Abstract:
  The leading explanation of the $\textit{Fermi}$ Galactic center $\gamma$-ray
excess is the extended emission from a unresolved population of millisecond
pulsars (MSPs) in the Galactic bulge. Such a population would, along with the
prompt $\gamma$ rays, also inject large quantities of electrons/positrons
($e^\pm$) into the interstellar medium. These $e^\pm$ could potentially
inverse-Compton (IC) scatter ambient photons into $\gamma$ rays that fall
within the sensitivity range of the upcoming Cherenkov Telescope Array (CTA).
In this article, we examine the detection potential of CTA to this signature by
making a realistic estimation of the systematic uncertainties on the Galactic
diffuse emission model at TeV-scale $\gamma$-ray energies. We forecast that, in
the event that $e^\pm$ injection spectra are harder than $E^{-2}$, CTA has the
potential to robustly discover the IC signature of a putative Galactic bulge
MSP population sufficient to explain the GCE for $e^\pm$ injection efficiencies
in the range $\approx 2.9-74.1\%$, or higher, depending on the level of
mismodeling of the Galactic diffuse emission components. On the other hand, for
spectra softer than $E^{-2.5}$, a reliable CTA detection would require an
unphysically large $e^\pm$ injection efficiency of $\gtrsim 158\%$. However,
even this pessimistic conclusion may be avoided in the plausible event that MSP
observational and/or modeling uncertainties can be reduced. We further find
that, in the event that an IC signal were detected, CTA can successfully
discriminate between an MSP and a dark matter origin for the radiating $e^\pm$.


Abstract:
  A useful application of event sensing is visual odometry, especially in
settings that require high-temporal resolution. The state-of-the-art method of
contrast maximisation recovers the motion from a batch of events by maximising
the contrast of the image of warped events. However, the cost scales with image
resolution and the temporal resolution can be limited by the need for large
batch sizes to yield sufficient structure in the contrast image. In this work,
we propose spatiotemporal registration as a compelling technique for
event-based rotational motion estimation. We theoretcally justify the approach
and establish its fundamental and practical advantages over contrast
maximisation. In particular, spatiotemporal registration also produces feature
tracks as a by-product, which directly supports an efficient visual odometry
pipeline with graph-based optimisation for motion averaging. The simplicity of
our visual odometry pipeline allows it to process more than 1 M events/second.
We also contribute a new event dataset for visual odometry, where motion
sequences with large velocity variations were acquired using a high-precision
robot arm.


Abstract:
  The mean of 430 visual magnitudes of VisorSats adjusted to a distance of
550-km (the operational altitude) is 5.92 +/-0.04. This is the characteristic
brightness of these satellites when observed at zenith. VisorSats average 1.29
magnitudes fainter than the original-design Starlink satellites and, thus, they
are 31% as bright.


Abstract:
  Lossy Image compression is necessary for efficient storage and transfer of
data. Typically the trade-off between bit-rate and quality determines the
optimal compression level. This makes the image quality metric an integral part
of any imaging system. While the existing full-reference metrics such as PSNR
and SSIM may be less sensitive to perceptual quality, the recently introduced
learning methods may fail to generalize to unseen data. In this paper we
propose the largest image compression quality dataset to date with human
perceptual preferences, enabling the use of deep learning, and we develop a
full reference perceptual quality assessment metric for lossy image compression
that outperforms the existing state-of-the-art methods. We show that the
proposed model can effectively learn from thousands of examples available in
the new dataset, and consequently it generalizes better to other unseen
datasets of human perceptual preference.


Abstract:
  This paper introduces WaveGrad 2, a non-autoregressive generative model for
text-to-speech synthesis. WaveGrad 2 is trained to estimate the gradient of the
log conditional density of the waveform given a phoneme sequence. The model
takes an input phoneme sequence, and through an iterative refinement process,
generates an audio waveform. This contrasts to the original WaveGrad vocoder
which conditions on mel-spectrogram features, generated by a separate model.
The iterative refinement process starts from Gaussian noise, and through a
series of refinement steps (e.g., 50 steps), progressively recovers the audio
sequence. WaveGrad 2 offers a natural way to trade-off between inference speed
and sample quality, through adjusting the number of refinement steps.
Experiments show that the model can generate high fidelity audio, approaching
the performance of a state-of-the-art neural TTS system. We also report various
ablation studies over different model configurations. Audio samples are
available at https://wavegrad.github.io/v2.


Abstract:
  The accuracy of a discrete-time channel model based on regular perturbation
is numerically studied for unamplified links. We analyse the distance between
discrete nonlinear interference points and show that such distance can be used
to estimate the effective channel memory.


Abstract:
  Text-to-speech (TTS) synthesis is the process of producing synthesized speech
from text or phoneme input. Traditional TTS models contain multiple processing
steps and require external aligners, which provide attention alignments of
phoneme-to-frame sequences. As the complexity increases and efficiency
decreases with every additional step, there is expanding demand in modern
synthesis pipelines for end-to-end TTS with efficient internal aligners. In
this work, we propose an end-to-end text-to-waveform network with a novel
reinforcement learning based duration search method. Our proposed generator is
feed-forward and the aligner trains the agent to make optimal duration
predictions by receiving active feedback from actions taken to maximize
cumulative reward. We demonstrate accurate alignments of phoneme-to-frame
sequence generated from trained agents enhance fidelity and naturalness of
synthesized audio. Experimental results also show the superiority of our
proposed model compared to other state-of-the-art TTS models with internal and
external aligners.


Abstract:
  We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial
Kaehler-Ricci solitons (KRS), both complete and not complete, which can be
Kaehler immersed into infinite dimensional complex space forms. This result
shows that the triviality of a KRS induced by a finite dimensional complex
space form proved in [12] does not hold when the ambient space is allowed to be
infinite dimensional. Moreover, we show that the radial potential of a radial
KRS induced by a non-elliptic complex space form is necessarily defined at the
origin.


Abstract:
  The ability to tailor laser light on a chip using integrated photonics has
allowed for extensive control over fundamental light-matter interactions in
manifold quantum systems including atoms, trapped ions, quantum dots, and
defect centers. Free electrons, enabling high-resolution microscopy for
decades, are increasingly becoming the subject of laser-based quantum
manipulation. Using free-space optical excitation and intense laser pulses,
this has led to the observation of free-electron quantum walks, attosecond
electron pulses, and imaging of electromagnetic fields. Enhancing the
interaction with electron beams through chip-based photonics promises unique
applications in nanoscale quantum control and sensing, but has yet to enter
electron microscopy. Here, we merge integrated photonics with electron
microscopy, demonstrating coherent phase modulation of an electron beam using a
silicon nitride microresonator driven by a continuous-wave laser. The high-Q
factor (~$10^6$) cavity enhancement and a waveguide designed for phase matching
lead to efficient electron-light scattering at unprecedentedly low,
few-microwatt optical powers. Specifically, we fully deplete the initial
electron state at a cavity-coupled power of 6 $\mu$W and create >500 photon
sidebands for only 38 mW in the bus waveguide. Moreover, we demonstrate $\mu$eV
electron energy gain spectroscopy (EEGS). Providing simultaneous optical and
electronic spectroscopy of the resonant cavity, the fiber-coupled photonic
structures feature single-mode electron-light interaction with full control
over the input and output channels. This approach establishes a versatile
framework for exploring free-electron quantum optics, with future developments
in strong coupling, local quantum probing, and electron-photon entanglement.
Our results highlight the potential of integrated photonics to efficiently
interface free electrons and light.


Abstract:
  Consumers only discover at the first seller which product best fits their
needs, then check its price online, then decide on buying. Switching sellers is
costly. Equilibrium prices fall in the switching cost, eventually to the
monopoly level, despite the exit of lower-value consumers when changing sellers
becomes costlier. More expensive switching makes some buyers exit the market,
leaving fewer inframarginal buyers to the sellers. Marginal buyers may change
in either direction, so for a range of parameters, all firms cut prices.


Abstract:
  The large-time behavior of a nonlinearly coupled pair of measure-valued
transport equations with discontinuous boundary conditions, parameterized by a
positive real-valued parameter $\lambda$, is considered. These equations
describe the hydrodynamic or fluid limit of many-server queues with reneging
(with traffic intensity $\lambda$), which model phenomena in diverse
disciplines, including biology and operations research. For a broad class of
reneging distributions with finite mean and service distributions with finite
mean and hazard rate function that is either decreasing or bounded away from
zero and infinity, it is shown that if the fluid equations have a unique
invariant state, then the Dirac measure at this state is the unique random
fixed point of the fluid equations, which implies that the stationary
distributions of scaled $N$-server systems converge to the unique invariant
state of the corresponding fluid equations. Moreover, when $\lambda\ne 1$, it
is shown that the solution to the fluid equation starting from any initial
condition converges to this unique invariant state in the large time limit. The
proof techniques are different under the two sets of assumptions on the service
distribution. When the hazard rate function is decreasing, a reformulation of
the dynamics in terms of a certain renewal equation is used, in conjunction
with recursive asymptotic estimates. When the hazard rate function is bounded
away from zero and infinity, the proof uses an extended relative entropy
functional as a Lyapunov function. Analogous large-time convergence results are
also established for a system of coupled measure-valued equations modeling a
multiclass queue.


Abstract:
  Reservoir simulation and adaptation (also known as history matching) are
typically considered as separate problems. While a set of models are aimed at
the solution of the forward simulation problem assuming all initial geological
parameters are known, the other set of models adjust geological parameters
under the fixed forward simulation model to fit production data. This results
in many difficulties for both reservoir engineers and developers of new
efficient computation schemes. We present a unified approach to reservoir
simulation and adaptation problems. A single neural network model allows a
forward pass from initial geological parameters of the 3D reservoir model
through dynamic state variables to well's production rates and backward
gradient propagation to any model inputs and variables. The model fitting and
geological parameters adaptation both become the optimization problem over
specific parts of the same neural network model. Standard gradient-based
optimization schemes can be used to find the optimal solution. Using real-world
oilfield model and historical production rates we demonstrate that the
suggested approach allows reservoir simulation and history matching with a
benefit of several orders of magnitude simulation speed-up. Finally, to
propagate this research we open-source a Python-based framework DeepField that
allows standard processing of reservoir models and reproducing the approach
presented in this paper.


Abstract:
  Domain knowledge is useful to improve the generalization performance of
learning machines. Sign constraints are a handy representation to combine
domain knowledge with learning machine. In this paper, we consider constraining
the signs of the weight coefficients in learning the linear support vector
machine, and develop two optimization algorithms for minimizing the empirical
risk under the sign constraints. One of the two algorithms is based on the
projected gradient method, in which each iteration of the projected gradient
method takes $O(nd)$ computational cost and the sublinear convergence of the
objective error is guaranteed. The second algorithm is based on the Frank-Wolfe
method that also converges sublinearly and possesses a clear termination
criterion. We show that each iteration of the Frank-Wolfe also requires $O(nd)$
cost. Furthermore, we derive the explicit expression for the minimal iteration
number to ensure an $\epsilon$-accurate solution by analyzing the curvature of
the objective function. Finally, we empirically demonstrate that the sign
constraints are a promising technique when similarities to the training
examples compose the feature vector.


Abstract:
  We consider tests of short-distance modifications of gravity based on neutron
interferometry in the scenario of large extra dimensions. Avoiding the
non-computability problem in the calculation of the internal gravitational
potential of extended sources, typical of models with zero-width brane, we
determine the neutron optical potential associated with the higher-dimension
gravitational interaction between the incident neutron and a material medium in
the context of thick brane theories. Proceeding this way, we identify the
physical quantity of the extra dimension model that the neutron interferometry
is capable of constraining. We also consider interferometric experiments in
which the phase shifter is an electric field, as in the test of the
Aharanov-Casher effect. We argue that this experiment, with this non-baryonic
source, can be viewed as a test of the short-range behavior of Post-Newtonian
parameters that measure the capacity of the pressure and the internal energy
for producing gravity.


Abstract:
  Topological signals defined on nodes, links and higher dimensional simplices
define the dynamical state of a network or of a simplicial complex. As such,
topological signals are attracting increasing attention in network theory,
dynamical systems, signal processing and machine learning. Topological signals
defined on the nodes are typically studied in network dynamics, while
topological signals defined on links are much less explored. Here we
investigate topological synchronization describing locally coupled topological
signals defined on the nodes and on the links of a network. The dynamics of
signals defined on the nodes is affected by a phase lag depending on the
dynamical state of nearby links and vice versa, the dynamics of topological
signals defined on the links is affected by a phase lag depending on the
dynamical state of nearby nodes. We show that topological synchronization on a
fully connected network is explosive and leads to a discontinuous forward
transition and a continuous backward transition. The analytical investigation
of the phase diagram provides an analytical expression for the critical
threshold of the discontinuous explosive synchronization. The model also
displays an exotic coherent synchronized phase, also called rhythmic phase,
characterized by having non-stationary order parameters which can shed light on
topological mechanisms for the emergence of brain rhythms.


Abstract:
  This paper investigates regularized estimation of Kronecker-structured
covariance matrices (CM) for complex elliptically symmetric (CES) data. To
obtain a well-conditioned estimate of the CM, we add penalty terms of
Kullback-Leibler divergence to the negative log-likelihood function of the
associated complex angular Gaussian (CAG) distribution. This is shown to be
equivalent to regularizing Tyler's fixed-point equations by shrinkage. A
sufficient condition that the solution exists is discussed. An iterative
algorithm is applied to solve the resulting fixed-point iterations and its
convergence is proved. In order to solve the critical problem of tuning the
shrinkage factors, we then introduce three methods by exploiting oracle
approximating shrinkage (OAS) and cross-validation (CV). When the training
samples are limited, the proposed estimator, referred to as the robust
shrinkage Kronecker estimator (RSKE), has better performance compared with
several existing methods. Simulations are conducted for validating the proposed
estimator and demonstrating its high performance.


Abstract:
  In this paper we introduce a method for stacking data cubelets extracted from
interferometric surveys of galaxies in the redshifted 21-cm H\,\textsc{i} line.
Unlike the traditional spectral stacking technique, which stacks
one-dimensional spectra extracted from data cubes, we examine a method based on
image domain stacks which makes deconvolution possible. To test the validity of
this assumption, we mock a sample of 3622 equatorial galaxies extracted from
the GAMA survey, recently imaged as part of a DINGO-VLA project. We first
examine the accuracy of the method using a noise-free simulation and note that
the stacked image and flux estimation are dramatically improved compared to
traditional stacking. The extracted H\,\textsc{i} mass from the deconvolved
image agrees with the average input mass to within 3\%. However, with
traditional spectral stacking, the derived H\,\textsc{i} is incorrect by
greater than a factor of 2. For a more realistic case of a stack with finite
S/N, we also produced 20 different noise realisations to closely mimic the
properties of the DINGO-VLA interferometric survey. We recovered the predicted
average H\,\textsc{i} mass to within $\sim$4\%. Compared with traditional
spectral stacking, this technique extends the range of science applications
where stacking can be used, and is especially useful for characterizing the
emission from extended sources with interferometers.


Abstract:
  Connected and autonomous vehicles (CAVs) are an innovative form of
traditional vehicles. Automotive Ethernet replaces the controller area network
and FlexRay to support the large throughput required by high-definition
applications. As CAVs have numerous functions, they exhibit a large attack
surface and an increased vulnerability to attacks. However, no previous studies
have focused on intrusion detection in automotive Ethernet-based networks. In
this paper, we present an intrusion detection method for detecting audio-video
transport protocol (AVTP) stream injection attacks in automotive Ethernet-based
networks. To the best of our knowledge, this is the first such method developed
for automotive Ethernet. The proposed intrusion detection model is based on
feature generation and a convolutional neural network (CNN). To evaluate our
intrusion detection system, we built a physical BroadR-Reach-based testbed and
captured real AVTP packets. The experimental results show that the model
exhibits outstanding performance: the F1-score and recall are greater than
0.9704 and 0.9949, respectively. In terms of the inference time per input and
the generation intervals of AVTP traffic, our CNN model can readily be employed
for real-time detection.


Abstract:
  The robust principles of treating interference as noise (TIN) when it is
sufficiently weak, and avoiding it when it is not, form the background of this
work. Combining TIN with the topological interference management (TIM)
framework that identifies optimal interference avoidance schemes, we formulate
a TIM-TIN problem for multilevel topological interference management, wherein
only a coarse knowledge of channel strengths and no knowledge of channel phases
is available to transmitters. To address the TIM-TIN problem, we first propose
an analytical baseline approach, which decomposes a network into TIN and TIM
components, allocates the signal power levels to each user in the TIN
component, allocates signal vector space dimensions to each user in the TIM
component, and guarantees that the product of the two is an achievable number
of signal dimensions available to each user in the original network. Next, a
distributed numerical algorithm called ZEST is developed. The convergence of
the algorithm is demonstrated, leading to the duality of the TIM-TIN problem
(in terms of GDoF). Numerical results are also provided to demonstrate the
superior sum-rate performance and fast convergence of ZEST.


Abstract:
  Federated learning is a new learning paradigm that decouples data collection
and model training via multi-party computation and model aggregation. As a
flexible learning setting, federated learning has the potential to integrate
with other learning frameworks. We conduct a focused survey of federated
learning in conjunction with other learning algorithms. Specifically, we
explore various learning algorithms to improve the vanilla federated averaging
algorithm and review model fusion methods such as adaptive aggregation,
regularization, clustered methods, and Bayesian methods. Following the emerging
trends, we also discuss federated learning in the intersection with other
learning paradigms, termed as federated x learning, where x includes multitask
learning, meta-learning, transfer learning, unsupervised learning, and
reinforcement learning. This survey reviews the state of the art, challenges,
and future directions.


Abstract:
  Observations have revealed that disturbances in the cold neutral atomic
hydrogen (HI) in galaxies are ubiquitous, but the reasons for these
disturbances remain unclear. While some studies suggest that asymmetries in
integrated HI spectra (global HI asymmetry) are higher in HI-rich systems,
others claim that they are preferentially found in HI-poor galaxies. In this
work, we utilise the ALFALFA and xGASS surveys, plus a sample of post-merger
galaxies, to clarify the link between global HI asymmetry and the gas
properties of galaxies. Focusing on star-forming galaxies in ALFALFA, we find
that elevated global HI asymmetry is not associated with a change in the HI
content of a galaxy, and that only the galaxies with the highest global HI
asymmetry show a small increase in specific star-formation rate (sSFR).
However, we show that the lack of a trend with HI content is because ALFALFA
misses the gas-poor tail of the star-forming main-sequence. Using xGASS to
obtain a sample of star-forming galaxies that is representative in both sSFR
and HI content, we find that global HI asymmetric galaxies are typically more
gas-poor than symmetric ones at fixed stellar mass, with no change in sSFR. Our
results highlight the complexity of the connection between galaxy properties
and global HI asymmetry. This is further confirmed by the fact that even
post-merger galaxies show both symmetric and asymmetric HI spectra,
demonstrating that merger activity does not always lead to an asymmetric global
HI spectrum.


Abstract:
  We introduce DBS, a new technique for user selection in downlink multi-user
communications with extra-large (XL) antenna arrays. DBS categorizes users
according to their equivalent distance to the antenna array. Such
categorization effectively accounts for inter-user interference while largely
reducing the computational burden. Results show that (i) DBS achieves the same
performance as the reference zero-forcing beamforming scheme with a lower
complexity; (ii) a simplified version of DBS achieves a similar performance
when realistic spherical-wavefront (SW) propagation features are considered;
(iii) SW propagation brings additional degrees of freedom, which allows for
increasing the number of served users.


Abstract:
  The emerging possibilities to steer and control electronic motion on subcycle
time scales with strong electric fields enable studying the nonperturbative
optical response and Bloch bands' topological properties, originated from
Berry's trilogy: connection, curvature, and phase. This letter introduces a
theoretical framework for the nonperturbative electron dynamics in
two-dimensional (2D) crystalline solids induced by the few-cycle and
strong-field optical lasers. In the presented model, the expression associated
with the Bloch band topology and broken crystal symmetry merges
self-consistently in the system observables such as High Harmonic Generation
(HHG). This singles out our work from recent HHG calculations from the
strongly-driven systems. Concisely, in our theoretical experiment on 2D
materials in the strong-field optical regime, we show that Bloch band topology
and broken symmetry manifest themselves in several ways: the momentum-resolved
attosecond interferometry of electron wave packets, anomalous and chiral
velocity in both intraband and interband dynamics, anomalous Hall current and
respective HHG highly sensitive to the laser waveform, multiple plateau-cutoff
structures in both longitudinal and transverse HHG, the formation of even
harmonics in the perpendicular polarization with respect to the driving laser,
singular jumps across the phase diagram of the HHG, attosecond chirp, and
ultrafast valley polarization induced by the chiral gauge field that is robust
to lattice imperfections and scattering. The link between HHG and solid-state
band geometry offers an all-optical reconstruction of electron band structure
by optical means, and accelerates studies on the non-equilibrium Floquet
engineering, topologically-protected nonlinear spin and edge currents,
valleytronics, quantum computing and high-temperature superconductivity on
sub-femtosecond time scales.


Abstract:
  We discuss a semi-discrete analogue of the Unified Transform Method,
introduced by A. S. Fokas, to solve initial-boundary-value problems for linear
evolution partial differential equations of constant coefficients. The
semi-discrete method is applied to various spacial discretizations of several
first and second-order linear equations on the half-line $x \geq 0$, producing
the exact solution for the semi-discrete problem, given appropriate initial and
boundary data. We additionally show how the Unified Transform Method treats
derivative boundary conditions and ghost points introduced by the choice of
discretization stencil. We consider the continuum limit of the semi-discrete
solutions and provide several numerical examples.


Abstract:
  Scalar bosonic stars (BSs) stand out as a multi-purpose model of exotic
compact objects. We enlarge the landscape of such (asymptotically flat,
stationary, everywhere regular) objects by considering multiple fields
(possibly) with different frequencies. This allows for new morphologies ${\it
and}$ a stabilization mechanism for different sorts of unstable BSs. First, any
odd number of complex fields, yields a continuous family of BSs departing from
the spherical, equal frequency, $\ell-$BSs. As the simplest illustration, we
construct the $\ell$ = ${\it 1}$ ${\it BSs}$ ${\it family}$, that includes
several single frequency solutions, including even parity (such as spinning BSs
and a toroidal, static BS) and odd parity (a dipole BS) limits. Second, these
limiting solutions are dynamically unstable, but can be stabilized by a ${\it
hybrid}$-$\ell$ construction: adding a sufficiently large fundamental $\ell=0$
BS of another field, with a different frequency. Evidence for this dynamical
robustness is obtained by non-linear numerical simulations of the corresponding
Einstein-(complex, massive) Klein-Gordon system, both in formation and
evolution scenarios, and a suggestive correlation between stability and energy
distribution is observed. Similarities and differences with vector BSs are
anticipated.


Abstract:
  We present Query2Prod2Vec, a model that grounds lexical representations for
product search in product embeddings: in our model, meaning is a mapping
between words and a latent space of products in a digital shop. We leverage
shopping sessions to learn the underlying space and use merchandising
annotations to build lexical analogies for evaluation: our experiments show
that our model is more accurate than known techniques from the NLP and IR
literature. Finally, we stress the importance of data efficiency for product
search outside of retail giants, and highlight how Query2Prod2Vec fits with
practical constraints faced by most practitioners.


Abstract:
  The thermal Sunyaev-Zeldovich effect contains information about the thermal
history of the universe, observable in maps of the Compton $y$ parameter;
however, it does not contain information about the redshift of the sources.
Recent papers have utilized a tomographic approach, cross-correlating the
Compton $y$ map with the locations of galaxies with known redshift, in order to
deproject the signal along the line of sight. In this paper, we test the
validity and accuracy of this tomographic approach to probe the thermal history
of the universe. We use the state-of-the-art cosmological hydrodynamical
simulation, Magneticum, for which the thermal history of the universe is a
known quantity. The key ingredient is the Compton-$y$-weighted halo bias,
$b_y$, computed from the halo model. We find that, at redshifts currently
available, the method reproduces the correct mean thermal pressure (or the
density-weighted mean temperature) to high accuracy, validating and confirming
the results of previous papers. At higher redshifts ($z\gtrsim 2.5$), there is
significant disagreement between $b_y$ from the halo model and the simulation.


Abstract:
  We consider a prototypical nonlinear parabolic equation whose flux has three
distinguished features: it is nonlinear with respect to both the unknown and
its gradient, it is homogeneous, and it depends only on the direction of the
gradient. For such equation, we obtain existence and uniqueness of entropy
solutions to the Dirichlet problem, the homogeneous Neumann problem, and the
Cauchy problem. Qualitative properties of solutions, such as finite speed of
propagation and the occurrence of waiting-time phenomena, with sharp bounds,
are shown. We also discuss the formation of jump discontinuities both at the
boundary of the solutions' support and in the bulk.


Abstract:
  We investigate the effect of the thermal imbalance on the structural
stability of the magnetohydrodynamic model of the preflare current layer
(Ledentsov, Sol. Phys. 296, 74, 2021). The piecewise homogeneous model of the
current layer is supplemented by a magnetic field longitudinal with respect to
the direction of the current. It is shown that the presence of a weak
longitudinal field does not change the previously calculated spatial period of
the thermal instability in the most expected range of the parameters of the
preflare current layer and, moreover, contributes to the formation of the
instability. On the other hand, a strong longitudinal magnetic field
contributes to the spatial stabilization of the current layer.


Abstract:
  This paper describes a KGD-type model of a hydraulic fracture created by
injecting fluid in weak, poorly consolidated rocks. The model is based on the
key assumption that the hydraulic fracture is propagating within a domain where
the hydraulic fields are quasi-stationary. By further assuming a negligible
toughness, the fracture is shown to grow as a square root of time. The
asymptotic fracture propagation regimes at small and large time are constructed
and the transient solution is computed by solving a nonlinear system of
algebraic equations formulated in terms of the fracture aperture. At early time
the fracture is hydraulically invisible and the injection pressure increases
with time $t$ as $\log t$, while at late time leak-off from the borehole is
negligible and the injection pressure decreases as $t^{-1/4}$. According to
this model, the peak injection pressure observed when injecting fluid in weak,
poorly consolidated rocks should not be interpreted as indicating a breakdown
of the formation, but rather as marking the transition between two asymptotic
flow regimes. The timescale that legislates the transition between the small
and large time asymptotic regimes is shown to be a strongly nonlinear function
of a dimensionless injection rate.


Abstract:
  With the heightened volatility in stock prices during the Covid-19 pandemic,
the need for price forecasting has become more critical. We investigated the
forecast performance of four models including Long-Short Term Memory, XGBoost,
Autoregression, and Last Value on stock prices of Facebook, Amazon, Tesla,
Google, and Apple in COVID-19 pandemic time to understand the accuracy and
predictability of the models in this highly volatile time region. To train the
models, the data of all stocks are split into train and test datasets. The test
dataset starts from January 2020 to April 2021 which covers the COVID-19
pandemic period. The results show that the Autoregression and Last value models
have higher accuracy in predicting the stock prices because of the strong
correlation between the previous day and the next day's price value.
Additionally, the results suggest that the machine learning models (Long-Short
Term Memory and XGBoost) are not performing as well as Autoregression models
when the market experiences high volatility.


Abstract:
  Large Transformer-based language models are pre-trained on corpora of varying
sizes, for a different number of steps and with different batch sizes. At the
same time, more fundamental components, such as the pre-training objective or
architectural hyperparameters, are modified. In total, it is therefore
difficult to ascribe changes in performance to specific factors. Since
searching the hyperparameter space over the full systems is too costly, we
pre-train down-scaled versions of several popular Transformer-based
architectures on a common pre-training corpus and benchmark them on a subset of
the GLUE tasks (Wang et al., 2018). Specifically, we systematically compare
three pre-training objectives for different shape parameters and model sizes,
while also varying the number of pre-training steps and the batch size. In our
experiments MLM + NSP (BERT-style) consistently outperforms MLM (RoBERTa-style)
as well as the standard LM objective. Furthermore, we find that additional
compute should be mainly allocated to an increased model size, while training
for more steps is inefficient. Based on these observations, as a final step we
attempt to scale up several systems using compound scaling (Tan and Le, 2019)
adapted to Transformer-based language models.


Abstract:
  Following Brown[1], we construct composite operators for the scalar $\phi^3$
theory in six dimensions using renormalisation group methods with dimensional
regularisation. We express bare scalar operators in terms of renormalised
composite operators of low dimension, then do this with traceless tensor
operators. We then express the bare energy momentum tensor in terms of the
renormalised composite operators, with some terms having divergent
coefficients. We subtract these away and obtain a manifestly finite energy
tensor. The subtracted terms are transverse, so this does not affect the
conservation of the energy momentum tensor. The trace of this finite improved
energy momentum tensor vanishes at the fixed point indicating conformal
invariance. Interestingly it is not RG-invariant except at the fixed point, but
can be made RG invariant everywhere by further addition of transverse terms,
whose coefficients vanish at the fixed point.


Abstract:
  The distributional reinforcement learning (RL) approach advocates for
representing the complete probability distribution of the random return instead
of only modelling its expectation. A distributional RL algorithm may be
characterised by two main components, namely the representation and
parameterisation of the distribution and the probability metric defining the
loss. This research considers the unconstrained monotonic neural network (UMNN)
architecture, a universal approximator of continuous monotonic functions which
is particularly well suited for modelling different representations of a
distribution (PDF, CDF, quantile function). This property enables the
decoupling of the effect of the function approximator class from that of the
probability metric. The paper firstly introduces a methodology for learning
different representations of the random return distribution. Secondly, a novel
distributional RL algorithm named unconstrained monotonic deep Q-network
(UMDQN) is presented. Lastly, in light of this new algorithm, an empirical
comparison is performed between three probability quasimetrics, namely the
Kullback-Leibler divergence, Cramer distance and Wasserstein distance. The
results call for a reconsideration of all probability metrics in distributional
RL, which contrasts with the dominance of the Wasserstein distance in recent
publications.


Abstract:
  We propose a self-consistent theoretical framework of chorus wave excitation,
which describes the evolution of the whistler fluctuation spectrum as well as
the supra-thermal electron distribution function. The renormalized hot electron
response is cast in the form of a Dyson-like equation, which then leads to
evolution equations for nonlinear fluctuation growth and frequency shift. This
approach allows us to analytically derive for the first time exactly the same
expression for the chorus chirping rate originally proposed by Vomvoridis et
al.,1982. Chorus chirping is shown to correspond to maximization of wave
particle power exchange, where each individual wave belonging to the whistler
wave packet is characterized by small nonlinear frequency shift. We also show
that different interpretations of chorus chirping proposed in published
literature have a consistent reconciliation within the present theoretical
framework, which further illuminates the analogy with similar phenomena in
fusion plasmas and free electron laser physics.


Abstract:
  Recent methods for long-tailed instance segmentation still struggle on rare
object classes with few training data. We propose a simple yet effective
method, Feature Augmentation and Sampling Adaptation (FASA), that addresses the
data scarcity issue by augmenting the feature space especially for rare
classes. Both the Feature Augmentation (FA) and feature sampling components are
adaptive to the actual training status -- FA is informed by the feature mean
and variance of observed real samples from past iterations, and we sample the
generated virtual features in a loss-adapted manner to avoid over-fitting. FASA
does not require any elaborate loss design, and removes the need for
inter-class transfer learning that often involves large cost and
manually-defined head/tail class groups. We show FASA is a fast, generic method
that can be easily plugged into standard or long-tailed segmentation
frameworks, with consistent performance gains and little added cost. FASA is
also applicable to other tasks like long-tailed classification with
state-of-the-art performance.


Abstract:
  ELECTRA pretrains a discriminator to detect replaced tokens, where the
replacements are sampled from a generator trained with masked language
modeling. Despite the compelling performance, ELECTRA suffers from the
following two issues. First, there is no direct feedback loop from
discriminator to generator, which renders replacement sampling inefficient.
Second, the generator's prediction tends to be over-confident along with
training, making replacements biased to correct tokens. In this paper, we
propose two methods to improve replacement sampling for ELECTRA pre-training.
Specifically, we augment sampling with a hardness prediction mechanism, so that
the generator can encourage the discriminator to learn what it has not
acquired. We also prove that efficient sampling reduces the training variance
of the discriminator. Moreover, we propose to use a focal loss for the
generator in order to relieve oversampling of correct tokens as replacements.
Experimental results show that our method improves ELECTRA pre-training on
various downstream tasks.


Abstract:
  For unramified reductive groups, we determine the connected components of
affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on
the work of Hamacher-Kim and Zhou, this result allows us to verify, in the
unramified group case, the He-Rapoport axioms, the ``almost product structure"
of Newton strata, and the precise description of mod $p$ isogeny classes
predicted by the Langlands-Rapoport conjecture, for the Kisin-Pappas integral
models of Shimura varieties of Hodge type with parahoric level structure.


Abstract:
  Generative Adversarial Networks (GANs) are able to generate high-quality
images, but it remains difficult to explicitly specify the semantics of
synthesized images. In this work, we aim to better understand the semantic
representation of GANs, and thereby enable semantic control in GAN's generation
process. Interestingly, we find that a well-trained GAN encodes image semantics
in its internal feature maps in a surprisingly simple way: a linear
transformation of feature maps suffices to extract the generated image
semantics. To verify this simplicity, we conduct extensive experiments on
various GANs and datasets; and thanks to this simplicity, we are able to learn
a semantic segmentation model for a trained GAN from a small number (e.g., 8)
of labeled images. Last but not least, leveraging our findings, we propose two
few-shot image editing approaches, namely Semantic-Conditional Sampling and
Semantic Image Editing. Given a trained GAN and as few as eight semantic
annotations, the user is able to generate diverse images subject to a
user-provided semantic layout, and control the synthesized image semantics. We
have made the code publicly available.


Abstract:
  The citizenship identities of a nation's occupants enable the state to
identify and authenticate them unquestionably. These documents help individuals
in recognizing themselves and to profit from the rights and advantages given to
them by the legislature or the constitution of the land. There are problems in
the traditional way of issuance f these identities and many hurdles that impede
people from getting their benefits or exercising their rights. These
paper-based identities can be forged easily and are hard to authenticate at
various civil end points. There are reports of identity thefts. In this paper,
we are discussing how Blockchain can be employed to overcome these problems and
makes these identities confidential, immutable, and secured. Blockchain
technology can help the governing bodies in maintaining and verifying these
identities in a quick manner with less chance for human errors, meaning more
reach for government plans and aid


Abstract:
  Let K be a cubic number field. In this paper, we study the Ramanujan sums
c_{J}(I), where I and J are integral ideals in O_{K}. The asymptotic behaviour
of sums of c_{J}(I) over both I and J is investigated.


Abstract:
  We study magnetohydrodynamic stability of neutron star core matter composed
of neutrons, protons and leptons threaded by a magnetar-strength magnetic field
$10^{14}$--$10^{17}$ G, where quantum electrodynamical effects and Landau
quantization of fermions are important. Stability is determined using the
Friedman--Schutz formalism for the canonical energy of fluid perturbations,
which we calculate for a magnetizable fluid with $H\neq B$. Using this and the
Euler--Heisenberg--Fermi--Dirac Lagrangian for a strongly magnetized fluid of
Landau-quantized charged fermions, we calculate the local stability criteria
for a fluid slab as a stand-in for a segment of a neutron star core, accounting
for magnetic and composition gradient buoyancy. The slab is threaded by a field
orthogonal to the gravitational field, the Cartesian analogy to a toroidal
field. We find that, for sufficiently strong fields $B\gtrsim10^{15}$ G, the
magnetized fluid is unstable to a magnetosonic-type instability with growth
times of order $10^{-3}$ s. The instability is triggered by sharp changes in
the second-order field derivative of the Euler--Heisenberg--Fermi--Dirac
Lagrangian which occur where additional Landau levels start being populated.
These sharp changes are divergent at zero temperature, but are finite for
nonzero temperature, so realistic neutron star core temperatures $5\times10^7$
K$<T<5\times10^8$ K are used. We conjecture that this mechanism could promote
the formation of magnetic domains as predicted by Blandford and Hernquist
(1982) and Suh and Mathews (2010).


Abstract:
  Several Ising-type magnetic van der Waals (vdW) materials exhibit stable
magnetic ground states. Despite these clear experimental demonstrations, a
complete theoretical and microscopic understanding of their magnetic anisotropy
is still lacking. In particular, the validity limit of identifying their
one-dimensional (1-D) Ising nature has remained uninvestigated in a
quantitative way. Here we performed the complete mapping of magnetic anisotropy
for a prototypical Ising vdW magnet FePS$_3$ for the first time. Combining
torque magnetometry measurements with their magnetostatic model analysis and
the relativistic density functional total energy calculations, we successfully
constructed the three-dimensional (3-D) mappings of the magnetic anisotropy in
terms of magnetic torque and energy. The results not only quantitatively
confirm that the easy axis is perpendicular to the $ab$ plane, but also reveal
the anisotropies within the $ab$, $ac$, and $bc$ planes. Our approach can be
applied to the detailed quantitative study of magnetism in vdW materials.


Abstract:
  Swarming behavior, where coherent motion emerges from the interactions of
many mobile agents, is ubiquitous in physics and biology. Moreover, there are
many efforts to replicate swarming dynamics in mobile robotic systems which
take inspiration from natural swarms. In particular, understanding how swarms
come apart, change their behavior, and interact with other swarms is a research
direction of special interest to the robotics and defense communities. Here we
develop a theoretical approach that can be used to predict the parameters under
which colliding swarms form a stable milling state. Our analytical methods rely
on the assumption that, upon collision, two swarms oscillate near a
limit-cycle, where each swarm rotates around the other while maintaining an
approximately constant density. Using our methods, we are able to predict the
critical swarm-swarm interaction coupling (below which two colliding swarms
merely scatter) for nearly aligned collisions as a function of physical swarm
parameters. We show that the critical coupling corresponds to a saddle-node
bifurcation of a limit-cycle in the constant-density approximation. Finally, we
show preliminary results from experiments in which two swarms of micro UAVs
collide and form a milling state, which is in general agreement with our
theory.


Abstract:
  We give an exposition of the hidden subgroup problem for dihedral groups from
the point of view of the standard hidden subgroup quantum algorithm for finite
groups. In particular, we recall the obstructions for strong Fourier sampling
to succeed, but at the same time, show how the standard algorithm can be
modified to establish polynomial quantum query complexity. Finally, we explain
a new connection between the dihedral coset problem and cloning of quantum
states.


Abstract:
  In this paper we examine the puzzle of neutron formation in atmospheric
discharge. While conventional explanation relies on photonuclear reactions,
voltages used to recreate such discharges in the lab (1 MV) are thought to be
not high enough to accelerate electrons beyond the threshold of photonuclear
reactions (10.5 MeV). We have proposed a solution to the neutron formation
puzzle and point out that rapidly changing magnetic vector potential creates
strong electrokinetic field that can accelerate free electrons to energies that
are much higher than what is possible with the voltage of the discharge. We
report on the development of highly sophisticated and extremely sensitive
neutron detector system that can reliably detect neutron fluxes smaller than
0.1 CPS above background and is completely impervious to EM noise. Finally, we
present measurements of weak yet statistically significant neutron fluxes
originating from sustained 20-30 kV / 20-30 mA X-ray producing discharge in
dilute atmosphere.


Abstract:
  We formulate a substantial improvement on Buchberger's algorithm for
Gr\"obner bases of zero-dimensional ideals. The improvement scales down the
phenomenon of intermediate expression swell as well as the complexity of
Buchberger's algorithm to a significant degree. The idea is to compute a new
type of bases over principal ideal rings instead of over fields like Gr\"obner
bases. The generalizations of Buchberger's algorithm from over fields to over
rings are abundant in the literature. However they are limited to either
computations of strong Gr\"obner bases or modular computations of the numeral
coefficients of ideal bases with no essential improvement on the algorithmic
complexity. In this paper we make pseudo-divisions with multipliers to enhance
computational efficiency. In particular, we develop a new methodology in
determining the authenticity of the factors of the pseudo-eliminant, i.e., we
compare the factors with the multipliers of the pseudo-divisions instead of the
leading coefficients of the basis elements. In order to find out the exact form
of the eliminant, we contrive a modular algorithm of proper divisions over
principal quotient rings with zero divisors. The pseudo-eliminant and proper
eliminants and their corresponding bases constitute a decomposition of the
original ideal. In order to address the ideal membership problem, we elaborate
on various characterizations of the new type of bases. In the complexity
analysis we devise a scenario linking the rampant intermediate coefficient
swell to B\'ezout coefficients, partially unveiling the mystery of hight-level
complexity associated with the computation of Gr\"obner bases. Finally we make
exemplary computations to demonstrate the conspicuous difference between
Gr\"obner bases and the new type of bases.


Abstract:
  We consider a peer-to-peer electricity market, where agents hold private
information that they might not want to share. The problem is modeled as a
noncooperative communication game, which takes the form of a Generalized Nash
Equilibrium Problem, where the agents determine their randomized reports to
share with the other market players, while anticipating the form of the
peer-to-peer market equilibrium. In the noncooperative game, each agent decides
on the deterministic and random parts of the report, such that (a) the distance
between the deterministic part of the report and the truthful private
information is bounded and (b) the expectation of the privacy loss random
variable is bounded. This allows each agent to change her privacy level. We
characterize the equilibrium of the game, prove the uniqueness of the
Variational Equilibria and provide a closed form expression of the privacy
price. In addition, we provide a closed form expression to measure the impact
of the privacy preservation caused by inclusion of random noise and
deterministic deviation from agents' true values. Numerical illustrations are
presented on the 14-bus IEEE network.


Abstract:
  It is well known that in the Noetherian local ring with infinite residue
field the reduction of $\mm$-primary ideal may be given in the form of a
sufficiently general linear combination of its generators. In the paper we give
a condition for the existence of such reduction in terms of the sum of degrees
of the ideal fiber cone prime divisors in the case of any Noetherian local
ring.


Abstract:
  Traditional bulk load flexibility options, such as load shifting and load
curtailment, for managing uncertainty in power markets limit the diversity of
options and ignore the preferences of the individual loads, thus reducing
efficiency and welfare. This paper proposes an alternative to bulk load
flexibility options for managing uncertainty in power markets: a reinforcement
learning based dynamic matching market. We propose a novel hybrid
learning-based model for maximizing social welfare in the dynamic matching
market. The key features of our model is a fixed rule-based function and a
learnable component that can be trained by data gathered online with no prior
knowledge or expert supervision. The output of the learnable component is a
probability distribution over the matching decisions for the individual
customers. The proposed hybrid model enables the learning algorithm to find an
effective matching policy that simultaneously satisfies the customers'
servicing preferences. The simulations show that the learning algorithm learns
an effective matching policy for different generation-consumption profiles and
exhibits better performance compared to standard online matching heuristics
such as Match on Arrival, Match to the Highest, and Match to the Earliest
Deadline policies.


Abstract:
  The availability of large spatial data geocoded at accurate locations has
fueled a growing interest in spatial modeling and analysis of point processes.
The proposed research is motivated by the intensity estimation problem for
large spatial point patterns on complex domains in $\mathbb{R}^2$ (e.g.,
domains with irregular boundaries, sharp concavities, and/or interior holes due
to geographic constraints) and linear networks, where many existing spatial
point process models suffer from the problems of "leakage" and computation. We
propose an efficient intensity estimation algorithm to estimate the spatially
varying intensity function and to study the varying relationship between
intensity and explanatory variables on complex domains. The method is built
upon a graph regularization technique and hence can be flexibly applied to
point patterns on complex domains such as regions with irregular boundaries and
holes, or linear networks. An efficient proximal gradient optimization
algorithm is proposed to handle large spatial point patterns. We also derive
the asymptotic error bound for the proposed estimator. Numerical studies are
conducted to illustrate the performance of the method. Finally, we apply the
method to study and visualize the intensity patterns of the accidents on the
Western Australia road network, and the spatial variations in the effects of
income, lights condition, and population density on the Toronto homicides
occurrences.


Abstract:
  The principles of density-functional theory are studied for finite lattice
systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn
theorem is found void in general, while many insights into the topological
structure of the density-potential mapping can be won. We give precise
conditions for a ground state to be uniquely v-representable and are able to
prove that this property holds for almost all densities. A set of examples
illustrates the theory and demonstrates the non-convexity of the pure-state
constrained-search functional.


Abstract:
  Coarse structural nested mean models are used to estimate treatment effects
from longitudinal observational data. Coarse structural nested mean models lead
to a large class of estimators. It turns out that estimates and standard errors
may differ considerably within this class. We prove that, under additional
assumptions, there exists an explicit solution for the optimal estimator within
the class of coarse structural nested mean models. Moreover, we show that even
if the additional assumptions do not hold, this optimal estimator is
doubly-robust: it is consistent and asymptotically normal not only if the model
for treatment initiation is correct, but also if a certain outcome-regression
model is correct.
  We compare the optimal estimator to some naive choices within the class of
coarse structural nested mean models in a simulation study. Furthermore, we
apply the optimal and naive estimators to study how the CD4 count increase due
to one year of antiretroviral treatment (ART) depends on the time between HIV
infection and ART initiation in recently infected HIV infected patients. Both
in the simulation study and in the application, the use of optimal estimators
leads to substantial increases in precision.


Abstract:
  Existing deep learning methods for solving mean-field games (MFGs) with
common noise fix the sampling common noise paths and then solve the
corresponding MFGs. This leads to a nested-loop structure with millions of
simulations of common noise paths in order to produce accurate solutions, which
results in prohibitive computational cost and limits the applications to a
large extent. In this paper, based on the rough path theory, we propose a novel
single-loop algorithm, named signatured deep fictitious play, by which we can
work with the unfixed common noise setup to avoid the nested-loop structure and
reduce the computational complexity significantly. The proposed algorithm can
accurately capture the effect of common uncertainty changes on mean-field
equilibria without further training of neural networks, as previously needed in
the existing machine learning algorithms. The efficiency is supported by three
applications, including linear-quadratic MFGs, mean-field portfolio game, and
mean-field game of optimal consumption and investment. Overall, we provide a
new point of view from the rough path theory to solve MFGs with common noise
with significantly improved efficiency and an extensive range of applications.
In addition, we report the first deep learning work to deal with extended MFGs
(a mean-field interaction via both the states and controls) with common noise.


Abstract:
  A group topology is said to be linear if open subgroups form a base of
neighborhoods of the identity element. It is proved that the existence of a
nondiscrete extremally disconnected group of Ulam nonmeasurable cardinality
with linear topology implies that of a nondiscrete extremally disconnected
group of cardinality at most $2^\omega$ with linear topology.


Abstract:
  The task of identifying emotions from a given music track has been an active
pursuit in the Music Information Retrieval (MIR) community for years. Music
emotion recognition has typically relied on acoustic features, social tags, and
other metadata to identify and classify music emotions. The role of lyrics in
music emotion recognition remains under-appreciated in spite of several studies
reporting superior performance of music emotion classifiers based on features
extracted from lyrics. In this study, we use the transformer-based approach
model using XLNet as the base architecture which, till date, has not been used
to identify emotional connotations of music based on lyrics. Our proposed
approach outperforms existing methods for multiple datasets. We used a robust
methodology to enhance web-crawlers' accuracy for extracting lyrics. This study
has important implications in improving applications involved in playlist
generation of music based on emotions in addition to improving music
recommendation systems.


Abstract:
  In this paper, we investigate some qualitative properties of solutions to the
Moore-Gibson-Thompson (MGT) equation and the Jordan-MGT (JMGT) equation with
memory of type I in the whole space $\mathbb{R}^n$, which are the fundamental
models for acoustic waves in relaxing hereditary fluids. First of all, we study
sharp estimates of solutions to the viscous and inviscid MGT equation with
memory, where regularity-loss decay properties appear in the inviscid case.
Then, not only formal expansion of solution with respect to the small sound
diffusivity but also rigorous justification of inviscid limit in
$L^{\infty}([0,\infty)\times\mathbb{R}^n)$ are derived by WKB analysis.
Concerning the viscous JMGT equation of Kuznetsov-type and Westervelt-type in
hereditary fluids, we prove global (in time) solvability and obtain some
estimates of them. This paper studies acoustic waves in hereditary fluids from
some different viewpoints comparing with the previous researches.


Abstract:
  We propose a postselecting parity-swap amplifier for Schr\"odinger cat states
that does not require the amplified state to be known a priori. The device is
based on a previously-implemented state comparison amplifier for coherent
states. It consumes only Gaussian resource states, which provides an advantage
over some cat state amplifiers. It requires simple Geiger-mode photodetectors
and works with high fidelity and approximately twofold gain.


Abstract:
  Visual Place Recognition (VPR) is often characterized as being able to
recognize the same place despite significant changes in appearance and
viewpoint. VPR is a key component of Spatial Artificial Intelligence, enabling
robotic platforms and intelligent augmentation platforms such as augmented
reality devices to perceive and understand the physical world. In this paper,
we observe that there are three "drivers" that impose requirements on spatially
intelligent agents and thus VPR systems: 1) the particular agent including its
sensors and computational resources, 2) the operating environment of this
agent, and 3) the specific task that the artificial agent carries out. In this
paper, we characterize and survey key works in the VPR area considering those
drivers, including their place representation and place matching choices. We
also provide a new definition of VPR based on the visual overlap -- akin to
spatial view cells in the brain -- that enables us to find similarities and
differences to other research areas in the robotics and computer vision fields.
We identify numerous open challenges and suggest areas that require more
in-depth attention in future works.


Abstract:
  Rate-Splitting Multiple Access (RSMA) has recently appeared as a powerful and
robust multiple access and interference management strategy for downlink
Multi-user (MU) multi-antenna communications. In this work, we study the
precoder design problem for RSMA scheme in downlink MU systems with both
perfect and imperfect Channel State Information at the Transmitter (CSIT) and
assess the role and benefits of transmitting multiple common streams. Unlike
existing works which have considered single-antenna receivers (Multiple-Input
Single-Output--MISO), we propose and extend the RSMA framework for
multi-antenna receivers (Multiple-Input Multiple-Output--MIMO) and formulate
the precoder optimization problem with the aim of maximizing the Weighted
Ergodic Sum-Rate (WESR). Precoder optimization is solved using Sample Average
Approximation (SAA) together with the proposed vectorization and Weighted
Minimum Mean Square Error (WMMSE) based approach. Achievable sum-Degree of
Freedom (DoF) of RSMA is derived for the proposed framework as an increasing
function of the number of transmitted common and private streams, which is
further validated by the Ergodic Sum Rate (ESR) performance using Monte Carlo
simulations. Conventional MU-MIMO based on linear precoders and Non-Orthogonal
Multiple Access (NOMA) schemes are considered as baselines. Numerical results
show that with imperfect CSIT, the sum-DoF and ESR performance of RSMA is
superior than that of the two baselines, and is increasing with the number of
transmitted common streams. Moreover, by better managing the interference, RSMA
not only has significant ESR gains over baseline schemes but is more robust to
CSIT inaccuracies, network loads and user deployments.


Abstract:
  Suppose that $X$ is a smooth projective variety and that $C$ is a general
member of a family of free rational curves on $X$. We prove several statements
showing that the Harder-Narasimhan filtration of $T_{X}|_{C}$ is approximately
the same as the restriction of the Harder-Narasimhan filtration of $T_{X}$ with
respect to the class of $C$. When $X$ is a Fano variety, we prove that the set
of all restricted tangent bundles for general free rational curves is
controlled by a finite set of data. We then apply our work to analyze Peyre's
"freeness" formulation of Manin's Conjecture in the setting of rational curves.


Abstract:
  This paper presents a cooperative dynamic task assignment framework for a
certain class of Autonomous Underwater Vehicles (AUVs) employed to control
outbreak of Crown-Of-Thorns Starfish (COTS) in Australia's Great Barrier Reef.
The problem of monitoring and controlling the COTS is transcribed into a
constrained task assignment problem in which eradicating clusters of COTS, by
the injection system of COTSbot AUVs, is considered as a task. A probabilistic
map of the operating environment including seabed terrain, clusters of COTS,
and coastlines is constructed. Then, a novel heuristic algorithm called
Heuristic Fleet Cooperation (HFC) is developed to provide a cooperative
injection of the COTSbot AUVs to the maximum possible COTS in an assigned
mission time. Extensive simulation studies together with quantitative
performance analysis are conducted to demonstrate the effectiveness and
robustness of the proposed cooperative task assignment algorithm in eradicating
the COTS in the Great Barrier Reef.


Abstract:
  Neural coupled oscillators are a useful building block in numerous models and
applications. They were analyzed extensively in theoretical studies and more
recently, in biologically realistic simulations of spiking neural networks. The
advent of mixed-signal analog/digital neuromorphic electronic circuits provides
new means for implementing neural coupled oscillators on compact low-power
spiking neural network hardware platforms. However, their implementation on
this noisy, low-precision and inhomogeneous computing substrate raises new
challenges with regards to stability and controllability. In this work, we
present a robust, spiking neural network model of neural coupled oscillators
and validate it with an implementation on a mixed-signal neuromorphic
processor. We demonstrate its robustness showing how to reliably control and
modulate the oscillator's frequency and phase shift, despite the variability of
the silicon synapse and neuron properties. We show how this ultra-low power
neural processing system can be used to build an adaptive cardiac pacemaker
modulating the heart rate with respect to the respiration phases and compare it
with surface ECG and respiratory signal recordings of dogs at rest. The
implementation of our model in neuromorphic electronic hardware shows its
robustness on a highly variable substrate and extends the toolbox for
applications requiring rhythmic outputs such as pacemakers.


Abstract:
  A basic requirement for a mathematical model is often that its solution
(output) shouldn't change much if the model's parameters (input) are perturbed.
This is important because the exact values of parameters may not be known and
one would like to avoid being mislead by an output obtained using incorrect
values. Thus, it's rarely enough to address an application by formulating a
model, solving the resulting optimization problem and presenting the solution
as the answer. One would need to confirm that the model is suitable, i.e.,
"good," and this can, at least in part, be achieved by considering a family of
optimization problems constructed by perturbing parameters of concern. The
resulting sensitivity analysis uncovers troubling situations with unstable
solutions, which we referred to as "bad" models, and indicates better model
formulations. Embedding an actual problem of interest within a family of
problems is also a primary path to optimality conditions as well as
computationally attractive, alternative problems, which under ideal
circumstances, and when properly tuned, may even furnish the minimum value of
the actual problem. The tuning of these alternative problems turns out to be
intimately tied to finding multipliers in optimality conditions and thus
emerges as a main component of several optimization algorithms. In fact, the
tuning amounts to solving certain dual optimization problems. In this tutorial,
we'll discuss the opportunities and insights afforded by this broad
perspective.


Abstract:
  By means of a truncation condition on the parameters, the elliptic
Ruijsenaars difference operators are restricted onto a finite lattice of points
encoded by bounded partitions. A corresponding orthogonal basis of joint
eigenfunctions is constructed in terms of polynomials on the joint spectrum. In
the trigonometric limit, this recovers the diagonalization of the truncated
Macdonald difference operators by a finite-dimensional basis of Macdonald
polynomials.


Abstract:
  Machine learning has enabled the prediction of quantum chemical properties
with high accuracy and efficiency, allowing to bypass computationally costly ab
initio calculations. Instead of training on a fixed set of properties, more
recent approaches attempt to learn the electronic wavefunction (or density) as
a central quantity of atomistic systems, from which all other observables can
be derived. This is complicated by the fact that wavefunctions transform
non-trivially under molecular rotations, which makes them a challenging
prediction target. To solve this issue, we introduce general SE(3)-equivariant
operations and building blocks for constructing deep learning architectures for
geometric point cloud data and apply them to reconstruct wavefunctions of
atomistic systems with unprecedented accuracy. Our model achieves speedups of
over three orders of magnitude compared to ab initio methods and reduces
prediction errors by up to two orders of magnitude compared to the previous
state-of-the-art. This accuracy makes it possible to derive properties such as
energies and forces directly from the wavefunction in an end-to-end manner. We
demonstrate the potential of our approach in a transfer learning application,
where a model trained on low accuracy reference wavefunctions implicitly learns
to correct for electronic many-body interactions from observables computed at a
higher level of theory. Such machine-learned wavefunction surrogates pave the
way towards novel semi-empirical methods, offering resolution at an electronic
level while drastically decreasing computational cost. Additionally, the
predicted wavefunctions can serve as initial guess in conventional ab initio
methods, decreasing the number of iterations required to arrive at a converged
solution, thus leading to significant speedups without any loss of accuracy or
robustness.


Abstract:
  Heterostructures between topological insulators (TI) and magnetic insulators
represent a pathway to realize the quantum anomalous Hall effect (QAHE). Using
density functional theory based systematic screening and investigation of
thermodynamic, magnetic and topological properties of heterostructures, we
demonstrate that forming a type-I heterostructure between a wide gap
antiferromagnetic insulator Cr$_2$O$_3$ and a TI-film, such as Sb$_2$Te$_3$,
can lead to pinning of the Fermi-level at the center of the gap, even when
magnetically doped. Cr-doping in the heterostructure increases the gap to
$\sim$ 64.5 meV, with a large Zeeman energy from the interfacial Cr dopants,
thus overcoming potential metallicity due to band bending effects. By fitting
the band-structure around the Fermi-level to a 4-band k.p model Hamiltonian, we
show that Cr doped Sb$_2$Te$_3$/Cr$_2$O$_3$ is a Chern insulator with a Chern
number C = -1. Transport calculations further show chiral edge-modes localized
at the top/bottom of the TI-film to be the dominant current carriers in the
material. Our predictions of a large interfacial magnetism due to Cr-dopants,
that coupled antiferromagnetically to the AFM substrate is confirmed by our
polarised neutron reflectometry measurements on MBE grown Cr doped
Sb$_2$Te$_3$/Cr$_2$O$_3$ heterostructures, and is consistent with a positive
exchange bias measured in such systems recently. Consequently, Cr doped
Sb$_2$Te$_3$/Cr$_2$O$_3$ heterostructure represents a promising platform for
the development of functional topological magnetic devices, with high
tunability.


Abstract:
  We present a novel approach to robustly detect and perceive vehicles in
different camera views as part of a cooperative vehicle-infrastructure system
(CVIS). Our formulation is designed for arbitrary camera views and makes no
assumptions about intrinsic or extrinsic parameters. First, to deal with
multi-view data scarcity, we propose a part-assisted novel view synthesis
algorithm for data augmentation. We train a part-based texture inpainting
network in a self-supervised manner. Then we render the textured model into the
background image with the target 6-DoF pose. Second, to handle various camera
parameters, we present a new method that produces dense mappings between image
pixels and 3D points to perform robust 2D/3D vehicle parsing. Third, we build
the first CVIS dataset for benchmarking, which annotates more than 1540 images
(14017 instances) from real-world traffic scenarios. We combine these novel
algorithms and datasets to develop a robust approach for 2D/3D vehicle parsing
for CVIS. In practice, our approach outperforms SOTA methods on 2D detection,
instance segmentation, and 6-DoF pose estimation, by 4.5%, 4.3%, and 2.9%,
respectively. More details and results are included in the supplement. To
facilitate future research, we will release the source code and the dataset on
GitHub.


Abstract:
  Markov chain Monte Carlo (MCMC) algorithms have long been the main workhorses
of Bayesian inference. Among them, Hamiltonian Monte Carlo (HMC) has recently
become very popular due to its efficiency resulting from effective use of the
gradients of the target distribution. In privacy-preserving machine learning,
differential privacy (DP) has become the gold standard in ensuring that the
privacy of data subjects is not violated. Existing DP MCMC algorithms either
use random-walk proposals, or do not use the Metropolis--Hastings (MH)
acceptance test to ensure convergence without decreasing their step size to
zero. We present a DP variant of HMC using the MH acceptance test that builds
on a recently proposed DP MCMC algorithm called the penalty algorithm, and adds
noise to the gradient evaluations of HMC. We prove that the resulting algorithm
converges to the correct distribution, and is ergodic. We compare DP-HMC with
the existing penalty, DP-SGLD and DP-SGNHT algorithms, and find that DP-HMC has
better or equal performance than the penalty algorithm, and performs more
consistently than DP-SGLD or DP-SGNHT.


Abstract:
  Electromyography (EMG) is a way of measuring the bioelectric activities that
take place inside the muscles. EMG is usually performed to detect abnormalities
within the nerves or muscles of a target area. The recent developments in the
field of Machine Learning allow us to use EMG signals to teach machines the
complex properties of human movements. Modern machines are capable of detecting
numerous human activities and distinguishing among them solely based on the EMG
signals produced by those activities. However, success in accomplishing this
task mostly depends on the learning technique used by the machine to analyze
EMG signals; and even the latest algorithms do not result in flawless
classification. In this study, a novel classification method has been described
employing a multichannel Convolutional Neural Network (CNN) that interprets
surface EMG signals by the properties they exhibit in the power domain. The
proposed method was tested on a well-established EMG dataset, and the result
yields very high classification accuracy. This learning model will help
researchers to develop prosthetic arms capable of detecting various hand
gestures to mimic them afterwards.


Abstract:
  Internet of Things (IoT) is considered as a key enabler of health
informatics. IoT-enabled devices are used for in-hospital and in-home patient
monitoring to collect and transfer biomedical data pertaining to blood
pressure, electrocardiography (ECG), blood sugar levels, body temperature, etc.
Among these devices, wearables have found their presence in a wide range of
healthcare applications. These devices generate data in real-time and transmit
them to nearby gateways and remote servers for processing and visualization.
The data transmitted by these devices are vulnerable to a range of adversarial
threats, and as such, privacy and integrity need to be preserved. In this
paper, we present LightIoT, a lightweight and secure communication approach for
data exchanged among the devices of a healthcare infrastructure. LightIoT
operates in three phases: initialization, pairing, and authentication. These
phases ensure the reliable transmission of data by establishing secure sessions
among the communicating entities (wearables, gateways and a remote server).
Statistical results exhibit that our scheme is lightweight, robust, and
resilient against a wide range of adversarial attacks and incurs much lower
computational and communication overhead for the transmitted data in the
presence of existing approaches.


Abstract:
  While complex numbers are essential in mathematics, they are not needed to
describe physical experiments, expressed in terms of probabilities, hence real
numbers. Physics however aims to explain, rather than describe, experiments
through theories. While most theories of physics are based on real numbers,
quantum theory was the first to be formulated in terms of operators acting on
complex Hilbert spaces. This has puzzled countless physicists, including the
fathers of the theory, for whom a real version of quantum theory, in terms of
real operators, seemed much more natural. In fact, previous works showed that
such "real quantum theory" can reproduce the outcomes of any multipartite
experiment, as long as the parts share arbitrary real quantum states. Thus, are
complex numbers really needed in the quantum formalism? Here, we show this to
be case by proving that real and complex quantum theory make different
predictions in network scenarios comprising independent states and
measurements. This allows us to devise a Bell-like experiment whose successful
realization would disprove real quantum theory, in the same way as standard
Bell experiments disproved local physics.


Abstract:
  With the increasing scale of search engine marketing, designing an efficient
bidding system is becoming paramount for the success of e-commerce companies.
The critical challenges faced by a modern industrial-level bidding system
include: 1. the catalog is enormous, and the relevant bidding features are of
high sparsity; 2. the large volume of bidding requests induces significant
computation burden to both the offline and online serving. Leveraging
extraneous user-item information proves essential to mitigate the sparsity
issue, for which we exploit the natural language signals from the users' query
and the contextual knowledge from the products. In particular, we extract the
vector representations of ads via the Transformer model and leverage their
geometric relation to building collaborative bidding predictions via
clustering. The two-step procedure also significantly reduces the computation
stress of bid evaluation and optimization. In this paper, we introduce the
end-to-end structure of the bidding system for search engine marketing for
Walmart e-commerce, which successfully handles tens of millions of bids each
day. We analyze the online and offline performances of our approach and discuss
how we find it as a production-efficient solution.


Abstract:
  COVID-19 pandemic has spread globally for months. Due to its long incubation
period and high testing cost, there is no clue showing its spread speed is
slowing down, and hence a faster testing method is in dire need. This paper
proposes an efficient Evolutionary Multi-objective neural ARchitecture Search
(EMARS) framework, which can automatically search for 3D neural architectures
based on a well-designed search space for COVID-19 chest CT scan
classification. Within the framework, we use weight sharing strategy to
significantly improve the search efficiency and finish the search process in 8
hours. We also propose a new objective, namely potential, which is of benefit
to improve the search process's robustness. With the objectives of accuracy,
potential, and model size, we find a lightweight model (3.39 MB), which
outperforms three baseline human-designed models, i.e., ResNet3D101 (325.21
MB), DenseNet3D121 (43.06 MB), and MC3\_18 (43.84 MB). Besides, our
well-designed search space enables the class activation mapping algorithm to be
easily embedded into all searched models, which can provide the
interpretability for medical diagnosis by visualizing the judgment based on the
models to locate the lesion areas.


Abstract:
  The idea of using lexical translations to define sense inventories has a long
history in lexical semantics. We propose a theoretical framework which allows
us to answer the question of why this apparently reasonable idea failed to
produce useful results. We formally prove several propositions on how the
translations of a word relate to its senses, as well as on the relationship
between synonymy and polysemy. We empirically validate our theoretical findings
on BabelNet, and demonstrate how they could be used to perform unsupervised
word sense disambiguation of a substantial fraction of the lexicon.


Abstract:
  We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion
in mathlib, which is a community-driven effort to build a unified mathematics
library for Lean. One goal of the mathlib project is to contain all of the
topics of a complete undergraduate mathematics education.
  We provide three presentations of the main theorem statement: in terms of
indexed families of finite sets, of relations on types, and of matchings in
bipartite graphs. We also formalize a version of K\H{o}nig's lemma (in terms of
inverse limits) to boost the theorem to the case of countably infinite index
sets. We give a description of the design of the recent mathlib library for
simple graphs, and we also give a necessary and sufficient condition for a
simple graph to carry a function.


Abstract:
  In this Letter, we describe how a spectrum of entropic perturbations
generated during a period of slow contraction can source a nearly
scale-invariant spectrum of curvature perturbations on length scales larger
than the Hubble radius during the transition from slow contraction to a
classical non-singular bounce (the `graceful exit' phase). The sourcing occurs
naturally through higher-order scalar field kinetic terms common to classical
(non-singular) bounce mechanisms. We present a concrete example in which, by
the end of the graceful exit phase, the initial entropic fluctuations have
become negligible and the curvature fluctuations have a nearly scale-invariant
spectrum with an amplitude consistent with observations.


Abstract:
  We generalize a terminating summation formula to a unilateral nonterminating,
and further, a bilateral summation formula by a property of analytic functions.
The unilateral one is proved to be a $q$-analogue of a $_4F_3$-summation
formula. And, an identity unifying Jacobi's triple product identity and the
quintuple product identity is obtained as a special case of the bilateral one.


Abstract:
  "Minimum Falling Path Sum" (MFPS) is classic question in programming - "Given
a grid of size $N{\times}N$ with integers in cells, return the minimum sum of a
falling path through grid. A falling path starts at any cell in the first row
and ends in last row, with the rule of motion - the next element after the cell
$(i,j)$ is one of the cells $(i+1,j-1),(i+1,j)$ and $(i+1,j+1)$". This problem
has linear solution (LS) (i.e. O($N^2$)) using dynamic programming method
(DPM). There is an Multi-Agent version of MFPS called "Cherry Pickup II" (CP2).
CP2 is a search for the maximum sum of 2 falling paths started from top
corners, where each covered cell summed up one time. All known fast solutions
of CP2 uses DPM, but have O($N^3$) time complexity on grid $N{\times}N$. Here
we offer a LS of CP2 (also using DPM) as finding maximum total weight of 2
vertex-disjoint paths. Also, we extend this LS for some extended version of CP2
with wider motion rules.


Abstract:
  Explainable Artificial Intelligence (XAI) has in recent years become a
well-suited framework to generate human understandable explanations of black
box models. In this paper, we present a novel XAI visual explanation algorithm
denoted SIDU that can effectively localize entire object regions responsible
for prediction in a full extend. We analyze its robustness and effectiveness
through various computational and human subject experiments. In particular, we
assess the SIDU algorithm using three different types of evaluations
(Application, Human and Functionally-Grounded) to demonstrate its superior
performance. The robustness of SIDU is further studied in presence of
adversarial attack on black box models to better understand its performance.


Abstract:
  Let H be a complex Lie group acting holomorphically on a complex analytic
space X such that the restriction to X_{\mathrm{red}} of every H-invariant
regular function on X is constant. We prove that an H-equivariant holomorphic
vector bundle E over X is $H$-finite, meaning f_1(E)= f_2(E) as H-equivariant
bundles for two distinct polynomials f_1 and f_2 whose coefficients are
nonnegative integers, if and only if the pullback of E along some H-equivariant
finite \'etale covering of X is trivial as an H-equivariant bundle.


Abstract:
  This work is devoted to review the modern geometric description of the
Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The
relation with the "classical" Hamiltonian approach using canonical
transformations is also analyzed. Furthermore, a more general framework for the
theory is also briefly explained. It is also shown how, from this generic
framework, the Lagrangian and Hamiltonian cases of the theory for dynamical
systems are recovered, and how the model can be extended to other types of
physical systems, such as higher-order dynamical systems and (first-order)
classical field theories in their multisymplectic formulation.


Abstract:
  In this paper, we prove the convergence from the atomistic model to the
Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex
lattice. We show that the displacement field of the dislocation solution of the
PN model converges to the dislocation solution of the atomistic model with
second-order accuracy. The consistency of PN model and the stability of
atomistic model are essential in our proof. The main idea of our approach is to
use several low-degree polynomials to approximate the energy due to atomistic
interactions of different groups of atoms of the complex lattice.


Abstract:
  We study asymptotic topological regularity of CAT(0) spaces. We prove that if
a purely n-dimensional, proper, geodesically complete CAT(0) space has small
volume growth, then it is homeomorphic to the n-dimensional Euclidean space. We
also discuss asymptotic geometry of proper, geodesically complete CAT(0) spaces
of small volume growth.


Abstract:
  In this paper, constructing a class of ideals of $B_1(X)$ from proper ideals
of $C(X)$ a formula for real maximal ideals of $C(X)$ is established and
utilizing these ideals of $B_1(X)$, closed maximal ideals in $B_1(X)$ are
introduced. It is observed that the real maximal ideals of $B_1(X)$ is that
subfamily of closed maximal ideals whose contraction in $C(X)$ is contained in
a real maximal ideal of $C(X)$. A one-one correspondence between the class of
real maximal ideals of $C(X)$ and those of $B_1(X)$ is proved. Also, it is
observed that an injective map from the class of hyper-real maximal ideals of
$C(X)$ into the class of hyper-real maximal ideals of $B_1(X)$ exists. These
observations finally lead to the conclusion that within the class of
non-discrete perfectly normal $T_1$ spaces, cardinality of the collection
$\MMM(C(X))$, of all maximal ideals of $C(X)$, is strictly less than the
cardinality of the collection $\MMM(B_1(X))$, of all maximal ideals of
$B_1(X)$. Finally, it is proved that Tychonoff space is real compact if and
only if every real maximal ideal of $B_1(X)$ is fixed. As a consequence, within
the class of perfectly normal $T_1$ real compact spaces $B_1(X) = {B_1}^*(X)$
if and only if $X$ is finite.


Abstract:
  Road infrastructure maintenance inspection is typically a labour-intensive
and critical task to ensure the safety of all the road users. In this work, we
propose a detailed methodology to use state-of-the-art techniques in artificial
intelligence and computer vision to automate a sizeable portion of the
maintenance inspection subtasks and reduce the labour costs. The proposed
methodology uses state-of-the-art computer vision techniques such as object
detection and semantic segmentation to automate inspections on primary road
structures such as the road surface, markings, barriers (guardrails) and
traffic signs. The models are mostly trained on commercially viable datasets
and augmented with proprietary data. We demonstrate that our AI models can not
only automate and scale maintenance inspections on primary road structures but
also result in higher recall compared to traditional manual inspections.


Abstract:
  Multi-Layer Perceptrons (MLPs) make powerful functional representations for
sampling and reconstruction problems involving low-dimensional signals like
images,shapes and light fields. Recent works have significantly improved their
ability to represent high-frequency content by using periodic activations or
positional encodings. This often came at the expense of generalization: modern
methods are typically optimized for a single signal. We present a new
representation that generalizes to multiple instances and achieves
state-of-the-art fidelity. We use a dual-MLP architecture to encode the
signals. A synthesis network creates a functional mapping from a
low-dimensional input (e.g. pixel-position) to the output domain (e.g. RGB
color). A modulation network maps a latent code corresponding to the target
signal to parameters that modulate the periodic activations of the synthesis
network. We also propose a local-functional representation which enables
generalization. The signal's domain is partitioned into a regular grid,with
each tile represented by a latent code. At test time, the signal is encoded
with high-fidelity by inferring (or directly optimizing) the latent code-book.
Our approach produces generalizable functional representations of images,
videos and shapes, and achieves higher reconstruction quality than prior works
that are optimized for a single signal.


Abstract:
  Verifying specifications for large-scale modern engineering systems can be a
time-consuming task, as most formal verification methods are limited to systems
of modest size. Recently, contract-based design and verification has been
proposed as a modular framework for specifications, and
linear-programming-based techniques have been presented for verifying that a
given system satisfies a given contract. In this paper, we extend this
assume/guarantee framework by presenting necessary and sufficient conditions
for a collection of contracts on individual components to refine a contract on
the composed system. These conditions can be verified by solving linear
programs, whose number grows linearly with the number of specifications defined
by the contracts. We exemplify the tools developed using a case study
considering safety in a car-following scenario, where noise and time-varying
delay are considered.


Abstract:
  We propose the use of physics-informed neural networks for solving the
shallow-water equations on the sphere. Physics-informed neural networks are
trained to satisfy the differential equations along with the prescribed initial
and boundary data, and thus can be seen as an alternative approach to solving
differential equations compared to traditional numerical approaches such as
finite difference, finite volume or spectral methods. We discuss the training
difficulties of physics-informed neural networks for the shallow-water
equations on the sphere and propose a simple multi-model approach to tackle
test cases of comparatively long time intervals. We illustrate the abilities of
the method by solving the most prominent test cases proposed by Williamson et
al. [J. Comput. Phys. 102, 211-224, 1992].


Abstract:
  Modern change detection (CD) has achieved remarkable success by the powerful
discriminative ability of deep convolutions. However, high-resolution remote
sensing CD remains challenging due to the complexity of objects in the scene.
Objects with the same semantic concept may show distinct spectral
characteristics at different times and spatial locations. Most recent CD
pipelines using pure convolutions are still struggling to relate long-range
concepts in space-time. Non-local self-attention approaches show promising
performance via modeling dense relations among pixels, yet are computationally
inefficient. Here, we propose a bitemporal image transformer (BIT) to
efficiently and effectively model contexts within the spatial-temporal domain.
Our intuition is that the high-level concepts of the change of interest can be
represented by a few visual words, i.e., semantic tokens. To achieve this, we
express the bitemporal image into a few tokens, and use a transformer encoder
to model contexts in the compact token-based space-time. The learned
context-rich tokens are then feedback to the pixel-space for refining the
original features via a transformer decoder. We incorporate BIT in a deep
feature differencing-based CD framework. Extensive experiments on three CD
datasets demonstrate the effectiveness and efficiency of the proposed method.
Notably, our BIT-based model significantly outperforms the purely convolutional
baseline using only 3 times lower computational costs and model parameters.
Based on a naive backbone (ResNet18) without sophisticated structures (e.g.,
FPN, UNet), our model surpasses several state-of-the-art CD methods, including
better than four recent attention-based methods in terms of efficiency and
accuracy. Our code is available at https://github.com/justchenhao/BIT\_CD.


Abstract:
  Let $G$ be a reductive linear algebraic group over an algebraically closed
field $\mathbb{K}$ of characteristic $2$. Fix a parabolic subgroup $P$ such
that the corresponding parabolic subgroup over $\mathbb{C}$ has abelian
unipotent radical and fix a Levi subgroup $L\subseteq P$. We parametrize the
orbits of a Borel $B\subseteq P$ over the Hermitian symmetric variety $G/L$
supposing the root system $\Phi$ is irreducible. For $\Phi$ simply laced we
prove a combinatorial characterization of the Bruhat order over these orbits.
We also prove a formula to compute the dimension of the orbits from
combinatorial characteristics of their representatives.


Abstract:
  Given a location-based social network, how to find the communities that are
highly relevant to query users and have top overall scores in multiple
attributes according to user preferences? Typically, in the face of such a
problem setting, we can model the network as a multi-attributed road-social
network, in which each user is linked with location information and $d$
($\geq\! 1$) numerical attributes. In practice, user preferences (i.e.,
weights) are usually inherently uncertain and can only be estimated with
bounded accuracy, because a human user is not able to designate exact values
with absolute precision. Inspired by this, we introduce a normative community
model suitable for multi-criteria decision making, called multi-attributed
community (MAC), based on the concepts of $k$-core and a novel dominance
relationship specific to preferences. Given uncertain user preferences, namely,
an approximate representation of weights, the MAC search reports the exact
communities for each of the possible weight settings. We devise an elegant
index structure to maintain the dominance relationships, based on which two
algorithms are developed to efficiently compute the top-$j$ MACs. The
efficiency and scalability of our algorithms and the effectiveness of MAC model
are demonstrated by extensive experiments on both real-world and synthetic
road-social networks.


Abstract:
  The Super-Scaling Approach (SuSA) model, based on the analogies between
electron and neutrino interactions with nuclei, is reviewed and its application
to the description of neutrino-nucleus scattering is presented. The
contribution of both one- and two-body relativistic currents is considered. A
selection of results is presented where theoretical predictions are compared
with cross section measurements from the main ongoing neutrino oscillation
experiments.


Abstract:
  Curated scientific databases play an important role in the scientific
endeavour and support is needed for the significant effort that goes into their
creation and maintenance. This demonstration and case study illustrate how
curation support has been developed in the Links cross-tier programming
language, a functional, strongly typed language with language-integrated query
and support for temporal databases. The chosen case study uses weekly released
Covid-19 fatality figures from the Scottish government which exhibit updates to
previously released data. This data allows the capture and query of update
provenance in our prototype. This demonstration will highlight the potential
for language-integrated support for curation to simplify and streamline
prototyping of web-applications in support of scientific databases


Abstract:
  The "particle in a box" problem is investigated for a relativistic particle
obeying the Klein-Gordon equation. To find the bound states, the standard
methods known from elementary non-relativistic quantum mechanics can only be
employed for "shallow" wells. For deeper wells, when the confining potentials
become supercritical, we show that a method based on a scattering expansion
accounts for Klein tunneling (undamped propagation outside the well) and the
Klein paradox (charge density increase inside the well). We will see that in
the infinite well limit, the wavefunction outside the well vanishes and Klein
tunneling is suppressed: quantization is thus recovered, similarly to the
non-relativistic particle in a box. In addition, we show how wavepackets can be
constructed semi-analytically from the scattering expansion, accounting for the
dynamics of Klein tunneling in a physically intuitive way