Abstract:
  A well-known formula of Whipple relates certain hypergeometric values
$_7F_6(1)$ and $_4F_3(1)$. In this paper we revisit this relation from the
viewpoint of the underlying hypergeometric data $HD$, to which there are also
associated hypergeometric character sums and Galois representations. We explain
a special structure behind Whipple's formula when the hypergeometric data $HD$
are primitive and self-dual. If the data are also defined over $\mathbb Q$, by
the work of Katz, Beukers, Cohen, and Mellit, there are compatible families of
$\ell$-adic representations of the absolute Galois group of $\mathbb Q$
attached to $HD$. For specialized choices of $HD$, these Galois representations
are shown to be decomposable and automorphic. As a consequence, the values of
the corresponding hypergeometric character sums can be explicitly expressed in
terms of Fourier coefficients of certain modular forms. We further relate the
hypergeometric values $_7F_6(1)$ in Whipple's formula to the periods of these
modular forms.


Abstract:
  A theory for analyzing the radiative and reactive energies for pulse
radiators in free space is presented. With the proposed definition of reactive
energies and radiative energies, power balance at arbitrarily chosen
observation surfaces are established, which intuitively shows that the Poynting
vector contains not only the power flux density associated with the radiative
energies, but also the influence of the fluctuation of the reactive energies
dragging by the sources. A new vector is defined for the radiative power flux
density. The radiative energies passing through observation surfaces enclosing
the radiator are accurately calculated. Numerical results verifies that the
proposed radiative flux density is more proper for expressing the radiative
power flux density than the Poynting vector.


Abstract:
  In this thesis we study the momentum space approach to the solution of the
CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the
essential steps needed to build tensor correlators starting from the scalar
solutions, for 3-point functions. In the case of 4-point functions, our
attention is centred around scalar correlators for which the CWI's are
sufficient to isolate the unique solution if we enhance the symmetry with the
addition of a dual conformal symmetry. Dual conformal symmetry in momentum
space is obtained once the momentum variables are rewritten in a dual form, as
the difference of coordinate-like variables and treated as ordinary correlators
in such variables, mirroring the action of coordinate space. This enhancement
of the symmetry is sufficient to fix the solutions also for such correlators.
The solution of the conformal constraints are given in terms of triple-$K$
integrals and are expressed in terms of a set of constants, specific for each
correlator and spacetime dimension. We present a discussion of the intermediate
steps in the description of two nontrivial correlators, the $TTO$ and the
$TTT$, in a more pedagogical way, offering details that could help extend such
methods to higher point function.


Abstract:
  Machine learning models are often implemented in cohort with humans in the
pipeline, with the model having an option to defer to a domain expert in cases
where it has low confidence in its inference. Our goal is to design mechanisms
for ensuring accuracy and fairness in such prediction systems that combine
machine learning model inferences and domain expert predictions. Prior work on
"deferral systems" in classification settings has focused on the setting of a
pipeline with a single expert and aimed to accommodate the inaccuracies and
biases of this expert to simultaneously learn an inference model and a deferral
system. Our work extends this framework to settings where multiple experts are
available, with each expert having their own domain of expertise and biases. We
propose a framework that simultaneously learns a classifier and a deferral
system, with the deferral system choosing to defer to one or more human experts
in cases of input where the classifier has low confidence. We test our
framework on a synthetic dataset and a content moderation dataset with biased
synthetic experts, and show that it significantly improves the accuracy and
fairness of the final predictions, compared to the baselines. We also collect
crowdsourced labels for the content moderation task to construct a real-world
dataset for the evaluation of hybrid machine-human frameworks and show that our
proposed learning framework outperforms baselines on this real-world dataset as
well.


Abstract:
  The global gravitational-wave detector network achieves higher detection
rates, better parameter estimates, and more accurate sky localisation, as the
number of detectors, $\mathcal{I}$ increases. This paper quantifies network
performance as a function of $\mathcal{I}$ for BayesWave, a source-agnostic,
wavelet-based, Bayesian algorithm which distinguishes between true
astrophysical signals and instrumental glitches. Detection confidence is
quantified using the signal-to-glitch Bayes factor,
$\mathcal{B}_{\mathcal{S},\mathcal{G}}$. An analytic scaling is derived for
$\mathcal{B}_{\mathcal{S},\mathcal{G}}$ versus $\mathcal{I}$, the number of
wavelets, and the network signal-to-noise ratio, SNR$_\text{net}$, which is
confirmed empirically via injections into detector noise of the
Hanford-Livingston (HL), Hanford-Livingston-Virgo (HLV), and
Hanford-Livingston-KAGRA-Virgo (HLKV) networks at projected sensitivities for
the fourth observing run (O4). The empirical and analytic scalings are
consistent; $\mathcal{B}_{\mathcal{S},\mathcal{G}}$ increases with
$\mathcal{I}$. The accuracy of waveform reconstruction is quantified using the
overlap between injected and recovered waveform, $\mathcal{O}_\text{net}$. The
HLV and HLKV network recovers $87\%$ and $86\%$ of the injected waveforms with
$\mathcal{O}_\text{net}>0.8$ respectively, compared to $81\%$ with the HL
network. The accuracy of BayesWave sky localisation is $\approx 10$ times
better for the HLV network than the HL network, as measured by the search area,
$\mathcal{A}$, and the sky areas contained within $50\%$ and $90\%$ confidence
intervals. Marginal improvement in sky localisation is also observed with the
addition of KAGRA.


Abstract:
  VI$_{3}$ is a ferromagnet with planar honeycomb sheets of bonded V$^{3+}$
ions held together by van der Waals forces. We apply neutron spectroscopy to
measure the two dimensional ($J/J_{c} \approx 17$) magnetic excitations in the
ferromagnetic phase, finding two energetically gapped ($\Delta \approx k_{B}
T_{c} \approx$ 55 K) and dispersive excitations. We apply a multi-level spin
wave formalism to describe the spectra in terms of two coexisting domains
hosting differing V$^{3+}$ orbital ground states built from contrasting
distorted octahedral environments. This analysis fits a common nearest neighbor
in-plane exchange coupling ($J$=-8.6 $\pm$ 0.3 meV) between V$^{3+}$ sites. The
distorted local crystalline electric field combined with spin-orbit coupling
provides the needed magnetic anisotropy for spatially long-ranged
two-dimensional ferromagnetism in VI$_{3}$.


Abstract:
  We introduce weak barycenters of a family of probability distributions, based
on the recently developed notion of optimal weak transport of mass by Gozlanet
al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical
analysis of this object and discuss its interpretation in the light of convex
ordering between probability measures. In particular, we show that, rather than
averaging the input distributions in a geometric way (as the Wasserstein
barycenter based on classic optimal transport does) weak barycenters extract
common geometric information shared by all the input distributions, encoded as
a latent random variable that underlies all of them. We also provide an
iterative algorithm to compute a weak barycenter for a finite family of input
distributions, and a stochastic algorithm that computes them for arbitrary
populations of laws. The latter approach is particularly well suited for the
streaming setting, i.e., when distributions are observed sequentially. The
notion of weak barycenter and our approaches to compute it are illustrated on
synthetic examples, validated on 2D real-world data and compared to standard
Wasserstein barycenters.


Abstract:
  In this paper, we compute the Bott connections and their curvature on
three-dimensional Lorentzian Lie groups with three different distributions, and
we classify affine Ricci solitons associated to the Bott connection on
three-dimensional Lorentzian Lie groups with three different distributions.


Abstract:
  The relative motion of three impenetrable particles on a ring, in our case
two identical fermions and one impurity, is isomorphic to a triangular quantum
billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses,
the billiards can be integrable or non-integrable (also referred to in the main
text as chaotic). To set the stage, we first investigate the energy level
distributions of the billiards as a function of $1/\kappa\in [0,1]$ and find no
evidence of integrable cases beyond the limiting values $1/\kappa=1$ and
$1/\kappa=0$. Then, we use machine learning tools to analyze properties of
probability distributions of individual quantum states. We find that
convolutional neural networks can correctly classify integrable and
non-integrable states.The decisive features of the wave functions are the
normalization and a large number of zero elements, corresponding to the
existence of a nodal line. The network achieves typical accuracies of 97%,
suggesting that machine learning tools can be used to analyze and classify the
morphology of probability densities obtained in theory or experiment.


Abstract:
  In this paper we study the effects of dynamic wetting on the immiscible
displacement of a high viscosity fluid subject to the radial injection of a
less viscous fluid in a Hele-Shaw cell. The displaced fluid can leave behind a
trailing film that coats the cell walls, dynamically affecting the pressure
drop at the fluid interface. By considering the non-linear pressure drop in a
boundary element formulation, we construct a Picard scheme to iteratively
predict the interfacial velocity and subsequent displacement in finite mobility
ratio flow regimes. Dynamic wetting delays the onset of finger bifurcation in
the late stages of interfacial growth, and at high local capillary numbers can
alter the fundamental mode of bifurcation, producing vastly different finger
morphologies. In low mobility ratio regimes, we see that finger interaction is
reduced and characteristic finger breaking mechanisms are delayed but never
fully inhibited. In high mobility ratio regimes, finger shielding is reduced
when dynamic wetting is present. Finger bifurcation is delayed which allows the
primary fingers to advance further into the domain before secondary fingers are
generated, reducing the level of competition.


Abstract:
  The symmetry axes of active galactic nuclei (AGN) are randomly distributed in
space but highly inclined sources are heavily obscured and are not seen as
quasars with broad emission lines. The obscuring torus geometry determines the
average viewing angle, and if the torus geometry changes with the redshift,
this average viewing angle will also change. Thus the ratio between the
isotropic luminosity and observed luminosity may change systematically with
redshift. Therefore, if we use quasars to measure the luminosity distance by
evaluating the isotropic absolute luminosity and measuring the observed flux,
we can have a redshift-dependent bias which can propagate to cosmological
parameters. We propose a toy model for testing the effect of viewing angle
uncertainty on measurement of the luminosity distance. The model is based on
analytical description of the obscuring torus applied to one-parameter
observational data. It illustrates the possible change of the torus covering
factor between the two chosen redshift ranges. We have estimated the possible
error on specific cosmological parameters (H0,Omega_m) for the flat Lambda-CDM
cosmology if a method is calibrated at low redshift and applied to the higher
redshift. The errors on cosmological parameters due to potential dependence of
viewing angle on redshift are found to be potentially significant, and the
effect will have to be accommodated in the future in all quasar-based
cosmological methods. A careful systematic study of AGN mean viewing angle
across redshift is necessary, with the use of appropriate samples and models
which uniquely determine the inclination of each source.


Abstract:
  The electric dipole moment (EDM) of electron is studied in the supersymmetric
$\rm A_4$ modular invariant theory of flavors with CP invariance. The CP
symmetry of the lepton sector is broken by fixing the modulus $\tau$. Lepton
mass matrices are completely consistent with observed lepton masses and mixing
angles in our model. In this framework, a fixed $\tau$ also causes the CP
violation in the soft SUSY breaking terms. The elecrton EDM arises from the CP
non-conserved soft SUSY breaking terms. The experimental upper bound of the
electron EDM excludes the SUSY mass scale below $2-6$ TeV for five cases of the
lepton mass matrices. In order to see the effect of CP phase of the modulus
$\tau$, we examine the correlation between the electron EDM and the decay rate
of the $\mu \rightarrow e \gamma$ decay, which is also predicted by the soft
SUSY breaking terms. The correlations are clearly predicted in contrast to
models of the conventional flavor symmetry. The SUSY mass scale will be
constrained by the future sensitivity of the electron EDM, $|d_e/e| \simeq
10^{-30}$. Indeed, it could probe the SUSY mass range of $10-20$ TeV in our
model. Thus, the electron EDM provides a severe test of the CP violation via
the modulus $\tau$ in the supersymmetric modular invariant theory of flavors.


Abstract:
  This paper is concerned with a class of nonlinear boundary value problem
involving fractional derivative in the $\varphi$-Riemann-Liouville sense. Some
Properties of the Green's function for this problem are mentioned. By means of
the Banach contraction principle in $b$-metric space and the technique of the
$\gamma$-$\psi$- Geraghty contractive maps, existence and uniqueness results
are obtained. Two examples are given to support the theoretical results.


Abstract:
  The Frank-Wolfe algorithm is a method for constrained optimization that
relies on linear minimizations, as opposed to projections. Therefore, a
motivation put forward in a large body of work on the Frank-Wolfe algorithm is
the computational advantage of solving linear minimizations instead of
projections. However, the discussions supporting this advantage are often too
succinct or incomplete. In this paper, we review the complexity bounds for both
tasks on several sets commonly used in optimization. Projection methods onto
the $\ell_p$-ball, $p\in\left]1,2\right[\cup\left]2,+\infty\right[$, and the
Birkhoff polytope are also proposed.


Abstract:
  In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption
that either $p^2 \nmid \chi(1)$ for all $\chi \in {\rm Irr}(G)$ or $p^2 \nmid
\phi(1)$ for all $\phi \in {\rm IBr}_p(G)$. This would settle two conjectures
raised by Lewis, Navarro, Tiep, and Tong-Viet.


Abstract:
  Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative
ring and $M$ a graded $R$-module. A proper graded submodule $N$ of $M$ is
called \textit{a graded semiprime submodule} if whenever $r\in h(R)$, $m\in
h(M)$ and $n\in Z^{+}$ with $r^{n}m\in N$, then $rm\in N$. In this paper, we
introduce the concept of graded quasi-semiprime submodule as a generalization
of graded semiprime submodule and show a number of results in this class. We
say that a proper graded submodule $N$ of $M$ is \emph{a graded quasi-semiprime
submodule} if $(N:_{R}M)$ is a graded semiprime ideal of $R$.


Abstract:
  In 2018, Solar Cycle 24 entered into a solar minimum phase. During this
period, 11 million zenithal night sky brightness (NSB) data were collected at
different dark sites around the planet, including astronomical observatories
and natural protected areas, with identical broadband Telescope Encoder and Sky
Sensor photometers (based on the Unihedron Sky Quality Meter TSL237 sensor). A
detailed observational review of the multiple effects that contribute to the
NSB measurement has been conducted with optimal filters designed to avoid
brightening effects by the Sun, the Moon, clouds, and other astronomical
sources (the Galaxy and zodiacal light). The natural NSB has been calculated
from the percentiles for 44 different photometers by applying these new
filters. The pristine night sky was measured to change with an amplitude of 0.1
mag/arcsec$^2$ in all the photometers, which is suggested to be due to NSB
variations on scales of up to months and to be compatible with semiannual
oscillations. We report the systematic observation of short-time variations in
NSB on the vast majority of the nights and find these to be related to airglow
events forming above the mesosphere.


Abstract:
  In this paper, the soft gluon resummation effect in double heavy quarkonium
production at the LHC is studied. By applying the transverse momentum dependent
factorization formalism, the large logarithms introduced by the small total
transverse momentum of heavy quarkonium pair final state system, are resummed
to all orders in the expansion of the strong interaction coupling at the
Next-to-Leading Logarithm accuracy. We also compare our result with the LHC
data. We find that the distribution shape predicted by resummation calculation
is consistent with experimental data very well. Since this process is mainly
initiated by gluon fusion, it supplies us an important channel to study the
gluon parton property in hadrons.


Abstract:
  This paper presents a machine learning approach for the automatic
identification of rip currents with breaking waves. Rip currents are dangerous
fast moving currents of water that result in many deaths by sweeping people out
to sea. Most people do not know how to recognize rip currents in order to avoid
them. Furthermore, efforts to forecast rip currents are hindered by lack of
observations to help train and validate hazard models. The presence of web cams
and smart phones have made video and still imagery of the coast ubiquitous and
provide a potential source of rip current observations. These same devices
could aid public awareness of the presence of rip currents. What is lacking is
a method to detect the presence or absence of rip currents from coastal
imagery. This paper provides expert labeled training and test data sets for rip
currents. We use Faster-RCNN and a custom temporal aggregation stage to make
detections from still images or videos with higher measured accuracy than both
humans and other methods of rip current detection previously reported in the
literature.


Abstract:
  The increased penetration of Electric Vehicles (EVs) in the transportation
sector has increased the requirement of Fast Charging Direct Current (FCDC)
stations to meet customer's speedy charging requirements. However, both
charging stations and EVs connection to the communication infrastructure as
well as the power grid makes it vulnerable to cyber attacks. In this paper, the
vulnerability of the EV charging process is initially studied. We then show how
a botnet of compromised EVs and FCDC stations can be utilized to launch cyber
attacks on the power grid resulting in an increase in the load at a specific
time. The effect of such attacks on the distribution network in terms of line
congestion and voltage limit violations is investigated. Moreover, the effect
of the botnet of the transmission network is also studied.


Abstract:
  We propose an alternate approach to quantifying how well language models
learn natural language: we ask how well they match the statistical tendencies
of natural language. To answer this question, we analyze whether text generated
from language models exhibits the statistical tendencies present in the
human-generated text on which they were trained. We provide a framework--paired
with significance tests--for evaluating the fit of language models to these
trends. We find that neural language models appear to learn only a subset of
the tendencies considered, but align much more closely with empirical trends
than proposed theoretical distributions (when present). Further, the fit to
different distributions is highly-dependent on both model architecture and
generation strategy. As concrete examples, text generated under the nucleus
sampling scheme adheres more closely to the type--token relationship of natural
language than text produced using standard ancestral sampling; text from LSTMs
reflects the natural language distributions over length, stopwords, and symbols
surprisingly well.


Abstract:
  The Galactic halo is supposed to form from merging with nearby dwarf
galaxies. In order to probe different components of the Galactic halo, we have
applied the Gaussian Mixture Models method to a selected sample of metal poor
stars with [Fe/H] $< -0.7$ dex in the APOGEE DR16 catalogue based on
four-parameters, metallicity, [Mg/Fe] ratio and spatial velocity
(\textit{$V_R$, $V_\phi$}). Nine groups are identified with four from the halo
(group 1, 3, 4 and 5), one from the thick disk (group 6), one from the thin
disk (group 8) and one from dwarf galaxies (group 7) by analyzing their
distributions in the ([M/H], [Mg/Fe]), ($V_R$, $V_\phi$), (\textit{Zmax},
\textit{eccentricity}), (\textit{Energy}, \textit{Lz}) and ([Mg/Mn], [Al/Fe])
coordinates. The rest two groups are respectively caused by observational
effect (group 9) and the cross section component (group 2) between the thin
disk and the thick disk. It is found that in the extremely outer accreted halo
(group 1), stars born in the Milky Way can not be distinguished from those
accreted from other galaxies either chemically or kinematically. In the
intermediate metallicity of $-$1.6 $<$ [Fe/H] $< -0.7$ dex, the accreted halo
mainly composed of the Gaia-Enceladus-Sausage substructure (group 5), which can
be easily distinguished from group 4 (the in-situ halo group) in both chemical
and kinematic space. Some stars of group 4 may come from the disk and some disk
stars can be scattered to high orbits by resonant effects as shown in the
\textit{Zmax} versus Energy coordinate. We also displayed the spatial
distribution of main components of the halo and the ratio of accreted
components do not show clear relation to Galactic radius.


Abstract:
  We present deep, narrowband imaging of the nearby spiral galaxy M101 and its
group environment to search for star-forming dwarf galaxies and outlying HII
regions. Using the Burrell Schmidt telescope, we target the brightest emission
lines of star-forming regions, H$\alpha$, H$\beta$, and [OIII], to detect
potential outlying star-forming regions. Our survey covers $\sim$6 square
degrees around M101, and we detect objects in emission down to an H$\alpha$
flux level of $5.7 \times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$ (equivalent to a
limiting SFR of $1.7 \times 10^{-6}$ $M_\odot$ yr$^{-1}$ at the distance of
M101). After careful removal of background contaminants and foreground M stars,
we detect 19 objects in emission in all three bands, and 8 objects in emission
in H$\alpha$ and [OIII]. We compare the structural and photometric properties
of the detected sources to Local Group dwarf galaxies and star-forming galaxies
in the 11HUGS and SINGG surveys. We find no large population of outlying HII
regions or undiscovered star-forming dwarfs in the M101 Group, as most sources
(93%) are consistent with being M101 outer disk HII regions. Only two sources
were associated with other galaxies: a faint star-forming satellite of the
background galaxy NGC 5486, and a faint outlying HII region near the M101
companion NGC 5474. We also find no narrowband emission associated with
recently discovered ultradiffuse galaxies and starless HI clouds near M101. The
lack of any hidden population of low luminosity star-forming dwarfs around M101
suggests a rather shallow faint end slope (as flat as $\alpha \sim -1.0$) for
the star-forming luminosity function in the M101 Group. We discuss our results
in the context of tidally-triggered star formation models and the interaction
history of the M101 Group.


Abstract:
  Human learners can readily understand speech, or a melody, when it is
presented slower or faster than usual. Although deep convolutional neural
networks (CNNs) are extremely powerful in extracting information from time
series, they require explicit training to generalize to different time scales.
This paper presents a deep CNN that incorporates a temporal representation
inspired by recent findings from neuroscience. In the mammalian brain, time is
represented by populations of neurons with temporal receptive fields.
Critically, the peaks of the receptive fields form a geometric series, such
that the population codes a set of temporal basis functions over log time.
Because memory for the recent past is a function of log time, rescaling the
input results in translation of the memory. The Scale-Invariant Temporal
History Convolution network (SITHCon) builds a convolutional layer over this
logarithmically-distributed temporal memory. A max-pool operation results in a
network that is invariant to rescalings of time modulo edge effects. We compare
performance of SITHCon to a Temporal Convolution Network (TCN). Although both
networks can learn classification and regression problems on both univariate
and multivariate time series f(t), only SITHCon generalizes to rescalings
f(at). This property, inspired by findings from contemporary neuroscience and
consistent with findings from cognitive psychology, may enable networks that
learn with fewer training examples, fewer weights and that generalize more
robustly to out of sample data.


Abstract:
  Emergency Departments (EDs) overcrowding is a well recognized worldwide
phenomenon. The consequences range from long waiting times for visits and
treatment of patients up to life-threatening health conditions. The
international community is devoting greater and greater efforts to analyze this
phenomenon aiming at reducing waiting times, improving the quality of the
service. Within this framework, we propose a Discrete Event Simulation (DES)
model to study the patient flows through a medium-size ED located in a region
of Central Italy recently hit by a severe earthquake. In particular, our aim is
to simulate unusual ED conditions, corresponding to critical events (like a
natural disaster) that cause a sudden spike in the number of patient arrivals.
The availability of detailed data concerning the ED processes enabled to build
an accurate DES model and to perform extensive scenario analyses. The model
provides a valid decision support system for the ED managers also in defining
specific emergency plans to be activated in case of mass casualty disasters.


Abstract:
  We consider an arbitrary metric graph, to which we glue another graph with
edges of lengths proportional to $\varepsilon$, where $\varepsilon$ is a small
positive parameter. On such graph, we consider a general self-adjoint second
order differential operator $\mathcal{H}_\varepsilon$ with varying coefficients
subject to general vertex conditions; all coefficients in differential
expression and vertex conditions are supposed to be analytic in $\varepsilon$.
We introduce a special operator on a certain graph obtained by rescaling the
aforementioned small edges and assume that it has no embedded eigenvalues at
the threshold of its essential spectrum. Under such assumption, we show that
certain parts of the resolvent of $\mathcal{H}_\varepsilon$ are analytic in
$\varepsilon$. This allows us to represent the resolvent of
$\mathcal{H}_\varepsilon$ by an uniformly converging Taylor-like series and its
partial sums can be used for approximating the resolvent up to an arbitrary
power of $\varepsilon$. In particular, the zero-order approximation reproduces
recent convergence results by G. Berkolaiko, Yu. Latushkin, S. Sukhtaiev and by
C. Cacciapuoti, but we additionally show that next-to-leading terms in
$\varepsilon$-expansions of the coefficients in the differential expression and
vertex conditions can contribute to the limiting operator producing the Robin
part at the vertices, to which small edges are incident. We also discuss
possible generalizations of our model including both the cases of a more
general geometry of the small parts of the graph and a non-analytic
$\varepsilon$-dependence of the coefficients in the differential expression and
vertex conditions.


Abstract:
  In this work, we consider the following elliptic partial differential
equations: \begin{equation*} \left\{ \begin{aligned}{}
  - b_{ij} \; \frac{\partial^{2} w}{\partial x_{i} \partial x_{j}} &= g
  \;\;\; \text{in} \;\; \Omega, w &= 0 \;\;\;\text{on} \;\partial \Omega,
\end{aligned} \right. \end{equation*} \noindent where the domain $\Omega
\subset \mathbb{R}^{n}$ is convex, the matrix $\big(b_{ij}\big)_{n \times n}$
satisfies the uniform ellipticity conditions. For $g$ in the scaling critical
Lorentz space $ L(n,\; 1)(\Omega)$, we establish boundary differentiability of
solutions to the above problem. We also prove $C^{\mathrm{Log-Lip}}$ regularity
estimate at a boundary point in the case when $g \in L^{n}(\Omega)$.


Abstract:
  Recent researches in data assimilation lead to the introduction of the
parametric Kalman filter (PKF): an implementation of the Kalman filter, where
the covariance matrices are approximated by a parameterized covariance model.
In the PKF, the dynamics of the covariance during the forecast step relies on
the prediction of the covariance parameters. Hence, the design of the parameter
dynamics is crucial while it can be tedious to do this by hand. This
contribution introduces a python package, SymPKF, able to compute PKF dynamics
for univariate statistics and when the covariance model is parameterized from
the variance and the local anisotropy of the correlations. The ability of
SymPKF to produce the PKF dynamics is shown on a non-linear diffusive advection
(Burgers equation) over a 1D domain and the linear advection over a 2D domain.
The computation of the PKF dynamics is performed at a symbolic level, but an
automatic code generator is also introduced to perform numerical simulations. A
final multivariate example illustrates the potential of SymPKF to go beyond the
univariate case.


Abstract:
  In this paper we study the multiplicity and concentration of positive
solutions for the following $(p, q)$-Laplacian problem: \begin{equation*}
\left\{ \begin{array}{ll} -\Delta_{p} u -\Delta_{q} u +V(\varepsilon x)
\left(|u|^{p-2}u + |u|^{q-2}u\right) = f(u) &\mbox{ in } \mathbb{R}^{N}, \\
u\in W^{1, p}(\mathbb{R}^{N})\cap W^{1, q}(\mathbb{R}^{N}), \quad u>0 \mbox{ in
} \mathbb{R}^{N}, \end{array} \right. \end{equation*} where $\varepsilon>0$ is
a small parameter, $1< p<q<N$, $\Delta_{r}u=\mbox{div}(|\nabla u|^{r-2}\nabla
u)$, with $r\in \{p, q\}$, is the $r$-Laplacian operator,
$V:\mathbb{R}^{N}\rightarrow \mathbb{R}$ is a continuous function satisfying
the global Rabinowitz condition, and $f:\mathbb{R}\rightarrow \mathbb{R}$ is a
continuous function with subcritical growth. Using suitable variational
arguments and Ljusternik-Schnirelmann category theory, we investigate the
relation between the number of positive solutions and the topology of the set
where $V$ attains its minimum for small $\varepsilon$.


Abstract:
  Building cross-lingual voice conversion (VC) systems for multiple speakers
and multiple languages has been a challenging task for a long time. This paper
describes a parallel non-autoregressive network to achieve bilingual and
code-switched voice conversion for multiple speakers when there are only
mono-lingual corpora for each language. We achieve cross-lingual VC between
Mandarin speech with multiple speakers and English speech with multiple
speakers by applying bilingual bottleneck features. To boost voice cloning
performance, we use an adversarial speaker classifier with a gradient reversal
layer to reduce the source speaker's information from the output of encoder.
Furthermore, in order to improve speaker similarity between reference speech
and converted speech, we adopt an embedding consistency loss between the
synthesized speech and its natural reference speech in our network.
Experimental results show that our proposed method can achieve high quality
converted speech with mean opinion score (MOS) around 4. The conversion system
performs well in terms of speaker similarity for both in-set speaker conversion
and out-set-of one-shot conversion.


Abstract:
  By using electrochemical etching, we fabricated conductive ultrathin SrVO3
(SVO) films that exhibited metallic behavior down to 3 monolayers (ML). From an
observed systematic change in transport properties with decreasing film
thickness, it was found that the disorder in the films remained nearly
unchanged during etching, and only the thickness was reduced. This is in
contrast to the insulating behavior found for as-deposited SVO ultrathin films.
For the etched films, the electron mobility at 200 K decreased with decreasing
film thickness below 10 ML, originating from an increased scattering rate and
electron effective mass near the metal-insulator transition. A slight upturn in
the resistivity and a positive magnetoresistance at low temperatures were
typically observed for the etched films down to 3 ML, which was explained by
weak anti-localization of electrons in a weakly disordered metal.


Abstract:
  We study the non-parametric isotonic regression problem for bivariate
elicitable functionals that are given as an elicitable univariate functional
and its Bayes risk. Prominent examples for functionals of this type are (mean,
variance) and (Value-at-Risk, Expected Shortfall), where the latter pair
consists of important risk measures in finance. We present our results for
totally ordered covariates but extenstions to partial orders are given in the
appendix.


Abstract:
  Characterizing the predicted environments of dwarf galaxies like the Large
Magellanic Cloud (LMC) is becoming increasingly important as next generation
surveys push sensitivity limits into this low-mass regime at cosmological
distances. We study the environmental effects of LMC-mass halos ($M_{200m} \sim
10^{11}$ M$_\odot$) on their populations of satellites ($M_\star \geq 10^4$
M$_\odot$) using a suite of zoom-in simulations from the Feedback In Realistic
Environments (FIRE) project. Our simulations predict significant hot coronas
with $T\sim10^5$ K and $M_\text{gas}\sim10^{9.5}$ M$_\odot$. We identify
signatures of environmental quenching in dwarf satellite galaxies, particularly
for satellites with intermediate mass ($M_\star = 10^{6-7}$ M$_\odot$). The gas
content of such objects indicates ram-pressure as the likely quenching
mechanism, sometimes aided by star formation feedback. Satellites of LMC-mass
hosts replicate the stellar mass dependence of the quiescent fraction found in
satellites of MW mass hosts (i.e. that the quiescent fraction increases as
stellar mass decreases). Satellites of LMC-mass hosts have a wider variety of
quenching times when compared to the strongly bi-modal distribution of
quenching times of nearby centrals. Finally, we identify significant tidal
stellar structures around four of our six LMC-analogs, suggesting that stellar
streams may be common. These tidal features originated from satellites on close
orbits, extend to $\sim$80 kpc from the central galaxy, and contain
$\sim10^{6-7}$ M$_\odot$~of stars.


Abstract:
  Optical metasurfaces have been heralded as the platform to integrate multiple
functionalities in a compact form-factor, potentially replacing bulky
components. A central stepping stone towards realizing this promise is the
demonstration of multifunctionality under several constraints (e.g. at multiple
incident wavelengths and/or angles) in a single device -- an achievement being
hampered by design limitations inherent to single-layer planar geometries.
Here, we propose a general framework for the inverse design of volumetric 3D
metaoptics via topology optimization, showing that even few-wavelength thick
devices can achieve high-efficiency multifunctionality. We embody our framework
in multiple closely-spaced patterned layers of a low-index polymer. We
experimentally demonstrate our approach with an inverse-designed 3d-printed
light concentrator working at five different non-paraxial angles of incidence.
Our framework paves the way towards realizing multifunctional ultra-compact 3D
nanophotonic devices.


Abstract:
  Recently, significant progress has been made on semantic segmentation.
However, the success of supervised semantic segmentation typically relies on a
large amount of labelled data, which is time-consuming and costly to obtain.
Inspired by the success of semi-supervised learning methods in image
classification, here we propose a simple yet effective semi-supervised learning
framework for semantic segmentation. We demonstrate that the devil is in the
details: a set of simple design and training techniques can collectively
improve the performance of semi-supervised semantic segmentation significantly.
Previous works [3, 27] fail to employ strong augmentation in pseudo label
learning efficiently, as the large distribution change caused by strong
augmentation harms the batch normalisation statistics. We design a new batch
normalisation, namely distribution-specific batch normalisation (DSBN) to
address this problem and demonstrate the importance of strong augmentation for
semantic segmentation. Moreover, we design a self correction loss which is
effective in noise resistance. We conduct a series of ablation studies to show
the effectiveness of each component. Our method achieves state-of-the-art
results in the semi-supervised settings on the Cityscapes and Pascal VOC
datasets.


Abstract:
  Given a group $G$ and an endomorphism $\varphi$ of $G$, two elements $x, y
\in G$ are said to be $\varphi$-conjugate if $x = gy \varphi(g)^{-1}$ for some
$g \in G$. The number of equivalence classes for this relation is the
Reidemeister number $R(\varphi)$ of $\varphi$. The set $\{R(\psi) \mid \psi \in
\mathrm{Aut}(G)\}$ is called the Reidemeister spectrum of $G$. We investigate
Reidemeister numbers and spectra on direct products of finitely many groups and
determine what information can be derived from the individual factors.


Abstract:
  Mobile communication via high-altitude platforms operating in the
stratosphere is an idea that has been on the table for decades. In the past few
years, however, with recent advances in technology and parallel progress in
standardization and regulatory bodies like 3GPP and ITU, these ideas have
gained considerable momentum. In this article, we present a comprehensive
overview of HIBS - High Altitude Platform Stations as IMT Base Stations. We lay
out possible use cases and summarize the current status of the development,
from a technological point of view as well as from standardization in 3GPP, and
regarding spectrum aspects. We then present preliminary system level simulation
results to shed light on the performance of HIBS. We conclude with pointing out
several directions for future research.


Abstract:
  If gravitational perturbations are quantized into gravitons in analogy with
the electromagnetic field and photons, the resulting graviton interactions
should lead to an entangling interaction between massive objects. We suggest a
test of this prediction. To do this, we introduce the concept of interactive
quantum information sensing. This novel sensing protocol is tailored to
provable verification of weak dynamical entanglement generation between a pair
of systems. We show that this protocol is highly robust to typical thermal
noise sources. The sensitivity can moreover be increased both using an initial
thermal state and/or an initial phase of entangling via a non-gravitational
interaction. We outline a concrete implementation testing the ability of the
gravitational field to generate entanglement between an atomic interferometer
and mechanical oscillator. Preliminary numerical estimates suggest that
near-term devices could feasibly be used to perform the experiment.


Abstract:
  Accelerating Entrepreneurial Decision-Making Through Hybrid Intelligence
DESIGN PARADIGMS AND PRINCIPLES FOR DECISIONAL GUIDANCE IN ENTREPRENEURSHIP


Abstract:
  Traditional numerical methods for calculating matrix eigenvalues are
prohibitively expensive for high-dimensional problems. Iterative random
sparsification methods allow for the estimation of a single dominant eigenvalue
at reduced cost by leveraging repeated random sampling and averaging. We
present a general approach to extending such methods for the estimation of
multiple eigenvalues and demonstrate its performance for several benchmark
problems in quantum chemistry.


Abstract:
  Impacts of dust grains on spacecraft are known to produce typical impulsive
signals in the voltage waveform recorded at the terminals of electric antennas.
Such signals are routinely detected by the Time Domain Sampler (TDS) system of
the Radio and Plasma Waves (RPW) instrument aboard Solar Orbiter. We
investigate the capabilities of RPW in terms of interplanetary dust studies and
present the first analysis of dust impacts recorded by this instrument. We
discuss previously developed models of voltage pulses generation after a dust
impact onto a spacecraft and present the relevant technical parameters for
Solar Orbiter RPW as a dust detector. Then we present the statistical analysis
of the dust impacts recorded by RPW/TDS from April 20th, 2020 to February 27th,
2021 between 0.5 AU and 1 AU. The study shows that the dust population studied
presents a radial velocity component directed outward from the Sun, the order
of magnitude of which can be roughly estimated as $v_{r, dust} \simeq 50$
km.$s^{-1}$. This is consistent with the flux of impactors being dominated by
$\beta$-meteoroids. We estimate the cumulative flux of these grains at 1 AU to
be roughly $F_\beta \simeq 8\times 10^{-5} $ m$^{-2}$s$^{-1}$, for particles of
radius $r \gtrsim 100$ nm. The power law index $\delta$ of the cumulative mass
flux of the impactors is evaluated by two differents methods (direct
observations of voltage pulses and indirect effect on the impact rate
dependency on the impact speed). Both methods give a result $\delta \simeq
0.3-0.4$. Solar Orbiter RPW proves to be a suitable instrument for
interplanetary dust studies. These first results are promising for the
continuation of the mission, in particular for the in-situ study of the dust
cloud outside the ecliptic plane, which Solar Orbiter will be the first
spacecraft to explore.


Abstract:
  Combining two classical notions in extremal combinatorics, the study of
Ramsey-Tur\'an theory seeks to determine, for integers $m\le n$ and $p \leq q$,
the number $\mathsf{RT}_p(n,K_q,m)$, which is the maximum size of an $n$-vertex
$K_q$-free graph in which every set of at least $m$ vertices contains a $K_p$.
  Two major open problems in this area from the 80s ask: (1) whether the
asymptotic extremal structure for the general case exhibits certain periodic
behaviour, resembling that of the special case when $p=2$; (2) constructing
analogues of Bollob\'as-Erd\H{o}s graphs with densities other than $1/2$.
  We refute the first conjecture by witnessing asymptotic extremal structures
that are drastically different from the $p=2$ case, and address the second
problem by constructing Bollob\'as-Erd\H{o}s-type graphs using high dimensional
complex spheres with all rational densities. Some matching upper bounds are
also provided.


Abstract:
  In order to further develop and implement novel drift scan imaging
experiments to undertake wide field, high time resolution surveys for
millisecond optical transients, an appropriate telescope drive system is
required. This paper describes the development of a simple and inexpensive
hardware and software system to monitor, characterise, and correct the primary
category of telescope drive errors, periodic errors due to imperfections in the
drive and gear chain. A model for the periodic errors is generated from direct
measurements of the telescope drive shaft rotation, verified by comparison to
astronomical measurements of the periodic errors. The predictive model is
generated and applied in real-time in the form of corrections to the drive
rate. A demonstration of the system shows that that inherent periodic errors of
peak-to-peak amplitude ~100'' are reduced to below the seeing limit of ~3''.
This demonstration allowed an estimate of the uncertainties on the transient
sensitivity timescales of the prototype survey of Tingay & Joubert (2021), with
the nominal timescale sensitivity of 21 ms revised to be in the range of 20 -
22 ms, which does not significantly affect the results of the experiment. The
correction system will be adopted into the final version of high cadence
imaging experiment, which is currently under construction. The correction
system is inexpensive (<$A100) and composed of readily available hardware, and
is readily adaptable to other applications. Design details and codes are
therefore made publicly available.


Abstract:
  We show that an invertible bilateral weighted shift is strongly structurally
stable if and only if it has the shadowing property. We also exhibit a
K{\"o}the sequence space supporting a frequently hypercyclic weighted shift,
but no chaotic weighted shifts.


Abstract:
  Simple, controllable models play an important role to learn how to manipulate
and control quantum resources. We focus here on quantum non-Markovianity and
model the evolution of open quantum systems by quantum renewal processes. This
class of quantum dynamics provides us with a phenomenological approach to
characterise dynamics with a variety of non-Markovian behaviours, here
described in terms of the trace distance between two reduced states. By
adopting a trajectory picture for the open quantum system evolution, we analyse
how non-Markovianity is influenced by the constituents defining the quantum
renewal process, namely the time-continuous part of the dynamics, the type of
jumps and the waiting time distributions. We focus not only on the mere value
of the non-Markovianity measure, but also on how different features of the
trace distance evolution are altered, including times and number of revivals.


Abstract:
  Security is of critical importance for the Internet of Things (IoT). Many IoT
devices are resource-constrained, calling for lightweight security protocols.
Physical unclonable functions (PUFs) leverage integrated circuits' variations
to produce responses unique for individual devices, and hence are not
reproducible even by the manufacturers. Implementable with simplistic circuits
of thousands of transistors and operable with low energy, Physical unclonable
functions are promising candidates as security primitives for
resource-constrained IoT devices. Arbiter PUFs (APUFs) are a group of
delay-based PUFs which are highly lightweight in resource requirements but
suffer from high susceptibility to machine learning attacks. To defend APUF
variants against machine learning attacks, we introduce challenge input
interface, which incurs low resource overhead. With the interface, experimental
attack study shows that all tested PUFs have substantially improved their
resistance against machine learning attacks, rendering interfaced APUF variants
promising candidates for security critical applications.


Abstract:
  We present explicit estimates of right and left tails and exact (up to
universal, multiplicative constants) estimates of tails and moments of hitting
times of Bessel processes. The latter estimates are obtained from more general
estimates of moments and tails established for convolutions of elementary
mixtures of exponential distributions.


Abstract:
  Modern information retrieval systems, including web search, ads placement,
and recommender systems, typically rely on learning from user feedback. Click
models, which study how users interact with a ranked list of items, provide a
useful understanding of user feedback for learning ranking models. Constructing
"right" dependencies is the key of any successful click model. However,
probabilistic graphical models (PGMs) have to rely on manually assigned
dependencies, and oversimplify user behaviors. Existing neural network based
methods promote PGMs by enhancing the expressive ability and allowing flexible
dependencies, but still suffer from exposure bias and inferior estimation. In
this paper, we propose a novel framework, Adversarial Imitation Click Model
(AICM), based on imitation learning. Firstly, we explicitly learn the reward
function that recovers users' intrinsic utility and underlying intentions.
Secondly, we model user interactions with a ranked list as a dynamic system
instead of one-step click prediction, alleviating the exposure bias problem.
Finally, we minimize the JS divergence through adversarial training and learn a
stable distribution of click sequences, which makes AICM generalize well across
different distributions of ranked lists. A theoretical analysis has indicated
that AICM reduces the exposure bias from $O(T^2)$ to $O(T)$. Our studies on a
public web search dataset show that AICM not only outperforms state-of-the-art
models in traditional click metrics but also achieves superior performance in
addressing the exposure bias and recovering the underlying patterns of click
sequences.


Abstract:
  We associate to a graphon $\gamma$ the sequence of $W$-random graphs
$(G_n(\gamma))_{n \geq 1}$. We say that the graphon is singular if, for any
finite graph $F$, the homomorphism density $t(F,G_n(\gamma))$ has a variance of
order $O(n^{-2})$. This behavior is singular because generically, the density
of a fixed finite graph $F$ in a $W$-random graph has a variance of order
$O(n^{-1})$. We conjecture that the only singular graphons are the constant
graphons $\gamma_p$ with $p \in [0,1]$, corresponding to the Erd\H{o}s-R\'enyi
random graphs $G(n,p)$. In this paper, we investigate the general properties of
the singular graphons, and we show that they share many properties with the
Erd\H{o}s-R\'enyi random graphs. In particular, if $\gamma$ is a singular
graphon, then the scaled densities
$n(t(F,G_n(\gamma))-\mathbb{E}[t(F,G_n(\gamma))])$ converge in joint
distribution. This generalises the central limit theorem satisfied by the
Erd\H{o}s-R\'enyi random graphs $G(n,p)$; however, the limiting distribution
might be non-Gaussian if the conjecture does not hold. We also establish an
equation satisfied by the characteristic polynomial of the Laplacian of the
graph $G_n(\gamma)$ associated to a singular graphon; this opens the way to a
spectral approach of the conjecture.


Abstract:
  Many businesses and industries nowadays rely on large quantities of time
series data making time series forecasting an important research area. Global
forecasting models that are trained across sets of time series have shown a
huge potential in providing accurate forecasts compared with the traditional
univariate forecasting models that work on isolated series. However, there are
currently no comprehensive time series archives for forecasting that contain
datasets of time series from similar sources available for the research
community to evaluate the performance of new global forecasting algorithms over
a wide variety of datasets. In this paper, we present such a comprehensive time
series forecasting archive containing 20 publicly available time series
datasets from varied domains, with different characteristics in terms of
frequency, series lengths, and inclusion of missing values. We also
characterise the datasets, and identify similarities and differences among
them, by conducting a feature analysis. Furthermore, we present the performance
of a set of standard baseline forecasting methods over all datasets across
eight error metrics, for the benefit of researchers using the archive to
benchmark their forecasting algorithms.


Abstract:
  Operads are algebraic devices offering a formalization of the concept of
operations with several inputs and one output. Such operations can be naturally
composed to form bigger and more complex ones. Coming historically from
algebraic topology, operads intervene now as important objects in computer
science and in combinatorics. The theory of operads, together with the
algebraic setting and the tools accompanying it, promises advances in these two
areas. On the one hand, operads provide a useful abstraction of formal
expressions, and also, provide connections with the theory of rewrite systems.
On the other hand, a lot of operads involving combinatorial objects highlight
some of their properties and allow to discover new ones.
  This book presents the theory of nonsymmetric operads under a combinatorial
point of view. It portrays the main elements of this theory and the links it
maintains with several areas of computer science and combinatorics. A lot of
examples of operads appearing in combinatorics are studied and some
constructions relating operads with known algebraic structures are presented.
The modern treatment of operads consisting in considering the space of formal
power series associated with an operad is developed. Enrichments of
nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.
  This text is addressed to any computer scientist or combinatorist who looks a
complete and a modern description of the theory of nonsymmetric operads.
Evenly, this book is intended to an audience of algebraists who are looking for
an original point of view fitting in the context of combinatorics.


Abstract:
  The (open-high-low-close) OHLC data is the most common data form in the field
of finance and the investigate object of various technical analysis. With
increasing features of OHLC data being collected, the issue of extracting their
useful information in a comprehensible way for visualization and easy
interpretation must be resolved. The inherent constraints of OHLC data also
pose a challenge for this issue. This paper proposes a novel approach to
characterize the features of OHLC data in a dataset and then performs dimension
reduction, which integrates the feature information extraction method and
principal component analysis. We refer to it as the pseudo-PCA method.
Specifically, we first propose a new way to represent the OHLC data, which will
free the inherent constraints and provide convenience for further analysis.
Moreover, there is a one-to-one match between the original OHLC data and its
feature-based representations, which means that the analysis of the
feature-based data can be reversed to the original OHLC data. Next, we develop
the pseudo-PCA procedure for OHLC data, which can effectively identify
important information and perform dimension reduction. Finally, the
effectiveness and interpretability of the proposed method are investigated
through finite simulations and the spot data of China's agricultural product
market.


Abstract:
  We introduce an algebraic system which can be used as a model for spaces with
geodesic paths between any two of their points. This new algebraic structure is
based on the notion of mobility algebra which has recently been introduced as a
model for the unit interval of real numbers. We show that there is a strong
connection between modules over a ring and affine mobility spaces over a
mobility algebra. However, geodesics in general fail to be affine thus giving
rise to the new algebraic structure of mobility space. We show that the so
called formula for spherical linear interpolation, which gives geodesics on the
n-sphere, is an example of a mobility space over the unit interval mobility
algebra.


Abstract:
  GANs largely increases the potential impact of generative models. Therefore,
we propose a novel knowledge transfer method for generative models based on
mining the knowledge that is most beneficial to a specific target domain,
either from a single or multiple pretrained GANs. This is done using a miner
network that identifies which part of the generative distribution of each
pretrained GAN outputs samples closest to the target domain. Mining effectively
steers GAN sampling towards suitable regions of the latent space, which
facilitates the posterior finetuning and avoids pathologies of other methods,
such as mode collapse and lack of flexibility. Furthermore, to prevent
overfitting on small target domains, we introduce sparse subnetwork selection,
that restricts the set of trainable neurons to those that are relevant for the
target dataset. We perform comprehensive experiments on several challenging
datasets using various GAN architectures (BigGAN, Progressive GAN, and
StyleGAN) and show that the proposed method, called MineGAN, effectively
transfers knowledge to domains with few target images, outperforming existing
methods. In addition, MineGAN can successfully transfer knowledge from multiple
pretrained GANs.


Abstract:
  The Peace-Athabasca Delta (PAD) of northwestern Alberta is one of the largest
inland freshwater deltas in the world, laying at the confluence of the Peace
and Athabasca Rivers. The PAD is recognized as a having unique ecological
significance and periodic ice jam flooding from both rivers is an important
feature of its current ecology. Past studies have debated whether a change in
ice jam flood (IJF) frequency on the Peace River has recently occurred, and
what factors might be driving any perceived changes. This study contributes to
this debate by addressing two questions: (1) what factors are most predictive
of Peace River IJFs, and (2) how might climate change impact IJF frequency?
This work starts with a physically-based conceptual model of the necessary
conditions for a large Peace River IJF, and the factors that indicate whether
those conditions are met. Logistic regression is applied to the historical
flood record to determine which combination of hydroclimatic and riverine
factors best predict IJFs and the uncertainty in those relationships given the
available data. Winter precipitation and temperature are most predictive of
Peace River IJFs, while freeze-up elevation contains little predictive power
and is not closely related to IJF occurrence. The best logistic regression
model is forced with downscaled climate change scenarios from multiple climate
models to project IJF frequency for a variety of plausible futures. Parametric
uncertainty in the best logistic regression model is propagated into the
projections using a parametric bootstrap to sample many plausible statistical
models. Although there is variability across emissions scenarios and climate
models, all projections indicate that the frequency of Peace River IJFs is
likely to decrease substantially in the coming decades, and that average
waiting times between future IJFs will likely surpass recent experience.


Abstract:
  We investigate the impact on cosmological observables of $f(Q)$-gravity, a
specific class of modified gravity models in which gravity is described by the
non-metricity scalar, $Q$. In particular we focus on a specific model which is
indistinguishable from the $\Lambda$-cold-dark-matter ($\Lambda$CDM) model at
the background level, while showing peculiar and measurable signatures at
linear perturbation level. These are attributed to a time-dependent Planck mass
and are regulated by a single dimensionless parameter, $\alpha$. In comparison
to the $\Lambda$CDM model, we find for positive values of $\alpha$ a suppressed
matter power spectrum and lensing effect on the Cosmic Microwave Background
radiation (CMB) angular power spectrum and an enhanced integrated-Sachs-Wolfe
tail of CMB temperature anisotropies. The opposite behaviors are present when
the $\alpha$ parameter is negative. We also investigate the modified
Gravitational Waves (GWs) propagation and show the prediction of the GWs
luminosity distance compared to the standard electromagnetic one. Finally, we
infer the accuracy on the free parameter of the model with standard sirens at
future GWs detectors.


Abstract:
  Sakurai et al. (J Comput Phys, 2019) presented a flux-based volume
penalization (VP) approach for imposing inhomogeneous Neumann boundary
conditions on embedded interfaces. The flux-based VP method modifies the
diffusion coefficient of the original elliptic (Poisson) equation and uses a
flux-forcing function as a source term in the equation to impose the Neumann
boundary conditions. As such, the flux-based VP method can be easily
incorporated into existing fictitious domain codes. Sakurai et al. relied on an
analytical construction of flux-forcing functions, which limits the
practicality of the approach. Because of the analytical approach taken in the
prior work, only (spatially) constant flux values on simple interfaces were
considered. In this paper, we present a numerical technique for constructing
flux-forcing functions for arbitrarily complex boundaries. The imposed flux
values are also allowed to vary spatially in our approach. Furthermore, the
flux-based VP method is extended to include (spatially varying) Robin boundary
conditions, which makes the flux-based VP method even more general. We consider
several two- and three-dimensional test examples to access the spatial accuracy
of the numerical solutions. The method is also used to simulate flux-driven
thermal convection in a concentric annular domain. We formally derive the
flux-based volume penalized Poisson equation satisfying Neumann/Robin boundary
condition in strong form; such a derivation was not presented in Sakurai et
al., where the equation first appeared for the Neumann problem. The derivation
reveals that the flux-based VP approach relies on a surface delta function to
impose inhomogeneous Neumann/Robin boundary conditions. However, explicit
construction of the delta function is not necessary for the flux-based VP
method, which makes it different from other diffuse domain equations presented
in the literature.


Abstract:
  Two extremely red main-belt asteroids: 203 Pompeja and 269 Justitia, were
identified from combined visible and near-infrared spectroscopic observations
collected at the IRTF and SAO observatories. These two asteroids have a redder
spectral slope than any other D-type body, which are the reddest objects in the
asteroid belt, and similar to RR and IR-class objects found in the outer Solar
System among trans-Neptunian objects and Centaurs. Spectroscopic results
suggest the presence of complex organic materials on the surface layer of these
asteroids, implying that they could have formed in the vicinity of Neptune and
been transplanted to the main belt region during a phase of planetary
migration. 203 Pompeia is the only very red asteroid known so far among the
~250 bodies with diameter larger than 110 km (i.e. presumably structurally
intact) found in the asteroid belt. These discoveries add another piece of
evidence that the main asteroid belt hosts a population of bodies that were
formed in the outskirt of the Solar System.


Abstract:
  Freestanding semiconductor nanowires have opened up new possibilities for
semiconductor devices, enabling geometries, material combinations and strain
states which were not previously possible. Along these lines, spontaneous
bending in asymmetric core-shell nanowire heterostructures has recently been
proposed as a means to realize previously unimagined device geometries, novel
strain-gradient engineering and bottom-up device fabrication. The synthesis of
these nanostructures exploits the nanowire geometry and the directionality of
the shell deposition process. Here, we explore the underlying mechanisms of
this bending process by modeling the evolution of nanowires during asymmetric
shell deposition. We show how bending can lead to dramatic local shell
thickness, curvature and strain variations along the length of the nanowire,
and we elucidate the dependence of shell growth and bending on parameters such
as the core and shell dimensions and materials, and angle of incidence of the
deposition source. In addition, deposition shadowing by neighboring nanowires
is explored. We show that shadowing can easily be employed to connect nanowire
pairs, which could be used to fabricate novel nanowire sensors. Model results
are compared with GaAs-InP and GaAs-(Al,In)As core-shell nanowire growth
experiments. These results can be used to guide future experiments and to help
pave the way to bent nanowire devices.


Abstract:
  We report on the Shubnikov de Haas (SdH) oscillations in the quasi
two-dimensional molecular conductor $\alpha-$(BETS)$_{2}$I$_{3}$ [BETS:
bis(ethylenedithio)tetraselenafulvalene] laminated on polyimide films at 1.7 K.
From the SdH phase factor, we verified experimentally that the material is in
the Dirac fermion phase under pressure. $\alpha-$(BETS)$_{2}$I$_{3}$ is in the
vicinity of the phase transition between strongly correlated insulating and
Dirac fermion phases, and is a possible candidate for an ambient-pressure
molecular Dirac fermion system. However, the SdH oscillations indicate that the
Berry phase is zero at ambient pressure. Under pressure, a $\pi$ Berry phase
emerges when the metal-insulator crossover is almost suppressed at $\sim$0.5
GPa. The results contrast those for the pioneering molecular Dirac fermion
system $\alpha-$(BEDT-TTF)$_{2}$I$_{3}$ [BEDT-TTF:
bis(ethylenedithio)tetrathiafulvalene] in which Dirac fermions and
semiconducting behavior are simultaneously observed.


Abstract:
  Variability is a general property of accretion discs and their associated
jets. We introduce a semi-analytic model for particle acceleration and radio
jet/lobe evolution and explore the effect of Myr timescale jet variability on
the particles accelerated by an AGN jet. Our work is motivated by the need for
local powerful ultrahigh energy cosmic ray (UHECR) sources and evidence for
variability in AGN and radio galaxies. Our main results are: i) UHECR and
nonthermal radiative luminosities track the jet power but with a response set
by the escape and cooling times, respectively; ii) jet variability produces
structure in the electron, synchrotron and UHECR spectra that deviates from
that produced for a constant jet power - in particular, spectral hardening
features may be signatures of variability; iii) the cutoff in the integrated CR
spectrum is stretched out due to the variation in jet power (and, consequently,
maximum CR energy). The resulting spectrum is the convolution of the jet power
distribution and the source term. We derive an approximate form for a
log-normal distribution of powers; iv) we introduce the idea of $\sim 10$ GeV
'proxy electrons' that are cooling at the same rate that UHECRs of rigidity 10
EV are escaping from the source, and determine the corresponding photon
frequencies that probe escaping UHECRs. Our results demonstrate the link
between the history of an astrophysical particle accelerator and its particle
contents, nonthermal emission and UHECR spectrum, with consequences for
observations of radio galaxies and UHECR source models.


Abstract:
  Optimal transport (OT), which provides a distance between two probability
distributions by considering their spatial locations, has been applied to
widely diverse applications. Computing an OT problem requires solution of
linear programming with tight mass-conservation constraints. This requirement
hinders its application to large-scale problems. To alleviate this issue, the
recently proposed relaxed-OT approach uses a faster algorithm by relaxing such
constraints. Its effectiveness for practical applications has been
demonstrated. Nevertheless, it still exhibits slow convergence. To this end,
addressing a convex semi-relaxed OT, we propose a fast block-coordinate
Frank-Wolfe (BCFW) algorithm, which gives sparse solutions. Specifically, we
provide their upper bounds of the worst convergence iterations, and equivalence
between the linearization duality gap and the Lagrangian duality gap. Three
fast variants of the proposed BCFW are also proposed. Numerical evaluations in
color transfer problem demonstrate that the proposed algorithms outperform
state-of-the-art algorithms across different settings.


Abstract:
  We are concerned below with the characterization in a unital commutative real
Banach algebra $\mathbb{A}$ of continuous solutions of the
Go{\l}\k{a}b-Schinzel functional equation (below), the general Popa groups they
generate and the associated Goldie functional equation. This yields general
structure theorems involving both linear and exponential homogeneity in
$\mathbb{A}$ for both these functional equations and also explict forms, in
terms of the recently developed theory of multi-Popa groups [BinO3,4], both for
the ring $C[0,1]$ and for the case of $\mathbb{R}^{d}$ with componentwise
product, clarifying the context of recent developments in [RooSW]. The case
$\mathbb{A}=\mathbb{C}$ provides a new viewpoint on continuous complex-valued
solutions of the primary equation by distinguishing analytic from real-analytic
ones.


Abstract:
  The LPMWPC can be used as the {\Delta}E detector for the low-energy charged
particle detection. In order to increase the transmittance, the wires were
adopted as the cathode. This work investigated the LPMWPC signal
characteristics of this configuration and measured the gas gain with a mixture
of 90%Ar and 10% CO2 from 1E3 to 1E5 Pa. From the test, the second pulse after
the avalanche signal was observed, which proved to be caused by the ions'
drifting near the cathode wire.


Abstract:
  We show that the position-momentum duality offers a transparent
interpretation of the band geometry at the topological band crossings. Under
this duality, the band geometry with Berry connection is dual to the
free-electron motion under gauge field. This identifies the trace of quantum
metric as the dual energy in momentum space. The band crossings with Berry
defects thus induce the dual energy quantization in the trace of quantum
metric. For a $\mathbb Z$ nodal-point or nodal-surface semimetal, a dual Landau
level quantization occurs owing to the Berry charge. Meanwhile, a nodal-loop
semimetal exhibits a Berry vortex line, leading to the quantized dual
rotational energy about the nodal loop. A $\mathbb Z_2$ monopole brings about
another dual rotational energy, which originates from the link with an
additional nodal line. Nontrivial band geometry generically induces finite
spread in the Wannier functions. While the spread manifests a quantized lower
bound in a $\mathbb Z$ nodal-point or nodal-surface semimetal, logarithmic
divergence occurs in a nodal-loop semimetal. The band geometry at the band
crossings may be probed experimentally by a periodic-drive measurement.


Abstract:
  In this paper, we introduce new generalizations of higher-order Changhee of
the first and second kind. Moreover, we derive some new results for these
numbers and polynomials. Furthermore, some interesting special cases of the
generalized higher-order Changhee numbers and polynomials are deduced.


Abstract:
  It is known that the right key of a Kashiwara-Nakashima tableau can be
computed using the Lecouvey-Sheats symplectic jeu de taquin. Motivated by
Willis' direct way of computing type A right keys, we also give a way of
computing symplectic right keys without the use of jeu de taquin.


Abstract:
  Atom-interferometer gravitational-wave (GW) observatory, as a new design of
ground-based GW detector for the near future, is sensitive at a relatively low
frequency for GW observations. Taking the proposed atom interferometer Zhaoshan
Long-baseline Atom Interferometer Gravitation Antenna (ZAIGA), and its
illustrative upgrade (Z+) as examples, we investigate how the atom
interferometer will complement ground-based laser interferometers in testing
the gravitational dipole radiation from binary neutron star (BNS) mergers. A
test of such kind is important for a better understanding of the strong
equivalence principle laying at the heart of Einstein's general relativity. To
obtain a statistically sound result, we sample BNS systems according to their
merger rate and population, from which we study the expected bounds on the
parameterized dipole radiation parameter $B$. Extracting BNS parameters and the
dipole radiation from the combination of ground-based laser interferometers and
the atom-interferometer ZAIGA/Z+, we are entitled to obtain tighter bounds on
$B$ by a few times to a few orders of magnitude, compared to ground-based laser
interferometers alone, ultimately reaching the levels of $|B| \lesssim 10^{-9}$
(with ZAIGA) and $|B| \lesssim 10^{-10}$ (with Z+).


Abstract:
  Grid turbulence is investigated using cross-correlation digital Particle
Image Velocimetry (PIV) over a range of Taylor Reynolds Number (Re{\lambda})
from 5 to 44. Instantaneous velocity is measured directly and vorticity and
velocity gradients are obtained indirectly. Measurements are taken at various
downstream locations from the generating grid. Probability distribution
functions (PDFs) are calculated for the fluctuating component of the velocity,
the spatial velocity gradients and vorticity. The PDF of the velocity
fluctuations has a Gaussian distribution while velocity gradients and vorticity
are found to have non-Gaussian PDF distributions. The structure of the flow is
investigated by calculating spatial autocorrelations for all measured and
derived data. The spatial velocity autocorrelations differ from previous
experimental measurements of grid turbulence, most of which have been
determined from single-point measurements. This difference is believed to be
due to differences in the way in which the measurements are made, and
particularly to differences in the spatial size of the experimental domain.


Abstract:
  Photosynthesis is the primary energy production process of ecosystem.
Throughout the green plants, two different types of chlorophylls, Chl-a and -b,
are bound to the light-harvesting complex for photosystem II. While the
structure and functional characteristics of the two types of chlorophylls have
been well documented as individual, the features of the coexistence has yet to
be understood clearly. Here, we present a principled framework for discerning
and quantifying the chlorophylls' role during the excited energy transfer. Our
approach combines network science and Monte Carlo Markov analysis based on the
Foerster resonance energy transfer rates between all the chlorophyll pairs in
the light-harvesting antennae for photosystem II. We find that the excitation
energy can be rapidly confined to the specific chlorophyll clusters in the
light-harvesting complex, where excess energy dissipation possibly takes place,
only when both chlorophyll species are involved. Comparing to other models with
hypothetical chlorophyll compositions, we show that the light harvesting system
with natural chlorophyll a and b ratio is the most advantageous for the
photosystem II supercomplex to balance the light-harvesting and photoprotection
capabilities.


Abstract:
  A class of models of long waves in dispersive media with coupled quadratic
nonlinearities on a periodic domain $\mathbb{T}$ are studied. We used two
distributed controls, supported in $\omega\subset\mathbb{T}$ and assumed to be
generated by a linear feedback law conserving the "mass" (or "volume"), to
prove global control results. The first result, using spectral analysis,
guarantees that the system in consideration is locally controllable in
$H^s(\mathbb{T})$, for $s\geq0$. After that, by certain properties of Bourgain
spaces we show a property of global exponential stability. This property
together with the local exact controllability ensures for the first time in the
literature that long waves in nonlinear dispersive media are globally exactly
controllable in large time. Precisely, our analysis relies strongly on the
bilinear estimates using the Fourier restriction spaces in two different
dispersions that will guarantee a global control result for coupled systems of
the Korteweg-de Vries type. This result, of independent interest in the area of
control of coupled dispersive systems, provides a necessary first step for the
study of global control properties to the coupled dispersive systems in
periodic domains.


Abstract:
  Using the unification of the chiral SU(3) model and QCD sum rules, we deduce
the in-medium properties of $K^\pm_1$ meson. Within the chiral SU(3) model,
medium modified gluon and quark condensates are evaluated through their
interactions with the scalar fields ($\sigma$, $\zeta$, $\delta$, and $\chi$).
These condensates are further used as input in the Borel transformed equations
of QCD sum rules to evaluate the in-medium mass of strange $K^\pm_1$ meson. The
in-medium property of the above meson can be used to study the restoration of
chiral symmetry in nuclear matter.


Abstract:
  As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and
steering play important roles in quantum-enhanced communication protocols.
Distributing such quantum resources among multiple remote users in a network is
a crucial precondition underlying various quantum tasks. We experimentally
demonstrate the deterministic distribution of two- and three-mode Gaussian
entanglement and steering by transmitting separable states in a network
consisting of a quantum server and multiple users. In our experiment, entangled
states are not prepared solely by the quantum server, but are created among
independent users during the distribution process. More specifically, the
quantum server prepares separable squeezed states and applies classical
displacements on them before spreading out, and users simply perform local
beam-splitter operations and homodyne measurements after they receive separable
states. We show that the distributed Gaussian entanglement and steerability are
robust against channel loss. Furthermore, one-way Gaussian steering is achieved
among users that is useful for further directional or highly asymmetric quantum
information processing.


Abstract:
  In the present paper, we prove that any finite non-trivial irreducible module
over a rank two Lie conformal algebra $\mathcal{H}$ is of rank one. We also
describe the actions of $\mathcal{H}$ on its finite irreducible modules
explicitly. Moreover, we show that all finite non-trivial irreducible modules
of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie
conformal algebra are of rank one.


Abstract:
  Predicting all applicable labels for a given image is known as multi-label
classification. Compared to the standard multi-class case (where each image has
only one label), it is considerably more challenging to annotate training data
for multi-label classification. When the number of potential labels is large,
human annotators find it difficult to mention all applicable labels for each
training image. Furthermore, in some settings detection is intrinsically
difficult e.g. finding small object instances in high resolution images. As a
result, multi-label training data is often plagued by false negatives. We
consider the hardest version of this problem, where annotators provide only one
relevant label for each image. As a result, training sets will have only one
positive label per image and no confirmed negatives. We explore this special
case of learning from missing labels across four different multi-label image
classification datasets for both linear classifiers and end-to-end fine-tuned
deep networks. We extend existing multi-label losses to this setting and
propose novel variants that constrain the number of expected positive labels
during training. Surprisingly, we show that in some cases it is possible to
approach the performance of fully labeled classifiers despite training with
significantly fewer confirmed labels.


Abstract:
  The Cayley-Klein (CK) formalism is applied to the real algebra ${so}(5)$ by
making use of four graded contraction parameters describing in a unified
setting 81 Lie algebras, which cover the (anti-)de Sitter, Poincar\'e,
Newtonian and Carrollian algebras. Starting with the Drinfel'd-Jimbo real Lie
bialgebra for ${so}(5)$ together with its Drinfel'd double structure, we obtain
the corresponding CK bialgebra and the CK $r$-matrix coming from a Drinfel'd
double. As a novelty, we construct the (first-order) noncommutative CK spaces
of points, lines, 2-planes and 3-hyperplanes, studying their structural
properties. By requiring to deal with real structures, it comes out that there
exist 63 specific real Lie bialgebras together with their sets of four
noncommutative spaces. Furthermore, we find 14 classical $r$-matrices coming
from Drinfel'd doubles, obtaining new results for the de Sitter ${so}(4,1)$ and
anti-de Sitter ${so}(3,2)$ and for some of their contractions. These geometric
results are exhaustively applied onto the (3+1)D kinematical algebras, not only
considering the usual (3+1)D spacetime but also the 6D space of lines. We
establish different assignations between the geometrical CK generators and the
kinematical ones which convey physical identifications for the CK contraction
parameters in terms of the cosmological constant/curvature $\Lambda$ and speed
of light $c$. We finally obtain four classes of kinematical $r$-matrices
together with their noncommutative spacetimes and spaces of lines, comprising
all $\kappa$-deformations as particular cases.


Abstract:
  In this paper, we revisit math word problems~(MWPs) from the cross-lingual
and multilingual perspective. We construct our MWP solvers over pretrained
multilingual language models using sequence-to-sequence model with copy
mechanism. We compare how the MWP solvers perform in cross-lingual and
multilingual scenarios. To facilitate the comparison of cross-lingual
performance, we first adapt the large-scale English dataset MathQA as a
counterpart of the Chinese dataset Math23K. Then we extend several English
datasets to bilingual datasets through machine translation plus human
annotation. Our experiments show that the MWP solvers may not be transferred to
a different language even if the target expressions have the same operator set
and constants. But for both cross-lingual and multilingual cases, it can be
better generalized if problem types exist on both source language and target
language.


Abstract:
  The black hole information paradox has been hotly debated for the last few
decades, without full resolution. This makes it desirable to find analogs of
this paradox in simple and experimentally accessible systems, whose resolutions
may shed light on this long-standing and fundamental problem. Here we identify
and resolve an apparent "information paradox" in a quantum Hall interface
between the Halperin-331 and Pfaffian states. Information carried by pseudospin
degree of freedom of the Abelian 331 quasiparticles gets scrambled when they
cross the interface to enter non-Abelian Pfaffian state, and becomes
inaccessible to local measurements; in this sense the Pfaffian region is an
analog of black hole interior while the interface plays a role similar to its
horizon. We demonstrate that the "lost" information gets recovered once the
"black hole" evaporates and the quasiparticles return to the 331 region, albeit
in a highly entangled form. Such recovery is quantified by the Page curve of
the entropy carried by these quasiparticles, which are analogs of Hawking
radiation.


Abstract:
  Modern deep Super-Resolution (SR) networks have established themselves as
valuable techniques in image reconstruction and enhancement. However, these
networks are normally trained and tested on benchmark image data that lacks the
typical image degrading noise present in real images. In this paper, we test
the feasibility of using deep SR in real remote sensing payloads by assessing
SR performance in reconstructing realistically degraded satellite images. We
demonstrate that a state-of-the-art SR technique called Enhanced Deep
Super-Resolution Network (EDSR), without domain specific pre-training, can
recover encoded pixel data on images with poor ground sampling distance,
provided the ground resolved distance is sufficient. However, this recovery
varies amongst selected geographical types. Our results indicate that custom
training has potential to further improve reconstruction of overhead imagery,
and that new satellite hardware should prioritise optical performance over
minimising pixel size as deep SR can overcome a lack of the latter but not the
former.


Abstract:
  Clock configuration within constrained general-purpose microcontrollers takes
a key role in tuning performance, power consumption, and timing accuracy of
applications in the Internet of Things (IoT). Subsystems governing the
underlying clock tree must nonetheless cope with a huge parameter space,
complex dependencies, and dynamic constraints. Manufacturers expose the
underlying functions in very diverse ways, which leads to specialized
implementations of low portability. In this paper, we propose FlexClock, an
approach for generic online clock reconfiguration on constrained IoT devices.
We argue that (costly) generic clock configuration of general purpose computers
and powerful mobile devices need to slim down to the lower end of the device
spectrum. In search of a generalized solution, we identify recurring patterns
and building blocks, which we use to decompose clock trees into independent,
reusable components. With this segmentation we derive an abstract
representation of vendor-specific clock trees, which then can be dynamically
reconfigured at runtime. We evaluate our implementation on common hardware. Our
measurements demonstrate how FlexClock significantly improves peak power
consumption and energy efficiency by enabling dynamic voltage and frequency
scaling (DVFS) in a platform-agnostic way.


Abstract:
  Top-N recommendation is a challenging problem because complex and sparse
user-item interactions should be adequately addressed to achieve high-quality
recommendation results. The local latent factor approach has been successfully
used with multiple local models to capture diverse user preferences with
different sub-communities. However, previous studies have not fully explored
the potential of local models, and failed to identify many small and coherent
sub-communities. In this paper, we present Local Collaborative Autoencoders
(LOCA), a generalized local latent factor framework. Specifically, LOCA adopts
different neighborhood ranges at the training and inference stages. Besides,
LOCA uses a novel sub-community discovery method, maximizing the coverage of a
union of local models and employing a large number of diverse local models. By
adopting autoencoders as the base model, LOCA captures latent non-linear
patterns representing meaningful user-item interactions within sub-communities.
Our experimental results demonstrate that LOCA is scalable and outperforms
state-of-the-art models on several public benchmarks, by 2.99~4.70% in Recall
and 1.02~7.95% in NDCG, respectively.


Abstract:
  We study the mod $p^r$ Milnor $K$-groups of $p$-adically complete and
$p$-henselian rings, establishing in particular a Nesterenko-Suslin style
description in terms of the Milnor range of syntomic cohomology. In the case of
smooth schemes over complete discrete valuation rings we prove the mod $p^r$
Gersten conjecture for Milnor $K$-theory locally in the Nisnevich topology. In
characteristic $p$ we show that the Bloch-Kato-Gabber theorem remains true for
valuation rings, and for regular formal schemes in a pro sense.


Abstract:
  Deterministic and randomized, row-action and column-action linear solvers
have become increasingly popular owing to their simplicity, low computational
and memory complexities, and ease of composition with other techniques.
Moreover, in order to achieve high-performance, such solvers must often be
adapted to the given problem structure and to the hardware platform on which
the problem will be solved. Unfortunately, determining whether such adapted
solvers will converge to a solution has required equally unique analyses. As a
result, adapted, reliable solvers are slow to be developed and deployed. In
this work, we provide a general set of assumptions under which such adapted
solvers are guaranteed to converge with probability one, and provide worst case
rates of convergence. As a result, we can provide practitioners with guidance
on how to design highly adapted, randomized or deterministic, row-action or
column-action linear solvers that are also guaranteed to converge.


Abstract:
  Deep neural networks (DNNs) have been found to be vulnerable to adversarial
examples. Adversarial examples are malicious images with visually imperceptible
perturbations. While these carefully crafted perturbations restricted with
tight $\Lp$ norm bounds are small, they are still easily perceivable by humans.
These perturbations also have limited success rates when attacking black-box
models or models with defenses like noise reduction filters. To solve these
problems, we propose Demiguise Attack, crafting ``unrestricted'' perturbations
with Perceptual Similarity. Specifically, we can create powerful and
photorealistic adversarial examples by manipulating semantic information based
on Perceptual Similarity. Adversarial examples we generate are friendly to the
human visual system (HVS), although the perturbations are of large magnitudes.
We extend widely-used attacks with our approach, enhancing adversarial
effectiveness impressively while contributing to imperceptibility. Extensive
experiments show that the proposed method not only outperforms various
state-of-the-art attacks in terms of fooling rate, transferability, and
robustness against defenses but can also improve attacks effectively. In
addition, we also notice that our implementation can simulate illumination and
contrast changes that occur in real-world scenarios, which will contribute to
exposing the blind spots of DNNs.


Abstract:
  Let $n,k,t$ be positive integers. What is the maximum number of arcs in a
digraph on $n$ vertices in which there are at most $t$ distinct walks of length
$k$ with the same endpoints? In this paper, we prove that the maximum number is
equal to $n(n-1)/2$ and the extremal digraph are the transitive tournaments
when $k\ge n-1\ge \max\{2t+1,2\left\lceil \sqrt{2t+9/4}+1/2\right\rceil+3\}$.
Based on this result, we may determine the maximum numbers and the extremal
digraphs for $k\ge \max\{2t+1,2\left\lceil \sqrt{2t+9/4}+1/2\right\rceil+3\}$
and $n$ is sufficiently large, which generalises the existing results. A
conjecture is also presented.


Abstract:
  We explore entanglement generation between multiple optically levitated
nanospheres interacting with a common optical cavity via the Coherent
Scattering optomechanical interaction. We derive the many-particle Hamiltonian
governing the unitary evolution of the system and show that it gives rise to
quantum correlations among the various partitions of the setup, following a
non-Markovian dynamics of entanglement birth, death and revivals. We also
consider the effects of coupling the system to external environments and show
that under reasonable experimental conditions entanglement between the
mechanical modes can survive even at room temperature. Its dependence upon the
number of nanoparticles, their initial temperature and coupling strength is
studied. A numerical toolbox to simulate the closed and open dynamics of
Gaussian optomechanical states and their informational measures is developed.


Abstract:
  The geometry of black hole spacetimes can be probed with exquisite precision
in the gravitational-wave window, and possibly also in the optical regime. We
study the accretion of bright spots -- objects which emit strongly in the
optical or in gravitational waves -- by non-spinning black holes. The emission
as the object falls down the hole is dominated by photons or gravitons orbiting
the light ring, causing the total luminosity to decrease exponentially as
${\cal L}_o\sim e^{-t/(3\sqrt{3}\,M)}$. Late-time radiation is blueshifted, due
to its having been emitted during the infall, trapped at the light ring and
subsequently re-emitted. These universal properties are a clear signature of
the existence of light rings in the spacetime, and not particularly sensitive
to near horizon details.


Abstract:
  One-shot neural architecture search (NAS) methods significantly reduce the
search cost by considering the whole search space as one network, which only
needs to be trained once. However, current methods select each operation
independently without considering previous layers. Besides, the historical
information obtained with huge computation cost is usually used only once and
then discarded. In this paper, we introduce a sampling strategy based on Monte
Carlo tree search (MCTS) with the search space modeled as a Monte Carlo tree
(MCT), which captures the dependency among layers. Furthermore, intermediate
results are stored in the MCT for the future decision and a better
exploration-exploitation balance. Concretely, MCT is updated using the training
loss as a reward to the architecture performance; for accurately evaluating the
numerous nodes, we propose node communication and hierarchical node selection
methods in the training and search stages, respectively, which make better uses
of the operation rewards and hierarchical information. Moreover, for a fair
comparison of different NAS methods, we construct an open-source NAS benchmark
of a macro search space evaluated on CIFAR-10, namely NAS-Bench-Macro.
Extensive experiments on NAS-Bench-Macro and ImageNet demonstrate that our
method significantly improves search efficiency and performance. For example,
by only searching $20$ architectures, our obtained architecture achieves
$78.0\%$ top-1 accuracy with 442M FLOPs on ImageNet. Code (Benchmark) is
available at: \url{https://github.com/xiusu/NAS-Bench-Macro}.


Abstract:
  The sources of IceCube neutrinos are as yet unknown. The multi-messenger
observation of their emission in $\gamma$-rays can be a guide to their
identification, as exemplified by the case of TXS 0506+056. We suggest a new
method of searching for $\gamma$-rays with Imaging Air Cherenkov Telescopes
from sources in coincidence with possible astrophysical neutrinos. We propose
that searches of $\gamma$-rays are extended, from the current practice of only
a few days, to up to one month from a neutrino alert. We test this strategy on
simulated sources modeled after the blazar \emph{TXS 0506+056-like}, emitting
neutrinos and $\gamma$-rays via photohadronic interactions: the $\gamma$-rays
are subsequently reprocessed in the VHE range. Using MAGIC as a benchmark
example, we show that current Cherenkov Telescopes should be able to
detect$\gamma$-ray counterparts to neutrino alerts with a rate of approximately
one per year. It has been proposed that the high-energy diffuse neutrino flux
can be explained by $\sim$ 5\% of all blazars flaring in neutrinos once every
10 years, with a neutrino luminosity similar to that of TXS 0506+056 during the
2014-2015 neutrino flare. The implementation of our strategy could lead, over a
timescale of one or few years, either to the detection of this subclass of
blazars contributing to the diffuse neutrino flux, or to a constraint on this
model.


Abstract:
  Deep Q Network (DQN) firstly kicked the door of deep reinforcement learning
(DRL) via combining deep learning (DL) with reinforcement learning (RL), which
has noticed that the distribution of the acquired data would change during the
training process. DQN found this property might cause instability for training,
so it proposed effective methods to handle the downside of the property.
Instead of focusing on the unfavourable aspects, we find it critical for RL to
ease the gap between the estimated data distribution and the ground truth data
distribution while supervised learning (SL) fails to do so. From this new
perspective, we extend the basic paradigm of RL called the Generalized Policy
Iteration (GPI) into a more generalized version, which is called the
Generalized Data Distribution Iteration (GDI). We see massive RL algorithms and
techniques can be unified into the GDI paradigm, which can be considered as one
of the special cases of GDI. We provide theoretical proof of why GDI is better
than GPI and how it works. Several practical algorithms based on GDI have been
proposed to verify the effectiveness and extensiveness of it. Empirical
experiments prove our state-of-the-art (SOTA) performance on Arcade Learning
Environment (ALE), wherein our algorithm has achieved 9620.98% mean human
normalized score (HNS), 1146.39% median HNS and 22 human world record
breakthroughs (HWRB) using only 200M training frames. Our work aims to lead the
RL research to step into the journey of conquering the human world records and
seek real superhuman agents on both performance and efficiency.


Abstract:
  Motivated by various possible generalizations of Taubes's \(SW=Gr\) theorem
[T] to Floer-theoretic setting, we prove certain variants of Taubes's
convergence theorem in \cite{T} (the first part of his proof of \(SW=Gr\)). In
place of the closed symplectic 4-manifold considered in [T], this article
considers non-compact manifolds with cylindrical ends, equipped with a
self-dual harmonic 2-form with non-degenerate zeroes. This extends and
simplifies some central technical ingredients of the author's prior work in
[LT] and [KLT5]. Other expected applications include: extending the \(HM=PFH\)
theorem in [T] and the \(HM=HF\) theorem in [KLT1]-[KLT5] to TQFTs on both
sides [L1]; definitions of large-perturbation Seiberg-Witten analogs of
Heegaard Floer theory's link Floer homologies and link cobordism invariants.


Abstract:
  Multimodal pre-training with text, layout, and image has achieved SOTA
performance for visually-rich document understanding tasks recently, which
demonstrates the great potential for joint learning across different
modalities. In this paper, we present LayoutXLM, a multimodal pre-trained model
for multilingual document understanding, which aims to bridge the language
barriers for visually-rich document understanding. To accurately evaluate
LayoutXLM, we also introduce a multilingual form understanding benchmark
dataset named XFUND, which includes form understanding samples in 7 languages
(Chinese, Japanese, Spanish, French, Italian, German, Portuguese), and
key-value pairs are manually labeled for each language. Experiment results show
that the LayoutXLM model has significantly outperformed the existing SOTA
cross-lingual pre-trained models on the XFUND dataset. The pre-trained
LayoutXLM model and the XFUND dataset are publicly available at
https://aka.ms/layoutxlm.