title:
Universality of the nodal length of bivariate random trigonometric
  polynomials

abstract:
  We consider random trigonometric polynomials of the form \[
f_n(x,y)=\sum_{1\le k,l \le n} a_{k,l} \cos(kx) \cos(ly), \] where the entries
$(a_{k,l})_{k,l\ge 1}$ are i.i.d. random variables that are centered with unit
variance. We investigate the length $\ell_K(f_n)$ of the nodal set $Z_K(f_n)$
of the zeros of $f_n$ that belong to a compact set $K \subset \mathbb R^2$. We
first establish a local universality result, namely we prove that, as $n$ goes
to infinity, the sequence of random variables $n\, \ell_{K/n}(f_n)$ converges
in distribution to a universal limit which does not depend on the particular
law of the entries. We then show that at a macroscopic scale, the expectation
of $\ell_{[0,\pi]^2}(f_n)/n$ also converges to an universal limit. Our approach
provides two main byproducts: (i) a general result regarding the continuity of
the volume of the nodal sets with respect to $C^1$-convergence which refines
previous findings of Rusakov et al., Iksanov et al. and Aza\"is et al., and
(ii) a new strategy for proving small ball estimates in random trigonometric
models, providing in turn uniform local controls of the nodal volumes.


title: End-to-end attention-based distant speech recognition with Highway LSTM

abstract:
  End-to-end attention-based models have been shown to be competitive
alternatives to conventional DNN-HMM models in the Speech Recognition Systems.
In this paper, we extend existing end-to-end attention-based models that can be
applied for Distant Speech Recognition (DSR) task. Specifically, we propose an
end-to-end attention-based speech recognizer with multichannel input that
performs sequence prediction directly at the character level. To gain a better
performance, we also incorporate Highway long short-term memory (HLSTM) which
outperforms previous models on AMI distant speech recognition task.


title: The Observable Signatures of GRB Cocoons

abstract:
  As a long GRB jet propagates within the surrounding stellar atmosphere it
creates a cocoon composed of an outer Newtonian shocked stellar material and an
inner (possibly relativistic) shocked jet material. The jet deposits
$10^{51}-10^{52}$ erg into this cocoon. This energy is comparable to the GRB's
energy and to the energy of the accompanying supernova, yet its signature has
been largely neglected so far. A fraction of the cocoon energy is released
during its expansion following the breakout from the star and later as it
interacts with the surrounding matter. We explore here the possible signatures
of the cocoon emission and outline a framework to calculate them from the
conditions of the cocoon at the time of the jet breakout. We show that the
cocoon signature depends strongly on the level of mixing between the shocked
jet and shocked stellar material that fills it, which is currently unknown. We
find that if there is no mixing at all then the $\gamma$-ray emission from the
cocoon is so bright that it should have been already detected, and the lack of
such detections indicates that mixing at some level must take place. We
calculate also the expected signal for partial and full mixing. While the
typical signals are weaker than GRBs' afterglows, the latter are highly beamed
while the former have wide angles. We predict that future optical, UV and X-ray
transient searches, like LSST, ZTF, ULTRASAT, ISS-Lobster and others will most
likely detect such signals, providing a wealth of information on the
progenitors and jets of GRBs. While we focus on long GRBs, we note that
analogous (but weaker) cocoons may arise in short GRBs as well. Their
signatures might be the most promising electromagnetic counterparts for
gravitational waves merger's signals.


title:
All-dielectric nanophotonics: fundamentals, fabrication, and
  applications

abstract:
  In this Article, we review a novel, rapidly developing field of modern light
science named all-dielectric nanophotonics. This branch of nanophotonics is
based on the properties of high-index dielectric nanoparticles which allow for
controlling both magnetic and electric responses of a nanostructured matter.
Here, we discuss optical properties of high-index dielectric nanoparticles,
methods of their fabrication, and recent advances in practical applications,
including the quantum source emission engineering, Fano resonances in
all-dielectric nanoclusters, surface enhanced spectroscopy and sensing,
coupled-resonator optical waveguides, metamaterials and metasurfaces, and
nonlinear nanophotonics.


title:
Topological quantum phase transition and superconductivity induced by
  pressure in the bismuth tellurohalide BiTeI

abstract:
  A pressure-induced topological quantum phase transition has been
theoretically predicted for the semiconductor BiTeI with giant Rashba spin
splitting. In this work, the evolution of the electrical transport properties
in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent
resistivity in a wide temperature range passes through a minimum at around 3
GPa, indicating the predicted transition in BiTeI. Superconductivity is
observed in both BiTeI and BiTeBr while the resistivity at higher temperatures
still exhibits semiconducting behavior. Theoretical calculations suggest that
the superconductivity may develop from the multi-valley semiconductor phase.
The superconducting transition temperature Tc increases with applied pressure
and reaches a maximum value of 5.2 K at 23.5 GPa for BiTeI (4.8 K at 31.7 GPa
for BiTeBr), followed by a slow decrease. Our results demonstrate that BiTeX (X
= I, Br) compounds with non-trivial topology of electronic states display new
ground states upon compression.


title: Structure of almost Abelian Lie algebras

abstract:
  An almost Abelian Lie algebra is a non-Abelian Lie algebra with a codimension
1 Abelian subalgebra. It is known that such an algebra necessarily has a
codimension 1 Abelian ideal. Almost Abelian Lie algebras are perhaps the next
simplest Lie algebras after Abelian Lie algebras. The present exposition
studies the structure and important algebraic properties of almost Abelian Lie
algebras of arbitrary dimension over any field of scalars.


title: Foot force models of crowd dynamics on a wobbly bridge

abstract:
  Modern pedestrian and suspension bridges are designed using industry-standard
packages, yet disastrous resonant vibrations are observed, necessitating
multi-million dollar repairs. Recent examples include pedestrian induced
vibrations during the openings of the Solf\'erino Bridge in Paris in 1999 and
the increased bouncing of the Squibb Park Bridge in Brooklyn in 2014. The most
prominent example of an unstable lively bridge is the London Millennium Bridge
which started wobbling as a result of pedestrian-bridge interactions.
Pedestrian phase-locking due to footstep phase adjustment, is suspected to be
the main cause of its large lateral vibrations; however, its role in the
initiation of wobbling was debated. In this paper, we develop foot force models
of pedestrians' response to bridge motion and detailed, yet analytically
tractable models of crowd phase-locking. We use bio-mechanically inspired
models of crowd lateral movement to investigate to what degree pedestrian
synchrony must be present for a bridge to wobble significantly and what is a
critical crowd size. Our results can be used as a safety guideline for
designing pedestrian bridges or limiting the maximum occupancy of an existing
bridge. The pedestrian models can be used as "crash test dummies" when
numerically probing a specific bridge design. This is particularly important
because the US code for designing pedestrian bridges does not contain explicit
guidelines that account for the collective pedestrian behavior.


title: The random matrix hard edge: rare events and a transition

abstract:
  We study probabilities of various rare events for the limiting point process
that appears at the random matrix hard edge. We also show a transition from
hard edge to bulk behavior. Asymptotic events studied include a central limit
theorem and large deviation result for the number of points in a growing
interval $[0,\lambda]$ as $\lambda \to \infty$. We study these results for the
square root of the hard edge process. In this setting many of these behaviors
mimic those of the Sine$_\beta$ process.


title: Monolithic CMOS-compatible zero-index metamaterials

abstract:
  Zero-index materials exhibit exotic optical properties that can be utilized
for integrated-optics applications. However, practical implementation requires
compatibility with complementary metallic-oxide-semiconductor (CMOS)
technologies. We demonstrate a CMOS-compatible zero-index metamaterial
consisting of a square array of air holes in a 220-nm-thick
silicon-on-insulator (SOI) wafer. This design is achieved through a Dirac-cone
dispersion. The metamaterial is entirely composed of silicon and offers
compatibility through low-aspect-ratio structures that can be simply fabricated
in a standard device layer. This platform enables mass adoption and exploration
of zero-index-based photonic devices at low cost and high fidelity.


title: The Final SDSS High-Redshift Quasar Sample of 52 Quasars at z>5.7

abstract:
  We present the discovery of nine quasars at $z\sim6$ identified in the Sloan
Digital Sky Survey (SDSS) imaging data. This completes our survey of $z\sim6$
quasars in the SDSS footprint. Our final sample consists of 52 quasars at
$5.7<z\le6.4$, including 29 quasars with $z_{\rm AB}\le20$ mag selected from
11,240 deg$^2$ of the SDSS single-epoch imaging survey (the main survey), 10
quasars with $20\le z_{\rm AB}\le20.5$ selected from 4223 deg$^2$ of the SDSS
overlap regions (regions with two or more imaging scans), and 13 quasars down
to $z_{\rm AB}\approx22$ mag from the 277 deg$^2$ in Stripe 82. They span a
wide luminosity range of $-29.0\le M_{1450}\le-24.5$. This well-defined sample
is used to derive the quasar luminosity function (QLF) at $z\sim6$. After
combining our SDSS sample with two faint ($M_{1450}\ge-23$ mag) quasars from
the literature, we obtain the parameters for a double power-law fit to the QLF.
The bright-end slope $\beta$ of the QLF is well constrained to be
$\beta=-2.8\pm0.2$. Due to the small number of low-luminosity quasars, the
faint-end slope $\alpha$ and the characteristic magnitude $M_{1450}^{\ast}$ are
less well constrained, with $\alpha=-1.90_{-0.44}^{+0.58}$ and
$M^{\ast}=-25.2_{-3.8}^{+1.2}$ mag. The spatial density of luminous quasars,
parametrized as $\rho(M_{1450}<-26,z)=\rho(z=6)\,10^{k(z-6)}$, drops rapidly
from $z\sim5$ to 6, with $k=-0.72\pm0.11$. Based on our fitted QLF and assuming
an IGM clumping factor of $C=3$, we find that the observed quasar population
cannot provide enough photons to ionize the $z\sim6$ IGM at $\sim90$\%
confidence. Quasars may still provide a significant fraction of the required
photons, although much larger samples of faint quasars are needed for more
stringent constraints on the quasar contribution to reionization.


title: An accurate metric for the spacetime around neutron stars

abstract:
  The problem of having an accurate description of the spacetime around neutron
stars is of great astrophysical interest. For astrophysical applications, one
needs to have a metric that captures all the properties of the spacetime around
a neutron star. Furthermore, an accurate appropriately parameterised metric,
i.e., a metric that is given in terms of parameters that are directly related
to the physical structure of the neutron star, could be used to solve the
inverse problem, which is to infer the properties of the structure of a neutron
star from astrophysical observations. In this work we present such an
approximate stationary and axisymmetric metric for the exterior of neutron
stars, which is constructed using the Ernst formalism and is parameterised by
the relativistic multipole moments of the central object. This metric is given
in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole
moments as free parameters and is shown to be extremely accurate in capturing
the physical properties of a neutron star spacetime as they are calculated
numerically in general relativity. Because the metric is given in terms of an
expansion, the expressions are much simpler and easier to implement, in
contrast to previous approaches. For the parameterisation of the metric in
general relativity, the recently discovered universal 3-hair relations are used
to produce a 3-parameter metric. Finally, a straightforward extension of this
metric is given for scalar-tensor theories with a massless scalar field, which
also admit a formulation in terms of an Ernst potential.


title: (2,2) Superconformal Bootstrap in Two Dimensions

abstract:
  We find a simple relation between two-dimensional BPS N=2 superconformal
blocks and bosonic Virasoro conformal blocks, which allows us to analyze the
crossing equations for BPS 4-point functions in unitary (2,2) superconformal
theories numerically with semidefinite programming. We constrain gaps in the
non-BPS spectrum through the operator product expansion of BPS operators, in
ways that depend on the moduli of exactly marginal deformations through chiral
ring coefficients. In some cases, our bounds on the spectral gaps are observed
to be saturated by free theories, by N=2 Liouville theory, and by certain
Landau-Ginzburg models.


title: The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

abstract:
  The validity of the vanishing viscosity limit, that is, whether solutions of
the Navier-Stokes equations modeling viscous incompressible flows converge to
solutions of the Euler equations modeling inviscid incompressible flows as
viscosity approaches zero, is one of the most fundamental issues in
mathematical fluid mechanics. The problem is classified into two categories:
the case when the physical boundary is absent, and the case when the physical
boundary is present and the effect of the boundary layer becomes significant.
The aim of this article is to review recent progress on the mathematical
analysis of this problem in each category.


title:
The SOFIA Massive (SOMA) Star Formation Survey. I. Overview and First
  Results

abstract:
  We present an overview and first results of the Stratospheric Observatory For
Infrared Astronomy Massive (SOMA) Star Formation Survey, which is using the
FORCAST instrument to image massive protostars from
$\sim10$--$40\:\rm{\mu}\rm{m}$. These wavelengths trace thermal emission from
warm dust, which in Core Accretion models mainly emerges from the inner regions
of protostellar outflow cavities. Dust in dense core envelopes also imprints
characteristic extinction patterns at these wavelengths, causing intensity
peaks to shift along the outflow axis and profiles to become more symmetric at
longer wavelengths. We present observational results for the first eight
protostars in the survey, i.e., multiwavelength images, including some
ancillary ground-based MIR observations and archival {\it{Spitzer}} and
{\it{Herschel}} data. These images generally show extended MIR/FIR emission
along directions consistent with those of known outflows and with shorter
wavelength peak flux positions displaced from the protostar along the
blueshifted, near-facing sides, thus confirming qualitative predictions of Core
Accretion models. We then compile spectral energy distributions and use these
to derive protostellar properties by fitting theoretical radiative transfer
models. Zhang and Tan models, based on the Turbulent Core Model of McKee and
Tan, imply the sources have protostellar masses $m_*\sim10$--50$\:M_\odot$
accreting at $\sim10^{-4}$--$10^{-3}\:M_\odot\:{\rm{yr}}^{-1}$ inside cores of
initial masses $M_c\sim30$--500$\:M_\odot$ embedded in clumps with mass surface
densities $\Sigma_{\rm{cl}}\sim0.1$--3$\:{\rm{g\:cm}^{-2}}$. Fitting Robitaille
et al. models typically leads to slightly higher protostellar masses, but with
disk accretion rates $\sim100\times$ smaller. We discuss reasons for these
differences and overall implications of these first survey results for massive
star formation theories.


title:
Stable computations with flat radial basis functions using vector-valued
  rational approximations

abstract:
  One commonly finds in applications of smooth radial basis functions (RBFs)
that scaling the kernels so they are `flat' leads to smaller discretization
errors. However, the direct numerical approach for computing with flat RBFs
(RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing
this ill-conditioning that is based on a new method for rational approximation
(RA) of vector-valued analytic functions with the property that all components
of the vector share the same singularities. This new algorithm (RBF-RA) is more
accurate, robust, and easier to implement than the Contour-Pad\'e method, which
is similarly based on vector-valued rational approximation. In contrast to the
stable RBF-QR and RBF-GA algorithms, which are based on finding a better
conditioned base in the same RBF-space, the new algorithm can be used with any
type of smooth radial kernel, and it is also applicable to a wider range of
tasks (including calculating Hermite type implicit RBF-FD stencils). We present
a series of numerical experiments demonstrating the effectiveness of this new
method for computing RBF interpolants in the flat regime. We also demonstrate
the flexibility of the method by using it to compute implicit RBF-FD formulas
in the flat regime and then using these for solving Poisson's equation in a 3D
spherical shell.


title:
Compact Linearization for Binary Quadratic Problems subject to
  Assignment Constraints

abstract:
  We prove new necessary and sufficient conditions to carry out a compact
linearization approach for a general class of binary quadratic problems subject
to assignment constraints as it has been proposed by Liberti in 2007. The new
conditions resolve inconsistencies that can occur when the original method is
used. We also present a mixed-integer linear program to compute a
minimally-sized linearization. When all the assignment constraints have
non-overlapping variable support, this program is shown to have a totally
unimodular constraint matrix. Finally, we give a polynomial-time combinatorial
algorithm that is exact in this case and can still be used as a heuristic
otherwise.


title: Probabilistic Safety Programs

abstract:
  Achieving safe control under uncertainty is a key problem that needs to be
tackled for enabling real-world autonomous robots and cyber-physical systems.
This paper introduces Probabilistic Safety Programs (PSP) that embed both the
uncertainty in the environment as well as invariants that determine safety
parameters. The goal of these PSPs is to evaluate future actions or
trajectories and determine how likely it is that the system will stay safe
under uncertainty. We propose to perform these evaluations by first compiling
the PSP to a graphical model then using a fast variational inference algorithm.
We highlight the efficacy of the framework on the task of safe control of
quadrotors and autonomous vehicles in dynamic environments.


title:
Optimizing Open-Ended Crowdsourcing: The Next Frontier in Crowdsourced
  Data Management

abstract:
  Crowdsourcing is the primary means to generate training data at scale, and
when combined with sophisticated machine learning algorithms, crowdsourcing is
an enabler for a variety of emergent automated applications impacting all
spheres of our lives. This paper surveys the emerging field of formally
reasoning about and optimizing open-ended crowdsourcing, a popular and
crucially important, but severely understudied class of crowdsourcing---the
next frontier in crowdsourced data management. The underlying challenges
include distilling the right answer when none of the workers agree with each
other, teasing apart the various perspectives adopted by workers when answering
tasks, and effectively selecting between the many open-ended operators
appropriate for a problem. We describe the approaches that we've found to be
effective for open-ended crowdsourcing, drawing from our experiences in this
space.


title: Redundant interdependencies boost the robustness of multilayer networks

abstract:
  In the analysis of the robustness of multiplex networks, it is commonly
assumed that a node is functioning only if its interdependent nodes are
simultaneously functioning. According to this model, a multiplex network
becomes more and more fragile as the number of layers increases. In this
respect, the addition of a new layer of interdependent nodes to a preexisting
multiplex network will never improve its robustness. Whereas such a model seems
appropriate to understand the effect of interdependencies in the simplest
scenario of a network composed of only two layers, it may seem not suitable to
characterize the robustness of real systems formed by multiple network layers.
It seems in fact unrealistic that a real system, evolved, through the
development of multiple layers of interactions, towards a fragile structure. In
this paper, we introduce a model of percolation where the condition that makes
a node functional is that the node is functioning in at least two of the layers
of the network. The model reduces to the commonly adopted percolation model for
multiplex networks when the number of layers equals two. For larger number of
layers, however, the model describes a scenario where the addition of new
layers boosts the robustness of the system by creating redundant
interdependencies among layers. We prove this fact thanks to the development of
a message-passing theory able to characterize the model in both synthetic and
real-world multiplex graphs.


title: 3D Higher spin gravity and the fractional quantum Hall effect

abstract:
  This article is based on the talk "Fractional Spin Gravity" presented in the
31st International Colloquium on Group Theoretical Methods in Physics, Rio de
Janeiro, 19-25th June 2016. There we emphasised an implication of the works
[1,2] by N. Boulanger, P. Sundell and the author on fractional spin extensions
of 2+1D higher spin gravity. This is that higher spin gravity may govern
interactions of pseudo-particles excitations in the (fractional) quantum Hall
effect. More generally, fractional spin currents in 2+1D source higher spin
gravity curvatures.


title:
Cancellation in the Additive Twists of Fourier Coefficients for
  $\mathrm{GL}_2$ and $\mathrm{GL}_3$ over Number Fields

abstract:
  In this article, we study the sum of additively twisted Fourier coefficients
of an irreducible cuspidal automorphic representation of $\mathrm{GL}_2$ or
$\mathrm{GL}_3$ over an arbitrary number field. When the representation is
unramified at all non-archimedean places, we prove the Wilton type bound for
$\mathrm{GL}_2$ and the Miller type bound for $\mathrm{GL}_3$ which are uniform
in terms of the additive character.


title: Fully Hodge-Newton decomposable Shimura varieties

abstract:
  The motivation for this paper is the study of arithmetic properties of
Shimura varieties, in particular the Newton stratification of the special fiber
of a suitable integral model at a prime with parahoric level structure. This is
closely related to the structure of Rapoport-Zink spaces and of affine
Deligne-Lusztig varieties.
  We prove a Hodge-Newton decomposition for affine Deligne-Lusztig varieties
and for the special fibres of Rapoport-Zink spaces, relating these spaces to
analogous ones defined in terms of Levi subgroups, under a certain condition
(Hodge-Newton decomposability) which can be phrased in combinatorial terms.
  Second, we study the Shimura varieties in which every non-basic
$\sigma$-isogeny class is Hodge-Newton decomposable. We show that (assuming the
axioms of \cite{HR}) this condition is equivalent to nice conditions on either
the basic locus, or on all the non-basic Newton strata of the Shimura
varieties. We also give a complete classification of Shimura varieties
satisfying these conditions.
  While previous results along these lines often have restrictions to
hyperspecial (or at least maximal parahoric) level structure, and/or
quasi-split underlying group, we handle the cases of arbitrary parahoric level
structure, and of possibly non-quasi-split underlying groups. This results in a
large number of new cases of Shimura varieties where a simple description of
the basic locus can be expected. As a striking consequence of the results, we
obtain that this property is independent of the parahoric subgroup chosen as
level structure.
  We expect that our conditions are closely related to the question whether the
weakly admissible and admissible loci coincide.


title:
Towards an automated tool to evaluate the impact of the nuclear
  modification of the gluon density on quarkonium, D and B meson production in
  proton-nucleus collisions

abstract:
  We propose a simple and model-independent procedure to account for the impact
of the nuclear modification of the gluon density as encoded in nuclear
collinear PDF sets on two-to-two partonic hard processes in proton-nucleus
collisions. This applies to a good approximation to quarkonium, D and B meson
production, generically referred to H. Our procedure consists in parametrising
the square of the parton scattering amplitude, A_{gg -> H X} and constraining
it from the proton-proton data. Doing so, we have been able to compute the
corresponding nuclear modification factors for J/psi, Upsilon and D^0 as a
function of y and P_T at sqrt(s_NN)=5 and 8 TeV in the kinematics of the
various LHC experiments in a model independent way. It is of course justified
since the most important ingredient in such evaluations is the probability of
each kinematical configuration. Our computations for D mesons can also be
extended to B meson production. To further illustrate the potentiality of the
tool, we provide --for the first time-- predictions for the nuclear
modification factor for eta_c production in pPb collisions at the LHC.


title:
Detection of intensity bursts using Hawkes processes: an application to
  high frequency financial data

abstract:
  Given a stationary point process, an intensity burst is defined as a short
time period during which the number of counts is larger than the typical count
rate. It might signal a local non-stationarity or the presence of an external
perturbation to the system. In this paper we propose a novel procedure for the
detection of intensity bursts within the Hawkes process framework. By using a
model selection scheme we show that our procedure can be used to detect
intensity bursts when both their occurrence time and their total number is
unknown. Moreover, the initial time of the burst can be determined with a
precision given by the typical inter-event time. We apply our methodology to
the mid-price change in FX markets showing that these bursts are frequent and
that only a relatively small fraction is associated to news arrival. We show
lead-lag relations in intensity burst occurrence across different FX rates and
we discuss their relation with price jumps.


title: A Short Guide to Anyons and Modular Functors

abstract:
  To the working physicist, anyon theory is meant to describe certain
quasi-particle excitations occurring in two dimensional topologically ordered
systems. A typical calculation using this theory will involve operations such
as $\otimes$ to combine anyons, $F^{abc}_{d}$ to re-associate such
combinations, and $R^{ab}_c$ to commute or braid these anyons. Although there
is a powerful string-diagram notation that greatly assists these manipulations,
we still appear to be operating on particles arranged on a one-dimensional
line, algebraically ordered from left to right. The obvious question is, where
is the other dimension? The topological framework for considering these anyons
as truly living in a two dimensional space is known as a modular functor, or
topological quantum field theory. In this work we show how the apparently
one-dimensional algebraic anyon theory is secretly the theory of anyons living
in a fully two-dimensional system. The mathematical literature covering this
secret is vast, and we try to distill this down into something more manageable.


title: Laser remote magnetometry using mesospheric sodium

abstract:
  We have demonstrated a remote magnetometer based on sodium atoms in the
Earth's mesosphere, at a 106-kilometer distance from our instrument. A
1.33-watt laser illuminated the atoms, and the magnetic field was inferred from
back-scattered light collected by a telescope with a 1.55-meter-diameter
aperture. The measurement sensitivity was 162 nT/$\sqrt{Hz}$. The value of
magnetic field inferred from our measurement is consistent with an estimate
based on the Earth's known field shape to within a fraction of a percent.
Projected improvements in optics could lead to sensitivity of 20
nT/$\sqrt{Hz}$, and the use of advanced lasers or a large telescope could
approach 1-nT/$\sqrt{Hz}$ sensitivity. All experimental and theoretical
sensitivity values are based on a 60$^\circ$ angle between the laser beam axis
and the magnetic field vector; at the optimal 90$^\circ$ angle sensitivity
would be improved by about a factor of two.

categories: astro-ph.IM astro-ph.EP physics.atom-ph physics.ins-det physics.space-ph


title:
Squeezing giant spin states via geometric phase control in
  cavity-assisted Raman transitions

abstract:
  Squeezing ensemble of spins provides a way to surpass the standard quantum
limit (SQL) in quantum metrology and test the fundamental physics as well, and
therefore attracts broad interest. Here we propose an experimentally accessible
protocol to squeeze a giant ensemble of spins via the geometric phase control.
Using the cavity-assisted Raman transitions in a double $\Lambda$-type system,
we realize an effective Dicke model. Under the condition of vanishing effective
spin transition frequency, we find a particular evolution time where the cavity
decouples from the spins and the spin ensemble is squeezed considerably. Our
scheme has the potential to improve the sensitivity in quantum metrology with
spins by about two orders.


title: Conjectures involving a generalization of the sums of powers of integers

abstract:
  Some class of sums which naturally include the sums of powers of integers is
considered. A number of conjectures concerning a representation of these sums
is made.


title: Quantum estimation in neutrino oscillations

abstract:
  Neutrino oscillations are at the forefront of advances in Physics beyond the
Standard Model. Increasing accuracy in measurements of the neutrino mixing
matrix is an important challenge in current experiments. It depends on
parameters that do not directly correspond to observables of the neutrino
system. This type of estimation problem is handled by Quantum Estimation Theory
(QET) via the Fisher Information (FI) and the Quantum Fisher Information (QFI).
In this work, we analyze two-flavor neutrino oscillations within the framework
of QET. We compute the QFI for the mixing angle $\theta$ and show that mass
measurements are the ones that achieve optimal precision. We also study the FI
associated with flavor measurements and show that they are optimized at
specific neutrino times-of-flight. Therefore, although the usual population
measurement does not realize the precision limit set by the QFI, it can in
principle be implemented with the best possible sensitivity to $\theta $. We
study how these quantifiers relate to the single-particle, mode entanglement.
We demonstrate that this form of entanglement does not enhance neither of them.
In particular, this shows that in single-particle settings, entanglement is not
directly connected with the optimal precision in metrological tasks.


title:
Singe-photon multi-ports router based on the coupled cavity
  optomechanical system

abstract:
  A scheme of single-photon multi-port router is put forward by coupling two
optomechanical cavities with waveguides. It is shown that the coupled two
optomechanical cavities can exhibit photon blockade effect, which is generated
from interference of three mode interaction. A single-photon travel along the
system is calculated. The results show that the single photon can be controlled
in the multi-port system because of the radiation pressure, which should be
useful for constructing quantum network.


title:
Explicit symplectic algorithms based on generating functions for
  relativistic charged particle dynamics in time-dependent electromagnetic
  field

abstract:
  Relativistic dynamics of a charged particle in time-dependent electromagnetic
fields has theoretical significance and a wide range of applications. It is
often multi-scale and requires accurate long-term numerical simulations using
symplectic integrators. For modern large-scale particle simulations in complex,
time-dependent electromagnetic field, explicit symplectic algorithms are much
more preferable. In this paper, we treat the relativistic dynamics of a
particle as a Hamiltonian system on the cotangent space of the space-time, and
construct for the first time explicit symplectic algorithms for relativistic
charged particles of order 2 and 3 using the sum-split technique and generating
functions.


title: Transport exponents of states with large support

abstract:
  We extend results of Damanik and Tcheremchantsev on estimating transport
exponents to initial states supported on more than one site. These general
results for upper and lower bounds are then applied to several classes of
models, including Sturmian, quiasi-periodic and substitution-generated
potentials, and random polymer model.


title:
AutoGP: Exploring the Capabilities and Limitations of Gaussian Process
  Models

abstract:
  We investigate the capabilities and limitations of Gaussian process models by
jointly exploring three complementary directions: (i) scalable and
statistically efficient inference; (ii) flexible kernels; and (iii) objective
functions for hyperparameter learning alternative to the marginal likelihood.
Our approach outperforms all previously reported GP methods on the standard
MNIST dataset; performs comparatively to previous kernel-based methods using
the RECTANGLES-IMAGE dataset; and breaks the 1% error-rate barrier in GP models
using the MNIST8M dataset, showing along the way the scalability of our method
at unprecedented scale for GP models (8 million observations) in classification
problems. Overall, our approach represents a significant breakthrough in kernel
methods and GP models, bridging the gap between deep learning approaches and
kernel machines.


title:
On the Stability of Satellite Planes I: Effects of Mass, Velocity, Halo
  Shape and Alignment

abstract:
  The recently discovered vast thin plane of dwarf satellites orbiting the
Andromeda Galaxy (M31) adds to the mystery of the small scale distribution of
the Local Group's galaxy population. Such well defined planar structures are
apparently rare occurrences in cold dark matter cosmological simulations, and
we lack a coherent explanation of their formation and existence. In this paper,
we explore the long-term survivability of thin planes of dwarfs in galactic
halos, focusing, in particular, on systems mimicking the observed Andromeda
distribution. The key results show that, in general, planes of dwarf galaxies
are fragile, sensitive to the shape of the dark matter halo and other
perturbing effects. In fact, long lived planes of satellites only exist in
polar orbits in spherical dark matter halos, presenting a challenge to the
observed Andromeda plane which is significantly tilted with respect to the
optical disk. Our conclusion is that, in standard cosmological models, planes
of satellites are generally short lived, and hence we must be located at a
relatively special time in the evolution of the Andromeda Plane, lucky enough
to see its coherent pattern.


title: Sequential Learning without Feedback

abstract:
  In many security and healthcare systems a sequence of features/sensors/tests
are used for detection and diagnosis. Each test outputs a prediction of the
latent state, and carries with it inherent costs. Our objective is to {\it
learn} strategies for selecting tests to optimize accuracy \& costs.
Unfortunately it is often impossible to acquire in-situ ground truth
annotations and we are left with the problem of unsupervised sensor selection
(USS). We pose USS as a version of stochastic partial monitoring problem with
an {\it unusual} reward structure (even noisy annotations are unavailable).
Unsurprisingly no learner can achieve sublinear regret without further
assumptions. To this end we propose the notion of weak-dominance. This is a
condition on the joint probability distribution of test outputs and latent
state and says that whenever a test is accurate on an example, a later test in
the sequence is likely to be accurate as well. We empirically verify that weak
dominance holds on real datasets and prove that it is a maximal condition for
achieving sublinear regret. We reduce USS to a special case of multi-armed
bandit problem with side information and develop polynomial time algorithms
that achieve sublinear regret.


title:
Diffusive stability of spatially periodic patterns with a conservation
  law

abstract:
  Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and
Schneider in their analysis of the fourth-order scalar Swift-Hohenberg
equation, we carry out a rigorous small-amplitude stability analysis of Turing
patterns for the model introduced by Matthews and Cox for pattern formation
with a conservation law. Our results confirm that stability is accurately
predicted in the small-amplitude limit by the formal modified Ginzburg-Lanadau
system (mGL) consisting of a coupled Ginzburg-Landau equation and mean mode
equation derived by Matthews and Cox, rigorously validating the standard weakly
unstable approximation.


title: Star Formation Law in the Milky Way

abstract:
  The Schmidt law (SF law) in the Milky Way was investigated using 3D
distribution maps of HII regions, HI and molecular (\Htwo) gases with spatial
resolutions of $\sim 1$ kpc in the Galactic plane and a few tens of pc in the
vertical direction. HII regions were shown to be distributed in a star-forming
(SF) disk with nearly constant vertical full thickness 92 pc in spatial
coincidence with the molecular gas disk. The vertically averaged volume star
formation rate (SFR) $\rho_{\rm SFR}$ in the SF disk is related to the surface
SFR $\Sigma_{\rm SFR}$ by $\rho_{\rm SFR} /[{\rm M_\odot y^{-1} kpc^{-3}}]
=9.26\times \Sigma_{\rm SFR}/[{\rm M_\odot y^{-1} kpc^{-2}}]$. The SF law
fitted by a single power law of gas density in the form of $\Sigma_{\rm SFR}
\propto \rho_{\rm SFR} \propto \rho_{\rm gas}^\alpha$ and $\propto \Sigma_{\rm
gas}^\beta$ showed indices of $\alpha=0.78 \pm 0.05$ for $\rho_{\rm H_2}$ and
$2.15 \pm 0.08$ for $\rho_{\rm total}$, and $\beta=1.14\pm 0.23$ for
$\Sigma_{\rm total}$, where $\rho$ and $\Sigma$ denote volume and surface
densities, respectively. The star formation rate is shown to be directly
related to the molecular gas, but indirectly to HI and total gas densities. The
dependence of the SF law on the gaseous phase is explained by the phase
transition theory between HI and H$_2$ gases.


title: An application of continuous logic to fixed point theory

abstract:
  In aiming to apply to a broader class of examples the Avigad-Iovino
"ultraproducts and metastability" approach to obtaining uniformity for
convergence of sequences, we construct a framework using continuous logic that
in particular is able to handle discontinuous functions in its domain of
discourse. This setup weakens the usual continuity requirements for functions,
but compensates for the loss of control by introducing a notion of "linear
structure" that captures in a quite general way the situation of having
geodesics between every pair of points, and has as a special case the vector
space structure of Banach spaces. We use this to apply the Avigad-Iovino method
to specific convergence results from functional analysis involving iterations
of discontinuous functions, and so obtain uniform metastable convergence in
those results.


title:
Localization of weakly interacting bosons in two dimensions: disorder vs
  lattice geometry effects

abstract:
  We investigate the effects of disorder and lattice geometry against
localisation phenomena in a weakly interacting ultracold bosonic gas confined
in a 2D optical lattice. The behaviour of the quantum fluid is studied at the
mean-field level performing computational experiments, as a function of
disorder strength for lattices of sizes similar to current experiments.
Quantification of localisation, away from the Bose glass phase, was obtained
directly from the stationary density profiles through a robust statistical
analysis of the condensate component, as a function of the disorder amplitude.
Our results show a smooth transition, or crossover, to localisation induced by
disorder in square and triangular lattices. In contrast, associated to its
larger tunneling amplitude, honeycomb lattices show absence of localisation for
the same range of disorder strengths and same lattice amplitude, while also
exhibiting partial localisation for large disorder amplitudes. We also conclude
that the coordination number z have a partial influence on how fast this smooth
transition occurs as the system size increases. Signatures of disorder are also
found in the ground state energy spectrum, where a continuous distribution
emerges instead of a distribution of sharp peaks proper to the system in the
absence of disorder.


title:
Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and
  Novel 2D Emergent Fermions

abstract:
  Tunable quantum phase transitions and novel emergent fermions in solid state
materials are fascinating subjects of research. Here, we propose a new stable
two-dimensional (2D) material, the blue phosphorene oxide (BPO), which exhibits
both. Based on first-principles calculations, we show that its equilibrium
state is a narrow-bandgap semiconductor with three bands at low energy.
Remarkably, a moderate strain can drive a semiconductor-to-semimetal quantum
phase transition in BPO. At the critical transition point, the three bands
cross at a single point at Fermi level, around which the quasiparticles are a
novel type of 2D pseudospin-1 fermions. Going beyond the transition, the system
becomes a symmetry-protected semimetal, for which the conduction and valence
bands touch quadratically at a single Fermi point that is protected by
symmetry, and the low-energy quasiparticles become another novel type of 2D
double Weyl fermions. We construct effective models characterizing the phase
transition and these novel emergent fermions, and we point out several exotic
effects, including super Klein tunneling, supercollimation, and universal
optical absorbance. Our result reveals BPO as an intriguing platform for the
exploration of fundamental properties of quantum phase transitions and novel
emergent fermions, and also suggests its great potential in nanoscale device
applications.


title:
Going off the Grid: Iterative Model Selection for Biclustered Matrix
  Completion

abstract:
  We consider the problem of performing matrix completion with side information
on row-by-row and column-by-column similarities. We build upon recent proposals
for matrix estimation with smoothness constraints with respect to row and
column graphs. We present a novel iterative procedure for directly minimizing
an information criterion in order to select an appropriate amount row and
column smoothing, namely perform model selection. We also discuss how to
exploit the special structure of the problem to scale up the estimation and
model selection procedure via the Hutchinson estimator. We present simulation
results and an application to predicting associations in imaging-genomics
studies.


title:
Uniquely solvable and energy stable decoupled schemes for
  Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry

abstract:
  We propose and analyze two novel decoupled numerical schemes for solving the
Cahn-Hilliard-Stokes-Darcy (CHSD) model for two-phase flows in karstic
geometry. In the first numerical scheme, we explore a fractional step method
(operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from
the velocity field (Stokes-Darcy fluid equations). To further decouple the
Stokes-Darcy system, we introduce a first order pressure stabilization term in
the Darcy solver in the second numerical scheme so that the Stokes system is
decoupled from the Darcy system and hence the CHSD system can be solved in a
fully decoupled manner. We show that both decoupled numerical schemes are
uniquely solvable, energy stable, and mass conservative. Ample numerical
results are presented to demonstrate the accuracy and efficiency of our
schemes.


title: VRPBench: A Vehicle Routing Benchmark Tool

abstract:
  The number of optimization techniques in the combinatorial domain is large
and diversified. Nevertheless, there is still a lack of real benchmarks to
validate optimization algorithms. In this work we introduce VRPBench, a tool to
create instances and visualize solutions to the Vehicle Routing Problem (VRP)
in a planar graph embedded in the Euclidean 2D space. We use VRPBench to model
a real-world mail delivery case of the city of Artur Nogueira. Such scenarios
were characterized as a multi-objective optimization of the VRP. We extracted a
weighted graph from a digital map of the city to create a challenging benchmark
for the VRP. Each instance models one generic day of mail delivery with
hundreds to thousands of delivery points, thus allowing both the comparison and
validation of optimization algorithms for routing problems.


title: Runaway gas accretion and gap opening versus type~I migration

abstract:
  Growing planets interact with their natal protoplanetary disc, which exerts a
torque onto them allowing them to migrate in the disc. Small mass planets do
not affect the gas profile and migrate in the fast type~I migration. Although
type~I migration can be directed outwards for planets smaller than $20-30
M_\oplus$, planets above this mass should be lost into the central star long
before the disc disperses. Massive planets open a gap and subsequently migrate
in the slower, type~II migration, which could save them from migrating all the
way to the star. Hence, growing giant planets can be saved if and only if they
can reach the gap opening mass, because this extends their migration
time-scale, allowing them to eventually survive at large orbits until the disc
itself disperses.
  However, most of the previous studies only measured the torques on planets
with fixed masses and orbits to determine the migration rate. Additionally, the
transition between type~I and type~II migration itself is not well studied.
Here we use isothermal 2D disc simulations with FARGO-2D1D to study the
migration behaviour of gas accreting protoplanets in discs. We find that
migrating giant planets always open gaps in the disc. We further show
analytically and numerically that planets growing in the runaway gas accretion
regime will reach gap opening masses before migrating all the way to the
central star if the disc is not extremely viscous and/or thick. An accretion
rate limited to the radial gas flow in the disc, in contrast, is not fast
enough. When gas accretion by the planet is taken into account, the gap opening
process is accelerated because the planet accretes material originating from
its horseshoe region. This allows an accreting planet to transition to type~II
migration before being lost even if gas fails to be provided for a rapid enough
growth and the gap opening mass is not reached.


title:
An Alternative Approach to Mean Field Game with Major and Minor Players,
  and Applications to Herders Impacts

abstract:
  The goal of the paper is to introduce a formulation of the mean field game
with major and minor players as a fixed point on a space of controls. This
approach emphasizes naturally the role played by McKean-Vlasov dynamics in some
of the players optimization problems. We apply this approach to linear
quadratic models for which we recover the existing solutions for open loop
equilibria, and we show that we can also provide solutions for closed loop
versions of the game. Finally, we implement numerically our theoretical results
on a simple model of flocking.


title: Homomorphism reductions on Polish groups

abstract:
  In an earlier paper, we introduced the following pre-order on the subgroups
of a given Polish group: if $G$ is a Polish group and $H,L \subseteq G$ are
subgroups, we say $H$ is {\em homomorphism reducible} to $L$ iff there is a
continuous group homomorphism $\varphi : G \rightarrow G$ such that $H =
\varphi^{-1} (L)$. We previously showed that there is a $K_\sigma$ subgroup,
$L$, of the countable power of any locally compact Polish group, $G$, such that
every $K_\sigma$ subgroup of $G^\omega$ is homomorphism reducible to $L$. In
the present work, we show that this fails in the countable power of the group
of increasing homeomorphisms of the unit interval.


title: Strong edge-colorings of sparse graphs with large maximum degree

abstract:
  A {\em strong $k$-edge-coloring} of a graph $G$ is a mapping from $E(G)$ to
$\{1,2,\ldots,k\}$ such that every two adjacent edges or two edges adjacent to
the same edge receive distinct colors. The {\em strong chromatic index}
$\chi_s'(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ admits a
strong $k$-edge-coloring. We give bounds on $\chi_s'(G)$ in terms of the
maximum degree $\Delta(G)$ of a graph $G$. when $G$ is sparse, namely, when $G$
is $2$-degenerate or when the maximum average degree ${\rm Mad}(G)$ is small.
We prove that the strong chromatic index of each $2$-degenerate graph $G$ is at
most $5\Delta(G) +1$. Furthermore, we show that for a graph $G$, if ${\rm
Mad}(G)< 8/3$ and $\Delta(G)\geq 9$, then $\chi_s'(G)\leq 3\Delta(G) -3$ (the
bound $3\Delta(G) -3$ is sharp) and if ${\rm Mad}(G)<3$ and $\Delta(G)\geq 7$,
then $\chi_s'(G)\leq 3\Delta(G)$ (the restriction ${\rm Mad}(G)<3$ is sharp).


title:
Contribution of the first galaxies to the cosmic
  far-infrared/sub-millimeter background - I. Mean background level

abstract:
  We study the contribution of the first galaxies to the
far-infrared/sub-millimeter (FIR/sub-mm) extragalactic background light (EBL)
by implementing an analytical model for dust emission. We explore different
dust models, assuming different grain size distributions and chemical
compositions. According to our findings, observed re-radiated emission from
dust in dwarf-size galaxies at $z \sim 10$ would peak at a wavelength of $\sim
500 \mu {\rm m}$ with observed fluxes of $\sim 10^{-3} - 10^{-2}$ nJy, which is
below the capabilities of current observatories. In order to be detectable,
model sources at these high redshifts should exhibit luminosities of $\gtrsim
10^{12} L_{\odot}$, comparable to that of local ultra-luminous systems. The
FIR/sub-mm EBL generated by primeval galaxies peaks at $\sim 500 \mu {\rm m}$,
with an intensity ranging from $\sim 10^{-4}$ to $10^{-3} {\rm nW \ m^{-2} \
sr^{-1}}$, depending on dust properties. These values are $\sim 3 - 4$ orders
of magnitude below the absolute measured cosmic background level, suggesting
that the first galaxies would not contribute significantly to the observed
FIR/sub-mm EBL. Our model EBL exhibits a strong correlation with the
dust-to-metal ratio, where we assume a fiducial value of $D = 0.005$,
increasing almost proportionally to it. Thus, measurements of the FIR/sub-mm
EBL could provide constraints on the amount of dust in the early Universe. Even
if the absolute signal from primeval dust emission may be undetectable, it
might still be possible to obtain information about it by exploring angular
fluctuations at $\sim 500 \mu {\rm m}$, close to the peak of dust emission from
the first galaxies.


title: Finite State Mean Field Games with Major and Minor Players

abstract:
  The goal of the paper is to develop the theory of finite state mean field
games with major and minor players when the state space of the game is finite.
We introduce the finite player games and derive a mean field game formulation
in the limit when the number of minor players tends to infinity. In this limit,
we prove that the value functions of the optimization problems are viscosity
solutions of PIDEs of the HJB type, and we construct the best responses for
both types of players. From there, we prove existence of Nash equilibria under
reasonable assumptions. Finally we prove that a form of propagation of chaos
holds in the present context and use this result to prove existence of
approximate Nash equilibria for the finite player games from the solutions of
the mean field games. this vindicate our formulation of the mean field game
problem.


title: Split Nash Equilibria for Related Games and Applications to Economics

abstract:
  In this paper we introduce the concept of split Nash equilibrium problems
associated with two related noncooperative strategic games. Then we apply the
Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium
problems of related noncooperative strategic games, in which the strategy sets
of the players are nonempty closed and convex subsets in Banach spaces. As
application of this existence to economics, an example is provided to study the
existence of split Nash equilibrium of utilities of two related economies. As
applications, we study the existence of split Nash equilibrium in the dual
extended Bertrant duopoly model of price competition


title: Two-scale analysis of solar magnetic helicity

abstract:
  We develop a two-scale formalism to determine global magnetic helicity
spectra in systems where the local magnetic helicity has opposite signs on both
sides of the equator, giving rise to cancelation with conventional methods. We
verify this approach using first a synthetic one-dimensional magnetic field and
then two-dimensional slices from a three-dimensional alpha effect-type
dynamo-generated magnetic field with forced turbulence of opposite helicity
above and below the midplane of the domain. We then apply this formalism to
global solar synoptic vector magnetograms. To improve the statistics, data from
three consecutive Carrington rotations (2161--2163) are combined into a single
map. We find that the spectral magnetic helicity representative of the northern
hemisphere is negative at all wavenumbers and peaks at ~ 0.06 Mm^{-1} (scales
around 100 Mm). There is no evidence of bihelical magnetic fields that are
found in three-dimensional turbulence simulations of helicity-driven alpha
effect-type dynamos.


title:
Gate-independent energy gap in non-covalently intercalated bilayer
  graphene on SiC(0001)

abstract:
  Our first-principles calculations show that an energy gap around 0.12-0.25 eV
can be engineered in epitaxial graphene on SiC(0001) through the non-covalent
intercalation of transition- or alkali-metals, yet originated from the distinct
mechanisms. The former is attributed to the combined effects of metal induced
perpendicular electric field and interaction while the latter is solely
attributed to the built-in electric field. A great advantage of this scheme is
that the gap size is almost independent of the gate voltage up to 1 V/nm, thus
reserving the electric means to tune the Fermi level of graphene when
configured as field-effect transistors. Given the recent progress in
experimental techniques on the intercalated graphene, our findings provide a
practical way to incorporate the graphene with the current semiconductor
industry.


title: Almost-Sure Reachability in Stochastic Multi-Mode System

abstract:
  A constant-rate multi-mode system is a hybrid system that can switch freely
among a finite set of modes, and whose dynamics is specified by a finite number
of real-valued variables with mode-dependent constant rates. We introduce and
study a stochastic extension of a constant-rate multi-mode system where the
dynamics is specified by mode-dependent compactly supported probability
distributions over a set of constant rate vectors. Given a tolerance
$\varepsilon > 0$, the almost-sure reachability problem for stochastic
multi-mode systems is to decide the existence of a control strategy that steers
the system almost-surely from an arbitrary start state to an
$\varepsilon$-neighborhood of an arbitrary target state while staying inside a
pre-specified safety set. We prove a necessary and sufficient condition to
decide almost-sure reachability and, using this condition, we show that
almost-sure reachability can be decided in polynomial time. Our algorithm can
be used as a path-following algorithm in combination with any off-the-shelf
path-planning algorithm to make a robot or an autonomous vehicle with noisy
low-level controllers follow a given path with arbitrary precision.


title:
Relative quantum coherence, incompatibility, and quantum correlations of
  states

abstract:
  Quantum coherence, incompatibility, and quantum correlations are fundamental
features of quantum physics. A unified view of those features is crucial for
revealing quantitatively their intrinsic connections. We define the relative
quantum coherence of two states as the coherence of one state in the reference
basis spanned by the eigenvectors of another one and establish its quantitative
connections with the extent of mutual incompatibility of two states. We also
show that the proposed relative quantum coherence, which can take any form of
measures such as $l_1$ norm and relative entropy, can be interpreted as or
connected to various quantum correlations such as quantum discord, symmetric
discord, entanglement of formation, and quantum deficits. Our results reveal
conceptual implications and basic connections of quantum coherence, mutual
incompatibility, and quantum correlations.


title: The rigidity of hypersurface in Euclidean space

abstract:
  In the present paper, we revisit the rigidity of hypersurfaces in Euclidean
space. We highlight Darboux equation and give new proof of rigidity of
hypersurfaces by energy method and maximal principle.


title: Weak Convergence (IA). Sequences of Random Vectors

abstract:
  (English) This monograph aims at presenting the core weak convergence theory
for sequences of random vectors with values in $\mathbb{R}^k$. In some places,
a more general formulation in metric spaces is provided. It lays out the
necessary foundation that paves the way to applications in particular subfields
of the theory. In particular, the needs of Asymptotic Statistics are addressed.
A whole chapter is devoted to weak convergence in $\mathbb{R}$ where specific
tools, for example for handling weak convergence of sequences using independent
and indentically distributed random variables such that the Renyi's
representations by means of standard uniform or exponential random variables,
are stated. The function empirical process is presented as a powerful tool for
solving a considerable number of asymptotic problems in Statistics. The text is
written in a self-contained approach whith the proofs of all used results at
the exception of the general Skorohod-Wichura Theorem.


title:
Refined Shapley-Folkman Lemma and Its Application in Duality Gap
  Estimation

abstract:
  Based on concepts like kth convex hull and finer characterization of
nonconvexity of a function, we propose a refinement of the Shapley-Folkman
lemma and derive a new estimate for the duality gap of nonconvex optimization
problems with separable objective functions. We apply our result to a network
flow problem and the dynamic spectrum management problem in communication
systems as examples to demonstrate that the new bound can be qualitatively
tighter than the existing ones. The idea is also applicable to cases with
general nonconvex constraints.


title:
Numeric Solution of Advection-Diffusion Equations by a Discrete Time
  Random Walk Scheme

abstract:
  Explicit numerical finite difference schemes for partial differential
equations are well known to be easy to implement but they are particularly
problematic for solving equations whose solutions admit shocks, blowups and
discontinuities. Here we present an explicit numerical scheme for solving
non-linear advection-diffusion equations admitting shock solutions that is both
easy to implement and stable. The numerical scheme is obtained by considering
the continuum limit of a discrete time and space stochastic process for
non-linear advection-diffusion. The stochastic process is well posed and this
guarantees the stability of the scheme. Several examples are provided to
highlight the importance of the formulation of the stochastic process in
obtaining a stable and accurate numerical scheme.


title: Analysis of the semileptonic decay \Lambda_c->ne^+\nu_e

abstract:
  The semileptonic weak decay process of the $\Lambda_c$ baryon to the neutron
$\Lambda_c\rightarrow ne^+\nu_e$ is examined. The transition form factors are
investigated with light-cone QCD sum rules. The differential decay width is
obtained in the dynamical region by fitting the sum rules-allowed results with
the dipole formula. The total decay width and the branching ratio are estimated
to be $\Gamma(\Lambda_c\rightarrow
ne^+\nu_e)=(8.57\pm0.41)\times10^{-15}\,\mbox{GeV}$ and
$\mbox{Br}(\Lambda_c\rightarrow ne^+\nu_e)=0.26\pm0.01\%$, respectively.


title:
A Joint Indoor WLAN Localization and Outlier Detection Scheme Using
  LASSO and Elastic-Net Optimization Techniques

abstract:
  In this paper, we introduce two indoor Wireless Local Area Network (WLAN)
positioning methods using augmented sparse recovery algorithms. These schemes
render a sparse user's position vector, and in parallel, minimize the distance
between the online measurement and radio map. The overall localization scheme
for both methods consists of three steps: 1) coarse localization, obtained from
comparing the online measurements with clustered radio map. A novel graph-based
method is proposed to cluster the offline fingerprints. In the online phase, a
Region Of Interest (ROI) is selected within which we search for the user's
location; 2) Access Point (AP) selection; and 3) fine localization through the
novel sparse recovery algorithms. Since the online measurements are subject to
inordinate measurement readings, called outliers, the sparse recovery methods
are modified in order to jointly estimate the outliers and user's position
vector. The outlier detection procedure identifies the APs whose readings are
either not available or erroneous. The proposed localization methods have been
tested with Received Signal Strength (RSS) measurements in a typical office
environment and the results show that they can localize the user with
significantly high accuracy and resolution which is superior to the results
from competing WLAN fingerprinting localization methods.


title:
Collective cell migration without proliferation: density determines cell
  velocity and wave velocity

abstract:
  Collective cell migration contributes to embryogenesis, wound healing and
tumor metastasis. Cell monolayer migration experiments help understanding what
determines the movement of cells far from the leading edge. Inhibiting cell
proliferation limits cell density increase and prevents jamming; we observe
long-duration migration and quantify space-time characteristics of the velocity
profile over large length- and time-scales. Velocity waves propagate backwards
and their frequency depends only on cell density at the moving front. Both cell
average velocity and wave velocity increase linearly with the cell effective
radius regardless of the distance to the front. Inhibiting lamellipodia
decreases cell velocity while waves either disappear or have a lower frequency.
Our model combines conservation laws, monolayer mechanical properties and a
phenomenological coupling between strain and polarity: advancing cells pull on
their followers which then become polarized. With reasonable values of
parameters, this model agrees with several of our experimental observations.
Together, our experiments and model disantangle the respective contributions of
active velocity and of proliferation in monolayer migration, explain how cells
maintain their polarity far from the moving front, and highlight the importance
of strain-polarity coupling and density in long-range information propagation.


title:
Structured Group Sparsity: A Novel Indoor WLAN Localization, Outlier
  Detection, and Radio Map Interpolation Scheme

abstract:
  This paper introduces novel schemes for indoor localization, outlier
detection, and radio map interpolation using Wireless Local Area Networks
(WLANs). The localization method consists of a novel multicomponent
optimization technique that minimizes the squared $\ell_{2}$-norm of the
residuals between the radio map and the online Received Signal Strength (RSS)
measurements, the $\ell_{1}$-norm of the user's location vector, and weighted
$\ell_{2}$-norms of layered groups of Reference Points (RPs). RPs are grouped
using a new criterion based on the similarity between the so-called Access
Point (AP) coverage vectors. In addition, since AP readings are prone to
containing inordinate readings, called outliers, an augmented optimization
problem is proposed to detect the outliers and localize the user with cleaned
online measurements. Moreover, a novel scheme to record fingerprints from a
smaller number of RPs and estimate the radio map at RPs without recorded
fingerprints is developed using sparse recovery techniques. All localization
schemes are tested on RSS fingerprints collected from a real environment. The
overall scheme has comparable complexity with competing approaches, while it
performs with high accuracy under a small number of APs and finer granularity
of RPs.


title: On subgroups of first homology

abstract:
  We prove several new theorems regarding first homology. Some dichotomies for
first homology of Peano continua are presented, as well as a notion of strong
abelianization for arbitrary path connected metric spaces. We also show that
the fundamental group of the Hawaiian earring has Borel subgroups of almost all
multiplicative and additive types.


title: Minimal models of compact symplectic semitoric manifolds

abstract:
  A symplectic semitoric manifold is a symplectic $4$-manifold endowed with a
Hamiltonian $(S^1 \times \mathbb{R})$-action satisfying certain conditions. The
goal of this paper is to construct a new symplectic invariant of symplectic
semitoric manifolds, the helix, and give applications. The helix is a
symplectic analogue of the fan of a nonsingular complete toric variety in
algebraic geometry, that takes into account the effects of the monodromy near
focus-focus singularities. We give two applications of the helix: first, we use
it to give a classification of the minimal models of symplectic semitoric
manifolds, where "minimal" is in the sense of not admitting any blowdowns. The
second application is an extension to the compact case of a well known result
of V\~{u} Ngoc about the constraints posed on a symplectic semitoric manifold
by the existence of focus-focus singularities. The helix permits to translate a
symplectic geometric problem into an algebraic problem, and the paper describes
a method to solve this type of algebraic problem.


title:
Modern WLAN Fingerprinting Indoor Positioning Methods and Deployment
  Challenges

abstract:
  Wireless Local Area Network (WLAN) has become a promising choice for indoor
positioning as the only existing and established infrastructure, to localize
the mobile and stationary users indoors. However, since WLAN has been initially
designed for wireless networking and not positioning, the localization task
based on WLAN signals has several challenges. Amongst the WLAN positioning
methods, WLAN fingerprinting localization has recently achieved great attention
due to its promising results. WLAN fingerprinting faces several challenges and
hence, in this paper, our goal is to overview these challenges and the
state-of-the-art solutions. This paper consists of three main parts: 1)
Conventional localization schemes; 2) State-of-the-art approaches; 3) Practical
deployment challenges. Since all the proposed methods in WLAN literature have
been conducted and tested in different settings, the reported results are not
equally comparable. So, we compare some of the main localization schemes in a
single real environment and assess their localization accuracy, positioning
error statistics, and complexity. Our results depict illustrative evaluation of
WLAN localization systems and guide to future improvement opportunities.


title:
Space group symmetries of the phases of (Pb0.94Sr0.06)(ZrxTi1-x)O3
  across the antiferrodistortive phase transition in the composition range
  0.620<x<0.940

abstract:
  The existing controversies about the space group symmetries of Pb(ZrxTi1-x)O3
(PZT) above and below antiferrodistortive (AFD) phase transition temperature
(TAFD) in the Zr4+- rich (0.620<x<0.940) compositions are addressed using the
results of dielectric, synchrotron x-ray powder diffraction (SXRPD) and neutron
powder diffraction (NPD) studies. These compositions undergo an AFD phase
transition above room temperature due to tilting of oxygen octahedral leading
to a superlattice phase of PZT. We have substituted 6% Sr2+ at Pb2+-site to
enhance the tilt angle and thereby the intensity of the superlattice peaks. The
real and imaginary parts of complex dielectric permittivity have been used to
locate the paraelectric to ferroelectric and ferroelectric to AFD phase
transitions. Rietveld analysis of SXRPD and NPD profiles unambiguously reject
the rhombohedral phases in R3c and R3m space groups below and above TAFD,
respectively, with or without a coexisting monoclinic phase in Cm space group,
and confirm that the true symmetries are monoclinic in Cc and Cm space groups
below and above TAFD, respectively. Based on these and previous findings a
phase diagram of PSZT for 0.40<x<0.90 showing stability fields of monoclinic Cc
and monoclinic Cm, tetragonal P4mm and cubic Pm3m phases has also been
presented.


title:
Critical Transitions in Public Opinion: A Case Study of American
  Presidential Election

abstract:
  At the tipping point, it is known that small incident can trigger dramatic
societal shift. Getting early-warning signals for such changes are valuable to
avoid detrimental outcomes such as riots or collapses of nations. However, it
is notoriously hard to capture the processes of such transitions in the
real-world. Here, we demonstrate the occurrence of a major shift in public
opinion in the form of political support. Instead of simple swapping of ruling
parties, we study the regime shift of a party popularity based on its
attractiveness by examining the American presidential elections during
1980-2012. A single irreversible transition is detected in 1991. Once a
transition happens, recovery to the original level of attractiveness does not
bring popularity of the political party back. Remarkably, this transition is
corroborated by tell-tale early-warning signature of critical slowing down. Our
approach is applicable to shifts in public attitude within any social system.


title:
Proximal Algorithms and Temporal Differences for Large Linear Systems:
  Extrapolation, Approximation, and Simulation

abstract:
  We consider large linear and nonlinear fixed point problems, and solution
with proximal algorithms. We show that there is a close connection between two
seemingly different types of methods from distinct fields: 1) Proximal
iterations for linear systems of equations, which are prominent in numerical
analysis and convex optimization, and 2) Temporal difference (TD) type methods,
such as TD(lambda), LSTD(lambda), and LSPE(lambda), which are central in
simulation-based approximate dynamic programming/reinforcement learning
(DP/RL), and its recent prominent successes in large-scale game contexts, among
others.
  One benefit of this connection is a new and simple way to accelerate the
standard proximal algorithm by extrapolation towards the TD iteration, which
generically has a faster convergence rate. Another benefit is the potential
integration into the proximal algorithmic context of several new ideas that
have emerged in the DP/RL context. We discuss some of the possibilities, and in
particular, algorithms that project each proximal iterate onto the subspace
spanned by a small number of basis functions, using low-dimensional
calculations and simulation. A third benefit is that insights and analysis from
proximal algorithms can be brought to bear on the enhancement of TD methods.
  The linear fixed point methodology can be extended to nonlinear fixed point
problems involving a contraction, thus providing guaranteed and potentially
substantial acceleration of the proximal and forward backward splitting
algorithms at no extra cost. Moreover, the connection of proximal and TD
methods can be extended to nonlinear (nondifferentiable) fixed point problems
through new proximal-like algorithms that involve successive linearization,
similar to policy iteration in DP.


title: Maxwell's equal area law for black holes in power Maxwell invariant

abstract:
  In this paper, we consider the phase transition of black hole in power
Maxwell invariant by means of Maxwell's equal area law. First, we review and
study the analogy of nonlinear charged black hole solutions with the Van der
Waals gas-liquid system in the extended phase space, and obtain isothermal
$P$-$v$ diagram. Then, using the Maxwell's equal area law we study the phase
transition of AdS black hole with different temperatures. Finally, we extend
the method to the black hole in the canonical (grand canonical) ensemble in
which charge (potential) is fixed at infinity. Interestingly, we find the phase
transition occurs in the both ensembles. We also study the effect of the
parameters of the black hole on the two-phase coexistence. The results show
that the black hole may go through a small-large phase transition similar to
those of usual non-gravity thermodynamic systems.


title:
Comparison between the continuum threshold and the Polyakov loop as
  deconfinement order parameters

abstract:
  We study the relation between the continuum threshold as function of the
temperature $s_0(T)$ within finite energy sum rules and the trace of the
Polyakov loop $\Phi$ in the framework of a nonlocal SU(2) chiral quark model,
establishing a contact between both deconfinement order parameters at finite
temperature $T$ and chemical potential $\mu$. In our analysis, we also include
the order parameter for the chiral symmetry restoration, the chiral quark
condensate.
  We found that $s_0$ and $\Phi$ providing us the same information for the
deconfinement transition, both for the zero and finite chemical potential
cases. At zero density, the critical temperatures for both quantities coincide
exactly and, at finite $\mu$ both order parameters provide evidence for the
appearance of a quarkyonic phase.


title: Vitali properties of Banach analytic manifolds

abstract:
  We discuss possible generalizations of Vitali convergence theorem when the
source and the target are Banach analytic manifolds. These results are then
applied to study behavior of holomorphic mappings between Banach analytic
manifolds. Explicit examples of manifolds having Vitali properties are also
provided.


title: Wireless Fractal Cellular Networks

abstract:
  With the seamless coverage of wireless cellular networks in modern society,
it is interesting to consider the shape of wireless cellular coverage. Is the
shape a regular hexagon, an irregular polygon, or another complex geometrical
shape? Based on fractal theory, the statistical characteristic of the wireless
cellular coverage boundary is determined by the measured wireless cellular data
collected from Shanghai, China. The measured results indicate that the wireless
cellular coverage boundary presents an extremely irregular geometrical shape,
which is also called a statistical fractal shape. Moreover, the statistical
fractal characteristics of the wireless cellular coverage boundary have been
validated by values of the Hurst parameter estimated in angular scales. The
statistical fractal characteristics of the wireless cellular coverage boundary
can be used to evaluate and design the handoff scheme of mobile user terminals
in wireless cellular networks.


title:
ARTiS: Appearance-based Action Recognition in Task Space for Real-Time
  Human-Robot Collaboration

abstract:
  To have a robot actively supporting a human during a collaborative task, it
is crucial that robots are able to identify the current action in order to
predict the next one. Common approaches make use of high-level knowledge, such
as object affordances, semantics or understanding of actions in terms of pre-
and post-conditions. These approaches often require hand-coded a priori
knowledge, time- and resource-intensive or supervised learning techniques.
  We propose to reframe this problem as an appearance-based place recognition
problem. In our framework, we regard sequences of visual images of human
actions as a map in analogy to the visual place recognition problem. Observing
the task for the second time, our approach is able to recognize pre-observed
actions in a one-shot learning approach and is thereby able to recognize the
current observation in the task space. We propose two new methods for creating
and aligning action observations within a task map. We compare and verify our
approaches with real data of humans assembling several types of IKEA flat
packs.


title:
Study of the Polarimetric Performance of a Si/CdTe Semiconductor Compton
  Camera for the Hitomi Satellite

abstract:
  Gamma-ray polarization offers a unique probes into the geometry of the
gamma-ray emission process in celestial objects. The Soft Gamma-ray Detector
(SGD) onboard the X-ray observatory Hitomi is a Si/CdTe Compton camera and is
expected to be an excellent polarimeter, as well as a highly sensitive
spectrometer due to its good angular coverage and resolution for Compton
scattering. A beam test of the final-prototype for the SGD Compton camera was
conducted to demonstrate its polarimetric capability and to verify and
calibrate the Monte Carlo simulation of the instrument. The modulation factor
of the SGD prototype camera, evaluated for the inner and outer parts of the
CdTe sensors as absorbers, was measured to be 0.649--0.701 (inner part) and
0.637--0.653 (outer part) at 122.2 keV and 0.610--0.651 (inner part) and
0.564--0.592 (outer part) at 194.5 keV at varying polarization angles with
respect to the detector. This indicates that the relative systematic
uncertainty of the modulation factor is as small as ~3%.


title:
A Tensor Network Kalman filter with an application in recursive MIMO
  Volterra system identification

abstract:
  This article introduces a Tensor Network Kalman filter, which can estimate
state vectors that are exponentially large without ever having to explicitly
construct them. The Tensor Network Kalman filter also easily accommodates the
case where several different state vectors need to be estimated simultaneously.
The key lies in rewriting the standard Kalman equations as tensor equations and
then implementing them using Tensor Networks, which effectively transforms the
exponential storage cost and computational complexity into a linear one. We
showcase the power of the proposed framework through an application in
recursive nonlinear system identification of high-order discrete-time
multiple-input multiple-output (MIMO) Volterra systems. The identification
problem is transformed into a linear state estimation problem wherein the state
vector contains all Volterra kernel coefficients and is estimated using the
Tensor Network Kalman filter. The accuracy and robustness of the scheme are
demonstrated via numerical experiments, which show that updating the Kalman
filter estimate of a state vector of length $10^9$ and its covariance matrix
takes about 0.007s on a standard desktop computer in Matlab.


title: On Optimizing Hierarchical Modulation in AWGN channel

abstract:
  Hierarchical modulation (HM) is able to provide different levels of
protection for data streams and achieve a rate region that cannot be realized
by traditional orthogonal schemes, such as time division (TD). Nevertheless,
criterions and algorithms for general HM design are not available in existing
literatures. In this paper, we jointly optimize the constellation positions and
binary labels for HM to be used in additive white gaussian noise (AWGN)
channel. Based on bit-interleaved coded modulation (BICM) with successive
interference cancellation (SIC) capacity, our main purpose is to maximize the
rate of one data stream, with power constrains and the constrain that the rate
of other data streams should be larger than given thresholds. Multi-start
interior-point algorithm is used to carry out the constellation optimization
problems and methods to reduce optimization complexity are also proposed in
this paper. Numerical results verify the performance gains of optimized HM
compared with optimized quadrature amplidude modulation (QAM) based HM and
other orthogonal transmission methods.


title: Fair Representation and a Linear Shapley Rule

abstract:
  When delegations to an assembly or council represent differently sized
constituencies, they are often allocated voting weights which increase in
population numbers (EU Council, US Electoral College, etc.). The Penrose square
root rule (PSRR) is the main benchmark for fair representation of all
bottom-tier voters in the top-tier decision making body, but rests on the
restrictive assumption of independent binary decisions. We consider intervals
of alternatives with single-peaked preferences instead, and presume positive
correlation of local voters. This calls for a replacement of the PSRR by a
linear Shapley rule: representation is fair if the Shapley value of the
delegates is proportional to their constituency sizes.


title: Mission Opportunities for Human Exploration of Nearby Planetary Bodies

abstract:
  We characterize mission profiles for human expeditions to near-Earth
asteroids, Venus, and Mars. Near-Earth objects (NEOs) are the closest
destinations beyond cis-lunar space and present a compelling target with
capabilities already under development by NASA and its partners. We present
manned NEO mission options that would require between 90 days and one year. We
next consider planetary flyby missions for Venus along the lines of plans that
were first drafted during the Apollo program for human exploration of Venus. We
also characterize a Mars flyby, and a double-flyby variant that would include
close passes to both Venus and Mars. Finally, we consider orbital missions to
Venus and Mars with capability for rendezvous with Phobos or Deimos. This would
be a truly new class of mission for astronauts and could serve as a precursor
to a human landing on Mars. We present launch opportunities, transit time,
requisite {\Delta}V, and approximate radiation environment parameters for each
mission class. We find that {\Delta}V requirements for each class of mission
match near-term chemical propulsion system capabilities.


title:
VLTI-AMBER velocity-resolved aperture-synthesis imaging of Eta Carinae
  with a spectral resolution of 12000. Studies of the primary star wind and
  innermost wind-wind collision

abstract:
  Context. The mass loss from massive stars is not understood well. Eta Car is
a unique object for studying the massive stellar wind during the LBV phase. It
is also an eccentric binary with a period of 5.54 yr. The nature of both stars
is uncertain, although we know from X-ray studies that there is a wind-wind
collision whose properties change with orbital phase.
  Methods. Observations of Eta Car were carried out with the ESO VLTI and the
AMBER instrument between approximately five and seven months before the August
2014 periastron passage. Velocity-resolved aperture-synthesis images were
reconstructed from the spectrally dispersed interferograms. Interferometric
studies can provide information on the binary orbit, the primary wind, and the
wind collision.
  Results. We present velocity-resolved aperture-synthesis images reconstructed
in more than 100 different spectral channels distributed across the Br Gamma
2.166 micrometer emission line. The intensity distribution of the images
strongly depends on wavelength. At wavelengths corresponding to radial
velocities of approximately -140 to -376 km/s measured relative to line center,
the intensity distribution has a fan-shaped structure. At the velocity of -277
km/s, the position angle of the symmetry axis of the fan is ~ 126 degree. The
fan-shaped structure extends approximately 8.0 mas (~ 18.8 au) to the southeast
and 5.8 mas (~ 13.6 au) to the northwest, measured along the symmetry axis at
the 16% intensity contour. The shape of the intensity distributions suggests
that the obtained images are the first direct images of the innermost wind-wind
collision zone. Therefore, the observations provide velocity-dependent image
structures that can be used to test three-dimensional hydrodynamical, radiative
transfer models of the massive interacting winds of Eta Car.


title:
Photospheric carbon and oxygen abundances of F-G type stars in the
  Pleiades cluster

abstract:
  In order to investigate the carbon-to-oxygen ratio of the young open cluster
M45 (Pleiades), the C and O abundances of selected 32 F-G type dwarfs (in the
effective temperature range of Teff~5800-7600K and projected rotational
velocity range of vesini~10-110km/s) belonging to this cluster were determined
by applying the synthetic spectrum-fitting technique to C I 5380 and O I 6156-8
lines. The non-LTE corrections for these C I and O I lines were found to be
practically negligible (less than a few hundredths dex). The resulting C and O
abundances (along with the Fe abundance) turned out nearly uniform without any
systematic dependence upon Teff or vesini. We found, however, in spite of
almost solar Fe abundance ([Fe/H]~0), carbon turned out to be slightly subsolar
([C/H]~-0.1) while oxygen slightly supersolar ([O/H]~+0.1). This lead to a
conclusion that [C/O] ratio was moderately subsolar (~-0.2) in the primordial
gas from which these Pleiades stars were formed ~120--130 Myr ago.
Interestingly, similarly young B-type stars are reported to show just the same
result ([C/O]~-0.2), while rather aged (~1-10 Gyr) field F-G stars of
near-solar metallicity yield almost the solar value ([C/O]~0) on the average.
Such a difference in the C/O ratio between two star groups of distinctly
different ages may be explained as a consequence of orbit migration mechanism
which Galactic stars may undergo over a long time.


title: Automatic monotonicity detection for Gaussian Processes

abstract:
  We propose a new method for automatically detecting monotonic input-output
relationships from data using Gaussian Process (GP) models with virtual
derivative observations. Our results on synthetic and real datasets show that
the proposed method detects monotonic directions from input spaces with high
accuracy. We expect the method to be useful especially for improving
explainability of the models and improving the accuracy of regression and
classification tasks, especially near the edges of the data or when
extrapolating.


title: Classical Weyl Transverse Gravity

abstract:
  We study various classical aspects of the Weyl transverse (WTDiff) gravity in
a general space-time dimension. First of all, we clarify a classical
equivalence among three kinds of gravitational theories, those are, the
conformally-invariant scalar tensor gravity, Einstein's general relativity and
the WTDiff gravity via the gauge fixing procedure. Secondly, we show that in
the WTDiff gravity the cosmological constant is a mere integration constant as
in unimodular gravity, but it does not receive any radiative corrections unlike
the unimodular gravity. A key point in this proof is to construct a covariantly
conserved energy-momentum tensor, which is achieved on the basis of this
equivalence relation. Thirdly, we demonstrate that the Noether current for the
Weyl transformation is identically vanishing, thereby implying that the Weyl
symmetry existing in both the conformally-invariant scalar tensor gravity and
the WTDiff gravity is a "fake" symmetry. We find it possible to extend this
proof to all matter fields, i.e. the Weyl invariant scalar, vector and spinor
fields. Fourthly, it is explicitly shown that in the WTDiff gravity the
Schwarzshild black hole metric and a charged black hole one are classical
solutions to the equations of motion only when they are expressed in the
Cartesian coordinate system. Finally, we consider the
Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact
solutions.


title:
Realization of Zero-Refractive-Index Lens with Ultralow Spherical
  Aberration

abstract:
  Optical complex materials offer unprecedented opportunity to engineer
fundamental band dispersion which enables novel optoelectronic functionality
and devices. Exploration of photonic Dirac cone at the center of momentum space
has inspired an exceptional characteristic of zero-index, which is similar to
zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index
photonic crystals provide an in-plane mechanism such that the energy of the
propagating waves can be well confined along the chip direction. A
straightforward example is to achieve the anomalous focusing effect without
longitudinal spherical aberration, when the size of zero-index lens is large
enough. Here, we designed and fabricated a prototype of zero-refractive-index
lens by comprising large-area silicon nanopillar array with plane-concave
profile. Near-zero refractive index was quantitatively measured near 1.55 um
through anomalous focusing effect, predictable by effective medium theory. The
zero-index lens was also demonstrated to perform ultralow longitudinal
spherical aberration. Such IC compatible device provides a new route to
integrate all-silicon zero-index materials into optical communication, sensing,
and modulation, and to study fundamental physics on the emergent fields of
topological photonics and valley photonics.


title:
Neural Network for Quantum Brain Dynamics: 4D CP$^1$+U(1) Gauge Theory
  on Lattice and its Phase Structure

abstract:
  We consider a system of two-level quantum quasi-spins and gauge bosons put on
a 3+1D lattice. As a model of neural network of the brain functions, these
spins describe neurons quantum-mechanically, and the gauge bosons describes
weights of synaptic connections. It is a generalization of the Hopfield model
to a quantum network with dynamical synaptic weights. At the microscopic level,
this system becomes a model of quantum brain dynamics proposed by Umezawa et
al., where spins and gauge field describe water molecules and photons,
respectively. We calculate the phase diagram of this system under quantum and
thermal fluctuations, and find that there are three phases; confinement,
Coulomb, and Higgs phases. Each phase is classified according to the ability to
learn patterns and recall them. By comparing the phase diagram with that of
classical networks, we discuss the effect of quantum fluctuations and thermal
fluctuations (noises in signal propagations) on the brain functions.


title:
Interstellar gas towards the TeV gamma-ray sources HESS J1640-465 and
  HESS J1641-463

abstract:
  We present a detailed analysis of the interstellar medium towards the TeV
$\gamma$-ray sources HESS J1640$-$465 and HESS J1641$-$463 using results from
the Mopra Southern Galactic Plane CO Survey and from a Mopra 7 mm-wavelength
study. The $\gamma$-ray sources are positionally coincident with two supernova
remnants G338.3$-$0.0 and G338.5+0.1 respectively. A bright complex of HII
regions connect the two SNRs and TeV objects. Observations in the CO(1-0)
transition lines reveal substantial amounts of diffuse gas positionally
coincident with the $\gamma$-ray sources at multiple velocities along the line
of sight, while 7 mm observations in CS, SiO, HC$_{3}$N and CH$_{3}$OH
transition lines reveal regions of dense, shocked gas. Archival HI data from
the Southern Galactic Plane Survey was used to account for the diffuse atomic
gas. Physical parameters of the gas towards the TeV sources were calculated
from the data. We find that for a hadronic origin for the $\gamma$-ray
emission, the cosmic-ray enhancement rates are $\sim 10^{3}$ and $10^{2}$ times
the local solar value for HESS J1640$-$465 and HESS J1641$-$463 respectively.


title: A weak variant of Hindman's Theorem stronger than Hilbert's Theorem

abstract:
  Hirst investigated a slight variant of Hindman's Finite Sums Theorem --
called Hilbert's Theorem -- and proved it equivalent over $\RCA_0$ to the
Infinite Pigeonhole Principle for all colors. This gave the first example of a
natural restriction of Hindman's Theorem provably much weaker than Hindman's
Theorem itself. We here introduce another natural variant of Hindman's Theorem
-- which we name the Adjacent Hindman's Theorem -- and prove it to be provable
from Ramsey's Theorem for pairs and strictly stronger than Hirst's Hilbert's
Theorem. The lower bound is obtained by a direct combinatorial implication from
the Adjacent Hindman's Theorem to the Increasing Polarized Ramsey's Theorem for
pairs introduced by Dzhafarov and Hirst. In the Adjacent Hindman's Theorem
homogeneity is required only for finite sums of adjacent elements.


title:
Provably Good Early Detection of Diseases using Non-Sparse
  Covariance-Regularized Linear Discriminant Analysis

abstract:
  To improve the performance of Linear Discriminant Analysis (LDA) for early
detection of diseases using Electronic Health Records (EHR) data, we propose
\TheName{} -- a novel framework for \emph{\underline{E}HR based
\underline{E}arly \underline{D}etection of \underline{D}iseases} on top of
\emph{Covariance-Regularized} LDA models. Specifically, \TheName\ employs a
\emph{non-sparse} inverse covariance matrix (or namely precision matrix)
estimator derived from graphical lasso and incorporates the estimator into LDA
classifiers to improve classification accuracy. Theoretical analysis on
\TheName\ shows that it can bound the expected error rate of LDA
classification, under certain assumptions. Finally, we conducted extensive
experiments using a large-scale real-world EHR dataset -- CHSN. We compared our
solution with other regularized LDA and downstream classifiers. The result
shows \TheName\ outperforms all baselines and backups our theoretical analysis.


title:
Hysteresis and phase transitions in a lattice regularization of an
  ill-posed forward-backward diffusion equation

abstract:
  We consider a lattice regularization for an ill-posed diffusion equation with
trilinear constitutive law and study the dynamics of phase interfaces in the
parabolic scaling limit. Our main result guarantees for a certain class of
single-interface initial data that the lattice solutions satisfy asymptotically
a free boundary problem with hysteretic Stefan condition. The key challenge in
the proof is to control the microscopic fluctuations that are inevitably
produced by the backward diffusion when a particle passes the spinodal region.


title:
Generalization error minimization: a new approach to model evaluation
  and selection with an application to penalized regression

abstract:
  We study model evaluation and model selection from the perspective of
generalization ability (GA): the ability of a model to predict outcomes in new
samples from the same population. We believe that GA is one way formally to
address concerns about the external validity of a model. The GA of a model
estimated on a sample can be measured by its empirical out-of-sample errors,
called the generalization errors (GE). We derive upper bounds for the GE, which
depend on sample sizes, model complexity and the distribution of the loss
function. The upper bounds can be used to evaluate the GA of a model, ex ante.
We propose using generalization error minimization (GEM) as a framework for
model selection. Using GEM, we are able to unify a big class of penalized
regression estimators, including lasso, ridge and bridge, under the same set of
assumptions. We establish finite-sample and asymptotic properties (including
$\mathcal{L}_2$-consistency) of the GEM estimator for both the $n \geqslant p$
and the $n < p$ cases. We also derive the $\mathcal{L}_2$-distance between the
penalized and corresponding unpenalized regression estimates. In practice, GEM
can be implemented by validation or cross-validation. We show that the GE
bounds can be used for selecting the optimal number of folds in $K$-fold
cross-validation. We propose a variant of $R^2$, the $GR^2$, as a measure of
GA, which considers both both in-sample and out-of-sample goodness of fit.
Simulations are used to demonstrate our key results.


title:
Fractional type multilinear commutators generated by fractional integral
  with rough variable kernel and local Campanato functions on generalized
  vanishing local Morrey spaces

abstract:
  In this paper, we consider the boundedness of fractional type multilinear
commutators generated by fractional integral with rough variable kernel and
local Campanato functions on both generalized local (central) Morrey spaces and
generalized vanishing local Morrey spaces, under generic size conditions which
are satisfied by most of the operators in harmonic analysis, respectively.


title: Searching chaotic saddles in high dimensions

abstract:
  We propose new methods to numerically approximate non-attracting sets
governing transiently-chaotic systems. Trajectories starting in a vicinity
$\Omega$ of these sets escape $\Omega$ in a finite time $\tau$ and the problem
is to find initial conditions ${\bf x} \in \Omega$ with increasingly large
$\tau= \tau({\bf x})$. We search points ${\bf x}'$ with $\tau({\bf
x}')>\tau({\bf x})$ in a {\it search domain} in $\Omega$. Our first method
considers a search domain with size that decreases exponentially in $\tau$,
with an exponent proportional to the largest Lyapunov exponent $\lambda_1$. Our
second method considers anisotropic search domains in the {\it tangent}
unstable manifold, where each direction scale as the inverse of the
corresponding {\it expanding} singular value of the Jacobian matrix of the
iterated map. We show that both methods outperform the state-of-the-art {\it
Stagger-and-Step} method (Sweet, Nusse, and York, Phys. Rev. Lett. {\bf 86},
2261, 2001) but that only the anisotropic method achieves an efficiency
independent of $\tau$ for the case of high-dimensional systems with multiple
positive Lyapunov exponents. We perform simulations in a chain of coupled
H\'enon maps in up to 24 dimensions ($12$ positive Lyapunov exponents). This
suggests the possibility of characterizing also non-attracting sets in
spatio-temporal systems.