title: Absence of Binding in the Nelson and Piezoelectric Polaron Models

abstract:
  In the context of the massless Nelson model, we prove that two
non-relativistic nucleons interacting with a massless meson field do not bind
when a sufficiently strong Coulomb repulsion between the nucleons is added to
the Hamiltonian. The result holds for both the renormalized and unrenormalized
theories, and can also be applied to the so-called piezoelectric polaron model,
which describes an electron interacting with the acoustical vibrational modes
of a crystal through the piezoelectric interaction. The result can then be
interpreted as well as a no-binding statement about piezoelectric bipolarons.
The methods used allow also for a significant reduction of about 30% over
previously known no-binding conditions for the optical bipolaron model of H.
Fr\"ohlich.


title: Symmetries and Critical Phenomena in Fluids

abstract:
  We show that given an initial vorticity which is bounded and $m$-fold
rotationally symmetric for $m \ge 3$, there is a unique global solution to the
2D Euler equation on the whole plane. That is, in the well-known $L^1 \cap
L^\infty$ theory of Yudovich, the $L^1$ assumption can be dropped upon having
an appropriate symmetry condition. This contains a class of radially
homogeneous solutions to the 2D Euler equation, which gives rise to a new 1D
fluid model. We discuss several interesting properties of this 1D system. Using
this framework, we construct time quasi-periodic solutions to the 2D Euler
equation exhibiting pendulum-like behavior. We also exhibit solutions with
compact support for which angular derivatives grow linearly in time or
exponential in time (the latter being in the presence of a boundary). A similar
study can be done for the surface quasi-geostrophic (SQG) equation. Using the
same symmetry condition, we prove local existence and uniqueness of solutions
which are merely Lipschitz continuous near the origin - though, without the
symmetry, Lipschitz initial data is expected to lose its Lipschitz continuity
immediately. Once more, a special class of radially homogeneous solutions is
considered and we extract a 1D model which bears great resemblance to the
so-called De Gregorio model. We then show that finite-time singularity
formation for the 1D model implies finite-time singularity formation in the
class of Lipschitz solutions to the SQG equation which are compact support.
While the study of special infinite energy solutions to fluid models is
classical, this appears to be the first case where they can be embedded into a
natural existence/uniqueness class for the equation. Moreover, these special
solutions approximate finite-energy solutions for long time and have a direct
bearing on the global regularity problem for finite-energy solutions.


title: Integration by differentiation: new proofs, methods and examples

abstract:
  Recently, new methods were introduced which allow one to solve ordinary
integrals by performing only derivatives. These studies were originally
motivated by the difficulties of the quantum field theoretic path integral, and
correspondingly, the results were derived by heuristic methods. Here, we give
rigorous proofs for the methods to hold on fully specified function spaces. We
then illustrate the efficacy of the new methods by applying them to the study
of the surprising behavior of so-called Borwein integrals.


title:
On the Control of Affine Systems with Safety Constraints: Relaxed
  In-Block Controllability

abstract:
  We consider affine systems defined on polytopes and study the cases where the
systems are not in-block controllable with respect to the given polytopes. That
are the cases in which we cannot fully control the affine systems within the
interior of a given polytope, representing the intersection of given safety
constraints. Instead, we introduce in this paper the notion of relaxed in-block
controllability (RIBC), which can be useful for the cases where one can
distinguish between soft and hard safety constraints. In particular, we study
whether all the states in the interior of a given polytope, formed by the
intersection of soft safety constraints, are mutually accessible through the
interior of a given bigger polytope, formed by the intersection of hard safety
constraints, by applying uniformly bounded control inputs. By exploring the
geometry of the problem, we provide necessary conditions for RIBC. We then show
when these conditions are also sufficient. Several illustrative examples are
also given to clarify the main results.


title: Feature-Augmented Neural Networks for Patient Note De-identification

abstract:
  Patient notes contain a wealth of information of potentially great interest
to medical investigators. However, to protect patients' privacy, Protected
Health Information (PHI) must be removed from the patient notes before they can
be legally released, a process known as patient note de-identification. The
main objective for a de-identification system is to have the highest possible
recall. Recently, the first neural-network-based de-identification system has
been proposed, yielding state-of-the-art results. Unlike other systems, it does
not rely on human-engineered features, which allows it to be quickly deployed,
but does not leverage knowledge from human experts or from electronic health
records (EHRs). In this work, we explore a method to incorporate
human-engineered features as well as features derived from EHRs to a
neural-network-based de-identification system. Our results show that the
addition of features, especially the EHR-derived features, further improves the
state-of-the-art in patient note de-identification, including for some of the
most sensitive PHI types such as patient names. Since in a real-life setting
patient notes typically come with EHRs, we recommend developers of
de-identification systems to leverage the information EHRs contain.


title:
Sounds of Failure: Passive Acoustic Measurements of Excited Vibrational
  Modes

abstract:
  Granular materials can fail through spontaneous events like earthquakes or
brittle fracture. However, measurements and analytic models which forecast
failure in this class of materials, while of both fundamental and practical
interest, remain elusive. Materials including numerical packings of spheres,
colloidal glasses, and granular materials have been known to develop an excess
of low-frequency vibrational modes as the confining pressure is reduced. Here,
we report experiments on sheared granular materials in which we monitor the
evolving density of excited modes via passive monitoring of acoustic emissions.
We observe a broadening of the distribution of excited modes coincident with
both bulk and local plasticity, and clear evolution in the shape of the
distribution before and after bulk failure. These results provide a new
interpretation of the changing state of the material on its approach to
stick-slip failure.


title: Breuil-Kisin Modules via crystalline cohomology

abstract:
  For a perfect field $k$ of characteristic $p>0$ and a smooth and proper
formal scheme $\mathscr{X}$ over the ring of integers of a finite and totally
ramified extension $K$ of $W(k)[1/p]$, we propose a cohomological construction
of the Breuil-Kisin modules attached to the $p$-adic \'etale cohomology
$H^i_{\mathrm{\'et}}(\mathscr{X}_{\overline{K}},\mathbf{Z}_p)$. We then prove
that our proposal works when $p>2$, $i < p-1$, and the crystalline cohomology
of the special fiber of $\mathscr{X}$ is torsion-free in degrees $i$ and $i+1$.


title: Shape phase mixing in critical point nuclei

abstract:
  Spectral properties of nuclei near the critical point of the quantum phase
transition between spherical and axially symmetric shapes are studied in a
hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid
collective conditions through a rigidity parameter. The model in the lower and
upper limits of the rigidity parameter recovers the X(5) and X(3) solutions
respectively, while in the equally mixed case it corresponds to the X(4)
critical point symmetry. Numerical applications of the model on nuclei from
regions known for critical behavior reveal a sizable shape phase mixing and its
evolution with neutron or proton numbers. The model also enables a better
description of energy spectra and electromagnetic transitions for these nuclei.


title: Complete Monopole Dominance of the Static Quark Potential

abstract:
  In earlier work, we used a gauge independent Abelian Decomposition to show
that Abelian degrees of freedom are wholly responsible for the static quark
potential. The restricted Abelian field can be split into two terms, a Maxwell
term and a $\theta$ (Dirac) term. The $\theta$ term's contribution to the
string tension can be analysed theoretically and numerically, and arises
because of the existence of a certain type of monopole. While the Abelian field
can be constructed without gauge fixing, its two component parts are
gauge-dependent, with a gauge transformation moving the topological features
from one part to another. This allows us to isolate and identify the
topological objects responsible for confinement by constructing a gauge where
the $\theta$ term wholly accounts for the string tension. We confirm the
presence of these monopoles in lattice simulations of SU(2) Yang-Mills theory.


title:
Blue Straggler Star Populations in Globular Clusters: II. Proper-Motion
  Cleaned HST Catalogs of BSSs in 38 Galactic GCs

abstract:
  We present new Blue Straggler Star (BSS) catalogs in 38 Milky Way globular
clusters (GCs) based on multi-passband and multi-epoch treasury survey data
from the Hubble Space Telescope. We measure precise astrometry and relative
proper motions of stars in all target clusters and performed a subsequent
cluster membership selection. We study the accuracy of our proper motion
measurements using estimates of central velocity dispersions and find very good
agreement with previous studies in the literature. Finally, we present a
homogeneous BSS selection method, that expands the classic BSS selection
parameter space to more evolved BSS evolutionary stages. We apply this method
to the proper-motion cleaned GC star catalogs in order to define proper-motion
cleaned BSS catalogs in all 38 GCs, which we make publicly available to enable
further study and follow-up observations.


title:
Time-Resolved Studies of the Spin-Transfer Reversal Mechanism in
  Perpendicularly Magnetized Magnetic Tunnel Junctions

abstract:
  Pulsed spin-torque switching has been studied using single-shot time-resolved
electrical measurements in perpendicularly magnetized magnetic tunnel junctions
as a function of pulse amplitude and junction size in 50 to 100 nm diameter
circular junctions. The mean switching time depends inversely on pulse
amplitude for all junctions studied. However, the switching dynamics is found
to be strongly dependent on junction size and pulse amplitude. In 50 nm
diameter junctions the switching onset is stochastic but the switching once
started, is fast; after being initiated it takes less than 2 ns to switch. In
larger diameter junctions the time needed for complete switching is strongly
dependent on the pulse amplitude, reaching times less than 2 ns at large pulse
amplitudes. Anomalies in the switching rate versus pulse amplitude are shown to
be associated with the long lived (> 2 ns) intermediate junction resistance
states.


title:
The Jacquet-Langlands correspondence for overconvergent Hilbert modular
  forms

abstract:
  We use results by Chenevier to interpolate the classical Jacquet-Langlands
correspondence for Hilbert modular forms, which gives us an extension of
Chenevier's results to totally real fields. From this we obtain an isomorphisms
between eigenvarieties attached Hilbert modular forms and those attached to
modular forms on a totally definite quaternion algebra over a totally real
field of even degree.


title:
Real-Time Image Distortion Correction: Analysis and Evaluation of
  FPGA-Compatible Algorithms

abstract:
  Image distortion correction is a critical pre-processing step for a variety
of computer vision and image processing algorithms. Standard real-time software
implementations are generally not suited for direct hardware porting, so
appropriated versions need to be designed in order to obtain implementations
deployable on FPGAs. In this paper, hardware-compatible techniques for image
distortion correction are introduced and analyzed in details. The considered
solutions are compared in terms of output quality by using a
geometrical-error-based approach, with particular emphasis on robustness with
respect to increasing lens distortion. The required amount of hardware
resources is also estimated for each considered approach.


title:
Remnant of binary black-hole mergers: New simulations and peak
  luminosity studies

abstract:
  We present the results of 61 new simulations of nonprecessing spinning black
hole binaries with mass ratios $q=m_1/m_2$ in the range $1/3\leq q\leq1$ and
individual spins covering the parameter space $-0.85\leq\alpha_{1,2}\leq0.85$.
We additionally perform 10 new simulations of nonspinning black hole binaries
with mass ratios covering the range $1/6\leq q<1$. We follow the evolution for
typically the last ten orbits before merger down to the formation of the final
remnant black hole. This allows for assessment of the accuracy of our previous
empirical formulae for relating the binary parameters to the remnant final
black hole mass, spin and recoil. We use the new simulation to improve the fit
to the above remnant formulae and add a formula for the peak luminosity of
gravitational waves, produced around the merger of the two horizons into one.
We find excellent agreement (typical errors $\sim0.1-0.2\%$) for the mass and
spin, and within $\sim5\%$ for the recoil and peak luminosity. These formulae
have direct application to parameter estimation techniques applied to LIGO
observations of gravitational waves from binary black hole mergers.


title:
Pricing variance swaps with stochastic volatility and stochastic
  interest rate under full correlation structure

abstract:
  This paper considers the case of pricing discretely-sampled variance swaps
under the class of equity-interest rate hybridization. Our modeling framework
consists of the equity which follows the dynamics of the Heston stochastic
volatility model, and the stochastic interest rate is driven by the
Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among
the state variables. This full correlation structure possess the limitation to
have fully analytical pricing formula for hybrid models of variance swaps, due
to the non-affinity property embedded in the model itself. We address this
issue by obtaining an efficient semi-closed form pricing formula of variance
swaps for an approximation of the hybrid model via the derivation of
characteristic functions. Subsequently, we implement numerical experiments to
evaluate the accuracy of our pricing formula. Our findings confirmed that the
impact of the correlation between the underlying and the interest rate is
significant for pricing discretely-sampled variance swaps.


title: On the equivalence of quaternionic contact structures

abstract:
  Following the Cartans's original method of equivalence supported by methods
of parabolic geometry, we provide a complete solution for the equivalence
problem of quaternionic contact structures, that is, the problem of finding a
complete system of differential invariants for two quaternionic contact
manifolds to be locally diffeomorphic. This includes an explicit construction
of the corresponding Cartan geometry and detailed information on all curvature
components.


title: Doubly Convolutional Neural Networks

abstract:
  Building large models with parameter sharing accounts for most of the success
of deep convolutional neural networks (CNNs). In this paper, we propose doubly
convolutional neural networks (DCNNs), which significantly improve the
performance of CNNs by further exploring this idea. In stead of allocating a
set of convolutional filters that are independently learned, a DCNN maintains
groups of filters where filters within each group are translated versions of
each other. Practically, a DCNN can be easily implemented by a two-step
convolution procedure, which is supported by most modern deep learning
libraries. We perform extensive experiments on three image classification
benchmarks: CIFAR-10, CIFAR-100 and ImageNet, and show that DCNNs consistently
outperform other competing architectures. We have also verified that replacing
a convolutional layer with a doubly convolutional layer at any depth of a CNN
can improve its performance. Moreover, various design choices of DCNNs are
demonstrated, which shows that DCNN can serve the dual purpose of building more
accurate models and/or reducing the memory footprint without sacrificing the
accuracy.


title: Symmetry-protected zero-mode laser with a tunable spatial profile

abstract:
  We propose to utilize symmetry-protected zero modes of a photonic lattice to
realize a single-mode, fixed-frequency, and spatially tunable laser. These
properties are the consequence of the underlying non-Hermitian particle-hole
symmetry, with which the energy spectrum satisfies
$\varepsilon_m=-\varepsilon_n^*$. Unlike in the Hermitian case, the symmetric
phase of particle-hole symmetry is no longer restricted to $\varepsilon=0$ but
extends along the imaginary-$\varepsilon$ axis, which is set by the
single-cavity frequency and symmetry-protected against position and coupling
disorder of the photonic lattice. By selectively pumping different cavities in
the photonic lattice, we control the spontaneous symmetry restoration process,
which provides a convenient method to tune the spatial profile of the laser
without changing its frequency.


title: Hamiltonian and symplectic symmetries: an introduction

abstract:
  Classical mechanical systems are modeled by a symplectic manifold
$(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on
$M$ by diffeomorphisms that preserves $\omega$. These actions, which are called
"symplectic", have been studied in the past forty years, following the works of
Atiyah, Delzant, Duistermaat, Guillemin, Heckman, Kostant, Souriau, and
Sternberg in the 1970s and 1980s on symplectic actions of compact abelian Lie
groups that are, in addition, of "Hamiltonian" type, i.e. they also satisfy
Hamilton's equations. Since then a number of connections with combinatorics,
finite dimensional integrable Hamiltonian systems, more general symplectic
actions, and topology, have flourished. In this paper we review classical and
recent results on Hamiltonian and non Hamiltonian symplectic group actions
roughly starting from the results of these authors. The paper also serves as a
quick introduction to the basics of symplectic geometry.


title: Surface plastic flow in polishing of rough surfaces

abstract:
  We report electron microscopy observations of the surface plastic flow in
polishing of rough metal surfaces with a controlled spherical asperity
structure. We show that asperity--abrasive sliding contacts exhibit viscous
behavior, where the material flows in the form of thin fluid-like layers.
Subsequent bridging of these layers among neighboring asperities result in
progressive surface smoothening. Our study provides new phenomenological
insights into the long-debated mechanism of polishing. The observations are of
broad relevance in tribology and materials processing.


title:
Evolutionary Fields Can Explain Patterns of High Dimensional Complexity
  in Ecology

abstract:
  One of the properties that make ecological systems so unique is the range of
complex behavioural patterns that can be exhibited by even the simplest
communities with only a few species. Much of this complexity is commonly
attributed to stochastic factors which have very high-degrees of freedom.
Orthodox study of the evolution of these simple networks has generally been
limited in its ability to explain complexity, since it restricts evolutionary
adaptation to an inertia-free process with few degrees of freedom in which only
gradual, moderately complex behaviours are possible. We propose a model
inspired by particle mediated field phenomena in classical physics in
combination with fundamental concepts in adaptation, that suggests that small
but high-dimensional chaotic dynamics near to the adaptive trait optimum could
help explain complex properties shared by most ecological datasets, such as
aperiodicity and pink, fractal noise spectra. By examining a simple
predator-prey model and appealing to real ecological data, we show that this
type of complexity could be easily confused for or confounded by stochasticity,
especially when spurred on or amplified by stochastic factors that share
variational and spectral properties with the underlying dynamics.


title:
Lee monoids are non-finitely based while the sets of their isoterms are
  finitely based

abstract:
  We establish a new sufficient condition under which a monoid is non-finitely
based and apply this condition to Lee monoids $L_\ell^1$, obtained by adjoining
an identity element to the semigroup generated by two idempotents $a$ and $b$
subjected to the relation $0=abab \cdots$ (length $\ell$).
  We show that every monoid which generates a variety containing $L_5^1$ and is
contained in the variety generated by $L_\ell^1$ for some $\ell \ge 5$ is
non-finitely based. We establish this result by analyzing $\tau$-terms for $M$
where $\tau$ is certain non-trivial congruence on the free semigroup, that is,
we analyze words $\bf u$ with the property that ${\bf u} \tau {\bf v}$ whenever
$M$ satisfies an identity ${\bf u} \approx {\bf v}$.
  We also show that if $\tau$ is the trivial congruence on the free semigroup
and $\ell \le 5$ then the $\tau$-terms (isoterms) for $L_\ell^1$ carry no
information about the non-finite basis property of $L_\ell^1$.


title:
Represent, Aggregate, and Constrain: A Novel Architecture for Machine
  Reading from Noisy Sources

abstract:
  In order to extract event information from text, a machine reading model must
learn to accurately read and interpret the ways in which that information is
expressed. But it must also, as the human reader must, aggregate numerous
individual value hypotheses into a single coherent global analysis, applying
global constraints which reflect prior knowledge of the domain.
  In this work we focus on the task of extracting plane crash event information
from clusters of related news articles whose labels are derived via distant
supervision. Unlike previous machine reading work, we assume that while most
target values will occur frequently in most clusters, they may also be missing
or incorrect.
  We introduce a novel neural architecture to explicitly model the noisy nature
of the data and to deal with these aforementioned learning issues. Our models
are trained end-to-end and achieve an improvement of more than 12.1 F$_1$ over
previous work, despite using far less linguistic annotation. We apply factor
graph constraints to promote more coherent event analyses, with belief
propagation inference formulated within the transitions of a recurrent neural
network. We show this technique additionally improves maximum F$_1$ by up to
2.8 points, resulting in a relative improvement of $50\%$ over the previous
state-of-the-art.


title:
A compact linear accelerator based on a scalable
  microelectromechanical-system RF-structure

abstract:
  A new approach for a compact radio-frequency (RF) accelerator structure is
presented. The new accelerator architecture is based on the Multiple
Electrostatic Quadrupole Array Linear Accelerator (MEQALAC) structure that was
first developed in the 1980s. The MEQALAC utilized RF resonators producing the
accelerating fields and providing for higher beam currents through parallel
beamlets focused using arrays of electrostatic quadrupoles (ESQs). While the
early work obtained ESQs with lateral dimensions on the order of a few
centimeters, using printed circuits board (PCB), we reduce the characteristic
dimension to the millimeter regime, while massively scaling up the potential
number of parallel beamlets. Using Microelectromechanical systems scalable
fabrication approaches, we are working on further reducing the characteristic
dimension to the sub-millimeter regime. The technology is based on
RF-acceleration components and ESQs implemented in PCB or silicon wafers where
each beamlet passes through beam apertures in the wafer. The complete
accelerator is then assembled by stacking these wafers. This approach has the
potential for fast and inexpensive batch fabrication of the components and
flexibility in system design for application specific beam energies and
currents. For prototyping the accelerator architecture, the components have
been fabricated using PCB. In this paper, we present proof of concept results
of the principal components using PCB: RF acceleration and ESQ focusing.
Ongoing developments on implementing components in silicon and scaling of the
accelerator technology to high currents and beam energies are discussed.


title:
Likelihood Inference for Large Scale Stochastic Blockmodels with
  Covariates based on a Divide-and-Conquer Parallelizable Algorithm with
  Communication

abstract:
  We consider a stochastic blockmodel equipped with node covariate information,
that is helpful in analyzing social network data. The key objective is to
obtain maximum likelihood estimates of the model parameters. For this task, we
devise a fast, scalable Monte Carlo EM type algorithm based on case-control
approximation of the log-likelihood coupled with a subsampling approach. A key
feature of the proposed algorithm is its parallelizability, by processing
portions of the data on several cores, while leveraging communication of key
statistics across the cores during each iteration of the algorithm. The
performance of the algorithm is evaluated on synthetic data sets and compared
with competing methods for blockmodel parameter estimation. We also illustrate
the model on data from a Facebook derived social network enhanced with node
covariate information.


title:
A new construction for the shortest non-trivial element in the lower
  central series

abstract:
  We provide a new upper bound for the length for the shortest non-trivial
element in the lower central series $\gamma_n(\mathbb{F}_2)$ of the free group
on two generators. We prove that it has an asymptotic behaviour of the form
$O(n^{\log_{\varphi}(2)})$, where $\varphi=1.618...$ is the golden ratio. This
new technique is used to provide new estimates on the length of laws for finite
groups and on almost laws for compact groups.


title: The Multi-fidelity Multi-armed Bandit

abstract:
  We study a variant of the classical stochastic $K$-armed bandit where
observing the outcome of each arm is expensive, but cheap approximations to
this outcome are available. For example, in online advertising the performance
of an ad can be approximated by displaying it for shorter time periods or to
narrower audiences. We formalise this task as a multi-fidelity bandit, where,
at each time step, the forecaster may choose to play an arm at any one of $M$
fidelities. The highest fidelity (desired outcome) expends cost
$\lambda^{(m)}$. The $m^{\text{th}}$ fidelity (an approximation) expends
$\lambda^{(m)} < \lambda^{(M)}$ and returns a biased estimate of the highest
fidelity. We develop MF-UCB, a novel upper confidence bound procedure for this
setting and prove that it naturally adapts to the sequence of available
approximations and costs thus attaining better regret than naive strategies
which ignore the approximations. For instance, in the above online advertising
example, MF-UCB would use the lower fidelities to quickly eliminate suboptimal
ads and reserve the larger expensive experiments on a small set of promising
candidates. We complement this result with a lower bound and show that MF-UCB
is nearly optimal under certain conditions.


title:
Asymptotic expansions of the Helmholtz equation solutions using
  approximations of the Dirichlet to Neumann operator

abstract:
  This paper is concerned with the asymptotic expansions of the amplitude of
the solution of the Helmholtz equation. The original expansions were obtained
using a pseudo-differential decomposition of the Dirichlet to Neumann operator.
This work uses first and second order approximations of this operator to derive
new asymptotic expressions of the normal derivative of the total field. The
resulting expansions can be used to appropriately choose the ansatz in the
design of high-frequency numerical solvers, such as those based on integral
equations, in order to produce more accurate approximation of the solutions
around the shadow and deep shadow regions than the ones based on the usual
ansatz.


title:
An Inexact Spingarn's Partial Inverse Method with Applications to
  Operator Splitting and Composite Optimization

abstract:
  We propose and study the iteration-complexity of an inexact version of the
Spingarn's partial inverse method. Its complexity analysis is performed by
viewing it in the framework of the hybrid proximal extragradient (HPE) method,
for which pointwise and ergodic iteration-complexity has been established
recently by Monteiro and Svaiter. As applications, we propose and analyze the
iteration-complexity of an inexact operator splitting algorithm -- which
generalizes the original Spingarn's splitting method -- and of a parallel
forward-backward algorithm for multi-term composite convex optimization.


title: Restricting Specht modules of cyclotomic Hecke algebras

abstract:
  This paper proves that the restriction of a Specht module for a (degenerate
or non-degenerate) cyclotomic Hecke algebra, or KLR algebra, of type A has a
Specht filtration.


title: Active Learning from Imperfect Labelers

abstract:
  We study active learning where the labeler can not only return incorrect
labels but also abstain from labeling. We consider different noise and
abstention conditions of the labeler. We propose an algorithm which utilizes
abstention responses, and analyze its statistical consistency and query
complexity under fairly natural assumptions on the noise and abstention rate of
the labeler. This algorithm is adaptive in a sense that it can automatically
request less queries with a more informed or less noisy labeler. We couple our
algorithm with lower bounds to show that under some technical conditions, it
achieves nearly optimal query complexity.


title: Trapping planar Brownian motion in a non circular trap

abstract:
  Brownian motion in the plane in the presence of a "trap" at which motion is
stopped is studied. If the trap $T$ is a connected compact set, it is shown
that the probability for planar Brownian motion to hit this set before a given
time $t$ is well approximated even at short times by the probability that
Brownian motion hits a disk of radius $r_T$ equal to the conformal radius of
the trap $T$.


title:
Reconstructing protein and gene phylogenies by extending the framework
  of reconciliation

abstract:
  The architecture of eukaryotic coding genes allows the production of several
different protein isoforms by genes. Current gene phylogeny reconstruction
methods make use of a single protein product per gene, ignoring information on
alternative protein isoforms. These methods often lead to inaccurate gene tree
reconstructions that require to be corrected before being used in phylogenetic
tree reconciliation analyses or gene products phylogeny reconstructions. Here,
we propose a new approach for the reconstruction of accurate gene trees and
protein trees accounting for the production of alternative protein isoforms by
the genes of a gene family. We extend the concept of reconciliation to protein
trees, and we define a new reconciliation problem called MinDRGT that consists
in finding a gene tree that minimizes a double reconciliation cost with a given
protein tree and a given species tree. We define a second problem called
MinDRPGT that consists in finding a protein tree and a gene tree minimizing a
double reconciliation cost, given a species tree and a set of protein subtrees.
We provide algorithmic exact and heuristic solutions for some versions of the
problems, and we present the results of an application to the correction of
gene trees from the Ensembl database. An implementation of the heuristic method
is available at https://github.com/UdeS-CoBIUS/Protein2GeneTree.


title: PCA meets RG

abstract:
  A system with many degrees of freedom can be characterized by a covariance
matrix; principal components analysis (PCA) focuses on the eigenvalues of this
matrix, hoping to find a lower dimensional description. But when the spectrum
is nearly continuous, any distinction between components that we keep and those
that we ignore becomes arbitrary; it then is natural to ask what happens as we
vary this arbitrary cutoff. We argue that this problem is analogous to the
momentum shell renormalization group (RG). Following this analogy, we can
define relevant and irrelevant operators, where the role of dimensionality is
played by properties of the eigenvalue density. These results also suggest an
approach to the analysis of real data. As an example, we study neural activity
in the vertebrate retina as it responds to naturalistic movies, and find
evidence of behavior controlled by a nontrivial fixed point. Applied to
financial data, our analysis separates modes dominated by sampling noise from a
smaller but still macroscopic number of modes described by a non--Gaussian
distribution.

categories: physics.bio-ph cond-mat.stat-mech q-bio.NC q-bio.QM


title:
Model-free bounds on Value-at-Risk using extreme value information and
  statistical distances

abstract:
  We derive bounds on the distribution function, therefore also on the
Value-at-Risk, of $\varphi(\mathbf X)$ where $\varphi$ is an aggregation
function and $\mathbf X = (X_1,\dots,X_d)$ is a random vector with known
marginal distributions and partially known dependence structure. More
specifically, we analyze three types of available information on the dependence
structure: First, we consider the case where extreme value information, such as
the distributions of partial minima and maxima of $\mathbf X$, is available. In
order to include this information in the computation of Value-at-Risk bounds,
we utilize a reduction principle that relates this problem to an optimization
problem over a standard Fr\'echet class, which can then be solved by means of
the rearrangement algorithm or using analytical results. Second, we assume that
the copula of $\mathbf X$ is known on a subset of its domain, and finally we
consider the case where the copula of $\mathbf X$ lies in the vicinity of a
reference copula as measured by a statistical distance. In order to derive
Value-at-Risk bounds in the latter situations, we first improve the
Fr\'echet--Hoeffding bounds on copulas so as to include this additional
information on the dependence structure. Then, we translate the improved
Fr\'echet--Hoeffding bounds to bounds on the Value-at-Risk using the so-called
improved standard bounds. In numerical examples we illustrate that the
additional information typically leads to a significant improvement of the
bounds compared to the marginals-only case.


title: Community detection with nodal information

abstract:
  Community detection is one of the fundamental problems in the study of
network data. Most existing community detection approaches only consider edge
information as inputs, and the output could be suboptimal when nodal
information is available. In such cases, it is desirable to leverage nodal
information for the improvement of community detection accuracy. Towards this
goal, we propose a flexible network model incorporating nodal information, and
develop likelihood-based inference methods. For the proposed methods, we
establish favorable asymptotic properties as well as efficient algorithms for
computation. Numerical experiments show the effectiveness of our methods in
utilizing nodal information across a variety of simulated and real network data
sets.


title:
A deep convolutional neural network using directional wavelets for
  low-dose X-ray CT reconstruction

abstract:
  Due to the potential risk of inducing cancers, radiation dose of X-ray CT
should be reduced for routine patient scanning. However, in low-dose X-ray CT,
severe artifacts usually occur due to photon starvation, beamhardening, etc,
which decrease the reliability of diagnosis. Thus, high quality reconstruction
from low-dose X-ray CT data has become one of the important research topics in
CT community. Conventional model-based denoising approaches are, however,
computationally very expensive, and image domain denoising approaches hardly
deal with CT specific noise patterns. To address these issues, we propose an
algorithm using a deep convolutional neural network (CNN), which is applied to
wavelet transform coefficients of low-dose CT images. Specifically, by using a
directional wavelet transform for extracting directional component of artifacts
and exploiting the intra- and inter-band correlations, our deep network can
effectively suppress CT specific noises. Moreover, our CNN is designed to have
various types of residual learning architecture for faster network training and
better denoising. Experimental results confirm that the proposed algorithm
effectively removes complex noise patterns of CT images, originated from the
reduced X-ray dose. In addition, we show that wavelet domain CNN is efficient
in removing the noises from low-dose CT compared to an image domain CNN. Our
results were rigorously evaluated by several radiologists and won the second
place award in 2016 AAPM Low-Dose CT Grand Challenge. To the best of our
knowledge, this work is the first deep learning architecture for low-dose CT
reconstruction that has been rigorously evaluated and proven for its efficacy.


title: Revitalized automatic proofs: demonstrations

abstract:
  We consider three problems from the recent issues of the American
Mathematical Monthly involving different versions of Catalan triangle. Our main
results offer generalizations of these identities and demonstrate automated
proofs with additional twists, and on occasion we furnish a combinatorial
proof.


title: Why are normal sub-Riemannian extremals locally minimizing?

abstract:
  It is well-known that normal extremals in sub-Riemannian geometry are curves
which locally minimize the energy functional. Most proofs of this fact do not
make, however, an explicit use of relations between local optimality and the
geometry of the problem. In this paper, we provide a new proof of that
classical result, which gives insight into direct geometric reasons of local
optimality. Also the relation of the regularity of normal extremals with their
optimality becomes apparent in our approach.


title: RKFD Methods - a short review

abstract:
  In this paper, a recently published method [Hussain, Ismail, Senua, Solving
directly special fourth-order ordinary differential equations using Runge-Kutta
type method, J. Comput. Appl. Math. 306 (2016) 179-199] for solving
fourth-order ordinary differential equations is summarized and reviewed. An
independant implementation of one of the published methods is also tested and
benchmarked against the RK4 method.


title: A New Polar Decomposition in a Scalar Product Space

abstract:
  There are various definitions of right and left polar decompositions of an
$m\times n$ matrix $F \in \mathbb{K}^{m\times n}$ (where
$\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$) with respect to bilinear or
sesquilinear products defined by nonsingular matrices $M\in \mathbb{K}^{m\times
m}$ and $N\in \mathbb{K}^{n\times n}$. The existence and uniqueness of such
decompositions under various assumptions on $F$, $M$, and $N$ have been
studied. Here we introduce a new form of right and left polar decompositions,
$F=WS$ and $F=S'W'$, respectively, where the matrix $W$ has orthonormal columns
($W'$ has orthonormal rows) with respect to suitably defined scalar products
which are functions of $M$, $N$, and $F$, and the matrix $S$ is selfadjoint
with respect to the same suitably defined scalar products and has eigenvalues
only in the open right half-plane. We show that our right and left
decompositions exist and are unique for any nonsingular matrices $M$ and $N$
when the matrix $F$ satisfies $(F^{[M,N]})^{[N,M]}=F$ and $F^{[M,N]}F$
($FF^{[M,N]}$, respectively) is nonsingular, where $F^{[M,N]}=N^{-1} F^\# M$
with $F^\#=F^T$ for real or complex bilinear forms and $F^\#=\bar{F}^T$ for
sesquilinear forms. When $M=N$, our results apply to nonsingular square
matrices $F$. Our assumptions on $F$, $M$, and $N$ are in some respects weaker
and in some respects stronger than those of previous work on polar
decompositions.


title: Coxeter categories and quantum groups

abstract:
  We define the notion of braided Coxeter category, which is informally a
tensor category carrying compatible, commuting actions of a generalised braid
group B_W and Artin's braid groups B_n on the tensor powers of its objects. The
data which defines the action of B_W bears a formal similarity to the
associativity constraints in a monoidal category, but is related to the
coherence of a family of fiber functors. We show that the quantum Weyl group
operators of a quantised Kac-Moody algebra U_h(g), together with the universal
R-matrices of its Levi subalgebras, give rise to a braided Coxeter structure on
integrable, category O-modules for U_h(g). By relying on the 2-categorical
extension of Etingof-Kazhdan quantisation obtained in arXiv:1610.09744, we then
prove that this structure can be transferred to integrable, category
O-representations of g. These results are used in arXiv:1512.03041 to give a
monodromic description of the quantum Weyl group operators of U_h(g) which
extends the one obtained by the second author for a semisimple Lie algebra.


title: Factorizations into Normal Matrices in Indefinite Inner Product Spaces

abstract:
  We show that any nonsingular (real or complex) square matrix can be
factorized into a product of at most three normal matrices, one of which is
unitary, another selfadjoint with eigenvalues in the open right half-plane, and
the third one is normal involutory with a neutral negative eigenspace (we call
the latter matrices normal neutral involutory). Here the words normal, unitary,
selfadjoint and neutral are understood with respect to an indefinite inner
product.


title: An Exploration of Graphical Password Authentication for Children

abstract:
  In this paper, we explore graphical passwords as a child-friendly alternative
for user authentication. We evaluate the usability of three variants of the
PassTiles graphical password scheme for children, and explore the similarities
and differences in performance and preferences between children and adults
while using these schemes. Children were most successful at recalling passwords
containing images of distinct objects. Both children and adults prefer
graphical passwords to their existing schemes, but password memorization
strategies differ considerably between the two groups. Based on our findings,
we provide recommendations for designing more child-friendly authentication
schemes.


title: A 2-categorical extension of Etingof-Kazhdan quantisation

abstract:
  Let k be a field of characteristic zero. Etingof and Kazhdan constructed a
quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice
of an associator Phi. They prove moreover that this quantisation is functorial
in b. Remarkably, the quantum group U_h(b) is endowed with a Tannakian
equivalence F_b from the braided tensor category of Drinfeld-Yetter modules
over b, with deformed associativity constraints given by Phi, to that of
Drinfeld-Yetter modules over U_h(b). In this paper, we prove that the
equivalence F_b is functorial in b.


title:
A new method for computing the expected hitting time between arbitrary
  different configurations of the multiple-urn Ehrenfest model

abstract:
  We study a multiple-urn version of the Ehrenfest model. In this setting, we
denote the n urns by Urn 1 to Urn n, where n>=2. Initially, M balls are
randomly placed in the n urns. At each subsequent step, a ball is selected and
put into the other n-1 urns with equal probability. The expected hitting time
leading to a change of the M balls' status is computed using the method of
stopping times. As a corollary, we obtain the expected hitting time of moving
all the M balls from Urn 1 to Urn 2. This proves a conjecture which was
recently made in Chen et al.(2017).


title:
Delta isobars in relativistic mean-field models with $\sigma$-scaled
  hadron masses and couplings

abstract:
  We extend the relativistic mean-field models with hadron masses and
meson-baryon coupling constants dependent on the scalar $\sigma$ field, studied
previously to incorporate $\Delta(1232)$ baryons. Available empirical
information is analyzed to put constraints on the couplings of $\Delta$s with
meson fields. Conditions for the appearance of $\Delta$s are studied. We
demonstrate that with inclusion of the $\Delta$s our equations of state
continue to fulfill majority of known empirical constraints including the
pressure-density constraint from heavy-ion collisions, the constraint on the
maximum mass of the neutron stars, the direct Urca and the gravitational-baryon
mass ratio constraints.


title:
Almost Sure Existence of Global Weak Solutions to the 3D Incompressible
  Navier-Stokes Equation

abstract:
  In this paper we prove the almost sure existence of global weak solution to
the 3D incompressible Navier-Stokes Equation for a set of large data in
$\dot{H}^{-\alpha}(\mathbb{R}^{3})$ or $\dot{H}^{-\alpha}(\mathbb{T}^{3})$ with
$0<\alpha\leq 1/2$. This is achieved by randomizing the initial data and
showing that the energy of the solution modulus the linear part keeps finite
for all $t\geq0$. Moreover, the energy of the solutions is also finite for all
$t>0$. This improves the recent result of Nahmod, Pavlovi\'{c} and Staffilani
on (SIMA, [1])in which $\alpha$ is restricted to $0<\alpha<\frac{1}{4}$.


title:
Scalar quanta in Fermi liquids: zero sounds, instabilities, Bose
  condensation, and a metastable state in dilute nuclear matter

abstract:
  Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a
local scalar interaction is investigated for various values and momentum
dependence of the scalar Landau parameter $f_0$ in the particle-hole channel.
For $f_0 >0$ the conditions are found when the phase velocity on the spectrum
of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$
there are only damped excitations, and for $f_0<-1$ the spectrum becomes
unstable against a growth of scalar-mode excitations. An effective Lagrangian
for the scalar excitation modes is derived after performing a bosonization
procedure. We demonstrate that the instability may be tamed by the formation of
a static Bose condensate of the scalar modes. The condensation may occur in a
homogeneous or inhomogeneous state relying on the momentum dependence of the
scalar Landau parameter. We show that in the isospin-symmetric nuclear matter
there may appear a metastable state at a subsaturation nuclear density owing to
the condensate. Then we consider a possibility of the condensation of the
zero-sound-like excitations in a state with a non-zero momentum in Fermi
liquids moving with overcritical velocities, provided an appropriate momentum
dependence of the Landau parameter $f_0 (k)>0$. We also argue that in
peripheral heavy-ion collisions the Pomeranchuk instability may occur already
for $f_0 >-1$.


title:
Spin-orbit interaction in InAs/GaSb heterostructures quantified by weak
  antilocalization

abstract:
  We study the spin-orbit interaction (SOI) in InAs/ GaSb and InAs quantum
wells. We show through temperature- and gate-dependent magnetotransport
measurements of weak antilocalization that the dominant spin-orbit relaxation
mechanism in our low-mobility heterostructures is Elliott-Yafet and not
Dyakonov-Perel in the form of the Rashba or Dresselhaus SOI as previously
suggested. We compare our findings with recent work on this material system and
show that the SOI length lies within the same range. The SOI length may be
controlled using an electrostatic gate, opening up prospects for developing
spintronic applications.


title:
Sequential Bayesian Learning for Merton's Jump Model with Stochastic
  Volatility

abstract:
  Jump stochastic volatility models are central to financial econometrics for
volatility forecasting, portfolio risk management, and derivatives pricing.
Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for
the sequential learning of volatility state variables and parameters, whereby
the investor must update all posterior and predictive densities as new
information arrives. We develop a particle filtering and learning algorithm to
sample posterior distribution in Merton's jump stochastic volatility. This
allows to filter spot volatilities and jump times, together with sequentially
updating (learning) of jump and volatility parameters. We illustrate our
methodology on Google's stock return. We conclude with directions for future
research.


title: Brownian Motion with Drift on Spaces with Varying Dimension

abstract:
  Many properties of Brownian motion on spaces with varying dimension (BMVD in
abbreviation) have been explored in [5]. In this paper, we study Brownian
motion with drift on spaces with varying dimension (BMVD with drift in
abbreviation). Such a process can be conveniently defined by a regular
Dirichlet form that is not necessarily symmetric. The drift term is in some
type of $L^{p}$ space with $p$ depending on the region of the state space. We
show BMVD with drift can be related to a BMVD without drift via Girsanov
transform. Through the method of Duhamel's principle, it is established in this
paper that the transition density of BMVD with drift has the same type of sharp
two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we
derive Green function estimate for BMVD with drift.


title: Universal Critical Behaviors in Non-Hermitian Phase Transitions

abstract:
  Quantum phase transitions also occur in non-Hermitian systems. In this work
we show that density functional theory, for the first time, uncovers universal
behaviors for phase transitions in non-Hermitian many-body systems. To be
specific, we first prove that the non-degenerate steady state of a
non-Hermitian quantum many-body system is a universal function of the first
derivative of the steady state energy with respect to the control parameter.
This finding has far-reaching consequences for non-Hermitian systems: (i) It
bridges the nonanalytic behavior in physical observable and nonanalytic
behavior of steady state energy, which explains why the quantum phase
transitions in non-Hermitian systems occur for finite systems. (ii) It predicts
universal scaling behaviors of any physical observable at non-Hermitian phase
transition point with scaling exponent being
$(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$ with $p$ being the number of
coalesced states at the exceptional point and $n$ being a positive integer.
(iii). It reveals that quantum entanglement in non-Hermitian phase transition
point presents universal scaling behaviors with critical exponents being
$(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$. These results uncover universal
critical behaviors in non-Hermitian phase transitions and provide profound
connections between entanglement and phase transition in non-Hermitian quantum
many-body physics and establish foundations for quantum metrology in
non-Hermitian systems.


title: Ricci flow from spaces with isolated conical singularities

abstract:
  Let $(M,g_0)$ be a compact $n$-dimensional Riemannian manifold with a finite
number of singular points, where the metric is asymptotic to a non-negatively
curved cone over $(\mathbb{S}^{n-1},g)$. We show that there exists a smooth
Ricci flow starting from such a metric with curvature decaying like C/t. The
initial metric is attained in Gromov-Hausdorff distance and smoothly away from
the singular points. In the case that the initial manifold has isolated
singularities asymptotic to a non-negatively curved cone over
$(\mathbb{S}^{n-1}/\Gamma,g)$, where $\Gamma$ acts freely and properly
discontinuously, we extend the above result by showing that starting from such
an initial condition there exists a smooth Ricci flow with isolated orbifold
singularities.


title: A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces

abstract:
  We extend our previous work on hypergeometric point count formulas by proving
that we can express the number of points on families of Dwork hypersurfaces
$$X_{\lambda}^d: \hspace{.1in} x_1^d+x_2^d+\ldots+x_d^d=d\lambda x_1x_2\cdots
x_d$$ over finite fields of order $q\equiv 1\pmod d$ in terms of Greene's
finite field hypergeometric functions. We prove that when $d$ is odd, the
number of points can be expressed as a sum of hypergeometric functions plus
$(q^{d-1}-1)/(q-1)$ and conjecture that this is also true when $d$ is even. The
proof rests on a result that equates certain Gauss sum expressions with finite
field hypergeometric functions. Furthermore, we discuss the types of
hypergeometric terms that appear in the point count formula and give an
explicit formula for Dwork threefolds.


title:
Dipolar effects on the critical fluctuations in Fe: Investigation by
  MIEZE

abstract:
  Iron is one of the archetypical ferromagnets to study the critical
fluctuations at a continuous phase transition thus serving as a model system
for the application of scaling theory. We report a comprehensive study of the
critical dynamics at the transition from the ferro- to the paramagnetic phase
in Fe, employing the high-resolution neutron spin echo technique MIEZE. The
results show that the dipolar interactions lead to an additional damping of the
critical spin fluctuations at small momentum transfers $\bf q$. The results
agree essentially with scaling theory if the dipolar interactions are taken
into account by means of the mode-coupling equations. However, in contrast to
expectations, the dipolar wavenumber $q_D$ that plays a central role in the
scaling function $f(\kappa/q,q_D/\kappa)$ becomes temperature dependent. In the
limit of small $\bf q$ the critical exponent $z$ crosses over from 2.5 to 2.0.


title:
Towards Deep Learning in Hindi NER: An approach to tackle the Labelled
  Data Scarcity

abstract:
  In this paper we describe an end to end Neural Model for Named Entity
Recognition NER) which is based on Bi-Directional RNN-LSTM. Almost all NER
systems for Hindi use Language Specific features and handcrafted rules with
gazetteers. Our model is language independent and uses no domain specific
features or any handcrafted rules. Our models rely on semantic information in
the form of word vectors which are learnt by an unsupervised learning algorithm
on an unannotated corpus. Our model attained state of the art performance in
both English and Hindi without the use of any morphological analysis or without
using gazetteers of any sort.


title: Galoisian approach to complex oscillation theory of some Hill equations

abstract:
  We apply Kovacic's algorithm from differential Galois theory to show that all
complex non-oscillatory solutions (finite exponential of convergence of zeros)
of certain Hill equations considered by Bank and Laine using Nevanlinna theory
must be Liouvillian solutions. That is, solutions are obtainable by suitable
differential field extensions construction. In particular, we have established
a full correspondence between solutions of non-oscillatory type and Liouvillian
solutions for a particular Hill equation. Explicit closed-form solutions are
obtained via both methods for this Hill equation whose potential has four
exponential functions in the Bank-Laine theory. The differential equation is a
periodic form of biconfluent Heun equation. We further show that these
Liouvillian solutions exhibit novel single and double orthogonality and a
Fredholm integral equation over suitable integration regions in $\mathbf{C}$
that mimic single/double orthogonality for the corresponding Liouvillian
solutions of the Lam\'e and Whittaker-Hill equations, discovered by Whittaker
and Ince almost a century ago.


title: An SYK-Like Model Without Disorder

abstract:
  Making use of known facts about "tensor models," it is possible to construct
a quantum system without quenched disorder that has the same large $n$ limit
for its correlation functions and thermodynamics as the SYK model. This might
be useful in further probes of this approach to holographic duality.


title: Towards a quantitative understanding of high $p_T$ flow harmonics

abstract:
  In this proceedings I briefly review the recent progress achieved on the
calculation of $v_n$ at high $p_T$ via the coupling of a jet energy loss model
with full event-by-event viscous hydrodynamics. It is shown that that this
framework can simultaneously describe experimental data for $R_{AA}$, $v_2$,
and $v_3$ at high $p_T$. High $p_T$ $v_2$ is found to be approximately linearly
correlated with the soft $v_2$ on an event-by-event basis, which opens up a new
way to correlate soft and hard observables in heavy ion collisions.


title:
Proton radius from electron-proton scattering and chiral perturbation
  theory

abstract:
  We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a
fit to low-$Q^2$ electron-proton elastic scattering cross section data with the
higher moments fixed (within uncertainties) to the values predicted by chiral
perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls
between the value obtained from muonic hydrogen analyses and the CODATA value
(based upon atomic hydrogen spectroscopy and electron-proton scattering
determinations).


title:
ARAPrototyper: Enabling Rapid Prototyping and Evaluation for
  Accelerator-Rich Architectures

abstract:
  Compared to conventional general-purpose processors, accelerator-rich
architectures (ARAs) can provide orders-of-magnitude performance and energy
gains and are emerging as one of the most promising solutions in the age of
dark silicon. However, many design issues related to the complex interaction
between general-purpose cores, accelerators, customized on-chip interconnects,
and memory systems remain unclear and difficult to evaluate.
  In this paper we design and implement the ARAPrototyper to enable rapid
design space explorations for ARAs in real silicons and reduce the tedious
prototyping efforts far down to manageable efforts. First, ARAPrototyper
provides a reusable baseline prototype with a highly customizable memory
system, including interconnect between accelerators and buffers, interconnect
between buffers and last-level cache (LLC) or DRAM, coherency choice at LLC or
DRAM, and address translation support. Second, ARAPrototyper provides a clean
interface to quickly integrate users' own accelerators written in high-level
synthesis (HLS) code. The whole design flow is highly automated to generate a
prototype of ARA on an FPGA system-on-chip (SoC). Third, to quickly develop
applications that run seamlessly on the ARA prototype, ARAPrototyper provides a
system software stack, abstracts the accelerators as software libraries, and
provides APIs for software developers. Our experimental results demonstrate
that ARAPrototyper enables a wide range of design space explorations for ARAs
at manageable prototyping efforts, which has 4,000X to 10,000X faster
evaluation time than full-system simulations. We believe that ARAPrototyper can
be an attractive alternative for ARA design and evaluation.


title: Discussion of a possible corrected black hole entropy

abstract:
  Einstein's equation could be interpreted as the first law of thermodynamic
near the spherically symmetric horizon. Through recalling the Einstein gravity
with a more general static spherical symmetric metric, we find that the entropy
would have a correction in Einstein gravity. By using this method, we
investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter
field, we can also derive the first law in EiBI gravity. With an
electromagnetic field, as the field equations have a more general spherically
symmetric solution in EiBI gravity, we find that correction of the entropy
could be generalized to EiBI gravity. Furthermore, we point out that the
Einstein gravity and EiBI gravity might be equivalent on the event horizon. At
last, under EiBI gravity with the electromagnetic field, a specific corrected
entropy of black hole is given.


title:
L\"uscher's finite volume test for two-baryon systems with attractive
  interactions

abstract:
  For the attractive interaction, the L\"uscher's finite volume formula gives
the phase shift at negative squared moment $k^2<0$ for the ground state in the
finite volume, which corresponds to the analytic continuation of the phase
shift at $k^2<0$ in the infinite volume. Using this fact, we reexamine
behaviors of phase shifts at $k^2 <0$ obtained directly from plateaux of
effective energy shifts in previous lattice studies for two nucleon systems on
various volumes. We have found that data, based on which existences of the
bound states are claimed, show singular behaviors of the phase shift at
$k^2<0$, which seem incompatible with smooth behaviors predicted by the
effective range expansion. This, together with the fake plateau problem for the
determination of the energy shift, brings a serious doubt on existences of the
$NN$ bound states claimed in previous lattice studies at pion masses heavier
than 300 MeV.


title: Gluing affine vortices

abstract:
  We construct a gluing map for stable affine vortices over the upper half
plane with the Lagrangian boundary condition at a rigid, regular, codimension
one configuration. This construction plays an important role in establishing
the relation between the gauged linear sigma model and the nonlinear sigma
model in the presence of Lagrangian branes.


title: The Maslov Index and the Spectra of Second Order Elliptic Operators

abstract:
  We consider second order elliptic differential operators on a bounded
Lipschitz domain $\Omega$. Firstly, we establish a natural one-to-one
correspondence between their self-adjoint extensions, with domains of
definition containing in $H^1(\Omega)$, and Lagrangian planes in
$H^{1/2}(\partial\Omega)\times H^{-1/2}(\partial\Omega)$. Secondly, we derive a
formula relating the spectral flow of the one-parameter families of such
operators to the Maslov index, the topological invariant counting the signed
number of conjugate points of paths of Lagrangian planes in
$H^{1/2}(\partial\Omega)\times H^{-1/2}(\partial\Omega)$. Furthermore, we
compute the Morse index, the number of negative eigenvalues, in terms of the
Maslov index for several classes of the second order operators: the
$\vec{\theta}-$periodic Schr\"odinger operators on a period cell $Q\subset
\mathbb{R}^n$, the elliptic operators with Robin-type boundary conditions, and
the abstract self-adjoint extensions of the Schr\"odinger operators on
star-shaped domains. Our work is built on the techniques recently developed by
B.Boo{\ss}-Bavnbek, K. Furutani, and C. Zhu, and extends the scope of validity
of their spectral flow formula by incorporating the self-adjoint extensions of
the second order operators with domains in the first order Sobolev space
$H^1(\Omega)$. In addition, we generalize the results concerning relations
between the Maslov and Morse indices quite recently obtained by G. Cox, J.
Deng, C. Jones, J. Marzuola, A. Sukhtayev and the authors. Finally, we describe
and study a link between the theory of abstract boundary triples and the
Lagrangian description of self-adjoint extensions of abstract symmetric
operators.


title:
A New Distance Measure for Non-Identical Data with Application to Image
  Classification

abstract:
  Distance measures are part and parcel of many computer vision algorithms. The
underlying assumption in all existing distance measures is that feature
elements are independent and identically distributed. However, in real-world
settings, data generally originate from heterogeneous sources even if they do
possess a common data-generating mechanism. Since these sources are not
identically distributed by necessity, the assumption of identical distribution
is inappropriate. Here, we use statistical analysis to show that feature
elements of local image descriptors are indeed non-identically distributed. To
test the effect of omitting the unified distribution assumption, we created a
new distance measure called the Poisson-Binomial Radius (PBR). PBR is a
bin-to-bin distance which accounts for the dispersion of bin-to-bin
information. PBR's performance was evaluated on twelve benchmark data sets
covering six different classification and recognition applications: texture,
material, leaf, scene, ear biometrics and category-level image classification.
Results from these experiments demonstrate that PBR outperforms
state-of-the-art distance measures for most of the data sets and achieves
comparable performance on the rest, suggesting that accounting for different
distributions in distance measures can improve performance in classification
and recognition tasks.


title: On Sequential Locally Repairable Codes

abstract:
  We consider the locally repairable codes (LRC), aiming at sequential
recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally
Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be
sequentially recovered, each one by r (2<=r<k) other code symbols. Sequential
recovering means that the erased symbols are recovered one by one, and an
already recovered symbol can be used to recover the remaining erased symbols.
This important recovering method, in contrast with the vastly studied parallel
recovering, is currently far from understanding, say, lacking codes constructed
for arbitrary t>=3 erasures and bounds to evaluate the performance of such
codes.
  We first derive a tight upper bound on the code rate of (n, k, r, t)-SLRC for
t=3 and r>=2. We then propose two constructions of binary (n, k, r, t)-SLRCs
for general r,t>=2 (Existing constructions are dealing with t<=7 erasures. The
first construction generalizes the method of direct product construction. The
second construction is based on the resolvable configurations and yields SLRCs
for any r>=2 and odd t>=3. For both constructions, the rates are optimal for t
in {2,3} and are higher than most of the existing LRC families for arbitrary
t>=4.


title:
Soft Phonon Modes and Diffuse Scattering in
  Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 Relaxor Ferroelectrics

abstract:
  Single crystals of a ternary relaxor ferroelectric system,
0.29Pb(In1/2Nb1/2)O3-0.45Pb(Mg1/3Nb2/3)O3-0.26PbTiO3, have been studied using
triple-axis based elastic and inelastic neutron scattering. Elastic diffuse
scattering confirms the presence of polar nano-regions (PNRs) in this system.
The PNRs emerge at the Burns temperature, TB = 630 K and then grow continuously
in population and correlation size as the crystal cools down to 100 K. At 300
K, characteristic 'butterfly' and ellipsoid shaped diffuse scattering patterns
are observed on the HK0 reciprocal space plane. Electrical poling along the
[110] direction produces a marked asymmetry in the diffuse scattering patterns,
with the parallel-to-the-field components enhanced while the
perpendicular-to-the-field components suppressed. Several low energy phonon
branches along the [001] and [111] directions were studied. Most significantly,
the PNR-acoustic phonon coupling is confirmed for the [110] transverse acoustic
(TA) phonons polarized along the [1-10] real space direction and the [100] TA
phonons. This coupling appears to be anisotropic and correlated with the
distribution of PNRs, and also affected by the relative length scales of the
PNRs and phonon wave vectors. The well-known 'waterfall' phenomenon is observed
on the [001] and [110] transverse optical (TO) branches, near the zone center.
The optical phonon measurements also reveal a lowest-energy, zone center soft
TO mode, whose squared phonon energy increase linearly with decreasing
temperature below the TB.


title:
Meta-Path Guided Embedding for Similarity Search in Large-Scale
  Heterogeneous Information Networks

abstract:
  Most real-world data can be modeled as heterogeneous information networks
(HINs) consisting of vertices of multiple types and their relationships. Search
for similar vertices of the same type in large HINs, such as bibliographic
networks and business-review networks, is a fundamental problem with broad
applications. Although similarity search in HINs has been studied previously,
most existing approaches neither explore rich semantic information embedded in
the network structures nor take user's preference as a guidance.
  In this paper, we re-examine similarity search in HINs and propose a novel
embedding-based framework. It models vertices as low-dimensional vectors to
explore network structure-embedded similarity. To accommodate user preferences
at defining similarity semantics, our proposed framework, ESim, accepts
user-defined meta-paths as guidance to learn vertex vectors in a user-preferred
embedding space. Moreover, an efficient and parallel sampling-based
optimization algorithm has been developed to learn embeddings in large-scale
HINs. Extensive experiments on real-world large-scale HINs demonstrate a
significant improvement on the effectiveness of ESim over several
state-of-the-art algorithms as well as its scalability.


title: Multiplicative richness of additively large sets in $\mathbb{Z}^d$

abstract:
  In their proof of the IP Szemer\'edi theorem, a far reaching extension of the
classic theorem of Szemer\'edi on arithmetic progressions, Furstenberg and
Katznelson introduced an important class of additively large sets called
$\text{IP}_{\text{r}}^*$ sets which underlies recurrence aspects in dynamics
and is instrumental to enhanced formulations of combinatorial results. The
authors recently showed that additive $\text{IP}_{\text{r}}^*$ subsets of
$\mathbb{Z}^d$ are multiplicatively rich with respect to every multiplication
on $\mathbb{Z}^d$ without zero divisors (e.g. multiplications induced by degree
$d$ number fields). In this paper, we explain the relationships between classes
of multiplicative largeness with respect to different multiplications on
$\mathbb{Z}^d$. We show, for example, that in contrast to the case for
$\mathbb{Z}$, there are infinitely many different notions of multiplicative
piecewise syndeticity for subsets of $\mathbb{Z}^d$ when $d \geq 2$. This is
accomplished by using the associated algebra representations to prove the
existence of sets which are large with respect to some multiplications while
small with respect to others. In the process, we give necessary and sufficient
conditions for a linear transformation to preserve a class of multiplicatively
large sets. One consequence of our results is that additive
$\text{IP}_{\text{r}}^*$ sets are multiplicatively rich in infinitely many
genuinely different ways. We conclude by cataloging a number of sources of
additive $\text{IP}_{\text{r}}^*$ sets from combinatorics and dynamics.


title:
On the interplay between notions of additive and multiplicative
  largeness and its combinatorial applications

abstract:
  Many natural notions of additive and multiplicative largeness arise from
results in Ramsey theory. In this paper, we explain the relationships between
these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic
structures. We show that multiplicative largeness begets additive largeness in
three ways and give a collection of examples demonstrating the optimality of
these results. We also give a variety of applications arising from the
connection between additive and multiplicative largeness. For example, we show
that given any $n, k \in \mathbb{N}$, any finite set with fewer than $n$
elements in a sufficiently large finite field can be translated so that each of
its elements becomes a non-zero $k^{\text{th}}$ power. We also prove a theorem
concerning Diophantine approximation along multiplicatively syndetic subsets of
$\mathbb{N}$ and a theorem showing that subsets of positive upper Banach
density in certain multiplicative sub-semigroups of $\mathbb{N}$ of zero
density contain arbitrarily long arithmetic progressions. Along the way, we
develop a new characterization of upper Banach density in a wide class of
amenable semigroups and make explicit the uniformity in recurrence theorems
from measure theoretic and topological dynamics. This in turn leads to
strengthened forms of classical theorems of Szemer\'edi and van der Waerden on
arithmetic progressions.


title:
Identification of the Lowest $T=2$, $J^{\pi=}0^+$ Isobaric Analog State
  in $^{52}$Co and Its Impact on the Understanding of $\beta$-Decay Properties
  of $^{52}$Ni

abstract:
  Masses of $^{52g,52m}$Co were measured for the first time with an accuracy of
$\sim 10$ keV, an unprecedented precision reached for short-lived nuclei in the
isochronous mass spectrometry. Combining our results with the previous
$\beta$-$\gamma$ measurements of $^{52}$Ni, the $T=2$, $J^{\pi}=0^+$ isobaric
analog state (IAS) in $^{52}$Co was newly assigned, questioning the
conventional identification of IASs from the $\beta$-delayed proton emissions.
Using our energy of the IAS in $^{52}$Co, the masses of the $T=2$ multiplet fit
well into the Isobaric Multiplet Mass Equation. We find that the IAS in
$^{52}$Co decays predominantly via $\gamma$ transitions while the proton
emission is negligibly small. According to our large-scale shell model
calculations, this phenomenon has been interpreted to be due to very low
isospin mixing in the IAS.


title: Nucleon structure from 2+1-flavor dynamical DWF ensembles

abstract:
  Nucleon isovector vector- and axialvector-current form factors, the
renormalized isovector transversity and scalar charge, and the bare quark
momentum and helicity moments of isovector structure functions are reported
with improved statistics from two recent RBC+UKQCD 2+1-flavor dynamical
domain-wall fermions ensembles: Iwasaki\(\times\)DSDR gauge \(32^3\times64\) at
inverse lattice spacing of 1.38 GeV and pion mass of 249 and 172 MeV.


title:
Lower Bounds on Davenport-Schinzel Sequences via Rectangular
  Zarankiewicz Matrices

abstract:
  An order-$s$ Davenport-Schinzel sequence over an $n$-letter alphabet is one
avoiding immediate repetitions and alternating subsequences with length $s+2$.
The main problem is to determine the maximum length of such a sequence, as a
function of $n$ and $s$. When $s$ is fixed this problem has been settled but
when $s$ is a function of $n$, very little is known about the extremal function
$\lambda(s,n)$ of such sequences.
  In this paper we give a new recursive construction of Davenport-Schinzel
sequences that is based on dense 0-1 matrices avoiding large all-1 submatrices
(aka Zarankiewicz's Problem.) In particular, we give a simple construction of
$n^{2/t} \times n$ matrices containing $n^{1+1/t}$ 1s that avoid $t\times 2$
all-1 submatrices.
  Our lower bounds on $\lambda(s,n)$ exhibit three qualitatively different
behaviors depending on the size of $s$ relative to $n$. When $s \le \log\log n$
we show that $\lambda(s,n)/n \ge 2^s$ grows exponentially with $s$. When $s =
n^{o(1)}$ we show $\lambda(s,n)/n \ge (\frac{s}{2\log\log_s n})^{\log\log_s n}$
grows faster than any polynomial in $s$. Finally, when
$s=\Omega(n^{1/t}(t-1)!)$, $\lambda(s,n) = \Omega(n^2 s/(t-1)!)$ matches the
trivial upper bound $O(n^2s)$ asymptotically, whenever $t$ is constant.


title: Ideals and quotients of diagonally quasi-symmetric functions

abstract:
  In 2004, J-C. Aval, F. Bergeron and N. Bergeron studied the algebra of
diagonally quasi-symmetric functions $\operatorname{\mathsf{DQSym}}$ in the
ring $\mathbb{Q}[\mathbf{x},\mathbf{y}]$ with two sets of variables. They made
conjectures on the structure of the quotient
$\mathbb{Q}[\mathbf{x},\mathbf{y}]/\langle\operatorname{\mathsf{DQSym}}^+\rangle$,
which is a quasi-symmetric analogue of the diagonal harmonic polynomials. In
this paper, we construct a Hilbert basis for this quotient when there are
infinitely many variables i.e. $\mathbf{x}=x_1,x_2,\dots$ and
$\mathbf{y}=y_1,y_2,\dots$. Then we apply this construction to the case where
there are finitely many variables, and compute the second column of its Hilbert
matrix.


title:
Mathematical aspects of the nuclear glory phenomenon: from backward
  focusing to Chebyshev polynomials

abstract:
  The angular dependence of the cumulative particles production off nuclei near
the kinematical boundary for multistep process is defined by characteristic
polynomials in angular variables $J_N^2(z_N^\theta)$, where $\theta$ is the
polar angle defining the momentum of the final (cumulative) particle,
$z_N^\theta = cos (\theta/N)$, the integer $N$ being the multiplicity of the
process (the number of interactions). Physical argumentation, exploring the
small phase space method, leads to the appearance of equations for these
polynomials $J_N^2[cos(\pi/N)]=0$. The recurrent relations between polynomials
with different $N$ are obtained, and their connection with known in mathematics
Chebyshev polynomials of 2-d kind is established. As a result of this equality,
differential cross section of the cumulative particle production has
characteristic behaviour $d\sigma \sim 1/ \sqrt {\pi - \theta}$ at $\theta \sim
\pi$ (the backward focusing effect). Such behaviour takes place for any
multiplicity of the interaction, beginning with $n=3$, elastic or inelastic
(with resonances excitations in intermediate states), and can be called the
nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.


title:
Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic
  control of a unitary Fermi gas

abstract:
  Coherent control of complex quantum systems is a fundamental requirement in
quantum information processing and engineering. Recently developed notion of
shortcut to adiabaticity (STA) has spawned intriguing prospects. So far, the
most experimental investigations of STA are implemented in the ideal thermal
gas or the weakly interacting ultracold Bose gases. Here we report the first
demonstration of a many-body STA in a 3D anisotropically trapped unitary Fermi
gas. A new dynamical scaling law is demonstrated on such a strongly interacting
quantum gas. By simply engineering the frequency aspect ratio of a harmonic
trap, the dynamics of the gas can be manipulated and the many-body state can be
transferred adiabatically from one stationary state to another one in short
time scale without the excitation. The universal scaling both for
non-interacting and unitary Fermi gas is also verified. This could be very
important for future many-body quantum engineering and the exploration of the
fundamental law of the thermodynamics.


title:
DPPred: An Effective Prediction Framework with Concise Discriminative
  Patterns

abstract:
  In the literature, two series of models have been proposed to address
prediction problems including classification and regression. Simple models,
such as generalized linear models, have ordinary performance but strong
interpretability on a set of simple features. The other series, including
tree-based models, organize numerical, categorical and high dimensional
features into a comprehensive structure with rich interpretable information in
the data.
  In this paper, we propose a novel Discriminative Pattern-based Prediction
framework (DPPred) to accomplish the prediction tasks by taking their
advantages of both effectiveness and interpretability. Specifically, DPPred
adopts the concise discriminative patterns that are on the prefix paths from
the root to leaf nodes in the tree-based models. DPPred selects a limited
number of the useful discriminative patterns by searching for the most
effective pattern combination to fit generalized linear models. Extensive
experiments show that in many scenarios, DPPred provides competitive accuracy
with the state-of-the-art as well as the valuable interpretability for
developers and experts. In particular, taking a clinical application dataset as
a case study, our DPPred outperforms the baselines by using only 40 concise
discriminative patterns out of a potentially exponentially large set of
patterns.


title:
Baryon interactions in lattice QCD: the direct method vs. the HAL QCD
  potential method

abstract:
  We make a detailed comparison between the direct method and the HAL QCD
potential method for the baryon-baryon interactions, taking the $\Xi\Xi$ system
at $m_\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark
sources. The energy shift $\Delta E_\mathrm{eff}(t)$ in the direct method shows
the strong dependence on the choice of quark source operators, which means that
the results with either (or both) source are false. The time-dependent HAL QCD
method, on the other hand, gives the quark source independent $\Xi\Xi$
potential, thanks to the derivative expansion of the potential, which absorbs
the source dependence to the next leading order correction. The HAL QCD
potential predicts the absence of the bound state in the $\Xi\Xi$($^1$S$_0$)
channel at $m_\pi= 0.51$ GeV, which is also confirmed by the volume dependence
of finite volume energy from the potential. We also demonstrate that the origin
of the fake plateau in the effective energy shift $\Delta E_\mathrm{eff}(t)$ at
$t \sim 1$ fm can be clarified by a few low-lying eigenfunctions and
eigenvalues on the finite volume derived from the HAL QCD potential, which
implies that the ground state saturation of $\Xi\Xi$($^1$S$_0$) requires $t
\sim 10$ fm in the direct method for the smeared source on $(4.3 \
\mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such a
problem.


title:
Flexible Models for Microclustering with Application to Entity
  Resolution

abstract:
  Most generative models for clustering implicitly assume that the number of
data points in each cluster grows linearly with the total number of data
points. Finite mixture models, Dirichlet process mixture models, and
Pitman--Yor process mixture models make this assumption, as do all other
infinitely exchangeable clustering models. However, for some applications, this
assumption is inappropriate. For example, when performing entity resolution,
the size of each cluster should be unrelated to the size of the data set, and
each cluster should contain a negligible fraction of the total number of data
points. These applications require models that yield clusters whose sizes grow
sublinearly with the size of the data set. We address this requirement by
defining the microclustering property and introducing a new class of models
that can exhibit this property. We compare models within this class to two
commonly used clustering models using four entity-resolution data sets.


title:
On the Newtonian and Spin-induced Perturbations felt by the Stars
  Orbiting around the Massive Black Hole in the Galactic Center

abstract:
  The S-stars discovered in the Galactic center (GC) are expected to provide
unique dynamical tests of the Kerr metric of the massive black hole (MBH)
orbited by them. In order to obtain unbiased measurements of its spin and the
related relativistic effects, a comprehensive understanding of the
gravitational perturbations of the stars and stellar remnants around the MBH is
quite essential. Here, we study the perturbations on the observables of a
typical target star, i.e., the apparent orbital motion and the redshift, due to
both the spin-induced relativistic effects and the Newtonian attractions of a
single or a cluster of disturbing object(s). We find that, in most cases, the
Newtonian perturbations on the observables are mainly attributed to the
perturbed orbital period of the target star, rather than the Newtonian orbital
precessions. The Newtonian perturbations have their unique features when they
peak around the pericenter passage in each revolution, which is quite different
from those of the spin-induced effects. Looking at the currently detected star
S2/S0-2, we find that its spin-induced effects on both the image position and
redshift are very likely obscured by the gravitational perturbations from the
star S0-102 alone. We also investigate and discuss the Newtonian perturbations
on a hypothetical S-star located inside the orbits of the currently detected
ones. By considering a number of possible stellar distributions near the
central MBH, we find that the spin-induced effects on the apparent position and
the redshift dominate over the stellar perturbations for target stars with
orbital semimajor axis smaller than $100-400$AU if the MBH is maximally
spinning. Our results suggest that, in principle, the stellar perturbations can
be removed as they have distinctive morphologies comparing to those of the
relativistic Kerr-type signatures.


title: Efficient Construction of Polar Codes

abstract:
  The construction of polar codes for channels other than BECs requires sorting
of all bit channels and then selecting the best $K$ of them for a block length
$N=2^n$. In this paper, two types of partial orders (PO) of polar codes are
incorporated in the construction process to decrease the required computations.
Three sets, corresponding to the good bit channels ($\mathcal{I}$), the frozen
bit channels ($\mathcal{F}$), and the undetermined bit channels
($\mathcal{U}$), are selected by applying PO relations. The POs are channel
independent and are therefore universal for all binary-input discrete
memoryless channels. For a given specific channel, a new process, called
Dimension Reduction (DR), is proposed in this paper to further reduce the size
of $\mathcal{U}$. Our studies show that for $N=10$ and the code rate $R=0.5$
(being the worst code rate), incorporating PO relations alone can determine 50%
of the bit channels ($|\mathcal{I}| + |\mathcal{F}| \approx N/2$). With our
proposed DR, this number of the determined bit channels goes up to 82%, which
brings a significant reduction of computations in the construction of polar
codes.


title: Hermitian-Randi\'c matrix and Hermitian-Randi\'c energy of mixed graphs

abstract:
  Let $M$ be a mixed graph and $H(M)$ be its Hermitian-adjacency matrix. If we
add every edge and arc in $M$ a Randi\'c weight, then we can get a new weighted
Hermitian-adjacency matrix. What are the properties of this new matrix?
Motivated by this, we define the Hermitian-Randi\'c matrix
$R_{H}(M)=(r_{h})_{kl}$ of a mixed graph $M$, where
$(r_{h})_{kl}=-(r_{h})_{lk}=\frac{\textbf{i}}{\sqrt{d_{k}d_{l}}}$
($\textbf{i}=\sqrt{-1}$) if $(v_{k},v_{l})$ is an arc of $M$,
$(r_{h})_{kl}=(r_{h})_{lk}=\frac{1}{\sqrt{d_{k}d_{l}}}$ if $v_{k}v_{l}$ is an
undirected edge of $M$, and $(r_{h})_{kl}=0$ otherwise.
  In this paper, firstly, we compute the characteristic polynomial of the
Hermitian-Randi\'c matrix of a mixed graph. Furthermore, we give bounds to the
Hermitian-Randi\'c energy of a general mixed graph. Finally, we give some
results about the Hermitian-Randi\'c energy of mixed trees.


title: Homology of Brownian loops

abstract:
  The purpose of this note is to extend to Brownian loops some homology and
holonomy results obtained in the case of discrete loops on a graph


title:
Generalized Solution for the Demodulation of Reaction Shift Keying
  Signals in Molecular Communication Networks

abstract:
  This paper considers a diffusion-based molecular communication system where
the transmitter uses Reaction Shift Keying (RSK) as the modulation scheme. We
focus on the demodulation of RSK signal at the receiver. The receiver consists
of a front-end molecular circuit and a back-end demodulator. The front-end
molecular circuit is a set of chemical reactions consisting of multiple
chemical species. The optimal demodulator computes the posteriori probability
of the transmitted symbols given the history of the observation. The derivation
of the optimal demodulator requires the solution to a specific Bayesian
filtering problem. The solution to this Bayesian filtering problem had been
derived for a few specific molecular circuits and specific choice(s) of
observed chemical species. The derivation of such solution is also lengthy. The
key contribution of this paper is to present a general solution to this
Bayesian filtering problem which can be applied to any molecular circuit and
any choice of observed species.


title: Stop Clickbait: Detecting and Preventing Clickbaits in Online News Media

abstract:
  Most of the online news media outlets rely heavily on the revenues generated
from the clicks made by their readers, and due to the presence of numerous such
outlets, they need to compete with each other for reader attention. To attract
the readers to click on an article and subsequently visit the media site, the
outlets often come up with catchy headlines accompanying the article links,
which lure the readers to click on the link. Such headlines are known as
Clickbaits. While these baits may trick the readers into clicking, in the long
run, clickbaits usually don't live up to the expectation of the readers, and
leave them disappointed.
  In this work, we attempt to automatically detect clickbaits and then build a
browser extension which warns the readers of different media sites about the
possibility of being baited by such headlines. The extension also offers each
reader an option to block clickbaits she doesn't want to see. Then, using such
reader choices, the extension automatically blocks similar clickbaits during
her future visits. We run extensive offline and online experiments across
multiple media sites and find that the proposed clickbait detection and the
personalized blocking approaches perform very well achieving 93% accuracy in
detecting and 89% accuracy in blocking clickbaits.


title: Edward: A library for probabilistic modeling, inference, and criticism

abstract:
  Probabilistic modeling is a powerful approach for analyzing empirical
information. We describe Edward, a library for probabilistic modeling. Edward's
design reflects an iterative process pioneered by George Box: build a model of
a phenomenon, make inferences about the model given data, and criticize the
model's fit to the data. Edward supports a broad class of probabilistic models,
efficient algorithms for inference, and many techniques for model criticism.
The library builds on top of TensorFlow to support distributed training and
hardware such as GPUs. Edward enables the development of complex probabilistic
models and their algorithms at a massive scale.


title:
Pseudo-marginal Metropolis--Hastings using averages of unbiased
  estimators

abstract:
  We consider a pseudo-marginal Metropolis--Hastings kernel $P_m$ that is
constructed using an average of $m$ exchangeable random variables, as well as
an analogous kernel $P_s$ that averages $s<m$ of these same random variables.
Using an embedding technique to facilitate comparisons, we show that the
asymptotic variances of ergodic averages associated with $P_m$ are lower
bounded in terms of those associated with $P_s$. We show that the bound
provided is tight and disprove a conjecture that when the random variables to
be averaged are independent, the asymptotic variance under $P_m$ is never less
than $s/m$ times the variance under $P_s$. The conjecture does, however, hold
when considering continuous-time Markov chains. These results imply that if the
computational cost of the algorithm is proportional to $m$, it is often better
to set $m=1$. We provide intuition as to why these findings differ so markedly
from recent results for pseudo-marginal kernels employing particle filter
approximations. Our results are exemplified through two simulation studies; in
the first the computational cost is effectively proportional to $m$ and in the
second there is a considerable start-up cost at each iteration.


title: Asymptotic expansions of solutions of fractional diffusion equations

abstract:
  In this paper we obtain the precise description of the asymptotic behavior of
the solution $u$ of $$ \partial_t
u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty),
\qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf R}^N, $$ where $0<\theta<2$ and
$\varphi\in L_K:=L^1({\bf R}^N,\,(1+|x|)^K\,dx)$ with $K\ge 0$. Furthermore, we
develop the arguments in [15] and [18] and establish a method to obtain the
asymptotic expansions of the solutions to a nonlinear fractional diffusion
equation $$ \partial_t
u+(-\Delta)^{\frac{\theta}{2}}u=|u|^{p-1}u\quad\mbox{in}\quad{\bf
R}^N\times(0,\infty), $$ where $0<\theta<2$ and $p>1+\theta/N$.


title:
Accessing the Full Superconducting Dome in Pristine YBa2Cu3O6+x Under
  Pressure

abstract:
  We attain the previously unaccessed full superconducting dome in a pristine
high temperature cuprate superconductor by applying pressures up to 280 kbar to
samples of near stoichiometric YBa2Cu3O7. The obtained superconducting phase
boundary as a function of hole doping closely follows the superconducting dome
in La2-xSrxCuO4. Measurements are now enabled to trace the evolution of various
entangled phases and the Fermi surface from the underdoped to overdoped regime
in a single high purity cuprate superconducting family of materials.


title: The arc length of a random lemniscate

abstract:
  A polynomial lemniscate is a curve in the complex plane defined by $\{z \in
\mathbb{C}:|p(z)|=t\}$. Erd\"os, Herzog, and Piranian posed the extremal
problem of determining the maximum length of a lemniscate $\Lambda=\{ z \in
\mathbb{C}:|p(z)|=1\}$ when $p$ is a monic polynomial of degree $n$. In this
paper, we study the length and topology of a random lemniscate whose defining
polynomial has independent Gaussian coefficients. In the special case of the
Kac ensemble we show that the length approaches a nonzero constant as $n
\rightarrow \infty$. We also show that the average number of connected
components is asymptotically $n$, and we observe a positive probability
(independent of $n$) of a giant component occurring.


title:
Strongly coupled $\mathcal{N}=4$ super Yang-Mills plasma on the Coulomb
  branch I: Thermodynamics

abstract:
  We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch
(cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The
dual geometry is the rotating black 3-brane Type IIB supergravity solution with
a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale
corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the
Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are
held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and
$<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$
cSYM at finite $T$, as well as the heavy quark-antiquark potential and the
quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By
computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy
quark-antiquark potential $V(L)$ to be the Cornell potential, which is
confining for large separation $L$. At $T\neq 0$, we find two black hole
branches: the large black hole and small black hole branches. For the large
black hole branch, that has positive specific heat, we find qualitatively
similar EoS to that of pure Yang-Mills theory on the lattice. For the small
black hole branch, that has negative specific heat, we find an EoS where the
entropy and energy densities decrease with $T$. We also find a second-order
phase transition between the large and small black hole branches with critical
temperature $T_c=T_{min}$.


title:
Strongly coupled $\mathcal{N}=4$ super Yang-Mills plasma on the Coulomb
  branch II: Transport coefficients and hard probe parameters

abstract:
  We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch
(cSYM) by using its Type IIB supergravity dual. We compute the transport
coefficients, and hard probe parameters of $\mathcal{N} = 4$ cSYM at finite
temperature $T$. We use the rotating black 3-brane solution of Type IIB
supergravity with a single non-zero rotation parameter $r_{0}$ after
analytically continuing $r_{0}\rightarrow -ir_{0}$, and in an ensemble where
the Hawking temperature $T$ and a scalar condensate $<\mathcal{O}>\sim r_{0}^4$
are held fixed. We find that the bulk viscosity to entropy density ratio of the
large black hole branch decreases with temperature and has a maxima around the
critical temperature $T_{c}$ while, for the small black hole branch, it
increases with temperature. The other transport coefficients and parameters of
hard probes, such as the conductivity, jet quenching parameter, drag force, and
momentum diffusion coefficients of the large black hole branch increase with
temperature and asymptote to their conformal value while, for the small black
hole branch, they decrease with temperature.


title: Willmore inequality on hypersurfaces in hyperbolic space

abstract:
  In this article, we prove a geometric inequality for star-shaped and
mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow.
This inequality can be considered as a generalization of Willmore inequality
for closed surface in hyperbolic $3$-space.


title:
Finding Minimum and Maximum Termination Time of Timed Automata Models
  with Cyclic Behaviour

abstract:
  The paper presents a novel algorithm for computing best and worst case
execution times (BCET/WCET) of timed automata models with cyclic behaviour. The
algorithms can work on any arbitrary diagonal-free TA and can handle more cases
than previously existing algorithms for BCET/WCET computations, as it can
handle cycles in TA and decide whether they lead to an infinite WCET. We show
soundness of the proposed algorithm and study its complexity. To our knowledge,
this is the first model checking algorithm that addresses comprehensively the
BCET/WCET problem of systems with cyclic behaviour. Behrmann et al. provide an
algorithm for computing the minimum cost/time of reaching a goal state in
priced timed automata (PTA). The algorithm has been implemented in the
well-known model checking tool UPPAAL to compute the minimum time for
termination of an automaton. However, we show that in certain circumstances,
when infinite cycles exist, the algorithm implemented in UPPAAL may not
terminate, and we provide examples which UPPAAL fails to verify.