Abstract:
  The development of an automatic way to extract user opinions about products,
movies, and foods from online social network (OSN) interactions is among the
main interests of sentiment analysis and opinion mining studies. Existing
approaches in the sentiment analysis domain mostly do not discriminate the
sentences of different types of users, even though some users are always
negative and some are always positive. Thus, finding a way to identify these
two types of user is significant because their attitudes can change the
analysis of user reviews of businesses and products. Due to the complexity of
natural language processing, pure text mining methods may lead to
misunderstandings about the exact nature of the sentiments expressed in review
text. In this study, we propose a neural network classifier to predict the
presence of biased users on the basis of users' psychological behaviors. The
identification of the psychological behaviors of users allows us to find overly
positive and overly negative users and to categorize these users' attitudes
regardless of the content of their review texts. The experiment result
indicates that the biased users can be predicted based on user behavior at an
accuracy rate of 89%, 67% and 81% for three different datasets.


Abstract:
  We investigate the structural, electronic and magnetic properties of the full
Heusler compounds Mn$_2$YSn (Y = Mo, Nb, Zr) by first-principles density
functional theory using the generalized gradient approximation. It is found
that the calculated lattice constants are in good agreement with the
theoretical values. We observe that the Cu$_2$MnAl-type structure is more
stable than the Hg$_2$CuTi type. The calculated total magnetic moments of
Mn$_2$NbSn and Mn$_2$ZrSn are 1 $\mu_{\text{B}}$ and 2 $\mu_{\text{B}}$ at the
equilibrium lattice constant of 6.18 \AA and 6.31 \AA, respectively, for the
Cu$_2$MnAl-type structure. Mn$_2$MoSn have a metallic character in both
Hg$_2$CuTi and Cu$_2$MnAl type structures. The total spin magnetic moment obeys
the Slater-Pauling rule. Half-metal exhibits 100% spin polarization at the
Fermi level. Thus, these alloys are promising magnetic candidates in spintronic
devices.


Abstract:
  A (positive definite and integral) quadratic form is called {\it an
isolation} of a quadratic form $f$ if it represents all subforms of $f$ except
for $f$ itself. The minimum rank of isolations of a quadratic form $f$ is
denoted, if it exists, by $\text{Iso}(f)$. In this article, we show that
$\text{Iso}(I_2)=5$ and $\text{Iso}(I_3)=6$, where $I_n=x_1^2+\dots+x_n^2$ is
the sum of $n$ squares for any positive integer $n$. After proving that there
always exists an isolation of $I_n$ for any positive integer $n$, we provide
some explicit lower and upper bounds for $\text{Iso}(I_n)$. In particular, we
show that $\text{Iso}(I_n) \in \Omega(n^{\frac32-\epsilon})$ for any
$\epsilon>0$.


Abstract:
  This article produces a complete list of all maximal subgroups of the finite
simple groups of type $F_4$, $E_6$ and twisted $E_6$ over all finite fields.
Along the way, we determine the collection of Lie primitive almost simple
subgroups of the corresponding algebraic groups. We give the stabilizers under
the actions of outer automorphisms, from which one can obtain complete
information about the maximal subgroups of all almost simple groups with socle
one of these groups. We also provide a new maximal subgroup of ${}^2\!F_4(8)$,
correcting the maximal subgroups for that group from the list of Malle. This
provides the first new exceptional groups of Lie type to have their maximal
subgroups enumerated for three decades.
  The techniques are a mixture of algebraic groups, representation theory,
computational algebra, and use of the trilinear form on the $27$-dimensional
minimal module for $E_6$. We provide a collection of auxiliary Magma files that
prove the author's computational claims, yielding existence and the number of
conjugacy classes of all maximal subgroups mentioned in the text.


Abstract:
  Magnetic nulls are ubiquitous in space plasmas, and are of interest as sites
of localized energy dissipation or magnetic reconnection. As such, a number of
methods have been proposed for detecting nulls in both simulation data and in
situ spacecraft data from Earth's magnetosphere. The same methods can be
applied to detect stagnation points in flow fields. In this paper we describe a
systematic comparison of different methods for finding magnetic nulls. The
Poincare index method, the first-order Taylor expansion (FOTE) method, and the
trilinear method are considered. We define a magnetic field containing fourteen
magnetic nulls whose positions and types are known to arbitrary precision.
Furthermore, we applied the selected techniques in order to find and classify
those nulls. Two situations are considered: one in which the magnetic field is
discretized on a rectangular grid, and the second in which the magnetic field
is discretized along synthetic `spacecraft trajectories' within the domain. At
present, FOTE and trilinear are the most reliable methods for finding nulls in
the spacecraft data and in numerical simulations on Cartesian grids,
respectively. The Poincare index method is suitable for simulations on both
tetrahedral and hexahedral meshes. The proposed magnetic field configuration
can be used for grading and benchmarking the new and existing tools for finding
magnetic nulls and flow stagnation points.


Abstract:
  Absolute camera pose regressors estimate the position and orientation of a
camera from the captured image alone. Typically, a convolutional backbone with
a multi-layer perceptron head is trained with images and pose labels to embed a
single reference scene at a time. Recently, this scheme was extended for
learning multiple scenes by replacing the MLP head with a set of fully
connected layers. In this work, we propose to learn multi-scene absolute camera
pose regression with Transformers, where encoders are used to aggregate
activation maps with self-attention and decoders transform latent features and
scenes encoding into candidate pose predictions. This mechanism allows our
model to focus on general features that are informative for localization while
embedding multiple scenes in parallel. We evaluate our method on commonly
benchmarked indoor and outdoor datasets and show that it surpasses both
multi-scene and state-of-the-art single-scene absolute pose regressors. We make
our code publicly available from
https://github.com/yolish/multi-scene-pose-transformer.


Abstract:
  We reconsider the evaluation of OOD detection methods for image recognition.
Although many studies have been conducted so far to build better OOD detection
methods, most of them follow Hendrycks and Gimpel's work for the method of
experimental evaluation. While the unified evaluation method is necessary for a
fair comparison, there is a question of if its choice of tasks and datasets
reflect real-world applications and if the evaluation results can generalize to
other OOD detection application scenarios. In this paper, we experimentally
evaluate the performance of representative OOD detection methods for three
scenarios, i.e., irrelevant input detection, novel class detection, and domain
shift detection, on various datasets and classification tasks. The results show
that differences in scenarios and datasets alter the relative performance among
the methods. Our results can also be used as a guide for practitioners for the
selection of OOD detection methods.


Abstract:
  We introduce new foundations for relative topos theory based on stacks. One
of the central results in our theory is an adjunction between the category of
toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that
of ${\mathcal{C}}$-indexed categories. This represents a wide generalization of
the classical adjunction between presheaves on a topological space and bundles
over it, and allows one to interpret several constructions on sheaves and
stacks in a geometrical way; in particular, it leads to fibrational
descriptions of direct and inverse images of sheaves and stacks, as well as to
a geometric understanding of the sheafification process. It also naturally
allows one to regard any Grothendieck topos as a 'petit' topos associated with
a 'gros' topos, thereby providing an answer to a problem posed by Grothendieck
in the seventies. Another key ingredient in our theory is a notion of relative
site, which allows one to represent arbitrary geometric morphisms towards a
fixed base topos of sheaves on a site as structure morphisms induced by
relative sites over that site.


Abstract:
  The main aim of decision support systems is to find solutions that satisfy
user requirements. Often, this leads to predictability of those solutions, in
the sense that having the input data and the model, an adversary or enemy can
predict to a great extent the solution produced by your decision support
system. Such predictability can be undesirable, for example, in military or
security timetabling, or applications that require anonymity. In this paper, we
discuss the notion of solution predictability and introduce potential
mechanisms to intentionally avoid it.


Abstract:
  Learning feature representation from discriminative local regions plays a key
role in fine-grained visual classification. Employing attention mechanisms to
extract part features has become a trend. However, there are two major
limitations in these methods: First, they often focus on the most salient part
while neglecting other inconspicuous but distinguishable parts. Second, they
treat different part features in isolation while neglecting their
relationships. To handle these limitations, we propose to locate multiple
different distinguishable parts and explore their relationships in an explicit
way. In this pursuit, we introduce two lightweight modules that can be easily
plugged into existing convolutional neural networks. On one hand, we introduce
a feature boosting and suppression module that boosts the most salient part of
feature maps to obtain a part-specific representation and suppresses it to
force the following network to mine other potential parts. On the other hand,
we introduce a feature diversification module that learns semantically
complementary information from the correlated part-specific representations.
Our method does not need bounding boxes/part annotations and can be trained
end-to-end. Extensive experimental results show that our method achieves
state-of-the-art performances on several benchmark fine-grained datasets.
Source code is available at https://github.com/chaomaer/FBSD.


Abstract:
  The production of hydrogen fuels, via water splitting, is of practical
relevance for meeting global energy needs and mitigating the environmental
consequences of fossil-fuel-based transportation. Water photoelectrolysis has
been proposed as a viable approach for generating hydrogen, provided that
stable and inexpensive photocatalysts with conversion efficiencies over 10% can
be discovered, synthesized at scale, and successfully deployed (Pinaud et al.,
Energy Environ. Sci., 2013, 6, 1983). While a number of first-principles
studies have focused on the data-driven discovery of photocatalysts, in the
absence of systematic experimental validation, the success rate of these
predictions may be limited. We address this problem by developing a screening
procedure with co-validation between experiment and theory to expedite the
synthesis, characterization, and testing of the computationally predicted, most
desirable materials. Starting with 70,150 compounds in the Materials Project
database, the proposed protocol yielded 71 candidate photocatalysts, 11 of
which were synthesized as single-phase materials. Experiments confirmed
hydrogen generation and favorable band alignment for 6 of the 11 compounds,
with the most promising ones belonging to the families of alkali and
alkaline-earth indates and orthoplumbates. This study shows the accuracy of a
nonempirical, Hubbard-corrected density-functional theory method to predict
band gaps and band offsets at a fraction of the computational cost of hybrid
functionals, and outlines an effective strategy to identify photocatalysts for
solar hydrogen generation.


Abstract:
  The main goal of this paper is to introduce the notion of twisted partial
action of groupoids. We generalize the theorem about the existence of an
enveloping action, also known as the globalization theorem, and show that the
crossed products of the twisted partial action and of its associated twisted
global action are Morita equivalent. Finally, we generalize the concepts of
partial projective representation and partial Schur multiplier for a groupoid,
and we show the interaction between groupoid partial projective representions
and groupoid twisted partial actions.


Abstract:
  We study the generalization of deep learning models in relation to the convex
hull of their training sets. A trained image classifier basically partitions
its domain via decision boundaries and assigns a class to each of those
partitions. The location of decision boundaries inside the convex hull of
training set can be investigated in relation to the training samples. However,
our analysis shows that in standard image classification datasets, all testing
images are considerably outside that convex hull, in the pixel space, in the
wavelet space, and in the internal representations learned by deep networks.
Therefore, the performance of a trained model partially depends on how its
decision boundaries are extended outside the convex hull of its training data.
From this perspective which is not studied before, over-parameterization of
deep learning models may be considered a necessity for shaping the extension of
decision boundaries. At the same time, over-parameterization should be
accompanied by a specific training regime, in order to yield a model that not
only fits the training set, but also its decision boundaries extend desirably
outside the convex hull. To illustrate this, we investigate the decision
boundaries of a neural network, with various degrees of parameters, inside and
outside the convex hull of its training set. Moreover, we use a polynomial
decision boundary to study the necessity of over-parameterization and the
influence of training regime in shaping its extensions outside the convex hull
of training set.


Abstract:
  Much of the information about the magnetic field in the Milky Way and other
galaxies comes from measurements which are path integrals, such as Faraday
rotation and the polarization of synchrotron radiation of cosmic ray electrons.
The measurement made at the radio telescope results from the contributions of
volume elements along a long line of sight. The inferred magnetic field is
therefore some sort of average over a long line segment. A magnetic field
measurement at a given spatial location is of much more physical significance.
In this paper, we point out that HII regions fortuitously offer such a
``point'' measurement, albeit of one component of the magnetic field, and
averaged over the sightline through the HII region. However, the line of sight
(LOS) through an HII region is much smaller (e.g. 30 - 50 pc) than one through
the entire Galactic disk, and thus constitutes a ``pseudo-local'' measurement.
We use published HII region Faraday rotation measurements to provide a new
constraint on the magnitude of magnetohydrodynamic (MHD) turbulence in the
Galaxy, as well as to raise intriguing speculations about the modification of
the Galactic field during the star formation process.


Abstract:
  In this paper we study a cross-diffusion system whose coefficient matrix is
non-symmetric and degenerate. The system arises in the study of tissue growth
with autophagy. The existence of a weak solution is established. We also
investigate the limiting behavior of solutions as the pressure gets stiff. The
so-called incompressible limit is a free boundary problem of Hele-Shaw type.
Our key new discovery is that the usual energy estimate still holds as long as
the time variable stays away from $0$.


Abstract:
  Compression and efficient storage of neural network (NN) parameters is
critical for applications that run on resource-constrained devices. Although NN
model compression has made significant progress, there has been considerably
less investigation in the actual physical storage of NN parameters.
Conventionally, model compression and physical storage are decoupled, as
digital storage media with error correcting codes (ECCs) provide robust
error-free storage. This decoupled approach is inefficient, as it forces the
storage to treat each bit of the compressed model equally, and to dedicate the
same amount of resources to each bit. We propose a radically different approach
that: (i) employs analog memories to maximize the capacity of each memory cell,
and (ii) jointly optimizes model compression and physical storage to maximize
memory utility. We investigate the challenges of analog storage by studying
model storage on phase change memory (PCM) arrays and develop a variety of
robust coding strategies for NN model storage. We demonstrate the efficacy of
our approach on MNIST, CIFAR-10 and ImageNet datasets for both existing and
novel compression methods. Compared to conventional error-free digital storage,
our method has the potential to reduce the memory size by one order of
magnitude, without significantly compromising the stored model's accuracy.


Abstract:
  We propose a B tree representation storing $n$ keys, each of $k$ bits, in
either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits
of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b)
$O(\lg n / \lg \lg n)$ time, respectively. We can augment each node with an
aggregate value such as the minimum value within its subtree, and maintain
these aggregate values within the same space and time complexities. Finally, we
give the sparse suffix tree as an application, and present a linear-time
algorithm computing the sparse longest common prefix array from the suffix AVL
tree of Irving et al. [JDA'2003].


Abstract:
  We analyze the robustness of the exponential stability of
infinite-dimensional sampled-data systems with unbounded control operators. The
unbounded perturbations we consider are the so-called Desch-Schappacher
perturbations, which arises, e.g., from the boundary perturbations of systems
described by partial differential equations. As the main result, we show that
the exponential stability of the sampled-data systems is preserved under all
Desch-Schappacher perturbations sufficiently small in a certain sense.


Abstract:
  A recent focus of quantum spin liquid (QSL) studies is how
disorder/randomness in a QSL candidate affects its true magnetic ground state.
The ultimate question is whether the QSL survives disorder or the disorder
leads to a "spin-liquid-like" state, such as the proposed random-singlet (RS)
state. Since disorder is a standard feature of most QSL candidates, this
question represents a major challenge for QSL candidates. YbMgGaO$_4$, a
triangular lattice antiferromagnet with effective spin-1/2 Yb$^{3+}$ ions, is
an ideal system to address this question, since it shows no long-range magnetic
ordering with Mg/Ga site disorder. Despite the intensive study, it remains
unresolved as to whether YbMgGaO$_4$ is a QSL or in the RS state. Here, through
ultralow-temperature thermal conductivity and magnetic torque measurements,
plus specific heat and DC magnetization data, we observed a residual
$\kappa_0/T$ term and series of quantum spin state transitions in the zero
temperature limit for YbMgGaO$_4$. These observations strongly suggest that a
QSL state with itinerant excitations and quantum spin fluctuations survives
disorder in YbMgGaO$_4$.


Abstract:
  Monte Carlo (MC) dropout is a simple and efficient ensembling method that can
improve the accuracy and confidence calibration of high-capacity deep neural
network models. However, MC dropout is not as effective as more
compute-intensive methods such as deep ensembles. This performance gap can be
attributed to the relatively poor quality of individual models in the MC
dropout ensemble and their lack of diversity. These issues can in turn be
traced back to the coupled training and substantial parameter sharing of the
dropout models. Motivated by this perspective, we propose a strategy to compute
an ensemble of subnetworks, each corresponding to a non-overlapping dropout
mask computed via a pruning strategy and trained independently. We show that
the proposed subnetwork ensembling method can perform as well as standard deep
ensembles in both accuracy and uncertainty estimates, yet with a computational
efficiency similar to MC dropout. Lastly, using several computer vision
datasets like CIFAR10/100, CUB200, and Tiny-Imagenet, we experimentally
demonstrate that subnetwork ensembling also consistently outperforms recently
proposed approaches that efficiently ensemble neural networks.


Abstract:
  Face recognition approaches often rely on equal image resolution for
verification faces on two images. However, in practical applications, those
image resolutions are usually not in the same range due to different image
capture mechanisms or sources. In this work, we first analyze the impact of
image resolutions on the face verification performance with a state-of-the-art
face recognition model. For images, synthetically reduced to $5\, \times 5\,
\mathrm{px}$ resolution, the verification performance drops from $99.23\%$
increasingly down to almost $55\%$. Especially, for cross-resolution image
pairs (one high- and one low-resolution image), the verification accuracy
decreases even further. We investigate this behavior more in-depth by looking
at the feature distances for every 2-image test pair. To tackle this problem,
we propose the following two methods: 1) Train a state-of-the-art
face-recognition model straightforward with $50\%$ low-resolution images
directly within each batch. \\ 2) Train a siamese-network structure and adding
a cosine distance feature loss between high- and low-resolution features. Both
methods show an improvement for cross-resolution scenarios and can increase the
accuracy at very low resolution to approximately $70\%$. However, a
disadvantage is that a specific model needs to be trained for every
resolution-pair ...


Abstract:
  To further understand the underlying mechanism of various reinforcement
learning (RL) algorithms and also to better use the optimization theory to make
further progress in RL, many researchers begin to revisit the linear-quadratic
regulator (LQR) problem, whose setting is simple and yet captures the
characteristics of RL. Inspired by this, this work is concerned with the
model-free design of stochastic LQR controller for linear systems subject to
Gaussian noises, from the perspective of both RL and primal-dual optimization.
From the RL perspective, we first develop a new model-free off-policy policy
iteration (MF-OPPI) algorithm, in which the sampled data is repeatedly used for
updating the policy to alleviate the data-hungry problem to some extent. We
then provide a rigorous analysis for algorithm convergence by showing that the
involved iterations are equivalent to the iterations in the classical policy
iteration (PI) algorithm. From the perspective of optimization, we first
reformulate the stochastic LQR problem at hand as a constrained non-convex
optimization problem, which is shown to have strong duality. Then, to solve
this non-convex optimization problem, we propose a model-based primal-dual
(MB-PD) algorithm based on the properties of the resulting Karush-Kuhn-Tucker
(KKT) conditions. We also give a model-free implementation for the MB-PD
algorithm by solving a transformed dual feasibility condition. More
importantly, we show that the dual and primal update steps in the MB-PD
algorithm can be interpreted as the policy evaluation and policy improvement
steps in the PI algorithm, respectively. Finally, we provide one simulation
example to show the performance of the proposed algorithms.


Abstract:
  We accelerate deep reinforcement learning-based training in visually complex
3D environments by two orders of magnitude over prior work, realizing
end-to-end training speeds of over 19,000 frames of experience per second on a
single GPU and up to 72,000 frames per second on a single eight-GPU machine.
The key idea of our approach is to design a 3D renderer and embodied navigation
simulator around the principle of "batch simulation": accepting and executing
large batches of requests simultaneously. Beyond exposing large amounts of work
at once, batch simulation allows implementations to amortize in-memory storage
of scene assets, rendering work, data loading, and synchronization costs across
many simulation requests, dramatically improving the number of simulated agents
per GPU and overall simulation throughput. To balance DNN inference and
training costs with faster simulation, we also build a computationally
efficient policy DNN that maintains high task performance, and modify training
algorithms to maintain sample efficiency when training with large mini-batches.
By combining batch simulation and DNN performance optimizations, we demonstrate
that PointGoal navigation agents can be trained in complex 3D environments on a
single GPU in 1.5 days to 97% of the accuracy of agents trained on a prior
state-of-the-art system using a 64-GPU cluster over three days. We provide
open-source reference implementations of our batch 3D renderer and simulator to
facilitate incorporation of these ideas into RL systems.


Abstract:
  We demonstrate dynamical topological phase transitions in evolving
Su-Schrieffer-Heeger (SSH) lattices made of interacting soliton arrays, which
are entirely driven by nonlinearity and thereby exemplify emergent nonlinear
topological phenomena. The phase transitions occur from topologically
trivial-to-nontrivial phase in periodic succession with crossovers from
topologically nontrivial-to-trivial regime. The signature of phase transition
is gap-closing and re-opening point, where two extended states are pulled from
the bands into the gap to become localized topological edge states. Crossovers
occur via decoupling of the edge states from the bulk of the lattice.


Abstract:
  Conditional quantile estimation is a key statistical learning challenge
motivated by the need to quantify uncertainty in predictions or to model a
diverse population without being overly reductive. As such, many models have
been developed for this problem. Adopting a meta viewpoint, we propose a
general framework (inspired by neural network optimization) for aggregating any
number of conditional quantile models in order to boost predictive accuracy. We
consider weighted ensembling strategies of increasing flexibility where the
weights may vary over individual models, quantile levels, and feature values.
An appeal of our approach is its portability: we ensure that estimated
quantiles at adjacent levels do not cross by applying simple transformations
through which gradients can be backpropagated, and this allows us to leverage
the modern deep learning toolkit for building quantile ensembles. Our
experiments confirm that ensembling can lead to big gains in accuracy, even
when the constituent models are themselves powerful and flexible.


Abstract:
  Internal oscillations in switched antenna transmitters cause undesirable
fluctuations of the stored energy in the system, reducing the effectiveness of
time-varying broadbanding methods, such as energy-synchronous direct antenna
modulation. To mitigate these parasitic oscillations, a modified direct antenna
modulation system with an auxiliary DC source is introduced to stabilize energy
storage on the antenna. A detailed circuit model for a direct antenna
modulation system is used to identify the origin of the oscillations and to
justify the selection of the DC source. Measured phase shift keyed waveforms
transmitted by the modified system show significant increases in signal
fidelity, including a 10-20 dB reduction in error vector magnitude compared to
a time-invariant system. Comparison to an equivalent, scalable time-invariant
antenna suggests that the switched transmitter behaves as though it has 2-3
times lower radiation Q-factor and 20% higher radiation efficiency.


Abstract:
  We define a product of pairs of double complex spaces $C^n_m(V, \mathcal{W},
\mathcal{F})$ for gradig-restricted vertex algebra cohomology of codimension
one foliation on a complex curve. We introduce a vertex algebra counterpart of
the classical %product-type cohomological class using the orthogonality
conditions on elements of double complex spaces with respect to the product we
introduced.


Abstract:
  Using the theory of Dirichlet forms we construct a large class of continuous
semimartingales on an open domain $E \subset \mathbb{R}^d$, which are governed
by rank-based, in addition to name-based, characteristics. Using the results of
Baur et al. [Potential Analysis, 38(4):1233-1258,2013] we obtain a strong
Feller property for this class of diffusions. As a consequence we are able to
establish the nonexistence of triple collisions and obtain a simplified formula
for the dynamics of its rank process. We also establish conditions under which
the process is ergodic. Our main motivation is Stochastic Portfolio Theory
(SPT), where rank-based diffusions of this type are used to model financial
markets. We show that three main classes of models studied in SPT -- Atlas
models, generalized volatility-stabilized models and polynomial models -- are
special cases of our framework.


Abstract:
  Multi-label text classification (MLTC) is an attractive and challenging task
in natural language processing (NLP). Compared with single-label text
classification, MLTC has a wider range of applications in practice. In this
paper, we propose a heterogeneous graph convolutional network model to solve
the MLTC problem by modeling tokens and labels as nodes in a heterogeneous
graph. In this way, we are able to take into account multiple relationships
including token-level relationships. Besides, the model allows a good
explainability as the token-label edges are exposed. We evaluate our method on
three real-world datasets and the experimental results show that it achieves
significant improvements and outperforms state-of-the-art comparison methods.


Abstract:
  Recent single-channel speech enhancement methods based on deep neural
networks (DNNs) have achieved remarkable results, but there are still
generalization problems in real scenes. Like other data-driven methods,
DNN-based speech enhancement models produce significant performance degradation
on untrained data. In this study, we make full use of the contribution of
multi-target joint learning to the model generalization capability, and propose
a lightweight and low-computing dilated convolutional network (DCN) model for a
more robust speech denoising task. Our goal is to integrate the masking target,
the mapping target, and the parameters of the traditional speech enhancement
estimator into a DCN model to maximize their complementary advantages. To do
this, we build a multi-stage learning framework to deal with multiple targets
in stages to achieve their joint learning, namely `MT-in-MS'. Our experimental
results show that compared with the state-of-the-art time domain and
time-frequency domain models, this proposed low-cost DCN model can achieve
better generalization performance in speaker, noise, and channel mismatch
cases.


Abstract:
  The importance of the chromosphere in the mass and energy transport within
the solar atmosphere is now widely recognised. This review discusses the
physics of magnetohydrodynamic (MHD) waves and instabilities in large-scale
chromospheric structures as well as in magnetic flux tubes. We highlight a
number of key observational aspects that have helped our understanding of the
role of the solar chromosphere in various dynamic processes and wave phenomena,
and the heating scenario of the solar chromosphere is also discussed. The
review focuses on the physics of waves and invokes the basics of plasma
instabilities in the context of this important layer of the solar atmosphere.
Potential implications, future trends and outstanding questions are also
delineated.


Abstract:
  Integrated optical amplifiers and light sources are of great significance for
photonic integrated circuits (PICs) and have attracted many research interests.
Doping rare-earth ions in materials as a solution to realize efficient optical
amplifiers and lasing has been investigated a lot. We investigate the
erbium-doped lithium niobate on insulator (LNOI). Here, spiral waveguide
amplifiers were fabricated on a 1-mol\% erbium-doped LNOI by CMOS-compatible
technique. We demonstrated a maximum internal net gain of 8.3 dB at 1530 nm
indicating a net gain per unit length of 15.6 dB/cm with a compact spiral
waveguide of 5.3 mm length and $ \sim $0.06 mm$ ^{2} $ footprint. The
erbium-doped integrated lithium niobate spiral waveguide amplifiers would pave
the way in the PICs of the lithium niobate platform, especially in achieving
efficient integration of active and passive devices on a lithium niobate thin
film, which will make full use of its excellent physical properties such as
remarkable photoacoustic, electro-optic, and piezoelectric characteristics.


Abstract:
  This paper aims at studying a generalized Camassa-Holm equation under random
perturbation. We establish a local well-posedness result in the sense of
Hadamard, i.e., existence, uniqueness and continuous dependence on initial
data, as well as blow-up criteria for pathwise solutions in the Sobolev spaces
$H^s$ with $s>3/2$ for two cases, i.e., $x\in\R$ and $x\in\T=(\R/2\pi\Z)$. The
analysis on continuous dependence on initial data for nonlinear stochastic
partial differential equations has gained less attention in the literature so
far. In this work, we first show that the solution map is continuous. Then we
introduce a notion of stability of exiting times. We provide an example showing
that one cannot improve the stability of the exiting time and simultaneously
improve the continuity of the dependence on initial data. Finally, we analyze
the regularization effect of nonlinear noise in preventing blow-up. Precisely,
we demonstrate that global existence holds true almost surely provided that the
noise is strong enough.


Abstract:
  Novel dynamical phases that violate ergodicity have been a subject of
extensive research in recent years. A periodically driven system is naively
expected to lose all memory of its initial state due to thermalization, yet
this can be avoided in the presence of many-body localization. A discrete time
crystal represents a driven system whose local observables spontaneously break
time translation symmetry and retain memory of the initial state indefinitely.
Here we report the observation of a discrete time crystal on a chain consisting
of 57 superconducting qubits on a state-of-the-art quantum computer. We probe
random initial states and compare the cases of vanishing and finite disorder to
distinguish many-body localization from pre-thermal dynamics. We further report
results on the dynamical phase transition between the discrete time crystal and
a thermal regime, which is observed via critical fluctuations in the system's
sub-harmonic frequency response and a significant speed-up of spin
depolarisation.


Abstract:
  "Deep Learning"/"Deep Neural Nets" is a technological marvel that is now
increasingly deployed at the cutting-edge of artificial intelligence tasks.
This dramatic success of deep learning in the last few years has been hinged on
an enormous amount of heuristics and it has turned out to be a serious
mathematical challenge to be able to rigorously explain them. In this thesis,
submitted to the Department of Applied Mathematics and Statistics, Johns
Hopkins University we take several steps towards building strong theoretical
foundations for these new paradigms of deep-learning. In chapter 2 we show new
circuit complexity theorems for deep neural functions and prove classification
theorems about these function spaces which in turn lead to exact algorithms for
empirical risk minimization for depth 2 ReLU nets. We also motivate a measure
of complexity of neural functions to constructively establish the existence of
high-complexity neural functions. In chapter 3 we give the first algorithm
which can train a ReLU gate in the realizable setting in linear time in an
almost distribution free set up. In chapter 4 we give rigorous proofs towards
explaining the phenomenon of autoencoders being able to do sparse-coding. In
chapter 5 we give the first-of-its-kind proofs of convergence for stochastic
and deterministic versions of the widely used adaptive gradient deep-learning
algorithms, RMSProp and ADAM. This chapter also includes a detailed empirical
study on autoencoders of the hyper-parameter values at which modern algorithms
have a significant advantage over classical acceleration based methods. In the
last chapter 6 we give new and improved PAC-Bayesian bounds for the risk of
stochastic neural nets. This chapter also includes an experimental
investigation revealing new geometric properties of the paths in weight space
that are traced out by the net during the training.


Abstract:
  We give a complexity dichotomy for the Quantified Constraint Satisfaction
Problem QCSP(H) when H is a reflexive tournament. It is well-known that
reflexive tournaments can be split into a sequence of strongly connected
components H_1,...,H_n so that there exists an edge from every vertex of H_i to
every vertex of H_j if and only if i<j. We prove that if H has both its initial
and final strongly connected component (possibly equal) of size 1, then QCSP(H)
is in NL and otherwise QCSP(H) is NP-hard.


Abstract:
  The boundaries of quantum materials can host a variety of exotic effects such
as topologically robust edge states or anyonic quasiparticles. Here, we show
that fermionic systems such as graphene that admit a low energy Dirac
description can exhibit counterintuitive relativistic effects at their
boundaries. As an example, we consider carbon nanotubes and demonstrate that
relativistic bulk spinor states can have non zero charge density on the
boundaries, in contrast to the sinusoidal distribution of non-relativistic wave
functions that are necessarily zero at the boundaries. This unusual property of
relativistic spinors is complementary to the linear energy dispersion relation
exhibited by Dirac materials and can influence their coupling to leads,
transport properties or their response to external fields.


Abstract:
  Most modern asset transfer systems use consensus to maintain a totally
ordered chain of transactions. It was recently shown that consensus is not
always necessary for implementing asset transfer. More efficient, asynchronous
solutions can be built using reliable broadcast instead of consensus. This
approach has been originally used in the closed (permissioned) setting. In this
paper, we extend it to the open (permissionless) environment. We present
Pastro, a permissionless and asynchronous asset-transfer implementation, in
which quorum systems, traditionally used in reliable broadcast, are replaced
with a weighted Proof-of-Stake mechanism. Pastro tolerates a dynamic adversary
that is able to adaptively corrupt participants based on the assets owned by
them.


Abstract:
  We present analysis of XMM-Newton Optical Monitor observations in the
near-ultraviolet of HD 189733, covering twenty primary transits of its hot
Jupiter planet. The transit is clearly detected with both the UVW2 and UVM2
filters, and our fits to the data reveal transit depths in agreement with that
observed optically. The measured depths correspond to radii of
$1.059^{+0.046}_{-0.050}$ and $0.94^{+0.15}_{-0.17}$ times the
optically-measured radius (1.187 R$_{\rm J}$ at 4950 \r{A}) in the UVW2 and
UVM2 bandpasses, respectively. We also find no statistically significant
variation in the transit depth across the 8 year baseline of the observations.
We rule out extended broadband absorption towards or beyond the Roche lobe at
the wavelengths investigated, although observations with higher spectral
resolution are required to determine if absorption out to those distances from
the planet is present in individual near-UV lines.


Abstract:
  Hawking has predicted that the formation of a black hole by gravitational
collapse causes quantum particle creation and the spectrum of the particles is
almost thermal. This phenomenon is called the Hawking radiation. Recently, it
has been predicted that the particle creation may drastically change from the
Hawking radiation to a strong double burst if the gravitational collapse
suddenly stops just before the formation of the event horizon. By contrast with
the Hawking radiation, the burst may be so strong that it can be of
observational interest even for collapsing objects with astrophysical mass
scales. However, the burst phenomenon has been predicted through the studies of
idealized models in which a spherical hollow shell begins to collapse, but
stops shrinking and eventually settles down to a static "star". Therefore, one
might guess that it could be particular to the hollow shell model. In this
paper, we study the particle creation due to the gravitational collapse of a
spherical object whose interior is filled with matter. In this model, we obtain
similar results to those in the case of the hollow shell model. This implies
that the double burst is a robust property of particle creation by the sudden
braking of gravitational collapse.


Abstract:
  Compositional disorder induces myriad captivating phenomena in perovskites.
Target-driven discovery of perovskite solid solutions has been a great
challenge due to the analytical complexity introduced by disorder. Here, we
demonstrate that an unsupervised deep learning strategy can find fingerprints
of disordered materials that embed perovskite formability and underlying
crystal structure information by learning only from the chemical composition,
manifested in (A1-xA'x)BO3 and A(B1-xB'x)O3 formulae. This phenomenon can be
capitalized to predict the crystal symmetry of experimental compositions,
outperforming several supervised machine learning (ML) algorithms. The educated
nature of material fingerprints has led to the conception of analogical
materials discovery that facilitates inverse exploration of promising
perovskites based on similarity investigation with known materials. The search
space of unstudied perovskites is screened from ~600,000 feasible compounds
using experimental data powered ML models and automated web mining tools at a
94% success rate. This concept further provides insights on possible phase
transitions and computational modelling of complex compositions. The proposed
quantitative analysis of materials analogies is expected to bridge the gap
between the existing materials literature and the undiscovered terrain.


Abstract:
  Recently the LARS and LAMB optimizers have been proposed for training neural
networks faster using large batch sizes. LARS and LAMB add layer-wise
normalization to the update rules of Heavy-ball momentum and Adam,
respectively, and have become popular in prominent benchmarks and deep learning
libraries. However, without fair comparisons to standard optimizers, it remains
an open question whether LARS and LAMB have any benefit over traditional,
generic algorithms. In this work we demonstrate that standard optimization
algorithms such as Nesterov momentum and Adam can match or exceed the results
of LARS and LAMB at large batch sizes. Our results establish new, stronger
baselines for future comparisons at these batch sizes and shed light on the
difficulties of comparing optimizers for neural network training more
generally.


Abstract:
  Datacenter power demand has been continuously growing and is the key driver
of its cost. An accurate mapping of compute resources (CPU, RAM, etc.) and
hardware types (servers, accelerators, etc.) to power consumption has emerged
as a critical requirement for major Web and cloud service providers. With the
global growth in datacenter capacity and associated power consumption, such
models are essential for important decisions around datacenter design and
operation. In this paper, we discuss two classes of statistical power models
designed and validated to be accurate, simple, interpretable and applicable to
all hardware configurations and workloads across hyperscale datacenters of
Google fleet. To the best of our knowledge, this is the largest scale power
modeling study of this kind, in both the scope of diverse datacenter planning
and real-time management use cases, as well as the variety of hardware
configurations and workload types used for modeling and validation. We
demonstrate that the proposed statistical modeling techniques, while simple and
scalable, predict power with less than 5% Mean Absolute Percent Error (MAPE)
for more than 95% diverse Power Distribution Units (more than 2000) using only
4 features. This performance matches the reported accuracy of the previous
started-of-the-art methods, while using significantly less features and
covering a wider range of use cases.


Abstract:
  Several neural network approaches for solving differential equations employ
trial solutions with a feedforward neural network. There are different means to
incorporate the trial solution in the construction, for instance one may
include them directly in the cost function. Used within the corresponding
neural network, the trial solutions define the so-called neural form. Such
neural forms represent general, flexible tools by which one may solve various
differential equations. In this article we consider time-dependent initial
value problems, which require to set up the neural form framework adequately.
The neural forms presented up to now in the literature for such a setting can
be considered as first order polynomials. In this work we propose to extend the
polynomial order of the neural forms. The novel collocation-type construction
includes several feedforward neural networks, one for each order. Additionally,
we propose the fragmentation of the computational domain into subdomains. The
neural forms are solved on each subdomain, whereas the interfacing grid points
overlap in order to provide initial values over the whole fragmentation. We
illustrate in experiments that the combination of collocation neural forms of
higher order and the domain fragmentation allows to solve initial value
problems over large domains with high accuracy and reliability.


Abstract:
  The variational quantum Monte Carlo (VQMC) method received significant
attention in the recent past because of its ability to overcome the curse of
dimensionality inherent in many-body quantum systems. Close parallels exist
between VQMC and the emerging hybrid quantum-classical computational paradigm
of variational quantum algorithms. VQMC overcomes the curse of dimensionality
by performing alternating steps of Monte Carlo sampling from a parametrized
quantum state followed by gradient-based optimization. While VQMC has been
applied to solve high-dimensional problems, it is known to be difficult to
parallelize, primarily owing to the Markov Chain Monte Carlo (MCMC) sampling
step. In this work, we explore the scalability of VQMC when autoregressive
models, with exact sampling, are used in place of MCMC. This approach can
exploit distributed-memory, shared-memory and/or GPU parallelism in the
sampling task without any bottlenecks. In particular, we demonstrate the
GPU-scalability of VQMC for solving up to ten-thousand dimensional
combinatorial optimization problems.


Abstract:
  Neural networks are sensitive to hyper-parameter and architecture choices.
Automated Machine Learning (AutoML) is a promising paradigm for automating
these choices. Current ML software libraries, however, are quite limited in
handling the dynamic interactions among the components of AutoML. For example,
efficientNAS algorithms, such as ENAS and DARTS, typically require an
implementation coupling between the search space and search algorithm, the two
key components in AutoML. Furthermore, implementing a complex search flow, such
as searching architectures within a loop of searching hardware configurations,
is difficult. To summarize, changing the search space, search algorithm, or
search flow in current ML libraries usually requires a significant change in
the program logic. In this paper, we introduce a new way of programming AutoML
based on symbolic programming. Under this paradigm, ML programs are mutable,
thus can be manipulated easily by another program. As a result, AutoML can be
reformulated as an automated process of symbolic manipulation. With this
formulation, we decouple the triangle of the search algorithm, the search space
and the child program. This decoupling makes it easy to change the search space
and search algorithm (without and with weight sharing), as well as to add
search capabilities to existing code and implement complex search flows. We
then introduce PyGlove, a new Python library that implements this paradigm.
Through case studies on ImageNet and NAS-Bench-101, we show that with PyGlove
users can easily convert a static program into a search space, quickly iterate
on the search spaces and search algorithms, and craft complex search flows to
achieve better results.


Abstract:
  We identify a quantum critical point with fractal symmetry whose effective
theory eludes the renormalization group framework. We consider the Newman-Moore
model with three-body interaction subjected to an external transverse field,
which exhibits a Kramers-Wannier type self-duality and a fractal $Z_2$ symmetry
with Ising charge conserved on a fractal subset of sites, i.e., on Sierpinski
gaskets. Using large-scale quantum Monte Carlo simulations, we identify a
continuous quantum phase transition between a phase with spontaneous fractal
symmetry breaking and a paramagnetic phase. This phase transition is
characterized by the emergence of a fractal scaling dimension $d=\ln(3)/\ln(2)$
at the quantum critical point, where the power-law exponent of the correlation
function is related to the fractal dimension of the Sierpinski triangle. We
develop a field theory to elucidate such quantum criticality and denote the
fractal scaling as a subsequence of UV-IR mixing, where the low energy modes at
the critical point are manipulated by short-wavelength physics due to the
fractal symmetry.


Abstract:
  The recent discovery of magnetic topological insulators has opened new
avenues to explore exotic states of matter that can emerge from the interplay
between topological electronic states and magnetic degrees of freedom, be it
ordered or strongly fluctuating. Motivated by the effects that the dynamics of
the magnetic moments can have on the topological surface states, we investigate
the magnetic fluctuations across the
(MnBi$_{\text{2}}$Te$_{\text{4}}$)(Bi$_{\text{2}}$Te$_{\text{3}}$)$_{\text{n}}$
family. Our paramagnetic electron spin resonance experiments reveal contrasting
Mn spin dynamics in different compounds, which manifests in a strongly
anisotropic Mn spin relaxation in MnBi$_{\text{2}}$Te$_{\text{4}}$ while being
almost isotropic in MnBi$_{\text{4}}$Te$_{\text{7}}$. Our density-functional
calculations explain these striking observations in terms of the sensitivity of
the local electronic structure to the Mn spin-orientation, and indicate that
the anisotropy of the magnetic fluctuations can be controlled by the carrier
density, which may directly affect the electronic topological surface states.


Abstract:
  We demonstrate fast and ultrasensitive charge detection with a
cavity-embedded Cooper pair transistor (cCPT) via dispersive readout of its
Josephson inductance. We report a minimum charge sensitivity of $14$ $\mu
e/\sqrt{\mathrm{Hz}}$ with a detection bandwidth on the order of $1$ MHz using
$16$ attowatts of power, corresponding to the single-photon level of the
cavity. In addition, our measured sensitivities are within a factor of $5$ of
the quantum limit for this device. The single-photon-level sensitivity of the
cCPT is comparable to that of the rf-SET, which typically operates using
picowatts of power corresponding to hundreds of thousands of photons in its
tank circuit. Our results support the feasibility of using the cCPT to mediate
an optomechanical interaction that reaches the single-photon strong coupling
regime.


Abstract:
  In this paper, we generalize the problem of single-index model to the context
of continual learning in which a learner is challenged with a sequence of tasks
one by one and the dataset of each task is revealed in an online fashion. We
propose a randomized strategy that is able to learn a common single-index
(meta-parameter) for all tasks and a specific link function for each task. The
common single-index allows to transfer the information gained from the previous
tasks to a new one. We provide a rigorous theoretical analysis of our proposed
strategy by proving some regret bounds under different assumption on the loss
function.


Abstract:
  This work is the first to propose the concept of a semantic numeration system
(SNS) as a certain class of context-based numeration methods. The development
of the SNS concept required the introduction of fundamentally new concepts such
as a cardinal abstract entity, a cardinal semantic operator, a cardinal
abstract object, a numeration space. The main attention is paid to the key
elements of semantic numeration systems - cardinal semantic operators. A
classification of semantic numeration systems is given.


Abstract:
  The preparation of low-entropy starting conditions is a key requirement for
many experiments involving neutral atoms. Here, we propose a method to
autonomously assemble arbitrary spatial configurations of atoms within arrays
of optical tweezers or lattice sites, enabled by a combination of tunneling and
ground-state laser cooling. In contrast to previous methods, our protocol does
not rely on either imaging or evaporative cooling. This circumvents limitations
associated with imaging fidelity and loss, especially in systems with small
spatial scales, while providing a substantial improvement in speed relative to
evaporative approaches. These features may make it well-suited for preparing
arbitrary initial conditions for Bose-Hubbard or Rydberg interacting systems.


Abstract:
  Abstract syntax tree (AST) mapping algorithms are widely used to analyze
changes in source code. Despite the foundational role of AST mapping
algorithms, little effort has been made to evaluate the accuracy of AST mapping
algorithms, i.e., the extent to which an algorihtm captures the evolution of
code. We observe that a program element often has only one best-mapped program
element. Based on this observation, we propose a hierarchical approach to
automatically compare the similarity of mapped statements and tokens by
different algorithms. By performing the comparison, we determine if each of the
compared algorithms generates inaccurate mappings for a statement or its
tokens. We invite 12 external experts to determine if three commonly used AST
mapping algorithms generate accurate mappings for a statement and its tokens
for 200 statements. Based on the experts' feedback,we observe that our approach
achieves a precision of 0.98--1.00 and a recall of 0.65--0.75. Furthermore, we
conduct a large-scale study with a dataset of ten Java projects, containing a
total of 263,165 file revisions. Our approach determines that GumTree, MTDiff
and IJM generate inaccurate mappings for 20%--29%, 25%--36% and 21%--30% of the
file revisions, respectively. Our experimental results show that state-of-art
AST mapping agorithms still need improvements.


Abstract: We compute the area of a generic d-sphere in a Snyder geometry.


Abstract:
  In this letter we generalize Spekkens' notion of measurement
non-contextuality (NC). We show that any non-contextual ontological model based
on this notion of contextuality fails to explain the statistics of outcomes of
a single carefully constructed POVM executed sequentially on a quantum system.
The POVM essentially forms a single measurement device. The context of
measurement arises from the different configurations in which the device can be
used. We develop an inequality from the non-contextual ontic model, and
construct corresponding quantum situations where the measurement outcomes from
the device violate this NC inequality. Our work brings out the hitherto
unexplored implications of contextuality for a single measurement device, and
paves the way for further study of consequences of contextuality for sequential
measurements.


Abstract:
  Travel speed is an intrinsic feature of transport, and enlarging the speed is
considered as beneficial. The benefit of a speed increase is generally assessed
as the value of the saved travel time. However, this approach conflicts with
the observation that time spent on travelling is rather constant and might not
be affected by speed changes. The paper aims to define the benefits of a speed
increase and addresses two research questions. First, how will a speed increase
in person transport work out, which factors are affected? Second, is the value
of time a good proxy for the value of speed? Based on studies on time spending
and research on the association between speed and land use, we argue that human
wealth could be the main affected factor by speed changes, rather than time or
access. Then the value of time is not a good proxy for the value of speed: the
benefits of a wealth increase are negatively correlated with prosperity
following the law of diminishing marginal utility, while the calculated
benefits of saved travel time prove to be positively correlated. The inadequacy
of the value of time is explained by some shortcomings with respect to the
willingness to pay that is generally used for assessing the value of time:
people do not predict correctly the personal benefits that will be gained from
a decision, and they neglect the social impacts.


Abstract:
  Superconductivity allows to construct and operate magnets at field values
beyond 2 Tesla, the practical limitation of normal-conducting magnets
exploiting ferro-magnetism. The field of superconducting magnets is dominated
by the field generated in the coil. The stored energy and the electromagnetic
forces generated by the coil are the main challenges to be overcome in the
design of these magnets. For further reading you may consult the following
books: [1], [2], [3], [4] or the proceedings of two specialized CAS courses:
[5] and [6].


Abstract:
  The convex body isoperimetric conjecture in the plane asserts that the least
perimeter to enclose given area inside a unit disk is greater than inside any
other convex set of area $\pi$. In this note we confirm two cases of the
conjecture: domains symmetric to both coordinate axes and perturbations of unit
disk.


Abstract:
  Most recent video super-resolution (SR) methods either adopt an iterative
manner to deal with low-resolution (LR) frames from a temporally sliding
window, or leverage the previously estimated SR output to help reconstruct the
current frame recurrently. A few studies try to combine these two structures to
form a hybrid framework but have failed to give full play to it. In this paper,
we propose an omniscient framework to not only utilize the preceding SR output,
but also leverage the SR outputs from the present and future. The omniscient
framework is more generic because the iterative, recurrent and hybrid
frameworks can be regarded as its special cases. The proposed omniscient
framework enables a generator to behave better than its counterparts under
other frameworks. Abundant experiments on public datasets show that our method
is superior to the state-of-the-art methods in objective metrics, subjective
visual effects and complexity. Our code will be made public.


Abstract:
  In this paper, we discuss the application of the Generalized Finite Element
Method (GFEM) to approximate the solutions of quasilinear elliptic equations
with multiple interfaces in one dimensional space. The problem is characterized
by spatial discontinuity of the elliptic coefficient that depends on the
unknown solution. It is known that unless the partition of the domain matches
the discontinuity configuration, accuracy of standard finite element techniques
significantly deteriorates and standard refinement of the partition may not
suffice. The GFEM is a viable alternative to overcome this predicament. It is
based on the construction of certain enrichment functions supplied to the
standard space that capture effects of the discontinuity. This approach is
called stable (SGFEM) if it maintains an optimal rate of convergence and the
conditioning of GFEM is not worse than that of the standard FEM. A convergence
analysis is derived and performance of the method is illustrated by several
numerical examples. Furthermore, it is known that typical global formulations
such as FEMs do not enjoy the numerical local conservation property that is
crucial in many conservation law-based applications. To remedy this issue, a
Lagrange multiplier technique is adopted to enforce the local conservation. A
numerical example is given to demonstrate the performance of proposed
technique.


Abstract:
  We present a protocol for the fully automated construction of quantum
mechanical-(QM)-classical hybrid models by extending our previously reported
approach on self-parametrizing system-focused atomistic models (SFAM) J. Chem.
Theory Comput. 2020, 16, 1646]. In this QM/SFAM approach, the size and
composition of the QM region is evaluated in an automated manner based on first
principles so that the hybrid model describes the atomic forces in the center
of the QM region accurately. This entails the automated construction and
evaluation of differently sized QM regions with a bearable computational
overhead that needs to be paid for automated validation procedures. Applying
SFAM for the classical part of the model eliminates any dependence on
pre-existing parameters due to its system-focused quantum mechanically derived
parametrization. Hence, QM/SFAM is capable of delivering a high fidelity and
complete automation. Furthermore, since SFAM parameters are generated for the
whole system, our ansatz allows for a convenient re-definition of the QM region
during a molecular exploration. For this purpose, a local re-parametrization
scheme is introduced, which efficiently generates additional classical
parameters on the fly when new covalent bonds are formed (or broken) and moved
to the classical region.


Abstract:
  We extend the notion of the Nieh-Yan invariant to generic metric-affine
geometries, where both torsion and nonmetricity are taken into account.
Notably, we show that the properties of projective invariance and topologicity
can be independently accommodated by a suitable choice of the parameters
featuring this new Nieh-Yan term. We then consider a special class of modified
theories of gravity able to promote the Immirzi parameter to a dynamical scalar
field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics
of the effective scalar tensor theory stemming from such a revised theoretical
framework. We focus, in particular, on cosmological Bianchi I models and we
derive classical solutions where the initial singularity is safely removed in
favor of a big-bounce, which is ultimately driven by the non-minimal coupling
with the Immirzi field. These solutions, moreover, turn out to be characterized
by finite time singularities, but we show that such critical points do not
spoil the geodesic completeness and wave regularity of these space-times.


Abstract:
  This paper explores a family of generalized sweeping preconditionners for
Helmholtz problems with non-overlapping checkerboard partition of the
computational domain. The domain decomposition procedure relies on high-order
transmission conditions and cross-point treatments, which cannot scale without
an efficient preconditioning technique when the number of subdomains increases.
With the proposed approach, existing sweeping preconditioners, such as the
symmetric Gauss-Seidel and parallel double sweep preconditioners, can be
applied to checkerboard partitions with different sweeping directions (e.g.
horizontal and diagonal). Several directions can be combined thanks to the
flexible version of GMRES, allowing for the rapid transfer of information in
the different zones of the computational domain, then accelerating the
convergence of the final iterative solution procedure. Several two-dimensional
finite element results are proposed to study and to compare the sweeping
preconditioners, and to illustrate the performance on cases of increasing
complexity.


Abstract:
  We study the global strong solutions to the compressible Navier-Stokes system
with potential temperature transport in $\mathbb{R}^n.$ Different from the
Navier-Stokes-Fourier system, the pressure is a nonlinear function of the
density and the potential temperature, we can not exploit the special
quasi-diagonalization structure of this system to capture any dissipation of
the density. Some new idea and delicate analysis involved in high or low
frequency decomposition in the Besov spaces have to be made to close the energy
estimates.


Abstract:
  This paper presents the system that we propose for the Reliable Intelligence
Indentification on Vietnamese Social Network Sites (ReINTEL) task of the
Vietnamese Language and Speech Processing 2020 (VLSP 2020) Shared Task. In this
task, the VLSP 2020 provides a dataset with approximately 6,000 trainning
news/posts annotated with reliable or unreliable labels, and a test set
consists of 2,000 examples without labels. In this paper, we conduct
experiments on different transfer learning models, which are bert4news and
PhoBERT fine-tuned to predict whether the news is reliable or not. In our
experiments, we achieve the AUC score of 94.52% on the private test set from
ReINTEL's organizers.


Abstract:
  This paper presents an efficient multi-scale vision Transformer, called ResT,
that capably served as a general-purpose backbone for image recognition. Unlike
existing Transformer methods, which employ standard Transformer blocks to
tackle raw images with a fixed resolution, our ResT have several advantages:
(1) A memory-efficient multi-head self-attention is built, which compresses the
memory by a simple depth-wise convolution, and projects the interaction across
the attention-heads dimension while keeping the diversity ability of
multi-heads; (2) Position encoding is constructed as spatial attention, which
is more flexible and can tackle with input images of arbitrary size without
interpolation or fine-tune; (3) Instead of the straightforward tokenization at
the beginning of each stage, we design the patch embedding as a stack of
overlapping convolution operation with stride on the 2D-reshaped token map. We
comprehensively validate ResT on image classification and downstream tasks.
Experimental results show that the proposed ResT can outperform the recently
state-of-the-art backbones by a large margin, demonstrating the potential of
ResT as strong backbones. The code and models will be made publicly available
at https://github.com/wofmanaf/ResT.


Abstract:
  In linear regression, SLOPE is a new convex analysis method that generalizes
the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized
more heavily. This magnitude-dependent regularization requires an input of
penalty sequence $\lambda$, instead of a scalar penalty as in the Lasso case,
thus making the design extremely expensive in computation. In this paper, we
propose two efficient algorithms to design the possibly high-dimensional SLOPE
penalty, in order to minimize the mean squared error. For Gaussian data
matrices, we propose a first order Projected Gradient Descent (PGD) under the
Approximate Message Passing regime. For general data matrices, we present a
zero-th order Coordinate Descent (CD) to design a sub-class of SLOPE, referred
to as the k-level SLOPE. Our CD allows a useful trade-off between the accuracy
and the computation speed. We demonstrate the performance of SLOPE with our
designs via extensive experiments on synthetic data and real-world datasets.


Abstract:
  Generating diverse populations of high quality solutions has gained interest
as a promising extension to the traditional optimization tasks. We contribute
to this line of research by studying evolutionary diversity optimization for
two of the most prominent permutation problems, namely the Traveling
Salesperson Problem (TSP) and Quadratic Assignment Problem (QAP). We explore
the worst-case performance of a simple mutation-only evolutionary algorithm
with different mutation operators, using an established diversity measure.
Theoretical results show most mutation operators for both problems ensure
production of maximally diverse populations of sufficiently small size within
cubic expected run-time. We perform experiments on QAPLIB instances in
unconstrained and constrained settings, and reveal much more optimistic
practical performances. Our results should serve as a baseline for future
studies.


Abstract:
  Two-dimensional molecular crystals have been beyond the reach of systematic
investigation because of the lack or instability of their well-defined forms.
Here, we demonstrate drastically enhanced photostability and Davydov splitting
in single and few-layer tetracene (Tc) crystals sandwiched between inorganic 2D
crystals of graphene or hexagonal BN. Molecular orientation and long-range
order mapped with polarized wide-field photoluminescence imaging and optical
second-harmonic generation revealed high crystallinity of the 2D Tc and its
distinctive orientational registry with the 2D inorganic crystals, which were
also verified with first-principles calculations. The reduced dielectric
screening in 2D space was manifested by enlarged Davydov splitting and
attenuated vibronic sidebands in the excitonic absorption and emission of
monolayer Tc crystals. Photostable 2D molecular crystals and their size effects
will lead to novel photophysical principles and photonic applications.


Abstract:
  A new paradigm for data-driven, model-agnostic new physics searches at
colliders is emerging, and aims to leverage recent breakthroughs in anomaly
detection and machine learning. In order to develop and benchmark new anomaly
detection methods within this framework, it is essential to have standard
datasets. To this end, we have created the LHC Olympics 2020, a community
challenge accompanied by a set of simulated collider events. Participants in
these Olympics have developed their methods using an R&D dataset and then
tested them on black boxes: datasets with an unknown anomaly (or not). This
paper will review the LHC Olympics 2020 challenge, including an overview of the
competition, a description of methods deployed in the competition, lessons
learned from the experience, and implications for data analyses with future
datasets as well as future colliders.


Abstract:
  In the present paper, we develop the algorithmic correspondence theory for
hybrid logic with binder. We define the class of Sahlqvist inequalities, each
inequality of which is shown to have a first-order frame correspondent
effectively computable by an algorithm ALBA.


Abstract:
  In protoplanetary discs and planetary atmospheres, dust grains coagulate to
form fractal dust aggregates. The geometric cross-section of these aggregates
is a crucial parameter characterizing aerodynamical friction, collision rates,
and opacities. However, numerical measurements of the cross-section are often
time-consuming as aggregates exhibit complex shapes. In this study, we derive a
novel analytic expression for geometric cross-sections of fractal aggregates.
If an aggregate consists of $N$ monomers of radius $R_0$, its geometric
cross-section $G$ is expressed as \begin{equation} \frac{G}{N\pi
R_0^2}=\frac{A}{1+(N-1)\tilde{\sigma}}, \nonumber
  \end{equation} where $\tilde{\sigma}$ is an overlapping efficiency, and $A$
is a numerical factor connecting the analytic expression to the small
non-fractal cluster limit. The overlapping efficiency depends on the fractal
dimension, fractal prefactor, and $N$ of the aggregate, and its analytic
expression is derived as well. The analytic expressions successfully reproduce
numerically measured cross-sections of aggregates. We also find that our
expressions are compatible with the mean-field light scattering theory of
aggregates in the geometrical optics limit. The analytic expressions greatly
simplify an otherwise tedious calculation and will be useful in model
calculations of fractal grain growth in protoplanetary discs and planetary
atmospheres.


Abstract:
  The complexity of comprehensive ocean models poses an important question for
parameterisations: is there a minimum set of equations that should be
parameterised, on the one hand, to reduce the development to a minimum, and, on
the other hand, to ensure an accurate representation of large-scale flow
patterns? This work seeks to answer this to assist modern parameterisations be
more selective in their targets. For this, we considered a North Atlantic
configuration of the MIT general circulation model and studied contributions of
different model equations to the accuracy of representation of the Gulf Stream
at low resolution. Our results suggest that it is enough to parameterise only
the tracer equations for temperature and salinity and leave the other equations
in the hydrodynamic part, as well as the atmospheric model unmodified.


Abstract:
  The increasing complexity of configuring cellular networks suggests that
machine learning (ML) can effectively improve 5G technologies. Deep learning
has proven successful in ML tasks such as speech processing and computational
vision, with a performance that scales with the amount of available data. The
lack of large datasets inhibits the flourish of deep learning applications in
wireless communications. This paper presents a methodology that combines a
vehicle traffic simulator with a raytracing simulator, to generate channel
realizations representing 5G scenarios with mobility of both transceivers and
objects. The paper then describes a specific dataset for investigating
beams-election techniques on vehicle-to-infrastructure using millimeter waves.
Experiments using deep learning in classification, regression and reinforcement
learning problems illustrate the use of datasets generated with the proposed
methodology


Abstract:
  Video deraining is an important task in computer vision as the unwanted rain
hampers the visibility of videos and deteriorates the robustness of most
outdoor vision systems. Despite the significant success which has been achieved
for video deraining recently, two major challenges remain: 1) how to exploit
the vast information among continuous frames to extract powerful
spatio-temporal features across both the spatial and temporal domains, and 2)
how to restore high-quality derained videos with a high-speed approach. In this
paper, we present a new end-to-end video deraining framework, named Enhanced
Spatio-Temporal Interaction Network (ESTINet), which considerably boosts
current state-of-the-art video deraining quality and speed. The ESTINet takes
the advantage of deep residual networks and convolutional long short-term
memory, which can capture the spatial features and temporal correlations among
continuing frames at the cost of very little computational source. Extensive
experiments on three public datasets show that the proposed ESTINet can achieve
faster speed than the competitors, while maintaining better performance than
the state-of-the-art methods.


Abstract:
  Deep learning has recently been applied to optical music recognition (OMR).
However, currently OMR processing from various sheet music images still lacks
precision to be widely applicable. Here, we present an MMdA (Measure-based
Multimodal deep learning (DL)-driven Assembly) method allowing for end-to-end
OMR processing from various images including inclined photo images. Using this
method, measures are extracted by a deep learning model, aligned, and resized
to be used for inference of given musical symbol components by using multiple
deep learning models in sequence or in parallel. Use of each standardized
measure enables efficient training of the models and accurate adjustment of
five staff lines in each measure. Multiple musical symbol component category
models with a small number of feature types can represent a diverse set of
notes and other musical symbols including chords. This MMdA method provides a
solution to end-to-end OMR processing with precision.


Abstract:
  Strategies based on Explainable Artificial Intelligence - XAI have emerged in
computing to promote a better understanding of predictions made by black box
models. Most XAI measures used today explain these types of models, generating
attribute rankings aimed at explaining the model, that is, the analysis of
Attribute Importance of Model. There is no consensus on which XAI measure
generates an overall explainability rank. For this reason, several proposals
for tools have emerged (Ciu, Dalex, Eli5, Lofo, Shap and Skater). An
experimental benchmark of explainable AI techniques capable of producing global
explainability ranks based on tabular data related to different problems and
ensemble models are presented herein. Seeking to answer questions such as "Are
the explanations generated by the different measures the same, similar or
different?" and "How does data complexity play along model explainability?" The
results from the construction of 82 computational models and 592 ranks shed
some light on the other side of the problem of explainability: dataset
complexity!


Abstract:
  We prove that any positive solution of the Yamabe equation on an
asymptotically flat $n$-dimensional manifold of flatness order at least
$\frac{n-2}{2}$ and $n\le 24$ must converge at infinity either to a fundamental
solution of the Laplace operator on the Euclidean space or to a radial Fowler
solution defined on the entire Euclidean space. The flatness order
$\frac{n-2}{2}$ is the minimal flatness order required to define ADM mass in
general relativity; the dimension $24$ is the dividing dimension of the
validity of compactness of solutions to the Yamabe problem. We also prove such
alternatives for bounded solutions when $n>24$.
  We prove these results by establishing appropriate asymptotic behavior near
an isolated singularity of solutions to the Yamabe equation when the metric has
a flatness order of at least $\frac{n-2}{2}$ at the singularity and $n<24$,
also when $n>24$ and the solution grows no faster than the fundamental solution
of the flat metric Laplacian at the singularity. These results extend earlier
results of L. Caffarelli, B. Gidas and J. Spruck, also of N. Korevaar, R.
Mazzeo, F. Pacard and R. Schoen, when the metric is conformally flat, and work
of C.C. Chen and C. S. Lin when the scalar curvature is a non-constant function
with appropriate flatness at the singular point, also work of F. Marques when
the metric is not necessarily conformally flat but smooth, and the dimension of
the manifold is three, four, or five, as well as recent similar results by the
second and third authors in dimension six.


Abstract:
  Recently, based on the phase-field modeling, it was predicted that Hf1-xZrxO2
(HZO) exhibits the morphotropic phase boundary (MPB) in its compositional phase
diagram. Here, we investigate the effect of structural changes between
tetragonal (t) and orthorhombic (o) phases on the ferroelectric and dielectric
properties of HZO films to probe the existence of MPB region. The structural
analysis show that by adjusting the ozone dosage during the atomic layer
deposition process and annealing conditions, different ratios of t- to o-phases
(f_(t/o) ) were achieved which consequently affect the ferroelectric and
dielectric properties of the samples. Polarization versus electric field
measurements show a remarkable increase in ferroelectric characteristics (Pr
and Ec) of the sample that contains the minimum t-phase fraction (f_(t/o)~
0.04). This sample shows the lowest dielectric constant compared to the other
samples which is due to the formation of ferroelectric o-phase. The sample that
contains the maximum f_(t/o)~ 0.41 demonstrates the highest dielectric
response. By adjusting the f_(t/o), a large dielectric constant of ~ 55 is
achieved. Our study reveals a direct relation between f_(t/o) and dielectric
constant of HZO thin films which can be understood by considering the density
of MPB region.


Abstract:
  When two Neutron Stars collide a multi-band electromagnetic emission, known
as Kilonova (KN), follows being powered by the radioactive decay of ejecta
products. In this contribution we discuss how the equation of state of dense
matter, impacts the mass and velocity in the KN ejecta and thus its light
curve. Using this information encoded in the stellar mass-radius relationship,
we ellaborate on how the future experimental observations in photon channels,
in addition to complementary multimessenger probes, could provide a new and
more detailed insight into the equation of state of nuclear matter.


Abstract:
  We consider mappings of domains of Riemannian manifolds that admit branch
points and satisfy a certain condition regarding the distortion of the modulus
of families of paths. We have established logarithmic estimates of distance
distortion under such mappings. A separate study relates to the situation when
the mappings are defined in metric spaces, and one of them is the Loewner
space. We also studied the question of equicontinuity of the families of the
indicated mappings in the closure of the domain. In addition, we have
established the possibility of continuous extension of these mappings to an
isolated point of the boundary.


Abstract:
  Ultrarelativistic collisions between heavy nuclei briefly generate the
quark-gluon plasma (QGP), a new state of matter characterized by deconfined
partons last seen microseconds after the Big Bang. The properties of the QGP
are of intense interest, and a large community has developed over several
decades, to produce, measure and understand this primordial plasma. The plasma
is now recognized to be a strongly-coupled fluid with remarkable properties,
and hydrodynamics is commonly used to quantify and model the system. An
important feature of any fluid is its vorticity, related to the local angular
momentum density; however, this degree of freedom has received relatively
little attention because no experimental signals of vorticity had been
detected. Thanks to recent high-statistics datasets from experiments with
precision tracking and complete kinemetic coverage at collider energies,
hyperon spin polarization measurements have begun to uncover the vorticity of
the QGP created at the Relativistic Heavy Ion Collider. The injection of this
new degree of freedom into a relatively mature field of research represents an
enormous opportunity to generate new insights into the physics of the QGP. The
community has responded with enthusiasm, and this book (to be published as a
volume of Lecture Notes in Physics series by Springer) represents some of the
diverse lines of inquiry into aspects of strongly interacting matter under
rotation.


Abstract:
  Electrons confined in silicon quantum dots exhibit orbital, spin, and valley
degrees of freedom. The valley degree of freedom originates from the bulk
bandstructure of silicon, which has six degenerate electronic minima. The
degeneracy can be lifted in silicon quantum wells due to strain and electronic
confinement, but the "valley splitting" of the two lowest lying valleys is
known to be sensitive to atomic-scale disorder. Large valley splittings are
desirable to have a well-defined spin qubit. In addition, an understanding of
the inter-valley tunnel coupling that couples different valleys in adjacent
quantum dots is extremely important, as the resulting gaps in the energy level
diagram may affect the fidelity of charge and spin transfer protocols in
silicon quantum dot arrays. Here we use microwave spectroscopy to probe spatial
variations in the valley splitting, and the intra- and inter-valley tunnel
couplings ($t_{ij}$ and $t'_{ij}$) that couple dots $i$ and $j$ in a triple
quantum dot (TQD). We uncover large spatial variations in the ratio of
inter-valley to intra-valley tunnel couplings $t_{12}'/t_{12}=0.90$ and
$t_{23}'/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that
$t'_{ij}$ scales linearly with $t_{ij}$, as expected from theory. The results
indicate strong interactions between different valley states on neighboring
dots, which we attribute to local inhomogeneities in the silicon quantum well.


Abstract:
  Progressively applying Gaussian noise transforms complex data distributions
to approximately Gaussian. Reversing this dynamic defines a generative model.
When the forward noising process is given by a Stochastic Differential Equation
(SDE), Song et al. (2021) demonstrate how the time inhomogeneous drift of the
associated reverse-time SDE may be estimated using score-matching. A limitation
of this approach is that the forward-time SDE must be run for a sufficiently
long time for the final distribution to be approximately Gaussian. In contrast,
solving the Schr\"odinger Bridge problem (SB), i.e. an entropy-regularized
optimal transport problem on path spaces, yields diffusions which generate
samples from the data distribution in finite time. We present Diffusion SB
(DSB), an original approximation of the Iterative Proportional Fitting (IPF)
procedure to solve the SB problem, and provide theoretical analysis along with
generative modeling experiments. The first DSB iteration recovers the
methodology proposed by Song et al. (2021), with the flexibility of using
shorter time intervals, as subsequent DSB iterations reduce the discrepancy
between the final-time marginal of the forward (resp. backward) SDE with
respect to the prior (resp. data) distribution. Beyond generative modeling, DSB
offers a widely applicable computational optimal transport tool as the
continuous state-space analogue of the popular Sinkhorn algorithm (Cuturi,
2013).


Abstract:
  Motivated by recent nanofluidics experiments, we use Brownian dynamics and
Monte Carlo simulations to study the conformation, organization and dynamics of
two polymer chains confined to a single box-like cavity. The polymers are
modeled as flexible hard-sphere chains, and the box has a square cross-section
of side length $L$ and a height that is small enough to compress the polymers
in that dimension. For sufficiently large $L$, the system behaviour approaches
that of an isolated polymer in a slit. However, the combined effects of
crowding and confinement on the polymer organization, conformation and
equilibrium dynamics become significant when $L/R_{{\rm g},xy}^*\lesssim 5$,
where $R_{{\rm g},xy}^*$ is the transverse radius of gyration for a slit
geometry. In this regime, the centre-of-mass probability distribution in the
transverse plane exhibits a depletion zone near the centre of the cavity
(except at very small $L$) and a 4-fold symmetry with quasi-discrete positions.
Reduction in polymer size with decreasing $L$ arises principally from
confinement rather than inter-polymer crowding. By contrast, polymer diffusion
and internal motion are strongly affected by inter-polymer crowding. The two
polymers tend to occupy opposite positions relative to the box centre, about
which they diffuse relatively freely. Qualitatively, this static and dynamical
behaviour differs significantly from that previously observed for confinement
of two polymers to a narrow channel. The simulation results for a suitably
chosen box width are qualitatively consistent with results from a recent
experimental study of two $\lambda$-DNA chains confined to a nanofluidic
cavity.


Abstract:
  For a quantum harmonic oscillator an explicit expression that describes the
energy distribution as a coordinate function is obtained. The presence of the
energy function poles is shown for the quantum system in domains where the
Wigner function has negative values.


Abstract:
  In this paper, some sufficient conditions for the differentiability of the
$n$-variable real-valued function are obtained, which are given based on the
differentiability of the $n-1$-variable real-valued function and are weaker
than classical conditions.


Abstract:
  We introduce the Australia Telescope Compact Array (ATCA) rapid-response mode
by presenting the first successful trigger on the short-duration gamma-ray
burst (GRB) 181123B. Early-time radio observations of short GRBs may provide
vital insights into the radio afterglow properties of Advanced LIGO- and
Virgo-detected gravitational wave events, which will in turn inform follow-up
strategies to search for counterparts within their large positional
uncertainties. The ATCA was on target within 12.6 hr post-burst, when the
source had risen above the horizon. While no radio afterglow was detected
during the 8.3 hr observation, we obtained force-fitted flux densities of $7
\pm 12$ and $15 \pm 11~\mu$Jy at 5.5 and 9 GHz, respectively. Afterglow
modelling of GRB 181123B showed that the addition of the ATCA force-fitted
radio flux densities to the Swift X-ray Telescope detections provided more
stringent constraints on the fraction of thermal energy in the electrons
(log$\epsilon_e = -0.75^{+0.39}_{-0.40}$ rather than log$\epsilon_e =
-1.13^{+0.82}_{-1.2}$ derived without the inclusion of the ATCA values), which
is consistent with the range of typical $\epsilon_e$ derived from GRB afterglow
modelling. This allowed us to predict that the forward shock may have peaked in
the radio band $\sim10$ days post-burst, producing detectable radio emission
$\gtrsim3-4$ days post-burst. Overall, we demonstrate the potential for
extremely rapid radio follow-up of transients and the importance of triggered
radio observations for constraining GRB blast wave properties, regardless of
whether there is a detection, via the inclusion of force-fitted radio flux
densities in afterglow modelling efforts.


Abstract:
  The excited-state structure of atomic nuclei can modify nuclear processes in
stellar environments. In this work, we study the influence of nuclear
excitations on Urca cooling (repeated back-and-forth beta decay and electron
capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars.
We provide for the first time an expression for Urca process neutrino
luminosity which accounts for excited states of both members of an Urca pair.
We use our new formula with state-of-the-art nuclear structure inputs to
compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear
inputs consist of the latest experimental data supplemented with calculations
using the projected shell model. We show that, in contrast with previous
results that only consider the ground states of both nuclei in the pair, our
calculated neutrino luminosities for different Urca pairs vary sensitively with
the environment temperature and can be radically different from those obtained
in the one transition approximation.


Abstract:
  We study the problem of stochastic bandits with adversarial corruptions in
the cooperative multi-agent setting, where $V$ agents interact with a common
$K$-armed bandit problem, and each pair of agents can communicate with each
other to expedite the learning process. In the problem, the rewards are
independently sampled from distributions across all agents and rounds, but they
may be corrupted by an adversary. Our goal is to minimize both the overall
regret and communication cost across all agents. We first show that an additive
term of corruption is unavoidable for any algorithm in this problem. Then, we
propose a new algorithm that is agnostic to the level of corruption. Our
algorithm not only achieves near-optimal regret in the stochastic setting, but
also obtains a regret with an additive term of corruption in the corrupted
setting, while maintaining efficient communication. The algorithm is also
applicable for the single-agent corruption problem, and achieves a high
probability regret that removes the multiplicative dependence of $K$ on
corruption level. Our result of the single-agent case resolves an open question
from Gupta et al. [2019].


Abstract:
  Mixtures of lipids and cholesterol are commonly used as model systems for
studying the formation of liquid-ordered ($L_o$) domains in heterogeneous
biological membranes. The simplest model system exhibiting coexistence between
$L_o$ domains and a liquid-disordered ($L_d$) matrix is that of a binary
mixture of saturated lipids like DPPC and cholesterol (Chol). DPPC/Chol
mixtures have been investigated for decades both experimentally, theoretically,
and recently also by means of atomistic simulations. Here, we present a minimal
lattice model that captures the correct behavior of this mixture across
multiple scales. On the macroscopic scales, we present simulation results of
mixtures of thousands of lipids and Chol molecules which show excellent
agreement with the phase diagram of the system. The simulations are conducted
on timescales of hundreds of microseconds and show the morphologies and
dynamics of the domains. On the molecular scales, the simulations reveal local
structures similar to those recently seen in atomistic simulations, including
the formation of gel-like nano-domains ($\sim$ 1-10 nm) within larger Chol-rich
$L_o$ domains ($\sim$ 10-100 nm). The observed multi-scale behavior is related
to the tendency of Chol to induce ordering of acyl chains on the one hand, and
disrupt their packing with each other, on the other hand.


Abstract:
  We approach the problem of hotel recognition with deep metric learning. We
overview the existing approaches and propose a modification to Contrastive loss
called Contrastive-Triplet loss. We construct a robust pipeline for
benchmarking metric learning models and perform experiments on Hotels-50K and
CUB200 datasets. Contrastive-Triplet loss is shown to achieve better retrieval
on Hotels-50k. We open-source our code.


Abstract:
  Style transfer aims to render the content of a given image in the
graphical/artistic style of another image. The fundamental concept underlying
NeuralStyle Transfer (NST) is to interpret style as a distribution in the
feature space of a Convolutional Neural Network, such that a desired style can
be achieved by matching its feature distribution. We show that most current
implementations of that concept have important theoretical and practical
limitations, as they only partially align the feature distributions. We propose
a novel approach that matches the distributions more precisely, thus
reproducing the desired style more faithfully, while still being
computationally efficient. Specifically, we adapt the dual form of Central
Moment Discrepancy (CMD), as recently proposed for domain adaptation, to
minimize the difference between the target style and the feature distribution
of the output image. The dual interpretation of this metric explicitly matches
all higher-order centralized moments and is therefore a natural extension of
existing NST methods that only take into account the first and second moments.
Our experiments confirm that the strong theoretical properties also translate
to visually better style transfer, and better disentangle style from semantic
image content.


Abstract:
  We investigate the ringdown waveform and reflectivity of a Lifshitz scalar
field around a fixed Schwarzschild black hole. The radial wave equation is
modified due to the Lorentz breaking terms, which leads to a diversity of
ringdown waveforms. Also, it turns out that Lifshitz waves scattered by the
Schwarzschild black hole exhibits superradiance. The Lorentz breaking terms
lead to superluminal propagation and high-frequency modes can enter and leave
the interior of the Killing horizon where negativity of energy is not
prohibited. This allows the Lifshitz waves to carry out additional positive
energy to infinity while leaving negative energy inside the Killing horizon,
similar to the Penrose process in the ergosphere of a Kerr spacetime. Another
interesting phenomenon is emergence of long-lived quasinormal modes, associated
with roton-type dispersion relations. These effects drastically modify the
greybody factor of a microscopic black hole, whose Hawking temperature is
comparable with or higher than the Lifshitz energy scale.


Abstract:
  In this paper, we prove a Poincar\'e inequality for any volume-constraint
local energy-minimizing sets, provided its singular set is of Hausdorff
dimension at most $n-3$. With this inequality, we prove that the only
volume-constraint local energy-minimizing sets in the Euclidean unit ball,
whose singular set is closed and of Hausdorff dimension at most $n-3$, are
totally geodesic balls or spherical caps intersecting the unit sphere with
constant contact angle; for stable sets in a wedge-shaped domain or in a half
space, provided the same condition of the singular set, must be spherical. In
particular, they are smooth.


Abstract:
  The superiority of variational quantum algorithms (VQAs) such as quantum
neural networks (QNNs) and variational quantum eigen-solvers (VQEs) heavily
depends on the expressivity of the employed ansatze. Namely, a simple ansatze
is insufficient to capture the optimal solution, while an intricate ansatze
leads to the hardness of the trainability. Despite its fundamental importance,
an effective strategy of measuring the expressivity of VQAs remains largely
unknown. Here, we exploit an advanced tool in statistical learning theory,
i.e., covering number, to study the expressivity of VQAs. In particular, we
first exhibit how the expressivity of VQAs with an arbitrary ansatze is upper
bounded by the number of quantum gates and the measurement observable. We next
explore the expressivity of VQAs on near-term quantum chips, where the system
noise is considered. We observe an exponential decay of the expressivity with
increasing circuit depth. We also utilize the achieved expressivity to analyze
the generalization of QNNs and the accuracy of VQE. We numerically verify our
theory employing VQAs with different levels of expressivity. Our work opens the
avenue for quantitative understanding of the expressivity of VQAs.