title: On the variety associated to the ring of theta constants in genus 3

abstract:
  Due to fundamental results of Igusa and Mumford the $N=2^{g-1}(2^g+1)$ even
theta constants define for each genus $g$ an injective holomorphic map of the
Satake compactification $X_g(4,8)=H_g/\Gamma_g[4,8]$ into the projective space
$P^{N-1}$. Moreover, this map is biholomorphic onto the image outside the
Satake boundary. It is not biholomorphic on the whole in the cases $g\ge 6$.
Igusa also proved that in the cases $g\le 2$ this map is biholomorphic onto the
image. In this paper we extend this result to the case $g=3$. So we show that
the theta map $$X_3(4,8)\to P^{35}$$ is biholomorphic onto the image. This is
equivalent to the statement that the image is a normal subvariety of $P^{35}$ .


title: Finite-time Stability Analysis for Random Nonlinear Systems

abstract:
  This paper presents an analysis approach to finite-time attraction in
probability concerns with nonlinear systems described by nonlinear random
differential equations (RDE). RDE provide meticulous physical interpreted
models for some applications contain stochastic disturbance. The existence and
the path-wise uniqueness of the finite-time solution are investigated through
nonrestrictive assumptions. Then a finite-time attraction analysis is
considered through the definition of the stochastic settling time function and
a Lyapunov based approach. A Lyapunov theorem provides sufficient conditions to
guarantee finite-time attraction in probability of random nonlinear systems. A
Lyapunov function ensures stability in probability and a finiteness of the
expectation of the stochastic settling time function. Results are demonstrated
employing the method for two examples to show potential of the proposed
technique.


title: Landau damping to partially locked states in the Kuramoto model

abstract:
  In the Kuramoto model of globally coupled oscillators, partially locked
states (PLS) are stationary solutions that incorporate the emergence of partial
synchrony when the interaction strength increases. While PLS have long been
considered, existing results on their stability are limited to neutral
stability of the linearized dynamics in strong topology, or to specific
invariant subspaces (obtained via the so-called Ott-Antonsen (OA) ansatz) with
specific frequency distributions for the oscillators. In the mean field limit,
the Kuramoto model shows various ingredients of the Landau damping mechanism in
the Vlasov equation. This analogy has been a source of inspiration for
stability proofs of regular Kuramoto equilibria. Besides, the major
mathematical issue with PLS asymptotic stability is that these states consist
of heterogeneous and singular measures. Here, we establish an explicit
criterion for their spectral stability and we prove their local asymptotic
stability in weak topology, for a large class of analytic frequency marginals.
The proof strongly relies on a suitable functional space that contains (Fourier
transforms of) singular measures, and for which the linearized dynamics is well
under control. For illustration, the stability criterion is evaluated in some
standard examples. We show in particular that no loss of generality results in
assuming the OA ansatz. To our best knowledge, our result provides the first
proof of Landau damping to heterogeneous and irregular equilibria, in absence
of dissipation.


title: On sofic approximations of Property (T) groups

abstract:
  We prove Bowen's conjecture that every sequence of finite graphs that locally
converges to the Cayley graph of a countably infinite group with Kazhdan
Property (T) is essentially a vertex-disjoint union of expander graphs. We
characterize graph sequences that are essentially a vertex-disjoint union of
expander graphs in terms of the Markov operator.


title:
Effects of flare definitions on the statistics of derived flare
  distributions

abstract:
  The statistical examination of solar flares is crucial to revealing their
global characteristics and behaviour. Such examinations can tackle large-scale
science questions or give context to detailed single-event studies. However,
they are often performed using standard but basic flare detection algorithms
relying on arbitrary thresholds. This arbitrariness may lead to important
scientific conclusions being drawn from results caused by subjective choices in
algorithms rather than the true nature of the Sun. In this paper, we explore
the effect of the arbitrary thresholds used in the GOES (Geostationary
Operational Environmental Satellite) event list and LYRA (Large Yield
RAdiometer) Flare Finder algorithms. We find that there is a small but
significant relationship between the power law exponent of the GOES flare peak
flux frequency distribution and the flare start thresholds of the algorithms.
We also find that the power law exponents of these distributions are not
stable, but appear to steepen with increasing peak flux. This implies that the
observed flare size distribution may not be a power law at all. We show that
depending on the true value of the exponent of the flare size distribution,
this deviation from a power law may be due to flares missed by the flare
detection algorithms. However, it is not possible determine the true exponent
from GOES/XRS observations. Additionally we find that the PROBA2/LYRA flare
size distributions are artificially steep and clearly non-power law. We show
that this is consistent with an insufficient degradation correction. This means
that PROBA2/LYRA should not be used for flare statistics or energetics unless
degradation is adequately accounted for. However, it can be used to study
variations over shorter timescales and for space weather monitoring.


title:
Multi-Tenant Virtual GPUs for Optimising Performance of a Financial Risk
  Application

abstract:
  Graphics Processing Units (GPUs) are becoming popular accelerators in modern
High-Performance Computing (HPC) clusters. Installing GPUs on each node of the
cluster is not efficient resulting in high costs and power consumption as well
as underutilisation of the accelerator. The research reported in this paper is
motivated towards the use of few physical GPUs by providing cluster nodes
access to remote GPUs on-demand for a financial risk application. We
hypothesise that sharing GPUs between several nodes, referred to as
multi-tenancy, reduces the execution time and energy consumed by an
application. Two data transfer modes between the CPU and the GPUs, namely
concurrent and sequential, are explored. The key result from the experiments is
that multi-tenancy with few physical GPUs using sequential data transfers
lowers the execution time and the energy consumed, thereby improving the
overall performance of the application.


title: Learning to learn by gradient descent by gradient descent

abstract:
  The move from hand-designed features to learned features in machine learning
has been wildly successful. In spite of this, optimization algorithms are still
designed by hand. In this paper we show how the design of an optimization
algorithm can be cast as a learning problem, allowing the algorithm to learn to
exploit structure in the problems of interest in an automatic way. Our learned
algorithms, implemented by LSTMs, outperform generic, hand-designed competitors
on the tasks for which they are trained, and also generalize well to new tasks
with similar structure. We demonstrate this on a number of tasks, including
simple convex problems, training neural networks, and styling images with
neural art.


title:
Open-system many-body dynamics through interferometric measurements and
  feedback

abstract:
  Light-matter interfaces enable the generation of entangled states of light
and matter which can be exploited to steer the quantum state of matter through
measurement of light and feedback. Here we consider continuous-time,
interferometric homodyne measurements of light on an array of light-matter
interfaces followed by local feedback acting on each material system
individually. While the systems are physically non-interacting, the feedback
master equation we derive describes driven-dissipative, interacting many-body
quantum dynamics, and comprises pairwise Hamiltonian interactions and
collective jump operators. We characterize the general class of
driven-dissipative many body systems which can be engineered in this way, and
derive necessary conditions on models supporting non-trivial quantum dynamics
beyond what can be generated by local operations and classical communication.
We provide specific examples of models which allow for the creation of
stationary many-particle entanglement, and the emulation of dissipative Ising
models. Since the interaction between the systems is mediated via feedback
only, there is no intrinsic limit on the range or geometry of the interaction,
making the scheme quite versatile.


title: Downlink Performance of Superimposed Pilots in Massive MIMO systems

abstract:
  In this paper, we investigate the downlink throughput performance of a
massive multiple-input multiple-output (MIMO) system that employs superimposed
pilots for channel estimation. The component of downlink (DL) interference that
results from transmitting data alongside pilots in the uplink (UL) is shown to
decrease at a rate proportional to the square root of the number of antennas at
the BS. The normalized mean-squared error (NMSE) of the channel estimate is
compared with the Bayesian Cram\'{e}r-Rao lower bound that is derived for the
system, and the former is also shown to diminish with increasing number of
antennas at the base station (BS). Furthermore, we show that staggered pilots
are a particular case of superimposed pilots and offer the downlink throughput
of superimposed pilots while retaining the UL spectral and energy efficiency of
regular pilots. We also extend the framework for designing a hybrid system,
consisting of users that transmit either regular or superimposed pilots, to
minimize both the UL and DL interference. The improved NMSE and DL rates of the
channel estimator based on superimposed pilots are demonstrated by means of
simulations.


title: Transport of magnetic turbulence in Supernova remnants

abstract:
  Context. Supernova remnants are known as sources of galactic cosmic rays for
their non-thermal emission of radio waves, X-rays, and gamma-rays. However, the
observed soft broken power-law spectra are hard to reproduce within standard
acceleration theory based on the assumption of Bohm diffusion and steady-state
calculations. Aims. We point out that a time-dependent treatment of the
acceleration process together with a self-consistent treatment of the
scattering turbulence amplification is necessary. Methods. We numerically solve
the coupled system of transport equations for cosmic rays and isotropic
Alfvenic turbulence. The equations are coupled through the growth rate of
turbulence determined by the cosmic-ray gradient and the spatial diffusion
coefficient of cosmic rays determined by the energy density of the turbulence.
The system is solved on a co-moving expanding grid extending upstream for
dozens of shock radii, allowing for the self-consistent study of cosmic-ray
diffusion in the vicinity of their acceleration site. The transport equation
for cosmic rays is solved in a test-particle approach. Results. We demonstrate
that the system is typically not in a steady state. In fact, even after several
thousand years of evolution, no equilibrium situation is reached. The resulting
time-dependent particle spectra strongly differ from those derived assuming a
steady state and Bohm diffusion. Our results indicate that proper accounting
for the evolution of the scattering turbulence and hence the particle diffusion
coefficient is crucial for the formation of the observed soft spectra. In any
case, the need to continuously develop magnetic turbulence upstream of the
shock introduces non-linearity in addition to that imposed by cosmic-ray
feedback.


title:
Bayesian Inference on Matrix Manifolds for Linear Dimensionality
  Reduction

abstract:
  We reframe linear dimensionality reduction as a problem of Bayesian inference
on matrix manifolds. This natural paradigm extends the Bayesian framework to
dimensionality reduction tasks in higher dimensions with simpler models at
greater speeds. Here an orthogonal basis is treated as a single point on a
manifold and is associated with a linear subspace on which observations vary
maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds
for various dimensionality reduction problems, explore the connection between
the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the
Grassmannian for the first time. We delineate in which situations either
manifold should be considered. Further, matrix manifold models are used to
yield scientific insight in the context of cognitive neuroscience, and we
conclude that our methods are suitable for basic inference as well as accurate
prediction.


title: Phase Transitions in the One-dimensional Coulomb Gas Ensembles

abstract:
  We consider the system of particles on a finite interval with pair-wise
nearest neighbours interaction and external force. This model was introduced by
Malyshev to study the flow of charged particles on a rigorous mathematical
level. It is a simplified version of a 3-dimensional classical Coulomb gas
model. We study Gibbs distribution at finite positive temperature extending
recent results on the zero temperature case (ground states) with external
force. We derive the asymptotic for the mean and for the variances of the
distances between the neighbouring charges. We prove that depending on the
strength of the external force there are several phase transitions in the local
structure of the configuration of the particles in the limit when the number of
particles goes to infinity.


title:
Electrically switchable cylindrical Fresnel lens based on holographic
  polymer-dispersed liquid crystals using a Michelson interferometer

abstract:
  Fabricating an electrically switchable cylindrical Fresnel lens based on
holographic polymer-dispersed liquid crystals (H-PDLC) using a Michelson
interferometer is reported. Simplicity of the method and possibility of
fabricating different focal length lenses in a single set up are among the
advantages of the method. It is demonstrated that the Fresnel structured zone
plate acts as a cylindrical lens and focuses light in one dimension. Its
electro-optical switching properties are also studied and it is found that at
an applied electric field of E=6 Vrms/{\mu}m across the sample, focusing
property of the sample eliminates with a response of about 1 ms in a reversible
manner.


title: Relativistic Landau Levels in the Rotating Cosmic String Spacetime

abstract:
  In the spacetime induced by a rotating cosmic string we compute the energy
levels of a massive spinless particle coupled covariantly to a homogeneous
magnetic field parallel to the string. Afterwards, we consider the addition of
a scalar potential with a Coulomb-type and a linear confining term and
completely solve the Klein-Gordon equations for each configuration. Finally,
assuming rigid-wall boundary conditions, we find the Landau levels when the
linear defect is itself magnetized. Remarkably, our analysis reveals that the
Landau quantization occurs even in the absence of gauge fields provided the
string is endowed with spin.


title: Linear correlations of multiplicative functions

abstract: We prove a Green--Tao theorem for multiplicative functions.


title:
Anomalous Damping of a Micro-electro-mechanical Oscillator in Superfluid
  $^3$He-B

abstract:
  The mechanical resonance properties of a micro-electro-mechanical oscillator
with a gap of 1.25 $\mu$m was studied in superfluid $^3$He-B at various
pressures. The oscillator was driven in the linear damping regime where the
damping coefficient is independent of the oscillator velocity. The quality
factor of the oscillator remains low ($Q\approx 80$) down to 0.1 $T_c$, 4
orders of magnitude less than the intrinsic quality factor measured in vacuum
at 4 K. In addition to the Boltzmann temperature dependent contribution to the
damping, a damping proportional to temperature was found to dominate at low
temperatures. We propose a multiple scattering mechanism of the surface Andreev
bound states to be a possible cause for the anomalous damping.


title:
Self-consistent scheme for optical response of large hybrid networks of
  semiconductor quantum dots and plasmonic metal nanoparticles

abstract:
  We discuss a self-consistent scheme for treating the optical response of
large, hybrid networks of semiconducting quantum dots (SQDs) and plasmonic
metallic nanoparticles (MNPs). Our method is efficient and scalable and becomes
exact in the limiting case of weakly interacting SQDs. The self-consistent
equations obtained for the steady state are analogous to the von Neumann
equations of motion for the density matrix of a SQD placed in an effective
electric field computed within the discrete dipole approximation. Illustrative
applications of the theory to square and honeycomb SQD, MNP, and hybrid SDQ-MNP
lattices as well as SQD-MNP dimers are presented. Our results demonstrate that
hybrid SQD-MNP lattices can provide flexible platforms for light manipulation
with tunable resonant characteristics.


title: Kepler-108: A Mutually Inclined Giant Planet System

abstract:
  The vast majority of well studied giant-planet systems, including the Solar
System, are nearly coplanar which implies dissipation within a primordial gas
disk. however, intrinsic instability may lead to planet-planet scattering,
which often produces non-coplanar, eccentric orbits. Planet scattering theories
have been developed to explain observed high eccentricity systems and also hot
Jupiters; thus far their predictions for mutual inclination (I) have barely
been tested. Here we characterize a highly mutually-inclined (I ~ 15-60
degrees), moderately eccentric (e >~ 0.1) giant planet system: Kepler-108. This
system consists of two approximately Saturn-mass planets with periods of ~49
and ~190 days around a star with a wide (~300AU) binary companion in an orbital
configuration inconsistent with a purely disk migration origin.


title: Lifted Convex Quadratic Programming

abstract:
  Symmetry is the essential element of lifted inference that has recently
demon- strated the possibility to perform very efficient inference in
highly-connected, but symmetric probabilistic models models. This raises the
question, whether this holds for optimisation problems in general. Here we show
that for a large class of optimisation methods this is actually the case. More
precisely, we introduce the concept of fractional symmetries of convex
quadratic programs (QPs), which lie at the heart of many machine learning
approaches, and exploit it to lift, i.e., to compress QPs. These lifted QPs can
then be tackled with the usual optimization toolbox (off-the-shelf solvers,
cutting plane algorithms, stochastic gradients etc.). If the original QP
exhibits symmetry, then the lifted one will generally be more compact, and
hence their optimization is likely to be more efficient.


title: Omnivore: An Optimizer for Multi-device Deep Learning on CPUs and GPUs

abstract:
  We study the factors affecting training time in multi-device deep learning
systems. Given a specification of a convolutional neural network, our goal is
to minimize the time to train this model on a cluster of commodity CPUs and
GPUs. We first focus on the single-node setting and show that by using standard
batching and data-parallel techniques, throughput can be improved by at least
5.5x over state-of-the-art systems on CPUs. This ensures an end-to-end training
speed directly proportional to the throughput of a device regardless of its
underlying hardware, allowing each node in the cluster to be treated as a black
box. Our second contribution is a theoretical and empirical study of the
tradeoffs affecting end-to-end training time in a multiple-device setting. We
identify the degree of asynchronous parallelization as a key factor affecting
both hardware and statistical efficiency. We see that asynchrony can be viewed
as introducing a momentum term. Our results imply that tuning momentum is
critical in asynchronous parallel configurations, and suggest that published
results that have not been fully tuned might report suboptimal performance for
some configurations. For our third contribution, we use our novel understanding
of the interaction between system and optimization dynamics to provide an
efficient hyperparameter optimizer. Our optimizer involves a predictive model
for the total time to convergence and selects an allocation of resources to
minimize that time. We demonstrate that the most popular distributed deep
learning systems fall within our tradeoff space, but do not optimize within the
space. By doing this optimization, our prototype runs 1.9x to 12x faster than
the fastest state-of-the-art systems.


title:
Directional Modulation via Symbol-Level Precoding: A Way to Enhance
  Security

abstract:
  Wireless communication provides a wide coverage at the cost of exposing
information to unintended users. As an information-theoretic paradigm, secrecy
rate derives bounds for secure transmission when the channel to the
eavesdropper is known. However, such bounds are shown to be restrictive in
practice and may require exploitation of specialized coding schemes. In this
paper, we employ the concept of directional modulation and follow a signal
processing approach to enhance the security of multi-user MIMO communication
systems when a multi-antenna eavesdropper is present. Enhancing the security is
accomplished by increasing the symbol error rate at the eavesdropper. Unlike
the information-theoretic secrecy rate paradigm, we assume that the legitimate
transmitter is not aware of its channel to the eavesdropper, which is a more
realistic assumption. We examine the applicability of MIMO receiving algorithms
at the eavesdropper. Using the channel knowledge and the intended symbols for
the users, we design security enhancing symbol-level precoders for different
transmitter and eavesdropper antenna configurations. We transform each design
problem to a linearly constrained quadratic program and propose two solutions,
namely the iterative algorithm and one based on non-negative least squares, at
each scenario for a computationally-efficient modulation. Simulation results
verify the analysis and show that the designed precoders outperform the
benchmark scheme in terms of both power efficiency and security enhancement.


title:
Expectations for high energy diffuse galactic neutrinos for different
  cosmic ray distributions

abstract:
  The interaction of cosmic rays with the gas contained in our Galaxy is a
guaranteed source of diffuse high energy neutrinos. We provide expectations for
this component by considering different assumptions for the cosmic ray
distribution in the Galaxy which are intended to cover the large uncertainty in
cosmic ray propagation models. We calculate the angular dependence of the
diffuse galactic neutrino flux and the corresponding rate of High Energy
Starting Events in IceCube by including the effect of detector angular
resolution. Moreover we discuss the possibility to discriminate the galactic
component from an isotropic astrophysical flux. We show that a statistically
significant excess of events from the galactic plane in present IceCube data
would favour models in which the cosmic ray density in the inner galactic
region is much larger than its local value, thus bringing relevant information
on the cosmic ray radial distribution.


title:
Nonequilibrium Electron Dynamics in a Solid with a Changing Nodal
  Excitation Gap

abstract:
  We develop a computationally inexpensive model to examine the dynamics of
boson-assisted electron relaxation in solids, studying nonequilibrium dynamics
in a metal, in a nodal superconductor with a stationary density of states, and
in a nodal superconductor where the gap dynamically opens. In the metallic
system, the electron population resembles a thermal population at all times,
but the presence of even a fixed nodal gap both invalidates a purely thermal
treatment and sharply curtails relaxation rates. For a gap that is allowed to
open as electron relaxation proceeds, effects are even more pronounced, and gap
dynamics become coupled to the dynamics of the electron population. Comparisons
to experiments reveal that phase-space restrictions in the presence of a gap
are likely to play a significant role in the widespread observation of
coexisting femtosecond and picosecond dynamics in the cuprate high-temperature
superconductors.


title: Origin of the metal-to-insulator crossover in cuprate superconductors

abstract:
  Superconductivity in cuprates peaks in the doping regime between a metal at
high p and an insulator at low p. Understanding how the material evolves from
metal to insulator is a fundamental and open question. Early studies in high
magnetic fields revealed that below some critical doping an insulator-like
upturn appears in the resistivity of cuprates at low temperature, but its
origin has remained a puzzle. Here we propose that this 'metal-to-insulator
crossover' is due to a drop in carrier density n associated with the onset of
the pseudogap phase at a critical doping p*. We use high-field resistivity
measurements on LSCO to show that the upturns are quantitatively consistent
with a drop from n=1+p above p* to n=p below p*, in agreement with high-field
Hall data in YBCO. We demonstrate how previously reported upturns in the
resistivity of LSCO, YBCO and Nd-LSCO are explained by the same universal
mechanism: a drop in carrier density by 1.0 hole per Cu atom.


title:
A Linearized Power Flow Model for Optimization in Unbalanced
  Distribution Systems

abstract:
  Optimal Power Flow (OPF) is an important tool used to coordinate assets in
electric power systems to ensure customer voltages are within pre-defined
tolerances and to improve distribution system operations. While convex
relaxations of Optimal Power Flow (OPF) problems have been proposed for both
balanced and unbalanced networks, these approaches do not provide universal
convexity guarantees and scale inefficiently as network size and the number of
constraints increase. To address these issues, we have recently explored a
novel linearized OPF formulation for unbalanced distribution systems. Our
approach is made possible in part by approximating the ratio of voltages across
phases throughout the network. In this work, we generalize the previous
formulation to allow arbitrary complex numbers to approximate voltage ratios at
different locations in the feeder. Furthermore, we continue the analysis of the
linearized OPF via comparison to results obtained through convex relaxations
and Semi-Definite Programming (SDP). Simulations of IEEE test feeders show that
the proposed formulation produces control decisions that closely approximate
those obtained via SDP relaxations. In a specific case, we show that the
linearized OPF is capable of solving certain problems which cannot be
formulated as SDPs.


title:
Some open problems in mathematical two-dimensional conformal field
  theory

abstract:
  We discuss some open problems in a program of constructing and studying
two-dimensional conformal field theories using the representation theory of
vertex operator algebras.


title:
Reducibility of 1-d Schroedinger equation with time quasiperiodic
  unbounded perturbations, I

abstract:
  We study the Schr\"odinger equation on $\R$ with a polynomial potential
behaving as $x^{2l}$ at infinity, $1\leq l\in\N$ and with a small time
quasiperiodic perturbation. We prove that if the symbol of the perturbation
grows at most like $(\xi^2+x^{2l})^{\beta/(2l)}$, with $\beta<l+1$, then the
system is reducible. Some extensions including cases with $\beta=2l$ are also
proved. The result implies boundedness of Sobolev norms. The proof is based on
pseudodifferential calculus and KAM theory.


title: Range Majorities and Minorities in Arrays

abstract:
  Karpinski and Nekrich (2008) introduced the problem of parameterized range
majority, which asks us to preprocess a string of length $n$ such that, given
the endpoints of a range, one can quickly find all the distinct elements whose
relative frequencies in that range are more than a threshold $\tau$. Subsequent
authors have reduced their time and space bounds such that, when $\tau$ is
fixed at preprocessing time, we need either $O(n \log (1 / \tau))$ space and
optimal $O(1 / \tau)$ query time or linear space and $O((1 / \tau) \log \log
\sigma)$ query time, where $\sigma$ is the alphabet size. In this paper we give
the first linear-space solution with optimal $O(1 / \tau)$ query time, even
with variable $\tau$ (i.e., specified with the query). For the case when
$\sigma$ is polynomial on the computer word size, our space is optimally
compressed according to the symbol frequencies in the string. Otherwise, either
the compressed space is increased by an arbitrarily small constant factor or
the time rises to any function in $(1/\tau)\cdot\omega(1)$. We obtain the same
results on the complementary problem of parameterized range minority introduced
by Chan et al. (2015), who had achieved linear space and $O(1 / \tau)$ query
time with variable $\tau$.


title: Effros, Baire, Steinhaus and Non-Separability

abstract:
  We give a short proof of an improved version of the Effros Open Mapping
Principle via a shift-compactness theorem (also with a short proof), involving
`sequential analysis' rather than separability, deducing it from the Baire
property in a general Baire-space setting (rather than under topological
completeness). It is applicable to absolutely-analytic normed groups (which
include complete metrizable topological groups), and via a Steinhaus-type
Sum-set Theorem (also a consequence of the shift-compactness theorem) includes
the classical Open Mapping Theorem (separable or otherwise).


title: A priority based noise tolerant jet framework and algorithm

abstract:
  We introduce a new framework for jet definitions called p-jets that matches
the computational speed of the currently used anti-k_T jet algorithm, but
avoids combining much of the energy from background pileup events with signal
jets. As a first illustration of the p-jet framework, we compare the
effectiveness of a p-jet algorithm to the anti-k_T algorithm in reconstructing
low energy jets from resonant Z boson production and 50 pileup events.


title: Reconstructing WKB from topological recursion

abstract:
  We prove that the topological recursion reconstructs the WKB expansion of a
quantum curve for all spectral curves whose Newton polygons have no interior
point (and that are smooth as affine curves). This includes nearly all
previously known cases in the literature, and many more; in particular, it
includes many quantum curves of order greater than two. We also explore the
connection between the choice of ordering in the quantization of the spectral
curve and the choice of integration divisor to reconstruct the WKB expansion.


title: Age and Structure of a Model Vapor-Deposited Glass

abstract:
  Glass films prepared by a process of physical vapor deposition have been
shown to have thermodynamic and kinetic stability comparable to those of
ordinary glasses aged for thousands of years. A central question in the study
of vapor-deposited glasses, particularly in light of new knowledge regarding
anisotropy in these materials, is whether the ultra-stable glassy films formed
by vapor deposition are ever equivalent to those obtained by liquid cooling. We
present a computational study of vapor deposition for a two-dimensional glass
forming liquid using a methodology which closely mimics experiment. We find
that for the model considered here, structures that arise in vapor-deposited
materials are statistically identical to those observed in ordinary glasses,
provided the two are compared at the same inherent structure energy. We also
find that newly deposited hot molecules produce cascades of hot particles that
propagate far into the film, possibly influencing the relaxation of the
material.


title: Structural and electronic properties of Fe(AlxGa1-x)3 system

abstract:
  FeGa3 is a well known d-p hybridization induced intermetallic bandgap
semiconductor. In this work, we present the experimental and theoretical
results on the effect of Al substitution in FeGa3, obtained by x-ray
diffraction (XRD), temperature dependent resistance measurement, room
temperature Mossbauer measurements and density functional theory based
electronic structure calculations. It is observed that upto x = 0.178 in
Fe(AlxGa1-x)3, which is the maximum range studied in this work, Al substitution
reduces the lattice parameters 'a' and 'c' preserving the parent tetragonal
P42/mnm crystal structure of FeGa3. The bandgap of Fe(AlxGa1-x)3 for x = 0.178
is reduced by ~ 24% as compared to FeGa3. Rietveld refinement of the XRD data
shows that the Al atoms replace Ga atoms located at the 8j sites in FeGa3. A
comparison of the trends of the lattice parameters and energy bandgap observed
in the calculations and the experiments also confirms that Al primarily
replaces the Ga atoms in the 8j site.


title:
Almost uniform convergence in noncommutative Dunford-Schwartz ergodic
  theorem

abstract:
  This article gives an affirmative solution to the problem whether the ergodic
Ces\'aro averages generated by a positive Dunford-Schwartz operator in a
noncommutative space $L^p(\mathcal M,\tau)$, $1\leq p<\infty$, converge almost
uniformly (in Egorov's sense). This problem goes back to the original paper of
Yeadon, published in 1977, where bilaterally almost uniform convergence of
these averages was established for $p=1$.


title: Enumeration of cyclic permutations in vector grid classes

abstract:
  A grid class consists of permutations whose pictorial depiction can be
partitioned into increasing and decreasing parts as determined by a given
matrix. In this paper, we introduce a method for enumerating cyclic
permutations in vector grid classes by establishing a bijective relationship
with certain necklaces. We use this method to complete the enumeration of
cyclic permutations in the length 3 vector grid classes. In addition, we define
an analog of Wilf-equivalence between these sets. We conclude by discussing
cyclic permutations in alternating grid classes.


title:
Shallow Discourse Parsing Using Distributed Argument Representations and
  Bayesian Optimization

abstract:
  This paper describes the Georgia Tech team's approach to the CoNLL-2016
supplementary evaluation on discourse relation sense classification. We use
long short-term memories (LSTM) to induce distributed representations of each
argument, and then combine these representations with surface features in a
neural network. The architecture of the neural network is determined by
Bayesian hyperparameter search.


title:
Optimising a balloon-borne polarimeter in the hard X-ray domain: from
  the PoGOLite Pathfinder to PoGO+

abstract:
  PoGOLite is a balloon-borne hard X-ray polarimeter dedicated to the study of
point sources. Compton scattered events are registered using an array of
plastic scintillator units to determine the polarisation of incident X-rays in
the energy range 20 - 240 keV. In 2013, a near circumpolar balloon flight of 14
days duration was completed after launch from Esrange, Sweden, resulting in a
measurement of the linear polarisation of the Crab emission. Building on the
experience gained from this Pathfinder flight, the polarimeter is being
modified to improve performance for a second flight in 2016. Such
optimisations, based on Geant4 Monte Carlo simulations, take into account the
source characteristics, the instrument response and the background environment
which is dominated by atmospheric neutrons. This paper describes the
optimisation of the polarimeter and details the associated increase in
performance. The resulting design, PoGO+, is expected to improve the Minimum
Detectable Polarisation (MDP) for the Crab from 19.8% to 11.1% for a 5 day
flight. Assuming the same Crab polarisation fraction as measured during the
2013 flight, this improvement in MDP will allow a 5{\sigma} constrained result.
It will also allow the study of the nebula emission only (Crab off-pulse) and
Cygnus X-1 if in the hard state.


title: Gluonic Transversity from Lattice QCD

abstract:
  We present an exploratory study of the gluonic structure of the $\phi$ meson
using lattice QCD (LQCD). This includes the first investigation of gluonic
transversity via the leading moment of the twist-two double-helicity-flip
gluonic structure function $\Delta(x,Q^2)$. This structure function only exists
for targets of spin $J\ge1$ and does not mix with quark distributions at
leading twist, thereby providing a particularly clean probe of gluonic degrees
of freedom. We also explore the gluonic analogue of the Soffer bound which
relates the helicity flip and non-flip gluonic distributions, finding it to be
saturated at the level of 80%. This work sets the stage for more complex LQCD
studies of gluonic structure in the nucleon and in light nuclei where
$\Delta(x,Q^2)$ is an 'exotic glue' observable probing gluons in a nucleus not
associated with individual nucleons.


title: Max-Margin Feature Selection

abstract:
  Many machine learning applications such as in vision, biology and social
networking deal with data in high dimensions. Feature selection is typically
employed to select a subset of features which im- proves generalization
accuracy as well as reduces the computational cost of learning the model. One
of the criteria used for feature selection is to jointly minimize the
redundancy and maximize the rele- vance of the selected features. In this
paper, we formulate the task of feature selection as a one class SVM problem in
a space where features correspond to the data points and instances correspond
to the dimensions. The goal is to look for a representative subset of the
features (support vectors) which describes the boundary for the region where
the set of the features (data points) exists. This leads to a joint
optimization of relevance and redundancy in a principled max-margin framework.
Additionally, our formulation enables us to leverage existing techniques for
optimizing the SVM objective resulting in highly computationally efficient
solutions for the task of feature selection. Specifically, we employ the dual
coordinate descent algorithm (Hsieh et al., 2008), originally proposed for
SVMs, for our formulation. We use a sparse representation to deal with data in
very high dimensions. Experiments on seven publicly available benchmark
datasets from a variety of domains show that our approach results in orders of
magnitude faster solutions even while retaining the same level of accuracy
compared to the state of the art feature selection techniques.


title:
Hierarchy of orientational phases and axial anisotropies in the gauge
  theoretical description of generalized nematics

abstract:
  The paradigm of spontaneous symmetry breaking encompasses the breaking of the
rotational symmetries $O(3)$ of isotropic space to a discrete subgroup, i.e. a
three-dimensional point group. The subgroups form a rich hierarchy and allow
for many different phases of matter with orientational order. Such spontaneous
symmetry breaking occurs in nematic liquid crystals and a highlight of such
anisotropic liquids are the uniaxial and biaxial nematics. Generalizing the
familiar uniaxial and biaxial nematics to phases characterized by an arbitrary
point group symmetry, referred to as \emph{generalized nematics}, leads to a
large hierarchy of phases and possible orientational phase transitions. We
discuss how a particular class of nematic phase transitions related to axial
point groups can be efficiently captured within a recently proposed gauge
theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J.
Slager, K. Wu, J. Zaanen, Phys. Rev. X {\bf 6}, 041025 (2016)]. These
transitions can be introduced in the model by considering anisotropic couplings
that do not break any additional symmetries. By and large this generalizes the
well-known uniaxial-biaxial nematic phase transition to any arbitrary axial
point group in three dimensions. We find in particular that the generalized
axial transitions are distinguished by two types of phase diagrams with
intermediate vestigial orientational phases and that the window of the
vestigial phase is intimately related to the amount of symmetry of the defining
point group due to inherently growing fluctuations of the order parameter. This
might explain the stability of the observed uniaxial-biaxial phases as compared
to the yet to be observed other possible forms of generalized nematic order
with higher point group symmetries.


title:
An effective-field-theory analysis of Efimov physics in heteronuclear
  mixtures of ultracold atomic gases

abstract:
  We use an effective-field-theory framework to analyze the Efimov effect in
heteronuclear three-body systems consisting of two species of atoms with a
large interspecies scattering length. In the leading-order description of this
theory, various three-body observables in heteronuclear mixtures can be
universally parameterized by one three-body parameter. We present the
next-to-leading corrections, which include the effects of the finite
interspecies effective range and the finite intraspecies scattering length, to
various three-body observables. We show that only one additional three-body
parameter is required to render the theory predictive at this order. By
including the effective range and intraspecies scattering length corrections,
we derive a set of universal relations that connect the different Efimov
features near the interspecies Feshbach resonance. Furthermore, we show that
these relations can be interpreted in terms of the running of the three-body
counterterms that naturally emerge from proper renormalization. Finally, we
make predictions for recombination observables of a number of atomic systems
that are of experimental interest.


title: The magnetorotational instability in debris-disc gas

abstract:
  Debris discs are commonly swathed in gas which can be observed in UV, in fine
structure lines in FIR, and in resolved maps of CO emission. Carbon and oxygen
are overabundant in such gas, but it is severely depleted in hydrogen. As a
consequence, its ionisation fraction is remarkably high, suggesting
magnetohydrodynamic (MHD) processes may be important. In particular, the gas
may be subject to the magnetorotational instability (MRI), and indeed recent
modelling of $\beta$ Pictoris requires an anomalous viscosity to explain the
gas's observed radial structure. In this paper we explore the possibility that
the MRI is active in debris-disc gas and responsible for the observed mass
transport. We find that non-ideal MHD and dust-gas interactions play a
subdominant role, and that linear instability is viable at certain radii.
However, owing to low gas densities, the outer parts of the disc could be
stabilised by a weak ambient magnetic field, though it is difficult to
constrain such a field. Even if the MRI is stabilised by too strong a field, a
magnetocentrifugal wind may be launched in its place and this could lead to
equivalent (non-turbulent) transport. Numerical simulations of the vertically
stratified MRI in conditions appropriate to the debris disc gas should be able
to determine the nature of the characteristic behaviour at different radii, and
decide on the importance of the MRI (and MHD more generally) on the evolution
of these discs.


title: The Origin and Evolution of Saturn, with Exoplanet Perspective

abstract:
  Saturn formed beyond the snow line in the primordial solar nebula that made
it possible for it to accrete a large mass. Disk instability and core accretion
models have been proposed for Saturn's formation, but core accretion is favored
on the basis of its volatile abundances, internal structure, hydrodynamic
models, chemical characteristics of protoplanetary disk, etc. The observed
frequency, properties and models of exoplanets provide additional supporting
evidence for core accretion. The heavy elements with mass greater than 4He make
up the core of Saturn, but are presently poorly constrained, except for carbon.
The C/H ratio is super-solar, and twice that in Jupiter. The enrichment of
carbon and other heavy elements in Saturn and Jupiter requires special delivery
mechanisms for volatiles to these planets. In this chapter we will review our
current understanding of the origin and evolution of Saturn and its atmosphere,
using a multi-faceted approach that combines diverse sets of observations on
volatile composition and abundances, relevant properties of the moons and
rings, comparison with the other gas giant planet, Jupiter, analogies to the
extrasolar giant planets, as well as pertinent theoretical models.


title: On the multiferroic skyrmion-host GaV4S8

abstract:
  The lacunar spinel GaV4S8 exhibits orbital ordering at 44 K and shows a
complex magnetic phase diagram below 12.7 K, which includes ferromagnetic and
cycloidal spin order. At low but finite external magnetic fields, N\'eel-type
skyrmions are formed in this material. Skyrmions are whirl-like spin vortices
that have received great theoretical interest because of their non-trivial spin
topology and that are also considered as basic entities for new data-storage
technologies. Interestingly, we found that the orbitally ordered phase shows
sizable ferroelectric polarization and that excess spin-driven polarizations
appear in all magnetic phases, including the skyrmion-lattice phase. Hence,
GaV4S8 shows simultaneous magnetic and polar order and belongs to the class of
multiferroics, materials that attracted enormous attention in recent years.
Here, we summarize the existing experimental information on the magnetic,
electronic, and dielectric properties of GaV4S8. By performing detailed
magnetic susceptibility, resistivity, specific heat, and dielectric
experiments, we complement the low-temperature phase diagram. Specifically, we
show that the low-temperature and low-field ground state of GaV4S8 seems to
have a more complex spin configuration than purely collinear ferromagnetic spin
order. In addition, at the structural Jahn-Teller transition the magnetic
exchange interaction changes from antiferromagnetic to ferromagnetic. We also
provide experimental evidence that the vanadium V4 clusters in GaV4S8 can be
regarded as molecular units with spin 1/2. However, at high temperatures
deviations in the susceptibility show up, indicating that either the magnetic
moments of the vanadium atoms fluctuate independently or excited states of the
V4 molecule become relevant.


title:
Why is Compiling Lifted Inference into a Low-Level Language so
  Effective?

abstract:
  First-order knowledge compilation techniques have proven efficient for lifted
inference. They compile a relational probability model into a target circuit on
which many inference queries can be answered efficiently. Early methods used
data structures as their target circuit. In our KR-2016 paper, we showed that
compiling to a low-level program instead of a data structure offers orders of
magnitude speedup, resulting in the state-of-the-art lifted inference
technique. In this paper, we conduct experiments to address two questions
regarding our KR-2016 results: 1- does the speedup come from more efficient
compilation or more efficient reasoning with the target circuit?, and 2- why
are low-level programs more efficient target circuits than data structures?


title: A note on the spectrum of the Neumann Laplacian in periodic waveguides

abstract:
  We study the Neumann Laplacian $-\Delta^N$ restricted to a periodic
waveguide. In this situation its spectrum $\sigma(-\Delta^N)$ presents a band
structure. Our goal and strategy is to get spectral information from an
analysis of the asymptotic behavior of these bands provided that the waveguide
is sufficiently thin.


title: On the degree-wise coherence of FI_G-modules

abstract:
  In this work we study a kind of coherence condition on FI_G-modules, which
generalizes the usual notion of finite generation. We prove that a module is
coherent, in the appropriate sense, if and only if its generators, as well as
its torsion, appears in only finitely many degrees. Using this technical
result, we prove that the category of coherent FI_G-modules is abelian,
independent of any assumptions on the group G, or the coefficient ring k.
Following this, we consider applications towards the local cohomology theory of
FI_G-modules, introduced by Li and the author in previous work.


title:
Enumerating graded ideals in graded rings associated to free nilpotent
  Lie rings

abstract:
  We compute the zeta functions enumerating graded ideals in the graded Lie
rings associated with the free $d$-generator Lie rings $\mathfrak{f}_{c,d}$ of
nilpotency class $c$ for all $c\leq2$ and for $(c,d)\in\{(3,3),(3,2),(4,2)\}$.
We apply our computations to obtain information about $\mathfrak{p}$-adic,
reduced, and topological zeta functions, in particular pertaining to their
degrees and some special values.


title: V\'enus selon Ibn al-Shatir

abstract:
  We attempt to grasp the mathematics behind the planetary theories of the
Syrian astronomer Ibn al-Shatir (1304-1375) in his treatise Nihayat al-Sul.
Following the Maragha school of astronomers, by composing circular movements
with constant angular velocity, Ibn al-Shatir attains two goals. He eliminates
the need of excentrics and equant points in astronomy; but he also describes
longitudes and latitudes with a unique method, with no more orbs than what is
strictly necessary to the longitudes. A better understanding of rotation as a
spatial transformation enables this ultimate economy of thought. In our
commentary, we take Venus as an example offering an interesting problem about
the latitudes. It is the opportunity to give the edition of the chapter of the
Nihayat al-Sul dedicated to the latitudes of Mercury and Venus.


title: Heavy right-handed neutrino dark matter and PeV neutrinos at IceCube

abstract:
  We discuss a simple non-supersymmetric model based on the electroweak gauge
group $SU(2)_L\times SU(2)^\prime\times U(1)_{B-L}$ where the lightest of the
right-handed neutrinos, which are part of the leptonic doublet of
$SU(2)^\prime$, play the role of a long-lived unstable dark matter with mass in
the multi-PeV range. We use a resonant $s$-channel annihilation to obtain the
correct thermal relic density and relax the unitarity bound on dark matter
mass. In this model, there exists a 3-body dark matter decay mode producing tau
leptons and neutrinos, which could be the source for the PeV cascade events
observed in the IceCube experiment. The model can be tested with more precise
flavor information of the highest-energy neutrino events in future data.


title:
Sparsely Connected and Disjointly Trained Deep Neural Networks for Low
  Resource Behavioral Annotation: Acoustic Classification in Couples' Therapy

abstract:
  Observational studies are based on accurate assessment of human state. A
behavior recognition system that models interlocutors' state in real-time can
significantly aid the mental health domain. However, behavior recognition from
speech remains a challenging task since it is difficult to find generalizable
and representative features because of noisy and high-dimensional data,
especially when data is limited and annotated coarsely and subjectively. Deep
Neural Networks (DNN) have shown promise in a wide range of machine learning
tasks, but for Behavioral Signal Processing (BSP) tasks their application has
been constrained due to limited quantity of data. We propose a
Sparsely-Connected and Disjointly-Trained DNN (SD-DNN) framework to deal with
limited data. First, we break the acoustic feature set into subsets and train
multiple distinct classifiers. Then, the hidden layers of these classifiers
become parts of a deeper network that integrates all feature streams. The
overall system allows for full connectivity while limiting the number of
parameters trained at any time and allows convergence possible with even
limited data. We present results on multiple behavior codes in the couples'
therapy domain and demonstrate the benefits in behavior classification
accuracy. We also show the viability of this system towards live behavior
annotations.


title:
Evidence for a postreproductive phase in female false killer whales
  Pseudorca crassidens

abstract:
  A substantial period of life after reproduction ends, known as
postreproductive lifespan (PRLS), is at odds with classical life history
theory. Prolonged PRLS has been confirmed in only two non-human mammals, both
odontocete cetaceans. We investigate the evidence for PRLS in a third species,
the false killer whale, Pseudorca crassidens, using a quantitative measure of
PRLS and morphological evidence from reproductive tissue. We examined specimens
from false killer whales from combined strandings (South Africa, 1981) and
harvest (Japan 1979-80) and found morphological evidence of changes in the
activity of the ovaries in relation to age. Ovulation had ceased in 50% of
whales over 45 years, and all whales over 55 years old had ovaries classified
as postreproductive. We also calculated a measure of PRLS, known as
postreproductive representation (PrR) as an indication of the effect of
inter-population demographic variability. PrR for the combined sample was 0.14,
whereas the mean of the simulated distribution for PrR under the null
hypothesis of no PRLS was 0.02. The 99th percentile of the simulated
distribution was 0.08 and no simulated value exceeded 0.13. These results
suggest that PrR was convincingly different from the measures simulated under
the null hypothesis. We found morphological and statistical evidence for PRLS
in South African and Japanese pods of false killer whales, suggesting that this
species is the third non-human mammal in which this phenomenon has been
demonstrated in wild populations. Our estimates for PrR in false killer whales
(0.12-0.37) spanned the single values available for the short-finned pilot
whale (0.28) and the killer whale (0.22) and are comparable to estimates for
historical or hunter-gather human populations (0.3-0.47).


title:
Selection Rules for Non-Radiative Carrier Relaxation Processes in
  Semiconductor Quantum Dots

abstract:
  Time resolved intensity cross-correlation measurements of radiative cascades
are used for studying non-radiative relaxation processes of excited carriers
confined in semiconductor quantum dots. We spectrally identify indirect
radiative cascades which include intermediate phonon assisted relaxations. The
energy of the first photon reveals the multicarrier configuration prior to the
non-radiative relaxation, while the energy of the second photon reveals the
configuration after the relaxation. The intensity cross correlation
measurements thus provide quantitative measures of the non-radiative processes
and their selection rules. We construct a model which accurately describes the
experimental observations in terms of the electron-phonon and electron-hole
exchange interactions. Our measurements and model provide a new tool for
engineering relaxation processes in semiconductor nanostructures.


title:
Training variance and performance evaluation of neural networks in
  speech

abstract:
  In this work we study variance in the results of neural network training on a
wide variety of configurations in automatic speech recognition. Although this
variance itself is well known, this is, to the best of our knowledge, the first
paper that performs an extensive empirical study on its effects in speech
recognition. We view training as sampling from a distribution and show that
these distributions can have a substantial variance. These results show the
urgent need to rethink the way in which results in the literature are reported
and interpreted.


title:
Two-Dimensional Multiferroics: Ferroelasticity, Ferroelectricity, Domain
  Wall, and Potential Mechano-Opto-Electronic Applications

abstract:
  Low-dimensional multiferroic materials hold great promises in miniaturized
device applications such as nanoscale transducers, actuators, sensors,
photovoltaics, and nonvolatile memories. Here, using first-principles theory we
predict that two-dimensional (2D) monolayer Group IV monochalcogenides
including GeS, GeSe, SnS, and SnSe are a class of 2D semiconducting
multiferroics with strongly coupled giant in-plane spontaneous ferroelectric
polarization and spontaneous ferroelastic lattice strain that are
thermodynamically stable at room temperature and beyond, and can be effectively
modulated by elastic strain engineering. Their optical absorption spectra
exhibit strong in-plane anisotropy with visible-spectrum excitonic gaps and
sizable exciton binding energies, rendering the unique characteristics of
low-dimensional semiconductors. More importantly, the predicted low domain wall
energy and small migration barrier together with the coupled multiferroic order
and anisotropic electronic structures suggest their great potentials for
tunable multiferroic functional devices by manipulating external electrical,
mechanical, and optical field to control the internal responses, and enable the
development of four device concepts including 2D ferroelectric memory, 2D
ferroelastic memory, and 2D ferroelastoelectric nonvolatile photonic memory as
well as 2D ferroelectric excitonic photovoltaics.

categories: cond-mat.mtrl-sci cond-mat.mes-hall physics.comp-ph physics.optics


title: Quantum-coherent mixtures of causal relations

abstract:
  Understanding the causal influences that hold among parts of a system is
critical both to explaining that system's natural behaviour and to controlling
it through targeted interventions. In a quantum world, understanding causal
relations is equally important, but the set of possibilities is far richer. The
two basic ways in which a pair of time-ordered quantum systems may be causally
related are by a cause-effect mechanism or by a common cause acting on both.
Here, we show a coherent mixture of these two possibilities. We realize this
nonclassical causal relation in a quantum optics experiment and derive a set of
criteria for witnessing the coherence based on a quantum version of Berkson's
effect, whereby two independent causes can become correlated upon observation
of their common effect. The interplay of causality and quantum theory lies at
the heart of challenging foundational puzzles, including Bell's theorem and the
search for quantum gravity.


title: On global and local minimizers of prestrained thin elastic rods

abstract:
  We study the stable configurations of a thin three-dimensional weakly
prestrained rod subject to a terminal load as the thickness of the section
vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and
show that isolated local minimizers of the limit model can be approached by
local minimizers of the three-dimensional model. In the case of isotropic
materials and for two-layers prestrained three-dimensional models the limit
energy further simplifies to that of a Kirchhoff rod-model of an intrinsically
curved beam. In this case we study the limit theory and investigate global
and/or local stability of straight and helical configurations. Through some
simple simulations we finally compare our results with real experiments.


title:
On the local existence for an active scalar equation in critical
  regularity setting

abstract:
  In this note, we address the local well-posedness for the active scalar
equation $\partial_t \theta + u\cdot \nabla \theta =0$, where $u = -
\nabla^\perp(-\Delta)^{-1+\beta/2}\theta$. The local existence of solutions in
the Sobolev class $H^{1+\beta+\epsilon}$, where $\epsilon>0$ and $\beta \in
(1,2)$, has been recently addressed in \cite{HKZ}. The critical case $\epsilon
=0$ has remained open. Using a different technique, we prove the local
well-posedness in the Besov space $B^{1+\beta}_{2,1}$, where $\beta \in (1,2)$.
The proof is based on log-Lipschitz estimates for the transport equation.


title: CCD photometry of the Globular Cluster NGC 6093

abstract:
  In this paper we present photometric CCD observations of the globular cluster
NGC 6093 (M80) in filters B, V , R and I. We produce the colour-magnitude
diagrams for this object and obtain values for its metallicity [Fe/H],
reddening E(V-B), E(V-I) and distance modulus (m - M)_0.


title:
The Extraordinary Amount of Substructure in the Hubble Frontier Fields
  Cluster Abell 2744

abstract:
  We present a joint optical/X-ray analysis of the massive galaxy cluster Abell
2744 (z=0.308). Our strong- and weak-lensing analysis within the central region
of the cluster, i.e., at R<1Mpc from the brightest cluster galaxy, reveals
eight substructures, including the main core. All of these dark-matter halos
are detected with a significance of at least 5sigma and feature masses ranging
from 0.5 to 1.4x10^{14}Msun within R<150kpc. Merten et al. (2011) and
Medezinski et al. (2016) substructures are also detected by us. We measure a
slightly higher mass for the main core component than reported previously and
attribute the discrepancy to the inclusion of our tightly constrained
strong-lensing mass model built on Hubble Frontier Fields data. X-ray data
obtained by XMM-Newton reveal four remnant cores, one of them a new detection,
and three shocks. Unlike Merten et al. (2011), we find all cores to have both
dark and luminous counterparts. A comparison with clusters of similar mass in
the MXXL simulations yields no objects with as many massive substructures as
observed in Abell 2744, confirming that Abell 2744 is an extreme system. We
stress that these properties still do not constitute a challenge to
$\Lambda$CDM, as caveats apply to both the simulation and the observations: for
instance, the projected mass measurements from gravitational lensing and the
limited resolution of the sub-haloes finders. We discuss implications of Abell
2744 for the plausibility of different dark-matter candidates and, finally,
measure a new upper limit on the self-interaction cross-section of dark matter
of sigma_{DM}<1.28cm2/g(68\% CL), in good agreement with previous results from
Harvey et al. (2015).


title:
The role of galactic cold gas in low-level supermassive black hole
  activity

abstract:
  The nature of the relationship between low-level supermassive black hole
(SMBH) activity and galactic cold gas, if any, is currently unclear. Here, we
test whether central black holes may feed at higher rates in gas-rich galaxies,
probing SMBH activity well below the active regime down to Eddington ratios of
~1e-7. We use a combination of radio data from the ALFALFA survey and from the
literature, along with archival X-ray flux measurements from the Chandra X-ray
observatory, to investigate this potential relationship. We construct a sample
of 129 late-type galaxies, with MB<-18 out to 50 Mpc, that have both HI masses
and sensitive X-ray coverage. Of these, 75 host a nuclear X-ray source, a 58%
detection fraction. There is a highly significant correlation between nuclear
X-ray luminosity LX and galaxy stellar mass Mstar with a slope of 1.7+/-0.3,
and a tentative correlation (significant at the 2.8 sigma level) between LX and
HI gas mass MHI. However, a joint fit to LX as a function of both Mstar and MHI
finds no significant dependence on MHI (slope 0.1+/00.3), and similarly the
residuals of LX-LX(Mstar) show no trend with MHI; the apparent correlation
between LX and MHI seems to be entirely driven by Mstar. We demonstrate
quantitatively that these results are robust against X-ray binary
contamination. We conclude that the galaxy-wide cold gas content in these
spirals does not strongly correlate with their low-level supermassive black
hole activity, and suggest fueling is a localized process.


title: Vaidya Spacetime for Galileon Gravity's Rainbow

abstract:
  In this paper, we analyze Vaidya spacetime with an energy dependent metric in
Galileon gravity's rainbow. This will be done using the rainbow functions which
are motivated from the results obtained in loop quantum gravity approach and
non-commutative geometry. We will investigate the Gravitational collapse in
this Galileon gravity's rainbow. We will discuss the behavior of singularities
formed from the gravitational collapse in this rainbow deformed Galileon
gravity.


title: Fusion and braiding in finite and affine Temperley-Lieb categories

abstract:
  Finite Temperley-Lieb (TL) algebras are diagram-algebra quotients of (the
group algebra of) the famous Artin's braid group $B_N$, while the affine TL
algebras arise as diagram algebras from a generalized version of the braid
group. We study asymptotic `$N\to\infty$' representation theory of these
quotients (parametrized by $q\in\mathbb{C}^{\times}$) from a perspective of
braided monoidal categories. Using certain idempotent subalgebras in the finite
and affine algebras, we construct infinite `arc' towers of the diagram algebras
and the corresponding direct system of representation categories, with terms
labeled by $N\in\mathbb{N}$. The corresponding direct-limit category is our
main object of studies.
  For the case of the finite TL algebras, we prove that the direct-limit
category is abelian and highest-weight at any $q$ and endowed with braided
monoidal structure. The most interesting result is when $q$ is a root of unity
where the representation theory is non-semisimple. The resulting braided
monoidal categories we obtain at different roots of unity are new and
interestingly they are not rigid. We observe then a fundamental relation of
these categories to a certain representation category of the Virasoro algebra
and give a conjecture on the existence of a braided monoidal equivalence
between the categories. This should have powerful applications to the study of
the `continuum' limit of critical statistical mechanics systems based on the TL
algebra.
  We also introduce a novel class of embeddings for the affine Temperley-Lieb
algebras and related new concept of fusion or bilinear $\mathbb{N}$-graded
tensor product of modules for these algebras. We prove that the fusion rules
are stable with the index $N$ of the tower and prove that the corresponding
direct-limit category is endowed with an associative tensor product. We also
study the braiding properties of this affine TL fusion.

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


title: The two-dimensional Jacobian Conjecture and unique factorization

abstract:
  The two-dimensional Jacobian Conjecture says that a $\mathbb{C}$-algebra
endomorphism $F:\mathbb{C}[x,y] \to \mathbb{C}[x,y]$ that has an invertible
Jacobian is an automorphism. We show that if a $\mathbb{C}$-algebra
endomorphism $F:\mathbb{C}[x,y] \to \mathbb{C}[x,y]$ has an invertible Jacobian
and if $v \in \mathbb{C}[F(x),F(y),x]$ is a product of prime elements of
$\mathbb{C}[F(x),F(y),x]$, then $F$ is an automorphism, where $v$ is such that
$y = u/v$, where $u \in \mathbb{C}[F(x),F(y),x]$.


title: Nondegenerate $2 \times k \times (k+1)$ Hypermatrices

abstract:
  We construct an extension of Gaussian elimination to show that if
$\mathbb{F}$ is a topological field, then there is a transitive, free, and
continuous action of a natural quotient of $GL_k(\mathbb{F}) \times
GL_{k+1}(\mathbb{F})$ on the set $M_k(\mathbb{F})$ of $2 \times k \times (k+1)$
hypermatrices over $\mathbb{F}$ with nonzero hyperdeterminant.
  We use this action to answer a number of questions including determining the
homotopy groups of $M_k(\mathbb{C})$, counting elements of $M_k(\mathbb{F}_q)$
(generalizing an unpublished result of Lewis and Sam), and computing
hyperdeterminants for $2 \times k \times (k+1)$ hypermatrices in $O(k^4)$ time,
which we use to compute explicit formulas in some special cases.


title: On functions without a normal order

abstract:
  The method of Tur\'an in establishing the normal order for the number of
prime divisors of a number is used to show that a certain class of arithmetic
functions do not have a normal order.


title:
Thermosensitive Cu2O-PNIPAM core-shell nanoreactors with tunable
  photocatalytic activity

abstract:
  We report a facile and novel method for the fabrication of Cu2O@PNIPAM
core-shell nanoreactors using Cu2O nanocubes as the core. The PNIPAM shell not
only effectively protects the Cu2O nanocubes from oxidation, but also improves
the colloidal stability of the system. The Cu2O@PNIPAM core-shell microgels can
work efficiently as photocatalyst for the decomposition of methyl orange under
visible light. A significant enhancement in the catalytic activity has been
observed for the core-shell microgels compared with the pure Cu2O nanocubes.
Most importantly, the photocatalytic activity of the Cu2O nanocubes can be
further tuned by the thermosensitive PNIPAM shell, as rationalized by our
recent theory.


title:
Efficient adaptation of complex-valued noiselet sensing matrices for
  compressed single-pixel imaging

abstract:
  Minimal mutual coherence of discrete noiselets and Haar wavelets makes this
pair of bases an essential choice for the measurement and compression matrices
in compressed-sensing-based single-pixel detectors. In this paper we propose an
efficient way of using complex-valued and non-binary noiselet functions for
object sampling in single-pixel cameras with binary spatial light modulators
and incoherent illumination. The proposed method allows to determine m complex
noiselet coefficients from m+1 binary sampling measurements. Further, we
introduce a modification to the complex fast noiselet transform, which enables
computationally-efficient real-time generation of the binary noiselet-based
patterns using efficient integer calculations on bundled patterns. The proposed
method is verified experimentally with a single-pixel camera system using a
binary spatial light modulator.


title:
O VI Emission Imaging of a Galaxy with the Hubble Space Telescope: a
  Warm Gas Halo Surrounding the Intense Starburst SDSS J115630.63+500822.1

abstract:
  We report results from a new HST study of the OVI 1032,1038\AA\ doublet in
emission around intensely star-forming galaxies. The programme aims to
characterize the energy balance in starburst galaxies and gas cooling in the
difficult-to-map coronal temperature regime of 2-5 x $10^5$K. We present the
first resolved image of gas emission in the OVI line. Our target, SDSS
J1156+5008, is very compact in the continuum but displays OVI emission to radii
of 23 kpc. The surface brightness profile is well fit by an exponential with a
scale of 7.5kpc. This is ten times the size of the photoionized gas, and we
estimate that 1/6 the total OVI luminosity comes from resonantly scattered
continuum radiation. Spectroscopy - which closely resembles a stacked sample of
archival spectra - confirms the OVI emission, and determines the column density
and outflow velocity from blueshifted absorption. The combination of
measurements enables several new calculations with few assumptions. The OVI
regions fill only ~$10^{-3}$ of the volume. By comparing the cooling time with
the cloud sound-crossing time, the cooling distance with the size, and the
pressure in the OVI and nebular gas, we conclude that the OVI-bearing gas
cannot have been lifted to the scale height at this temperature, and must be
cooling in situ through this coronal temperature regime. The coronal phase
contains ~1% of the ionized mass, and its kinetic energy is currently ~1% of
the budget set by supernova feedback. However a much larger amount of the gas
must have cooled through this phase during the star formation episode. The
outflow exceeds the escape velocity and the gas may become unbound, but it will
recombine before it escapes and become visible to Lyman (and OI) spectroscopy.
The mapping of this gas represents a crucial step in further constraining
galaxy formation scenarios and guiding the development of future satellites.


title: Linearity of Holographic Entanglement Entropy

abstract:
  We consider the question of whether the leading contribution to the
entanglement entropy in holographic CFTs is truly given by the expectation
value of a linear operator as is suggested by the Ryu-Takayanagi formula. We
investigate this property by computing the entanglement entropy, via the
replica trick, in states dual to superpositions of macroscopically distinct
geometries and find it consistent with evaluating the expectation value of the
area operator within such states. However, we find that this fails once the
number of semi-classical states in the superposition grows exponentially in the
central charge of the CFT. Moreover, in certain such scenarios we find that the
choice of surface on which to evaluate the area operator depends on the density
matrix of the entire CFT. This nonlinearity is enforced in the bulk via the
homology prescription of Ryu-Takayanagi. We thus conclude that the homology
constraint is not a linear property in the CFT. We also discuss the existence
of entropy operators in general systems with a large number of degrees of
freedom.


title:
A DECam Search for an Optical Counterpart to the LIGO Gravitational Wave
  Event GW151226

abstract:
  We report the results of a Dark Energy Camera (DECam) optical follow-up of
the gravitational wave (GW) event GW151226, discovered by the Advanced LIGO
detectors. Our observations cover 28.8 deg$^2$ of the localization region in
the $i$ and $z$ bands (containing 3% of the BAYESTAR localization probability),
starting 10 hours after the event was announced and spanning four epochs at
$2-24$ days after the GW detection. We achieve $5\sigma$ point-source limiting
magnitudes of $i\approx21.7$ and $z\approx21.5$, with a scatter of $0.4$ mag,
in our difference images. Given the two day delay, we search this area for a
rapidly declining optical counterpart with $\gtrsim 3\sigma$ significance
steady decline between the first and final observations. We recover four
sources that pass our selection criteria, of which three are cataloged AGN. The
fourth source is offset by $5.8$ arcsec from the center of a galaxy at a
distance of 187 Mpc, exhibits a rapid decline by $0.5$ mag over $4$ days, and
has a red color of $i-z\approx 0.3$ mag. These properties roughly match the
expectations for a kilonova. However, this source was detected several times,
starting $94$ days prior to GW151226, in the Pan-STARRS Survey for Transients
(dubbed as PS15cdi) and is therefore unrelated to the GW event. Given its
long-term behavior, PS15cdi is likely a Type IIP supernova that transitioned
out of its plateau phase during our observations, mimicking a kilonova-like
behavior. We comment on the implications of this detection for contamination in
future optical follow-up observations.


title:
Detection and localization of continuous gravitational waves with pulsar
  timing arrays: the role of pulsar terms

abstract:
  A pulsar timing array is a Galactic-scale detector of nanohertz gravitational
waves (GWs). Its target signals contain two components: the `Earth term' and
the `pulsar term' corresponding to GWs incident on the Earth and pulsar
respectively. In this work we present a Frequentist method for the detection
and localization of continuous waves that takes into account the pulsar term
and is significantly faster than existing methods. We investigate the role of
pulsar terms by comparing a full-signal search with an Earth-term-only search
for non-evolving black hole binaries. By applying the method to synthetic data
sets, we find that (i) a full-signal search can slightly improve the detection
probability (by about five percent); (ii) sky localization is biased if only
Earth terms are searched for and the inclusion of pulsar terms is critical to
remove such a bias; (iii) in the case of strong detections (with
signal-to-noise ratio $\gtrsim$ 30), it may be possible to improve pulsar
distance estimation through GW measurements.


title:
A close look at secular evolution: Boxy/peanut bulges reduce gas inflow
  to the central kiloparsec

abstract:
  In this letter we investigate the effect of boxy/peanut (b/p) bulges on
bar-induced gas inflow to the central kiloparsec, which plays a crucial role on
the evolution of disc galaxies. We carry out hydrodynamic gas response
simulations in realistic barred galaxy potentials, including or not the
geometry of a b/p bulge, to investigate the amount of gas inflow induced in the
different models. We find that b/p bulges can reduce the gas inflow rate to the
central kiloparsec by more than an order of magnitude, which leads to a
reduction in the amount of gas available in the central regions. We also
investigate the effect of the dark matter halo concentration on these results,
and find that for maximal discs, the effect of b/p bulges on gas inflow remains
significant. The reduced amount of gas reaching the central regions due to the
presence of b/p bulges could have significant repercussions on the formation of
discy- (pseudo-) bulges, on the amount of nuclear star formation and feedback,
on the fuel reservoir for AGN activity, and on the overall secular evolution of
galaxies.


title:
Search for light scalar dark matter with atomic gravitational wave
  detectors

abstract:
  We show that gravitational wave detectors based on a type of atom
interferometry are sensitive to ultralight scalar dark matter. Such dark matter
can cause temporal oscillations in fundamental constants with a frequency set
by the dark matter mass, and amplitude determined by the local dark matter
density. The result is a modulation of atomic transition energies. This signal
is ideally suited to a type of gravitational wave detector that compares two
spatially separated atom interferometers referenced by a common laser. Such a
detector can improve on current searches for electron-mass or electric-charge
modulus dark matter by up to 10 orders of magnitude in coupling, in a frequency
band complementary to that of other proposals. It demonstrates that this class
of atomic sensors is qualitatively different from other gravitational wave
detectors, including those based on laser interferometry. By using
atomic-clock-like interferometers, laser noise is mitigated with only a single
baseline. These atomic sensors can thus detect scalar signals in addition to
tensor signals.


title:
Effect of long-range hopping and interactions on entanglement dynamics
  and many-body localization

abstract:
  We numerically investigate the dynamics of entanglement in a chain of
spinless fermions with nonrandom but long-range hopping and interactions, and
with random on-site energies. For moderate disorder in the absence of
interactions, the chain hosts delocalized states at the top of the band which
undergo a delocalization-localization transition with increasing disorder. We
find an interesting regime in this noninteracting disordered chain where the
long-time entanglement entropy scales as $S(t) \sim \ln t$ and the saturated
entanglement entropy scales with system size $L$ as $S(L,t \to {\infty}) \sim
\ln L$. We further study the interplay of long-range hopping and interactions
on the growth of entanglement and the many-body localization (MBL) transition
in this system. We develop an analogy to higher-dimensional short-range systems
to compare and contrast such behavior with the physics of MBL in a higher
dimension.


title: Dirac Neutrinos and Dark Matter Stability from Lepton Quarticity

abstract:
  We propose to relate dark matter stability to the possible Dirac nature of
neutrinos. The idea is illustrated in a simple scheme where small Dirac
neutrino masses arise from a type--I seesaw mechanism as a result of a $Z_4$
discrete lepton number symmetry. The latter implies the existence of a viable
WIMP dark matter candidate, whose stability arises from the same symmetry which
ensures the Diracness of neutrinos.


title:
Classification of symmetry fractionalization in gapped $\mathbb Z_2$
  spin liquids

abstract:
  In quantum spin liquids, fractional spinon excitations carry half-integer
spins and other fractional quantum numbers of lattice and time-reversal
symmetries. Different patterns of symmetry fractionalization distinguish
different spin liquid phases. In this work, we derive a general constraint on
the symmetry fractionalization of spinons in a gapped spin liquid, realized in
a system with an odd number of spin-$1/2$ per unit cell. In particular, when
applied to kagome/triangular lattices, we obtain a complete classification of
symmetric gapped $\mathbb{Z_2}$ spin liquids.


title:
The scatter and evolution of the global hot gas properties of simulated
  galaxy cluster populations

abstract:
  We use the cosmo-OWLS suite of cosmological hydrodynamical simulations to
investigate the scatter and evolution of the global hot gas properties of large
simulated populations of galaxy groups and clusters. Our aim is to compare the
predictions of different physical models and to explore the extent to which
commonly-adopted assumptions in observational analyses (e.g. self-similar
evolution) are violated. We examine the relations between (true) halo mass and
the X-ray temperature, X-ray luminosity, gas mass, Sunyaev-Zel'dovich (SZ)
flux, the X-ray analogue of the SZ flux ($Y_X$) and the hydrostatic mass. For
the most realistic models, which include AGN feedback, the slopes of the
various mass-observable relations deviate substantially from the self-similar
ones, particularly at late times and for low-mass clusters. The amplitude of
the mass-temperature relation shows negative evolution with respect to the
self-similar prediction (i.e. slower than the prediction) for all models,
driven by an increase in non-thermal pressure support at higher redshifts. The
AGN models predict strong positive evolution of the gas mass fractions at low
halo masses. The SZ flux and $Y_X$ show positive evolution with respect to
self-similarity at low mass but negative evolution at high mass. The scatter
about the relations is well approximated by log-normal distributions, with
widths that depend mildly on halo mass. The scatter decreases significantly
with increasing redshift. The exception is the hydrostatic mass-halo mass
relation, for which the scatter increases with redshift. Finally, we discuss
the relative merits of various hot gas-based mass proxies.


title: Asymptotic Freedom versus Open/Closed Duality in Large-N QCD

abstract:
  The solution of the large-N 't Hooft limit of QCD is universally believed to
be a String Theory of Closed Strings in the Glueball Sector and of Open Strings
in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of
QCD with massless quarks, or more generally, that the large-N limit of a vast
class of confining, i.e. with a Mass Gap in the Glueball Sector,
asymptotically-free Gauge Theories coupled to matter fields with no mass scale
in perturbation theory cannot be a canonically-defined String Theory of Closed
and Open Strings, i.e. admitting Open/Closed Duality. The no-go theorem occurs
because Open/Closed Duality, implying that the ultraviolet divergences of
annulus diagrams in the Open Sector arise from infrared divergences of tadpoles
of massless particles in the Closed Sector, turns out to be incompatible with
the existence of the Mass Gap in the Glueball Sector of confining
asymptotically-free theories with no mass scale in perturbation theory in
which, as for example in QCD, the first coefficient of the beta function for 't
Hooft gauge coupling gets $1/N$ corrections due to the matter fields. Moreover,
we suggest a way-out to the no-go theorem on the basis of a new non-canonical
construction of the String S-matrix for asymptotically-free Gauge Theories such
as large-N QCD, involving Topological Strings on Non-Commutative Twistor Space.


title: Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase

abstract:
  We analyze the interplay of longitudinal and transverse fluctuations in a
$U(1)$ symmetric two-dimensional $\phi^4$-theory. To this end, we derive
coupled renormalization group equations for both types of fluctuations obtained
from a linear (cartesian) decomposition of the order parameter field.
Discarding the longitudinal fluctuations, the expected
Berezinskii-Kosterlitz-Thouless (BKT) phase characterized by a finite stiffness
and an algebraic decay of order parameter correlations is recovered.
Renormalized by transverse fluctuations, the longitudinal mass scales to zero,
so that longitudinal fluctuations become increasingly important for small
momenta. Within our expansion of the effective action, they generate a
logarithmic decrease of the stiffness, in agreement with previous functional
renormalization group calculations. The logarithmic terms imply a deviation
from the vanishing beta-function for the stiffness in the non-linear sigma
model describing the phase fluctuations at three-loop order. To gain further
insight, we also compute the flow of the parameters characterizing longitudinal
and transverse fluctuations from a density-phase representation of the order
parameter field, with a cutoff on phase fluctuations. The power-law flow of the
longitudinal mass and other quantities is thereby confirmed, but the stiffness
remains finite in this approach. We conclude that the marginal flow of the
stiffness obtained in the cartesian representation is an artifact of the
truncated expansion of momentum dependences.

categories: cond-mat.stat-mech cond-mat.quant-gas cond-mat.supr-con hep-th


title: The Frontier Fields Lens Modeling Comparison Project

abstract:
  Gravitational lensing by clusters of galaxies offers a powerful probe of
their structure and mass distribution. Deriving a lens magnification map for a
galaxy cluster is a classic inversion problem and many methods have been
developed over the past two decades to solve it. Several research groups have
developed techniques independently to map the predominantly dark matter
distribution in cluster lenses. While these methods have all provided
remarkably high precision mass maps, particularly with exquisite imaging data
from the Hubble Space Telescope (HST), the reconstructions themselves have
never been directly compared. In this paper, we report the results of comparing
various independent lens modeling techniques employed by individual research
groups in the community. Here we present for the first time a detailed and
robust comparison of methodologies for fidelity, accuracy and precision. For
this collaborative exercise, the lens modeling community was provided simulated
cluster images -- of two clusters Ares and Hera -- that mimic the depth and
resolution of the ongoing HST Frontier Fields. The results of the submitted
reconstructions with the un-blinded true mass profile of these two clusters are
presented here. Parametric, free-form and hybrid techniques have been deployed
by the participating groups and we detail the strengths and trade-offs in
accuracy and systematics that arise for each methodology. We note in conclusion
that lensing reconstruction methods produce reliable mass distributions that
enable the use of clusters as extremely valuable astrophysical laboratories and
cosmological probes.


title: An electroweak basis for neutrinoless double $\beta$ decay

abstract:
  A discovery of neutrinoless double-$\beta$ decay would be profound, providing
the first direct experimental evidence of $\Delta L=2$ lepton number violating
processes. While a natural explanation is provided by an effective Majorana
neutrino mass, other new physics interpretations should be carefully evaluated.
At low--energies such new physics could manifest itself in the form of color
and $SU(2)_L \times U(1)_{Y}$ invariant higher dimension operators. Here we
determine a complete set of electroweak invariant dimension--9 operators, and
our analysis supersedes those that only impose $U(1)_{em}$ invariance. Imposing
electroweak invariance implies: 1) a significantly reduced set of leading order
operators compared to only imposing $U(1)_{em}$ invariance; and 2) other
collider signatures. Prior to imposing electroweak invariance we find a minimal
basis of 24 dimension-9 operators, which is reduced to 11 electroweak invariant
operators at leading order in the expansion in the Higgs vacuum expectation
value. We set up a systematic analysis of the hadronic realization of the
4-quark operators using chiral perturbation theory, and apply it to determine
which of these operators have long-distance pion enhancements at leading order
in the chiral expansion. We also find at dimension--11 and dimension--13 the
electroweak invariant operators that after electroweak symmetry breaking
produce the remaining $\Delta L=2$ operators that would appear at dimension--9
if only $U(1)_{em}$ is imposed.


title:
Settling the complexity of computing approximate two-player Nash
  equilibria

abstract:
  We prove that there exists a constant $\epsilon>0$ such that, assuming the
Exponential Time Hypothesis for PPAD, computing an $\epsilon$-approximate Nash
equilibrium in a two-player (nXn) game requires quasi-polynomial time,
$n^{\log^{1-o(1)} n}$. This matches (up to the o(1) term) the algorithm of
Lipton, Markakis, and Mehta [LMM03].
  Our proof relies on a variety of techniques from the study of
probabilistically checkable proofs (PCP); this is the first time that such
ideas are used for a reduction between problems inside PPAD.
  En route, we also prove new hardness results for computing Nash equilibria in
games with many players. In particular, we show that computing an
$\epsilon$-approximate Nash equilibrium in a game with n players requires
$2^{\Omega(n)}$ oracle queries to the payoff tensors. This resolves an open
problem posed by Hart and Nisan [HN13], Babichenko [Bab14], and Chen et al.
[CCT15]. In fact, our results for n-player games are stronger: they hold with
respect to the $(\epsilon,\delta)$-WeakNash relaxation recently introduced by
Babichenko et al. [BPR16].


title:
TMAC: A Toolbox of Modern Async-Parallel, Coordinate, Splitting, and
  Stochastic Methods

abstract:
  TMAC is a toolbox written in C++11 that implements algorithms based on a set
of modern methods for large-scale optimization. It covers a variety of
optimization problems, which can be both smooth and nonsmooth, convex and
nonconvex, as well as constrained and unconstrained. The algorithms implemented
in TMAC, such as the coordinate up- date method and operator splitting method,
are scalable as they decompose a problem into simple subproblems. These
algorithms can run in a multi-threaded fashion, either synchronously or
asynchronously, to take advantages of all the cores available. TMAC
architecture mimics how a scientist writes down an optimization algorithm.
Therefore, it is easy for one to obtain a new algorithm by making simple
modifications such as adding a new operator and adding a new splitting, while
maintaining the multicore parallelism and other features. The package is
available at https://github.com/uclaopt/TMAC.


title:
A New Approach to Dimensionality Reduction for Anomaly Detection in Data
  Traffic

abstract:
  The monitoring and management of high-volume feature-rich traffic in large
networks offers significant challenges in storage, transmission and
computational costs. The predominant approach to reducing these costs is based
on performing a linear mapping of the data to a low-dimensional subspace such
that a certain large percentage of the variance in the data is preserved in the
low-dimensional representation. This variance-based subspace approach to
dimensionality reduction forces a fixed choice of the number of dimensions, is
not responsive to real-time shifts in observed traffic patterns, and is
vulnerable to normal traffic spoofing. Based on theoretical insights proved in
this paper, we propose a new distance-based approach to dimensionality
reduction motivated by the fact that the real-time structural differences
between the covariance matrices of the observed and the normal traffic is more
relevant to anomaly detection than the structure of the training data alone.
Our approach, called the distance-based subspace method, allows a different
number of reduced dimensions in different time windows and arrives at only the
number of dimensions necessary for effective anomaly detection. We present
centralized and distributed versions of our algorithm and, using simulation on
real traffic traces, demonstrate the qualitative and quantitative advantages of
the distance-based subspace approach.


title:
Fast Reconstruction Algorithm for Perturbed Compressive Sensing Based on
  Total Least-Squares and Proximal Splitting

abstract:
  We consider the problem of finding a sparse solution for an underdetermined
linear system of equations when the known parameters on both sides of the
system are subject to perturbation. This problem is particularly relevant to
reconstruction in fully-perturbed compressive-sensing setups where both the
projected measurements of an unknown sparse vector and the knowledge of the
associated projection matrix are perturbed due to noise, error, mismatch, etc.
We propose a new iterative algorithm for tackling this problem. The proposed
algorithm utilizes the proximal-gradient method to find a sparse total
least-squares solution by minimizing an l1-regularized Rayleigh-quotient cost
function. We determine the step-size of the algorithm at each iteration using
an adaptive rule accompanied by backtracking line search to improve the
algorithm's convergence speed and preserve its stability. The proposed
algorithm is considerably faster than a popular previously-proposed algorithm,
which employs the alternating-direction method and coordinate-descent
iterations, as it requires significantly fewer computations to deliver the same
accuracy. We demonstrate the effectiveness of the proposed algorithm via
simulation results.


title:
Interaction-Driven Distinctive Electronic States of Artificial Atoms at
  the ZnO Interface

abstract:
  We have investigated the electronic states of planar quantum dots at the ZnO
interface containing a few interacting electrons in an externally applied
magnetic field. In these systems, the electron-electron interaction effects are
expected to be much stronger than in traditional semiconductor quantum systems,
such as in GaAs or InAs quantum dots. In order to highlight that stronger
Coulomb effects in the ZnO quantum dots, we have compared the energy spectra
and the magnetization in this system to those of the InAs quantum dots. We have
found that in the ZnO quantum dots, the signatures of stronger Coulomb
interaction manifests in an unique ground state that has very different
properties than the corresponding ones in the InAs dot. Our results for the
magnetization also exhibits behaviors never before observed in a quantum dot:
We have found a stronger temperature dependence and other unexpected features,
such as paramagnetic-like behavior at high temperatures for a quantum-dot
helium.


title: Cycle transversal flag domains of Hodge type

abstract:
  Flag domains are open orbits of real semisimple Lie groups in flag manifolds
of their complexification. A special class of flag domains constitute the
classifying spaces for variations of Hodge structure, namely period domains or
more generally Mumford-Tate domains. In this paper we classify all proper,
equivariant embeddings of a flag domain of Hodge type, required to satisfy a
certain transversality condition, in a period domain and show that any such
flag domain must be a Hermitian symmetric space of non-compact type of
classical type. In particular, the classification describes also the proper,
equivariant embeddings of a flag domain of Hodge type in a period domain
satisfying Griffiths transversality.


title:
HAT-P-47b AND HAT-P-48b: Two Low Density Sub-Saturn-Mass Transiting
  Planets on the Edge of the Period--Mass Desert

abstract:
  We report the discovery of two new transiting extrasolar planets orbiting
moderately bright (V = 10.7 and 12.2 mag) F stars (masses of 1.39 Msun and 1.10
Msun, respectively). The planets have periods of P = 4.7322 d and 4.4087 d, and
masses of 0.21 MJ and 0.17 MJ which are almost half-way between those of
Neptune and Saturn. With radii of 1.31 RJ and 1.13 RJ, these very low density
planets are the two lowest mass planets with radii in excess that of Jupiter.
Comparing with other recent planet discoveries, we find that sub-Saturns
(0.18MJ < Mp < 0.3MJ) and super-Neptunes (0.05MJ < Mp < 0.18MJ) exhibit a wide
range of radii, and their radii exhibit a weaker correlation with irradiation
than higher mass planets. The two planets are both suitable for measuring the
Rossiter-McLaughlin effect and for atmospheric characterization. Measuring the
former effect would allow an interesting test of the theory that star-planet
tidal interactions are responsible for the tendency of close-in giant planets
around convective envelope stars to be on low obliquity orbits. Both planets
fall on the edge of the short period Neptunian desert in the semi-major
axis-mass plane.


title:
Flexible superconducting Nb transmission lines on thin film polyimide
  for quantum computing applications

abstract:
  We describe progress and initial results achieved towards the goal of
developing integrated multi-conductor arrays of shielded controlled-impedance
flexible superconducting transmission lines with ultra-miniature cross sections
and wide bandwidths (dc to >10 GHz) over meter-scale lengths. Intended
primarily for use in future scaled-up quantum computing systems, such flexible
thin-film Nb/polyimide ribbon cables provide a physically compact and ultra-low
thermal conductance alternative to the rapidly increasing number of discrete
coaxial cables that are currently used by quantum computing experimentalists to
transmit signals between the low-temperature stages (from ~ 4 K down to ~ 20
mK) of a dilution refrigerator. S-parameters are presented for 2-metal layer Nb
microstrip structures with lengths ranging up to 550 mm. Weakly coupled
open-circuit microstrip resonators provided a sensitive measure of the overall
transmission line loss as a function of frequency, temperature, and power. Two
common polyimide dielectrics, one conventional and the other photo-definable
(PI-2611 and HD-4100, respectively) were compared. Our most striking result,
not previously reported to our knowledge, was that the dielectric loss tangents
of both polyimides are remarkably low at deep cryogenic temperatures, typically
100$\times$ smaller than corresponding room temperature values. This enables
fairly long-distance transmission of microwave signals without excessive
attenuation and permits usefully high rf power levels to be transmitted without
creating excessive dielectric heating. We observed loss tangents as low as
2.2$\times$10$^{-5}$ at 20 mK. Our fabrication techniques could be extended to
more complex structures such as multiconductor, multi-layer stripline or
rectangular coax, and integrated attenuators and thermalization structures.