
the mirror symmetry breaking induces the large Rashba spin splitting around the
Gamma point, which, however, can be easily tuned by applying the in-plane
biaxial strain. Through a relatively small strain (from -2% to 2%), a large
tunability (from around -50% to 50%) of Rashba SOC can be obtained due to the
modified orbital overlap, which can in turn modulate the intrinsic electric
field. The orbital selective external potential method further confirms the
significance of the orbital overlap between W-dz2 and Se-pz in Rashba SOC. In
addition, we also explore the influence of the external electric field on
Rashba SOC in the WSeTe monolayer, which is less effective than strain. The
large Rashba spin splitting, together with the valley spin splitting in MXY
monolayers may make a special contribution to semiconductor spintronics and
valleytronics.


title: Flexible discrete space models of animal movement

abstract:
  Movement drives the spread of infectious disease, gene flow, and other
critical ecological processes. To study these processes we need models for
movement that capture complex behavior that changes over time and space in
response to biotic and abiotic factors. Penalized likelihood approaches, such
as penalized semiparametric spline expansions and LASSO regression, allow
inference on complex models without overfitting. Continuous-time Markov chains
(CTMCs) have been recently introduced as a flexible discrete-space model for
animal movement. Modeling with CTMCs involves discretizing an animal's path to
the resolution of a raster grid. The resulting stochastic process model can
easily incorporate environmental and other covariates, represented as raster
layers, that affect directional bias and overall movement rate. We introduce a
weighted likelihood approach that allows for modeling movement using CTMCs,
with path uncertainty due to missing data modeled by imputing continuous-time
paths between telemetry locations. The framework we introduce allows for
inference on CTMC movement models using existing software for fitting Poisson
regression models, including penalized versions of Poisson regression. The
result is a flexible, powerful, and accessible framework for modeling a wide
range of animal movement behavior.


title:
A Physics Informed Machine Learning Approach for Reconstructing Reynolds
  Stress Modeling Discrepancies Based on DNS Data

abstract:
  Turbulence modeling is a critical component in numerical simulations of
industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations.
However, after decades of efforts in the turbulence modeling community,
universally applicable RANS models with predictive capabilities are still
lacking. Recently, data-driven methods have been proposed as a promising
alternative to the traditional approaches of turbulence model development. In
this work we propose a data-driven, physics-informed machine learning approach
for predicting discrepancies in RANS modeled Reynolds stresses. The
discrepancies are formulated as functions of the mean flow features. By using a
modern machine learning technique based on random forests, the discrepancy
functions are first trained with benchmark flow data and then used to predict
Reynolds stresses discrepancies in new flows. The method is used to predict the
Reynolds stresses in the flow over periodic hills by using two training flow
scenarios of increasing difficulties: (1) the flow in the same periodic hills
geometry yet at a lower Reynolds number, and (2) the flow in a different hill
geometry with a similar recirculation zone. Excellent predictive performances
were observed in both scenarios, demonstrating the merits of the proposed
method. Improvement of RANS modeled Reynolds stresses enabled by the proposed
method is an important step towards predictive turbulence modeling, where the
ultimate goal is to predict the quantities of interest (e.g., velocity field,
drag, lift) more accurately by solving RANS equations with the Reynolds
stresses obtained therefrom.


title:
Building the Web of Knowledge with Smart IoT Applications (Extended
  Version)

abstract:
  The Internet of Things (IoT) is experiencing fast adoption in the society,
from industrial to home applications. The number of deployed sensors and
connected devices to the Internet is changing our perspective and the way we
understand the world. The development and generation of IoT applications is
just starting and they will modify our physical and virtual lives, from how we
control remotely appliances at home to how we deal with insurance companies in
order to start insurance schemes via smart cards. This massive deployment of
IoT devices represents a tremendous economic impact and at the same time offers
multiple opportunities. However, the potential of IoT is underexploited and day
by day this gap between devices and useful applications is getting bigger.
Additionally, the physical and cyber worlds are largely disconnected, requiring
a lot of manual efforts to integrate, find, and use information in a meaningful
way.
  To build a connection between the physical and the virtual, we need a
knowledge framework that allow bilateral understandings, devices producing
data, information systems managing the data and applications transforming
information into meaningful knowledge. The first column in this series in the
previous issue of this magazine titled "Internet of Things to Smart IoT Through
Semantic, Cognitive, and Perceptual Computing," reviews IoT growth and
potential that have energized research and technology development, centered on
aspects of Artificial Intelligence to build future intelligent system. This
column steps back and demonstrates the benefits of using semantic web
technologies to get meaningful knowledge from sensor data to design smart
systems.


title: Twist-induced Magnetosphere Reconfiguration for Intermittent Pulsars

abstract:
  We propose that the magnetosphere reconfiguration induced by magnetic twists
in the closed field line region can account for the mode-switching of
intermittent pulsars. We carefully investigate the properties of axisymmetric
force-free pulsar magnetospheres with magnetic twists in closed field line
region around the polar caps. The magnetosphere with twisted closed lines leads
to enhanced spin-down rates. The enhancement in spin-down rate depends on the
size of region with twisted closed lines. Typically, it is increased by a
factor of $\sim2$, which is consistent with the intermittent pulsars' spin down
behavior during the `off' and `on' states. We find there is a threshold of
maximal twist angle $\Delta\phi_{\rm thres}\sim1$. The magnetosphere is stable
only if the closed line twist angle is less than $\Delta\phi_{\rm thres}$.
Beyond this value, the magnetosphere becomes unstable and gets untwisted. The
spin-down rate would reduce to its off-state value. The quasi-periodicity in
spin-down rate change can be explained by long-term activities in star's crust
and the untwisting induced by MHD instability. The estimated duration time of
on-state is about one week, consistent with observations. Due to the MHD
instability, there exists an upper limit for the spin down ratio ($f\sim3$)
between the on-state and the off-state, if the Y-point remains at the light
cylinder.


title:
Tailoring optical metamaterials to tune the atom-surface Casimir-Polder
  interaction

abstract:
  Metamaterials are fascinating tools that can structure not only surface
plasmons and electromagnetic waves but also electromagnetic vacuum
fluctuations. The possibility of shaping the quantum vacuum is a powerful
concept that ultimately allows engineering the interaction between macroscopic
surfaces and quantum emitters such as atoms, molecules or quantum dots. The
long-range atom-surface interaction, known as Casimir-Polder interaction, is of
fundamental importance in quantum electrodynamics but also attracts a
significant interest for platforms that interface atoms with nanophotonic
devices. Here we perform a spectroscopic selective reflection measurement of
the Casimir-Polder interaction between a Cs(6P_{3/2}) atom and a nanostructured
metallic planar metamaterial. We show that by engineering the near-field
plasmonic resonances of the metamaterial, we can successfully tune the
Casimir-Polder interaction, demonstrating both a strong enhancement and
reduction with respect to its non-resonant value. We also show an enhancement
of the atomic spontaneous emission rate due to its coupling with the evanescent
modes of the nanostructure. Probing excited state atoms next to nontrivial
tailored surfaces is a rigorous test of quantum electrodynamics. Engineering
Casimir-Polder interactions represents a significant step towards atom trapping
in the extreme near field, possibly without the use of external fields.


title: Self-Contained Cross-Cutting Pipeline Software Architecture

abstract:
  Layered software architecture contains several intra-layer and inter-layer
dependencies. Each layer depends on shared components making it difficult to
release a code change, bug fix or feature without exhaustive testing and having
to build the entire software code base. This paper proposed self-contained,
cross-cutting pipeline architecture (SCPA) that is independent of existing
layers. We chose 2 open source projects and 3 internal intern projects that
used n-tier architecture and applied the SCPA to release subsequent feature
additions and any bug fixes. The SCPA decreased the release time by 42.99%. The
lines of delivered code (LOC), increased by 22.58%. The number of defects found
in existing functionality decreased by 85.54%. The SCPA also provided ability
to roll back or switch off the new feature quickly. SCPA proved a suitable
architecture for agile software development and continuous deployment.


title:
Faster Coreset Construction for Projective Clustering via Low-Rank
  Approximation

abstract:
  In this work, we present a randomized coreset construction for projective
clustering, which involves computing a set of $k$ closest $j$-dimensional
linear (affine) subspaces of a given set of $n$ vectors in $d$ dimensions. Let
$A \in \mathbb{R}^{n\times d}$ be an input matrix. An earlier deterministic
coreset construction of Feldman \textit{et. al.} relied on computing the SVD of
$A$. The best known algorithms for SVD require $\min\{nd^2, n^2d\}$ time, which
may not be feasible for large values of $n$ and $d$. We present a coreset
construction by projecting the rows of matrix $A$ on some orthonormal vectors
that closely approximate the right singular vectors of $A$. As a consequence,
when the values of $k$ and $j$ are small, we are able to achieve a faster
algorithm, as compared to the algorithm of Feldman \textit{et. al.}, while
maintaining almost the same approximation. We also benefit in terms of space as
well as exploit the sparsity of the input dataset. Another advantage of our
approach is that it can be constructed in a streaming setting quite
efficiently.


title:
Learning for Biomedical Information Extraction: Methodological Review of
  Recent Advances

abstract:
  Biomedical information extraction (BioIE) is important to many applications,
including clinical decision support, integrative biology, and
pharmacovigilance, and therefore it has been an active research. Unlike
existing reviews covering a holistic view on BioIE, this review focuses on
mainly recent advances in learning based approaches, by systematically
summarizing them into different aspects of methodological development. In
addition, we dive into open information extraction and deep learning, two
emerging and influential techniques and envision next generation of BioIE.


title: Isotropic submanifolds and coadjoint orbits of the Hamiltonian group

abstract:
  We describe a class of coadjoint orbits of the group of Hamiltonian
diffeomorphisms of a symplectic manifold $(M,\omega)$ by implementing
symplectic reduction for the dual pair associated to the Hamiltonian
description of ideal fluids. The description is given in terms of nonlinear
Grassmannians (manifolds of submanifolds) with additional geometric structures.
Reduction at zero momentum yields the identification of coadjoint orbits with
Grassmannians of isotropic volume submanifolds, slightly generalizing the
results in Weinstein [1990] and Lee [2009]. At the other extreme, the case of a
nondegenerate momentum recovers the identification of connected components of
the nonlinear symplectic Grassmannian with coadjoint orbits, thereby recovering
the result of Haller and Vizman [2004]. We also comment on the intermediate
cases which correspond to new classes of coadjoint orbits. The description of
these coadjoint orbits as well as their orbit symplectic form is obtained in a
systematic way by exploiting the general properties of dual pairs of momentum
maps. We also show that whenever the symplectic manifold $(M,\omega)$ is
prequantizable, the coadjoint orbits that consist of isotropic submanifolds
with total volume $a\in\mathbb{Z}$ are prequantizable. The prequantum bundle is
constructed explicitly and, in the Lagrangian case, recovers the Berry bundle
constructed in Weinstein [1990].


title:
Efficient data augmentation for fitting stochastic epidemic models to
  prevalence data

abstract:
  Stochastic epidemic models describe the dynamics of an epidemic as a disease
spreads through a population. Typically, only a fraction of cases are observed
at a set of discrete times. The absence of complete information about the time
evolution of an epidemic gives rise to a complicated latent variable problem in
which the state space size of the epidemic grows large as the population size
increases. This makes analytically integrating over the missing data infeasible
for populations of even moderate size. We present a data augmentation Markov
chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic
epidemic model parameters, in which measurements are augmented with
subject-level disease histories. In our MCMC algorithm, we propose each new
subject-level path, conditional on the data, using a time-inhomogeneous
continuous-time Markov process with rates determined by the infection histories
of other individuals. The method is general, and may be applied, with minimal
modifications, to a broad class of stochastic epidemic models. We present our
algorithm in the context of multiple stochastic epidemic models in which the
data are binomially sampled prevalence counts, and apply our method to data
from an outbreak of influenza in a British boarding school.


title:
Tailoring Kinetics on a Topological Insulator Surface by Defect-Induced
  Strain: Pb Mobility on Bi2Te3

abstract:
  Heteroepitaxial structures based on Bi$_{2}$Te$_{3}$-type topological
insulators (TIs) exhibit exotic quantum phenomena. For optimal characterization
of these phenomena, it is desirable to control the interface structure during
film growth on such TIs. In this process, adatom mobility is a key factor. We
demonstrate that Pb mobility on the Bi$_{2}$Te$_{3}$(111) surface can be
modified by the engineering local strain, {\epsilon}, which is induced around
the point-like defects intrinsically forming in the Bi$_{2}$Te$_{3}$(111) thin
film grown on a Si(111)-7 $\times$ 7 substrate. Scanning tunneling microscopy
observations of Pb adatom and cluster distributions and first-principles
density functional theory (DFT) analyses of the adsorption energy and diffusion
barrier E$_{d}$ of Pb adatom on Bi$_{2}$Te$_{3}$(111) surface show a
significant influence of {\epsilon}. Surprisingly, E$_d$ reveals a cusp-like
dependence on {\epsilon} due to a bifurcation in the position of the stable
adsorption site at the critical tensile strain {\epsilon}$_{c}$ $ \approx $
0.8%. This constitutes a very different strain-dependence of diffusivity from
all previous studies focusing on conventional metal or semiconductor surfaces.
Kinetic Monte Carlo simulations of Pb deposition, diffusion, and irreversible
aggregation incorporating the DFT results reveal adatom and cluster
distributions compatible with our experimental observations.


title: Properties of Strongly Balanced Tilings by Convex Polygons

abstract:
  Every normal periodic tiling is a strongly balanced tiling. The properties of
periodic tilings by convex polygons are rearranged from the knowledge of
strongly balanced tilings. From the results, we show the properties of
representative periodic tilings by a convex pentagonal tile.


title: Cohn-Leavitt Path Algebras and the Invariant Basis Number Property

abstract:
  We give the necessary and sufficient condition for a separated Cohn-Leavitt
path algebra of a finite digraph to have IBN. As a consequence, separated Cohn
path algebras have IBN. We determine the non-stable K-theory of a corner ring
in terms of the non-stable K-theory of the ambient ring. We give a necessary
condition for a corner algebra of a separated Cohn-Leavitt path algebra of a
finite graph to have IBN. We provide Morita equivalent rings which are non-IBN,
but are of different types.


title:
Real-space characterization of reactivity towards water at Bi2Te3(111)
  surface

abstract:
  Surface reactivity is important in modifying the physical and chemical
properties of surface sensitive materials, such as the topological insulators
(TIs). Even though many studies addressing the reactivity of TIs towards
external gases have been reported, it is still under heavy debate whether and
how the topological insulators react with H$_2$O. Here, we employ scanning
tunneling microscopy (STM) to directly probe the surface reaction of
Bi$_2$Te$_3$ towards H$_2$O. Surprisingly, it is found that only the top
quintuple layer is reactive to H$_2$O, resulting in a hydrated Bi bilayer as
well as some Bi islands, which passivate the surface and prevent from the
subsequent reaction. A reaction mechanism is proposed with H$_2$Te and hydrated
Bi as the products. Unexpectedly, our study indicates the reaction with water
is intrinsic and not dependent on any surface defects. Since water inevitably
exists, these findings provide key information when considering the reactions
of Bi$_2$Te$_3$ with residual gases or atmosphere.


title: (CaO)(FeSe): A Layered Wide Gap Oxychalcogenide Semiconductor

abstract:
  A new iron-oxychalcogenide (CaO)(FeSe) was obtained which crystallizes in the
orthorhombic space group Pnma (No. 62) with a = 5.9180(12) {\AA}, b = 3.8802(8)
{\AA}, c = 13.193(3) {\AA}. The unique structure of (CaO)(FeSe) is built up of
a quasi-two-dimensional network of corrugated infinite layers of corner-shared
FeSe2O2 tetrahedra that extend in the ab-plane. The corrugated layers composed
of corner-shared FeSe2O2 tetrahedra stack along the c-axis with Ca2+ cations
sandwiched between the layers. Optical spectroscopy and resistivity
measurements reveal semiconducting behavior with an indirect optical band gap
of around 1.8 eV and an activation energy of 0.19(1) eV. Electronic band
structure calculations at the density function level predict a magnetic
configuration as ground state and confirm the presence of an indirect wide gap
in (CaO)(FeSe).


title: Enumeration of graphs with given weighted number of connected components

abstract:
  We give a generating function for the number of graphs with given numerical
properties and prescribed weighted number of connected components. As an
application, we give a generating function for the number of bipartite graphs
of given order, size and number of connected components.


title: La1-xBi1+xS3 (x~0.08): An n-Type Semiconductor

abstract:
  The new bismuth chalcogenide La0.92Bi1.08S3 crystallizes in the monoclinic
space group C2/m with a = 28.0447(19) {\AA}, b = 4.0722(2) {\AA}, c =
14.7350(9) {\AA}, and $\beta$ = 118.493(5){\deg}. The structure of
La0.92Bi1.08S3 is built up of NaCl-type Bi2S5 blocks, and BiS4 and LaS5
infinitely long chains forming a compact three-dimensional framework with
parallel tunnels. Optical spectroscopy and resistivity measurements reveal a
semiconducting behavior with a band gap of ~ 1 eV and activation energy for
transport of 0.36(1) eV. Thermopower measurements suggest the majority carriers
of La0.92Bi1.08S3 are electrons. Heat capacity measurements indicate no phase
transitions from 2 to 300 K. Band structure calculations at the density
functional theory level confirm the semiconducting nature and the indirect gap
of La0.92Bi1.08S3.


title: Functional Distributional Semantics

abstract:
  Vector space models have become popular in distributional semantics, despite
the challenges they face in capturing various semantic phenomena. We propose a
novel probabilistic framework which draws on both formal semantics and recent
advances in machine learning. In particular, we separate predicates from the
entities they refer to, allowing us to perform Bayesian inference based on
logical forms. We describe an implementation of this framework using a
combination of Restricted Boltzmann Machines and feedforward neural networks.
Finally, we demonstrate the feasibility of this approach by training it on a
parsed corpus and evaluating it on established similarity datasets.


title:
Energy Quantization of Willmore surfaces at the boundary of the Moduli
  Space

abstract:
  We establish an energy quantization result for sequences of Willmore surfaces
when the underlying sequence of Riemann surfaces is degenerating in the moduli
space. we notably exhibit a new residue which quantifies the potential loss of
energy in collar regions. Thanks to these residues, we also prove compactness
of Willmore immersion with bounded conformal class and energy below $12\pi$.


title: Linear Stability of the Non-Extreme Kerr Black Hole

abstract:
  It is proven that for smooth initial data with compact support outside the
event horizon, the solution of every azimuthal mode of the Teukolsky equation
for general spin decays pointwise in time.


title:
Resonant inelastic scattering spectra at the Ir $L$-edge in
  Na$_2$IrO$_3$

abstract:
  We analyze resonant x-ray scattering (RIXS) spectra in Na$_2$IrO$_3$ on the
basis of the itinerant electron picture. Employing a multi-orbital
tight-binding model on a honeycomb lattice, we find that the zigzag magnetic
order is the most stable with sizable energy gap in the one-electron band
within the Hartree-Fock approximation. We derive the RIXS spectra, which are
connected to the generalized density-density correlation function. We calculate
the spectra as a function of excitation energy $\omega$, within the random
phase approximation. The spectra consist of the peaks with $\omega$ $<20$ meV,
and of the peaks with $0.4<\omega<0.8$ eV. The former peaks are composed of
four bound states in the density-density correlation function, and may be
identified as the magnetic excitations, while the latter peaks are composed of
sixteen bound states below the energy continuum of individual electron-hole
pair excitations, and may be identified as the excitonic excitations. The
calculated spectra agree qualitatively with the recent RIXS experiment.


title:
Gate-controlled conductance enhancement from quantum Hall channels along
  graphene p-n junctions

abstract:
  The formation of quantum Hall channels inside the bulk of graphene is studied
using various contact and gate geometries. p-n junctions are created along the
longitudinal direction of samples, and enhanced conductance is observed in the
case of bipolar doping due to new conducting channels forming in the bulk,
whose position, propagating direction and, in one geometry, coupling to
electrodes are determined by the gate-controlled filling factor across the
device. This effect could be exploited to probe the behavior and interaction of
quantum Hall channels protected against uncontrolled scattering at the edges.


title: Interactive Image Segmentation From A Feedback Control Perspective

abstract:
  Image segmentation is a fundamental problem in computational vision and
medical imaging. Designing a generic, automated method that works for various
objects and imaging modalities is a formidable task. Instead of proposing a new
specific segmentation algorithm, we present a general design principle on how
to integrate user interactions from the perspective of feedback control theory.
Impulsive control and Lyapunov stability analysis are employed to design and
analyze an interactive segmentation system. Then stabilization conditions are
derived to guide algorithm design. Finally, the effectiveness and robustness of
proposed method are demonstrated.


title: Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

abstract:
  In this paper, we investigate the recovery of a sparse weight vector
(parameters vector) from a set of noisy linear combinations. However, only
partial information about the matrix representing the linear combinations is
available. Assuming a low-rank structure for the matrix, one natural solution
would be to first apply a matrix completion on the data, and then to solve the
resulting compressed sensing problem. In big data applications such as massive
MIMO and medical data, the matrix completion step imposes a huge computational
burden. Here, we propose to reduce the computational cost of the completion
task by ignoring the columns corresponding to zero elements in the sparse
vector. To this end, we employ a technique to initially approximate the support
of the sparse vector. We further propose to unify the partial matrix completion
and sparse vector recovery into an augmented four-step problem. Simulation
results reveal that the augmented approach achieves the best performance, while
both proposed methods outperform the natural two-step technique with
substantially less computational requirements.


title: Quantum-Logic Synthesis of Hermitian Gates

abstract:
  In this paper, the problem of synthesizing a general Hermitian quantum gate
into a set of primary quantum gates is addressed. To this end, an extended
version of the Jacobi approach for calculating the eigenvalues of Hermitian
matrices in linear algebra is considered as the basis of the proposed synthesis
method. The quantum circuit synthesis method derived from the Jacobi approach
and its optimization challenges are described. It is shown that the proposed
method results in multiple-control rotation gates around the y axis,
multiple-control phase shift gates, multiple-control NOT gates and a middle
diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z
gates. Using the proposed approach, it is shown how multiple-control U gates,
where U is a single-qubit Hermitian quantum gate, can be implemented using a
linear number of elementary gates in terms of circuit lines with the aid of one
auxiliary qubit in an arbitrary state.


title: Motion by curvature of networks with two triple junctions

abstract:
  We consider the evolution by curvature of a general embedded network with two
triple junctions. We classify the possible singularities and we discuss the
long time existence of the evolution.


title: Yang-Mills correlators across the deconfinement phase transition

abstract:
  We compute the finite temperature ghost and gluon propagators of Yang-Mills
theory in the Landau-DeWitt gauge. The background field that enters the
definition of the latter is intimately related with the (gauge-invariant)
Polyakov loop and serves as an equivalent order parameter for the deconfinement
transition. We use an effective gauge-fixed description where the
nonperturbative infrared dynamics of the theory is parametrized by a gluon mass
which, as argued elsewhere, may originate from the Gribov ambiguity. In this
scheme, one can perform consistent perturbative calculations down to infrared
momenta, which have been shown to correctly describe the phase diagram of
Yang-Mills theories in four dimensions as well as the zero-temperature
correlators computed in lattice simulations. In this article, we provide the
one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon
propagators for a large class of gauge groups and present explicit results for
the SU(2) case. These are substantially different from those previously
obtained in the Landau gauge, which corresponds to a vanishing background
field. The nonanalyticity of the order parameter across the transition is
directly imprinted onto the propagators in the various color modes. In the
SU(2) case, this leads, for instance, to a cusp in the electric and magnetic
gluon susceptibilities as well as similar signatures in the ghost sector. We
mention the possibility that such distinctive features of the transition could
be measured in lattice simulations in the background field gauge studied here.


title: Model for Topological Phononics and Phonon Diode

abstract:
  The quantum anomalous Hall effect, an exotic topological state first
theoretically predicted by Haldane and recently experimentally observed, has
attracted enormous interest for low-power-consumption electronics. In this
work, we derived a Schr{\"o}dinger-like equation of phonons, where
topology-related quantities, time reversal symmetry and its breaking can be
naturally introduced similar as for electrons. Furthermore, we proposed a
phononic analog of the Haldane model, which gives the novel quantum (anomalous)
Hall-like phonon states characterized by one-way gapless edge modes immune to
scattering. The topologically nontrivial phonon states are useful not only for
conducting phonons without dissipation but also for designing highly efficient
phononic devices, like an ideal phonon diode, which could find important
applications in future phononics.


title: Some lower bounds in parameterized ${\rm AC}^0$

abstract:
  We demonstrate some lower bounds for parameterized problems via parameterized
classes corresponding to the classical ${\rm AC}^0$. Among others, we derive
such a lower bound for all fpt-approximations of the parameterized clique
problem and for a parameterized halting problem, which recently turned out to
link problems of computational complexity, descriptive complexity, and proof
theory. To show the first lower bound, we prove a strong ${\rm AC}^0$ version
of the planted clique conjecture: ${\rm AC}^0$-circuits asymptotically almost
surely can not distinguish between a random graph and this graph with a
randomly planted clique of any size $\le n^\xi$ (where $0 \le \xi < 1$).


title: A non-vanishing result for the CMC flux

abstract:
  We prove the non-vanishing of the CMC flux of the boundaries of certain
Riemannian manifolds with constant mean curvature.


title:
Asymptotic enumeration by Khintchine-Meinardus method: Necessary and
  sufficient conditions for sub exponential growth

abstract:
  In this paper we prove the necessity of the main sufficient condition of
Meinardus for sub exponential rate of growth of the number of structures,
having multiplicative generating functions of a general form and establish a
new necessary and suffcient condition for normal local limit theorem for
aforementioned structures. The latter result allows to encompass in our study
structures with weights having gaps in their supports.


title: Projective linear groups as automorphism groups of chiral polytopes

abstract:
  It is already known that the automorphism group of a chiral polyhedron is
never isomorphic to $PSL(2,q)$ or $PGL(2,q)$ for any prime power $q$. In this
paper, we show that $PSL(2,q)$ and $PGL(2,q)$ are never automorphism groups of
chiral polytopes of rank at least $5$. Moreover, we show that $PGL(2,q)$ is the
automorphism group of at least one chiral polytope of rank $4$ for every
$q\geq5$. Finally, we determine for which values of $q$ the group $PSL(2,q)$ is
the automorphism group of a chiral polytope of rank $4$, except when
$q=p^d\equiv3\pmod{4}$ where $d>1$ is not a prime power, in which case the
problem remains unsolved.


title:
On symmetries of generalized Robertson-Walker Space-times and
  applications

abstract:
  The purpose of the present article is to study and characterize sev- eral
types of symmetries of generalized Robertson-Walker space-times. Con- formal
vector fields, curvature and Ricci collineations are studied. Many im-
plications for existence of these symmetries on generalied Robertson-Walker
spacetimes are obtained. Finally, Ricci solitons on generalized Robertson-
Walker space-times admitting conformal vector fields are investigated.


title:
Phase sensitive parametric interactions in a $Ga_{0.5}In_{0.5}P$
  photonic crystal waveguide

abstract:
  We report phase sensitive amplification in a 1.5mm long, $Ga_{0.5}In_{0.5}P$
dispersion engineered photonic crystal waveguide which has a flattened
dispersion profile. A signal degenerate configuration with pulsed pumps whose
total peak power is only 0.5W yields a phase sensitive extinction ratio of
10dB.


title:
Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and
  qq-character for 5d Super Yang-Mills

abstract:
  The instanton partition functions of $\mathcal{N}=1$ 5d super Yang-Mills are
built using elements of the representation theory of quantum
$\mathcal{W}_{1+\infty}$ algebra: Gaiotto state, intertwiner, vertex operator.
This algebra is also known under the names of Ding-Iohara-Miki and quantum
toroidal $\widehat{\mathfrak{gl}}(1)$ algebra. Exploiting the explicit action
of the algebra on the partition function, we prove the regularity of the 5d
qq-characters. These characters provide a solution to the Schwinger-Dyson
equations, and they can also be interpreted as a quantum version of the
Seiberg-Witten curve.

categories: hep-th math-ph math.AG math.MP math.QA math.RT


title: The Liouville function in short intervals [after Matomaki and Radziwill]

abstract:
  This is a copy of my Bourbaki Seminar on the work of Matomaki and Radziwill
showing that the Liouville function exhibits cancelation in almost all short
intervals as soon as the length of the interval tends to infinity.


title:
Constant factor Approximation Algorithms for Uniform Hard Capacitated
  Facility Location Problems: Natural LP is not too bad

abstract:
  In this paper, we give first constant factor approximation for capacitated
knapsack median problem (CKM) for hard uniform capacities, violating the budget
only by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost of
a facility opened by the optimal and violating capacities by $(2+\epsilon)$
factor. Natural LP for the problem is known to have an unbounded integrality
gap when any one of the two constraints is allowed to be violated by a factor
less than $2$. Thus, we present a result which is very close to the best
achievable from the natural LP. To the best of our knowledge, the problem has
not been studied earlier.
  For capacitated facility location problem with uniform capacities, a constant
factor approximation algorithm is presented violating the capacities a little
($1 + \epsilon$). Though constant factor results are known for the problem
without violating the capacities, the result is interesting as it is obtained
by rounding the solution to the natural LP, which is known to have an unbounded
integrality gap without violating the capacities. Thus, we achieve the best
possible from the natural LP for the problem. The result shows that natural LP
is not too bad.
  Finally, we raise some issues with the proofs of the results presented in
\cite{capkmByrkaFRS2013} for capacitated $k$-facility location problem
(C$k$FLP). \cite{capkmByrkaFRS2013} presents $O(1/\epsilon^2)$ approximation
violating the capacities by a factor of $(2 + \epsilon)$ using dependent
rounding. We first fix these issues using our techniques. Also, it can be
argued that (deterministic) pipage rounding cannot be used to open the
facilities instead of dependent rounding. Our techniques for CKM provide a
constant factor approximation for CkFLP violating the capacities by $(2 +
\epsilon)$.


title: Searching with Advice: Robot Fence-Jumping

abstract:
  We study a new search problem on the plane involving a robot and an immobile
treasure, initially placed at distance $1$ from each other. The length $\beta$
of an arc (a fence) within the perimeter of the corresponding circle, as well
as the promise that the treasure is outside the fence, is given as part of the
input. The goal is to device movement trajectories so that the robot locates
the treasure in minimum time. Notably, although the presence of the fence
limits searching uncertainty, the location of the fence is unknown, and in the
worst case analysis is determined adversarially. Nevertheless, the robot has
the ability to move in the interior of the circle. In particular the robot can
attempt a number of chord-jump moves if it happens to be within the fence or if
an endpoint of the fence is discovered.
  The optimal solution to our question can be obtained as a solution to a
complicated optimization problem, which involves trigonometric functions, and
trigonometric equations that do not admit closed form solutions. For the 1-Jump
Algorithm, we fully describe the optimal trajectory, and provide an analysis of
the associated cost as a function of $\beta$. Our analysis indicates that the
optimal k-Jump Algorithm requires that the robot has enough memory and
computation power to compute the optimal chord-jumps. Motivated by this, we
give an abstract performance analysis for every k-Jump Algorithm. Subsequently,
we present a highly efficient Halving Heuristic k-Jump Algorithm that can
effectively approximate the optimal k-Jump Algorithm, with very limited memory
and computation requirements.


title: Stochastic Domination in Space-Time for the Contact Process

abstract:
  Liggett and Steif (2006) proved that, for the supercritical contact process
on certain graphs, the upper invariant measure stochastically dominates an
i.i.d.\ Bernoulli product measure. In particular, they proved this for
$\mathbb{Z}^d$ and (for infection rate sufficiently large) $d$-ary homogeneous
trees $T_d$.
  In this paper we prove some space-time versions of their results. We do this
by combining their methods with specific properties of the contact process and
general correlation inequalities.
  One of our main results concerns the contact process on $T_d$ with $d\geq2$.
We show that, for large infection rate, there exists a subset $\Delta$ of the
vertices of $T_d$, containing a "positive fraction" of all the vertices of
$T_d$, such that the following holds: The contact process on $T_d$ observed on
$\Delta$ stochastically dominates an independent spin-flip process. (This is
known to be false for the contact process on graphs having subexponential
growth.)
  We further prove that the supercritical contact process on $\mathbb{Z}^d$
observed on certain $d$-dimensional space-time slabs stochastically dominates
an i.i.d.\ Bernoulli product measure, from which we conclude strong mixing
properties important in the study of certain random walks in random
environment.


title: Twin peaks

abstract:
  We study random labelings of graphs conditioned on a small number (typically
one or two) peaks, i.e., local maxima. We show that the boundaries of level
sets of a random labeling of a square with a single peak have dimension 2, in a
suitable asymptotic sense. The gradient line of a random labeling of a long
ladder graph conditioned on a single peak consists mostly of straight line
segments. We show that for some tree-graphs, if a random labeling is
conditioned on exactly two peaks then the peaks can be very close to each
other. We also study random labelings of regular trees conditioned on having
exactly two peaks. Our results suggest that the top peak is likely to be at the
root and the second peak is equally likely, more or less, to be any vertex not
adjacent to the root.


title: On Schatten-class perturbations of Toeplitz operators

abstract:
  We characterize the commutant of the analytic Toeplitz operators modulo
operators of Schatten-p-class on suitable multivariable domains. We show that a
result of J. Xia on compact perturbations of Toeplitz operators on the unit
disc remains true on strictly pseudoconvex and symmetric domains in C^n if the
ideal of compact operators is replaced by the Schatten-p-classes with p
strictly less than infinity.


title:
Star-planet interactions: II. Is planet engulfment the origin of fast
  rotating red giants?

abstract:
  Context. Fast rotating red giants in the upper part of the red giant branch
have surface velocities that cannot be explained by single star evolution.
  Aims. We check whether tides between a star and a planet followed by planet
engulfment can indeed accelerate the surface rotation of red giants for a
sufficient long time in order to produce these fast rotating red giants.
  Methods. Using rotating stellar models, accounting for the redistribution of
the angular momentum inside the star by different transport mechanisms, for the
exchanges of angular momentum between the planet orbit and the star before the
engulfment and for the deposition of angular momentum inside the star at the
engulfment, we study how the surface rotation velocity at the stellar surface
evolves.
  Results. We show that the surface velocities reached at the end of the
orbital decay due to tidal forces and planet engulfment can be similar to
values observed for fast rotating red giants. This surface velocity then
decreases when the star evolves along the red giant branch but at a
sufficiently slow pace for allowing stars to be detected with such a high
velocity. More quantitatively, star-planet interaction can produce a rapid
acceleration of the surface of the star, above values equal to 8 km s$^{-1}$,
for periods lasting up to more than 30% the red giant branch phase. The changes
of the surface carbon isotopic ratios produced by the dilution of the planetary
material into the convective envelope is quite modest. Much more important
might be the increase of the lithium abundance due to this effect. However
lithium may be affected by many different, still uncertain, processes.
  Conclusions. The acceleration of the stellar surface to rotation velocities
above limits that depend on the surface gravity does appear at the moment as
the clearest signature of a star-planet interaction.[abridged]


title: Squashed entanglement and approximate private states

abstract:
  The squashed entanglement is a fundamental entanglement measure in quantum
information theory, finding application as an upper bound on the distillable
secret key or distillable entanglement of a quantum state or a quantum channel.
This paper simplifies proofs that the squashed entanglement is an upper bound
on distillable key for finite-dimensional quantum systems and solidifies such
proofs for infinite-dimensional quantum systems. More specifically, this paper
establishes that the logarithm of the dimension of the key system (call it
$\log_{2}K$) in an $\varepsilon$-approximate private state is bounded from
above by the squashed entanglement of that state plus a term that depends only
$\varepsilon$ and $\log_{2}K$. Importantly, the extra term does not depend on
the dimension of the shield systems of the private state. The result holds for
the bipartite squashed entanglement, and an extension of this result is
established for two different flavors of the multipartite squashed
entanglement.


title: Variations on inversion theorems for Newton-Puiseux series

abstract:
  Let $f(x,y)$ be a complex irreducible formal power series without constant
term. One may solve the equation $f(x,y)=0$ by choosing either $x$ or $y$ as
independent variable, getting two finite sets of Newton-Puiseux series. In 1967
and 1968, Abhyankar and Zariski published proofs of an \emph{inversion
theorem}, expressing the \emph{characteristic exponents} of one set of series
in terms of those of the other ones. In fact, a more general theorem, stated by
Halphen in 1876 and proved by Stolz in 1879, relates also the
\emph{coefficients} of the characteristic terms of both sets of series. This
theorem seems to have been completely forgotten. We give two new proofs of it
and we generalize it to a theorem concerning equations with an arbitrary number
of variables.


title: Revisiting $B\to D \ell \nu$

abstract:
  We re-examine the determination of $|V_{cb}|$ from $B\to D \ell \nu$ in view
of recent experimental and theoretical progress, discussing the
parameterization of the form factors and studying the role played by the
unitarity constraints. Our fit to experimental and lattice results for $B\to D
\ell \nu$ gives $|V_{cb}|=40.49(97)\ 10^{-3}$ and to $R(D)= 0.299(3)$.


title: Bouncing black holes in quantum gravity and the Fermi gamma-ray excess

abstract:
  Non-perturbative quantum-gravity effects can change the fate of black holes
and make them bounce in a time scale shorter than the Hawking evaporation time.
In this article, we show that this hypothesis can account for the GeV excess
observed from the galactic center by the Fermi satellite. By carefully taking
into account the secondary component due to the decay of unstable hadrons, we
show that the model is fully self-consistent. This phenomenon presents a
specific redshift-dependance that could allow to distinguish it from other
astrophysical phenomena possibly contributing to the GeV excess.


title:
Hyperfine coupling constants from internally contracted multireference
  perturbation theory

abstract:
  We present an accurate method for calculating hyperfine coupling constants
(HFCCs) based on the complete active space second-order perturbation theory
(CASPT2) with full internal contraction. The HFCCs are computed as a
first-order property using the relaxed CASPT2 spin-density matrix that takes
into account orbital and configurational relaxation due to dynamical electron
correlation. The first-order unrelaxed spin-density matrix is calculated from
one- and two-body spin-free counterparts that are readily available in the
CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys.
142, 051103 (2015)], whereas the second-order part is computed directly using
the newly extended automatic code generator. The relaxation contribution is
then calculated from the so-called Z-vectors that are available in the CASPT2
nuclear gradient program. Numerical results are presented for the CN and AlO
radicals, for which the CASPT2 values are comparable (or, even superior in some
cases) to the ones computed by the coupled-cluster and density matrix
renormalization group methods. The HFCCs for the hexaaqua complexes with VII,
CrIII, and MnII are also presented to demonstrate the accuracy and efficiency
of our code.


title: On Two OEIS Conjectures

abstract:
  Stephan (Prove or Disprove 100 Conjectures from the OES, arXiv:math/0409509v4
[math.CO])enumerates a number of conjectures regarding integer sequences
contained in Sloane's On-line Encyclopedia of Integer Sequences (N. J. A.
Sloane, editor, The On-Line Encyclopedia of Integer Sequences, published
electronically at https://oeis.org). In this paper, we prove two of these
conjectures.


title:
Visibility of Shafarevich-Tate group of abelian varieties over number
  field extensions

abstract:
  Given an abelian variety J and an abelian subvariety A of J over a number
field K, we study the visible elements of the Shafarevich-Tate group of A with
respect to J over certain number field extension M of K. The notion of visible
elements in Shafarevich-Tate group of an abelian variety was introduced by
Mazur. In this article, we study the image of Visible elements of A with
respect to J under the natural restriction map of the Galois cohomology of A
over K to the Galois cohomology of A over M. In particular, for a fixed odd
prime p, we investigate the conditions under which visible elements of order p
can be produced over a quadratic extension or a degree p extension M of K.


title:
Analytical Solutions Of The Schr\"{o}dinger Equation For The Hulth\'en
  Potential Within SUSY Quantum Mechanics

abstract:
  The analytical solution of the modified radial Schr\"{o}dinger equation for
the Hulth\'en potential is obtained within ordinary quantum mechanics by
applying the Nikiforov-Uvarov method and supersymmetric quantum mechanics by
applying the shape invariance consept that was introduced by Gendenshtein
method by using the improved approximation scheme to the centrifugal potential
for arbitrary $l$ states. The energy levels are worked out and the
corresponding normalized eigenfunctions are obtained in terms of orthogonal
polynomials for arbitrary $l$ states.


title: The bounded and precise word problems for presentations of groups

abstract:
  We introduce and study the bounded word problem and the precise word problem
for groups given by means of generators and defining relations. For example,
for every finitely presented group, the bounded word problem is in NP, i.e., it
can be solved in nondeterministic polynomial time, and the precise word problem
is in PSPACE. The main technical result of the paper states that, for certain
finite presentations of groups, which include the Baumslag-Solitar one-relator
groups and free products of cyclic groups, the bounded word problem and the
precise word problem can be solved in polylogarithmic space. As consequences of
developed techniques that can be described as calculus of brackets, we obtain
polylogarithmic space bounds for the computational complexity of the diagram
problem for free groups, for the width problem for elements of free groups, and
for computation of the area defined by polygonal singular closed curves in the
plane. We also obtain polynomial time bounds for these problems.


title: Combinatorial interpretations of Ramanujan's tau function

abstract:
  We use a q-series identity by Ramanujan to give a combinatorial
interpretation of Ramanujan's tau function which involves t-cores and a new
class of partitions which we call (m,k)-capsids. The same method can be applied
in conjunction with other related identities yielding alternative combinatorial
interpretations of the tau function.


title:
Weakly nonlinear models for internal waves: inverse scattering transform
  and solitary wave contents

abstract:
  The time evolution emanating from "internal dam-break" initial conditions is
studied for a class of models of stratified Euler fluids in configurations
close to two-homogeneous layers separated by a thin diffused interface. Direct
numerical simulations and experiments in wave tanks show that such initial
conditions eventually give rise to coherent structures that are close to
solitary-wave solutions moving ahead of a region of dispersive wave motion and
turbulent mixing close to the location of the initial dam step. A priori
theoretical predictions of the main features of these solitary waves, such as
their amplitudes and speeds, appear to be unavailable, even for simplified
models of wave evolution in stratified fluids. With the aim of providing
estimates of the existence, amplitude and speed of such solitary waves, an
approach based on Inverse Scattering Transform (IST) for completely integrable
models is developed here and tested against direct numerical simulations of
Euler fluids and some of their models based on long wave asymptotics. In
particular, a novel regularized version of the Kaup model is developed to cure
its mathematical ill-posedness, thereby making possible the use of its
analytical predictions on the solitary-waves "content" emanating from step-like
initial conditions. The a priori estimates of the new regularized model are
found to be in reasonable agreement with the direct numerical simulations for
weakly nonlinear regimes, this significantly improves predictions based on
unidirectional models such as the Korteweg-de Vries equation.


title:
Sets of minimal distances and characterizations of class groups of Krull
  monoids

abstract:
  Let $H$ be a Krull monoid with finite class group $G$ such that every class
contains a prime divisor. Then every non-unit $a \in H$ can be written as a
finite product of atoms, say $a=u_1 \cdot \ldots \cdot u_k$. The set $\mathsf L
(a)$ of all possible factorization lengths $k$ is called the set of lengths of
$a$. There is a constant $M \in \mathbb N$ such that all sets of lengths are
almost arithmetical multiprogressions with bound $M$ and with difference $d \in
\Delta^* (H)$, where $\Delta^* (H)$ denotes the set of minimal distances of
$H$. We study the structure of $\Delta^* (H)$ and establish a characterization
when $\Delta^*(H)$ is an interval.
  The system $\mathcal L (H) = \{ \mathsf L (a) \mid a \in H \}$ of all sets of
lengths depends only on the class group $G$, and a standing conjecture states
that conversely the system $\mathcal L (H)$ is characteristic for the class
group. We confirm this conjecture (among others) if the class group is
isomorphic to $C_n^r$ with $r,n \in \mathbb N$ and $\Delta^*(H)$ is not an
interval.


title: Hybrid Riemann Solvers for Large Systems of Conservation Laws

abstract:
  In this paper we present a new family of approximate Riemann solvers for the
numerical approximation of solutions of hyperbolic conservation laws. They are
approximate, also referred to as incomplete, in the sense that the solvers
avoid computing the characteristic decomposition of the flux Jacobian. Instead,
they require only an estimate of the globally fastest wave speeds in both
directions. Thus, this family of solvers is particularly efficient for large
systems of conservation laws, i.e. with many different propagation speeds, and
when no explicit expression for the eigensystem is available. Even though only
fastest wave speeds are needed as input values, the new family of Riemann
solvers reproduces all waves with less dissipation than HLL, which has the same
prerequisites, requiring only one additional flux evaluation.


title: Atomic quantum gases in periodically driven optical lattices

abstract:
  Time periodic forcing in the form of coherent radiation is a standard tool
for the coherent manipulation of small quantum systems like single atoms. In
the last years, periodic driving has more and more also been considered as a
means for the coherent control of many-body systems. In particular, experiments
with ultracold quantum gases in optical lattices subjected to periodic driving
in the lower kilohertz regime have attracted a lot of attention. Milestones
include the observation of dynamic localization, the dynamic control of the
quantum phase transition between a bosonic superfluid and a Mott insulator, as
well as the dynamic creation of strong artificial magnetic fields and
topological band structures. This article reviews these recent experiments and
their theoretical description. Moreover, fundamental properties of periodically
driven many-body systems are discussed within the framework of Floquet theory,
including heating, relaxation dynamics, anomalous topological edge states, and
the response to slow parameter variations.


title:
Numerical Semigroups with two coprime generators: James J. Sylvester's
  proof

abstract:
  This paper examines in a new way some known facts about numerical semigroups
especially when the number of minimal generators (that is the embedding
dimension) is at most three and at least two minimal generators are coprime;
for such semigroups an algorithm is re-investigated to find the
pseudo-Frobenius numbers. We consider particular $\langle a,a+1,a+p\rangle$ for
some $p\ge 2$, $\langle ab+a+1,bc+b+1,ca+c+1\rangle$ and $\langle
n^2,(n+1)^2,(n+2)^2\rangle$ semigroups; a certain family of $n$ dimensional
numerical semigroups of type at most $n-1$ is also given.


title: On Douglas general $(\alpha,\beta)$-metrics

abstract:
  Douglas metrics are metrics with vanishing Douglas curvature which is an
important projective invariant in Finsler geometry. To find more Douglas
metrics, in this paper we consider a class of Finsler metrics called general
$(\alpha,\beta)$-metrics, which are defined by a Riemannian metric
$\alpha=\sqrt{a_{ij}(x)y^iy^j}$ and a $1$-form $\beta=b_i(x)y^i$. We obtain the
differential equations that characterizes these metrics with vanishing Douglas
curvature. By solving the equivalent PDEs, the metrics in this class are
totally determined. Then many new Douglas metrics are constructed.


title:
Functional central limit theorems for certain statistics in an infinite
  urn scheme

abstract:
  We investigate a specific infinite urn scheme first considered by Karlin
(1967). We prove functional central limit theorems for the total number of urns
with at least k balls for different k.


title:
Proton-skins in momentum space and neutron-skins in coordinate space in
  heavy nuclei

abstract:
  Neutron-skins in coordinate space and proton-skins in momentum space are
predicted to coexist in heavy nuclei and their correlation is governed by
Liouville's theorem and Heisenberg's uncertainty principle. An analysis of
their correlation within a further extended Thomas-Fermi (ETF$^+$)
approximation incorporating effects of nucleon short-range correlations reveals
generally that protons move faster than neutrons in neutron-skins of heavy
nuclei.


title: Discriminating sample groups with multi-way data

abstract:
  High-dimensional linear classifiers, such as the support vector machine (SVM)
and distance weighted discrimination (DWD), are commonly used in biomedical
research to distinguish groups of subjects based on a large number of features.
However, their use is limited to applications where a single vector of features
is measured for each subject. In practice data are often multi-way, or measured
over multiple dimensions. For example, metabolite abundance may be measured
over multiple regions or tissues, or gene expression may be measured over
multiple time points, for the same subjects. We propose a framework for linear
classification of high-dimensional multi-way data, in which coefficients can be
factorized into weights that are specific to each dimension. More generally,
the coefficients for each measurement in a multi-way dataset are assumed to
have low-rank structure. This framework extends existing classification
techniques, and we have implemented multi-way versions of SVM and DWD. We
describe informative simulation results, and apply multi-way DWD to data for
two very different clinical research studies. The first study uses metabolite
magnetic resonance spectroscopy data over multiple brain regions to compare
patients with and without spinocerebellar ataxia, the second uses publicly
available gene expression time-course data to compare treatment responses for
patients with multiple sclerosis. Our method improves performance and
simplifies interpretation over naive applications of full rank linear
classification to multi-way data. An R package is available at
https://github.com/lockEF/MultiwayClassification .


title:
Nikishin systems on star-like sets: algebraic properties and weak
  asymptotics of the associated multiple orthogonal polynomials

abstract:
  Polynomials $Q_n(z)$, $n=0,1,\ldots,$ that are multi-orthogonal with respect
to a Nikishin system of $p\geq 1$ compactly supported measures over the
star-like set of $p+1$ rays $S_+:=\{z\in \mathbb{C}: z^{p+1}\geq 0 \}$ are
investigated. We prove that the Nikishin system is normal, that the polynomials
satisfy a three-term recurrence relation of order $p+1$ of the form $z
Q_{n}(z)=Q_{n+1}(z)+a_{n}\,Q_{n-p}(z)$ with $a_n>0$ for all $n\geq p$, and that
the nonzero roots of $Q_n$ are all simple and located in $S_+$. Under the
assumption of regularity (in the sense of Stahl and Totik) of the measures
generating the Nikishin system, we describe the asymptotic zero distribution
and weak behavior of the polynomials $Q_n$ in terms of a vector equilibrium
problem for logarithmic potentials. Under the same regularity assumptions, a
theorem on the convergence of the Hermite-Pad\'e approximants to the Nikishin
system of Cauchy transforms is proven.


title: When is the sum of complemented subspaces complemented?

abstract:
  We provide a sufficient condition for the sum of a finite number of
complemented subspaces of a Banach space to be complemented. Under this
condition a formula for a projection onto the sum is given. We also show that
the condition is sharp (in a certain sense). As applications, we get (1)
sufficient conditions for the complementability of sums of marginal subspaces
in $L^p$ and sums of tensor powers of subspaces in a tensor power of a Banach
space and (2) quantitative results on stability of the complementability
property of the sum of linearly independent subspaces.


title:
Horizon Areas and Logarithmic Correction to the Charged Accelerating
  Black Hole Entropy

abstract:
  It has been shown by explicit and exact calculation that the geometric
product formula i.e. horizon area (or entropy) product formula of outer horizon
(${\cal H}^{+}$) and inner horizon (${\cal H}^{-}$) for charged accelerating
black hole (BH) should \emph{ neither be mass-independent nor it be quantized}.
This implies that the horizon area (or entropy ) product is mass-independent
conjecture has been~\emph{broken down} for charged accelerating BH. This also
further implies that the mass-independent feature of the area product of ${\cal
H}^{\pm}$ is \emph{not} a generic feature at all. We also compute that the
\emph{Cosmic-Censorship-Inequality} for this BH. Indeed it is violated for this
BH. Moreover, we compute the specific heat for this BH to determine the local
thermodynamic stability of this BH. Under certain criterion, the BH shows the
second order phase transition. Furthermore, we compute logarithmic corrections
to the entropy for the said BH due to small statistical fluctuations around the
thermal equilibrium.


title: From discrete to continuous percolation in dimensions 3 to 7

abstract:
  We propose a method of studying the continuous percolation of aligned objects
as a limit of a corresponding discrete model. We show that the convergence of a
discrete model to its continuous limit is controlled by a power-law dependency
with a universal exponent $\theta = 3/2$. This allows us to estimate the
continuous percolation thresholds in a model of aligned hypercubes in
dimensions $d = 3,\ldots,7$ with accuracy far better than that attained using
any other method before. We also report improved values of the correlation
length critical exponent $\nu$ in dimensions $d = 4,5$ and the values of
several universal wrapping probabilities for $d=4,\ldots,7$.


title:
Training LDCRF model on unsegmented sequences using Connectionist
  Temporal Classification

abstract:
  Many machine learning problems such as speech recognition, gesture
recognition, and handwriting recognition are concerned with simultaneous
segmentation and labeling of sequence data. Latent-dynamic conditional random
field (LDCRF) is a well-known discriminative method that has been successfully
used for this task. However, LDCRF can only be trained with pre-segmented data
sequences in which the label of each frame is available apriori. In the realm
of neural networks, the invention of connectionist temporal classification
(CTC) made it possible to train recurrent neural networks on unsegmented
sequences with great success. In this paper, we use CTC to train an LDCRF model
on unsegmented sequences. Experimental results on two gesture recognition tasks
show that the proposed method outperforms LDCRFs, hidden Markov models, and
conditional random fields.


title:
Model-based Differentially Private Data Synthesis and Statistical
  Inference in Multiply Synthetic Differentially Private Data

abstract:
  We propose the approach of model-based differentially private synthesis
(modips) in the Bayesian framework for releasing individual-level
surrogate/synthetic datasets with privacy guarantees given the original data.
The modips technique integrates the concept of differential privacy into
model-based data synthesis. We introduce several variants for the general
modips approach and different procedures to obtaining privacy-preserving
posterior samples, a key step in modips. The uncertainty from the sanitization
and synthetic process in modips can be accounted for by releasing multiple
synthetic datasets and quantified via an inferential combination rule that is
proposed in this paper. We run empirical studies to examine the impacts of the
number of synthetic sets and the privacy budget allocation schemes on the
inference based on synthetic data.


title:
Pulkovo Compilation of Radial Velocities for 35495 Hipparcos Stars in a
  Common System

abstract:
  The Pulkovo Compilation of Radial Velocities (PCRV) has been made to study
the stellar kinematics in the local spiral arm. The PCRV contains weighted mean
absolute radial velocities for 35 495 Hipparcos stars of various spectral types
and luminosity classes over the entire celestial sphere mainly within 500 pc of
the Sun. The median accuracy of the radial velocities obtained is 0.7 km
s$^{-1}$. Results from 203 publications were used in the catalogue. Four of
them were used to improve the radial velocities of standard stars from the IAU
list. The radial velocities of 155 standard stars turned out to be constant
within 0.3 km s$^{-1}$. These stars were used to analyze 47 768 mean radial
velocities for 37 200 stars from 12 major publications ($\sim80\%$ of all the
data used). Zero-point discrepancies and systematic dependences on radial
velocity, $(B-V)$ color index, right ascension, and declination were found in
radial velocity differences of the form "publication minus IAU list of
standards". These discrepancies and dependences were approximated and taken
into account when calculating the weighted mean radial velocities. 1128 stars
whose independent radial-velocity determinations were available at least in
three of these publications and agreed within 3 km s$^{-1}$ were chosen as the
work list of secondary standards. Radial-velocity differences of the form
"publication minus list of secondary standards" were used by analogy to correct
the zero points and systematic dependences in the radial velocities from 33
more publications (~13\% of the data used). In addition, the radial velocities
from 154 minor publications ($\sim7\%$ of the data used) pertaining to
well-known instruments were used without any corrections.


title:
Modeling galaxy clustering on small scales to tighten constraints on
  dark energy and modified gravity

abstract:
  We present a new approach to measuring cosmic expansion history and growth
rate of large scale structure using the anisotropic two dimensional galaxy
correlation function (2DCF) measured from data; it makes use of the empirical
modeling of small-scale galaxy clustering derived from numerical simulations by
Zheng et al. (2013). We validate this method using mock catalogues, before
applying it to the analysis of the CMASS sample from the Sloan Digital Sky
Survey Data Release 10 (DR10) of the Baryon Oscillation Spectroscopic Survey
(BOSS). We find that this method enables accurate and precise measurements of
cosmic expansion history and growth rate of large scale structure. Modeling the
2DCF fully including nonlinear effects and redshift space distortions (RSD) in
the scale range of 16 to 144 Mpc/h, we find H(0.57)r_s(z_d)/c=0.0459 +/-
0.0006, D_A(0.57)/r_s(z_d)=9.011 +/- 0.073, and f_g(0.57)\sigma_8(0.57)=0.476
+/- 0.050, which correspond to precisions of 1.3%, 0.8%, and 10.5%
respectively. We have defined r_s(z_d) to be the sound horizon at the drag
epoch computed using a simple integral, f_g(z) as the growth rate at redshift
z, and \sigma_8(z) as the matter power spectrum normalization on 8Mpc/h scale
at z. We find that neglecting the small-scale information significantly weakens
the constraints on H(z) and D_A(z), and leads to a biased estimate of f_g(z).
Our results indicate that we can significantly tighten constraints on dark
energy and modified gravity by reliably modeling small-scale galaxy clustering.


title:
$R_{II}$ type recurrence, generalized eigenvalue problem and orthogonal
  polynomials on the unit circle

abstract:
  We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a
special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple
and lie on the real line. It turns out that the polynomial $P_n$, for any $n
\geq 2$, is the characteristic polynomial of a simple $n \times n$ generalized
eigenvalue problem. It is shown that with this $R_{II}$ type recurrence
relation one can always associate a positive measure on the unit circle. The
orthogonality property satisfied by $P_n$ with respect to this measure is also
obtained. Finally, examples are given to justify the results.


title:
Redshift factor and the first law of binary black hole mechanics in
  numerical simulations

abstract:
  The redshift factor $z$ is an invariant quantity of fundamental interest in
post-Newtonian and self-force descriptions of compact binaries. It connects
different approximation schemes, and plays a central role in the first law of
binary black hole mechanics, which links local quantities to asymptotic
measures of energy and angular momentum in these systems. Through this law, the
redshift factor is conjectured to have a close relation to the surface gravity
of the event horizons of black holes in circular orbits. We propose and
implement a novel method for extracting the redshift factor on apparent
horizons in numerical simulations of quasicircular binary inspirals. Our
results confirm the conjectured relationship between $z$ and the surface
gravity of the holes and that the first law holds to a remarkable degree for
binary inspirals. The redshift factor enables tests of analytic predictions for
$z$ in spacetimes where the binary is only approximately circular, giving a new
connection between analytic approximations and numerical simulations.


title: Fast Incremental Learning for Off-Road Robot Navigation

abstract:
  A promising approach to autonomous driving is machine learning. In such
systems, training datasets are created that capture the sensory input to a
vehicle as well as the desired response. A disadvantage of using a learned
navigation system is that the learning process itself may require a huge number
of training examples and a large amount of computing. To avoid the need to
collect a large training set of driving examples, we describe a system that
takes advantage of the huge number of training examples provided by ImageNet,
but is able to adapt quickly using a small training set for the specific
driving environment.


title:
Bianchi VIII and IX vacuum cosmologies: Almost every solution forms
  particle horizons and converges to the Mixmaster attractor

abstract:
  Bianchi models are posited by the BKL picture to be essential building blocks
towards an understanding of generic cosmological singularities. We study the
behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi
type VIII and IX, as they approach the big bang singularity. It is known since
2001 that generic Bianchi IX spacetimes converge towards the so-called
Mixmaster attractor as time goes towards the singularity. We extend this result
to the case of Bianchi VIII vacuum. The BKL picture suggests that particle
horizons should form, i.e. spatially separate regions should causally decouple.
We prove that this decoupling indeed occurs, for Lebesgue almost every Bianchi
VIII and IX vacuum spacetime.


title: Spatial asymptotic expansions in the incompressible Euler equation

abstract:
  In this paper we prove that the Euler equation describing the motion of an
ideal fluid in $\R^d$ is well-posed in a class of functions allowing spatial
asymptotic expansions as $|x|\to\infty$ of any a priori given order. These
asymptotic expansions can involve log terms and lead to a family of
conservation laws. Typically, the solutions of the Euler equation with initial
data in the Schwartz class develop non-trivial spatial asymptotic expansions of
the type considered here.


title:
Continuum limit of a mesoscopic model with elasticity of step motion on
  vicinal surfaces

abstract:
  This work considers the rigorous derivation of continuum models of step
motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model
following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the
lattice parameter goes to zero, for a finite time interval, a modified discrete
model converges to the strong solution of the limiting PDE with first order
convergence rate.


title:
Exact gradient updates in time independent of output size for the
  spherical loss family

abstract:
  An important class of problems involves training deep neural networks with
sparse prediction targets of very high dimension D. These occur naturally in
e.g. neural language models or the learning of word-embeddings, often posed as
predicting the probability of next words among a vocabulary of size D (e.g.
200,000). Computing the equally large, but typically non-sparse D-dimensional
output vector from a last hidden layer of reasonable dimension d (e.g. 500)
incurs a prohibitive O(Dd) computational cost for each example, as does
updating the $D \times d$ output weight matrix and computing the gradient
needed for backpropagation to previous layers. While efficient handling of
large sparse network inputs is trivial, the case of large sparse targets is
not, and has thus so far been sidestepped with approximate alternatives such as
hierarchical softmax or sampling-based approximations during training. In this
work we develop an original algorithmic approach which, for a family of loss
functions that includes squared error and spherical softmax, can compute the
exact loss, gradient update for the output weights, and gradient for
backpropagation, all in $O(d^{2})$ per example instead of $O(Dd)$, remarkably
without ever computing the D-dimensional output. The proposed algorithm yields
a speedup of up to $D/4d$ i.e. two orders of magnitude for typical sizes, for
that critical part of the computations that often dominates the training time
in this kind of network architecture.


title:
Comment on 'Symmetry and random sampling of symmetry independent
  configurations for the simulation of disordered solids'

abstract:
  The proposed algorithm by Philippe D'Arco et al. 2013 J. Phys.: Condens.
Matter 25 355401 was not well compared with other possible solutions for
symmetry independent configuration (SIC) generation. In this comment, three
well known solutions of SIC searching are discussed: exhaustive explorations,
pure random sampling and "symmetry imposed" approaches. It is shown, that the
advantages of the algorithm published by Philippe D'Arco et al. are
questionable.


title:
Enhancing Transparency and Control when Drawing Data-Driven Inferences
  about Individuals

abstract:
  Recent studies have shown that information disclosed on social network sites
(such as Facebook) can be used to predict personal characteristics with
surprisingly high accuracy. In this paper we examine a method to give online
users transparency into why certain inferences are made about them by
statistical models, and control to inhibit those inferences by hiding
("cloaking") certain personal information from inference. We use this method to
examine whether such transparency and control would be a reasonable goal by
assessing how difficult it would be for users to actually inhibit inferences.
Applying the method to data from a large collection of real users on Facebook,
we show that a user must cloak only a small portion of her Facebook Likes in
order to inhibit inferences about their personal characteristics. However, we
also show that in response a firm could change its modeling of users to make
cloaking more difficult.


title: Reflections on the projection of ions in atom probe tomography

abstract:
  There are two main projections used to transform, and reconstruct, field ion
micrographs or atom probe tomography data into atomic coordinates at the
specimen surface and, subsequently, in three-dimensions. In this article, we
present a perspective on the strength of the azimuthal equidistant projection
in comparison to the more widely used and well-established point-projection(or
pseudo-stereographic projection), which underpins data reconstruction in most
software packages currently in use across the community. After an overview of
the reconstruction methodology, we demonstrate that the azimuthal equidistant
is more robust with regards to errors on the parameters used to perform the
reconstruction and is therefore more likely to yield more accurate tomographic
reconstructions.


title: Face Card: An Information-sharing Framework on Google Glass

abstract:
  Wearable devices such as Google Glass can provide an efficient way to get
around users information. We present Face Card, a system builds on Google Glass
to provide information-sharing service with around people. With a look at
Google Glass, users can quickly get information of nearby and coming users.
Utilizing Bluetooth Low Energy (BLE) and proper user interface, Face Card
demonstrates the potential of being an efficient information sharing system
framework.


title: Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions

abstract:
  We prove an analogue of Sogge's local $L^p$ estimates for $L^p$ norms of
restrictions of eigenfunctions to submanifolds, and use it to show that for
quantum ergodic eigenfunctions one can get improvements of the results of
Burq-G\'erard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on
negatively curved manifolds (without boundary) and by $o(1)$ for manifolds
(with or without boundary) with ergodic geodesic flows. In the case of ergodic
billiards with piecewise smooth boundary, we get $o(1)$ improvements on
$L^\infty$ estimates of Cauchy data away from a shrinking neighborhood of the
corners, and as a result using the methods of Ghosh-Reznikov-Sarnak and
Jung-Zelditch, we get that the number of nodal domains of two dimensional
ergodic billiards tends to infinity as $\lambda \to \infty$. These results work
only for a full density subsequence of any given orthonormal basis of
eigenfunctions.
  We also present an extension of the $L^p$ estimates of
Burq-G\'erard-Tzvetkov, Hu, and Chen-Sogge, for the restrictions of Dirichlet
and Neumann eigenfunctions to compact submanifolds of the interior of manifolds
with piecewise smooth boundary. This part does not assume ergodicity on the
manifolds.


title:
Helicity in Proton-Proton Elastic Scattering and the Spin Structure of
  the Pomeron

abstract:
  We discuss different models for the spin structure of the nonperturbative
pomeron: scalar, vector, and rank-2 symmetric tensor. The ratio of
single-helicity-flip to helicity-conserving amplitudes in polarised high-energy
proton-proton elastic scattering, known as the complex r_5 parameter, is
calculated for these models. We compare our results to experimental data from
the STAR experiment. We show that the spin-0 (scalar) pomeron model is clearly
excluded by the data, while the vector pomeron is inconsistent with the rules
of quantum field theory. The tensor pomeron is found to be perfectly consistent
with the STAR data.


title: Statistical analysis of acoustic wave parameters near active regions

abstract:
  In order to quantify the influence of magnetic fields on acoustic mode
parameters and flows in and around active regions, we analyse the differences
in the parameters in magnetically quiet regions nearby an active region (which
we call `nearby regions'), compared with those of quiet regions at the same
disc locations for which there are no neighboring active regions. We also
compare the mode parameters in active regions with those in comparably located
quiet regions. Our analysis is based on ring diagram analysis of all active
regions observed by HMI during almost five years. We find that the frequency at
which the mode amplitude changes from attenuation to amplification in the quiet
nearby regions is around 4.2 mHz, in contrast to the active regions, for which
it is about 5.1 mHz. This amplitude enhancement (the `acoustic halo effect') is
as large as that observed in the active regions, and has a very weak dependence
on the wave propagation direction. The mode energy difference in nearby regions
also changes from a deficit to an excess at around 4.2 mHz, but averages to
zero over all modes. The frequency difference in nearby regions increases with
increasing frequency until a point at which the frequency shifts turn over
sharply as in active regions. However, this turnover occurs around 4.9 mHz,
significantly below the acoustic cutoff frequency. Inverting the horizontal
flow parameters in the direction of the neighboring active regions, we find
flows that are consistent with a model of the thermal energy flow being blocked
directly below the active region.