title: An Algorithm to Find Sums of Consecutive Powers of Primes

abstract:
  We present and analyze an algorithm to enumerate all integers $n\le x$ that
can be written as the sum of consecutive $k$th powers of primes, for $k>1$. We
show that the number of such integers $n$ is asymptotically bounded by a
constant times $$ c_k \frac{ x^{2/(k+1)} }{ (\log x)^{2k/(k+1)} }, $$ where
$c_k$ is a constant depending solely on $k$, roughly $k^2$ in magnitude. This
also bounds the asymptotic running time of our algorithm. We also present some
computational results, using our algorithm, that imply this bound is, at worst,
off by a constant factor near 0.6. Our work extends the previous work by
Tongsomporn, Wananiyakul, and Steuding (2022) who examined consecutive sums of
squares of primes.


title: MCSE: Multimodal Contrastive Learning of Sentence Embeddings

abstract:
  Learning semantically meaningful sentence embeddings is an open problem in
natural language processing. In this work, we propose a sentence embedding
learning approach that exploits both visual and textual information via a
multimodal contrastive objective. Through experiments on a variety of semantic
textual similarity tasks, we demonstrate that our approach consistently
improves the performance across various datasets and pre-trained encoders. In
particular, combining a small amount of multimodal data with a large text-only
corpus, we improve the state-of-the-art average Spearman's correlation by 1.7%.
By analyzing the properties of the textual embedding space, we show that our
model excels in aligning semantically similar sentences, providing an
explanation for its improved performance.


title:
Listing, Verifying and Counting Lowest Common Ancestors in DAGs:
  Algorithms and Fine-Grained Lower Bounds

abstract:
  The AP-LCA problem asks, given an $n$-node directed acyclic graph (DAG), to
compute for every pair of vertices $u$ and $v$ in the DAG a lowest common
ancestor (LCA) of $u$ and $v$ if one exists. In this paper we study several
interesting variants of AP-LCA, providing both algorithms and fine-grained
lower bounds for them. The lower bounds we obtain are the first conditional
lower bounds for LCA problems higher than $n^{\omega-o(1)}$, where $\omega$ is
the matrix multiplication exponent. Some of our results include:
  - In any DAG, we can detect all vertex pairs that have at most two LCAs and
list all of their LCAs in $O(n^\omega)$ time. This algorithm extends a result
of [Kowaluk and Lingas ESA'07] which showed an $\tilde{O}(n^\omega)$ time
algorithm that detects all pairs with a unique LCA in a DAG and outputs their
corresponding LCAs.
  - Listing $7$ LCAs per vertex pair in DAGs requires $n^{3-o(1)}$ time under
the popular assumption that 3-uniform 5-hyperclique detection requires
$n^{5-o(1)}$ time. This is surprising since essentially cubic time is
sufficient to list all LCAs (if $\omega=2$).
  - Counting the number of LCAs for every vertex pair in a DAG requires
$n^{3-o(1)}$ time under the Strong Exponential Time Hypothesis, and
$n^{\omega(1,2,1)-o(1)}$ time under the $4$-Clique hypothesis. This shows that
the algorithm of [Echkardt, M\"{u}hling and Nowak ESA'07] for listing all LCAs
for every pair of vertices is likely optimal.
  - Given a DAG and a vertex $w_{u,v}$ for every vertex pair $u,v$, verifying
whether all $w_{u,v}$ are valid LCAs requires $n^{2.5-o(1)}$ time assuming
3-uniform 4-hyperclique requires $n^{4 - o(1)}$ time. This defies the common
intuition that verification is easier than computation since returning some LCA
per vertex pair can be solved in $O(n^{2.447})$ time [Grandoni et al. SODA'21].


title: A Tale of Two Models: Constructing Evasive Attacks on Edge Models

abstract:
  Full-precision deep learning models are typically too large or costly to
deploy on edge devices. To accommodate to the limited hardware resources,
models are adapted to the edge using various edge-adaptation techniques, such
as quantization and pruning. While such techniques may have a negligible impact
on top-line accuracy, the adapted models exhibit subtle differences in output
compared to the original model from which they are derived. In this paper, we
introduce a new evasive attack, DIVA, that exploits these differences in edge
adaptation, by adding adversarial noise to input data that maximizes the output
difference between the original and adapted model. Such an attack is
particularly dangerous, because the malicious input will trick the adapted
model running on the edge, but will be virtually undetectable by the original
model, which typically serves as the authoritative model version, used for
validation, debugging and retraining. We compare DIVA to a state-of-the-art
attack, PGD, and show that DIVA is only 1.7-3.6% worse on attacking the adapted
model but 1.9-4.2 times more likely not to be detected by the the original
model under a whitebox and semi-blackbox setting, compared to PGD.


title: Baxos: Backing off for Robust and Efficient Consensus

abstract:
  Leader-based consensus algorithms are vulnerable to liveness and performance
downgrade attacks. We explore the possibility of replacing leader election in
Multi-Paxos with random exponential backoff (REB), a simpler approach that
requires minimum modifications to the two phase Synod Paxos and achieves better
resiliency under attacks. We propose Baxos, a new resilient consensus protocol
that leverages a random exponential backoff scheme as a replacement for leader
election in consensus algorithms. Our backoff scheme addresses the common
challenges of random exponential backoff such as scalability and robustness to
changing wide area latency. We extensively evaluate Baxos to illustrate its
performance and robustness against two liveness and performance downgrade
attacks using an implementation running on Amazon EC2 in a wide area network
and a combination of a micro benchmark and YCSB-A workload on Redis. Our
results show that Baxos offers more robustness to liveness and performance
downgrade attacks than leader-based consensus protocols. Baxos outperforms
Multi-Paxos and Raft up to 185% in throughput under liveness and performance
downgrade attacks under worst case contention scenarios where each replica
proposes requests concurrently while only incurring a 7% reduction on the
maximum throughput in the synchronous attack-free scenario.


title: Certifiable Robot Design Optimization using Differentiable Programming

abstract:
  There is a growing need for computational tools to automatically design and
verify autonomous systems, especially complex robotic systems involving
perception, planning, control, and hardware in the autonomy stack.
Differentiable programming has recently emerged as powerful tool for modeling
and optimization. However, very few studies have been done to understand how
differentiable programming can be used for robust, certifiable end-to-end
design optimization. In this paper, we fill this gap by combining
differentiable programming for robot design optimization with a novel
statistical framework for certifying the robustness of optimized designs. Our
framework can conduct end-to-end optimization and robustness certification for
robotics systems, enabling simultaneous optimization of navigation, perception,
planning, control, and hardware subsystems.
  Using simulation and hardware experiments, we show how our tool can be used
to solve practical problems in robotics. First, we optimize sensor placements
for robot navigation (a design with 5 subsystems and 6 tunable parameters) in
under 5 minutes to achieve an 8.4x performance improvement compared to the
initial design. Second, we solve a multi-agent collaborative manipulation task
(3 subsystems and 454 parameters) in under an hour to achieve a 44% performance
improvement over the initial design. We find that differentiable programming
enables much faster (32% and 20x, respectively for each example) optimization
than approximate gradient methods. We certify the robustness of each design and
successfully deploy the optimized designs in hardware. An open-source
implementation is available at https://github.com/MIT-REALM/architect


title:
Counterfactual Learning To Rank for Utility-Maximizing Query
  Autocompletion

abstract:
  Conventional methods for query autocompletion aim to predict which completed
query a user will select from a list. A shortcoming of this approach is that
users often do not know which query will provide the best retrieval performance
on the current information retrieval system, meaning that any query
autocompletion methods trained to mimic user behavior can lead to suboptimal
query suggestions. To overcome this limitation, we propose a new approach that
explicitly optimizes the query suggestions for downstream retrieval
performance. We formulate this as a problem of ranking a set of rankings, where
each query suggestion is represented by the downstream item ranking it
produces. We then present a learning method that ranks query suggestions by the
quality of their item rankings. The algorithm is based on a counterfactual
learning approach that is able to leverage feedback on the items (e.g., clicks,
purchases) to evaluate query suggestions through an unbiased estimator, thus
avoiding the assumption that users write or select optimal queries. We
establish theoretical support for the proposed approach and provide
learning-theoretic guarantees. We also present empirical results on publicly
available datasets, and demonstrate real-world applicability using data from an
online shopping store.


title:
Doping a Mott insulator with excitons in moir\'e bilayer: fractional
  superfluid, neutral Fermi surface and Mott transition

abstract:
  In this paper we explore possible phases arising from doping neutral excitons
into a Mott insulator in the context of moir\'e bilayers. We consider two
moir\'e layers coupled together only through inter-layer repulsion and there is
a U(2)$\times$ U(2) symmetry. The densities of the two layers can be tuned to
be $n_t=x,n_b=1-x$ with $n_t+n_b=1$. $x=0$ limit is a layer polarized Mott
insulator and small $x$ regime can be reached by doping inter-layer excitons at
density $x$. Charge gap can remain finite at small $x$, as is demonstrated
experimentally in the WSe$_2$-hBN-WSe$_2$/WS$_2$ system. To capture the
intertwinement of the spin and exciton degree of freedom, we propose a
four-flavor spin model. In addition to the obvious possibility of single
exciton condensation phase, we also identified more exotic physics with
fractionalization: (I) We define spin gap $\Delta_t, \Delta_b$ for the two
layers respectively. As long as the spin gap at either layer is finite, single
exciton condensation is impossible and we can only have paired exciton
condensation. If both spin gaps are finite, it can be a fractional exciton
superfluid with paired exciton condensation coexisting with $Z_2$ spin liquid.
Numerical evidences for such a phase will be provided. (II) If the layer
polarized Mott insulator at $x=0$ is in a U(1) spin liquid with spinon Fermi
surface, the natural phase at $x>0$ hosts neutral Fermi surface formed by
fermionic excitons. There are metallic counter-flow transport and also Friedel
oscillations in layer polarization in this exotic phase. Our numerical
simulation in one dimension observes an analog of this neutral Fermi surface
phase. (III) There could be a metal-insulator transition (MIT) by tuning $x$ in
the universality class of a bandwidth tuned MIT. We provide one theory for such
a continuous Mott transition and predicted a universal drag resistivity.


title: A Multi-level Alignment Training Scheme for Video-and-Language Grounding

abstract:
  To solve video-and-language grounding tasks, the key is for the network to
understand the connection between the two modalities. For a pair of video and
language description, their semantic relation is reflected by their encodings'
similarity. A good multi-modality encoder should be able to well capture both
inputs' semantics and encode them in the shared feature space where embedding
distance gets properly translated into their semantic similarity. In this work,
we focused on this semantic connection between video and language, and
developed a multi-level alignment training scheme to directly shape the
encoding process. Global and segment levels of video-language alignment pairs
were designed, based on the information similarity ranging from high-level
context to fine-grained semantics. The contrastive loss was used to contrast
the encodings' similarities between the positive and negative alignment pairs,
and to ensure the network is trained in such a way that similar information is
encoded closely in the shared feature space while information of different
semantics is kept apart. Our multi-level alignment training can be applied to
various video-and-language grounding tasks. Together with the task-specific
training loss, our framework achieved comparable performance to previous
state-of-the-arts on multiple video QA and retrieval datasets.


title: Unified Pretraining Framework for Document Understanding

abstract:
  Document intelligence automates the extraction of information from documents
and supports many business applications. Recent self-supervised learning
methods on large-scale unlabeled document datasets have opened up promising
directions towards reducing annotation efforts by training models with
self-supervised objectives. However, most of the existing document pretraining
methods are still language-dominated. We present UDoc, a new unified
pretraining framework for document understanding. UDoc is designed to support
most document understanding tasks, extending the Transformer to take multimodal
embeddings as input. Each input element is composed of words and visual
features from a semantic region of the input document image. An important
feature of UDoc is that it learns a generic representation by making use of
three self-supervised losses, encouraging the representation to model
sentences, learn similarities, and align modalities. Extensive empirical
analysis demonstrates that the pretraining procedure learns better joint
representations and leads to improvements in downstream tasks.


title:
Balancing Fairness and Accuracy in Sentiment Detection using Multiple
  Black Box Models

abstract:
  Sentiment detection is an important building block for multiple information
retrieval tasks such as product recommendation, cyberbullying detection, and
misinformation detection. Unsurprisingly, multiple commercial APIs, each with
different levels of accuracy and fairness, are now available for sentiment
detection. While combining inputs from multiple modalities or black-box models
for increasing accuracy is commonly studied in multimedia computing literature,
there has been little work on combining different modalities for increasing
fairness of the resulting decision. In this work, we audit multiple commercial
sentiment detection APIs for the gender bias in two actor news headlines
settings and report on the level of bias observed. Next, we propose a "Flexible
Fair Regression" approach, which ensures satisfactory accuracy and fairness by
jointly learning from multiple black-box models. The results pave way for fair
yet accurate sentiment detectors for multiple applications.


title: Reflected Brownian Motion with Drift in a Wedge

abstract:
  We study reflecting Brownian motion with drift constrained to a wedge in the
plane. Our first set of results provide necessary and sufficient conditions for
existence and uniqueness of a solution to the corresponding submartingale
problem with drift, and show that its solution possesses the Markov and Feller
properties. Next, we study a version of the problem with absorption at the
vertex of the wedge. In this case, we provide a condition for existence and
uniqueness of a solution to the problem and some results on the probability of
the vertex being reached.


title:
Evaluation of Multi-Scale Multiple Instance Learning to Improve Thyroid
  Cancer Classification

abstract:
  Thyroid cancer is currently the fifth most common malignancy diagnosed in
women. Since differentiation of cancer sub-types is important for treatment and
current, manual methods are time consuming and subjective, automatic
computer-aided differentiation of cancer types is crucial. Manual
differentiation of thyroid cancer is based on tissue sections, analysed by
pathologists using histological features. Due to the enormous size of gigapixel
whole slide images, holistic classification using deep learning methods is not
feasible. Patch based multiple instance learning approaches, combined with
aggregations such as bag-of-words, is a common approach. This work's
contribution is to extend a patch based state-of-the-art method by generating
and combining feature vectors of three different patch resolutions and
analysing three distinct ways of combining them. The results showed
improvements in one of the three multi-scale approaches, while the others led
to decreased scores. This provides motivation for analysis and discussion of
the individual approaches.


title: FPGA-based AI Smart NICs for Scalable Distributed AI Training Systems

abstract:
  Rapid advances in artificial intelligence (AI) technology have led to
significant accuracy improvements in a myriad of application domains at the
cost of larger and more compute-intensive models. Training such models on
massive amounts of data typically requires scaling to many compute nodes and
relies heavily on collective communication algorithms, such as all-reduce, to
exchange the weight gradients between different nodes. The overhead of these
collective communication operations in a distributed AI training system can
bottleneck its performance, with more pronounced effects as the number of nodes
increases. In this paper, we first characterize the all-reduce operation
overhead by profiling distributed AI training. Then, we propose a new smart
network interface card (NIC) for distributed AI training systems using
field-programmable gate arrays (FPGAs) to accelerate all-reduce operations and
optimize network bandwidth utilization via data compression. The AI smart NIC
frees up the system's compute resources to perform the more compute-intensive
tensor operations and increases the overall node-to-node communication
efficiency. We perform real measurements on a prototype distributed AI training
system comprised of 6 compute nodes to evaluate the performance gains of our
proposed FPGA-based AI smart NIC compared to a baseline system with regular
NICs. We also use these measurements to validate an analytical model that we
formulate to predict performance when scaling to larger systems. Our proposed
FPGA-based AI smart NIC enhances overall training performance by 1.6x at 6
nodes, with an estimated 2.5x performance improvement at 32 nodes, compared to
the baseline system using conventional NICs.


title:
Converting One-Way Streets to Two-Way Streets to Improve Transportation
  Network Efficiency and Reduce Vehicle Distance Traveled

abstract:
  Planning scholars have identified economic, safety, and social benefits of
converting one-way streets to two-way. Less is known about how conversions
could impact vehicular distances traveled - of growing relevance in an era of
fleet automation, electrification, and ride-hailing. We simulate such a
conversion in San Francisco, California. We find that its current street
network's average intra-city trip is about 1.7% longer than it would be with
all two-way streets, corresponding to 27 million kilometers of annual surplus
travel. As transportation technologies evolve, planners must consider different
facets of network efficiency to align local policy and street design with
sustainability and other societal goals.

categories: physics.soc-ph cs.CY econ.GN q-fin.EC stat.AP


title:
Noncooperative Herding With Control Barrier Functions: Theory and
  Experiments

abstract:
  In this paper, we consider the problem of protecting a high-value unit from
inadvertent attack by a group of agents using defending robots. Specifically,
we develop a control strategy for the defending agents that we call "dog
robots" to prevent a flock of "sheep agents" from breaching a protected zone.
We take recourse to control barrier functions to pose this problem and exploit
the interaction dynamics between the sheep and dogs to find dogs' velocities
that result in the sheep getting repelled from the zone. We solve a QP
reactively that incorporates the defending constraints to compute the desired
velocities for all dogs. Owing to this, our proposed framework is composable
\textit{i.e.} it allows for simultaneous inclusion of multiple protected zones
in the constraints on dog robots' velocities. We provide a theoretical proof of
feasibility of our strategy for the one dog/one sheep case. Additionally, we
provide empirical results of two dogs defending the protected zone from upto
ten sheep averaged over a hundred simulations and report high success rates. We
also demonstrate this algorithm experimentally on non-holonomic robots. Videos
of these results are available at https://tinyurl.com/4dj2kjwx.


title:
Evaluation of Monte-Carlo-based System Response Matrix Completeness and
  its Impact on Image Quality in Positron Emission Tomography

abstract:
  A major strength of iterative algorithms used in positron emission tomography
(PET) lies in their abilities to introduce precise models of the physics at
play, which includes the statistical nature of the detection processes, and a
detailed description of the radiation-matter interactions. The process of data
acquisition by the imaging system is described in a system response model, or
system response matrix (SRM). In PET, elements of this matrix correspond to a
probability of a coincident pair of gamma emitted from a certain element of the
imaged volume (voxel) to be detected by the apparatus along a given pair of
detection elements (e.g. a pair of scintillating crystals), or line of response
(LoR). The number of voxels involved for each line of response and the
statistical error on each matrix element are directly dependent on the number
of coincident events simulated to generate the SRM. The main goal of this paper
is to first evaluate the behavior of these two parameters and secondly to
estimate their impact on the overall image quality in preclinical PET imaging.
Our results show the direct impact of the statistical variance of the
Monte-Carlo generated System Response Matrices used in iterative reconstruction
algorithms on image quality.


title: DC-driven positive streamer coronas in airflow

abstract:
  An experimental study of the effect of laminar airflow on positive
self-pulsating streamer coronas in a needle-to-plate geometry is presented. The
experiments are performed in an open return wind tunnel with winds up to 30 m/s
orthogonal to the needle. The experimental data is presented in terms of
statistical properties of the discharge, inferred from high resolution, large
sample-size current waveforms. The key properties of the current pulsations,
namely inter-pulse period, peak current, deposited energy, and pulse width are
analyzed as a function of wind speed and applied DC voltage. All parameters
increase in dispersion with wind speed. The mean of the inter-pulse period
decreases with wind speed and the mean pulsation frequency increases. The peak
currents and energies per pulsation have a general tendency to decrease in
magnitude but also higher-current, higher-energy, streamer bursts are observed.
At low wind speeds, streamers preferentially propagate in the downwind
direction but, as the wind speed is increased, more streamers can propagate
upwind. Synchronized imaging reveals correlations between the streamer
direction and the electrical characteristics.


title:
Incompatibility of local measurements provide advantage in local quantum
  state discrimination

abstract:
  A pack of quantum measurements that cannot be measured simultaneously is said
to form a set of incompatible measurements. Every set of incompatible
measurements have advantage over the compatible ones in a quantum state
discrimination task where one prepares a state from an ensemble and sends it to
another party, and the latter tries to detect the state using available
measurements. We consider the local quantum state discrimination task where a
sender prepares a bipartite state and sends the subsystems to two receivers.
The receivers try to detect the sent state using locally incompatible
measurements. We analyze the ratio of the probability of successfully guessing
the state using incompatible measurements and the maximum probability of
successfully guessing the state using compatible measurements. We find that
this ratio is upper bounded by a simple function of robustnesses of
incompatibilities of the local measurements. Interestingly, corresponding to
every pair of sets of incompatible measurements, there exists at least one
local state discrimination task where this bound can be achieved. We argue that
the optimal local quantum state discrimination task does not present any
"nonlocality", where the term is used in the sense of a difference between the
ratios, of probabilities of successful detection via incompatible and
compatible measurements, in global and local state discriminations. The results
can be generalized to the regime of multipartite local quantum state
distinguishing tasks.


title: The Dark Souls of Archaeology: Recording Elden Ring

abstract:
  Archaeology can be broadly defined as the study and interpretation of the
past through material remains. Videogame worlds, though immaterial in nature,
can also afford opportunities to study the people who existed within them based
on what they leave behind. In this paper we present the first formal
archaeological survey of a predominantly single-player game, by examining the
player-generated content that is asynchronously distributed to players in the
videogame Elden Ring.


title: Multiples of integral points on Mordell curves

abstract:
  Let $P$ be a non torsion integral point on the minimal Mordell curve
$E_B:y^2=x^3+B$. In this paper, we study integral multiples $[n]P$ of $P$.
Among other results, we show that $P$ has at most three integral multiples with
$n>1$. This result is sharp in the sense that there are points $P$ with exactly
three integral multiples $[n]P$ and $n>1$. As an application, we discuss the
number of integral points on minimal Mordell curves of rank 1.


title:
Bounded generation and commutator width of Chevalley groups: function
  case

abstract:
  We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and
over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a
finite field, are boundedly elementarily generated. Using this we produce
explicit bounds of the commutator width of these groups. Under some additional
assumptions, we prove similar results for other classes of Chevalley groups
over Dedekind rings of arithmetic rings in positive characteristic. As a
corollary, we produce explicit estimates for the commutator width of affine
Kac--Moody groups defined over finite fields. The paper contains also a broader
discussion of the bounded generation problem for groups of Lie type, some
applications and a list of unsolved problems in the field.


title:
A note on the $f$-divergences between multivariate location-scale
  families with either prescribed scale matrices or location parameters

abstract:
  We extend the result of Ali and Silvey [Journal of the Royal Statistical
Society: Series B, 28.1 (1966), 131-142] who first reported that any
$f$-divergence between two isotropic multivariate Gaussian distributions
amounts to a corresponding strictly increasing scalar function of their
corresponding Mahalanobis distance. We report sufficient conditions on the
standard probability density function generating a multivariate location-scale
family and the generator $f$ in order to generalize this result. In that case,
one can compare exactly $f$-divergences between densities of these location
families via their Mahalanobis distances. In particular, this proves useful
when the $f$-divergences are not available in closed-form as it is the case for
example for the Jensen-Shannon divergence between multivariate isotropic
Gaussian distributions. Furthermore, we show that the $f$-divergences between
these multivariate location-scale families amount equivalently to
$f$-divergences between corresponding univariate location-scale families. We
present several applications of these results.


title: Transparency of Fast Radio Burst Waves in Magnetar Magnetospheres

abstract:
  It is widely believed that at least some fast radio bursts (FRBs) are
produced by magnetars. Even though mounting observational evidence points
towards a magnetospheric origin of FRB emission, the question of the location
for FRB generation continues to be debated. One argument recently suggested
against the magnetospheric origin of bright FRBs is that the radio waves
associated with an FRB may lose most of their energy before escaping the
magnetosphere because the cross-section for $e^\pm$ to scatter large-amplitude
EM waves in the presence of a strong magnetic field is much larger than the
Thompson cross-section. We have investigated this suggestion in this work, and
find that FRB radiation traveling through the open field line region of a
magnetar's magnetosphere does not suffer much loss due to two previously
ignored factors. First, the plasma in the outer magnetosphere ($r \gta 10^9 \
$cm), where the losses are potentially most severe, is likely to be flowing
outward at a high Lorentz factor $\gamma_p \geq 10^3$. Second, the angle
between the wave vector and the magnetic field vector, $\theta_B$, in the outer
magnetosphere is likely of the order of 0.1 radian or smaller due in part to
the intense FRB pulse that tilts open magnetic field lines so that they get
aligned with the pulse propagation direction. Both these effects reduce the
interaction between the FRB pulse and the plasma substantially. We find that a
bright FRB with an isotropic luminosity $L_{\rm frb} \gta 10^{42} \ {\rm erg \
s^{-1}}$ can escape the magnetosphere unscathed for a large section of the
$\gamma_p-\theta_B$ parameter space, and therefore conclude that the generation
of FRBs in magnetar magnetosphere passes this test.


title:
A new proof of existence in the L3-setting of solutions to the
  Navier-Stokes Cauchy problem

abstract:
  We investigate on the existence of solutions with initial datum U0 in L3. Our
chief goal is to establish the existence interval (0,T) uniquely considering
the size and the absolute continuity of |U0(x)|3.


title: Root vectors of polynomial and rational matrices: theory and computation

abstract:
  The notion of root polynomials of a polynomial matrix $P(\lambda)$ was
thoroughly studied in [F. Dopico and V. Noferini, Root polynomials and their
role in the theory of matrix polynomials, Linear Algebra Appl. 584:37--78,
2020]. In this paper, we extend such a systematic approach to general rational
matrices $R(\lambda)$, possibly singular and possibly with coalescent pole/zero
pairs. We discuss the related theory for rational matrices with coefficients in
an arbitrary field. As a byproduct, we obtain sensible definitions of
eigenvalues and eigenvectors of a rational matrix $R(\lambda)$, without any
need to assume that $R(\lambda)$ has full column rank or that the eigenvalue is
not also a pole. Then, we specialize to the complex field and provide a
practical algorithm to compute them, based on the construction of a minimal
state space realization of the rational matrix $R(\lambda)$ and then using the
staircase algorithm on the linearized pencil to compute the null space as well
as the root polynomials in a given point $\lambda_0$. If $\lambda_0$ is also a
pole, then it is necessary to apply a preprocessing step that removes the pole
while making it possible to recover the root vectors of the original matrix: in
this case, we study both the relevant theory (over a general field) and an
algorithmic implementation (over the complex field), still based on minimal
state space realizations.


title:
Auction Design in an Auto-bidding Setting: Randomization Improves
  Efficiency Beyond VCG

abstract:
  Auto-bidding is an area of increasing importance in the domain of online
advertising. We study the problem of designing auctions in an auto-bidding
setting with the goal of maximizing welfare at system equilibrium. Previous
results showed that the price of anarchy (PoA) under VCG is 2 and also that
this is tight even with two bidders. This raises an interesting question as to
whether VCG yields the best efficiency in this setting, or whether the PoA can
be improved upon. We present a prior-free randomized auction in which the PoA
is approx. 1.896 for the case of two bidders, proving that one can achieve an
efficiency strictly better than that under VCG in this setting. We also provide
a stark impossibility result for the problem in general as the number of
bidders increases -- we show that no (randomized) anonymous truthful auction
can have a PoA strictly better than 2 asymptotically as the number of bidders
per query increases. While it was shown in previous work that one can improve
on the PoA of 2 if the auction is allowed to use the bidder's values for the
queries in addition to the bidder's bids, we note that our randomized auction
is prior-free and does not use such additional information; our impossibility
result also applies to auctions without additional value information.


title: The Lack of Convexity of the Relevance-Compression Function

abstract:
  In this paper we investigate the convexity of the relevance-compression
function for the Information Bottleneck and the Information Distortion
problems. This curve is an analog of the rate-distortion curve, which is
convex. In the problems we discuss in this paper, the distortion function is
not a linear function of the quantizer, and the relevance-compression function
is not necessarily convex (concave), but can change its convexity. We relate
this phenomena with existence of first order phase transitions in the
corresponding Lagrangian as a function of the annealing parameter.


title: Towards Privacy-Preserving Neural Architecture Search

abstract:
  Machine learning promotes the continuous development of signal processing in
various fields, including network traffic monitoring, EEG classification, face
identification, and many more. However, massive user data collected for
training deep learning models raises privacy concerns and increases the
difficulty of manually adjusting the network structure. To address these
issues, we propose a privacy-preserving neural architecture search (PP-NAS)
framework based on secure multi-party computation to protect users' data and
the model's parameters/hyper-parameters. PP-NAS outsources the NAS task to two
non-colluding cloud servers for making full advantage of mixed protocols
design. Complement to the existing PP machine learning frameworks, we redesign
the secure ReLU and Max-pooling garbled circuits for significantly better
efficiency ($3 \sim 436$ times speed-up). We develop a new alternative to
approximate the Softmax function over secret shares, which bypasses the
limitation of approximating exponential operations in Softmax while improving
accuracy. Extensive analyses and experiments demonstrate PP-NAS's superiority
in security, efficiency, and accuracy.


title: HRPlanes: High Resolution Airplane Dataset for Deep Learning

abstract:
  Airplane detection from satellite imagery is a challenging task due to the
complex backgrounds in the images and differences in data acquisition
conditions caused by the sensor geometry and atmospheric effects. Deep learning
methods provide reliable and accurate solutions for automatic detection of
airplanes; however, huge amount of training data is required to obtain
promising results. In this study, we create a novel airplane detection dataset
called High Resolution Planes (HRPlanes) by using images from Google Earth (GE)
and labeling the bounding box of each plane on the images. HRPlanes include GE
images of several different airports across the world to represent a variety of
landscape, seasonal and satellite geometry conditions obtained from different
satellites. We evaluated our dataset with two widely used object detection
methods namely YOLOv4 and Faster R-CNN. Our preliminary results show that the
proposed dataset can be a valuable data source and benchmark data set for
future applications. Moreover, proposed architectures and results of this study
could be used for transfer learning of different datasets and models for
airplane detection.


title:
Inducing spin-order with an impurity: phase diagram of the magnetic Bose
  polaron

abstract:
  We investigate the formation of magnetic Bose polaron, an impurity atom
dressed by spin-wave excitations, in a one-dimensional spinor Bose gas. In
terms of an effective potential model the impurity is strongly confined by the
host excitations which can even overcome the impurity-medium repulsion leading
to a self-localized quasi-particle state. The phase diagram of the attractive
and self-bound repulsive magnetic polaron, repulsive non-magnetic (Fr{\"
o}hlich-type) polaron and impurity-medium phase-separation regimes is explored
with respect to the Rabi-coupling between the spin components, spin-spin
interactions and impurity-medium coupling. The residue of such magnetic
polarons decreases substantially in both strong attractive and repulsive
branches with strong impurity-spin interactions, illustrating significant
dressing of the impurity. The impurity can be used to probe and maneuver the
spin polarization of the magnetic medium while suppressing ferromagnetic
spin-spin correlations. It is shown that mean-field theory fails as the spinor
gas approaches immiscibility since the generated spin-wave excitations are
prominent. Our findings illustrate that impurities can be utilized to generate
controllable spin-spin correlations and magnetic polaron states which can be
realized with current cold atom setups.

categories: cond-mat.quant-gas cond-mat.other physics.atom-ph quant-ph


title: SEIRDV Model for QATAR COVID-19 Outbreak: A Case Study

abstract:
  The Covid-19 outbreak of 2020 has required many governments to develop
mathematical-statistical models of the outbreak for policy and planning
purposes. This work provides a tutorial on building a compartmental model using
Susceptibles, Exposed, Infected, Recovered, Deaths and Vaccinated (SEIRDV)
status through time. A Bayesian Framework is utilized to perform both parameter
estimation and predictions. This model uses interventions to quantify the
impact of various government attempts to slow the spread of the virus.
Predictions are also made to determine when the peak Active Infections will
occur.


title: Visual Attention Emerges from Recurrent Sparse Reconstruction

abstract:
  Visual attention helps achieve robust perception under noise, corruption, and
distribution shifts in human vision, which are areas where modern neural
networks still fall short. We present VARS, Visual Attention from Recurrent
Sparse reconstruction, a new attention formulation built on two prominent
features of the human visual attention mechanism: recurrency and sparsity.
Related features are grouped together via recurrent connections between
neurons, with salient objects emerging via sparse regularization. VARS adopts
an attractor network with recurrent connections that converges toward a stable
pattern over time. Network layers are represented as ordinary differential
equations (ODEs), formulating attention as a recurrent attractor network that
equivalently optimizes the sparse reconstruction of input using a dictionary of
"templates" encoding underlying patterns of data. We show that self-attention
is a special case of VARS with a single-step optimization and no sparsity
constraint. VARS can be readily used as a replacement for self-attention in
popular vision transformers, consistently improving their robustness across
various benchmarks. Code is released on GitHub (https://github.com/bfshi/VARS).


title:
Local Gaussian process extrapolation for BART models with applications
  to causal inference

abstract:
  Bayesian additive regression trees (BART) is a semi-parametric regression
model offering state-of-the-art performance on out-of-sample prediction.
Despite this success, standard implementations of BART typically provide
inaccurate prediction and overly narrow prediction intervals at points outside
the range of the training data. This paper proposes a novel extrapolation
strategy that grafts Gaussian processes to the leaf nodes in BART for
predicting points outside the range of the observed data. The new method is
compared to standard BART implementations and recent frequentist
resampling-based methods for predictive inference. We apply the new approach to
a challenging problem from causal inference, wherein for some regions of
predictor space, only treated or untreated units are observed (but not both).
In simulations studies, the new approach boasts superior performance compared
to popular alternatives, such as Jackknife+.


title:
Statistical inference of travelers' route choice preferences with
  system-level data

abstract:
  Traditional network models encapsulate travel behavior among all
origin-destination pairs based on a simplified and generic utility function.
Typically, the utility function consists of travel time solely and its
coefficients are equated to estimates obtained from stated preference data.
While this modeling strategy is reasonable, the inherent sampling bias in
individual-level data may be further amplified over network flow aggregation,
leading to inaccurate flow estimates. This data must be collected from surveys
or travel diaries, which may be labor intensive, costly and limited to a small
time period. To address these limitations, this study extends classical
bi-level formulations to estimate travelers' utility functions with multiple
attributes using system-level data. We formulate a methodology grounded on
non-linear least squares to statistically infer travelers' utility function in
the network context using traffic counts, traffic speeds, traffic incidents and
sociodemographic information, among other attributes. The analysis of the
mathematical properties of the optimization problem and of its pseudo-convexity
motivate the use of normalized gradient descent. We also develop a hypothesis
test framework to examine statistical properties of the utility function
coefficients and to perform attributes selection. Experiments on synthetic data
show that the coefficients are consistently recovered and that hypothesis tests
are a reliable statistic to identify which attributes are determinants of
travelers' route choices. Besides, a series of Monte-Carlo experiments suggest
that statistical inference is robust to noise in the Origin-Destination matrix
and in the traffic counts, and to various levels of sensor coverage. The
methodology is also deployed at a large scale using real-world multi-source
data in Fresno, CA collected before and during the COVID-19 outbreak.


title:
CLIP-Dissect: Automatic Description of Neuron Representations in Deep
  Vision Networks

abstract:
  In this paper, we propose CLIP-Dissect, a new technique to automatically
describe the function of individual hidden neurons inside vision networks.
CLIP-Dissect leverages recent advances in multimodal vision/language models to
label internal neurons with open-ended concepts without the need for any
labeled data or human examples, which are required for existing tools to
succeed. We show that CLIP-Dissect provides more accurate descriptions than
existing methods for neurons where the ground-truth is available as well as
qualitatively good descriptions for hidden layer neurons. In addition, our
method is very flexible: it is model agnostic, can easily handle new concepts
and can be extended to take advantage of better multimodal models in the
future. Finally CLIP-Dissect is computationally efficient and labels all
neurons of a layer in a large vision model in tens of minutes.


title:
Observation of Dirac hierarchy in three-dimensional acoustic topological
  insulators

abstract:
  Dirac cones (DCs) play a pivotal role in various unique phenomena ranging
from massless electrons in graphene to robust surface states in topological
insulators (TIs). Recent studies have theoretically revealed a full Dirac
hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold
hinge DC, associated with a hierarchy of topological phases including
first-order to third-order three-dimensional (3D) topological insulators, using
the same 3D base lattice. Here, we report the first experimental observation of
the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we
unambiguously reveal that lifting of multifold DCs in each hierarchy can induce
two-dimensional (2D) topological surface states with a fourfold DC in a
first-order 3D TI, one-dimensional (1D) topological hinge states with a twofold
DC in a second-order 3D TI, and zero-dimensional (0D) topological corner states
in a third-order 3D TI. Our work not only expands the fundamental research
scope of Dirac physics, but also opens up a new route for multidimensional
robust wave manipulation.


title:
Groupes de Brauer alg\'ebriques modulo les constants d'espaces
  homog\`enes et leurs compactifications

abstract:
  Let $X$ be a smooth, geometrically integral variety over a field $K$. Then
the quotient of the "algebraic" Brauer group of $X$ by $\operatorname{Br} K$
injects into $\textrm{H}^1(K,\textrm{Pic} \bar{X})$. We show that this
inclusion is not always an isomorphism, even in the case where $X$ is a
homogeneous space of a connected linear algebraic group over $K$. A similar
result for the smooth compactifications of $X$ is also given.
  --
  Soit $X$ une vari\'et\'e lisse, g\'eom\'etriquement int\`egre sur un corps
$K$. Alors le quotient du groupe Brauer "alg\'ebrique" de $X$ par
$\operatorname{Br} K$ s'injecte dans $\textrm{H}^1(K,\operatorname{Pic}
\bar{X})$. Nous montrons que cette inclusion n'est pas toujours un isomorphisme
m\^eme dans le cas o\`u $X$ est un espace homog\`ene d'un groupe alg\'ebrique
lin\'eaire connexe sur $K$. Un r\'esultat similaire pour les compactifications
lisses de $X$ est aussi donn\'e.


title: Cooperative colorings of forests

abstract:
  Given a family $\mathcal G$ of graphs spanning a common vertex $V$, a
cooperative coloring of $\mathcal G$ is a collection of one independent set
from each graph of $\mathcal G$ such that the union of these independent sets
equals $V$. We prove that when $d$ is large, there exists a family $\mathcal G$
of $(1+o(1)) \frac{\log d}{\log \log d}$ forests of maximum degree $d$ that
admits no cooperative coloring, which significantly improves a result of
Aharoni, Berger, Chudnovsky, Havet, and Jiang (Electronic Journal of
Combinatorics, 2020). Our family $\mathcal G$ consists entirely of star
forests, and we show that this value for $|\mathcal G|$ is asymptotically best
possible in the case that $\mathcal G$ is a family of star forests.


title:
When Doubly Robust Methods Meet Machine Learning for Estimating
  Treatment Effects from Real-World Data: A Comparative Study

abstract:
  Observational cohort studies are increasingly being used for comparative
effectiveness research and to assess the safety of therapeutics. Recently,
various doubly robust methods have been proposed for average treatment effect
estimation by combining the treatment model and the outcome model via different
vehicles, such as matching, weighting, and regression. The key advantage of the
doubly robust estimators is that they require either the treatment model or the
outcome model to be correctly specified to obtain a consistent estimator of the
average treatment effect, and therefore lead to a more accurate and often more
precise inference. However, little work has been done to understand how doubly
robust estimators differ due to their unique strategies of using the treatment
and outcome models and how machine learning techniques can be combined with
these estimators to boost their performance. Also, little has been understood
about the challenges of covariates selection, overlapping of the covariate
distribution, and treatment effect heterogeneity on the performance of these
doubly robust estimators. Here we examine multiple popular doubly robust
methods in the categories of matching, weighting, or regression, and compare
their performance using different treatment and outcome modeling via extensive
simulations and a real-world application. We found that incorporating machine
learning with doubly robust estimators such as the targeted maximum likelihood
estimator outperforms. Practical guidance on how to apply doubly robust
estimators is provided.


title:
Unsupervised Restoration of Weather-affected Images using Deep Gaussian
  Process-based CycleGAN

abstract:
  Existing approaches for restoring weather-degraded images follow a
fully-supervised paradigm and they require paired data for training. However,
collecting paired data for weather degradations is extremely challenging, and
existing methods end up training on synthetic data. To overcome this issue, we
describe an approach for supervising deep networks that are based on CycleGAN,
thereby enabling the use of unlabeled real-world data for training.
Specifically, we introduce new losses for training CycleGAN that lead to more
effective training, resulting in high-quality reconstructions. These new losses
are obtained by jointly modeling the latent space embeddings of predicted clean
images and original clean images through Deep Gaussian Processes. This enables
the CycleGAN architecture to transfer the knowledge from one domain
(weather-degraded) to another (clean) more effectively. We demonstrate that the
proposed method can be effectively applied to different restoration tasks like
de-raining, de-hazing and de-snowing and it outperforms other unsupervised
techniques (that leverage weather-based characteristics) by a considerable
margin.


title:
An Efficient Approach for Optimizing the Cost-effective Individualized
  Treatment Rule Using Conditional Random Forest

abstract:
  Evidence from observational studies has become increasingly important for
supporting healthcare policy making via cost-effectiveness (CE) analyses.
Similar as in comparative effectiveness studies, health economic evaluations
that consider subject-level heterogeneity produce individualized treatment
rules (ITRs) that are often more cost-effective than one-size-fits-all
treatment. Thus, it is of great interest to develop statistical tools for
learning such a cost-effective ITR (CE-ITR) under the causal inference
framework that allows proper handling of potential confounding and can be
applied to both trials and observational studies. In this paper, we use the
concept of net-monetary-benefit (NMB) to assess the trade-off between health
benefits and related costs. We estimate CE-ITR as a function of patients'
characteristics that, when implemented, optimizes the allocation of limited
healthcare resources by maximizing health gains while minimizing
treatment-related costs. We employ the conditional random forest approach and
identify the optimal CE-ITR using NMB-based classification algorithms, where
two partitioned estimators are proposed for the subject-specific weights to
effectively incorporate information from censored individuals. We conduct
simulation studies to evaluate the performance of our proposals. We apply our
top-performing algorithm to the NIH-funded Systolic Blood Pressure Intervention
Trial (SPRINT) to illustrate the CE gains of assigning customized intensive
blood pressure therapy.


title: GRM: Gradient Rectification Module for Visual Place Retrieval

abstract:
  Visual place retrieval aims to search images in the database that depict
similar places as the query image. However, global descriptors encoded by the
network usually fall into a low dimensional principal space, which is harmful
to the retrieval performance. We first analyze the cause of this phenomenon,
pointing out that it is due to degraded distribution of the gradients of
descriptors. Then, a new module called Gradient Rectification Module(GRM) is
proposed to alleviate this issue. It can be appended after the final pooling
layer. This module can rectify the gradients to the complement space of the
principal space. Therefore, the network is encouraged to generate descriptors
more uniformly in the whole space. At last, we conduct experiments on multiple
datasets and generalize our method to classification task under prototype
learning framework.


title: Detecting Recolored Image by Spatial Correlation

abstract:
  Image forensics, aiming to ensure the authenticity of the image, has made
great progress in dealing with common image manipulation such as copy-move,
splicing, and inpainting in the past decades. However, only a few researchers
pay attention to an emerging editing technique called image recoloring, which
can manipulate the color values of an image to give it a new style. To prevent
it from being used maliciously, the previous approaches address the
conventional recoloring from the perspective of inter-channel correlation and
illumination consistency. In this paper, we try to explore a solution from the
perspective of the spatial correlation, which exhibits the generic detection
capability for both conventional and deep learning-based recoloring. Through
theoretical and numerical analysis, we find that the recoloring operation will
inevitably destroy the spatial correlation between pixels, implying a new prior
of statistical discriminability. Based on such fact, we generate a set of
spatial correlation features and learn the informative representation from the
set via a convolutional neural network. To train our network, we use three
recoloring methods to generate a large-scale and high-quality data set.
Extensive experimental results in two recoloring scenes demonstrate that the
spatial correlation features are highly discriminative. Our method achieves the
state-of-the-art detection accuracy on multiple benchmark datasets and exhibits
well generalization for unknown types of recoloring methods.


title: DIMIX: DIminishing MIXing for Sloppy Agents

abstract:
  We study non-convex distributed optimization problems where a set of agents
collaboratively solve a separable optimization problem that is distributed over
a time-varying network. The existing methods to solve these problems rely on
(at most) one time-scale algorithms, where each agent performs a diminishing or
constant step-size gradient descent at the average estimate of the agents in
the network. However, if possible at all, exchanging exact information, that is
required to evaluate these average estimates, potentially introduces a massive
communication overhead. Therefore, a reasonable practical assumption to be made
is that agents only receive a rough approximation of the neighboring agents'
information. To address this, we introduce and study a \textit{two time-scale}
decentralized algorithm with a broad class of \textit{lossy} information
sharing methods (that includes noisy, quantized, and/or compressed information
sharing) over \textit{time-varying} networks. In our method, one time-scale
suppresses the (imperfect) incoming information from the neighboring agents,
and one time-scale operates on local cost functions' gradients. We show that
with a proper choices for the step-sizes' parameters, the algorithm achieves a
convergence rate of $\mathcal{O}({T}^{-1/3 + \epsilon})$ for non-convex
distributed optimization problems over time-varying networks, for any
$\epsilon>0$. Our simulation results support the theoretical results of the
paper.


title: Spherical Rotation Dimension Reduction with Geometric Loss Functions

abstract:
  Modern datasets witness high-dimensionality and nontrivial geometries of
spaces they live in. It would be helpful in data analysis to reduce the
dimensionality while retaining the geometric structure of the dataset.
Motivated by this observation, we propose a general dimension reduction method
by incorporating geometric information. Our Spherical Rotation Component
Analysis (SRCA) is a dimension reduction method that uses spheres or
ellipsoids, to approximate a low-dimensional manifold. This method not only
generalizes the Spherical Component Analysis (SPCA) method in terms of theories
and algorithms and presents a comprehensive comparison of our method, as an
optimization problem with theoretical guarantee and also as a structural
preserving low-rank representation of data. Results relative to
state-of-the-art competitors show considerable gains in ability to accurately
approximate the subspace with fewer components and better structural
preserving. In addition, we have pointed out that this method is a specific
incarnation of a grander idea of using a geometrically induced loss function in
dimension reduction tasks.


title: Discovering Intrinsic Reward with Contrastive Random Walk

abstract:
  The aim of this paper is to demonstrate the efficacy of using Contrastive
Random Walk as a curiosity method to achieve faster convergence to the optimal
policy.Contrastive Random Walk defines the transition matrix of a random walk
with the help of neural networks. It learns a meaningful state representation
with a closed loop. The loss of Contrastive Random Walk serves as an intrinsic
reward and is added to the environment reward. Our method works well in
non-tabular sparse reward scenarios, in the sense that our method receives the
highest reward within the same iterations compared to other methods. Meanwhile,
Contrastive Random Walk is more robust. The performance doesn't change much
with different random initialization of environments. We also find that
adaptive restart and appropriate temperature are crucial to the performance of
Contrastive Random Walk.


title: Rigidity method for automorphic forms over function fields

abstract:
  These are lectures given at the 2022 Arizona Winter School. It gives an
introduction to the rigidity method for constructing automorphic forms for
semisimple groups over function fields. The rigidity method leads to explicit
constructions of local systems that are Langlands parameters of automorphic
forms. The examples of local systems produced in this way have applications to
algebraic geometry and number theory.


title:
All-optical graph representation learning using integrated diffractive
  photonic computing units

abstract:
  Photonic neural networks perform brain-inspired computations using photons
instead of electrons that can achieve substantially improved computing
performance. However, existing architectures can only handle data with regular
structures, e.g., images or videos, but fail to generalize to graph-structured
data beyond Euclidean space, e.g., social networks or document co-citation
networks. Here, we propose an all-optical graph representation learning
architecture, termed diffractive graph neural network (DGNN), based on the
integrated diffractive photonic computing units (DPUs) to address this
limitation. Specifically, DGNN optically encodes node attributes into strip
optical waveguides, which are transformed by DPUs and aggregated by on-chip
optical couplers to extract their feature representations. Each DPU comprises
successive passive layers of metalines to modulate the electromagnetic optical
field via diffraction, where the metaline structures are learnable parameters
shared across graph nodes. DGNN captures complex dependencies among the node
neighborhoods and eliminates the nonlinear transition functions during the
light-speed optical message passing over graph structures. We demonstrate the
use of DGNN extracted features for node and graph-level classification tasks
with benchmark databases and achieve superior performance. Our work opens up a
new direction for designing application-specific integrated photonic circuits
for high-efficiency processing of large-scale graph data structures using deep
learning.


title: Smoothed Online Combinatorial Optimization Using Imperfect Predictions

abstract:
  Smoothed online combinatorial optimization considers a learner who repeatedly
chooses a combinatorial decision to minimize an unknown changing cost function
with a penalty on switching decisions in consecutive rounds. We study smoothed
online combinatorial optimization problems when an imperfect predictive model
is available, where the model can forecast the future cost functions with
uncertainty. We show that using predictions to plan for a finite time horizon
leads to regret dependent on the total predictive uncertainty and an additional
switching cost. This observation suggests choosing a suitable planning window
to balance between uncertainty and switching cost, which leads to an online
algorithm with guarantees on the upper and lower bounds of the cumulative
regret. Lastly, we provide an iterative algorithm to approximately solve the
planning problem in real-time. Empirically, our algorithm shows a significant
improvement in cumulative regret compared to other baselines in synthetic
online distributed streaming problems.


title: Special cycles for Shtukas are closed

abstract:
  In this paper we give a different proof of a theorem of Paul Breutmann: for a
Bruhat-Tits group scheme $\mathcal{H}$ over a smooth projective curve $X$ and a
closed embedding into another smooth affine group scheme $\mathcal{G}$, the
induced map on the moduli of Shtukas $Sht^{r}_{\mathcal{H}}\to
Sht^{r}_{\mathcal{G}}$ is schematic, finite and unramified. This result enables
one to define special cycles on the moduli stack of Shtukas.


title: Distributed Dynamic Safe Screening Algorithms for Sparse Regularization

abstract:
  Distributed optimization has been widely used as one of the most efficient
approaches for model training with massive samples. However, large-scale
learning problems with both massive samples and high-dimensional features
widely exist in the era of big data. Safe screening is a popular technique to
speed up high-dimensional models by discarding the inactive features with zero
coefficients. Nevertheless, existing safe screening methods are limited to the
sequential setting. In this paper, we propose a new distributed dynamic safe
screening (DDSS) method for sparsity regularized models and apply it on
shared-memory and distributed-memory architecture respectively, which can
achieve significant speedup without any loss of accuracy by simultaneously
enjoying the sparsity of the model and dataset. To the best of our knowledge,
this is the first work of distributed safe dynamic screening method.
Theoretically, we prove that the proposed method achieves the linear
convergence rate with lower overall complexity and can eliminate almost all the
inactive features in a finite number of iterations almost surely. Finally,
extensive experimental results on benchmark datasets confirm the superiority of
our proposed method.


title: Continuity and Additivity Properties of Information Decompositions

abstract:
  Information decompositions quantify how the Shannon information about a given
random variable is distributed among several other random variables. Various
requirements have been proposed that such a decomposition should satisfy,
leading to different candidate solutions. Curiously, however, only two of the
original requirements that determined the Shannon information have been
considered, namely monotonicity and normalization. Two other important
properties, continuity and additivity, have not been considered. In this
contribution, we check which of the decompositions satisfy these two
properties. While most of them satisfy continuity, only one of them satisfies
additivity.


title: Federated Contrastive Learning for Volumetric Medical Image Segmentation

abstract:
  Supervised deep learning needs a large amount of labeled data to achieve high
performance. However, in medical imaging analysis, each site may only have a
limited amount of data and labels, which makes learning ineffective. Federated
learning (FL) can help in this regard by learning a shared model while keeping
training data local for privacy. Traditional FL requires fully-labeled data for
training, which is inconvenient or sometimes infeasible to obtain due to high
labeling cost and the requirement of expertise. Contrastive learning (CL), as a
self-supervised learning approach, can effectively learn from unlabeled data to
pre-train a neural network encoder, followed by fine-tuning for downstream
tasks with limited annotations. However, when adopting CL in FL, the limited
data diversity on each client makes federated contrastive learning (FCL)
ineffective. In this work, we propose an FCL framework for volumetric medical
image segmentation with limited annotations. More specifically, we exchange the
features in the FCL pre-training process such that diverse contrastive data are
provided to each site for effective local CL while keeping raw data private.
Based on the exchanged features, global structural matching further leverages
the structural similarity to align local features to the remote ones such that
a unified feature space can be learned among different sites. Experiments on a
cardiac MRI dataset show the proposed framework substantially improves the
segmentation performance compared with state-of-the-art techniques.


title:
Deep Reinforcement Learning-based Radio Resource Allocation and Beam
  Management under Location Uncertainty in 5G mmWave Networks

abstract:
  Millimeter Wave (mmWave) is an important part of 5G new radio (NR), in which
highly directional beams are adapted to compensate for the substantial
propagation loss based on UE locations. However, the location information may
have some errors such as GPS errors. In any case, some uncertainty, and
localization error is unavoidable in most settings. Applying these distorted
locations for clustering will increase the error of beam management. Meanwhile,
the traffic demand may change dynamically in the wireless environment.
Therefore, a scheme that can handle both the uncertainty of localization and
dynamic radio resource allocation is needed. In this paper, we propose a
UK-means-based clustering and deep reinforcement learning-based resource
allocation algorithm (UK-DRL) for radio resource allocation and beam management
in 5G mmWave networks. We first apply UK-means as the clustering algorithm to
mitigate the localization uncertainty, then deep reinforcement learning (DRL)
is adopted to dynamically allocate radio resources. Finally, we compare the
UK-DRL with K-means-based clustering and DRL-based resource allocation
algorithm (K-DRL), the simulations show that our proposed UK-DRL-based method
achieves 150% higher throughput and 61.5% lower delay compared with K-DRL when
traffic load is 4Mbps.


title:
Federated Learning with Lossy Distributed Source Coding: Analysis and
  Optimization

abstract:
  Recently, federated learning (FL), which replaces data sharing with model
sharing, has emerged as an efficient and privacy-friendly paradigm for machine
learning (ML). A main challenge of FL is its huge uplink communication cost. In
this paper, we tackle this challenge from an information-theoretic perspective.
Specifically, we put forth a distributed source coding (DSC) framework for FL
uplink, which unifies the encoding, transmission, and aggregation of the local
updates as a lossy DSC problem, thus providing a systematic way to exploit the
correlation between local updates to improve the uplink efficiency. Under this
DSC-FL framework, we propose an FL uplink scheme based on the modified
Berger-Tung coding (MBTC), which supports separate encoding and joint decoding
by modifying the achievability scheme of the Berger-Tung inner bound. The
achievable region of the MBTC-based uplink scheme is also derived. To unleash
the potential of the MBTC-based FL scheme, we carry out a convergence analysis
and then formulate a convergence rate maximization problem to optimize the
parameters of MBTC. To solve this problem, we develop two algorithms,
respectively for small- and large-scale FL systems, based on the
majorization-minimization (MM) technique. Numerical results demonstrate the
superiority of the MBTC-based FL scheme in terms of aggregation distortion,
convergence performance, and communication cost, revealing the great potential
of the DSC-FL framework.


title:
Regrets of Proximal Method of Multipliers for Online Non-convex
  Optimization with Long Term Constraints

abstract:
  The online optimization problem with non-convex loss functions over a closed
convex set, coupled with a set of inequality (possibly non-convex) constraints
is a challenging online learning problem. A proximal method of multipliers with
quadratic approximations (named as OPMM) is presented to solve this online
non-convex optimization with long term constraints.
  Regrets of the violation of Karush-Kuhn-Tucker conditions of OPMM for solving
online non-convex optimization problems are analyzed. Under mild conditions, it
is shown that this algorithm exhibits ${\cO}(T^{-1/8})$ Lagrangian gradient
violation regret, ${\cO}(T^{-1/8})$ constraint violation regret and
${\cO}(T^{-1/4})$ complementarity residual regret if parameters in the
algorithm are properly chosen, where $T$ denotes the number of time periods.
For the case that the objective is a convex quadratic function, we demonstrate
that the regret of the objective reduction can be established even the feasible
set is non-convex. For the case when the constraint functions are convex, if
the solution of the subproblem in OPMM is obtained by solving its dual, OPMM is
proved to be an implementable projection method for solving the online
non-convex optimization problem.


title: Koopman-based Policy Iteration for Robust Optimal Control

abstract:
  Classically, the optimal control problem in the presence of an adversary is
formulated as a two-player zero-sum differential game or an $H_\infty$ control
problem. The solution to these problems can be obtained by solving the
Hamilton-Jacobi-Issac equation (HJIE). We provide a novel Koopman-based
expression of the HJIE, where the solutions can be obtained through the
approximation of the Koopman operator itself. In particular, we developed a
data-driven and model based policy iteration algorithm for approximating the
optimal value function using a finite-dimensional approximation of the Koopman
operator and generator.


title:
Stability analysis of circular orbits around a traversable wormhole with
  massless conformally coupled scalar field

abstract:
  We study the stability of circular orbits in the background of a traversable
wormhole (TWH) spacetime obtained as a solution of Einstein's field equations
coupled conformally to a massless scalar field. The Lyapunov stability approach
is employed to determine the stability of circular orbits (timelike and null)
of non-spinning test particles around a TWH spacetime. In the case of timelike
geodesics, the particle is confined to move in four different types of
effective potentials depending on various values of the angular momentum L with
both centrifugal and gravitational part. The effective potential for null
geodesics consists of only a centrifugal part. Further, we characterize each
fixed point according to its Lyapunov stability, and thus classify the circular
orbits at the fixed point into stable center and unstable saddle points by
depicting the corresponding phase-portraits.


title: Dialogue Meaning Representation for Task-Oriented Dialogue Systems

abstract:
  Dialogue meaning representation formulates natural language utterance
semantics in their conversational context in an explicit and machine-readable
form. Previous work typically follows the intent-slot framework, which is easy
for annotation yet limited on scalability for complex linguistic expressions. A
line of works alleviates the representation issue by introducing hierarchical
structures but challenging to express complex compositional semantics, such as
negation and coreference. We propose Dialogue Meaning Representation (DMR), a
flexible and easily extendable representation for task-oriented dialogue. Our
representation contains a set of nodes and edges with inheritance hierarchy to
represent rich semantics for compositional semantics and task-specific
concepts. We annotated DMR-FastFood, a multi-turn dialogue dataset with more
than 70k utterances, with DMR. We propose two evaluation tasks to evaluate
different machine learning based dialogue models, and further propose a novel
coreference resolution model GNNCoref for the graph-based coreference
resolution task. Experiments show that DMR can be parsed well with pretrained
Seq2Seq model, and GNNCoref outperforms the baseline models by a large margin.


title:
STC-IDS: Spatial-Temporal Correlation Feature Analyzing based Intrusion
  Detection System for Intelligent Connected Vehicles

abstract:
  Intrusion detection is an important defensive measure for the security of
automotive communications. Accurate frame detection models assist vehicles to
avoid malicious attacks. Uncertainty and diversity regarding attack methods
make this task challenging. However, the existing works have the limitation of
only considering local features or the weak feature mapping of multi-features.
To address these limitations, we present a novel model for automotive intrusion
detection by spatial-temporal correlation features of in-vehicle communication
traffic (STC-IDS). Specifically, the proposed model exploits an
encoding-detection architecture. In the encoder part, spatial and temporal
relations are encoded simultaneously. To strengthen the relationship between
features, the attention-based convolution network still captures spatial and
channel features to increase the receptive field, while attention-LSTM build
important relationships from previous time series or crucial bytes. The encoded
information is then passed to the detector for generating forceful
spatial-temporal attention features and enabling anomaly classification. In
particular, single-frame and multi-frame models are constructed to present
different advantages respectively. Under automatic hyper-parameter selection
based on Bayesian optimization, the model is trained to attain the best
performance. Extensive empirical studies based on a real-world vehicle attack
dataset demonstrate that STC-IDS has outperformed baseline methods and cables
fewer false-positive rates while maintaining efficiency.


title: A new perspective on semi-retractions and the Ramsey property

abstract:
  We investigate the notion of a semi-retraction between two first order
structures (in typically different languages) that was introduced by the second
author as a link between the Ramsey property and generalized indiscernible
sequences. We further these connections between combinatorics and model theory,
and look at semi-retractions through a new lens establishing transfers of the
Ramsey property and finite Ramsey degrees under quite general conditions that
are optimal as demonstrated by counterexamples. Finally, we compare
semi-retractions to the category theoretic notion of a pre-adjunction.


title: Energy fluctuations in one dimensional Zhang sandpile model

abstract:
  We consider the Zhang sandpile model in one-dimension (1D) with locally
conservative (or dissipative) dynamics and examine its total energy
fluctuations at the external drive time scale. The bulk-driven system leads to
Lorentzian spectra, with a cutoff time $T$ growing linearly with the system
size $L$. The fluctuations show $1/f^{\alpha}$ behavior with $\alpha \sim 1$
for the boundary drive, and the cutoff time varies non-linearly. For
conservative local dynamics, the cutoff time shows a power-law growth $T \sim
L^{\lambda}$ that differs from an exponential form $ \sim \exp(\mu L)$ observed
for the nonconservative case. We suggest that the local dissipation is not a
necessary ingredient of the system in 1D to get the $1/f$ noise, and the cutoff
time can reveal the distinct nature of the local dynamics. We also discuss the
energy fluctuations for locally nonconservative dynamics with random
dissipation.


title:
TerrainMesh: Metric-Semantic Terrain Reconstruction from Aerial Images
  Using Joint 2D-3D Learning

abstract:
  This paper considers outdoor terrain mapping using RGB images obtained from
an aerial vehicle. While feature-based localization and mapping techniques
deliver real-time vehicle odometry and sparse keypoint depth reconstruction, a
dense model of the environment geometry and semantics (vegetation, buildings,
etc.) is usually recovered offline with significant computation and storage.
This paper develops a joint 2D-3D learning approach to reconstruct a local
metric-semantic mesh at each camera keyframe maintained by a visual odometry
algorithm. Given the estimated camera trajectory, the local meshes can be
assembled into a global environment model to capture the terrain topology and
semantics during online operation. A local mesh is reconstructed using an
initialization and refinement stage. In the initialization stage, we estimate
the mesh vertex elevation by solving a least squares problem relating the
vertex barycentric coordinates to the sparse keypoint depth measurements. In
the refinement stage, we associate 2D image and semantic features with the 3D
mesh vertices using camera projection and apply graph convolution to refine the
mesh vertex spatial coordinates and semantic features based on joint 2D and 3D
supervision. Quantitative and qualitative evaluation using real aerial images
show the potential of our method to support environmental monitoring and
surveillance applications.


title:
MuCGEC: a Multi-Reference Multi-Source Evaluation Dataset for Chinese
  Grammatical Error Correction

abstract:
  This paper presents MuCGEC, a multi-reference multi-source evaluation dataset
for Chinese Grammatical Error Correction (CGEC), consisting of 7,063 sentences
collected from three Chinese-as-a-Second-Language (CSL) learner sources. Each
sentence is corrected by three annotators, and their corrections are carefully
reviewed by a senior annotator, resulting in 2.3 references per sentence. We
conduct experiments with two mainstream CGEC models, i.e., the
sequence-to-sequence model and the sequence-to-edit model, both enhanced with
large pretrained language models, achieving competitive benchmark performance
on previous and our datasets. We also discuss CGEC evaluation methodologies,
including the effect of multiple references and using a char-based metric. Our
annotation guidelines, data, and code are available at
\url{https://github.com/HillZhang1999/MuCGEC}.


title:
Impact of Pauli-blocking effect on optical limiting properties of WSe2
  thin films

abstract:
  We present a detailed investigation on thickness-dependent third-order
(\c{hi}^(3)) nonlinear optical properties of RF-sputtered WSe2 thin-films using
ultrashort pulses centered at different excitation wavelengths. The single-beam
Z-scan based investigation in the visible spectrum reveals the prominent role
of Pauli-blocking towards inducing saturable absorption or optical limiting in
WSe2 thin-films of various thicknesses. The study also explores the dispersion
in third-order nonlinear susceptibility (\c{hi}^(3)) in WSe2 thin films.
Interestingly, WSe2 thin-films of any thickness exhibit a self-focusing effect
depicting a positive nonlinear refractive index (n2 > 0). The
frequency-dependent nonlinear absorption (\b{eta}) bear distinct correlations
with the bandgap of the films which is also investigated through
density-functional-theory (DFT) based simulations. The alteration in
bandstructure is primarily due to the Se-deficiency induced defect bands in
WSe2 thin-films which has discernible impact on the optical limiting
characteristics.


title: Pairs of MOLS of order ten satisfying non-trivial relations

abstract:
  A relation on a $k$-net$(n)$ (or, equivalently, a set of $k-2$ mutually
orthogonal Latin squares of order $n$) is an $\mathbb{F}_{2}$ linear dependence
within the incidence matrix of the net. Dukes and Howard (2014) showed that any
6-net(10) satisfies at least two non-trivial relations, and classified the
relations that could appear in such a net. We find that, up to equivalence,
there are $18\,526\,320$ pairs of MOLS satisfying at least one non-trivial
relation. None of these pairs extend to a triple. We also rule out one other
relation on a set of $3$-MOLS from Dukes and Howard's classification.


title:
Cerebral Palsy Prediction with Frequency Attention Informed Graph
  Convolutional Networks

abstract:
  Early diagnosis and intervention are clinically considered the paramount part
of treating cerebral palsy (CP), so it is essential to design an efficient and
interpretable automatic prediction system for CP. We highlight a significant
difference between CP infants' frequency of human movement and that of the
healthy group, which improves prediction performance. However, the existing
deep learning-based methods did not use the frequency information of infants'
movement for CP prediction. This paper proposes a frequency attention informed
graph convolutional network and validates it on two consumer-grade RGB video
datasets, namely MINI-RGBD and RVI-38 datasets. Our proposed frequency
attention module aids in improving both classification performance and system
interpretability. In addition, we design a frequency-binning method that
retains the critical frequency of the human joint position data while filtering
the noise. Our prediction performance achieves state-of-the-art research on
both datasets. Our work demonstrates the effectiveness of frequency information
in supporting the prediction of CP non-intrusively and provides a way for
supporting the early diagnosis of CP in the resource-limited regions where the
clinical resources are not abundant.


title: Circle actions on 6-dimensional oriented manifolds with 4 fixed points

abstract:
  In this paper, we classify the fixed point data (weights and signs at the
fixed points), of a circle action on a 6-dimensional compact oriented manifold
with 4 fixed points. We prove that it agrees with that of a disjoint union of
rotations on two 6-spheres, or that of a linear action on $\mathbb{CP}^3$. The
former case includes that of Petrie's exotic action on $\mathbb{CP}^3$.


title:
Triggering a global density wave instability in graphene via local
  symmetry-breaking

abstract:
  Two-dimensional quantum materials offer a robust platform for investigating
the emergence of symmetry-broken ordered phases owing to the high tuneability
of their electronic properties. For instance, the ability to create new
electronic band structures in graphene through moir\'e superlattices from
stacked and twisted structures has led to the discovery of several correlated
and topological phases. Here we report an alternative method to induce an
incipient symmetry-broken phase in graphene at the millimetre scale. We show
that an extremely dilute concentration ($<\!0.3\% $) of surface adatoms can
self-assemble and trigger the collapse of the graphene atomic lattice into a
distinct Kekul\'e bond density wave phase, whereby the carbon C-C bond symmetry
is broken globally. Using complementary momentum-resolved techniques such as
angle-resolved photoemission spectroscopy (ARPES) and low-energy electron
diffraction (LEED), we directly probe the presence of this density wave phase
and confirm the opening of an energy gap at the Dirac point. We further show
that this Kekul\'e density wave phase occurs for various Fermi surface sizes
and shapes, suggesting that this lattice instability is driven by strong
electron-lattice interactions. Our results demonstrate that dilute
concentrations of self-assembled adsorbed atoms offer an attractive alternative
route towards designing novel quantum phases in two-dimensional materials.

categories: cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.str-el quant-ph


title:
Stability of the non-critical spectral properties I: arithmetic absolute
  continuity of the integrated density of states

abstract:
  We prove absolute continuity of the integrated density of states for
frequency-independent analytic perturbations of the non-critical almost Mathieu
operator under arithmetic conditions on frequency.


title: Incompressible limit for a fluid mixture

abstract:
  In this paper we discuss the incompressible limit for multicomponent fluids
in the isothermal ideal case. Both a direct limit-passage in the equation of
state and the low Mach-number limit in rescaled PDEs are investigated. Using
the relative energy inequality, we obtain convergence results for the densities
and the velocity-field under the condition that the incompressible model
possesses a sufficiently smooth solution, which is granted at least for a short
time. Moreover, in comparison to single-component flows, uniform estimates and
the convergence of the pressure are needed in the multicomponent case because
the incompressible velocity field is not divergence-free. We show that certain
constellations of the mobility tensor allow to control gradients of the
entropic variables and yield the convergence of the pressure in L1.


title: Stability of circular geodesics in equatorial plane of Kerr spacetime

abstract:
  We analyze the stability of circular geodesics for timelike as well as null
geodesics of the Kerr BH spacetime with rotation parameter on the equatorial
plane by Lyapunov stability analysis. Also, we verify the results of stability
by presenting the phase portrait for both timelike and null geodesics. Further,
by reviewing the Kosambi-Cartan-Chern (KCC) theory, we analyze the Jacobi
stability for Kerr spacetime and present a comparative study of the methods
used for stability analysis of geodesics.


title:
Light bending and gravitational lensing in energy-momentum-squared
  gravity

abstract:
  In the present work, we derive the motion of light in the weak-field limit of
energy-momentum-squared gravity (EMSG). To do so, we introduce the
post-Newtonian (PN) expansion of this modified theory of gravity. It is shown
that in addition to the Newtonian potential, a new EMSG potential affects the
trajectory of photons. As a result, in this theory, photons do not behave as
predicted by general relativity (GR). To evaluate the EMSG theory by the solar
system tests, we study light deflection and Shapiro time delay. Regarding the
results obtained in \cite{bertotti2003test,shapiro2004measurement}, we restrict
the free parameter of the theory and show that it lies within the range
$-4.0\times 10^{-27}\, \text{m}\,\text{s}^2\,\text{kg}^{-1} < f_0' < 8.7\times
10^{-26}\,\text{m}\,\text{s}^2\,\text{kg}^{-1}$. This interval is in agreement
with those derived in \cite{nazari2020Constraining,akarsu2018constraint}. This
consistency manifests that this theory passes these solar system tests with
flying colors. Interestingly, it turns out that the magnitude of the EMSG
correction strongly depends on the density of the deflector. So, we investigate
the possible effects of EMSG on images of a light source microlensed by a
compact dense object such as neutron stars. It is estimated that the EMSG
correction to the position of lensed images could be as large as $(1-0.1)$
micro-arcseconds which may be detected by future high-resolution missions.
Moreover, the total magnification and the shape of light curves are obtained in
the EMSG theory. It is revealed that except for a small deviation, the overall
behavior of the EMSG light curves is similar to that in GR.


title: Training and challenging models for text-guided fashion image retrieval

abstract:
  Retrieving relevant images from a catalog based on a query image together
with a modifying caption is a challenging multimodal task that can particularly
benefit domains like apparel shopping, where fine details and subtle variations
may be best expressed through natural language. We introduce a new evaluation
dataset, Challenging Fashion Queries (CFQ), as well as a modeling approach that
achieves state-of-the-art performance on the existing Fashion IQ (FIQ) dataset.
CFQ complements existing benchmarks by including relative captions with
positive and negative labels of caption accuracy and conditional image
similarity, where others provided only positive labels with a combined meaning.
We demonstrate the importance of multimodal pretraining for the task and show
that domain-specific weak supervision based on attribute labels can augment
generic large-scale pretraining. While previous modality fusion mechanisms lose
the benefits of multimodal pretraining, we introduce a residual attention
fusion mechanism that improves performance. We release CFQ and our code to the
research community.


title: A CubeSat platform for space based quantum key distribution

abstract:
  Satellite nodes are an enabler of global quantum networks by overcoming the
distance limitations of fiber and free-space links on ground. The design of
quantum sources and receivers for satellites, however, is challenging in terms
of size, weight, and power consumption, as well as mechanical and thermal
stability. This is all the more true for cost-efficient nanosatellites such as
the popular CubeSat platform standard.
  Here we report on the follow-up mission of SpooQy-1, a 3U CubeSat that
successfully demonstrated the generation of polarization-entangled photons in
orbit. The next iteration of the mission will showcase satellite-to-ground
quantum key distribution based on a compact source of polarization-entangled
photon-pairs, and we have recently completed the integration of a fully
functional demonstrator as a milestone towards the flight model.
  We also briefly describe the design of the optical ground station that we are
currently building in Singapore for receiving the quantum signal. We present
the most important subsystems and illustrate the concept of operation.


title:
In silico evaluation of Paxlovid's pharmacometrics for SARS-CoV-2: a
  multiscale approach

abstract:
  Paxlovid is a promising, orally bioavailable novel drug for SARS--CoV--2 with
excellent safety profiles. Our main goal here is to explore the pharmacometric
features of this new antiviral. To provide a detailed assessment of Paxlovid,
we propose a hybrid multiscale mathematical approach. We demonstrate that the
results of the present \textit{in silico} evaluation match the clinical
expectations remarkably well: on the one hand, our computations successfully
replicate the outcome of an actual \textit{in vitro} experiment; on the other
hand we verify both the sufficiency and the necessity of Paxlovid's two main
components (nirmatrelvir and ritonavir) for a simplified \textit{in vivo} case.
Moreover, in the simulated context of our computational framework we visualize
the importance of early interventions, and identify the time window where a
unit--length delay causes the highest level of tissue damage. Finally, the
results' sensitivity to the diffusion coefficient of the virus is explored in
details.


title: Synthetic U(1) Gauge Invariance in a Spin-1 Bose Gas

abstract:
  Recent experimental realizations of the lattice Schwinger model [Nature 587,
392 (2020) and Science 367, 1128 (2020)] open a door for quantum simulation of
elementary particles and their interactions using ultracold atoms, in which the
matter and gauge fields are constrained by a local U(1) gauge invariance known
as the Gauss's law. Stimulated by such exciting progress, we propose a new
scenario in simulating the lattice Schwinger model in a spin-1 Bose-Einstein
condensate. It is shown that our model naturally contains an interaction of the
matter fields which respects the U(1) gauge symmetry but has no counterpart in
the conventional Schwinger model. In addition to the Z2-ordered phase
identified in the previous work, this additional interaction leads to a new
Z3-ordered phase. We map out a rich phase diagram and identify that the
continuous phase transitions from the disordered to the Z2-ordered and the
Z3-ordered phases belong to the Ising and the 3-state Potts universality
classes, respectively. Furthermore, the two ordered phases each possess a set
of quantum scars which give rise to anomalous quantum dynamics when quenched to
a special point in the phase diagram. Our proposal provides a novel platform
for extracting emergent physics in cold-atom-based quantum simulators with
gauge symmetries.


title:
Long-term Spatio-temporal Forecasting via Dynamic Multiple-Graph
  Attention

abstract:
  Many real-world ubiquitous applications, such as parking recommendations and
air pollution monitoring, benefit significantly from accurate long-term
spatio-temporal forecasting (LSTF). LSTF makes use of long-term dependency
between spatial and temporal domains, contextual information, and inherent
pattern in the data. Recent studies have revealed the potential of multi-graph
neural networks (MGNNs) to improve prediction performance. However, existing
MGNN methods cannot be directly applied to LSTF due to several issues: the low
level of generality, insufficient use of contextual information, and the
imbalanced graph fusion approach. To address these issues, we construct new
graph models to represent the contextual information of each node and the
long-term spatio-temporal data dependency structure. To fuse the information
across multiple graphs, we propose a new dynamic multi-graph fusion module to
characterize the correlations of nodes within a graph and the nodes across
graphs via the spatial attention and graph attention mechanisms. Furthermore,
we introduce a trainable weight tensor to indicate the importance of each node
in different graphs. Extensive experiments on two large-scale datasets
demonstrate that our proposed approaches significantly improve the performance
of existing graph neural network models in LSTF prediction tasks.


title:
3D Simulations of Strongly Magnetised Non-Rotating Supernovae: Explosion
  Dynamics and Remnant Properties

abstract:
  We investigate the impact of strong initial magnetic fields in core-collapse
supernovae of non-rotating progenitors by simulating the collapse and explosion
of a 16.9 Msun star for a strong- and weak-field case assuming a twisted-torus
field with initial central field strengths of ~1012 G and ~106 G. The
strong-field model has been set up with a view to the fossil-field scenario for
magnetar formation and emulates a pre-collapse field configuration that may
occur in massive stars formed by a merger. This model undergoes shock revival
already 100 s after bounce and reaches an explosion energy of 9.3 x 10^50 erg
at 310 ms, in contrast to a more delayed and less energetic explosion in the
weak-field model. The strong magnetic fields help trigger a neutrino-driven
explosion early on, which results in a rapid rise and saturation of the
explosion energy. Dynamically, the strong initial field leads to a fast
build-up of magnetic fields in the gain region to 40% of kinetic equipartition
and also creates sizable pre-shock ram pressure perturbations that are known to
be conducive to asymmetric shock expansion. For the strong-field model, we find
an extrapolated neutron star kick of ~350 km/s, a spin period of ~70 ms, and no
spin-kick alignment. The dipole field strength of the proto-neutron star is 2 x
10^14 G by the end of the simulation with a declining trend. Surprisingly, the
surface dipole field in the weak-field model is stronger, which argues against
a straightforward connection between pre-collapse fields and the birth magnetic
fields of neutron stars.


title:
GFCL: A GRU-based Federated Continual Learning Framework against
  Adversarial Attacks in IoV

abstract:
  The integration of ML in 5G-based Internet of Vehicles (IoV) networks has
enabled intelligent transportation and smart traffic management. Nonetheless,
the security against adversarial attacks is also increasingly becoming a
challenging task. Specifically, Deep Reinforcement Learning (DRL) is one of the
widely used ML designs in IoV applications. The standard ML security techniques
are not effective in DRL where the algorithm learns to solve sequential
decision-making through continuous interaction with the environment, and the
environment is time-varying, dynamic, and mobile. In this paper, we propose a
Gated Recurrent Unit (GRU)-based federated continual learning (GFCL) anomaly
detection framework against adversarial attacks in IoV. The objective is to
present a lightweight and scalable framework that learns and detects the
illegitimate behavior without having a-priori training dataset consisting of
attack samples. We use GRU to predict a future data sequence to analyze and
detect illegitimate behavior from vehicles in a federated learning-based
distributed manner. We investigate the performance of our framework using
real-world vehicle mobility traces. The results demonstrate the effectiveness
of our proposed solution for different performance metrics.


title:
A Novel Splitting Criterion Inspired by Geometric Mean Metric Learning
  for Decision Tree

abstract:
  Decision tree (DT) attracts persistent research attention due to its
impressive empirical performance and interpretability in numerous applications.
However, the growth of traditional yet widely-used univariate decision trees
(UDTs) is quite time-consuming as they need to traverse all the features to
find the splitting value with the maximal reduction of the impurity at each
internal node. In this paper, we newly design a splitting criterion to speed up
the growth. The criterion is induced from Geometric Mean Metric Learning (GMML)
and then optimized under its diagonalized metric matrix constraint,
consequently, a closed-form rank of feature discriminant abilities can at once
be obtained and the top 1 feature at each node used to grow an intent DT
(called as dGMML-DT, where d is an abbreviation for diagonalization). We
evaluated the performance of the proposed methods and their corresponding
ensembles on benchmark datasets. The experiment shows that dGMML-DT achieves
comparable or better classification results more efficiently than the UDTs with
10x average speedup. Furthermore, dGMML-DT can straightforwardly be extended to
its multivariable counterpart (dGMML-MDT) without needing laborious operations.