Abstract:
  Plastic scintillators are widely used in particle detectors when precise
timing information is required. As a basis for comparing different detectors we
use such a characteristic as the time resolution per 1MeV detected energy, i.e.
the expected time resolution assuming the deposited energy in the scintillator
equals to 1MeV and all the scintillation light is collected to the photosensor.
In this work we measure this parameter with BC422 plastic scintillator read out
by different SiPMs. The best obtained value is about 6ps, which is almost a
factor of 3 better compared to our earlier result from 2012. Such an
improvement represents the progress in the development of SiPMs made over these
years and, driven by this progress, an improved knowledge and know-how on such
detectors.


Abstract:
  Semi-supervision in Machine Learning can be used in searches for new physics
where the signal plus background regions are not labelled. This strongly
reduces model dependency in the search for signals Beyond the Standard Model.
This approach displays the drawback in that over-fitting can give rise to fake
signals. Tossing toy Monte Carlo (MC) events can be used to estimate the
corresponding trials factor through a frequentist inference. However, MC events
that are based on full detector simulations are resource intensive. Generative
Adversarial Networks (GANs) can be used to mimic MC generators. GANs are
powerful generative models, but often suffer from training instability. We
henceforth show a review of GANs. We advocate the use of Wasserstein GAN (WGAN)
with weight clipping and WGAN with gradient penalty (WGAN-GP) where the norm of
gradient of the critic is penalized with respect to its input. Following the
emergence of multi-lepton anomalies, we apply GANs for the generation of
di-leptons final states in association with $b$-quarks at the LHC. A good
agreement between the MC and the WGAN-GP generated events is found for the
observables selected in the study.


Abstract:
  Detection of entanglement in quantum states is one of the most important
problems in quantum information processing. However, it is one of the most
challenging tasks to find a universal scheme which is also desired to be
optimal to detect entanglement for all states of a specific class--as always
preferred by experimentalists. Although, the topic is well studied at least in
case of lower dimensional compound systems, e.g., two-qubit systems, but in the
case of continuous variable systems, this remains as an open problem. Even in
the case of two-mode Gaussian states, the problem is not fully solved. In our
work, we have tried to address this issue. At first, a limited number of
Hermitian operators is given to test the necessary and sufficient criterion on
the covariance matrix of separable two-mode Gaussian states. Thereafter, we
present an interferometric scheme to test the same separability criterion in
which the measurements are being done via Stokes-like operators. In such case,
we consider only single-copy measurements on a two-mode Gaussian state at a
time and the scheme amounts to the full state tomography. Although this latter
approach is a linear optics based one, nevertheless it is not an economic
scheme. Resource-wise a more economical scheme than the full state tomography
is obtained if we consider measurements on two copies of the state at a time.
However, optimality of the scheme is not yet known.


Abstract:
  In this paper we study the $\mathbb{C}^*$-fixed points in moduli spaces of
Higgs bundles over a compact Riemann surface for a complex semisimple Lie group
and its real forms. These fixed points are called Hodge bundles and correspond
to complex variations of Hodge structure. We introduce a topological invariant
for Hodge bundles that generalizes the Toledo invariant appearing for Hermitian
Lie groups. A main result of this paper is a bound on this invariant which
generalizes both the Milnor-Wood inequality of the Hermitian case and the
Arakelov inequalities of classical variations of Hodge structure. When the
generalized Toledo invariant is maximal, we establish rigidity results for the
associated variations of Hodge structure which generalize known rigidity
results for maximal Higgs bundles and their associated maximal representations
in the Hermitian case.


Abstract:
  We derive conditions for the existence of fixed points of nonnegative neural
networks, an important research objective to understand the behavior of neural
networks in modern applications involving autoencoders and loop unrolling
techniques, among others. In particular, we show that neural networks with
nonnegative inputs and nonnegative parameters can be recognized as monotonic
and (weakly) scalable functions within the framework of nonlinear
Perron-Frobenius theory. This fact enables us to derive conditions for the
existence of a nonempty fixed point set of the nonnegative neural networks, and
these conditions are weaker than those obtained recently using arguments in
convex analysis, which are typically based on the assumption of nonexpansivity
of the activation functions. Furthermore, we prove that the shape of the fixed
point set of monotonic and weakly scalable neural networks is often an
interval, which degenerates to a point for the case of scalable networks. The
chief results of this paper are verified in numerical simulations, where we
consider an autoencoder-type network that first compresses angular power
spectra in massive MIMO systems, and, second, reconstruct the input spectra
from the compressed signals.


Abstract:
  We present a first-principles computational study of cation-Se $\Sigma$3
(112) grain boundaries in CuGaSe$_2$. We discuss the structure of these grain
boundaries, as well as the effect of native defects and Na impurities on their
electronic properties. The formation energies show that the defects will tend
to form preferentially at the grain boundaries, rather than in the grain
interiors. We find that in Ga-rich growth conditions Cu vacancies as well as Ga
at Cu and Cu at Ga antisites are mainly responsible for having the equilibrium
Fermi level pinned toward the middle of the gap, resulting in carrier
depletion. The Na at Cu impurity in its +1 charge state contributes to this. In
Ga-poor growth conditions, on the other hand, the formation energies of Cu
vacancies and Ga at Cu antisites are comparatively too high for any significant
influence on carrier density or on the equilibrium Fermi level position. Thus,
under these conditions, the Cu at Ga antisites give rise to a $p$-type grain
boundary. Also, their formation energy is lower than the formation energy of Na
at Cu impurities. Thus, the latter will fail to act as a hole barrier
preventing recombination at the grain boundary, in contrast to what occurs in
CuInSe$_2$ grain boundaries. We also discuss the effect of the defects on the
electronic properties of bulk CuGaSe$_2$, which we assume reflect the
properties of the grain interiors.


Abstract:
  Background and Objective: The new type of coronavirus is also called
COVID-19. It began to spread at the end of 2019 and has now spread across the
world. Until October 2020, It has infected around 37 million people and claimed
about 1 million lives. We propose a deep learning model that can help
radiologists and clinicians use chest X-rays to diagnose COVID-19 cases and
show the diagnostic features of pneumonia. Methods: The approach in this study
is: 1) we propose a data enhancement method to increase the diversity of the
data set, thereby improving the generalization performance of the model. 2) Our
deep convolution neural network model DPN-SE adds a self-attention mechanism to
the DPN network. The addition of a self-attention mechanism has greatly
improved the performance of the network. 3) Use the Lime interpretable library
to mark the feature regions on the X-ray medical image that helps doctors more
quickly diagnose COVID-19 in people. Results: Under the same network model, the
data with and without data enhancement is put into the model for training
respectively. At last, comparing two experimental results: among the 10 network
models with different structures, 7 network models have improved their effects
after using data enhancement, with an average improvement of 1% in recognition
accuracy. We propose that the accuracy and recall rates of the DPN-SE network
are 93% and 98% of cases (COVID vs. pneumonia bacteria vs. viral pneumonia vs.
normal). Compared with the original DPN, the respective accuracy is improved by
2%. Conclusion: The data augmentation method we used has achieved effective
results on a small amount of data set, showing that a reasonable data
augmentation method can improve the recognition accuracy without changing the
sample size and model structure. Overall, the proposed method and model can
effectively become a very useful tool for clinical radiologists.


Abstract:
  This paper has three main aims: first, to give a pedagogical introduction to
Noether's two theorems and their implications for energy conservation in
general relativity, which was a central point of discussion between Hilbert,
Klein, Noether and Einstein. Second, it introduces and compares two proposals
for gravitational energy and momentum, one of which is very influential in
physics: and, so far as I know, neither of the two has been discussed in the
philosophical literature. Third, it assesses these proposals in connection with
recent philosophical discussions of energy and momentum in general relativity.
  After briefly reviewing the debates about energy conservation between
Hilbert, Klein, Noether and Einstein, I give Noether's two theorems. I show
that Einstein's gravitational energy-momentum pseudo-tensor, including its
superpotential, is fixed, through Noether's theorem, by the boundary terms in
the action. That is, the freedom to add an arbitrary superpotential to the
gravitational pseudo-tensor corresponds to the freedom to add boundary terms to
the action without changing the equations of motion. This freedom is fixed in
the same way for both problems. I also review two proposals for energy and
momentum in GR, of which one is a quasi-local alternative to the local
expressions, and the other builds on Einstein's local pseudo-tensor approach. I
discuss the recent philosophical literature on the conservation of energy and
momentum in general relativity, and I assess and compare the two proposals in
the light of this literature: especially, in light of questions about
diffeomorphism invariance and background-independence.


Abstract:
  It is well-known that the chances of success of SETI depend on the longevity
of technological civilizations or, more broadly, on the duration of the signs
of their existence, or technosignatures. Here, we re-examine this general tenet
in more detail, and we show that its broader implications were not given the
proper significance. In particular, an often overlooked aspect is that the
duration of a technosignature is in principle almost entirely separable from
the age of the civilization that produces it. We propose a classification
scheme of technosignatures based on their duration and, using Monte Carlo
simulations, we show that, given an initial generic distribution of Galactic
technosignatures, only the ones with the longest duration are likely to be
detected. This tells us, among other things, that looking for a large number of
short-lived technosignatures is a weaker observational strategy than focusing
the search on a few long-lived ones. It also suggests to abandon any
anthropocentric bias in approaching the question of extraterrestrial
intelligence. We finally give some ideas of possible pathways that can lead to
the establishment of long-lived technosignatures.


Abstract:
  We apply the specialization technique based on the decomposition of the
diagonal to find an explicit example over $\mathbb{Q}$ of a quadric and cubic
hypersurface in $\mathbb{P}^6$ such that their intersection is a smooth stably
irrational fourfold. Using the same degeneration, Nicaise and Ottem have
already proven that the the very general complete intersection of this type is
stably irrational using the motivic volume.


Abstract:
  A constellation of $N=d-1$ Majorana stars represents an arbitrary pure
quantum state of dimension $d$ or a permutation-symmetric state of a system
consisting of $n$ qubits. We generalize the latter construction to represent in
a similar way an arbitrary symmetric pure state of $k$ subsystems with $d$
levels each. For $d\geq 3$, such states are equivalent, as far as rotations are
concerned, to a collection of various spin states, with definite relative
complex weights. Following Majorana's lead, we introduce a multiconstellation,
consisting of the Majorana constellations of the above spin states, augmented
by an auxiliary, "spectator" constellation, encoding the complex weights.
Examples of stellar representations of symmetric states of four qutrits, and
two spin-$3/2$ systems, are presented. We revisit the Hermite and Murnaghan
isomorphisms, which relate multipartite states of various spins, number of
parties, and even symmetries. We show how the tools introduced can be used to
analyze multipartite entanglement and to identify optimal quantum rotosensors,
i.e., pure states which are maximally sensitive to rotations around a specified
axis, or averaged over all axes.


Abstract:
  Recently, pre-training multilingual language models has shown great potential
in learning multilingual representation, a crucial topic of natural language
processing. Prior works generally use a single mixed attention (MA) module,
following TLM (Conneau and Lample, 2019), for attending to intra-lingual and
cross-lingual contexts equivalently and simultaneously. In this paper, we
propose a network named decomposed attention (DA) as a replacement of MA. The
DA consists of an intra-lingual attention (IA) and a cross-lingual attention
(CA), which model intralingual and cross-lingual supervisions respectively. In
addition, we introduce a language-adaptive re-weighting strategy during
training to further boost the model's performance. Experiments on various
cross-lingual natural language understanding (NLU) tasks show that the proposed
architecture and learning strategy significantly improve the model's
cross-lingual transferability.


Abstract:
  Considering Limit Cycles as one of the limits of Lienard equation, an analyis
analogous to centre manifold analysis has been done for a $3-D$ nonlinear
system exhibiting Limit Cycle. A rigorous study on radius of the Limit Cycle
orbit has been done by considering $\lambda-\omega$ equations for the
particular system and subsequently converting the system equations from
cartesian to polar form. It has been shown through an analysis analogous to
Centre Manifold Analysis and reduction of the system dynamics on a lower
dimensional space, the Limit cycle radius undergoes an increment change. One
example is provided to support the theoretical predictions.


Abstract:
  In this paper, we propose to use the HLL finite volume scheme combined with
implicit techniques for modelling the coupled surface and subsurface water
flows. In our approach, we used the shallow water equations modelling surface
water flow with different source terms such as variable bottom topography,
friction effect, precipitation and infiltration. For subsurface water flow, the
Green-Amp equation is used to simulate the infiltration process through soils.
For solving the resulting nonlinear-coupled system of shallow water flow and
the Green-Ampt infiltration equations, the HLL finite volume schemes with
linear reconstructions of the solutions at the discrete level are implemented
in order to achieve the second-order accuracy of the scheme. Appropriate
discretization techniques are used for the source terms to guarantee the
well-balanced property of our numerical scheme. Numerical experiments are
performed to test the capability of the developed numerical scheme to simulate
the coupled surface and subsurface water flows.


Abstract:
  The UNESCO World Heritage List (WHL) includes the exceptionally valuable
cultural and natural heritage to be preserved for mankind. Evaluating and
justifying the Outstanding Universal Value (OUV) is essential for each site
inscribed in the WHL, and yet a complex task, even for experts, since the
selection criteria of OUV are not mutually exclusive. Furthermore, manual
annotation of heritage values and attributes from multi-source textual data,
which is currently dominant in heritage studies, is knowledge-demanding and
time-consuming, impeding systematic analysis of such authoritative documents in
terms of their implications on heritage management. This study applies
state-of-the-art NLP models to build a classifier on a new dataset containing
Statements of OUV, seeking an explainable and scalable automation tool to
facilitate the nomination, evaluation, research, and monitoring processes of
World Heritage sites. Label smoothing is innovatively adapted to improve the
model performance by adding prior inter-class relationship knowledge to
generate soft labels. The study shows that the best models fine-tuned from BERT
and ULMFiT can reach 94.3% top-3 accuracy. A human study with expert evaluation
on the model prediction shows that the models are sufficiently generalizable.
The study is promising to be further developed and applied in heritage research
and practice.


Abstract:
  Motivated by the recent discovery of a dispersive-to-nondispersive transition
for linear waves in shear flows, we accurately explored the wavenumber-Reynolds
number parameter map of the plane Poiseuille flow, in the limit of least-damped
waves. We have discovered the existence of regions of the map where the
dispersion and propagation features vary significantly from their surroundings.
These regions are nested in the dispersive, low-wavenumber part of the map.
This complex dispersion scenario demonstrates the existence of linear
dispersive focusing in wave envelopes evolving out of an initial, spatially
localized, three-dimensional perturbation. An asymptotic wave packet's
representation, based on the saddle-point method, allows to enlighten the
nature of the packet's morphology, in particular the arrow-shaped structure and
spatial spreading rates. A correlation is also highlighted between the regions
of largest dispersive focusing and the regions which are most subject to strong
nonlinear coupling in observations.


Abstract:
  In this article we compute analytically the number of Nash Equilibria (NE)
for a two-choice game played on a (circular) ladder graph with $2n$ players. We
consider a set of games with generic payoff parameters, with the only
requirement that a NE occurs if the players choose opposite strategies
(anti-coordination game). The results show that for both, the ladder and
circular ladder, the number of NE grows exponentially with (half) the number of
players $n$, as $N_{NE}(2n)\sim C(\varphi)^n$, where $\varphi=1.618..$ is the
golden ratio and $C_{circ}>C_{ladder}$. In addition, the value of the scaling
factor $C_{ladder}$ depends on the value of the payoff parameters. However,
that is no longer true for the circular ladder (3-degree graph), that is
$C_{circ}$ is constant, which might suggest that the topology of the graph
indeed plays an important role for setting the number of NE.


Abstract:
  We consider solving a generalized Allen-Cahn equation coupled with a passive
convection for a given incompressible velocity field. The numerical scheme
consists of the first order accurate stabilized implicit explicit time
discretization and a fourth order accurate finite difference scheme, which is
obtained from the finite difference formulation of the $Q^2$ spectral element
method. We prove that the discrete maximum principle holds under suitable mesh
size and time step constraints. The same result also applies to construct a
bound-preserving scheme for any passive convection with an incompressible
velocity field.


Abstract:
  We propose a new method for estimating the relative pose between two images,
where we jointly learn keypoint detection, description extraction, matching and
robust pose estimation. While our architecture follows the traditional pipeline
for pose estimation from geometric computer vision, all steps are learnt in an
end-to-end fashion, including feature matching. We demonstrate our method for
the task of visual localization of a query image within a database of images
with known pose. Pairwise pose estimation has many practical applications for
robotic mapping, navigation, and AR. For example, the display of persistent AR
objects in the scene relies on a precise camera localization to make the
digital models appear anchored to the physical environment. We train our
pipeline end-to-end specifically for the problem of visual localization. We
evaluate our proposed approach on localization accuracy, robustness and runtime
speed. Our method achieves state of the art localization accuracy on the 7
Scenes dataset.


Abstract:
  We investigate how symmetries and conserved quantities relate to the
occurrence of the boundary time crystal (BTC) phase in a generalized spin model
with Lindblad dissipation. BTCs are a non-equilibrium phase of matter in which
the system, coupled to an external environment, breaks the continuous time
translational invariance. We perform a detailed mean-field study aided by a
finite-size analysis of the quantum model of a p,q-spin-interaction system, a
generalized p-spin interaction system, which can be implemented in
fully-connected spin-1/2 ensembles. We find the following conditions for the
observation of the BTC phase: First, the BTC appears when the discrete symmetry
held by the Hamiltonian, $\mathbb{Z}_2$ in the considered models, is explicitly
broken by the Lindblad jump operators. Second, the system must be coupled
uniformly to the same bath in order to preserve the total angular momentum
during the time evolution. If these conditions are not satisfied, any
oscillatory behavior appears only as a transient in the dynamics and a
time-independent stationary state is eventually reached. Our results suggest
that these two elements may be general requirements for the observation of a
stable BTC phase relating symmetries and conserved quantities in arbitrary spin
models.


Abstract:
  We establish a non-local integral difference quotient representation for
symmetric gradient semi-norms in $BD(\Omega)$ and $LD(\Omega)$, which does not
require the manipulation of distributional derivatives. Our representation
extends the formulas for the symmetric gradient established by Mengesha for
vector-fields in $W^{1,p}(\Omega;\mathbb R^d)$, which are inspired by the
gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in
$W^{1,p}(\Omega)$ and by D\'avila in $BV(\Omega)$.


Abstract:
  In this paper, we develop a family of third order asymptotic-preserving (AP)
and asymptotically accurate (AA) diagonally implicit Runge-Kutta (DIRK) time
discretization methods for the stiff hyperbolic relaxation systems and kinetic
Bhatnagar-Gross-Krook (BGK) model in the semi-Lagrangian (SL) setting. The
methods are constructed based on an accuracy analysis of the SL scheme for
stiff hyperbolic relaxation systems and kinetic BGK model in the limiting fluid
regime when the Knudsen number approaches $0$. An extra order condition for the
asymptotic third order accuracy in the limiting regime is derived. Linear Von
Neumann stability analysis of the proposed third order DIRK methods are
performed to a simplified two-velocity linear kinetic model. Extensive
numerical tests are presented to demonstrate the AA, AP and stability
properties of our proposed schemes.


Abstract:
  We study families of depth measures defined by natural sets of axioms. We
show that any such depth measure is a constant factor approximation of Tukey
depth. We further investigate the dimensions of depth regions, showing that the
Cascade conjecture, introduced by Kalai for Tverberg depth, holds for all depth
measures which satisfy our most restrictive set of axioms, which includes Tukey
depth. Along the way, we introduce and study a new depth measure called
enclosing depth, which we believe to be of independent interest, and show its
relation to a constant-fraction Radon theorem on certain two-colored point
sets.


Abstract:
  Following the recent surge in adoption of machine learning (ML), the negative
impact that improper use of ML can have on users and society is now also widely
recognised. To address this issue, policy makers and other stakeholders, such
as the European Commission or NIST, have proposed high-level guidelines aiming
to promote trustworthy ML (i.e., lawful, ethical and robust). However, these
guidelines do not specify actions to be taken by those involved in building ML
systems. In this paper, we argue that guidelines related to the development of
trustworthy ML can be translated to operational practices, and should become
part of the ML development life cycle. Towards this goal, we ran a multi-vocal
literature review, and mined operational practices from white and grey
literature. Moreover, we launched a global survey to measure practice adoption
and the effects of these practices. In total, we identified 14 new practices,
and used them to complement an existing catalogue of ML engineering practices.
Initial analysis of the survey results reveals that so far, practice adoption
for trustworthy ML is relatively low. In particular, practices related to
assuring security of ML components have very low adoption. Other practices
enjoy slightly larger adoption, such as providing explanations to users. Our
extended practice catalogue can be used by ML development teams to bridge the
gap between high-level guidelines and actual development of trustworthy ML
systems; it is open for review and contribution


Abstract:
  Distribution network topology detection and state estimation in real-time are
critical for modern distribution systems management and control. However,
number of sensors in distribution networks are limited and communication links
between switch devices and distribution management system are not
well-established. In this regard, this paper proposes mixed-integer quadratic
programming (MIQP) formulations to determine the topology of distribution
network and estimate distribution system states simultaneously using
micro-phasor measurement units (micro-PMUs) and smart meter data. Two
approaches based on AC optimal power flow are proposed and analyzed: (i) polar
power-voltage (PPV) formulation, and (ii) rectangular current-voltage (RIV)
formulation. The proposed models include convex objective function while
constraints are linearized using first-order approximation of Taylor series and
Big M method. The proposed models can identify multiple simultaneous switching
actions at each time instant and different topology configurations including
radial and meshed networks. Only measurement data at each time interval is
needed to identify topology and states of the system correctly. The proposed
models are tested on a modified IEEE-33 bus system with realistic load data
from Pecan Street Inc. database. The results confirm that both models can
identify system topology and states with remarkable accuracy in real-time,
while RIV model outperforms PPV model.


Abstract:
  In the present study, simulations are directed to capture the dynamics of
evacuating inner gas of a bubble bursting at the free surface, using Eulerian
based volume of fluid (VOF) method. The rate by which surrounding air rushing
inside the bubble cavity through the inner gas evacuation is estimated and
compared by the collapsing bubble cavity during the sequential stages of the
bubble bursting at the free surface. Further, the reachability of inner gas
over the free surface is evaluated by establishing the comparison of the same
through various horizontal planes, lying at different altitudes above the
unperturbed surface. The evacuating inner gas accompanies vortex rings, which
entrains the surrounding gas-phase. During the successive stages of air
entrainment, spatiotemporal characteristics of the vortex ring are obtained. At
low Bond numbers (< 1), after comparing the phase contours of evacuating inner
gas from the bubble cavity, the consequences at the axial growth of gas jet and
the radial expansion of the jet tip is discussed separately. Furthermore, under
the respiration process, the axial growth of rising inner gas over the free
surface and the radial expansion of vortex rings of a bubble bursting at the
free surface is compared with the quiescent surrounding air. At last, the
effects of various possible asymmetric perforation of the bubble cap keeping
the same Bo are studied. The cause of bent gas jet, as a consequence of
perforation of the bubble cap, asymmetrically, is explained by plotting the
velocity vectors.


Abstract:
  Thanks to the combination of state-of-the-art accelerators and highly
optimized open software frameworks, there has been tremendous progress in the
performance of deep neural networks. While these developments have been
responsible for many breakthroughs, progress towards solving large-scale
problems, such as video encoding and semantic segmentation in 3D, is hampered
because access to on-premise memory is often limited. Instead of relying on
(optimal) checkpointing or invertibility of the network layers -- to recover
the activations during backpropagation -- we propose to approximate the
gradient of convolutional layers in neural networks with a multi-channel
randomized trace estimation technique. Compared to other methods, this approach
is simple, amenable to analyses, and leads to a greatly reduced memory
footprint. Even though the randomized trace estimation introduces stochasticity
during training, we argue that this is of little consequence as long as the
induced errors are of the same order as errors in the gradient due to the use
of stochastic gradient descent. We discuss the performance of networks trained
with stochastic backpropagation and how the error can be controlled while
maximizing memory usage and minimizing computational overhead.


Abstract:
  We present ASTRODEEP-GS43, a new multiwavelength photometric catalogue of the
GOODS-South field, which builds and improves upon the previously released
CANDELS catalogue. We provide photometric fluxes and corresponding
uncertainties in 43 optical and infrared bands (25 wide and 18 medium filters),
as well as photometric redshifts and physical properties of the 34930 CANDELS
$H$-detected objects, plus an additional sample of 178 $H$-dropout sources, of
which 173 are $Ks$-detected and 5 IRAC-detected. We keep the CANDELS photometry
in 7 bands (CTIO $U$, Hubble Space Telescope WFC3 and ISAAC-$K$), and measure
from scratch the fluxes in the other 36 (VIMOS, HST ACS, HAWK-I $Ks$, Spitzer
IRAC, and 23 from Subaru SuprimeCAM and Magellan-Baade Fourstar) with
state-of-the-art techniques of template-fitting. We then compute new
photometric redshifts with three different software tools, and take the median
value as best estimate. We finally evaluate new physical parameters from SED
fitting, comparing them to previously published ones. Comparing to a sample of
3931 high quality spectroscopic redshifts, for the new photo-$z$'s we obtain a
normalized median absolute deviation (NMAD) of 0.015 with 3.01$\%$ of outliers
(0.011, 0.22$\%$ on the bright end at $I814$<22.5), similarly to the best
available published samples of photometric redshifts, such as the COSMOS
UltraVISTA catalogue. The ASTRODEEP-GS43 results are in qualitative agreement
with previously published catalogues of the GOODS-South field, improving on
them particularly in terms of SED sampling and photometric redshift estimates.
The catalogue is available for download from the Astrodeep website.


Abstract:
  In chemical graph theory, caterpillar trees have been an appealing model to
represent the molecular structures of benzenoid hydrocarbon. Meanwhile,
topological index has been thought of as a powerful tool for modeling
quantitative structure-property relationship and quantitative
structure-activity between molecules in chemical compounds. In this article, we
consider a class of caterpillar trees that are incorporated with randomness,
called random caterpillars, and investigate several popular topological indices
of this random class, including Zagreb index, Randi\'{c} index and Wiener
index, etc. Especially, a central limit theorem is developed for the asymptotic
distribution of the Zagreb index of random caterpillars.


Abstract:
  Quasi-one-dimensional (1D) materials provide a superior platform for
characterizing and tuning topological phases for two reasons: i) existence for
multiple cleavable surfaces that enables better experimental identification of
topological classification, and ii) stronger response to perturbations such as
strain for tuning topological phases compared to higher dimensional crystal
structures. In this paper, we present experimental evidence for a
room-temperature topological phase transition in the quasi-1D material
Bi$_4$I$_4$, mediated via a first order structural transition between two
distinct stacking orders of the weakly-coupled chains. Using high resolution
angle-resolved photoemission spectroscopy on the two natural cleavable
surfaces, we identify the high temperature $\beta$ phase to be the first weak
topological insulator with gapless Dirac cones on the (100) surface and no
Dirac crossing on the (001) surface, while in the low temperature $\alpha$
phase, the topological surface state on the (100) surface opens a gap,
consistent with a recent theoretical prediction of a higher-order topological
insulator beyond the scope of the established topological materials databases
that hosts gapless hinge states. Our results not only identify a rare
topological phase transition between first-order and second-order topological
insulators but also establish a novel quasi-1D material platform for exploring
unprecedented physics.


Abstract:
  This paper develops new tools to quantify uncertainty in optimal decision
making and to gain insight into which variables one should collect information
about given the potential cost of measuring a large number of variables. We
investigate simultaneous inference to determine if a group of variables is
relevant for estimating an optimal decision rule in a high-dimensional
semiparametric framework. The unknown link function permits flexible modeling
of the interactions between the treatment and the covariates, but leads to
nonconvex estimation in high dimension and imposes significant challenges for
inference. We first establish that a local restricted strong convexity
condition holds with high probability and that any feasible local sparse
solution of the estimation problem can achieve the near-oracle estimation error
bound. We further rigorously verify that a wild bootstrap procedure based on a
debiased version of the local solution can provide asymptotically honest
uniform inference for the effect of a group of variables on optimal decision
making. The advantage of honest inference is that it does not require the
initial estimator to achieve perfect model selection and does not require the
zero and nonzero effects to be well-separated. We also propose an efficient
algorithm for estimation. Our simulations suggest satisfactory performance. An
example from a diabetes study illustrates the real application.


Abstract:
  We study a simple lattice model with local symmetry, whose construction is
based on a crossed module of finite groups. Its dynamical degrees of freedom
are associated both to links and faces of a four-dimensional lattice. In
special limits the discussed model reduces to certain known topological quantum
field theories. In this work we focus on its dynamics, which we study both
analytically and using Monte Carlo simulations. We prove a factorization
theorem which reduces computation of correlation functions of local observables
to known, simpler models. This, combined with standard Krammers-Wannier type
dualities, allows us to propose a detailed phase diagram, which form is then
confirmed in numerical simulations. We describe also topological charges
present in the model, its symmetries and symmetry breaking patterns. The
corresponding order parameters are the Polyakov loop and its generalization,
which we call a Polyakov surface. The latter is particularly interesting, as it
is beyond the scope of the factorization theorem. As shown by the numerical
results, expectation value of Polyakov surface may serve to detects all phase
transitions and is sensitive to a value of the topological charge.


Abstract:
  Despite the proliferation of mobile devices in various wide-area Internet of
Things applications (e.g., smart city, smart farming), current Low-Power
Wide-Area Networks (LPWANs) are not designed to effectively support mobile
nodes. In this paper, we propose to handle mobility in SNOW (Sensor Network
Over White spaces), an LPWAN that operates in the TV white spaces. SNOW
supports massive concurrent communication between a base station (BS) and
numerous low-power nodes through a distributed implementation of OFDM. In SNOW,
inter-carrier interference (ICI) is more pronounced under mobility due to its
OFDM based design. Geospatial variation of white spaces also raises challenges
in both intra- and inter-network mobility as the low-power nodes are not
equipped to determine white spaces. To handle mobility impacts on ICI, we
propose a dynamic carrier frequency offset estimation and compensation
technique which takes into account Doppler shifts without requiring to know the
speed of the nodes. We also propose to circumvent the mobility impacts on
geospatial variation of white space through a mobility-aware spectrum
assignment to nodes. To enable mobility of the nodes across different SNOWs, we
propose an efficient handoff management through a fast and energy-efficient BS
discovery and quick association with the BS by combining time and frequency
domain energy-sensing. Experiments through SNOW deployments in a large
metropolitan city and indoors show that our proposed approaches enable mobility
across multiple different SNOWs and provide robustness in terms of reliability,
latency, and energy consumption under mobility.


Abstract:
  A long-standing goal of materials science is to understand, predict and
control the evolution of microstructures in crystalline materials. Most
microstructure evolution is controlled by interface motion; hence, the
establishment of rigorous interface equations of motion is a universal goal of
materials science. We present a new model for the motion of arbitrarily curved
interfaces that respects the underlying crystallography of the two
phases/domains meeting at the interface and is consistent with microscopic
mechanisms of interface motion; i.e., disconnection migration (line defects in
the interface with step and dislocation character). We derive the equation of
motion for interface migration under the influence of a wide range of driving
forces. In Part II of this paper [Salvalaglio, Han and Srolovitz, 2021], we
implement the interface model and the equation of motion proposed in this paper
in a diffuse interface simulation approach for complex morphology and
microstructure evolution.


Abstract:
  We identify a class of modal solutions for spatio-temporal optical vortex
(STOV) electromagnetic pulses propagating in dispersive media with orbital
angular momentum (OAM) orthogonal to propagation. We find that symmetric STOVs
in vacuum can carry half-integer intrinsic orbital angular momentum (OAM); for
general asymmetric STOVs in a dispersive medium, the OAM is quantized in
integer multiples of a parameter that depends on the STOV symmetry and the
group velocity dispersion. Our results suggest that STOVs propagating in
dispersive media are accompanied by a polariton-like quasiparticle. The modal
theory is in excellent agreement with measurements of free space propagation of
STOVs.


Abstract:
  In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$
zero rest-mass equations on Minkowski spacetime by using the conformal
geometric method. In our strategy, we prove the wellposedness of the Cauchy
problem in Einstein's cylinder. Then we establish pointwise decays of the
fields and prove the energy equalities of the conformal fields between the null
conformal boundaries $\scri^\pm$ and the hypersurface $\Sigma_0=\left\{ t=0
\right\}$. Finally, we prove the wellposedness of the Goursat problem in the
partial conformal compactification by using the energy equalities and the
generalisation of H\"ormander's result.


Abstract:
  Recent work demonstrated the lack of robustness of optical flow networks to
physical, patch-based adversarial attacks. The possibility to physically attack
a basic component of automotive systems is a reason for serious concerns. In
this paper, we analyze the cause of the problem and show that the lack of
robustness is rooted in the classical aperture problem of optical flow
estimation in combination with bad choices in the details of the network
architecture. We show how these mistakes can be rectified in order to make
optical flow networks robust to physical, patch-based attacks. Additionally, we
take a look at global white-box attacks in the scope of optical flow. We find
that targeted white-box attacks can be crafted to bias flow estimation models
towards any desired output, but this requires access to the input images and
model weights. Our results indicate that optical flow networks are robust to
universal attacks.


Abstract:
  In this paper, for a family of second-order elliptic equations with rapidly
oscillating periodic coefficients, we are interested in a Carleman-type
inequality for these solutions satisfying an additional growth condition in
elliptic periodic homogenization, which implies a three-ball inequality without
an error term at a macroscopic scale. Moreover, if we replace the additional
growth condition by the doubling condition at a macroscopic scale, then the
three-ball inequality without an error term holds at any scale. The proof
relies on the convergence of $H^1$-norm for the solution and the compactness
argument.


Abstract:
  A detailed numerical study on the phenomenon of Shock Wave focusing in air is
carried out. The focusing phenomenon is achieved with the help of a shock tube
and a converging section attached to it. The planar shock generated inside the
shock tube is converted to spherical shock with the help of the converging
section and is focused to a point. High-temperature effects like
temperature-dependent Cp variation and chemical reactions corresponding to
dissociated air are included in the simulation. The chemical reactions
including the dissociation, recombination and ionization of nine species of air
including three ions (N2, O2, N, O, NO, Ar, NO+, O+ and Ar+) are monitored
throughout the simulation. The effect of driven section filling conditions such
as initial pressure and temperature on focusing parameters is studied. The
variation in the initial fill temperature is found to affect the flow
properties much more as compared to the change in initial fill pressure, while
maintaining the same shock strength. The effect of incident shock strength on
shock wave focusing is also investigated. It is observed that as the strength
of the shock increases, the conditions like temperature and pressure at the
focusing point increases and thereby increasing the reaction rate of all the
reactions.


Abstract:
  In this paper, we propose a Monocular 3D Single Stage object Detector
(M3DSSD) with feature alignment and asymmetric non-local attention. Current
anchor-based monocular 3D object detection methods suffer from feature
mismatching. To overcome this, we propose a two-step feature alignment
approach. In the first step, the shape alignment is performed to enable the
receptive field of the feature map to focus on the pre-defined anchors with
high confidence scores. In the second step, the center alignment is used to
align the features at 2D/3D centers. Further, it is often difficult to learn
global information and capture long-range relationships, which are important
for the depth prediction of objects. Therefore, we propose a novel asymmetric
non-local attention block with multi-scale sampling to extract depth-wise
features. The proposed M3DSSD achieves significantly better performance than
the monocular 3D object detection methods on the KITTI dataset, in both 3D
object detection and bird's eye view tasks.


Abstract:
  In this article, we estimate the cost of simulating electrolyte molecules in
Li-ion batteries on a fault-tolerant quantum computer, focusing on the
molecules that can provide practical solutions to industrially relevant
problems. Our resource estimate is based on the fusion-based quantum computing
scheme using photons, but can be modified easily to the more conventional
gate-based model as well. We find the cost of the magic state factory to
constitute no more than $\sim 2\%$ of the total footprint of the quantum
computer, which suggests that it is more advantageous to use algorithms that
consume many magic states at the same time. We suggest architectural and
algorithmic changes that can accommodate such a capability. On the architecture
side, we propose a method to consume multiple magic states at the same time,
which can potentially lead to an order of magnitude reduction in the overall
computation time without incurring additional expense in the footprint. This is
based on a fault-tolerant measurement of a Pauli product operator in constant
time, which may be useful in other contexts as well. We also introduce a method
to implement an arbitrary fermionic basis change in logarithmic depth, which
may be of independent interest.


Abstract:
  The extreme miniaturization of a cold-atom interferometer accelerometer
requires the development of novel technologies and architectures for the
interferometer subsystems. We describe several component technologies and a
laser system architecture to enable a path to such miniaturization. We
developed a custom, compact titanium vacuum package containing a
microfabricated grating chip for a tetrahedral grating magneto-optical trap
(GMOT) using a single cooling beam. The vacuum package is integrated into the
optomechanical design of a compact cold-atom sensor head with fixed optical
components. In addition, a multichannel laser system driven by a single seed
laser has been implemented with time-multiplexed frequency shifting using
single sideband modulators, reducing the number of optical channels connected
to the sensor head. This laser system architecture is compatible with a highly
miniaturized photonic integrated circuit approach, and by demonstrating
atom-interferometer operation with this laser system, we show feasibility for
the integrated photonic approach. In the compact sensor head, sub-Doppler
cooling in the GMOT produces 15 uK temperatures, which can operate at a 20 Hz
data rate for the atom interferometer sequence. After validating atomic
coherence with Ramsey interferometry, we demonstrate a light-pulse atom
interferometer in a gravimeter configuration without vibration isolation for 10
Hz measurement cycle rate and T = 0 - 4.5 ms interrogation time, resulting in
$\Delta$g / g = 2.0e-6. All these efforts demonstrate progress towards
deployable cold-atom inertial sensors under large amplitude motional dynamics.


Abstract:
  Offensive language detection is an ever-growing natural language processing
(NLP) application. This growth is mainly because of the widespread usage of
social networks, which becomes a mainstream channel for people to communicate,
work, and enjoy entertainment content. Many incidents of sharing aggressive and
offensive content negatively impacted society to a great extend. We believe
contributing to improving and comparing different machine learning models to
fight such harmful contents is an important and challenging goal for this
thesis. We targeted the problem of offensive language detection for building
efficient automated models for offensive language detection. With the recent
advancements of NLP models, specifically, the Transformer model, which tackled
many shortcomings of the standard seq-to-seq techniques. The BERT model has
shown state-of-the-art results on many NLP tasks. Although the literature still
exploring the reasons for the BERT achievements in the NLP field. Other
efficient variants have been developed to improve upon the standard BERT, such
as RoBERTa and ALBERT. Moreover, due to the multilingual nature of text on
social media that could affect the model decision on a given tween, it is
becoming essential to examine multilingual models such as XLM-RoBERTa trained
on 100 languages and how did it compare to unilingual models. The RoBERTa based
model proved to be the most capable model and achieved the highest F1 score for
the tasks. Another critical aspect of a well-rounded offensive language
detection system is the speed at which a model can be trained and make
inferences. In that respect, we have considered the model run-time and
fine-tuned the very efficient implementation of FastText called BlazingText
that achieved good results, which is much faster than BERT-based models.


Abstract:
  In this work we study 35 stellar clusters in the Small Magellanic Cloud (SMC)
in order to provide their mean metallicities and ages. We also provide mean
metallicities of the fields surrounding the clusters. We used Str\"omgren
photometry obtained with the 4.1 m SOAR telescope and take advantage of $(b -
y)$ and $m1$ colors for which there is a metallicity calibration presented in
the literature. The spatial metallicity and age distributions of clusters
across the SMC are investigated using the results obtained by Str\"omgren
photometry. We confirm earlier observations that younger, more metal-rich star
clusters are concentrated in the central regions of the galaxy, while older,
more metal-poor clusters are located farther from the SMC center. We construct
the age-metallicity relation for the studied clusters and find good agreement
with theoretical models of chemical enrichment, and with other literature age
and metallicity values for those clusters. We also provide the mean
metallicities for old and young populations of the field stars surrounding the
clusters, and find the latter to be in good agreement with recent studies of
the SMC Cepheid population. Finally, the Str\"omgren photometry obtained for
this study is made publicly available.


Abstract:
  Although much has been published regarding street protests on social media,
few works have attempted to characterize social media users' spatial behavior
in such events. The research reported here uses spatial capture-recapture
methods to determine the influence of the built environment, physical proximity
to protest location, and collective posting rhythm on variations in users'
spatial detectability and density during a protest in Mexico City. The
best-obtained model, together with explaining the spatial density of users,
shows that there is high variability in the detectability of social media user
protest supporters and that the collective posting rhythm and the day of
observation are significant explanatory factors. The implication is that
studies of collective spatial behavior would benefit by focussing on users'
activity centres and their urban environment, rather than their physical
proximity to the protest location, the latter being unable to adequately
explain spatial variations in users' detectability and density during the
protest event.


Abstract:
  Let $\boldsymbol{X}$ be a $d$-dimensional random array on $[n]$ whose entries
take values in a finite set $\mathcal{X}$, that is, $\boldsymbol{X}=\langle
X_s:s\in {[n]\choose d}\rangle$ is an $\mathcal{X}$-valued stochastic process
indexed by the set ${[n]\choose d}$ of all $d$-element subsets of
$[n]:=\{1,\dots,n\}$. We give easily checked conditions on $\boldsymbol{X}$
which ensure, for instance, that for \emph{every} function $f\colon
\mathcal{X}^{{[n]\choose d}}\to\mathbb{R}$ which satisfies
$\mathbb{E}[f(\boldsymbol{X})]=0$ and $\|f(\boldsymbol{X})\|_{L_p}=1$ for some
$p>1$, the random variable $f(\boldsymbol{X})$ becomes concentrated after
conditioning it on a large subarray of $\boldsymbol{X}$. These conditions cover
several classes of random arrays with not necessarily independent entries.
Applications are given in combinatorics, and examples are also presented which
show~the optimality of various aspects of the results.


Abstract:
  Across the United States, a growing number of school districts are turning to
matching algorithms to assign students to public schools. The designers of
these algorithms aimed to promote values such as transparency, equity, and
community in the process. However, school districts have encountered practical
challenges in their deployment. In fact, San Francisco Unified School District
voted to stop using and completely redesign their student assignment algorithm
because it was not promoting educational equity in practice. We analyze this
system using a Value Sensitive Design approach and find that one reason values
are not met in practice is that the system relies on modeling assumptions about
families' priorities, constraints, and goals that clash with the real world.
These assumptions overlook the complex barriers to ideal participation that
many families face, particularly because of socioeconomic inequalities. We
argue that direct, ongoing engagement with stakeholders is central to aligning
algorithmic values with real world conditions. In doing so we must broaden how
we evaluate algorithms while recognizing the limitations of purely algorithmic
solutions in addressing complex socio-political problems.


Abstract:
  Learning from non-stationary data streams and overcoming catastrophic
forgetting still poses a serious challenge for machine learning research.
Rather than aiming to improve state-of-the-art, in this work we provide insight
into the limits and merits of rehearsal, one of continual learning's most
established methods. We hypothesize that models trained sequentially with
rehearsal tend to stay in the same low-loss region after a task has finished,
but are at risk of overfitting on its sample memory, hence harming
generalization. We provide both conceptual and strong empirical evidence on
three benchmarks for both behaviors, bringing novel insights into the dynamics
of rehearsal and continual learning in general. Finally, we interpret important
continual learning works in the light of our findings, allowing for a deeper
understanding of their successes.


Abstract:
  We study the coherent properties of fully screened and overscreened Kondo
effects based on the Nozieres local Fermi-liquid theory and Affleck-Ludwig
boundary conformal-field-theory approach, respectively. Coherent transports
through an SU($N)$ generalization of fully screened and the
multi-$\mathcal{K}$-channel overscreened Kondo impurities at and beyond the
particle-hole (PH) symmetric point are thoroughly investigated. We report
distinctive Fermi-liquid coefficients characterizing the finite temperature
correction to the transmission phase shift and normalized visibility in fully
screened Kondo regime, which can be measured with the existing experimental
setups. Our work equally uncovers the significance of temperature correction to
the transmission phase shift and visibility in non Fermi-liquid regime
associated with the PH asymmetric overscreened Kondo effects with an arbitrary
number of conduction channels $\mathcal{K}$. We propose viable roots of
verifying our predictions in connection to the recent experiments, in
particular with the experiments studying highly symmetric forms of fully
screened Kondo effects and two-channel overscreened Kondo effects realized in
quantum dot nano-structures.


Abstract:
  In this letter, we study the resource allocation for a multiuser intelligent
reflecting surface (IRS)-aided simultaneous wireless information and power
transfer (SWIPT) system. Specifically, a multi-antenna base station (BS)
transmits energy and information signals simultaneously to multiple energy
harvesting receivers (EHRs) and information decoding receivers (IDRs) assisted
by an IRS. Under this setup, we introduce a multi-objective optimization (MOOP)
framework to investigate the fundamental trade-off between the data sum-rate
maximization and the total harvested energy maximization, by jointly optimizing
the energy/information beamforming vectors at the BS and the phase shifts at
the IRS. This MOOP problem is first converted to a single-objective
optimization problem (SOOP) via the $\epsilon$-constraint method and then
solved by majorization minimization (MM) and inner approximation (IA)
techniques. Simulation results unveil a non-trivial trade-off between the
considered competing objectives, as well as the superior performance of the
proposed scheme as compared to various baseline schemes.


Abstract:
  We discuss the application of random projections to conic programming:
notably linear, second-order and semidefinite programs. We prove general
approximation results on feasibility and optimality using the framework of
formally real Jordan algebras. We then discuss some computational experiments
on randomly generated semidefinite programs in order to illustrate the
practical applicability of our ideas


Abstract:
  Let $R$ be a commutative ring: we explain the Beilinson-Bernstein
localisation mechanism for sheaves of homogeneous twisted differential
operators defined over a smooth, separated, locally of finite type $R$-scheme.
As an application, we give a new proof of Duflo's theorem characterising the
primitive ideals of the enveloping algebra of a complex semisimple Lie algebra.


Abstract:
  Frequent Subgraph Mining (FSM) is the key task in many graph mining and
machine learning applications. Numerous systems have been proposed for FSM in
the past decade. Although these systems show good performance for small
patterns (with no more than four vertices), we found that they have difficulty
in mining larger patterns. In this work, we propose a novel two-vertex
exploration strategy to accelerate the mining process. Compared with the
single-vertex exploration adopted by previous systems, our two-vertex
exploration avoids the large memory consumption issue and significantly reduces
the memory access overhead. We further enhance the performance through an
index-based quick pattern technique that reduces the overhead of isomorphism
checks, and a subgraph sampling technique that mitigates the issue of subgraph
explosion. The experimental results show that our system achieves significant
speedups against the state-of-the-art graph pattern mining systems and supports
larger pattern mining tasks that none of the existing systems can handle.


Abstract:
  In the diffraction-limited near-field propagation regime, free-space optical
quantum key distribution (QKD) systems can employ multiple spatial modes to
improve their key rate. Here, we analyze QKD using the non-orthogonal flat-top
focused beams. Although they suffer from a rate penalty, their ease of
implementation makes them an attractive alternative to the well-studied
orthonormal Laguerre-Gauss (LG) modes. Indeed, in the presence of turbulence,
the non-orthogonal modes may achieve higher QKD rate than the LG modes.


Abstract:
  Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple
equilibrium states as a consequence of bottom topography in their pioneering
work on the quasi-geostrophic barotropic flow over topography in a
$\beta$-plane channel. In the present paper, we prove that the basic flow is
asymptotically stable in a parameter region, including the flat topography
situation, which excludes the existence of multiple equilibrium states therein.
Moreover, we show that an additional condition on the average zonal force or
the average zonal velocity is indispensable to the well-posedness of the
Charney-DeVore quasi-geostrophic equation. Coexistence of at least three
equilibrium states is confirmed by a pseudo-arclength continuation method for
different topographic amplitudes. The stabilities of the equilibrium states are
examined by high-resolution direct numerical simulations.


Abstract:
  Over the last several decades, software has been woven into the fabric of
every aspect of our society. As software development surges and code
infrastructure of enterprise applications ages, it is now more critical than
ever to increase software development productivity and modernize legacy
applications. Advances in deep learning and machine learning algorithms have
enabled numerous breakthroughs, motivating researchers to leverage AI
techniques to improve software development efficiency. Thus, the fast-emerging
research area of AI for Code has garnered new interest and gathered momentum.
In this paper, we present a large-scale dataset CodeNet, consisting of over 14
million code samples and about 500 million lines of code in 55 different
programming languages, which is aimed at teaching AI to code. In addition to
its large scale, CodeNet has a rich set of high-quality annotations to
benchmark and help accelerate research in AI techniques for a variety of
critical coding tasks, including code similarity and classification, code
translation between a large variety of programming languages, and code
performance (runtime and memory) improvement techniques. Additionally, CodeNet
provides sample input and output test sets for 98.5% of the code samples, which
can be used as an oracle for determining code correctness and potentially guide
reinforcement learning for code quality improvements. As a usability feature,
we provide several pre-processing tools in CodeNet to transform source code
into representations that can be readily used as inputs into machine learning
models. Results of code classification and code similarity experiments using
the CodeNet dataset are provided as a reference. We hope that the scale,
diversity and rich, high-quality annotations of CodeNet will offer
unprecedented research opportunities at the intersection of AI and Software
Engineering.


Abstract:
  Consider a compact surface of genus $\geq 2$ equipped with a metric that is
flat everywhere except at finitely many cone points with angles greater than
$2\pi$. Following the technique in the work of Burns, Climenhaga, Fisher, and
Thompson, we prove that sufficiently regular potential functions have unique
equilibrium states if the singular set does not support the full pressure.
Moreover, we show that the pressure gap holds for any potential which is
locally constant on a neighborhood of the singular set. Finally, we establish
that the corresponding equilibrium states have the $K$-property, and closed
regular geodesics equidistribute.


Abstract:
  By restricting the spatial energy transmission of an electromagnetic wave,
dielectric waveguides transmit light over long distances at sustained
intensity. Waveguides have been used in the microwave and optical range to
maintain strong signal intensities in connection with lasers, but guiding of
intense short-wavelength radiation such as x-rays has proven more cumbersome.
Here we investigate theoretically how tapered x-ray waveguides can focus and
guide radiation from x-ray free electron lasers. Elliptical waveguides using a
cladding material with high atomic number such as platinum can maintain an
x-ray intensity up to three orders of magnitude larger than in free space. This
feature can be used to significantly enhance resonant interactions of x-rays,
for instance driving nuclear transitions up to transient nuclear population
inversion. This could be the first breakthrough in nuclear state population
control. Our results anticipate the important role of tapered x-ray waveguides
in the emerging field of x-ray quantum optics with nuclear transitions.


Abstract:
  Tukey's halfspace depth can be seen as a stochastic program and as such it is
not guarded against optimizer's curse, so that a limited training sample may
easily result in a poor out-of-sample performance. We propose a generalized
halfspace depth concept relying on the recent advances in distributionally
robust optimization, where every halfspace is examined using the respective
worst-case distribution in the Wasserstein ball of radius $\delta\geq 0$
centered at the empirical law. This new depth can be seen as a smoothed and
regularized classical halfspace depth which is retrieved as $\delta\downarrow
0$. It inherits most of the main properties of the latter and, additionally,
enjoys various new attractive features such as continuity and strict positivity
beyond the convex hull of the support. We provide numerical illustrations of
the new depth and its advantages, and develop some fundamental theory. In
particular, we study the upper level sets and the median region including their
breakdown properties.


Abstract:
  This year marks the eightieth anniversary of the invention of the finite
element method (FEM). FEM has become the computational workhorse for
engineering design analysis and scientific modeling of a wide range of physical
processes, including material and structural mechanics, fluid flow and heat
conduction, various biological processes for medical diagnosis and surgery
planning, electromagnetics and semi-conductor circuit and chip design and
analysis, additive manufacturing, i.e. virtually every conceivable problem that
can be described by partial differential equations (PDEs). FEM has
fundamentally revolutionized the way we do scientific modeling and engineering
design, ranging from automobiles, aircraft, marine structures, bridges,
highways, and high-rise buildings. Associated with the development of finite
element methods has been the concurrent development of an engineering science
discipline called computational mechanics, or computational science and
engineering.
  In this paper, we present a historical perspective on the developments of
finite element methods mainly focusing on its applications and related
developments in solid and structural mechanics, with limited discussions to
other fields in which it has made significant impact, such as fluid mechanics,
heat transfer, and fluid-structure interaction. To have a complete storyline,
we divide the development of the finite element method into four time periods:
I. (1941-1965) Early years of FEM; II. (1966-1991) Golden age of FEM; III.
(1992-2017) Large scale, industrial applications of FEM and development of
material modeling, and IV (2018-) the state-of-the-art FEM technology for the
current and future eras of FEM research. Note that this paper may not strictly
follow the chronological order of FEM developments, because often time these
developments were interwoven across different time periods.


Abstract:
  We study soluble groups G in which each subnormal subgroup H with infinite
rank is commensurable with a normal subgroup, i.e. there exists a normal
subgroup N such that the intersection of H and N has finite index in both H and
N. We show that if such a G is periodic, then all subnormal subgroups are
commensurable with a normal subgroup, provided either the Hirsch-Plotkin
radical of G has infinite rank or G is nilpotent-by-abelian (and has infinite
rank).


Abstract:
  A right Engel sink of an element $g$ of a group $G$ is a set ${\mathscr
R}(g)$ such that for every $x\in G$ all sufficiently long commutators
$[...[[g,x],x],\dots ,x]$ belong to ${\mathscr R}(g)$. (Thus, $g$ is a right
Engel element precisely when we can choose ${\mathscr R}(g)=\{ 1\}$.) We prove
that if a profinite group $G$ admits a coprime automorphism $\varphi $ of prime
order such that every fixed point of $\varphi $ has a finite right Engel sink,
then $G$ has an open locally nilpotent subgroup.
  A left Engel sink of an element $g$ of a group $G$ is a set ${\mathscr E}(g)$
such that for every $x\in G$ all sufficiently long commutators
$[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. (Thus, $g$ is a left
Engel element precisely when we can choose ${\mathscr E}(g)=\{ 1\}$.) We prove
that if a profinite group $G$ admits a coprime automorphism $\varphi $ of prime
order such that every fixed point of $\varphi $ has a finite left Engel sink,
then $G$ has an open pronilpotent-by-nilpotent subgroup.


Abstract:
  Representing surfaces as zero level sets of neural networks recently emerged
as a powerful modeling paradigm, named Implicit Neural Representations (INRs),
serving numerous downstream applications in geometric deep learning and 3D
vision. Training INRs previously required choosing between occupancy and
distance function representation and different losses with unknown limit
behavior and/or bias. In this paper we draw inspiration from the theory of
phase transitions of fluids and suggest a loss for training INRs that learns a
density function that converges to a proper occupancy function, while its log
transform converges to a distance function. Furthermore, we analyze the limit
minimizer of this loss showing it satisfies the reconstruction constraints and
has minimal surface perimeter, a desirable inductive bias for surface
reconstruction. Training INRs with this new loss leads to state-of-the-art
reconstructions on a standard benchmark.


Abstract:
  In 1989 Kusuoka started the study of probability measures on the shift space
that are defined with the help of products of matrices. In particular, he
derived a sufficient condition for the ergodicity of such measures, which have
since been referred to as Kusuoka measures. We observe that repeated
measurements of a unitarily evolving quantum system generate a Kusuoka measure
on the space of sequences of measurement outcomes. We show that if the
measurement consists of scaled projections, then Kusuoka's sufficient
ergodicity condition can be significantly simplified. We then prove that this
condition is also necessary for ergodicity if the measurement consists of
uniformly scaled rank-1 projections (i.e., it is a rank-1 POVM), or of exactly
two projections, one of which is rank-1. For the latter class of measurements
we also show that the Kusuoka measure is reversible in the sense that every
string of outcomes has the same probability of being emitted by the system as
its reverse.


Abstract:
  In this paper, we investigate the constraint typology of mixed-integer linear
programming MILP formulations. MILP is a commonly used mathematical programming
technique for modelling and solving real-life scheduling, routing, planning,
resource allocation, timetabling optimization problems, providing optimized
business solutions for industry sectors such as: manufacturing, agriculture,
defence, healthcare, medicine, energy, finance, and transportation. Despite the
numerous real-life Combinatorial Optimization Problems found and solved, and
millions yet to be discovered and formulated, the number of types of
constraints, the building blocks of a MILP, is relatively much smaller. In the
search of a suitable machine readable knowledge representation for MILPs, we
propose an optimization modelling tree built based upon an MILP ontology that
can be used as a guidance for automated systems to elicit an MILP model from
end-users on their combinatorial business optimization problems.


Abstract:
  In this study different types of intuitionistic fuzzy continuities (IFCs) and
intuitionistic fuzzy boundedness (IFBs) in intuitionistic fuzzy pseudo normed
linear spaces are studied. Relations (intra and inter) on intuitionistic fuzzy
continuities and intuitionistic fuzzy boundedness are investigated.


Abstract:
  We consider one-loop five-point QCD amplitudes in next-to-multi-Regge
kinematics, and evaluate the one-loop impact factor for the emission of two
gluons. This is the last ingredient which is necessary to evaluate the
gluon-jet impact factor at NNLO accuracy in $\as$. It is also the first
instance in which loop-level QCD amplitudes are evaluated in
next-to-multi-Regge kinematics, which requires to apply a different
reggeisation ansatz to each colour-ordered amplitude.


Abstract:
  Interferometers provide a highly sensitive means to investigate and exploit
the coherence properties of light in metrology applications. However,
interferometers come in various forms and exploit different properties of the
optical states within. In this paper, we introduce a classification scheme that
characterizes any interferometer based on the number of involved nonlinear
elements by studying their influence on single-photon and photon-pair states.
Several examples of specific interferometers from these more general classes
are discussed, and the theory describing the expected first-order and
second-order coherence measurements for single-photon and single-photon-pair
input states is summarized and compared. These theoretical predictions are then
tested in an innovative experimental setup that is easily able to switch
between implementing an interferometer consisting of only one or two nonlinear
elements. The resulting singles and coincidence rates are measured in both
configurations and the results are seen to fit well with the presented theory.
The measured results of coherence are tied back to the presented classification
scheme, revealing that our experimental design can be useful in gaining insight
into the properties of the various interferometeric setups containing different
degrees of nonlinearity.


Abstract:
  Methods for global measurement of transcript abundance such as microarrays
and RNA-seq generate datasets in which the number of measured features far
exceeds the number of observations. Extracting biologically meaningful and
experimentally tractable insights from such data therefore requires
high-dimensional prediction. Existing sparse linear approaches to this
challenge have been stunningly successful, but some important issues remain.
These methods can fail to select the correct features, predict poorly relative
to non-sparse alternatives, or ignore any unknown grouping structures for the
features. We propose a method called SuffPCR that yields improved predictions
in high-dimensional tasks including regression and classification, especially
in the typical context of omics with correlated features. SuffPCR first
estimates sparse principal components and then estimates a linear model on the
recovered subspace. Because the estimated subspace is sparse in the features,
the resulting predictions will depend on only a small subset of genes. SuffPCR
works well on a variety of simulated and experimental transcriptomic data,
performing nearly optimally when the model assumptions are satisfied. We also
demonstrate near-optimal theoretical guarantees.


Abstract:
  A decentralized federated learning architecture is proposed to apply to the
Businesses-to-Businesses scenarios by introducing the consortium blockchain in
this paper. We introduce a model verification mechanism to ensure the quality
of local models trained by participators. To analyze the latency of the system,
a latency model is constructed by considering the work flow of the
architecture. Finally the experiment results show that our latency model does
well in quantifying the actual delays.


Abstract:
  Deep convolutional neural networks (DCNN) aided high dynamic range (HDR)
imaging recently received a lot of attention. The quality of DCNN generated HDR
images have overperformed the traditional counterparts. However, DCNN is prone
to be computationally intensive and power-hungry. To address the challenge, we
propose LightFuse, a lightweight CNN-based algorithm for extreme dual-exposure
image fusion, which can be implemented on various embedded computing platforms
with limited power and hardware resources. Two sub-networks are utilized: a
GlobalNet (G) and a DetailNet (D). The goal of G is to learn the global
information on the spatial dimension, whereas D aims to enhance local details
on the channel dimension. Both G and D are based solely on depthwise
convolution (D Conv) and pointwise convolution (P Conv) to reduce required
parameters and computations. Experimental results display that the proposed
technique could generate HDR images with plausible details in extremely exposed
regions. Our model outperforms other state-of-the-art approaches in PSNR score
by 0.7 to 8.5 while achieving 1.4 to 25.9 times parameter reduction.


Abstract:
  We report the detection of two lines at millimetre wavelengths towards the
immediate surroundings of the post-giant and most likely post-common-envelope
star HD101584 using high-angular-resolution ALMA observations. The
circumstellar environment of this object is rich in different molecular
species, but we find no viable identifications in terms of molecular lines.
  We aim to determine whether or not these lines can be attributed to the
Rydberg transitions -- X30alpha and X26alpha -- of neutral atoms of elements
heavier than carbon.
  A simple model in strict local thermodynamic equilibrium for a warm-gas
environment of the moderate-temperature star (T_eff about 8500 K) was
constructed to corroborate our findings. A geometrically thin, disc-like
geometry seen face-on was chosen and a distance of 1 kpc.
  The observed flux densities of the lines and the continuum at 232 and 354 GHz
can be reproduced using 10^(-3) M_sun of gas at a temperature of about 2800 K
and a hydrogen density of about 10^(12) cm(-3), assuming solar abundances for
the elements. The gas lies within a distance of about 5 au from the star
(assuming a distance of 1 kpc). The ionisation fraction is low, about
3x10^(-5). The origin of such a region is not clear, but it may be related to a
common-envelope-evolution phase. With these conditions, the line emissions are
dominated by Rydberg transitions within the stable isotopes of Mg. A turbulent
velocity field in the range 5.5 - 7.5 km s^(-1) is required to fit the Gaussian
line shapes. An upper limit to the average magnetic field in the line-emitting
region of 1G is set using the Zeeman effect in these lines.
  We speculate that Rydberg transitions of heavy elements may be an interesting
probe for the close-in environments of other moderate-temperature objects like
AGB stars, red supergiants, yellow hypergiants, and binaries of various types.


Abstract:
  Bereg et al. (2012) introduced the Boxes Class Cover problem, which has its
roots in classification and clustering applications: Given a set of n points in
the plane, each colored red or blue, find the smallest cardinality set of
axis-aligned boxes whose union covers the red points without covering any blue
point. In this paper we give an alternative proof of APX-hardness for this
problem, which also yields an explicit lower bound on its approximability. Our
proof also directly applies when restricted to sets of points in general
position and to the case where so-called half-strips are considered instead of
boxes, which is a new result.
  We also introduce a symmetric variant of this problem, which we call
Simultaneous Boxes Class Cover and can be stated as follows: Given a set S of n
points in the plane, each colored red or blue, find the smallest cardinality
set of axis-aligned boxes which together cover S such that all boxes cover only
points of the same color and no box covering a red point intersects a box
covering a blue point. We show that this problem is also APX-hard and give a
polynomial-time constant-factor approximation algorithm.


Abstract:
  The vertical shear instability (VSI) is a hydrodynamical instability that
requires rapid gas cooling and has been suggested to operate in outer regions
of protoplanetary disks. The VSI drives turbulence with strong vertical
motions, which could regulate the dust growth and settling. However, dust
growth and settling can regulate the VSI because dust depletion makes gas
cooling inefficient in outer disk regions that are optically thin to their own
thermal emission. In this study, we quantify this potentially stabilizing
effects of dust evolution on the VSI based on the linear analysis. We construct
a model for calculating the cooling timescale, taking into account dust growth
beyond micron sizes and size-dependent settling. Combining the model with the
linear stability analysis, we map the region where the VSI operates, which we
call the VSI zone, and estimate the maximum growth rate at each radial
position. We find that dust growth as well as settling makes the VSI zone more
confined around the midplane. This causes a decrease in the growth rate because
the vertical shear of the rotation velocity, which is the source of the
instability, is weaker at lower altitude. In our default disk model with 0.01
solar masses, dust growth from 10 micron to 1 mm causes a decrease in the
growth rate by a factor of more than 10. The suppression of VSI-driven
turbulence by dust evolution may promote further dust evolution in the outer
regions and also explain a high degree of dust settling observed in the disk
around HL Tau.


Abstract:
  We posit a new mechanism for cooperation in multi-agent reinforcement
learning (MARL) based upon any nonlinear function of the team's long-term
state-action occupancy measure, i.e., a \emph{general utility}. This subsumes
the cumulative return but also allows one to incorporate risk-sensitivity,
exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow
Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy
evaluation (critic), weighted averaging with neighbors (information mixing),
and local gradient updates for their policy parameters (actor). DSAC augments
the classic critic step by requiring agents to (i) estimate their local
occupancy measure in order to (ii) estimate the derivative of the local utility
with respect to their occupancy measure, i.e., the "shadow reward". DSAC
converges to $\epsilon$-stationarity in $\mathcal{O}(1/\epsilon^{2.5})$
(Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/\epsilon^{2})$
(Corollary \ref{corollary:communication}) steps with high probability,
depending on the amount of communications. We further establish the
non-existence of spurious stationary points for this problem, that is, DSAC
finds the globally optimal policy (Corollary \ref{corollary:global}).
Experiments demonstrate the merits of goals beyond the cumulative return in
cooperative MARL.


Abstract:
  Phase wrapping is a major problem in direction-of-arrival (DOA) estimation
using phase-difference observations. For a sensor pair with an inter-sensor
spacing greater than half of the wavelength ($\lambda/2$) of the signal, phase
wrapping occurs at certain DOA angles leading to phase-difference ambiguities.
Existing phase unwrapping methods exploit either frequency or spatial
diversity. These techniques work by imposing restrictions on the utilized
frequencies or the receiver array geometry. In addition to sensitivity to noise
and calibration errors, these methods may also have high computational
complexity. We propose a grid-less \emph{phase-difference projection} (PDP) DOA
algorithm to overcome these issues. The concept of \emph{wrapped
phased-difference pattern} (WPDP) is introduced, which allows the proposed
algorithm to compute most of the parameters required for DOA estimation in an
offline manner, hence resulting in a superior computational speed in realtime.
Simulation results demonstrate the excellent performance of the proposed
algorithm, both in terms of accuracy and speed.


Abstract:
  This paper presents a new collision avoidance procedure for unmanned aerial
vehicles in the presence of static and moving obstacles. The proposed procedure
is based on a new form of local parametrized guidance vector fields, called
collision avoidance vector fields, that produce smooth and intuitive maneuvers
around obstacles. The maneuvers follow nominal collision-free paths which we
refer to as streamlines of the collision avoidance vector fields. In the case
of multiple obstacles, the proposed procedure determines a mixed vector field
that blends the collision avoidance vector field of each obstacle and assumes
its form whenever a pre-defined distance threshold is reached. Then, in
accordance to the computed guidance vector fields, different collision
avoidance controllers that generate collision-free maneuvers are developed.
Furthermore, it is shown that any tracking controller with convergence
guarantees can be used with the avoidance controllers to track the streamlines
of the collision avoidance vector fields. Finally, numerical simulations
demonstrate the efficacy of the proposed approach and its ability to avoid
collisions with static and moving pop-up threats in three different practical
scenarios.


Abstract:
  In this paper, we study how the evaporation of PBHs can affect the production
of dark matter (DM) particles through thermal processes. We consider fermionic
DM interacting with Standard Model particles via a spin-1 mediator in the
context of a Freeze-Out or Freeze-In mechanism. We show that when PBHs
evaporate after dominating the Universe's energy density, PBHs act as a source
of DM and continuously inject entropy into the visible sector that can affect
the thermal production in three qualitatively different ways. We compute the
annihilation cross-sections which account for the interactions between and
within the PBH produced and thermally produced DM populations, and establish a
set of Boltzmann equations which we solve to obtain the correct relic abundance
in those different regimes and confront the results with a set of different
cosmological constraints. We provide analytic formulae to calculate the relic
abundance for the Freeze-Out and Freeze-In mechanism in a PBH dominated early
Universe. We identify regions of the parameter space where the PBHs dilute the
relic density and thermalization occurs. Furthermore, we have made our code
that numerically solves the Boltzmann equations publicly available.


Abstract:
  We study the influence of the factor of electron-ion collisions on the
solution of the Cauchy problem in the one-dimensional relativistic model of
cold plasma and show that, depending on their intensity and initial data, two
scenarios are possible: either the solution remains smooth and stabilizes to a
stationary state, or during a finite time the oscillations blowup.
  In contrast to the nonrelativistic model, when exact conditions can be
obtained separating the two behaviors, in a much more complicated relativistic
situation, it turns out to be possible to analytically estimate from below the
time during which the existence of a smooth solution and the guaranteed number
of oscillations during this time. In addition, we show that in contrast to the
relativistic case without taking into account collisions, when oscillations
corresponding to arbitrarily small deviations from the zero equilibrium
position blow up, the presence of electron collisions can suppress the blow-up
of sufficiently small oscillations. Further, based on the analysis of
characteristics, a numerical algorithm is constructed, the order of accuracy of
which is determined only by the smoothness of the initial data. Numerical
experiments are presented to illustrate the theoretical results. The initial
conditions are chosen as reasonably as possible from the point of view of
full-scale physical experiments.


Abstract:
  We construct a new factorized waveform including
$(l,|m|)=(2,2),(2,1),(3,3),(4,4)$ modes based on effective-one-body (EOB)
formalism, which is valid for spinning binary black holes (BBH) in general
equatorial orbit. When combined with the dynamics of $\texttt{SEOBNRv4}$, the
$(l,|m|)=(2,2)$ mode waveform generated by this new waveform can fit the
original $\texttt{SEOBNRv4}$ waveform very well in the case of a quasi-circular
orbit. We have calibrated our new waveform model to the Simulating eXtreme
Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in
$(20,200)M_\odot$ using Advanced LIGO designed sensitivity. For the
quasi-circular cases we have compared our $(2,2)$ mode waveforms to the 281
numerical relativity (NR) simulations of BBH along quasi-circular orbits. All
of the matching factors are bigger than 98\%. For the elliptical cases, 24
numerical relativity simulations of BBH along an elliptic orbit are used. For
each elliptical BBH system, we compare our modeled gravitational polarizations
against the NR results for different combinations of the inclination angle, the
initial orbit phase and the source localization in the sky. We use the the
minimal matching factor respect to the inclination angle, the initial orbit
phase and the source localization to quantify the performance of the higher
modes waveform. We found that after introducing the high modes, the minimum of
the minimal matching factor among the 24 tested elliptical BBHs increases from
90\% to 98\%. Following our previous $\texttt{SEOBNRE}$ waveform model, we call
our new waveform model $\texttt{SEOBNREHM}$. Our $\texttt{SEOBNREHM}$ waveform
model can match all tested 305 SXS waveforms better than 98\% including highly
spinning ($\chi=0.99$) BBH, highly eccentric ($e\approx0.15$) BBH and large
mass ratio ($q=10$) BBH.


Abstract:
  We develop a mathematical model to capture the web dynamics of slingshot
spiders (Araneae: Theridiosomatidae), which utilize a tension line to deform
their orb webs into conical springs to hunt flying insects. Slingshot spiders
are characterized by their ultrafast launch speeds and accelerations (exceeding
1300 $m/s^2$), however a theoretical approach to characterize the underlying
spatiotemporal web dynamics remains missing. To address this knowledge gap, we
develop a 2D-coupled damped oscillator model of the web. Our model reveals
three key insights into the dynamics of slingshot motion. First, the tension
line plays a dual role: enabling the spider to load elastic energy into the web
for a quick launch (in milliseconds) to displacements of 10-15 body lengths,
but also enabling the spider to halt quickly, attenuating inertial
oscillations. Second, the dominant energy dissipation mechanism is viscous drag
by the silk lines - acting as a low Reynolds number parachute. Third, the web
exhibits underdamped oscillatory dynamics through a finely-tuned balance
between the radial line forces, the tension line force and viscous drag
dissipation. Together, our work suggests that the conical geometry and
tension-line enables the slingshot web to act as both an elastic spring and a
shock absorber, for the multi-functional roles of risky predation and
self-preservation.


Abstract:
  In this work we present a gauge-invariant three-dimensional teleparallel
supergravity theory using the Chern-Simons formalism. The present construction
is based on a supersymmetric extension of a particular deformation of the
Poincar\'e algebra. At the bosonic level the theory describes a non-Riemannian
geometry with a non-vanishing torsion. In presence of supersymmetry, the
teleparallel supergravity theory is characterized by a non-vanishing
super-torsion in which the cosmological constant can be seen as a source for
the torsion. We show that the teleparallel supergravity theory presented here
reproduces the Poincar\'e supergravity in the vanishing cosmological limit. The
extension of our results to $\mathcal{N}=p+q$ supersymmetries is also explored.


Abstract:
  In this article, we obtain several new weighted bounds for the numerical
radius of a Hilbert space operator. The significance of the obtained results is
the way they generalize many existing results in the literature; where certain
values of the weights imply some known results, or refinements of these
results. In the end, we present some numerical examples that show how our
results refine the well known results in the literature, related to this topic.


Abstract:
  White dwarfs with metal-polluted atmospheres have been studied widely in the
context of the accretion of rocky debris from evolved planetary systems. One
open question is the geometry of accretion and how material arrives and mixes
in the white dwarf surface layers. Using the 3D radiation-hydrodynamics code
CO$^5$BOLD, we present the first transport coefficients in degenerate star
atmospheres which describe the advection-diffusion of a passive scalar across
the surface-plane. We couple newly derived horizontal diffusion coefficients
with previously published vertical diffusion coefficients to provide
theoretical constraints on surface spreading of metals in white dwarfs. Our
grid of 3D simulations probes the vast majority of the parameter space of
convective white dwarfs, with pure-hydrogen atmospheres in the effective
temperature range 6000-18000 K and pure-helium atmospheres in the range
12000-34000 K. Our results suggest that warm hydrogen-rich atmospheres (DA;
$\gtrsim$13000 K) and helium-rich atmospheres (DB, DBA; $\gtrsim$30000 K) are
unable to efficiently spread the accreted metals across their surface,
regardless of the time dependence of accretion. This result may be at odds with
the current non-detection of surface abundance variations at white dwarfs with
debris discs. For cooler hydrogen- and helium-rich atmospheres, we predict a
largely homogeneous distribution of metals across the surface within a vertical
diffusion timescale. This is typically less than 0.1 per cent of disc lifetime
estimates, a quantity which is revisited in this paper using the overshoot
results. These results have relevance for studies of the bulk composition of
evolved planetary systems and models of accretion disc physics.


Abstract:
  Responsible AI is becoming critical as AI is widely used in our everyday
lives. Many companies that deploy AI publicly state that when training a model,
we not only need to improve its accuracy, but also need to guarantee that the
model does not discriminate against users (fairness), is resilient to noisy or
poisoned data (robustness), is explainable, and more. In addition, these
objectives are not only relevant to model training, but to all steps of
end-to-end machine learning, which include data collection, data cleaning and
validation, model training, model evaluation, and model management and serving.
Finally, responsible AI is conceptually challenging, and supporting all the
objectives must be as easy as possible. We thus propose three key research
directions towards this vision - depth, breadth, and usability - to measure
progress and introduce our ongoing research. First, responsible AI must be
deeply supported where multiple objectives like fairness and robust must be
handled together. To this end, we propose FR-Train, a holistic framework for
fair and robust model training in the presence of data bias and poisoning.
Second, responsible AI must be broadly supported, preferably in all steps of
machine learning. Currently we focus on the data pre-processing steps and
propose Slice Tuner, a selective data acquisition framework for training fair
and accurate models, and MLClean, a data cleaning framework that also improves
fairness and robustness. Finally, responsible AI must be usable where the
techniques must be easy to deploy and actionable. We propose FairBatch, a batch
selection approach for fairness that is effective and simple to use, and Slice
Finder, a model evaluation tool that automatically finds problematic slices. We
believe we scratched the surface of responsible AI for end-to-end machine
learning and suggest research challenges moving forward.


Abstract:
  We study the problem of incentivizing exploration for myopic users in linear
bandits, where the users tend to exploit arm with the highest predicted reward
instead of exploring. In order to maximize the long-term reward, the system
offers compensation to incentivize the users to pull the exploratory arms, with
the goal of balancing the trade-off among exploitation, exploration and
compensation. We consider a new and practically motivated setting where the
context features observed by the user are more informative than those used by
the system, e.g., features based on users' private information are not
accessible by the system. We propose a new method to incentivize exploration
under such information gap, and prove that the method achieves both sublinear
regret and sublinear compensation. We theoretical and empirically analyze the
added compensation due to the information gap, compared with the case that the
system has access to the same context features as the user, i.e., without
information gap. We also provide a compensation lower bound of our problem.


Abstract:
  Leibniz algebras are a non-anticommutative version of Lie algebras. They play
an important role in different areas of mathematics and physics and have
attracted much attention over the last thirty years. In this paper we
investigate whether conditions such as being a Lie algebra, cyclic, simple,
semisimple, solvable, supersolvable or nilpotent in such an algebra are
preserved by lattice isomorphisms.


Abstract:
  We propose a study of the Adaptive Biasing Force method's robustness under
generic (possibly non-conservative) forces. We first ensure the flat histogram
property is satisfied in all cases. We then introduce a fixed point problem
yielding the existence of a stationary state for both the Adaptive Biasing
Force and Projected Adapted Biasing Force algorithms, relying on generic bounds
on the invariant probability measures of homogeneous diffusions. Using
classical entropy techniques, we prove the exponential convergence of both
biasing force and law as time goes to infinity, for both the Adaptive Biasing
Force and the Projected Adaptive Biasing Force methods.


Abstract:
  A network is said to have the properties of a small world if a suitably
defined average distance between any two nodes is proportional to the logarithm
of the number of nodes, $N$. In this paper, we present a novel derivation of
the small-world property for Gilbert-Erd\"os-Renyi random networks. We employ a
mean field approximation that permits the analytic derivation of the
distribution of shortest paths that exhibits logarithmic scaling away from the
phase transition, inferable via a suitably interpreted order parameter. We
begin by framing the problem in generality with a formal generating functional
for undirected weighted random graphs with arbitrary disorder, recovering the
result that the free energy associated with an ensemble of Gilbert graphs
corresponds to a system of non-interacting fermions identified with the edge
states. We then present a mean field solution for this model and extend it to
more general realizations of network randomness. For a two family class of
stochastic block models that we refer to as dimorphic networks, which allow for
links within the different families to be drawn from two independent discrete
probability distributions, we find the mean field approximation maps onto a
spin chain combinatorial problem and again yields useful approximate analytic
expressions for mean path lengths. Dimorophic networks exhibit a richer phase
structure, where distinct small world regimes separate in analogy to the
spinodal decomposition of a fluid. We find that is it possible to induce small
world behavior in sub-networks that by themselves would not be in the
small-world regime.