Abstract:
  The increasing number of Photovoltaic (PV) systems connected to the power
grid are vulnerable to the projection of shadows from moving clouds. Global
Solar Irradiance (GSI) forecasting allows smart grids to optimize the energy
dispatch, preventing energy shortages caused by occlusion of the sun. This
investigation compares the performances of machine learning algorithms (not
requiring labelled images for training) for real-time segmentation of clouds in
images acquired using a ground-based infrared sky imager. Real-time
segmentation is utilized to extract cloud features using only the pixels in
which clouds are detected.


Abstract:
  In computer vision, recovering spatial information by filling in masked
regions, e.g., inpainting, has been widely investigated for its usability and
wide applicability to other various applications: image inpainting, image
extrapolation, and environment map estimation. Most of them are studied
separately depending on the applications. Our focus, however, is on
accommodating the opposite task, e.g., image outpainting, which would benefit
the target applications, e.g., image inpainting. Our self-supervision method,
In-N-Out, is summarized as a training approach that leverages the knowledge of
the opposite task into the target model. We empirically show that In-N-Out --
which explores the complementary information -- effectively takes advantage
over the traditional pipelines where only task-specific learning takes place in
training. In experiments, we compare our method to the traditional procedure
and analyze the effectiveness of our method on different applications: image
inpainting, image extrapolation, and environment map estimation. For these
tasks, we demonstrate that In-N-Out consistently improves the performance of
the recent works with In-N-Out self-supervision to their training procedure.
Also, we show that our approach achieves better results than an existing
training approach for outpainting.


Abstract:
  The natural night sky brightness is a relevant input for monitoring the light
pollution evolution at observatory sites, by subtracting it from the overall
sky brightness determined by direct measurements. It is also instrumental for
assessing the expected darkness of the pristine night skies. The natural
brightness of the night sky is determined by the sum of the spectral radiances
coming from astrophysical sources, including zodiacal light, and the
atmospheric airglow. The resulting radiance is modified by absorption and
scattering before it reaches the observer. Therefore, the natural night sky
brightness is a function of the location, time and atmospheric conditions. We
present in this work GAMBONS (GAia Map of the Brightness Of the Natural Sky), a
model to map the natural night brightness of the sky in cloudless and moonless
nights. Unlike previous maps, GAMBONS is based on the extra-atmospheric star
radiance obtained from the Gaia catalogue. The Gaia-DR2 archive compiles
astrometric and photometric information for more than 1.6 billion stars up to G
= 21 magnitude. For the brightest stars, not included in Gaia-DR2, we have used
the Hipparcos catalogue instead. After adding up to the star radiance the
contributions of the diffuse galactic and extragalactic light, zodiacal light
and airglow, and taking into account the effects of atmospheric attenuation and
scattering, the radiance detected by ground-based observers can be estimated.
This methodology can be applied to any photometric band, if appropriate
transformations from the Gaia bands are available. In particular, we present
the expected sky brightness for V (Johnson), and visual photopic and scotopic
passbands.


Abstract:
  We report the detection of 376.05 Hz (2.66 ms) coherent X-ray pulsations in
NICER observations of a transient outburst of the low-mass X-ray binary IGR
J17494-3030 in 2020 October/November. The system is an accreting millisecond
X-ray pulsar in a 75 minute ultracompact binary. The mass donor is most likely
a $\simeq 0.02 M_\odot$ finite-entropy white dwarf composed of He or C/O. The
fractional rms pulsed amplitude is 7.4%, and the soft (1-3 keV) X-ray pulse
profile contains a significant second harmonic. The pulsed amplitude and pulse
phase lag (relative to our mean timing model) are energy-dependent, each having
a local maximum at 4 keV and 1.5 keV, respectively. We also recovered the X-ray
pulsations in archival 2012 XMM-Newton observations, allowing us to measure a
long-term pulsar spin-down rate of $\dot\nu = -2.1(7)\times10^{-14}$ Hz/s and
to infer a pulsar surface dipole magnetic field strength of $\simeq 10^9$ G. We
show that the mass transfer in the binary is likely non-conservative, and we
discuss various scenarios for mass loss from the system.


Abstract:
  SVD serves as an exploratory tool in identifying the dominant features in the
form of top rank-r singular factors corresponding to the largest singular
values. For Big Data applications it is well known that Singular Value
Decomposition (SVD) is restrictive due to main memory requirements. However, a
number of applications such as community detection, clustering, or bottleneck
identification in large scale graph data-sets rely upon identifying the lowest
singular values and the singular corresponding vectors. For example, the lowest
singular values of a graph Laplacian reveal the number of isolated clusters
(zero singular values) or bottlenecks (lowest non-zero singular values) for
undirected, acyclic graphs. A naive approach here would be to perform a full
SVD however, this quickly becomes infeasible for practical big data
applications due to the enormous memory requirements. Furthermore, for such
applications only a few lowest singular factors are desired making a full
decomposition computationally exorbitant. In this work, we trivially extend the
previously proposed Range-Net to \textbf{Tail-Net} for a memory and compute
efficient extraction of lowest singular factors of a given big dataset and a
specified rank-r. We present a number of numerical experiments on both
synthetic and practical data-sets for verification and bench-marking using
conventional SVD as the baseline.


Abstract:
  Efficient video action recognition remains a challenging problem. One large
model after another takes the place of the state-of-the-art on the Kinetics
dataset, but real-world efficiency evaluations are often lacking. In this work,
we fill this gap and investigate the use of transformers for efficient action
recognition. We propose a novel, lightweight action recognition architecture,
VideoLightFormer. In a factorized fashion, we carefully extend the 2D
convolutional Temporal Segment Network with transformers, while maintaining
spatial and temporal video structure throughout the entire model. Existing
methods often resort to one of the two extremes, where they either apply huge
transformers to video features, or minimal transformers on highly pooled video
features. Our method differs from them by keeping the transformer models small,
but leveraging full spatiotemporal feature structure. We evaluate
VideoLightFormer in a high-efficiency setting on the temporally-demanding
EPIC-KITCHENS-100 and Something-Something-V2 (SSV2) datasets and find that it
achieves a better mix of efficiency and accuracy than existing state-of-the-art
models, apart from the Temporal Shift Module on SSV2.


Abstract:
  One of the ways blind people understand their surroundings is by clicking
images and relying on descriptions generated by image captioning systems.
Current work on captioning images for the visually impaired do not use the
textual data present in the image when generating captions. This problem is
critical as many visual scenes contain text. Moreover, up to 21% of the
questions asked by blind people about the images they click pertain to the text
present in them. In this work, we propose altering AoANet, a state-of-the-art
image captioning model, to leverage the text detected in the image as an input
feature. In addition, we use a pointer-generator mechanism to copy the detected
text to the caption when tokens need to be reproduced accurately. Our model
outperforms AoANet on the benchmark dataset VizWiz, giving a 35% and 16.2%
performance improvement on CIDEr and SPICE scores, respectively.


Abstract:
  Preprint for a book chapter introducing Audio Content Analysis. With a focus
on Music Information Retrieval systems, this chapter defines musical audio
content, introduces the general process of audio content analysis, and surveys
basic approaches to audio content analysis. The various tasks in Audio Content
Analysis are categorized into three classes: music transcription, music
performance analysis, and music identification and categorization. The examples
for music transcription systems include music key detection, fundamental
frequency detection, and music structure detection. Music performance analysis
systems feature an overview of beat and tempo detection approaches as well as
music performance assessment. The covered music classification systems are
audio fingerprinting, music genre classification, and music emotion
recognition. The chapter concludes with a discussion and current challenges in
the field and a speculation on future perspectives.


Abstract:
  In this work, we address the question whether a sufficiently deep quantum
neural network can approximate a target function as accurate as possible. We
start with simple but typical physical situations that the target functions are
physical observables, and then we extend our discussion to situations that the
learning targets are not directly physical observables, but can be expressed as
physical observables in an enlarged Hilbert space with multiple replicas, such
as the Loshimidt echo and the Renyi entropy. The main finding is that an
accurate approximation is possible only when the input wave functions in the
dataset do not exhaust the entire Hilbert space that the quantum circuit acts
on, and more precisely, the Hilbert space dimension of the former has to be
less than half of the Hilbert space dimension of the latter. In some cases,
this requirement can be satisfied automatically because of the intrinsic
properties of the dataset, for instance, when the input wave function has to be
symmetric between different replicas. And if this requirement cannot be
satisfied by the dataset, we show that the expressivity capabilities can be
restored by adding one ancillary qubit where the wave function is always fixed
at input. Our studies point toward establishing a quantum neural network
analogy of the universal approximation theorem that lays the foundation for
expressivity of classical neural networks.


Abstract:
  The CM carbonaceous chondrite meteorites provide a record of low temperature
aqueous reactions in the early solar system. A number of CM chondrites also
experienced short-lived, post-hydration thermal metamorphism at temperatures of
200C to over 750C. The exact conditions of thermal metamorphism and the
relationship between the unheated and heated CM chondrites are not well
constrained but are crucial to understanding the formation and evolution of
hydrous asteroids. Here we have used position-sensitive-detector X-ray
diffraction (PSD-XRD), thermogravimetric analysis (TGA) and transmission
infrared (IR) spectroscopy to characterise the mineralogy and water contents of
14 heated CM and ungrouped carbonaceous chondrites. We show that heated CM
chondrites underwent the same degree of aqueous alteration as the unheated CMs,
however upon thermal metamorphism their mineralogy initially (300 to 500C)
changed from hydrated phyllosilicates to a dehydrated amorphous phyllosilicate
phase. At higher temperatures (over 500C) we observe recrystallisation of
olivine and Fe-sulphides and the formation of metal. Thermal metamorphism also
caused the water contents of heated CM chondrites to decrease from 13 wt
percent to 3 wt percent and a subsequent reduction in the intensity of the 3
micron feature in IR spectra. We estimate that the heated CM chondrites have
lost 15 to 65 percent of the water they contained at the end of aqueous
alteration. If impacts were the main cause of metamorphism, this is consistent
with shock pressures of 20 to 50 GPa. However, not all heated CM chondrites
retain shock features suggesting that some were instead heated by solar
radiation. Evidence from the Hayabusa2 and ORSIRS-REx missions suggest that
dehydrated materials may be common on the surfaces of primitive asteroids and
our results will support upcoming analysis of samples returned from asteroids
Ryugu and Bennu.


Abstract:
  Dense semantic forecasting anticipates future events in video by inferring
pixel-level semantics of an unobserved future image. We present a novel
approach that is applicable to various single-frame architectures and tasks.
Our approach consists of two modules. Feature-to-motion (F2M) module forecasts
a dense deformation field that warps past features into their future positions.
Feature-to-feature (F2F) module regresses the future features directly and is
therefore able to account for emergent scenery. The compound F2MF model
decouples the effects of motion from the effects of novelty in a task-agnostic
manner. We aim to apply F2MF forecasting to the most subsampled and the most
abstract representation of a desired single-frame model. Our design takes
advantage of deformable convolutions and spatial correlation coefficients
across neighbouring time instants. We perform experiments on three dense
prediction tasks: semantic segmentation, instance-level segmentation, and
panoptic segmentation. The results reveal state-of-the-art forecasting accuracy
across three dense prediction tasks.


Abstract:
  The ongoing COVID-19 pandemic is the first epidemic in human history in which
digital contact-tracing has been deployed at a global scale. Tracking and
quarantining all the contacts of individuals who test positive to a virus can
help slowing-down an epidemic, but the impact of contact-tracing is severely
limited by the generally low adoption of contact-tracing apps in the
population. We derive here an analytical expression for the effectiveness of
contact-tracing app installation strategies in a SIR model on a given contact
graph. We propose a decentralised heuristic to improve the effectiveness of
contact tracing under fixed adoption rates, which targets a set of individuals
to install contact-tracing apps, and can be easily implemented. Simulations on
a large number of real-world contact networks confirm that this heuristic
represents a feasible alternative to the current state of the art.


Abstract:
  Extending the discovery by Giles Gardam of a concrete counterexample to
Kaplansky's unit conjecture in characteristic 2, a family of counterexamples
for every prime characteristic is presented.


Abstract:
  The role of the tensor part of the nuclear interaction is actively
investigated in recent years due to experimental advancement yielding new data
in nuclei far from the $\beta$-stability line. In this article we study the
effect of this part of the nuclear interaction on deformed neutron magic
numbers in the rare-earth region within the Skyrme energy-density functional
for various TIJ \cite{lesinski:2007} parametrizations. Two quantities signaling
magic numbers are considered: two-neutron separation energies and
single-particle energies. They are calculated in isotopic series involving
well-deformed rare-earth nuclei ranging from $Z=64$ to $Z=72$ in the $N=100$
region. Obtained results show that, whereas the neutron-proton tensor
contribution to binding energies is important to reproduce neutron sub-shell
closure at $N = 104$ in heavier rare earths Yb ($Z=70$) and Hf ($Z=72$)
isotopes, like-particle tensor also plays a role in the single-particle
spectrum around Fermi level and is even favored in lighter Gd ($Z=64$) and Dy
($Z=66$) rare-earth isotopes.


Abstract:
  In this paper, we introduce a generalization of a class of tilings which
appear in the literature: the tilings over which a height function can be
defined (for example, the famous tilings of polyominoes with dominoes). We show
that many properties of these tilings can be seen as the consequences of
properties of the generalized tilings we introduce. In particular, we show that
any tiling problem which can be modelized in our generalized framework has the
following properties: the tilability of a region can be constructively decided
in polynomial time, the number of connected components in the undirected
flip-accessibility graph can be determined, and the directed flip-accessibility
graph induces a distributive lattice structure. Finally, we give a few examples
of known tiling problems which can be viewed as particular cases of the new
notions we introduce.


Abstract:
  We present a survey of ways in which domain-knowledge has been included when
constructing models with neural networks. The inclusion of domain-knowledge is
of special interest not just to constructing scientific assistants, but also,
many other areas that involve understanding data using human-machine
collaboration. In many such instances, machine-based model construction may
benefit significantly from being provided with human-knowledge of the domain
encoded in a sufficiently precise form. This paper examines two broad
approaches to encode such knowledge--as logical and numerical constraints--and
describes techniques and results obtained in several sub-categories under each
of these approaches.


Abstract:
  High-order topological phases, such as those with nontrivial quadrupole
moments, protect edge states that are themselves topological insulators in
lower dimensions. So far, most quadrupole phases of light are explored in
linear optical systems, which are protected by spatial symmetries or synthetic
symmetries. Here we present Floquet quadrupole phases in driven nonlinear
photonic crystals (PhCs) that are protected by space-time screw symmetries. We
start by illustrating space-time symmetries by tracking the trajectory of
instantaneous optical axes of the driven media. Our Floquet quadrupole phase is
then confirmed in two independent ways: symmetry indices at high-symmetry
momentum points and calculations of the nested Wannier bands. Our work presents
a general framework to analyze symmetries in driven optical materials and paves
the way to further exploring symmetry-protected topological phases in Floquet
systems and their optoelectronic applications.


Abstract:
  In this paper we present the outcome of the first international comparison in
the terahertz frequency range among three different kinds of spectrometers. A
Fourier-Transform infrared spectrometer, a Vector Network Analyzer and a
Time-Domain Spectrometer have been employed for measuring the complex
refractive index of three travelling standards made of selected dielectric
materials in order to offer a wide enough range of parameters to be measured.
The three spectrometers have been compared in terms of measurement capability
and uncertainty.


Abstract:
  The interplay between the spin-orbit and Zeeman interactions acting on a
spinful Su-Schrieffer-Heeger model is studied based on an InAs nanowire
subjected to a periodic gate potential along the axial direction. It is shown
that a nontrivial topological phase can be achieved by regulating the
confining-potential configuration. In the absence of the Zeeman field, we prove
that the topology of the chain is not affected by the Rashba spin-orbit
interaction due to the persisting chiral symmetry. The energies of the edge
modes can be manipulated by varying the magnitude and direction of the external
magnetic field. Remarkably, the joint effect of the two spin-related
interactions leads to novel edge states that appear in the gap formed by the
anti-crossing of the bands of a finite spinful dimerized chain, and can be
merged into the bulk states by tilting the magnetic-field direction.


Abstract:
  Speech enhancement has benefited from the success of deep learning in terms
of intelligibility and perceptual quality. Conventional time-frequency (TF)
domain methods focus on predicting TF-masks or speech spectrum,via a naive
convolution neural network or recurrent neural network.Some recent studies were
based on Complex spectral Mapping convolution recurrent neural network (CRN) .
These models skiped directly from encoder layers' output and decoder layers'
input ,which maybe thoughtless. We proposed an attention mechanism based skip
connection between encoder and decoder layers,namely Complex Spectral Mapping
With Attention Based Convolution Recurrent Neural Network (CARN).Compared with
CRN model,the proposed CARN model improved more than 10% relatively at several
metrics such as PESQ,CBAK,COVL,CSIG and son,and outperformed the place 1st
model in both real time and non-real time track of the DNS Challenge 2020 at
these metrics.


Abstract:
  In this paper, a three-dimensional (3D) geometry based stochastic model
(GBSM) for a massive multiple-input multiple-output (MIMO) communication system
employing practical discrete intelligent reflecting surface (IRS) is proposed.
The proposed channel model supports the scenario where both transceivers and
environments move. The evolution of clusters in the space domain and the
practical discrete phase shifts are considered in the channel model. The
steering vector is set at the base station for the cooperation with IRS.
Through studying statistical properties, the non-stationary properties are
verified. We find that IRS plays a role in separating the whole channel and
make the absolute value of time autocorrelation function (ACF) larger than the
situation without employing IRS. Time ACF of the case using discrete phase
shifts is also compared with the continuous case.


Abstract:
  Training high-accuracy object detection models requires large and diverse
annotated datasets. However, creating these data-sets is time-consuming and
expensive since it relies on human annotators. We design, implement, and
evaluate TagMe, a new approach for automatic object annotation in videos that
uses GPS data. When the GPS trace of an object is available, TagMe matches the
object's motion from GPS trace and the pixels' motions in the video to find the
pixels belonging to the object in the video and creates the bounding box
annotations of the object. TagMe works using passive data collection and can
continuously generate new object annotations from outdoor video streams without
any human annotators. We evaluate TagMe on a dataset of 100 video clips. We
show TagMe can produce high-quality object annotations in a fully-automatic and
low-cost way. Compared with the traditional human-in-the-loop solution, TagMe
can produce the same amount of annotations at a much lower cost, e.g., up to
110x.


Abstract:
  Based on the Kazama-Suzuki type coset construction and its inverse coset
between the subregular $\mathcal{W}$-algebras for $\mathfrak{sl}_n$ and the
principal $\mathcal{W}$-superalgebras for $\mathfrak{sl}_{1|n}$, we prove
weight-wise linear equivalences of their representation categories. Our main
results are then improvements of these correspondences incorporating the
monoidal structures. Firstly, in the rational case, we obtain the
classification of simple modules and their fusion rules via simple current
extensions from their Heisenberg cosets. Secondly, beyond the rational case, we
use certain kernel VOAs together with relative semi-infinite cohomology
functors to get functors from categories of modules for the subregular
$\mathcal{W}$-algebras for $\mathfrak{sl}_n$ to categories of modules for the
principal $\mathcal{W}$-superalgebras for $\mathfrak{sl}_{1|n}$ and vice versa.
We study these functors and in particular prove isomorphisms between the
superspaces of logarithmic intertwining operators. As a corollary, we obtain
correspondences of representation categories in the monoidal sense beyond the
rational case as well.


Abstract:
  We introduce a data set called DCH-2, which contains 4,390 real
customer-helpdesk dialogues in Chinese and their English translations. DCH-2
also contains dialogue-level annotations and turn-level annotations obtained
independently from either 19 or 20 annotators. The data set was built through
our effort as organisers of the NTCIR-14 Short Text Conversation and NTCIR-15
Dialogue Evaluation tasks, to help researchers understand what constitutes an
effective customer-helpdesk dialogue, and thereby build efficient and helpful
helpdesk systems that are available to customers at all times. In addition,
DCH-2 may be utilised for other purposes, for example, as a repository for
retrieval-based dialogue systems, or as a parallel corpus for machine
translation in the helpdesk domain.


Abstract:
  As Machine Learning (ML) is now widely applied in many domains, in both
research and industry, an understanding of what is happening inside the black
box is becoming a growing demand, especially by non-experts of these models.
Several approaches had thus been developed to provide clear insights of a model
prediction for a particular observation but at the cost of long computation
time or restrictive hypothesis that does not fully take into account
interaction between attributes. This paper provides methods based on the
detection of relevant groups of attributes -- named coalitions -- influencing a
prediction and compares them with the literature. Our results show that these
coalitional methods are more efficient than existing ones such as SHapley
Additive exPlanation (SHAP). Computation time is shortened while preserving an
acceptable accuracy of individual prediction explanations. Therefore, this
enables wider practical use of explanation methods to increase trust between
developed ML models, end-users, and whoever impacted by any decision where
these models played a role.


Abstract:
  This paper presents a generalized and robust face manipulation detection
method based on the edge region features appearing in images. Most contemporary
face synthesis processes include color awkwardness reduction but damage the
natural fingerprint in the edge region. In addition, these color correction
processes do not proceed in the non-face background region. We also observe
that the synthesis process does not consider the natural properties of the
image appearing in the time domain. Considering these observations, we propose
a facial forensic framework that utilizes pixel-level color features appearing
in the edge region of the whole image. Furthermore, our framework includes a
3D-CNN classification model that interprets the extracted color features
spatially and temporally. Unlike other existing studies, we conduct
authenticity determination by considering all features extracted from multiple
frames within one video. Through extensive experiments, including real-world
scenarios to evaluate generalized detection ability, we show that our framework
outperforms state-of-the-art facial manipulation detection technologies in
terms of accuracy and robustness.


Abstract:
  The electromagnetic character of the $\Delta I=1$ transitions connecting the
one- to zero-phonon and the two- to one-phonon wobbling bands should be
dominated by an $E2$ component, due to the collective motion of the entire
nuclear charge. In the present work it is shown, based on combined angular
correlation and linear polarization measurements, that the mixing ratios of all
analyzed connecting transitions between low-lying bands in $^{135}$Pr
interpreted as zero-, one-, and two-phonon wobbling bands, have absolute values
smaller than one. This indicates predominant $M1$ magnetic character, which is
incompatible with the proposed wobbling nature. All experimental observables
are instead in good agreement with quasiparticle-plus-triaxial-rotor model
calculations, which describe the bands as resulting from a rapid re-alignment
of the total angular momentum from the short to the intermediate nuclear axis.


Abstract:
  The development of an optical clock with ultimate accuracy and stability
requires lasers with very narrow linewidth. We present two ultrastable laser
systems based on 48 cm long Fabry-Perot cavities made of ULE glass in
horizontal and vertical configurations operating at 698 nm. Fractional
frequency instability of the beat signal between two lasers reaches 1.6e-15 at
the averaging time of 1 s. We experimentally characterized the contribution of
the different noise sources (power fluctuations, residual amplitude modulation,
the Doppler noise, sensitivity to the shock impact) and found that in our case
the laser frequency instability to a large extent is determined by an
optoelectronic feedback loop. Although the vertical configuration proved to be
easier to manufacture and to transport, it turned out that it is much more
sensitive to acoustics and horizontal accelerations compared to the horizontal
one. Both laser systems were transported over a 60 km distance from the Lebedev
Physical Institute to the Russian National Metrology Institute (VNIIFTRI) where
they serve as local oscillators for spectroscopy of the clock transition in the
recently developed strontium optical clock.


Abstract:
  Based on $14.7~\textrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected with
the BESIII detector at the BEPCII collider at 17 different center-of-mass
energies between $3.7730~\textrm{GeV}$ and $4.5995~\textrm{GeV}$, Born cross
sections of the two processes $e^+e^- \to p\bar{p}\eta$ and $e^+e^- \to
p\bar{p}\omega$ are measured for the first time. No indication of resonant
production through a vector state $V$ is observed, and upper limits on the Born
cross sections of $e^+e^- \to V \to p\bar{p}\eta$ and $e^+e^- \to V \to
p\bar{p}\omega$ at the $90\%$ confidence level are calculated for a large
parameter space in resonance masses and widths. For the current world average
parameters of the $\psi(4230)$ of $m=4.2187~\textrm{GeV}/c^{2}$ and
$\Gamma=44~\textrm{MeV}$, we find upper limits on resonant production of the
$p\bar{p}\eta$ and $p\bar{p}\omega$ final states of $7.5~\textrm{pb}$ and
$10.4~\textrm{pb}$ at the $90\%$ CL, respectively.


Abstract:
  We study the release of energy during the gradual phase of a flare,
characterized by faint bursts of non-thermal hard X-ray (HXR) emission
associated with decimetric radio spikes and type III radio bursts starting at
high frequencies and extending to the heliosphere. We characterize the site of
electron acceleration in the corona and study the radial evolution of radio
source sizes in the high corona. Imaging and spectroscopy of the HXR emission
with Fermi and RHESSI provide a diagnostic of the accelerated electrons in the
corona as well as a lower limit on the height of the acceleration region. Radio
observations in the decimetric range with the ORFEES spectrograph provide radio
diagnostics close to the acceleration region. Radio spectro-imaging with LOFAR
in the meter range provide the evolution of the radio source sizes with their
distance from the Sun, in the high corona. Non-thermal HXR bursts and radio
spikes are well correlated on short timescales. The spectral index of
non-thermal HXR emitting electrons is -4 and their number is about $2\times
10^{33}$ electrons/s. The density of the acceleration region is constrained
between $1-5 \times 10^9$ cm$^{-3}$. Electrons accelerated upward rapidly
become unstable to Langmuir wave production, leading to high starting
frequencies of the type III radio bursts, and the elongation of the radio beam
at its source is between 0.5 and 11.4 Mm. The radio source sizes and their
gradient observed with LOFAR are larger than the expected size and gradient of
the size of the electron beam, assuming it follows the expansion of the
magnetic flux tubes. These observations support the idea that the fragmentation
of the radio emission into spikes is linked to the fragmentation of the
acceleration process itself. The combination of HXR and radio diagnostics in
the corona provides strong constrains on the site of electron acceleration.


Abstract:
  Quality control (QC) in medical image analysis is time-consuming and
laborious, leading to increased interest in automated methods. However, what is
deemed suitable quality for algorithmic processing may be different from
human-perceived measures of visual quality. In this work, we pose MR image
quality assessment from an image reconstruction perspective. We train Bayesian
CNNs using a heteroscedastic uncertainty model to recover clean images from
noisy data, providing measures of uncertainty over the predictions. This
framework enables us to divide data corruption into learnable and non-learnable
components and leads us to interpret the predictive uncertainty as an
estimation of the achievable recovery of an image. Thus, we argue that quality
control for visual assessment cannot be equated to quality control for
algorithmic processing. We validate this statement in a multi-task experiment
combining artefact recovery with uncertainty prediction and grey matter
segmentation. Recognising this distinction between visual and algorithmic
quality has the impact that, depending on the downstream task, less data can be
excluded based on ``visual quality" reasons alone.


Abstract:
  We construct the generating function for products of inverse central binomial
coefficients with harmonic numbers.


Abstract:
  We study the cosmology of a quadratic metric-compatible torsionful gravity
theory in the presence of a perfect hyperfluid. The gravitational action is an
extension of the Einstein-Cartan theory given by the usual Einstein-Hilbert
contribution plus all the admitted quadratic parity even torsion scalars and
the matter action also exhibits a dependence on the connection. The equations
of motion are obtained by regarding the metric and the metric-compatible
torsionful connection as independent variables. We then consider a
Friedmann-Lema\^itre-Robertson-Walker background, analyze the conservation
laws, and derive the torsion modified Friedmann equations for our theory.
Remarkably, we are able to provide exact analytic solutions for the torsionful
cosmology.


Abstract:
  The paper is devoted to a comprehensive study of smoothness of inertial
manifolds for abstract semilinear parabolic problems. It is well known that in
general we cannot expect more than $C^{1,\varepsilon}$-regularity for such
manifolds (for some positive, but small $\varepsilon$). Nevertheless, as shown
in the paper, under the natural assumptions, the obstacles to the existence of
a $C^n$-smooth inertial manifold (where $n\in\mathbb N$ is any given number)
can be removed by increasing the dimension and by modifying properly the
nonlinearity outside of the global attractor (or even outside the
$C^{1,\varepsilon}$-smooth IM of a minimal dimension). The proof is strongly
based on the Whitney extension theorem.


Abstract:
  We present the characteristic polynomial for the transition matrix of a
vertex-face walk on a graph, and obtain its spectra. Furthermore, we express
the characteristic polynomial for the transition matrix of a vertex-face walk
on the 2-dimensional torus by using its adjacency matrix, and obtain its
spectra. As an application, we define a new walk-type zeta function with
respect to the transition matrix of a vertex-face walk on the 2-dimensional
torus, and present its explicit formula.


Abstract:
  $\Gamma$-maximin, $\Gamma$-maximax and inteval dominance are familiar
decision criteria for making decisions under severe uncertainty, when
probability distributions can only be partially identified. One can apply these
three criteria by solving sequences of linear programs. In this study, we
present new algorithms for these criteria and compare their performance to
existing standard algorithms. Specifically, we use efficient ways, based on
previous work, to find common initial feasible points for these algorithms.
Exploiting these initial feasible points, we develop early stopping criteria to
determine whether gambles are either $\Gamma$-maximin, $\Gamma$-maximax or
interval dominant. We observe that the primal-dual interior point method
benefits considerably from these improvements. In our simulation, we find that
our proposed algorithms outperform the standard algorithms when the size of the
domain of lower previsions is less or equal to the sizes of decisions and
outcomes. However, our proposed algorithms do not outperform the standard
algorithms in the case that the size of the domain of lower previsions is much
larger than the sizes of decisions and outcomes.


Abstract:
  During the last decades, scientific community has been investigating both
biological and hydrographic processes that affect fisheries. Such an
interdisciplinary and synergic approach is nowadays giving a fundamental
contribution, in particular, in connecting the dots between hydrographic
phenomena and biomass variability and distribution of small pelagic fish. Here
we estimate impacts of hydrographic fluctuations on small pelagic fishery,
focusing on the inter-annual variability that characterizes connectivity
between spawning and recruiting areas for the European anchovy (Engraulis
encrasicolus, Linnaues 1758), in the Northern side of the Sicily Channel
(Mediterranean Sea). Results show that coastal transport dynamics of a specific
year largely affect the biomass recorded the following year. Our work,
moreover, quantifies the specific monetary impacts on landings of European
anchovy fishery due to hydrodynamics variability, connecting biomass
fluctuations with fishery economics in a highly dynamic and exploited marine
environment as the Sicily Channel. In particular, we build a model that
attributes a monetary value to the hydrographic phenomena (i.e., cross-shore
vs. alongshore eggs and larvae transport), registered in the FAO Geographical
Sub-Area (GSA) 16 (Southern Sicily). This allows us to provide a monetary
estimation of catches, derived from different transport dynamics. Our results
highlight the paramount importance that hydrographic phenomena can have over
the socio-economic performance of a fishery.


Abstract:
  We introduce simplified models for enhancements in the matter power spectrum
at small scales and study their implications for dark matter substructure and
gravitational observables. These models capture the salient aspects of a
variety of early universe scenarios that predict enhanced small-scale
structure, such as axion-like particle dark matter, light vector dark matter,
and epochs of early matter domination. We use a model-independent,
semi-analytic treatment to map bumps in the matter power spectrum to
early-forming sub-solar mass dark matter halos and estimate their evolution,
disruption, and contribution to substructure of clusters and galaxies at late
times. We discuss the sensitivity of gravitational observables, including
pulsar timing arrays and caustic microlensing, to both the presence of bumps in
the power spectrum and variations in their basic properties.


Abstract:
  We explore methodologies to improve the robustness of generative adversarial
imitation learning (GAIL) algorithms to observation noise. Towards this
objective, we study the effect of local Lipschitzness of the discriminator and
the generator on the robustness of policies learned by GAIL. In many robotics
applications, the learned policies by GAIL typically suffer from a degraded
performance at test time since the observations from the environment might be
corrupted by noise. Hence, robustifying the learned policies against the
observation noise is of critical importance. To this end, we propose a
regularization method to induce local Lipschitzness in the generator and the
discriminator of adversarial imitation learning methods. We show that the
modified objective leads to learning significantly more robust policies.
Moreover, we demonstrate --- both theoretically and experimentally --- that
training a locally Lipschitz discriminator leads to a locally Lipschitz
generator, thereby improving the robustness of the resultant policy. We perform
extensive experiments on simulated robot locomotion environments from the
MuJoCo suite that demonstrate the proposed method learns policies that
significantly outperform the state-of-the-art generative adversarial imitation
learning algorithm when applied to test scenarios with noise-corrupted
observations.


Abstract:
  In most nuclear many-body methods, observables are calculated using many-body
wave functions explicitly. The variational two-particle reduced density matrix
method is one of the few exceptions to the rule. Ground-state energies of both
closed-shell and open-shell nuclear systems can indeed be evaluated by
minimizing a constrained linear functional of the two-particle reduced density
matrix. However, it has virtually never been used in nuclear theory, because
nuclear ground states were found to be well overbound, contrary to those of
atoms and molecules. Consequently, we introduced new constraints in the nuclear
variational two-particle reduced density matrix method, developed recently for
atomic and molecular systems. Our calculations then show that this approach can
provide a proper description of nuclear systems where only valence neutrons are
included. For the nuclear systems where both neutrons and protons are active,
however, the energies obtained with the variational two-particle reduced
density matrix method are still overbound. The possible reasons for the noticed
discrepancies and solutions to this problem will be discussed.


Abstract:
  Vesicle budding induced by protein binding that generates an isotropic
spontaneous curvature is studied using a mean-field theory. Many spherical buds
are formed via protein binding. As the binding chemical potential increases,
the proteins first bind to the buds and then to the remainder of the vesicle.
For a high spontaneous curvature and/or high bending rigidity of the bound
membrane, it is found that a first-order transition occurs between a small
number of large buds and a large number of small buds. These two states coexist
around the transition point. The proposed scheme is simple and easily
applicable to many interaction types, so we investigate the effects of
inter-protein interactions, the protein-insertion-induced changes in area, the
variation of the saddle-splay-modulus, and the area-difference-elasticity
energy. The differences in the preferred curvatures for curvature sensing and
generation are also clarified.


Abstract:
  The variational determination of the two-fermion reduced density matrix is
described for trapped, ultracold few-fermion systems in one dimension with
equal spin populations. This is accomplished by formulating the problem as a
semi-definite program, with the two-fermion reduced density matrix being
subject to the D, Q, G, T1, and T2 $N$-representability conditions. The
ground-state energies of $N=2,4$, and $8$ fermion systems are found by
utilising an augmented Lagrangian method for semi-definite programming. The
ground-state energies are found to match extremely well to those determined by
full-configuration interaction and coupled-cluster calculations. This
demonstrates the utility of the reduced density matrix approach to strongly
correlated, ultracold few-fermion systems.


Abstract:
  Similarities in the chemical composition of two of the closest Milky Way
satellites, namely the Large Magellanic Cloud (LMC) and the Sagittarius (Sgr)
dwarf galaxy, have been proposed in the literature, suggesting similar chemical
enrichment histories between the two galaxies. This proposition, however, rests
on different abundance analyses, which likely introduce various systematics
that hamper a fair comparison among the different data sets. In order to bypass
this issue (and highlight real similarities and differences between their
abundance patterns), we present a homogeneous chemical analysis of 30 giant
stars in LMC, 14 giant stars in Sgr and 14 giants in the Milky Way, based on
high-resolution spectra taken with the spectrograph UVES-FLAMES. The LMC and
Sgr stars, in the considered metallicity range ([Fe/H]>-1.1 dex), show very
similar abundance ratios for almost all the elements, with differences only in
the heavy s-process elements Ba, La and Nd, suggesting a different contribution
by asymptotic giant branch stars. On the other hand, the two galaxies have
chemical patterns clearly different from those measured in the Galactic stars,
especially for the elements produced by massive stars. This finding suggests
the massive stars contributed less to the chemical enrichment of these galaxies
with respect to the Milky Way. The derived abundances support similar chemical
enrichment histories for the LMC and Sgr.


Abstract:
  In this paper, a comprehensive examination of the temperature- and
bias-dependent diffusion regimes of underdamped Brownian particles is
presented. A temperature threshold for a transition between anomalous and
normal diffusive behaviors is located, yielding a new phase diagram for the
system. In the low-temperature regime, the system exhibits an apparent negative
differential mobility due to persistent, long-time subdiffusion at low-bias; at
high temperature (or critical bias,) the system rapidly approaches normal
diffusion below an intermediate barrier height, $U_o \sim k_B T$. By
consideration of numerical results, comparison to the overdamped case, and the
related Kramers multistable escape problems, it is demonstrated that the
low-bias non-monotonic temperature dependence of the diffusivity, persistent
subdiffusion, and negative differential mobility can be traced to inertial
effects, which are evident in the oscillatory modes of the velocity power
spectra at low bias. In the giant diffusion regime, the velocity power spectra
exhibit coupling between the ``locked" and ``running" states, with a
characteristic frequency corresponding to the principal frequency of the limit
cycles of a damped, driven plane pendulum near critical bias. Non-linear second
harmonic generation, corresponding to oscillatory transient anomalous
diffusivity, is observed with increasing bias and decreasing temperature,
further emphasizing that the low-noise diffusion problem converges to
noise-free dynamics, complementing analytic results for the average velocity
[L. Cheng and N.K. Yip, Physica D, 2015].


Abstract:
  Synthesizing tabular data is attracting much attention these days for various
purposes. With sophisticate synthetic data, for instance, one can augment its
training data. For the past couple of years, tabular data synthesis techniques
have been greatly improved. Recent work made progress to address many problems
in synthesizing tabular data, such as the imbalanced distribution and
multimodality problems. However, the data utility of state-of-the-art methods
is not satisfactory yet. In this work, we significantly improve the utility by
designing our generator and discriminator based on neural ordinary differential
equations (NODEs). After showing that NODEs have theoretically preferred
characteristics for generating tabular data, we introduce our designs. The
NODE-based discriminator performs a hidden vector evolution trajectory-based
classification rather than classifying with a hidden vector at the last layer
only. Our generator also adopts an ODE layer at the very beginning of its
architecture to transform its initial input vector (i.e., the concatenation of
a noisy vector and a condition vector in our case) onto another latent vector
space suitable for the generation process. We conduct experiments with 13
datasets, including but not limited to insurance fraud detection, online news
article prediction, and so on, and our presented method outperforms other
state-of-the-art tabular data synthesis methods in many cases of our
classification, regression, and clustering experiments.


Abstract:
  An \emph{additive $+\beta$ spanner} of a graph $G$ is a subgraph which
preserves distances up to an additive $+\beta$ error. Additive spanners are
well-studied in unweighted graphs but have only recently received attention in
weighted graphs [Elkin et al.\ 2019 and 2020, Ahmed et al.\ 2020]. This paper
makes two new contributions to the theory of weighted additive spanners.
  For weighted graphs, [Ahmed et al.\ 2020] provided constructions of sparse
spanners with \emph{global} error $\beta = cW$, where $W$ is the maximum edge
weight in $G$ and $c$ is constant. We improve these to \emph{local} error by
giving spanners with additive error $+cW(s,t)$ for each vertex pair $(s,t)$,
where $W(s, t)$ is the maximum edge weight along the shortest $s$--$t$ path in
$G$. These include pairwise $+(2+\eps)W(\cdot,\cdot)$ and $+(6+\eps) W(\cdot,
\cdot)$ spanners over vertex pairs $\Pc \subseteq V \times V$ on
$O_{\eps}(n|\Pc|^{1/3})$ and $O_{\eps}(n|\Pc|^{1/4})$ edges for all $\eps > 0$,
which extend previously known unweighted results up to $\eps$ dependence, as
well as an all-pairs $+4W(\cdot,\cdot)$ spanner on $\widetilde{O}(n^{7/5})$
edges.
  Besides sparsity, another natural way to measure the quality of a spanner in
weighted graphs is by its \emph{lightness}, defined as the total edge weight of
the spanner divided by the weight of an MST of $G$. We provide a $+\eps
W(\cdot,\cdot)$ spanner with $O_{\eps}(n)$ lightness, and a $+(4+\eps)
W(\cdot,\cdot)$ spanner with $O_{\eps}(n^{2/3})$ lightness. These are the first
known additive spanners with nontrivial lightness guarantees. All of the above
spanners can be constructed in polynomial time.


Abstract:
  Surface plasmon enhanced processes and hot-carrier dynamics in plasmonic
nanostructures are of great fundamental interest to reveal light-matter
interactions at the nanoscale. Using plasmonic tunnel junctions as a platform
supporting both electrically- and optically excited localized surface plasmons,
we report a much greater (over 1000x) plasmonic light emission at upconverted
photon energies under combined electro-optical excitation, compared with
electrical or optical excitation separately. Two mechanisms compatible with the
form of the observed spectra are interactions of plasmon-induced hot carriers
and electronic anti-Stokes Raman scattering. Our measurement results are in
excellent agreement with a theoretical model combining electro-optical
generation of hot carriers through non-radiative plasmon excitation and
hot-carrier relaxation. We also discuss the challenge of distinguishing
relative contributions of hot carrier emission and the anti-Stokes electronic
Raman process. This observed increase in above-threshold emission in plasmonic
systems may open avenues in on-chip nanophotonic switching and hot carrier
photocatalysis.


Abstract:
  Reasoning the human-object interactions (HOI) is essential for deeper scene
understanding, while object affordances (or functionalities) are of great
importance for human to discover unseen HOIs with novel objects. Inspired by
this, we introduce an affordance transfer learning approach to jointly detect
HOIs with novel objects and recognize affordances. Specifically, HOI
representations can be decoupled into a combination of affordance and object
representations, making it possible to compose novel interactions by combining
affordance representations and novel object representations from additional
images, i.e. transferring the affordance to novel objects. With the proposed
affordance transfer learning, the model is also capable of inferring the
affordances of novel objects from known affordance representations. The
proposed method can thus be used to 1) improve the performance of HOI
detection, especially for the HOIs with unseen objects; and 2) infer the
affordances of novel objects. Experimental results on two datasets, HICO-DET
and HOI-COCO (from V-COCO), demonstrate significant improvements over recent
state-of-the-art methods for HOI detection and object affordance detection.
Code is available at https://github.com/zhihou7/HOI-CL


Abstract:
  Due to the COVID-19 pandemic, the focus on everydays mobility has been
shifted from traditional means of transport to how to safely commute for work
and/or move around the neighbourhood. Maintaining the safe distance among
pedestrian becomes crucial in big pedestrian networks. Looking at personal
goals, such as walking through the shortest path, could lead to congestion
phenomena on both roadsand crossroads violating the imposed regulations. We
suggest a centralized multi-objective approach able to assign alternative fair
paths for users while maintaining the congestion level as lower as possible.
Computational results show that, even considering paths that are not longer
than the 1% with respect to the shortest path for each pedestrian, the
congestion phenomena are reduced of more than the 50%


Abstract:
  This paper introduces multiuser multiple-input multiple-output (MU-MIMO)
architectures based on non-linear precoding and stream combining techniques
using rate-splitting (RS), where the transmitter often has only partial
knowledge of the channel state information (CSI). In contrast to existing
works, we consider deployments where the receivers may be equipped with
multiple antennas. This allows us to employ linear combining techniques based
on the Min-Max, the maximum ratio and the minimum mean-square error criteria
along with Tomlinson-Harashima precoders (THP) for RS-based MU-MIMO systems to
enhance the sum-rate performance. Moreover, we incorporate the Multi-Branch
(MB) concept into the RS architecture to further improve the sum-rate
performance. Closed-form expressions for the signal-to-interference-plus-noise
ratio and the sum-rate at the receiver end are devised through statistical
analysis. Simulation results show that the proposed RS-THP schemes achieve
better performance than conventional linear and THP precoders.


Abstract:
  Coupled nonlinear systems have promise for parallel computing architectures.
En route to realizing complex networks for Ising machines, we report an
experimental and theoretical study of two coupled parametric resonators
(parametrons). The coupling severely impacts the bifurcation topology and the
number of available solutions of the system; in part of the stability diagram,
we can access fewer solutions than expected. When applying noise to probe the
stability of the states, we find that the switching rates and the phase-space
trajectories of the system depend on the detuning in surprising ways. We
present a theoretical framework that heralds the existence of 'ghost
bifurcations'. These bifurcations involve only unstable solutions and lead to
avoided zones in phase space. The emergence of such ghost bifurcations is an
important feature of parametron networks that can influence their application
for parallel logic operations.


Abstract:
  We study the emergence of cooperation in large spatial public goods games.
Without employing severe social-pressure against "defectors", or alternatively,
significantly rewarding "cooperators", theoretical models typically predict a
system collapse in a way that is reminiscent of the "tragedy-of-the-commons"
metaphor. Drawing on a dynamic network model, this paper demonstrates how
cooperation can emerge when the social-pressure is mild. This is achieved with
the aid of an additional behavior called "hypocritical", which appears to be
cooperative from the external observer's perspective but in fact hardly
contributes to the social-welfare. Our model assumes that social-pressure is
induced over both defectors and hypocritical players, but the extent of which
may differ. Our main result indicates that the emergence of cooperation highly
depends on the extent of social-pressure applied against hypocritical players.
Setting it to be at some intermediate range below the one employed against
defectors allows a system composed almost exclusively of defectors to transform
into a fully cooperative one quickly. Conversely, when the social-pressure
against hypocritical players is either too low or too high, the system remains
locked in a degenerate configuration.


Abstract:
  Two-parameter perturbation theory (2PPT) is a framework designed to include
the relativistic gravitational effects of small-scale nonlinear structures on
the large-scale properties of the Universe. In this paper we use the 2PPT
framework to calculate and study the bispectrum of matter in a spatially-flat
$\Lambda$CDM cosmology. This is achieved by deploying Newtonian perturbation
theory to model the gravitational fields of quasi-nonlinear structures, and
then subsequently using them as source terms for the large-scale cosmological
perturbations. We find that our approach reproduces some of the expected
relativistic effects from second-order cosmological perturbation theory, but
not all. This work therefore provides a first step in deploying a formalism
that can simultaneously model the weak gravitational fields of both linear and
nonlinear structures in a realistic model of the Universe.


Abstract:
  For a subspace $X$ of functions from $L_2$ we consider the minimal number $m$
of nodes necessary for the exact discretization of the $L_2$-norm of the
functions in $X$. We construct a subspace such that for any exact
discretization with $m$ nodes there is at least one negative weight.


Abstract:
  We propose POLAR, a \textbf{pol}ynomial \textbf{ar}ithmetic framework that
leverages polynomial overapproximations with interval remainders for
bounded-time reachability analysis of neural network-controlled systems
(NNCSs). Compared with existing arithmetic approaches that use standard Taylor
models, our framework uses a novel approach to iteratively overapproximate the
neuron output ranges layer-by-layer with a combination of Bernstein polynomial
interpolation for continuous activation functions and Taylor model arithmetic
for the other operations. This approach can overcome the main drawback in the
standard Taylor model arithmetic, i.e. its inability to handle functions that
cannot be well approximated by Taylor polynomials, and significantly improve
the accuracy and efficiency of reachable states computation for NNCSs. To
further tighten the overapproximation, our method keeps the Taylor model
remainders symbolic under the linear mappings when estimating the output range
of a neural network. We show that POLAR can be seamlessly integrated with
existing Taylor model flowpipe construction techniques, and demonstrate that
POLAR significantly outperforms the current state-of-the-art techniques on a
suite of benchmarks.


Abstract:
  For a Calabi-Yau manifold $X$, the Kawamata - Morrison movable cone
conjecture connects the convex geometry of the movable cone
$\overline{\mathrm{Mov}}(X)$ to the birational automorphism group. Using the
theory of Coxeter groups, Cantat and Oguiso proved that the conjecture is true
for general varieties of Wehler type, and they described explicitly
$\mathrm{Bir}(X)$. We generalize their argument to prove the conjecture and
describe $\mathrm{Bir}(X)$ for general complete intersections of ample divisors
in arbitrary products of projective spaces. Then, under a certain condition, we
give a description of the boundary of $\overline{\mathrm{Mov}}(X)$ and an
application connected to the numerical dimension of divisors.


Abstract:
  Accelerated MRI shortens acquisition time by subsampling in the measurement
k-space. Recovering a high-fidelity anatomical image from subsampled
measurements requires close cooperation between two components: (1) a sampler
that chooses the subsampling pattern and (2) a reconstructor that recovers
images from incomplete measurements. In this paper, we leverage the sequential
nature of MRI measurements, and propose a fully differentiable framework that
jointly learns a sequential sampling policy simultaneously with a
reconstruction strategy. This co-designed framework is able to adapt during
acquisition in order to capture the most informative measurements for a
particular target (Figure 1). Experimental results on the fastMRI knee dataset
demonstrate that the proposed approach successfully utilizes intermediate
information during the sampling process to boost reconstruction performance. In
particular, our proposed method outperforms the current state-of-the-art
learned k-space sampling baseline on up to 96.96% of test samples. We also
investigate the individual and collective benefits of the sequential sampling
and co-design strategies. Code and more visualizations are available at
http://imaging.cms.caltech.edu/seq-mri


Abstract:
  This paper is concerned with the recovery of (approximate) solutions to
parabolic problems from incomplete and possibly inconsistent observational
data, given on a time-space cylinder that is a strict subset of the
computational domain under consideration. Unlike previous approaches to this
and related problems our starting point is a regularized least squares
formulation in a continuous infinite-dimensional setting that is based on
stable variational time-space formulations of the parabolic PDE. This allows us
to derive a priori as well as a posteriori error bounds for the recovered
states with respect to a certain reference solution. In these bounds the
regularization parameter is disentangled from the underlying discretization. An
important ingredient for the derivation of a posteriori bounds is the
construction of suitable Fortin operators which allow us to control oscillation
errors stemming from the discretization of dual norms. Moreover, the
variational framework allows us to contrive preconditioners for the discrete
problems whose application can be performed in linear time, and for which the
condition numbers of the preconditioned systems are uniformly proportional to
that of the regularized continuous problem.
  In particular, we provide suitable stopping criteria for the iterative
solvers based on the a posteriori error bounds. The presented numerical
experiments quantify the theoretical findings and demonstrate the performance
of the numerical scheme in relation with the underlying discretization and
regularization.


Abstract:
  Across machine learning, the use of curricula has shown strong empirical
potential to improve learning from data by avoiding local optima of training
objectives. For reinforcement learning (RL), curricula are especially
interesting, as the underlying optimization has a strong tendency to get stuck
in local optima due to the exploration-exploitation trade-off. Recently, a
number of approaches for an automatic generation of curricula for RL have been
shown to increase performance while requiring less expert knowledge compared to
manually designed curricula. However, these approaches are seldomly
investigated from a theoretical perspective, preventing a deeper understanding
of their mechanics. In this paper, we present an approach for automated
curriculum generation in RL with a clear theoretical underpinning. More
precisely, we formalize the well-known self-paced learning paradigm as inducing
a distribution over training tasks, which trades off between task complexity
and the objective to match a desired task distribution. Experiments show that
training on this induced distribution helps to avoid poor local optima across
RL algorithms in different tasks with uninformative rewards and challenging
exploration requirements.


Abstract:
  In this paper, we derive a formula to express the maximum number of
non-intersecting diagonals of arbitrary length that can be drawn in n x n
square arrays, where n is a multiple of l+1.


Abstract:
  In this work we explicitly show that the perturbative unitarity of analytic
infinite derivative (AID) scalar field theories can be achieved using a
modified prescription for computing scattering amplitudes. The crux of the new
prescription is the analytic continuation of a result obtained in the Euclidean
signature to the Minkowski external momenta. We explicitly elaborate an example
of a non-local $\phi^4$ model for various infinite derivative operators.
General UV properties of amplitudes in non-local theories are discussed.


Abstract:
  We initiate the use of a multi-layer neural network to model two-sided
matching and to explore the design space between strategy-proofness and
stability. It is well known that both properties cannot be achieved
simultaneously but the efficient frontier in this design space is not
understood. We show empirically that it is possible to achieve a good
compromise between stability and strategy-proofness-substantially better than
that achievable through a convex combination of deferred acceptance (stable and
strategy-proof for only one side of the market) and randomized serial
dictatorship (strategy-proof but not stable).


Abstract:
  Platooning on highways with connected and automated vehicles (CAVs) has
attracted considerable attention, while how to mange and coordinate platoons in
urban networks remains largely an open question. This scientific gap mainly
results from the maneuver complexity on urban roads, making it difficult to
model the platoon formation process. Inspired by flocking behaviors in nature,
this paper proposed a two-dimensional model to describe CAV group dynamics. The
model is formulated based on potential fields in planar coordinates, which is
composed of the inter-vehicle potential field and the cross-section potential
field. The inter-vehicle potential field enables CAVs to attract each other
when vehicle gaps are larger than the equilibrium distance, and repel each
other otherwise. It also generates incentives for lane change maneuvers to join
a platoon or to comply with the traffic management layer. The cross-section
potential field is able to mimic lane keeping behavior and it also creates
resistance to avoid unnecessary lane changes at very low incentives. These
modeling principles can also be applied to human-driven vehicles in the mixed
traffic environment. Behavioral plausibility of the model in terms of
car-following rationality and car-following safety is demonstrated analytically
and further verified with simulation in typical driving scenarios. The model is
computationally efficient and can provide insights into platoon operations in
urban networks.


Abstract:
  Graph drawing beyond planarity focuses on drawings of high visual quality for
non-planar graphs which are characterized by certain forbidden edge
configurations. A natural criterion for the quality of a drawing is the number
of edge crossings. The question then arises whether beyond-planar drawings have
a significantly larger crossing number than unrestricted drawings. Chimani et
al. [GD'19] gave bounds for the ratio between the crossing number of three
classes of beyond-planar graphs and the unrestricted crossing number. In this
paper we extend their results to the main currently known classes of
beyond-planar graphs characterized by forbidden edge configurations and answer
several of their open questions.


Abstract:
  Radial superlattices are nanostructured materials obtained by rolling-up thin
solid films into spiral-like tubular structures. The formation of these
"high-order" superlattices from two-dimensional crystals or ultrathin films is
expected to result in a transition of transport characteristics from
two-dimensional to one-dimensional. Here, we show that a transport hallmark of
radial superlattices is the appearance of magnetoconductance modulations in the
presence of externally applied axial magnetic fields. This phenomenon
critically relies on electronic interlayer tunneling processes that activates
an unconventional Aharonov-Bohm-like effect. Using a combination of density
functional theory calculations and low-energy continuum models, we determine
the electronic states of a paradigmatic single-material radial superlattice --
a two-winding carbon nanoscroll -- and indeed show momentum-dependent
oscillations of the magnetic states in axial configuration, which we
demonstrate to be entirely due to hopping between the two windings of the
spiral-shaped scroll.


Abstract:
  Purpose: To implement and evaluate a sequential approach to obtain
semi-quantitative T1-weighted MPRAGE images, unbiased by B1 inhomogeneities at
7T.
  Methods: In the reference gradient echo used for normalization of the MPRAGE
image, flip angle (aGE) and acquisition voxel size (Vref) was varied to
optimize tissue contrast and acquisition time (Tacq). The finalized protocol
was implemented at three different resolutions and the reproducibility was
evaluated. Maps of T1 were derived based on the normalized MPRAGE through
forward signal modelling.
  Results: A good compromise between tissue contrast and SNR was reached at
aGE=3{\deg}. A reduction of the reference GE Tacq by a factor of 4, at the cost
of negligible bias, was obtained by increasing Vref with a factor of 8 relative
the MPRAGE resolution. The coefficient-of-variation in segmented WM was 9+/-5%
after normalization, compared to 24+/-12% before. The T1 maps showed no obvious
bias and had reasonable values with regard to literature, especially after
optional B1 correction through separate flip angle mapping.
  Conclusion: A non-interleaved acquisition for normalization of MPRAGE offers
a simple alternative to MP2RAGE to obtain semi-quantitative purely T1-weighted
images. These images can be converted to T1 maps analogously to the established
MP2RAGE approach. Scan time can be reduced by increasing Vref which has a
miniscule effect on image quality.


Abstract:
  Due to the fractal nature of retinal blood vessels, the retinal fractal
dimension is a natural parameter for researchers to explore and has garnered
interest as a potential diagnostic tool. This review aims to summarize the
current scientific evidence regarding the relationship between fractal
dimension and retinal pathology and thus assess the clinical value of retinal
fractal dimension. Following the PRISMA guidelines, a literature search for
research articles was conducted in several internet databases (Embase, PubMed,
Web of Science, Scopus). This led to a result of 28 studies included in the
final review, which were analyzed via meta-analysis to determine whether the
fractal dimension changes significantly in retinal disease versus normal
individuals


Abstract:
  We prove that in each degree divisible by 2 or 3, there are infinitely many
totally real number fields that require universal quadratic forms to have
arbitrarily large rank.


Abstract:
  A new discontinuous model of computation called one-way jumping finite
automata was defined by H. Chigahara et. al. This model was a restricted
version of the model jumping finite automata. These automata read an input
symbol-by-symbol and jump only in one direction. A generalized linear one-way
jumping finite automaton makes jumps after deleting a substring of an input
string and then changes its state. These automata can make sequence of jumps in
only one direction on an input string either from left to right or from right
to left. We show that newly defined model is powerful than its original
counterpart. We define and compare the variants, generalized right linear
one-way jumping finite automata and generalized left linear one-way jumping
finite automata. We also compare the newly defined models with Chomsky
hierarchy. Finally, we explore closure properties of the model.


Abstract:
  In this paper, we explore the stability of the energy landscape of an Ising
Hamiltonian when subjected to two kinds of perturbations: a perturbation on the
coupling coefficients and external fields, and a perturbation on the underlying
graph structure. We give sufficient conditions so that the ground states of a
given Hamiltonian are stable under perturbations of the first kind in terms of
order preservation. Here by order preservation we mean that the ordering of
energy corresponding to two spin configurations in a perturbed Hamiltonian will
be preserved in the original Hamiltonian up to a given error margin. We also
estimate the probability that the energy gap between ground states for the
original Hamiltonian and the perturbed Hamiltonian is bounded by a given error
margin when the coupling coefficients and local external magnetic fields of the
original Hamiltonian are i.i.d. Gaussian random variables. In the end we show a
concrete example of a system which is stable under perturbations of the second
kind.


Abstract:
  Similarity search is a fundamental problem for many data analysis techniques.
Many efficient search techniques rely on the triangle inequality of metrics,
which allows pruning parts of the search space based on transitive bounds on
distances. Recently, Cosine similarity has become a popular alternative choice
to the standard Euclidean metric, in particular in the context of textual data
and neural network embeddings. Unfortunately, Cosine similarity is not metric
and does not satisfy the standard triangle inequality. Instead, many search
techniques for Cosine rely on approximation techniques such as locality
sensitive hashing. In this paper, we derive a triangle inequality for Cosine
similarity that is suitable for efficient similarity search with many standard
search structures (such as the VP-tree, Cover-tree, and M-tree); show that this
bound is tight and discuss fast approximations for it. We hope that this spurs
new research on accelerating exact similarity search for cosine similarity, and
possible other similarity measures beyond the existing work for distance
metrics.


Abstract:
  Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates.
The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly
interacting Bose-Einstein condensates. The GP equation has a form of the
Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii
equations are used to describe some mixtures of Bose-Einstein condensates. In
this paper, we will show some numerical results of coupled Gross-Pitaevskii
equations without self-interaction, which has a form of nonlinearly-coupled
Schroedinger equations. We demonstrate that the macroscopic oscillation and the
interference of two quantum wave packets decay in time owing to mutual
interaction, which is analogous to the decoherence in quantum mechanics of many
particles.


Abstract:
  This paper proposes a very simple deterministic mathematical model, which, by
using a power-law, is a \emph{non-integer power model} (or \emph{fractional
power model (FPM)}). Such a model, in non-integer power of time, namely $t^m$
up to constants, enables representing at each day, with a good precision, the
totality of the contaminated individuals. Despite being enriched with knowledge
through an internal structure based on a geometric sequence "with variable
ratio", the model (in its non-integer representation) has only three
parameters, among which the non-integer power, $m$, that determines on its own,
according to its value, an aggravation or an improvement of the viral
spreading. Its simplicity comes from the power-law, $t^m$, which simply
expresses the singular dynamics of the operator of non-integer differentiation
or integration, of high parametric compactness, that governs diffusion
phenomena and, as shown in this paper, the spreading phenomena by
contamination. The proposed model is indeed validated with the official data of
Ministry of Health on the COVID-19 spreading. Used in prediction, it well
enables justifying the choice of a lockdown, without which the spreading would
have highly worsened. The comparison of this model in $t^m$ with two known
models having the same number of parameters, well shows that its
representativity of the real data is better or more general. Finally, in a more
fundamental context and particularly in terms of complexity and simplicity, a
self-filtering action enables showing the compatibility between the
\emph{internal complexity} that the internal structure and its stochastic
behavior present, and the \emph{global simplicity} that the model in $t^m$
offers in a deterministic manner: it is true that the non-integer power of a
power-law is well a marker of complexity.


Abstract:
  This work focuses on low-energy collision avoidance and formation maintenance
in autonomous swarms of drones. Here, the two main problems are: 1) how to
avoid collisions by temporarily breaking the formation, i.e., collision
avoidance reformation, and 2) how do such reformation while minimizing the
deviation resulting in minimization of the overall time and energy consumption
of the drones. To address the first question, we use cellular automata based
technique to find an efficient formation that avoids the obstacle while
minimizing the time and energy. Concerning the second question, a near-optimal
reformation of the swarm after successful collision avoidance is achieved by
applying a temperature function reduction technique, originally used in the
point set registration process. The goal of the reformation process is to
remove the disturbance while minimizing the overall time it takes for the swarm
to reach the destination and consequently reducing the energy consumption
required by this operation. To measure the degree of formation disturbance due
to collision avoidance, deviation of the centroid of the swarm formation is
used, inspired by the concept of the center of mass in classical mechanics.
Experimental results show the efficiency of the proposed technique, in terms of
performance and energy.


Abstract:
  Despite extensive investigations of dissipation and deformation processes in
micro- and nano- sized metallic samples, the mechanisms at play during
deformation of systems with ultimate, molecular size remain elusive. While
metallic nanojunctions, obtained by stretching metallic wires down to the
atomic level are a system of choice to explore atomic scale contacts, it has
not been possible up to now to extract the full equilibrium and out of
equilibrium rheological flow properties of matter at such scales. Here, by
using a quartz-tuning fork based Atomic Force Microscope (TF-AFM), we combine
electrical and rheological measurement on angstr\"om-size gold junctions to
study the non linear rheology of this model atomic system. By submitting the
junction to increasing sub-nanometric deformations we uncover a transition from
a purely elastic regime to a plastic, and eventually to a viscous-like
fluidized regime, akin to the rheology of soft yielding materials, though
orders of magnitude difference in length scale. The fluidized state furthermore
highlights capillary attraction, as expected for liquid capillary bridges. This
shear fluidization cannot be captured by classical models of friction between
atomic planes, pointing to unexpected dissipative behavior of defect-free
metallic junctions at the ultimate scales. Atomic rheology is therefore a
powerful tool to probe the structural reorganization of atomic contacts.


Abstract:
  Sampling-based motion planners perform exceptionally well in robotic
applications that operate in high-dimensional space. However, most works often
constrain the planning workspace rooted at some fixed locations, do not
adaptively reason on strategy in narrow passages, and ignore valuable local
structure information. In this paper, we propose Rapidly-exploring Random
Forest (RRF*) -- a generalised multi-trees motion planner that combines the
rapid exploring property of tree-based methods and adaptively learns to deploys
a Bayesian local sampling strategy in regions that are deemed to be
bottlenecks. Local sampling exploits the local-connectivity of spaces via
Markov Chain random sampling, which is updated sequentially with a Bayesian
proposal distribution to learns the local structure from past observations. The
trees selection problem is formulated as a multi-armed bandit problem, which
efficiently allocates resources on the most promising tree to accelerate
planning runtime. RRF* learns the region that is difficult to perform tree
extensions and adaptively deploys local sampling in those regions to maximise
the benefit of exploiting local structure. We provide rigorous proofs of
completeness and optimal convergence guarantees, and we experimentally
demonstrate that the effectiveness of RRF*'s adaptive multi-trees approach
allows it to performs well in a wide range of problems.


Abstract:
  We present spatially resolved ($0.1'' - 1.0''$) radio maps of Neptune taken
from the Very Large Array and Atacama Large Submillimeter/Millimeter Array
between $2015-2017$. Combined, these observations probe from just below the
main methane cloud deck at $\sim 1$ bar down to the NH$_4$SH cloud at $\sim50$
bar. Prominent latitudinal variations in the brightness temperature are seen
across the disk. Depending on wavelength, the south polar region is $5-40$ K
brighter than the mid-latitudes and northern equatorial region. We use
radiative transfer modeling coupled to Markov Chain Monte Carlo methods to
retrieve H$_2$S, NH$_3$, and CH$_4$ abundance profiles across the disk, though
only strong constraints can be made for H$_2$S. Below all cloud formation, the
data are well fit by $53.8^{+18.9}_{-13.4}\times$ and $3.9^{+2.1}_{-3.1}\times$
protosolar enrichment in the H$_2$S and NH$_3$ abundances, respectively,
assuming a dry adiabat. Models in which the radio-cold mid-latitudes and
northern equatorial region are supersaturated in H$_2$S are statistically
favored over models following strict thermochemical equilibrium. H$_2$S is more
abundant at the equatorial region than at the poles, indicative of strong,
persistent global circulation. Our results imply that Neptune's
sulfur-to-nitrogen ratio exceeds unity as H$_2$S is more abundant than NH$_3$
in every retrieval. The absence of NH$_3$ above 50 bar can be explained either
by partial dissolution of NH$_3$ in an ionic ocean at GPa pressures or by a
planet formation scenario in which hydrated clathrates preferentially delivered
sulfur rather than nitrogen onto planetesimals, or a combination of these
hypotheses.


Abstract:
  In this article, we use the theory of (non-abelian) exterior product of
Hom-Lie algebras to prove the Hopf formula for these algebras. As an
application, we construct an eight-term sequence in the homology of Hom-Lie
algebras. We also investigate the capability property of Hom-Lie algebras via
the exterior product.


Abstract:
  Earth Trojan Asteroids are an important but elusive population that co-orbit
with Earth at the L4 and L5 Lagrange points. There is only one known, but a
large population is theoretically stable and could provide insight into our
solar system's past and present as well as planetary defense. In this paper, we
present the results of an Earth Trojan survey that uses a novel shift-and-stack
detection method on two nights of data from the Dark Energy Camera. We find no
new Earth Trojan Asteroids. We calculate an upper limit on the population that
is consistent with previous searches despite much less sky coverage.
Additionally, we elaborate on previous upper limit calculations using current
asteroid population statistics and an extensive asteroid simulation to provide
the most up to date population constraints. We find an L4 Earth Trojan
population of NET < 1 for H = 13.93, NET < 7 for H = 16, and NET < 938 for H =
22.


Abstract:
  The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on
compact K\"ahler manifolds that corresponds to the special Lagrangian equation
in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen
proved that the existence of the solution is equivalent to a uniform stability
condition in terms of holomorphic intersection numbers along test families. In
this paper, we establish an analogous stability result not involving a uniform
constant in accordance with a recent work on the $J$-equation by Song, which
makes further progress toward Collins-Jacob-Yau's original conjecture in the
supercritical phase case. In particular, we confirm this conjecture for
projective manifolds in the supercritical phase case.


Abstract:
  The mathematical analysis of random phylogenetic networks via analytic and
algorithmic methods has received increasing attention in the past years. In the
present work we introduce branching process methods to their study. This
approach appears to be new in this context. Our main results focus on random
level-$k$ networks with $n$ labelled leaves. Although the number of
reticulation vertices in such networks is typically linear in $n$, we prove
that their asymptotic global and local shape is tree-like in a well-defined
sense. We show that the depth process of vertices in a large network converges
towards a Brownian excursion after rescaling by $n^{-1/2}$. We also establish
Benjamini--Schramm convergence of large random level-$k$ networks towards a
novel random infinite network.


Abstract:
  The capabilities of natural neural systems have inspired new generations of
machine learning algorithms as well as neuromorphic very large-scale integrated
(VLSI) circuits capable of fast, low-power information processing. However, it
has been argued that most modern machine learning algorithms are not
neurophysiologically plausible. In particular, the workhorse of modern deep
learning, the backpropagation algorithm, has proven difficult to translate to
neuromorphic hardware. In this study, we present a neuromorphic, spiking
backpropagation algorithm based on synfire-gated dynamical information
coordination and processing, implemented on Intel's Loihi neuromorphic research
processor. We demonstrate a proof-of-principle three-layer circuit that learns
to classify digits from the MNIST dataset. To our knowledge, this is the first
work to show a Spiking Neural Network (SNN) implementation of the
backpropagation algorithm that is fully on-chip, without a computer in the
loop. It is competitive in accuracy with off-chip trained SNNs and achieves an
energy-delay product suitable for edge computing. This implementation shows a
path for using in-memory, massively parallel neuromorphic processors for
low-power, low-latency implementation of modern deep learning applications.


Abstract:
  This paper introduces decorated merge trees (DMTs) as a novel invariant for
persistent spaces. DMTs combine both $\pi_0$ and $H_n$ information into a
single data structure that distinguishes filtrations that merge trees and
persistent homology cannot distinguish alone. Three variants on DMTs, which
emphasize category theory, representation theory and persistence barcodes,
respectively, offer different advantages in terms of theory and computation.
Two notions of distance -- an interleaving distance and bottleneck distance --
for DMTs are defined and a hierarchy of stability results that both refine and
generalize existing stability results is proved here. To overcome some of the
computational complexity inherent in these distances, we provide a novel use of
Gromov-Wasserstein couplings to compute optimal merge tree alignments for a
combinatorial version of our interleaving distance which can be tractably
estimated. We introduce computational frameworks for generating, visualizing
and comparing decorated merge trees derived from synthetic and real data.
Example applications include comparison of point clouds, interpretation of
persistent homology of sliding window embeddings of time series, visualization
of topological features in segmented brain tumor images and topology-driven
graph alignment.


Abstract:
  CaCo$_{2-y}$As$_2$ is an unusual itinerant magnet with signatures of extreme
magnetic frustration. The conditions for establishing magnetic order in such
itinerant frustrated magnets, either by reducing frustration or increasing
electronic correlations, is an open question. Here we use results from
inelastic neutron scattering and magnetic susceptibility measurements and
density functional theory calculations to show that hole doping in
Ca(Co$_{1-x}$Fe$_{x}$)$_{2-y}$As$_{2}$ suppresses magnetic order by quenching
the magnetic moment while maintaining the same level of magnetic frustration.
The suppression is due to tuning the Fermi energy away from a peak in the
electronic density of states originating from a flat conduction band. This
results in the complete elimination of the magnetic moment by $x\approx0.25$,
providing a clear example of a Stoner-type transition.


Abstract:
  In a recent work it was shown that conformal Carroll geometries are
canonically equipped with a null-tractor bundle generalizing the tractor bundle
of conformal geometry. We here show that in the case of the conformal boundary
of an asymptotically flat space-time of any dimension d>=3, this null-tractor
bundle over null-infinity can be canonically derived from the bulk geometry. As
was previously discussed, compatible normal connections on the null-tractor
bundle are not unique: We prove that they are in fact in one-to-one
correspondence with the germ of the asymptotically flat space-time to leading
order.
  In dimension d=3 the tractor connection invariantly encodes a choice of mass
and angular momentum aspect, in dimension d>=4 a choice of asymptotic shear. In
dimension $d=4$ the presence of tractor curvature correspond to gravitational
radiations.
  Even thought the construction is by construction geometrical and coordinate
invariant, we give explicit expressions in BMS coordinates for concreteness.


Abstract:
  Abstract. We present a tool to automatically perform the data-size analysis
of imperative programs written in C. This tool, called pymwp, is inspired by a
classical work on complexity analysis [10], and allows to certify that the size
of the values computed by a program will be bounded by a polynomial in the
program's inputs. Strategies to provide meaningful feedback on non-polynomial
programs and to ``tame'' the non-determinism of the original analysis were
implemented following recent progresses [3], but required particular care to
accommodate the growing complexity of the analysis. The Python source code is
intensively documented, and our numerous example files encompass the original
examples as well as multiple test cases. A pip package should make it easy to
install pymwp on any plat-form, but an on-line demo is also available for
convenience.


Abstract:
  At this paper, it is considered to find a way for defining non-commutative
spaces by ordinary commutative ones and vice versa. A novel parameter which has
not been considered so far is represented. This parameter describes equivalent
spaces. Also, we searched concepts of these new parameters with one problem.
Noncommutativity in total space is important here because it could explain more
concepts. As we knew SW method (Seiberg-Witten) explained noncommutativity so
here, we showed that it was not suitable for some conditions.in the end we
considered Hamiltonian of free particle in new noncommutativity and we found
concepts of new parameters.


Abstract:
  Convolutional Neural Networks (CNNs) are the go-to model for computer vision.
Recently, attention-based networks, such as the Vision Transformer, have also
become popular. In this paper we show that while convolutions and attention are
both sufficient for good performance, neither of them are necessary. We present
MLP-Mixer, an architecture based exclusively on multi-layer perceptrons (MLPs).
MLP-Mixer contains two types of layers: one with MLPs applied independently to
image patches (i.e. "mixing" the per-location features), and one with MLPs
applied across patches (i.e. "mixing" spatial information). When trained on
large datasets, or with modern regularization schemes, MLP-Mixer attains
competitive scores on image classification benchmarks, with pre-training and
inference cost comparable to state-of-the-art models. We hope that these
results spark further research beyond the realms of well established CNNs and
Transformers.


Abstract:
  We use linear perturbation theory to study perturbations in dynamical dark
energy models. We compare quintessence and tachyonic dark energy models with
identical background evolution. We write the corresponding equations for
different models in a form that makes it easier to see that the two models are
very hard to distinguish in the linear regime, especially for models with $(1 +
w) \ll 1$. We use Cosmic Microwave Background data and parametric
representations for the two models to illustrate that they cannot be
distinguished for the same background evolution with existing observations.
Further, we constrain tachyonic models with the Planck data. We do this
analysis for exponential and inverse square potentials and find that the
intrinsic parameters of the potentials remain very weakly constrained. In
particular, this is true in the regime allowed by low redshift observations.


Abstract:
  In this article, we study the impact of a change in the type of boundary
conditions of an elliptic boundary value problem. In the context of the
conductivity equation we consider a reference problem with mixed homogeneous
Dirichlet and Neumann boundary conditions. Two different perturbed versions of
this ``background'' situation are investigated, when (i) The homogeneous
Neumann boundary condition is replaced by a homogeneous Dirichlet boundary
condition on a ``small'' subset $\omega_\varepsilon$ of the Neumann boundary;
and when (ii) The homogeneous Dirichlet boundary condition is replaced by a
homogeneous Neumann boundary condition on a ``small'' subset
$\omega_\varepsilon $ of the Dirichlet boundary. The relevant quantity that
measures the ``smallness'' of the subset $\omega_\varepsilon $ differs in the
two cases: while it is the harmonic capacity of $\omega_\varepsilon $ in the
former case, we introduce a notion of ``Neumann capacity'' to handle the
latter. In the first part of this work we derive representation formulas that
catch the structure of the first non trivial term in the asymptotic expansion
of the voltage potential, for a general $\omega_\varepsilon $, under the sole
assumption that it is ``small'' in the appropriate sense. In the second part,
we explicitly calculate the first non trivial term in the asymptotic expansion
of the voltage potential, in the particular geometric situation where the
subset $\omega_\varepsilon $ is a vanishing surfacic ball.


Abstract:
  Recent advances in Computer Vision and Deep Learning have enabled astonishing
results in a variety of fields and applications. Motivated by this success, the
SkyCam Dataset aims to enable image-based Deep Learning solutions for
short-term, precise prediction of solar radiation on a local level. For the
span of a year, three different cameras in three topographically different
locations in Switzerland are acquiring images of the sky every 10 seconds.
Thirteen high resolution images with different exposure times are captured and
used to create an additional HDR image. The images are paired with highly
precise irradiance values gathered from a high-accuracy pyranometer.


Abstract:
  Zero-shot learning (ZSL) aims at understanding unseen categories with no
training examples from class-level descriptions. To improve the discriminative
power of ZSL, we model the visual learning process of unseen categories with
inspiration from the psychology of human creativity for producing novel art.
First, we propose CIZSL-v1 as a creativity inspired model for generative ZSL.
We relate ZSL to human creativity by observing that ZSL is about recognizing
the unseen, and creativity is about creating a likable unseen. We introduce a
learning signal inspired by creativity literature that explores the unseen
space with hallucinated class-descriptions and encourages careful deviation of
their visual feature generations from seen classes while allowing knowledge
transfer from seen to unseen classes. Second, CIZSL-v2 is proposed as an
improved version of CIZSL-v1 for generative zero-shot learning. CIZSL-v2
consists of an investigation of additional inductive losses for unseen classes
along with a semantic guided discriminator. Empirically, we show consistently
that CIZSL losses can improve generative ZSL models on the challenging task of
generalized ZSL from a noisy text on CUB and NABirds datasets. We also show the
advantage of our approach to Attribute-based ZSL on AwA2, aPY, and SUN
datasets. We also show that CIZSL-v2 has improved performance compared to
CIZSL-v1.


Abstract:
  Let $n > 1$. Let $\{U_{ij}\}_{1 \leq i < j \leq n}$ be $\binom{n}{2}$
commuting unitaries on some Hilbert space $\mathcal{H}$, and suppose $U_{ji} :=
U_{ij}^*$, $1 \leq i < j \leq n$. An $n$-tuple of isometries $V = (V_1, \ldots
,V_n)$ on $\mathcal{H}$ is called $\mathcal{U}_n$-twisted isometry with respect
to $\{U_{ij}\}_{i<j}$ (or simply $\mathcal{U}_n$-twisted isometry if
$\{U_{ij}\}_{i<j}$ is clear from the context) if $V_i$'s are in the commutator
$\{U_{st}: s \neq t\}'$, and $V_i^*V_j=U_{ij}^*V_jV_i^*$, $i \neq j$
  We prove that each $\mathcal{U}_n$-twisted isometry admits a von Neumann-Wold
type orthogonal decomposition, and prove that the universal $C^*$-algebra
generated by $\mathcal{U}_n$-twisted isometry is nuclear. We exhibit concrete
analytic models of $\mathcal{U}_n$-twisted isometries, and establish
connections between unitary equivalence classes of the irreducible
representations of the $C^*$-algebras generated by $\mathcal{U}_n$-twisted
isometries and the unitary equivalence classes of the non-zero irreducible
representations of twisted noncommutative tori. Our motivation of
$\mathcal{U}_n$-twisted isometries stems from the classical rotation
$C^*$-algebras, Heisenberg group $C^*$-algebras, and a recent work of de Jeu
and Pinto.


Abstract:
  This note shows that the category of truncated spaces with finite homotopy
invariants (aka truncated coherent spaces, or truncated pi-finite spaces) has
many of the expected features of what should be an elementary infinity-topos.
It should be thought as the natural higher analogue of the elementary topos of
finite sets.


Abstract:
  As a step to establish the blockwise Alperin weight conjecture for all finite
groups, we verify the inductive blockwise Alperin weight condition introduced
by Navarro--Tiep and Sp\"ath for simple groups of Lie type $\mathsf A$, split
or twisted. Key to the proofs is to reduce the verification of the inductive
condition to the isolated (that means unipotent) blocks, using the Jordan
decomposition for blocks of finite reductive groups given by Bonnaf\'e, Dat and
Rouquier.


Abstract:
  In this article, we establish a near-optimal convergence rate for the CLT of
linear eigenvalue statistics of Wigner matrices, in Kolmogorov-Smirnov
distance. For all test functions $f\in C^5(\mathbb R)$, we show that the
convergence rate is either $N^{-1/2+\varepsilon}$ or $N^{-1+\varepsilon}$,
depending on the first Chebyshev coefficient of $f$ and the third moment of the
diagonal matrix entries. The condition that distinguishes these two rates is
necessary and sufficient. For a general class of test functions, we further
identify matching lower bounds for the convergence rates. In addition, we
identify an explicit, non-universal contribution in the linear eigenvalue
statistics, which is responsible for the slow rate $N^{-1/2+\varepsilon}$ for
non-Gaussian ensembles. By removing this non-universal part, we show that the
shifted linear eigenvalue statistics have the unified convergence rate
$N^{-1+\varepsilon}$ for all test functions.