title:
Planar Hamiltonian systems: index theory and applications to the
  existence of subharmonics

abstract:
  We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$,
where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic
in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z
H(t,z)$ is asymptotically linear for $\vert z \vert \to +\infty$. After
revisiting the index theory for linear planar Hamiltonian systems, by using the
Poincar\'e-Birkhoff fixed point theorem we prove that the above nonlinear
system has subharmonic solutions of any order $k$ large enough, whenever the
rotation numbers (or, equivalently, the mean Conley-Zehnder indices) of the
linearizations of the system at zero and at infinity are different.
Applications are given to the case of planar Hamiltonian systems coming from
second order scalar ODEs.


title: The Lingering Death of Periodic Near-Sun Comet 323P/SOHO

abstract:
  We observed near-Sun comet 323P/SOHO for the first time using ground and
space telescopes. In late December 2020, the object was recovered at Subaru
showing no cometary features on its way to perihelion. However, in our
postperihelion observations it developed a long narrow tail mimicking a
disintegrating cometary debris cloud. The ejecta, comprised of at least
mm-sized dust with power-law size distribution index $3.2 \pm 0.2$, was
impulsively produced shortly after the perihelion passage, during which
$\gtrsim$0.1-10% of the nucleus mass was shed due to excessive thermal stress
and rotational disruption. Two fragments of $\sim$20 m in radius (assuming a
geometric albedo of 0.15) were seen in HST observations from early March 2021.
The nucleus, with an effective radius of $86 \pm 3$ m (the same albedo assumed)
and an aspect ratio of $\lesssim$0.7, has a rotation period of 0.522 hr, which
is the shortest for known comets in the solar system and implies cohesive
strength $\gtrsim$10-100 Pa in the interior. The colour of the object was
peculiar, and how it changed temporally has never been previously observed.
Using our astrometry, we found a strong nongravitational effect following a
heliocentric dependency of $r_{\rm H}^{-8.5}$ in the transverse motion of the
object. Our N-body integration reveals that 323P has a likelihood of 99.7% to
collide with the Sun in the next two millennia driven by the $\nu_6$ secular
resonance.


title:
ScQ cloud quantum computation for generating Greenberger-Horne-Zeilinger
  states of up to 10 qubits

abstract:
  We introduce an online for public quantum computation platform, named as ScQ,
based on a 1D array of 10-qubit superconducting processor. Single qubit
rotation gates can be performed on each qubit. Controlled-NOT (CNOT) gates
between nearest-neighbor sites on the 1D array of 10 qubits are available. We
show online preparation and verification of Greenberger-Horne-Zeilinger (GHZ)
states of up to 10 qubits by this platform, for all possible blocks of qubits
in the chain. Both graphic interface and the quantum assembly language methods
are presented to achieve the above tasks, which rely on a parameter scanning
feature implemented on ScQ. Performance of this quantum computation platform,
such as fidelities of the logic gates and details of the superconducting
device, are presented.


title: Quantum Simulations of Vibrational Strong Coupling via Path Integrals

abstract:
  A quantum simulation of vibrational strong coupling (VSC) in the collective
regime via thermostatted ring-polymer molecular dynamics (TRPMD) is reported.
For a collection of liquid-phase water molecules resonantly coupled to a single
lossless cavity mode, the simulation shows that, as compared with a fully
classical calculation, the inclusion of nuclear and photonic quantum effects
does not lead to a change in the Rabi splitting but does broaden polaritonic
linewidths roughly by a factor of two. Moreover, under thermal equilibrium,
both quantum and classical simulations predict that the static dielectric
constant of liquid water is largely unchanged inside versus outside the cavity.
This result disagrees with a recent experiment demonstrating that the static
dielectric constant of liquid water can be resonantly enhanced under VSC,
suggesting either limitations of our approach or perhaps other experimental
factors that have not yet been explored.


title: The Formation of Globular Clusters as a Case of Overcooling

abstract:
  Driven by recent observational findings, we select massive interactive
binaries as the most suitable among the existing candidates for producing the
chemical patterns typical of multiple populations of Galactic globular
clusters. Still, to avoid supernova contamination we are further driven to
endorse the notion that above a critical mass stars fail to produce supernova
events, but rather eventually sink into black holes without ejecting much
energy and heavy metals. This assumption has the attractive implication of
suppressing star formation feedback for some 5--10 million years, in practice
leading to runaway star formation, analog to {\it overcooling} that in absence
of feedback would have turned most baryons into stars in the early Universe.
Under such conditions, multiple episodes of stars formation, incorporating
binary star ejecta from previous episodes, appear to be unavoidable, thus
accounting for the ubiquity of the multiple population phenomenon in globular
clusters.


title:
Offline Deep Reinforcement Learning for Dynamic Pricing of Consumer
  Credit

abstract:
  We introduce a method for pricing consumer credit using recent advances in
offline deep reinforcement learning. This approach relies on a static dataset
and requires no assumptions on the functional form of demand. Using both real
and synthetic data on consumer credit applications, we demonstrate that our
approach using the conservative Q-Learning algorithm is capable of learning an
effective personalized pricing policy without any online interaction or price
experimentation.


title:
Low-Complexity Beamforming Design for IRS-Aided NOMA Communication
  System with Imperfect CSI

abstract:
  Intelligent reflecting surface (IRS) as a promising technology rendering high
throughput in future communication systems is compatible with various
communication techniques such as non-orthogonal multiple-access (NOMA). In this
paper, the downlink transmission of IRS-assisted NOMA communication is
considered while undergoing imperfect channel state information (CSI).
Consequently, a robust IRS-aided NOMA design is proposed by solving the
sum-rate maximization problem to jointly find the optimal beamforming vectors
for the access point and the passive reflection matrix for the IRS, using the
penalty dual decomposition (PDD) scheme. This problem can be solved through an
iterative algorithm, with closed-form solutions in each step, and it is shown
to have very close performance to its upper bound obtained from perfect CSI
scenario. We also present a trellis-based method for optimal discrete phase
shift selection of IRS which is shown to outperform the conventional
quantization method. Our results show that the proposed algorithms, for both
continuous and discrete IRS, have very low computational complexity compared to
other schemes in the literature. Furthermore, we conduct a performance
comparison from achievable sum-rate standpoint between IRS-aided NOMA and
IRS-aided orthogonal multiple access (OMA), which demonstrates superiority of
NOMA compared to OMA in case of a tolerated channel uncertainty.


title: Semantic-Aware Latent Space Exploration for Face Image Restoration

abstract:
  For image restoration, most existing deep learning based methods tend to
overfit the training data leading to bad results when encountering unseen
degradations out of the assumptions for training. To improve the robustness,
generative adversarial network (GAN) prior based methods have been proposed,
revealing a promising capability to restore photo-realistic and high-quality
results. But these methods suffer from semantic confusion, especially on
semantically significant images such as face images. In this paper, we propose
a semantic-aware latent space exploration method for image restoration (SAIR).
By explicitly modeling referenced semantics information, SAIR can consistently
restore severely degraded images not only to high-resolution highly-realistic
looks but also to correct semantics. Quantitative and qualitative experiments
collectively demonstrate the effectiveness of the proposed SAIR. Our code can
be found in https://github.com/Liamkuo/SAIR.


title: Large cycles in generalized Johnson graphs

abstract:
  We count cycles of an unbounded length in generalized Johnson graphs.
Asymptotics of the number of such cycles is obtained for certain growth rates
of the cycle length.


title: The case for a new quark with a mass under 1 TeV

abstract:
  The latest measurements of the CKM matrix suggest that the W boson may have
interactions with some right-handed quarks. One way to reproduce measured
3-sigma variances from the Standard Model would be if one of these interactions
connected the right-handed charm quark with a new fourth-generation down-type
quark. Such a connection would also help explain the fact that high energy
collisions consistently produce more charm quarks than predicted by QCD. With
these data as a backdrop, it would be interesting to search for a new down-type
quark with a mass of under 1 TeV that decays to a W boson and a right-handed
charm quark. Direct searches do not rule out such a quark.


title:
Exploring Unfairness on Proof of Authority: Order Manipulation Attacks
  and Remedies

abstract:
  Proof of Authority (PoA) is a type of permissioned consensus algorithm with a
fixed committee. PoA has been widely adopted by communities and industries due
to its better performance and faster finality. In this paper, we explore the
\textit{unfairness} issue existing in the current PoA implementations. We have
investigated 2,500+ \textit{in the wild} projects and selected 10+ as our main
focus (covering Ethereum, Binance smart chain, etc.). We have identified two
types of order manipulation attacks to separately break the transaction-level
(a.k.a. transaction ordering) and the block-level (sealer position ordering)
fairness. Both of them merely rely on honest-but-\textit{profitable} sealer
assumption without modifying original settings. We launch these attacks on the
forked branches under an isolated environment and carefully evaluate the
attacking scope towards different implementations. To date (as of Nov 2021),
the potentially affected PoA market cap can reach up to $681,087$ million USD.
Besides, we further dive into the source code of selected projects, and
accordingly, propose our recommendation for the fix. To the best of knowledge,
this work provides the first exploration of the \textit{unfairness} issue in
PoA algorithms.


title: Coresets for Data Discretization and Sine Wave Fitting

abstract:
  In the \emph{monitoring} problem, the input is an unbounded stream
$P={p_1,p_2\cdots}$ of integers in $[N]:=\{1,\cdots,N\}$, that are obtained
from a sensor (such as GPS or heart beats of a human). The goal (e.g., for
anomaly detection) is to approximate the $n$ points received so far in $P$ by a
single frequency $\sin$, e.g. $\min_{c\in C}cost(P,c)+\lambda(c)$, where
$cost(P,c)=\sum_{i=1}^n \sin^2(\frac{2\pi}{N} p_ic)$, $C\subseteq [N]$ is a
feasible set of solutions, and $\lambda$ is a given regularization function.
For any approximation error $\varepsilon>0$, we prove that \emph{every} set $P$
of $n$ integers has a weighted subset $S\subseteq P$ (sometimes called
core-set) of cardinality $|S|\in O(\log(N)^{O(1)})$ that approximates
$cost(P,c)$ (for every $c\in [N]$) up to a multiplicative factor of
$1\pm\varepsilon$. Using known coreset techniques, this implies streaming
algorithms using only $O((\log(N)\log(n))^{O(1)})$ memory. Our results hold for
a large family of functions. Experimental results and open source code are
provided.


title:
Inverse problems for fractional equations with a minimal number of
  measurements

abstract:
  In this paper, we study several inverse problems associated with a fractional
differential equation of the following form:
  \[
  (-\Delta)^s u(x)+\sum_{k=0}^N a^{(k)}(x) [u(x)]^k=0,\ \ 0<s<1,\
N\in\mathbb{N}\cup\{0\}\cup\{\infty\},
  \]
  which is given in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq 1$.
For any finite $N$, we show that $a^{(k)}(x)$, $k=0,1,\ldots, N$, can be
uniquely determined by $N+1$ different pairs of Cauchy data in
$\Omega_e:=\mathbb{R}^n\backslash\overline{\Omega}$. If $N=\infty$, the
uniqueness result is established by using infinitely many pairs of Cauchy data.
The results are highly intriguing in that it generally does not hold true in
the local case, namely $s=1$, even for the simplest case when $N=0$, a fortiori
$N\geq 1$. The nonlocality plays a key role in establishing the uniqueness
result. We also establish several other unique determination results by making
use of a minimal number of measurements. Moreover, in the process we derive a
novel comparison principle for nonlinear fractional differential equations as a
significant byproduct.


title: On the generalized of p-harmonic maps

abstract:
  In this paper, we extend the definition of p-harmonic and p-biharmonic maps
between Riemannian manifolds. We present some new properties for the
generalized stable p-harmonic maps.


title: Control of the linearized Stefan problem in a periodic box

abstract:
  In this paper we consider the linearized one-phase Stefan problem with
surface tension, set in the strip $\mathbb{T}\times(-1,1)$, thus with periodic
boundary conditions respect to the horizontal direction $x_1\in\mathbb{T}$.
When the support of the control is not localized in $x_1$, namely, is of the
form $\omega=\mathbb{T}\times(c,d)$, we prove that the system is
null-controllable in any positive time. We rely on a Fourier decomposition with
respect to $x_1$, and controllability results which are uniform with respect to
the Fourier frequency parameter for the resulting family of one-dimensional
systems.
  The latter results are also novel, as we compute the full spectrum of the
underlying operator for the non-zero Fourier modes. The zeroth mode system, on
the other hand, is seen as a controllability problem for the linear heat
equation with a finite-dimensional constraint.
  We extend the controllability result to the setting of controls with a
support localized in a box: $\omega=(a,b)\times(c,d)$, through an argument
inspired by the method of Lebeau and Robbiano, under the assumption that the
initial data are of zero mean. Numerical experiments motivate several
challenging open problems, foraying even beyond the specific setting we deal
with herein.


title: Unbiased Estimation using a Class of Diffusion Processes

abstract:
  We study the problem of unbiased estimation of expectations with respect to
(w.r.t.) $\pi$ a given, general probability measure on
$(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with
respect to a standard Gaussian measure. We focus on simulation associated to a
particular class of diffusion processes, sometimes termed the
Schr\"odinger-F\"ollmer Sampler, which is a simulation technique that
approximates the law of a particular diffusion bridge process $\{X_t\}_{t\in
[0,1]}$ on $\mathbb{R}^d$, $d\in \mathbb{N}_0$. This latter process is
constructed such that, starting at $X_0=0$, one has $X_1\sim \pi$. Typically,
the drift of the diffusion is intractable and, even if it were not, exact
sampling of the associated diffusion is not possible. As a result,
\cite{sf_orig,jiao} consider a stochastic Euler-Maruyama scheme that allows the
development of biased estimators for expectations w.r.t.~$\pi$. We show that
for this methodology to achieve a mean square error of
$\mathcal{O}(\epsilon^2)$, for arbitrary $\epsilon>0$, the associated cost is
$\mathcal{O}(\epsilon^{-5})$. We then introduce an alternative approach that
provides unbiased estimates of expectations w.r.t.~$\pi$, that is, it does not
suffer from the time discretization bias or the bias related with the
approximation of the drift function. We prove that to achieve a mean square
error of $\mathcal{O}(\epsilon^2)$, the associated cost is, with high
probability, $\mathcal{O}(\epsilon^{-2}|\log(\epsilon)|^{2+\delta})$, for any
$\delta>0$. We implement our method on several examples including Bayesian
inverse problems.


title:
Learnable Irrelevant Modality Dropout for Multimodal Action Recognition
  on Modality-Specific Annotated Videos

abstract:
  With the assumption that a video dataset is multimodality annotated in which
auditory and visual modalities both are labeled or class-relevant, current
multimodal methods apply modality fusion or cross-modality attention. However,
effectively leveraging the audio modality in vision-specific annotated videos
for action recognition is of particular challenge. To tackle this challenge, we
propose a novel audio-visual framework that effectively leverages the audio
modality in any solely vision-specific annotated dataset. We adopt the language
models (e.g., BERT) to build a semantic audio-video label dictionary (SAVLD)
that maps each video label to its most K-relevant audio labels in which SAVLD
serves as a bridge between audio and video datasets. Then, SAVLD along with a
pretrained audio multi-label model are used to estimate the audio-visual
modality relevance during the training phase. Accordingly, a novel learnable
irrelevant modality dropout (IMD) is proposed to completely drop out the
irrelevant audio modality and fuse only the relevant modalities. Moreover, we
present a new two-stream video Transformer for efficiently modeling the visual
modalities. Results on several vision-specific annotated datasets including
Kinetics400 and UCF-101 validated our framework as it outperforms most relevant
action recognition methods.


title: Emerging chimera states under non-identical counter-rotating oscillators

abstract:
  Frequency plays a crucial role in exhibiting various collective dynamics in
the coexisting co- and counter-rotating (CR) systems. To illustrate the impact
of CR frequencies, we consider a network of non-identical and globally coupled
Stuart-Landau oscillators with additional perturbation. Primarily, we
investigate the dynamical transitions in the absence of perturbation,
demonstrating that the transition from desynchronized state to cluster
oscillatory state occurs through an interesting partial synchronization state.
Followed by this, the system dynamics transits to amplitude death and
oscillation death states. Importantly, we find that the observed dynamical
states do not preserve the parity(P) symmetry in the absence of perturbation.
When the perturbation is increased one can note that the system dynamics
exhibits a new kind of transition which corresponds to a change from incoherent
mixed synchronization to coherent mixed synchronization through chimera state.
In particular, incoherent mixed synchronization and coherent mixed
synchronization states completely preserve the P-symmetry, whereas the chimera
state preserves the P-symmetry only partially. To demonstrate the occurrence of
such partial symmetry breaking (chimera) state, we use basin stability analysis
and discover that PSB exists as a result of the coexistence of symmetry
preserving and symmetry breaking behavior in the initial state space. Further,
a measure of the strength of P-symmetry is established to quantify the
P-symmetry in the observed dynamical states. Finally, by increasing the network
size, the robustness of the chimera is also inspected and we find that the
chimera state is robust even in networks of larger sizes. We also show the
generality of the above results in the related phase reduced model as well as
in other coupled models such as the globally coupled van der Pol and R\"ossler
oscillators.


title:
Statistical Properties of Radio Halos in Galaxy Clusters and Origin of
  Seed Electrons for Reacceleration

abstract:
  One of the most promising mechanisms for producing radio halos (RHs) in
galaxy clusters is the reacceleration of cosmic-ray electrons by turbulences.
However, the origin of the seed electrons for the reacceleration is still
poorly constrained. In the secondary scenario, most of the seed electrons are
injected via collision of proton cosmic-rays, while high-energy electrons are
directly injected in the primary scenario. In this paper, we examine the two
scenarios for the seed electrons with the observed statistical properties of
RHs, combining two methods: following the temporal evolutions of the electron
energy and radial distributions in a cluster, and the merger history of
clusters. We find that the RH lifetime largely depends on the seed origin, as
it could be longer than the cosmological timescale in the secondary scenario.
We study the condition for the onset of RHs with the observed RH fraction and
the RH lifetime we obtained, and find that long-lived RHs in the secondary
scenario should be originated from major mergers with a mass ratio of
$\xi\sim0.1$, while the short lifetime in the primary scenario requires more
frequent onsets by minor mergers with $\xi\sim0.01$. Our simple model of the
turbulence acceleration can reproduce the observed radio luminosity-mass
relation. The RH luminosity functions we obtained suggest that the expected RH
number count with the ASKAP survey will detect $\approx10^3$ RHs in both the
scenarios.


title:
A Composable Framework for Policy Design, Learning, and Transfer Toward
  Safe and Efficient Industrial Insertion

abstract:
  Delicate industrial insertion tasks (e.g., PC board assembly) remain
challenging for industrial robots. The challenges include low error tolerance,
delicacy of the components, and large task variations with respect to the
components to be inserted. To deliver a feasible robotic solution for these
insertion tasks, we also need to account for hardware limits of existing
robotic systems and minimize the integration effort. This paper proposes a
composable framework for efficient integration of a safe insertion policy on
existing robotic platforms to accomplish these insertion tasks. The policy has
an interpretable modularized design and can be learned efficiently on hardware
and transferred to new tasks easily. In particular, the policy includes a safe
insertion agent as a baseline policy for insertion, an optimal configurable
Cartesian tracker as an interface to robot hardware, a probabilistic inference
module to handle component variety and insertion errors, and a safe learning
module to optimize the parameters in the aforementioned modules to achieve the
best performance on designated hardware. The experiment results on a UR10 robot
show that the proposed framework achieves safety (for the delicacy of
components), accuracy (for low tolerance), robustness (against perception error
and component defection), adaptability and transferability (for task
variations), as well as task efficiency during execution plus data and time
efficiency during learning.


title: RAPTOR: Rapid Aerial Pickup and Transport of Objects by Robots

abstract:
  Rapid aerial grasping promises vast applications that utilize the dynamic
picking up and placing of objects by robots. Rigid grippers traditionally used
in aerial manipulators require very high precision and specific object
geometries for successful grasping. We propose RAPTOR, a quadcopter platform
combined with a custom Fin Ray gripper to enable a more flexible grasping of
objects with different geometries, leveraging the properties of soft materials
to increase the contact surface between the gripper and the objects. To reduce
the communication latency, we present a novel FastDDS-based middleware solution
as an alternative to ROS (Robot Operating System). We show that RAPTOR achieves
an average of 83% grasping efficacy in a real-world setting for four different
object geometries while moving at an average velocity of 1 m/s during grasping,
which is approximately five times faster than the state-of-the-art while
supporting up to four times the payload. Our results further solidify the
potential of quadcopters in warehouses and other automated pick-and-place
applications over longer distances where speed and robustness become essential.


title:
A counterexample to a conjecture on the chromatic number of r-stable
  Kneser hypergraphs

abstract:
  The main purpose of this note is to give a counterexample to the following
conjecture, raised by Florian Frick [\textit{Int. Math. Res. Not. IMRN 2020
(13), 4037-4061 (2020)}].
  Conjecture. Let $r\geq 3$ and let $\mathcal{F}$ be a set system. Then
  $$\chi\left(\textrm{KG}^r\left(\mathcal{F}_{r-stab}\right)\right)\geq\left\lceil\frac{cd_r\left(\mathcal{F}\right)}{r-1}\right\rceil.$$


title: Optimal regimes for algorithm-assisted human decision-making

abstract:
  We introduce optimal regimes for algorithm-assisted human decision-making.
Such regimes are decision functions of measured pre-treatment variables and
enjoy a "superoptimality" property whereby they are guaranteed to outperform
conventional optimal regimes currently considered in the literature. A key
feature of these superoptimal regimes is the use of natural treatment values as
input to the decision function. Importantly, identification of the superoptimal
regime and its value require exactly the same assumptions as identification of
conventional optimal regimes in several common settings, including instrumental
variable settings. As an illustration, we study superoptimal regimes in an
example that has been presented in the optimal regimes literature.


title:
Hierarchically Structured Scheduling and Execution of Tasks in a
  Multi-Agent Environment

abstract:
  In a warehouse environment, tasks appear dynamically. Consequently, a task
management system that matches them with the workforce too early (e.g., weeks
in advance) is necessarily sub-optimal. Also, the rapidly increasing size of
the action space of such a system consists of a significant problem for
traditional schedulers. Reinforcement learning, however, is suited to deal with
issues requiring making sequential decisions towards a long-term, often remote,
goal. In this work, we set ourselves on a problem that presents itself with a
hierarchical structure: the task-scheduling, by a centralised agent, in a
dynamic warehouse multi-agent environment and the execution of one such
schedule, by decentralised agents with only partial observability thereof. We
propose to use deep reinforcement learning to solve both the high-level
scheduling problem and the low-level multi-agent problem of schedule execution.
Finally, we also conceive the case where centralisation is impossible at test
time and workers must learn how to cooperate in executing the tasks in an
environment with no schedule and only partial observability.


title: HEAR 2021: Holistic Evaluation of Audio Representations

abstract:
  What audio embedding approach generalizes best to a wide range of downstream
tasks across a variety of everyday domains without fine-tuning? The aim of the
HEAR 2021 NeurIPS challenge is to develop a general-purpose audio
representation that provides a strong basis for learning in a wide variety of
tasks and scenarios. HEAR 2021 evaluates audio representations using a
benchmark suite across a variety of domains, including speech, environmental
sound, and music. In the spirit of shared exchange, each participant submitted
an audio embedding model following a common API that is general-purpose,
open-source, and freely available to use. Twenty-nine models by thirteen
external teams were evaluated on nineteen diverse downstream tasks derived from
sixteen datasets. Open evaluation code, submitted models and datasets are key
contributions, enabling comprehensive and reproducible evaluation, as well as
previously impossible longitudinal studies. It still remains an open question
whether one single general-purpose audio representation can perform as
holistically as the human ear.


title:
Symmetric functions and a natural framework for combinatorial and number
  theoretic sequences

abstract:
  Certain triples of power series, considered by I. Macdonald, give a natural
framework for many combinatorial and number theoretic sequences, such as the
Stirling, Bernoulli and harmonic numbers and partitions of different kinds. The
power series in such a triple are closely linked by identities coming from the
theory of symmetric functions. We extend the work of Z-H. Sun, who developed
similar ideas, and Macdonald, revealing more of the structure of these triples.
De Moivre polynomials play a key role in this study.


title:
Enhancing associative memory recall in non-equilibrium materials through
  activity

abstract:
  Associative memory, a form of content-addressable memory, facilitates
information storage and retrieval in many biological and physical systems. In
statistical mechanics models, associative memory at equilibrium is represented
through attractor basins in the free energy landscape. Here, we use the
Hopfield model, a paradigmatic model to describe associate memory, to
investigate the effect of non-equilibrium activity on memory retention and
recall. We introduce activity into the system as gaussian-colored noise which
breaks detailed balance and forces the system out of equilibrium. We observe
that, under these non-equilibrium conditions, the Hopfield network has a higher
storage capacity than that allowed at equilibrium. Using analytical and
numerical techniques, we show that the rate of entropy production modifies the
energy landscape and helps the system to access memory regions which were
previously inaccessible.


title:
Spread and asymmetry of typical quantum coherence and their inhibition
  in response to glassy disorder

abstract:
  We consider the average quantum coherences of typical redits and qudits -
vectors of real and complex Hilbert spaces - with the analytical forms stemming
from the symmetry of Haar-uniformly distributed random pure states. We
subsequently study the response to disorder in spread of the typical quantum
coherence in response to glassy disorder. The disorder is inserted in the state
parameters. Even in the absence of disorder, the quantum coherence
distributions of redits and qudits are not uniform over the range of quantum
coherence, and the spreads are lower for higher dimensions. On insertion of
disorder, the spreads decrease. This decrease in the spread of quantum
coherence distribution in response to disorder is seen to be a generic feature
of typical pure states: we observe the feature for different strengths of
disorder and for various types of disorder distributions, viz. Gaussian,
uniform, and Cauchy-Lorentz. We also find that the quantum coherence
distributions become less asymmetric with increase in dimension and with
infusion of glassy disorder.


title: A global large deviation principle for discrete $\beta$-ensembles

abstract:
  We consider discrete $\beta$-ensembles, as introduced by Borodin, Gorin and
Guionnet in (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017).
Under general assumptions, we establish a large deviation principle for the
empirical (or spectral) measures corresponding to these models. Our results
apply in the cases when the potential of the model depends on the number of
particles, and/or has slow growth near infinity, leading to an equilibrium
measure with infinite support.


title:
Recurrence properties for linear dynamical systems: an approach via
  invariant measures

abstract:
  We study different pointwise recurrence notions for linear dynamical systems
from the Ergodic Theory point of view. We show that from any reiteratively
recurrent vector $x_0$, for an adjoint operator $T$ on a separable dual Banach
space $X$, one can construct a $T$-invariant probability measure which contains
$x_0$ in its support. This allows us to establish some equivalences, for these
operators, between some strong pointwise recurrence notions which in general
are completely distinguished. In particular, we show that (in our framework)
reiterative recurrence coincides with frequent recurrence; for complex Hilbert
spaces uniform recurrence coincides with the property of having a spanning
family of unimodular eigenvectors; and the same happens for power-bounded
operators on complex reflexive Banach spaces. These (surprising) properties are
easily generalized to product and inverse dynamical systems, which implies some
relations with the respective hypercyclicity notions. Finally we study how
typical is an operator with a non-zero reiteratively recurrent vector in the
sense of Baire category.


title:
Monotone methods in counterparty risk models with non-linear
  Black-Scholes-type equations

abstract:
  A non-linear Black-Scholes-type equation is studied within counterparty risk
models. The classical hypothesis on the uniform Lipschitz-continuity of the
non-linear reaction function allows for an equivalent transformation of the
semi-linear Black-Scholes equation into a standard parabolic problem with a
monotone non-linear reaction function and an inhomogeneous linear diffusion
equation. This setting allows us to construct a scheme of monotone, increasing
or decreasing, iterations that converge monotonically to the true solution. As
typically any numerical solution of this problem uses most computational power
for computing an approximate solution to the inhomogeneous linear diffusion
equation, we discuss also this question and suggest several solution methods,
including those based on Monte Carlo and finite differences/elements.


title:
Hall coefficient in amorphous alloys: critical behavior and quantitative
  test of quantum corrections due to weak localization and electron-electron
  interactions

abstract:
  Here, we present the measurements of $R_H$ in a series of $Ti_xSi_{100-x}$
amorphous reaching the critical concentration, $x_c\approx9-9.5$. For
$x\geq17$, the Hall coefficient displays the behavior predicted by the
perturbation theory, $R_H^{-1}\left(T\right)=R_H^{-1}\left(0\right)+bT^{1/2}$,
which extends up to the temperature 150 K. The temperature dependence gets
stronger in alloys with lower $x$; $R_H\left(0\right)$ diverges at $x_c$
displaying critical behavior. We used the combined conductivity and Hall
coefficient data for alloys with high Ti content to test the theories of
quantum corrections to conductivity. We found that the correction due to weak
localization is dominated by the electron-phonon scattering with the rate
varying with temperature as $\tau_{ep}^{-1}=A_{ep}T^2$. The extracted parameter
$A_{ep}$ is in good agreement with the theory that considers the incomplete
drag of impurities by lattice vibrations. The spin-orbit scattering time
extracted from the weak localization correction was found to be two orders of
magnitude larger than the time given by the standard estimate
$\tau_{so}\approx\tau\left(\hbar c/e^2Z\right)^4$. The theory of the EEI
quantum correction was tested using the Hall coefficient and specific heat data
for Ti-Si and $\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ amorphous alloys,
which allowed us to estimate all microscopic parameters needed by the theory.
We found that, within the accuracy of our measurements, the EEI theory works
exactly for alloys that follow the free electron model
[$\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ with $x\le50$.] The deviation from
the theory observed in all Ti-Si alloys and in Ag-Cu-Ge alloys with $x\geq60$
can be qualitatively explained by weakening of the electron screening in the
systems.


title:
Deep Reinforcement Learning based Model-free On-line Dynamic
  Multi-Microgrid Formation to Enhance Resilience

abstract:
  Multi-microgrid formation (MMGF) is a promising solution to enhance power
system resilience. This paper proposes a new deep reinforcement learning (RL)
based model-free on-line dynamic multi-MG formation (MMGF) scheme. The dynamic
MMGF problem is formulated as a Markov decision process, and a complete deep RL
framework is specially designed for the topology-transformable micro-grids. In
order to reduce the large action space caused by flexible switch operations, a
topology transformation method is proposed and an action-decoupling Q-value is
applied. Then, a CNN based multi-buffer double deep Q-network (CM-DDQN) is
developed to further improve the learning ability of original DQN method. The
proposed deep RL method provides real-time computing to support on-line dynamic
MMGF scheme, and the scheme handles a long-term resilience enhancement problem
using adaptive on-line MMGF to defend changeable conditions. The effectiveness
of the proposed method is validated using a 7-bus system and the IEEE 123-bus
system. The results show strong learning ability, timely response for varying
system conditions and convincing resilience enhancement.


title:
Propagation of moments for large data and semiclassical limit to the
  relativistic Vlasov equation

abstract:
  We investigate the semiclassical limit from the semi-relativistic
Hartree-Fock equation describing the time evolution of a system of fermions in
the mean-field regime with a relativistic dispersion law and interacting
through a singular potential of the form $K(x)=\gamma\frac{1}{|x|^a}$, $a \in
\left( \max \left\{ \frac{d}{2} -2 , - 1 \right\}, d-2 \right]$, $d\in\{2,3\}$
and $\gamma\in\mathbb{R}$, with the convention $K(x)=\gamma\log(|x|)$ if $a=0$.
For mixed states, we show convergence in Schatten norms with explicit rate
towards the Weyl transform of a solution to the relativistic Vlasov equation
with singular potentials, thus generalizing [J. Stat. Phys. 172 (2), 398--433
(2018)] where the case of smooth potentials has been treated. Moreover, we
provide new results on the well-posedness theory of the relativistic Vlasov
equations with singular interactions.


title: Weighted-average quantile regression

abstract:
  In this paper, we introduce the weighted-average quantile regression
framework, $\int_0^1 q_{Y|X}(u)\psi(u)du = X'\beta$, where $Y$ is a dependent
variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of
the conditional distribution of $Y$ given $X$, $\psi$ is a weighting function,
and $\beta$ is a vector of parameters. We argue that this framework is of
interest in many applied settings and develop an estimator of the vector of
parameters $\beta$. We show that our estimator is $\sqrt T$-consistent and
asymptotically normal with mean zero and easily estimable covariance matrix,
where $T$ is the size of available sample. We demonstrate the usefulness of our
estimator by applying it in two empirical settings. In the first setting, we
focus on financial data and study the factor structures of the expected
shortfalls of the industry portfolios. In the second setting, we focus on wage
data and study inequality and social welfare dependence on commonly used
individual characteristics.


title:
Spreading pressure bumps in gas-dust discs can stall planet migration
  via planet-vortex interactions

abstract:
  We investigate the gravitational interaction between low- to
intermediate-mass planets ($M_p \in[0.06-210]\,M_{\oplus}$) and two previously
formed pressure bumps in a gas-dust protoplanetary disc. We explore how the
disc structure changes due to planet-induced perturbations and also how the
appearance of vortices affects planet migration. We use multifluid 2D
hydrodynamical simulations and the dust is treated in the pressureless-fluid
approximation, assuming a single grain size of $5\,\mu{\mathrm{m}}$. The
initial surface density profiles containing two bumps are motivated by recent
observations of the protoplanetary disc HD163296. When planets are allowed to
migrate, either a single planet from the outer pressure maximum or two planets
from each pressure maximum, the initial pressure bumps quickly spread and merge
into a single bump which is radially wide and has a very low amplitude. The
redistribution of the disc material is accompanied by the Rossby Wave
Instability (RWI) and an appearance of mini-vortices that merge in a short
period of time to form a large vortex. The large vortex induces perturbations
with a spiral wave pattern that propagate away from the vortex as density
waves. We found that these vortex-induced spiral waves strongly interact with
the spiral waves generated by the planet and we called this mechanism the
"\textit{Faraway Interaction}". It facilitates much slower and/or stagnant
migration of the planets and it excites their orbital eccentricities in some
cases. Our study provides a new explanation for how rocky planets can come to
have a slow migration in protoplanetary discs where vortex formation occurs.


title:
A Unified View of SDP-based Neural Network Verification through
  Completely Positive Programming

abstract:
  Verifying that input-output relationships of a neural network conform to
prescribed operational specifications is a key enabler towards deploying these
networks in safety-critical applications. Semidefinite programming (SDP)-based
approaches to Rectified Linear Unit (ReLU) network verification transcribe this
problem into an optimization problem, where the accuracy of any such
formulation reflects the level of fidelity in how the neural network
computation is represented, as well as the relaxations of intractable
constraints. While the literature contains much progress on improving the
tightness of SDP formulations while maintaining tractability, comparatively
little work has been devoted to the other extreme, i.e., how to most accurately
capture the original verification problem before SDP relaxation. In this work,
we develop an exact, convex formulation of verification as a completely
positive program (CPP), and provide analysis showing that our formulation is
minimal -- the removal of any constraint fundamentally misrepresents the neural
network computation. We leverage our formulation to provide a unifying view of
existing approaches, and give insight into the source of large relaxation gaps
observed in some cases.


title:
Study of CP violation in hyperon decays at Super Charm-Tau Factories
  with a polarized electron beam

abstract:
  Non-leptonic two-body weak decays of baryons are an important tool to probe
the combined charge-conjugation--parity symmetry (CP) violation. We explain why
the decays of strange baryons provide complementary information to the decays
of kaons. A model-independent parameterization of the non-leptonic decays of
the $\Lambda$- and $\Xi$-baryons is reviewed, and the amplitudes are updated
according to the latest experimental input. We demonstrate the potential of
performing precision tests in strange baryon decays at the next generation
electron-positron $J/\psi$ factories with luminosity of $10^{35}$
cm$^{-2}$s$^{-1}$. The copious production of spin-entangled hyperon-antihyperon
pairs via the $J/\psi$ resonance allows for a direct comparison of the baryon
and antibaryon decay properties. Using analytic approximations and numerical
calculations, we study the quantitative impact of spin correlations and
polarization in such CP tests. We show that by using a longitudinally-polarized
electron beam, the statistical precision of the CP tests can be significantly
improved compared to the experiments without polarized beams. Furthermore, we
map out further directions for possible improvements, like analysis of
incompletely reconstructed events or a combination of the isospin related
processes. Altogether, these methods are promising for the observation of a
statistically significant CP-violation signal with a strength corresponding to
the standard model predictions. Our conclusions should encourage more detailed
feasibility studies, including optimisation of the measurement methods and
studies of systematic effects. Finally, our results call for an update of the
theory predictions with increased precision.


title:
Frames for Graph Signals on the Symmetric Group: A Representation
  Theoretic Approach

abstract:
  An important problem in the field of graph signal processing is developing
appropriate overcomplete dictionaries for signals defined on different families
of graphs. The Cayley graph of the symmetric group has natural applications in
ranked data analysis, as its vertices represent permutations, while the
generating set formalizes a notion of distance between rankings. Taking
advantage of the rich theory of representations of the symmetric group, we
study a particular class of frames, called Frobenius-Schur frames, where every
atom belongs to the coefficient space of only one irreducible representation of
the symmetric group. We provide a characterization for all Frobenius-Schur
frames on the group algebra of the symmetric group which are "compatible" with
respect to the generating set. Such frames have been previously studied for the
permutahedron, the Cayley graph of the symmetric group with the generating set
of adjacent transpositions, and have proved to be capable of producing
meaningful interpretation of the ranked data set via the analysis coefficients.
Our results generalize frame constructions for the permutahedron to any
inverse-closed generating set.


title: Some Collatz quadratic prime sequences

abstract:
  We consider some quadratic variations of the recursive sequence introduced by
Lothar Collatz in 1937.


title:
Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic
  Nonlinear Systems in Uncertain Environments

abstract:
  We address the risk bounded trajectory optimization problem of stochastic
nonlinear robotic systems. More precisely, we consider the motion planning
problem in which the robot has stochastic nonlinear dynamics and uncertain
initial locations, and the environment contains multiple dynamic uncertain
obstacles with arbitrary probabilistic distributions. The goal is to plan a
sequence of control inputs for the robot to navigate to the target while
bounding the probability of colliding with obstacles. Existing approaches to
address risk bounded trajectory optimization problems are limited to particular
classes of models and uncertainties such as Gaussian linear problems. In this
paper, we deal with stochastic nonlinear models, nonlinear safety constraints,
and arbitrary probabilistic uncertainties, the most general setting ever
considered. To address the risk bounded trajectory optimization problem, we
first formulate the problem as an optimization problem with stochastic dynamics
equations and chance constraints. We then convert probabilistic constraints and
stochastic dynamics constraints on random variables into a set of deterministic
constraints on the moments of state probability distributions. Finally, we
solve the resulting deterministic optimization problem using nonlinear
optimization solvers and get a sequence of control inputs. To our best
knowledge, it is the first time that the motion planning problem to such a
general extent is considered and solved. To illustrate the performance of the
proposed method, we provide several robotics examples.


title:
Landau-Ginzburg mirror, quantum differential equations and qKZ
  difference equations for a partial flag variety

abstract:
  We consider the system of quantum differential equations for a partial flag
variety and construct a basis of solutions in the form of multidimensional
hypergeometric functions, that is, we construct a Landau-Ginzburg mirror for
that partial flag variety. In our construction, the solutions are labeled by
elements of the $K$-theory algebra of the partial flag variety.
  To establish these facts we consider the equivariant quantum differential
equations for a partial flag variety and introduce a compatible system of
difference equations, which we call the qKZ equations. We construct a basis of
solutions of the joint system of the equivariant quantum differential equations
and qKZ difference equations in the form of multidimensional hypergeometric
functions. Then the facts about the non-equivariant quantum differential
equations are obtained from the facts about the equivariant quantum
differential equations by a suitable limit.
  Analyzing these constructions we obtain a formula for the fundamental Levelt
solution of the quantum differential equations for a partial flag variety.


title: Modelplasticity and Abductive Decision Making

abstract:
  `All models are wrong but some are useful' (George Box 1979). But, how to
find those useful ones starting from an imperfect model? How to make informed
data-driven decisions equipped with an imperfect model? These fundamental
questions appear to be pervasive in virtually all empirical fields -- including
economics, finance, marketing, healthcare, climate change, defense planning,
and operations research. This article presents a modern approach (builds on two
core ideas: abductive thinking and density-sharpening principle) and practical
guidelines to tackle these issues in a systematic manner.


title: Highly Accurate Dichotomous Image Segmentation

abstract:
  We present a systematic study on a new task called dichotomous image
segmentation (DIS), which aims to segment highly accurate objects from natural
images. To this end, we collected the first large-scale dataset, called DIS5K,
which contains 5,470 high-resolution (e.g., 2K, 4K or larger) images covering
camouflaged, salient, or meticulous objects in various backgrounds. All images
are annotated with extremely fine-grained labels. In addition, we introduce a
simple intermediate supervision baseline (IS-Net) using both feature-level and
mask-level guidance for DIS model training. Without tricks, IS-Net outperforms
various cutting-edge baselines on the proposed DIS5K, making it a general
self-learned supervision network that can help facilitate future research in
DIS. Further, we design a new metric called human correction efforts (HCE)
which approximates the number of mouse clicking operations required to correct
the false positives and false negatives. HCE is utilized to measure the gap
between models and real-world applications and thus can complement existing
metrics. Finally, we conduct the largest-scale benchmark, evaluating 16
representative segmentation models, providing a more insightful discussion
regarding object complexities, and showing several potential applications
(e.g., background removal, art design, 3D reconstruction). Hoping these efforts
can open up promising directions for both academic and industries. We will
release our DIS5K dataset, IS-Net baseline, HCE metric, and the complete
benchmark results.


title:
Review of sterile neutrino searches at very short-baseline reactor
  experiments

abstract:
  Search for New Physics beyond the Standard Model is the main direction in
particle physics nowadays. There are several experimental hints of New Physics.
The most statistically significant (5-6$\sigma$) are the hints of eV mass scale
sterile neutrinos. They come from antineutrino disappearance in reactor
experiments, $\nu_e$ disappearance in experiments with very powerful
radioactive sources, and electron (anti)neutrino appearance in the muon
(anti)neutrino beams. Very important results in this field were obtained in
2021 by the BEST, MicroBooNE, and Neutrino-4 collaborations as well as by
several other experiments. However, the situation is still or maybe even more
controversial. We review these indications of New Physics and prospects for the
next few years with the emphasis on reactor experiments.


title: High Speed Emulation in a Vehicle-in-the-Loop Driving Simulator

abstract:
  Rendering accurate multisensory feedback is critical to ensure natural user
behavior in driving simulators. In this work, we present a virtual reality
(VR)-based Vehicle-in-the-Loop (ViL) simulator that provides visual,
vestibular, and haptic feedback to drivers in high speed driving conditions.
Designing our simulator around a four-wheel steer-by-wire vehicle enables us to
emulate the dynamics of a vehicle traveling significantly faster than the test
vehicle and to transmit corresponding haptic steering feedback to the driver.
By scaling the speed of the test vehicle through a combination of VR visuals,
vehicle dynamics emulation, and steering wheel force feedback, we can safely
and immersively run experiments up to highway speeds within a limited driving
space. In double lane change and highway weaving experiments, our high speed
emulation method tracks yaw motion within human perception limits and provides
sensory feedback comparable to the same maneuvers driven manually.


title: Speculation in Procurement Auctions

abstract:
  A speculator can take advantage of a procurement auction by acquiring items
for sale before the auction. The accumulated market power can then be exercised
in the auction and may lead to a large enough gain to cover the acquisition
costs. I show that speculation always generates a positive expected profit in
second-price auctions but could be unprofitable in first-price auctions. In the
case where speculation is profitable in first-price auctions, it is more
profitable in second-price auctions. This comparison in profitability is driven
by different competition patterns in the two auction mechanisms. In terms of
welfare, speculation causes private value destruction and harms efficiency.
Sellers benefit from the acquisition offer made by the speculator. Therefore,
speculation comes at the expense of the auctioneer.


title:
Engine-fed Kilonovae (Mergernovae) -- I. Dynamical Evolution and Energy
  Injection / Heating Efficiencies

abstract:
  A binary neutron star merger is expected to be associated by a kilonova,
transient optical emission powered by radioactive decay of the neutron-rich
ejecta. If the post-merger remnant is a long-lived neutron star, additional
energy injection to the ejecta is possible. Hence, a long-lived neutron star
can serve as the engine of the kilonova. In this first paper of a series, we
study the dynamical evolution of the engine-fed kilonova (mergernova) ejecta in
detail. We perform a semi-analytical study of the problem by adopting a
modified mechanical blastwave model that invokes interaction between a
Poynting-flux-dominated flow and a non-magnetized massive ejecta. Shortly after
the engine is turned on, a pair of shocks would be excited. The reverse shock
quickly reaches the wind-acceleration region and disappears, whereas the
forward shock soon breaks out from the ejecta and continues to propagate in the
surrounding interstellar medium. Most of the energy injected into the blastwave
from the engine is stored as magnetic energy and kinetic energy. The internal
energy fraction is $f_{\rm int} < 0.3$ for an ejecta mass equal to
$10^{-3}M_{\odot}$. Overall, the energy injecting efficiency $\xi$ is at most
$\sim 0.6$ and can be as small as $\sim 0.04$ at later times. Contrary to the
previous assumption, efficient heating only happens before the forward shock
breaks out of the ejecta with a heating efficiency $\xi_t \sim (0.006 - 0.3)$,
which rapidly drops to $\sim 0$ afterwards. The engine-fed kilonova lightcurves
will be carefully studied in Paper II.


title: Dot products in ${\Bbb F}_q^3$ and the Vapnik-Chervonenkis dimension

abstract:
  Given a set $E \subset {\Bbb F}_q^3$, where ${\Bbb F}_q$ is the field with
$q$ elements. Consider a set of "classifiers" ${\mathcal H}^3_t(E)=\{h_y: y \in
E\}$, where $h_y(x)=1$ if $x \cdot y=t$, $x \in E$, and $0$ otherwise. We are
going to prove that if $|E| \ge Cq^{\frac{11}{4}}$, with a sufficiently large
constant $C>0$, then the Vapnik-Chervonenkis dimension of ${\mathcal H}^3_t(E)$
is equal to $3$. In particular, this means that for sufficiently large subsets
of ${\Bbb F}_q^3$, the Vapnik-Chervonenkis dimension of ${\mathcal H}^3_t(E)$
is the same as the Vapnik-Chervonenkis dimension of ${\mathcal H}^3_t({\Bbb
F}_q^3)$. In some sense the proof leads us to consider the most complicated
possible configuration that can always be embedded in subsets of ${\Bbb F}_q^3$
of size $\ge Cq^{\frac{11}{4}}$.


title: Recent Advances in Neural Text Generation: A Task-Agnostic Survey

abstract:
  In recent years much effort has been devoted to applying neural models to the
task of natural language generation. The challenge is to generate natural
human-like text, and to control the generation process. This paper presents a
task-agnostic survey of recent advances in neural text generation. These
advances have been achieved by numerous developments, which we group under the
following four headings: data construction, neural frameworks, training and
inference strategies, and evaluation metrics. Finally we discuss the future
directions for the development of neural text generation including neural
pipelines and exploiting back-ground knowledge.


title:
Scalable Uncertainty Quantification for Deep Operator Networks using
  Randomized Priors

abstract:
  We present a simple and effective approach for posterior uncertainty
quantification in deep operator networks (DeepONets); an emerging paradigm for
supervised learning in function spaces. We adopt a frequentist approach based
on randomized prior ensembles, and put forth an efficient vectorized
implementation for fast parallel inference on accelerated hardware. Through a
collection of representative examples in computational mechanics and climate
modeling, we show that the merits of the proposed approach are fourfold. (1) It
can provide more robust and accurate predictions when compared against
deterministic DeepONets. (2) It shows great capability in providing reliable
uncertainty estimates on scarce data-sets with multi-scale function pairs. (3)
It can effectively detect out-of-distribution and adversarial examples. (4) It
can seamlessly quantify uncertainty due to model bias, as well as noise
corruption in the data. Finally, we provide an optimized JAX library called
{\em UQDeepONet} that can accommodate large model architectures, large ensemble
sizes, as well as large data-sets with excellent parallel performance on
accelerated hardware, thereby enabling uncertainty quantification for DeepONets
in realistic large-scale applications.


title: Variational formalism for generic shells in general relativity

abstract:
  We investigate the variational principle for the gravitational field in the
presence of thin shells of completely unconstrained signature (generic shells).
Such variational formulations have been given before for shells of timelike and
null signatures separately, but so far no unified treatment exists. We identify
the shell equation as the natural boundary condition associated with a broken
extremal problem along a hypersurface where the metric tensor is allowed to be
nondifferentiable. Since the second order nature of the Einstein-Hilbert action
makes the boundary value problem associated with the variational formulation
ill-defined, regularization schemes need to be introduced. We investigate
several such regularization schemes and prove their equivalence. We show that
the unified shell equations derived from this variational procedure reproduce
past results obtained via distribution theory by Barrabes and Israel for
hypersurfaces of fixed causal type and by Mars and Senovilla for generic
shells. These results are expected to provide a useful guide to formulating
thin shell equations and junction conditions along generic hypersurfaces in
modified theories of gravity.


title: Operator $K$-theory algebra spectra of $C^*$-algebras

abstract:
  We construct commutative algebra spectra that represent the operator
$K$-theory of $C^*$-algebras, which are algebras over the commutative ring
spectra that represent topological $K$-theory. The spectral multiplicative
structure introduces a new graded commutative ring structure on the $K$-groups,
generalizing the well-known graded ring structure of commutative
$C^*$-algebras. This last structure reflects the multiplicative structure of
topological $K$-theory via Gelfand duality, Swan's theorem and the fiber tensor
product.
  We introduce $\mathscr L$-permutative categories, a generalization of
bipermutative categories, which are permutative categories equipped with a
multiplicative structures induced by coherent actions of the linear isometries
operad. The main class of examples of interest are categories whose objects are
projection matrices of the unitization of the stabilizations
$\widetilde{\mathfrak{KA}}$ of a $C^*$-algebras $\mathfrak A$, and morphisms
partial isometries witnessing the Murray-von Neumann relation.
  We then construct $E_\infty$-ring spaces out of them by adapting the usual
method applied to bipermutative categories. The delooping functor of the
recognition principle, the homotopical augmentation ideal and localization at
the Bott element then give us our algebra spectra.


title:
Estimation of a Factor-Augmented Linear Model with Applications Using
  Student Achievement Data

abstract:
  In many longitudinal settings, economic theory does not guide practitioners
on the type of restrictions that must be imposed to solve the rotational
indeterminacy of factor-augmented linear models. We study this problem and
offer several novel results on identification using internally generated
instruments. We propose a new class of estimators and establish large sample
results using recent developments on clustered samples and high-dimensional
models. We carry out simulation studies which show that the proposed approaches
improve the performance of existing methods on the estimation of unknown
factors. Lastly, we consider three empirical applications using administrative
data of students clustered in different subjects in elementary school, high
school and college.


title: Cone Vertex Algebras, Mock Theta Functions, and Umbral Moonshine Modules

abstract:
  We describe a family of indefinite theta functions of signature $(1,1)$ that
can be expressed in terms of trace functions of vertex algebras built from
cones in lattices. The family of indefinite theta functions considered has
interesting connections with mock theta functions and Appell-Lerch sums. We use
these relations to write the McKay-Thompson series of umbral moonshine at
lambency $\ell=8,12,16$ in terms of trace functions of vertex algebras modules,
and thereby provide the modules for these instances of umbral moonshine.


title: Time-of-Flight Quantum Tomography of Single Atom Motion

abstract:
  Time of flight is an intuitive way to determine the velocity of particles and
lies at the heart of many capabilities ranging from mass spectrometry to fluid
flow measurements. Here we show time-of-flight imaging can realize tomography
of a quantum state of motion of a single trapped atom. Tomography of motion
requires studying the phase space spanned by both position and momentum. By
combining time-of-flight imaging with coherent evolution of the atom in an
optical tweezer trap, we are able to access arbitrary quadratures in phase
space without relying on coupling to a spin degree of freedom. To create
non-classical motional states, we harness quantum tunneling in the versatile
potential landscape of optical tweezers, and our tomography both demonstrates
Wigner function negativity and assesses coherence of non-stationary states. Our
demonstrated tomography concept has wide applicability to a range of particles
and will enable characterization of non-classical states of more complex
systems or massive dielectric particles.


title:
Verification of Bitcoin's Smart Contracts in Agda using Weakest
  Preconditions for Access Control

abstract:
  This paper addresses the verification of Bitcoin smart contracts using the
interactive theorem prover Agda. It focuses on two standard smart contracts
that govern the distribution of Bitcoins, Pay to Public Key Hash (P2PKH) and
Pay to Multisig (P2MS). Both are written in Bitcoin's low-level language
script, and provide the security property of access control to the distribution
of Bitcoins. The paper introduces an operational semantics of the script
commands used in P2PKH and P2MS, and formalises it in the Agda proof assistant
using Hoare triples. It advocates weakest preconditions in the context of Hoare
triples as the appropriate notion for verifying access control. Two
methodologies for obtaining human-readable weakest preconditions are discussed
in order to close the validation gap between user requirements and formal
specification of smart contracts: (1) a step-by-step approach, which works
backwards instruction by instruction through a script, sometimes stepping over
several instructions in one go; (2) symbolic execution of the code and
translation into a nested case distinction, which allows to read off weakest
preconditions as the disjunction of accepting paths. A syntax for equational
reasoning with Hoare Triples is defined in order to formalise those approaches
in Agda.
  Keywords and phrases Blockchain; Cryptocurrency; Bitcoin; Ethereum; Agda;
Coq; Verification; Hoare logic; Script; P2PKH; Multi signature; Security;
Weakest precondition; Correctnes; Proof; Smart Contract


title:
A cryogenic tracking detector for antihydrogen detection in the AEgIS
  experiment

abstract:
  We present the commissioning of the Fast Annihilation Cryogenic Tracker
detector (FACT), installed around the antihydrogen production trap inside the 1
T superconducting magnet of the AE\=gIS experiment. FACT is designed to detect
pions originating from the annihilation of antiprotons. Its 794 scintillating
fibers operate at 4 K and are read out by silicon photomultipliers (MPPCs) at
near room temperature. FACT provides the antiproton/antihydrogen annihilation
position information with a few ns timing resolution. We present the hardware
and software developments which led to the successful operation of the detector
for antihydrogen detection and the results of an antiproton-loss based
efficiency assessment. The main background to the antihydrogen signal is that
of the positrons impinging onto the positronium conversion target and creating
a large amount of gamma rays which produce a sizeable signal in the MPPCs
shortly before the antihydrogen signal is expected. We detail the
characterization of this background signal and its impact on the antihydrogen
detection efficiency.


title:
Detection of chiral domains and linear electro-optical response in
  planar-aligned cells of an achiral rod-like ferro-electric nematic liquid
  crystal

abstract:
  Chiral domains of opposite chirality are observed surprisingly in a nematic
phase of an achiral rod-like liquid crystalline mesogen that shows
ferroelectric nematic and antiferroelectric smectic phases. The observations of
chiral domains of opposite chirality are enabled by application of a weak
electric field across a planar-aligned cell. However once domains of opposite
chirality are created, these stay permanently even if the field is removed. The
observed phenomenon is due to the symmetry breaking of achiral mesogens of
rod-shaped molecules. These domains are similarly observed in the Nx phase.
However for temperatures close or in the NF, the size of domains is reduced
significantly below the wavelength of visible light. There is either a single
domain with dipole moments parallel to the surface or domains antiparallel in
the NF phase, not possible to determine in this experiment.


title:
Social-Implicit: Rethinking Trajectory Prediction Evaluation and The
  Effectiveness of Implicit Maximum Likelihood Estimation

abstract:
  Best-of-N (BoN) Average Displacement Error (ADE)/ Final Displacement Error
(FDE) is the most used metric for evaluating trajectory prediction models. Yet,
the BoN does not quantify the whole generated samples, resulting in an
incomplete view of the model's prediction quality and performance. We propose a
new metric, Average Mahalanobis Distance (AMD) to tackle this issue. AMD is a
metric that quantifies how close the whole generated samples are to the ground
truth. We also introduce the Average Maximum Eigenvalue (AMV) metric that
quantifies the overall spread of the predictions. Our metrics are validated
empirically by showing that the ADE/FDE is not sensitive to distribution
shifts, giving a biased sense of accuracy, unlike the AMD/AMV metrics. We
introduce the usage of Implicit Maximum Likelihood Estimation (IMLE) as a
replacement for traditional generative models to train our model,
Social-Implicit. IMLE training mechanism aligns with AMD/AMV objective of
predicting trajectories that are close to the ground truth with a tight spread.
Social-Implicit is a memory efficient deep model with only 5.8K parameters that
runs in real time of about 580Hz and achieves competitive results. Interactive
demo of the problem can be seen here
\url{https://www.abduallahmohamed.com/social-implicit-amdamv-adefde-demo}. Code
is available at \url{https://github.com/abduallahmohamed/Social-Implicit}.


title: Relaxed Paxos: Quorum Intersection Revisited (Again)

abstract:
  Distributed consensus, the ability to reach agreement in the face of
failures, is a fundamental primitive for constructing reliable distributed
systems. The Paxos algorithm is synonymous with consensus and widely utilized
in production. Paxos uses two phases: phase one and phase two, each requiring a
quorum of acceptors, to reach consensus during a round of the protocol.
Traditionally, Paxos requires that all quorums, regardless of phase or round,
intersect and majorities are often used for this purpose. Flexible Paxos proved
that it is only necessary for phase one quorum of a given round to intersect
with the phase two quorums of all previous rounds.
  In this paper, we re-examine how Paxos approaches the problem of consensus.
We look again at quorum intersection in Flexible Paxos and observe that quorum
intersection can be safely weakened further. Most notably, we observe that if a
proposer learns that a value was proposed in some previous round then its phase
one no longer needs to intersect with the phase two quorums from that round or
from any previous rounds. Furthermore, in order to provide an intuitive
explanation of our results, we propose a novel abstraction for reasoning about
Paxos which utilizes write-once registers.


title:
Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta
  Learning, Provably?

abstract:
  Meta learning aims at learning a model that can quickly adapt to unseen
tasks. Widely used meta learning methods include model agnostic meta learning
(MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling
uncertainty, Bayesian MAML often has advantageous empirical performance.
However, the theoretical understanding of Bayesian MAML is still limited,
especially on questions such as if and when Bayesian MAML has provably better
performance than MAML. In this paper, we aim to provide theoretical
justifications for Bayesian MAML's advantageous performance by comparing the
meta test risks of MAML and Bayesian MAML. In the meta linear regression, under
both the distribution agnostic and linear centroid cases, we have established
that Bayesian MAML indeed has provably lower meta test risks than MAML. We
verify our theoretical results through experiments.


title: Do higher-order interactions promote synchronization?

abstract:
  Understanding how nonpairwise interactions alter dynamical processes in
networks is of fundamental importance to the characterization and control of
many coupled systems. Recent discoveries of hyperedge-enhanced synchronization
under various settings raised speculations that such enhancements might be a
general phenomenon. Here, we demonstrate that even for simple systems such as
Kuramoto oscillators, the effects of higher-order interactions are highly
representation-dependent. Specifically, we show numerically and analytically
that hyperedges typically enhance synchronization in random hypergraphs, but
have the opposite effect in simplicial complexes. As an explanation, we
identify higher-order degree heterogeneity as the key structural determinant of
synchronization stability in systems with a fixed coupling budget. Our findings
highlight the importance of appropriate representations in describing
higher-order interactions. In particular, the choice of simplicial complexes or
hypergraphs has significant ramifications and should not be purely motivated by
technical conveniences.

categories: nlin.AO cond-mat.dis-nn cs.SY eess.SY math.DS physics.soc-ph


title: Bounding Vanishing at the Central Point of Cuspidal Newforms

abstract:
  The Katz-Sarnak Density Conjecture states that zeros of families of
$L$-functions are well-modeled by eigenvalues of random matrix ensembles. For
suitably restricted test functions, this correspondence yields upper bounds for
the families' order of vanishing at the central point. We generalize previous
results on the $n$\textsuperscript{th} centered moment of the distribution of
zeros to allow arbitrary test functions. On the computational side, we use our
improved formulas to obtain significantly better bounds on the order of
vanishing for cuspidal newforms, setting world records for the quality of the
bounds. We also discover better test functions that further optimize our
bounds. We see improvement as early as the $5$\textsuperscript{th} order, and
our bounds improve rapidly as the rank grows (more than one order of magnitude
better for rank 10 and more than four orders of magnitude for rank 50).


title: Story Point Effort Estimation by Text Level Graph Neural Network

abstract:
  Estimating the software projects' efforts developed by agile methods is
important for project managers or technical leads. It provides a summary as a
first view of how many hours and developers are required to complete the tasks.
There are research works on automatic predicting the software efforts,
including Term Frequency Inverse Document Frequency (TFIDF) as the traditional
approach for this problem. Graph Neural Network is a new approach that has been
applied in Natural Language Processing for text classification. The advantages
of Graph Neural Network are based on the ability to learn information via graph
data structure, which has more representations such as the relationships
between words compared to approaches of vectorizing sequence of words. In this
paper, we show the potential and possible challenges of Graph Neural Network
text classification in story point level estimation. By the experiments, we
show that the GNN Text Level Classification can achieve as high accuracy as
about 80 percent for story points level classification, which is comparable to
the traditional approach. We also analyze the GNN approach and point out
several current disadvantages that the GNN approach can improve for this
problem or other problems in software engineering.


title: Heisenberg Algebra and String Theory

abstract:
  If the algebra of the Poincar\'e generators is enlarged by the spacetime
position operator $X=(X_0,\dots, X_{D-1})$ then the spectra of the momentum $P$
and the mass $P^2$ are unbounded and continuous. In particular, the constraint
$(P^2 - m^2)\Psi_{phys}=0$ of the covariant string has no solution in the space
which admits $X$: All physical states vanish, $\Psi_{phys}=0$. Vice versa, a
space spanned by mass eigenstates does not admit the position operator $X$ in
$D$ dimensions.
  A Heisenberg pair $X^-$ and $P^+=(P^0 + P_z)/\sqrt{2}$ with $ [P^+,X^-] = i
$, as it occurs in the light cone string, implies that the massless and massive
particles of positive energy are paired with negative energy particles. The
other way round, if all energies of massive and massless states are positive,
then $X^-$ does not exist.
  Also on tachyon states the algebra generated by the transverse position $\vec
X_{T}$ together with $X^-$, $e^{i\,b\,X^-}$ and the momenta $\vec P_{T},\, P^+$
and $P^-$ is inconsistent: there is no space of states on which the iterated
composition of these operators exists and defines a product. Hence the
algebraic calculation of the critical dimension $D=26$ of the bosonic string is
meaningless.
  A massless particle does not allow a spatial position operator $\vec X$.


title: Complex Field Formulation of the Quantum Estimation Theory

abstract:
  We present a complex field formulation of the quantum Fisher estimation
theory that works natively with complex statistics on the dependence of complex
parameters. This states new complex versions of the main quantities and results
of the estimation theory depending on complex parameters, such as Fisher
information matrices and Cram\'er-Rao bounds. This can be useful in contexts
where the quantum states are described through complex parameters, as coherent
states or squeezed states. We show an application of our theory in quantum
communication with coherent states.


title: Classical Evolution Without Evolution

abstract:
  The well known argument of Page and Wootters demonstrates how to "derive" the
usual quantum dynamics of a subsystem in a global state which is an eigenstate
of the total Hamiltonian. I show how the same argument can be made in classical
physics, by using a formalism that closely resembles the quantum one. This is
not surprising since the Hamilton-Jacobi formulation of classical dynamics is
precisely motivated by the logic of timeless dynamics. Ultimately, the key to
obtaining dynamics without dynamics is the principle of energy conservation
which leads to correlations between times pertaining to different subsystems.
The same can, of course, be said about all other conserved quantities and we
show how to address this problem in its full generality so as to realise
rotation without rotation, translation without translation and so on. The
classical and quantum interpretations do, however, have one major difference
and this is the Church of the Higher Hilbert Space interpretation of mixtures,
which only exists in quantum physics. We discuss a few consequences of this
point.


title:
A generalised time-evolution model for contact problems with wear and
  its analysis

abstract:
  In this paper, we revisit some classical and recent works on modelling
slide-contact with wear and propose their generalisation. Namely, we upgrade
the relation between the pressure and the wear rate by incorporating some
non-local time-dependence. To this effect, we use a combination of fractional
calculus and relaxation effects. Moreover, we consider a possibility when the
load is not constant in time. The proposed model is analysed and solved. The
results are illustrated numerically and comparison with similar models is
discussed.


title: Deep Learning From Four Vectors

abstract:
  An early example of the ability of deep networks to improve the statistical
power of data collected in particle physics experiments was the demonstration
that such networks operating on lists of particle momenta (four-vectors) could
outperform shallow networks using features engineered with domain knowledge. A
benchmark case is described, with extensions to parameterized networks. A
discussion of data handling and architecture is presented, as well as a
description of how to incorporate physics knowledge into the network
architecture.


title: Diversifying Agent's Behaviors in Interactive Decision Models

abstract:
  Modelling other agents' behaviors plays an important role in decision models
for interactions among multiple agents. To optimise its own decisions, a
subject agent needs to model what other agents act simultaneously in an
uncertain environment. However, modelling insufficiency occurs when the agents
are competitive and the subject agent can not get full knowledge about other
agents. Even when the agents are collaborative, they may not share their true
behaviors due to their privacy concerns. In this article, we investigate into
diversifying behaviors of other agents in the subject agent's decision model
prior to their interactions. Starting with prior knowledge about other agents'
behaviors, we use a linear reduction technique to extract representative
behavioral features from the known behaviors. We subsequently generate their
new behaviors by expanding the features and propose two diversity measurements
to select top-K behaviors. We demonstrate the performance of the new techniques
in two well-studied problem domains. This research will contribute to
intelligent systems dealing with unknown unknowns in an open artificial
intelligence world.


title:
Banking Deserts," City Size, and Socioeconomic Characteristics in Medium
  and Large U.S. Cities

abstract:
  A lack of financial access, which is often an issue in many central-city U.S.
neighborhoods, can be linked to higher interest rates as well as negative
health and psychological outcomes. A number of analyses of "banking deserts"
have also found these areas to be poorer and less White than other parts of the
city. While previous research has examined specific cities, or has classified
areas by population densities, no study to date has examined a large set of
individual cities. This study looks at 319 U.S. cities with populations greater
than 100,000 and isolates areas with fewer than 0.318 banks per square mile
based on distances from block-group centroids. The relative shares of these
"deserts" appears to be independent of city population across the sample, and
there is little relationship between these shares and socioeconomic variables
such as the poverty rate or the percentage of Black residents. One plausible
explanation is that only a subset of many cities' poorest, least White block
groups can be classified as banking deserts; nearby block groups with similar
socioeconomic characteristics are therefore non-deserts. Outside of the
Northeast, non-desert areas tend to be poorer than deserts, suggesting that
income- and bank-poor neighborhoods might not be as prevalent as is commonly
assumed.


title: Goh conditions for minima of nonsmooth problems with unbounded controls

abstract:
  Higher order necessary conditions for a minimizer of an optimal control
problem are generally obtained for systems whose dynamics is continuously
differentiable in the state variable. Here, by making use of the notion of
set-valued Lie bracket we obtain a Goh-type condition for a control affine
system with Lipschitz continuous dynamics and unbounded controls. In order to
manage the simultaneous lack of smoothness of the adjoint equation and of the
Lie bracket-like variations we make use of the notion of Quasi Differential
Quotient. We conclude the paper with a worked out example where the established
higher order condition is capable to rule out the optimality of a control
verifying the standard maximum principle.


title:
The Infrared Database of Extragalactic Observables from Spitzer. -- II.
  The Database & The Diagnostic Power of Crystalline Silicate Features in
  Galaxy Spectra

abstract:
  We present the Infrared Database of Extragalactic Observables from Spitzer
(IDEOS), a homogeneous, publicly available, database of 77 fitted mid-infrared
observables in the 5.4-36um range, comprising measurements for 3335 galaxies
observed in the low-resolution staring mode of the Infrared Spectrometer
onboard the Spitzer Space Telescope. Among the included observables are PAH
fluxes and their equivalent widths, the strength of the 9.8um silicate feature,
emission line fluxes, solid-state features, rest frame continuum fluxes,
synthetic photometry, and a mid-infrared spectral classification. The IDEOS
spectra were selected from the Cornell Atlas of Spitzer-IRS Sources. To our
surprise we have detected at a >95% confidence level crystalline silicates in
the spectra of 786 IDEOS galaxies. The detections range from single band
detections to detections of all fitted crystalline bands (16, 19, 23, 28 and
33um). We find the strength of the crystalline silicate bands to correlate with
the amorphous silicate strength, and the change from an emission to an
absorption feature to occur at higher obscuration as the wavelength of the
crystalline silicate band is longer. These observed characteristics are
consistent with an origin for the amorphous and crystalline silicate features
in a centrally heated dust geometry, either an edge-on disk or a cocoon. We
find the 23 and 33um crystalline silicate bands to be well-suited to classify
the obscuration level of galactic nuclei, even in the presence of strong
circumnuclear star formation. Based on our detection statistics, we conclude
that crystalline silicates are a common component of the interstellar medium of
galactic nuclei.


title: Leashing the Inner Demons: Self-Detoxification for Language Models

abstract:
  Language models (LMs) can reproduce (or amplify) toxic language seen during
training, which poses a risk to their practical application. In this paper, we
conduct extensive experiments to study this phenomenon. We analyze the impact
of prompts, decoding strategies and training corpora on the output toxicity.
Based on our findings, we propose a simple yet effective method for language
models to "detoxify" themselves without an additional large corpus or external
discriminator. Compared to a supervised baseline, our proposed method shows
better toxicity reduction with good generation quality in the generated content
under multiple settings. Warning: some examples shown in the paper may contain
uncensored offensive content.


title: ILDAE: Instance-Level Difficulty Analysis of Evaluation Data

abstract:
  Knowledge of questions' difficulty level helps a teacher in several ways,
such as estimating students' potential quickly by asking carefully selected
questions and improving quality of examination by modifying trivial and hard
questions. Can we extract such benefits of instance difficulty in NLP? To this
end, we conduct Instance-Level Difficulty Analysis of Evaluation data (ILDAE)
in a large-scale setup of 23 datasets and demonstrate its five novel
applications: 1) conducting efficient-yet-accurate evaluations with fewer
instances saving computational cost and time, 2) improving quality of existing
evaluation datasets by repairing erroneous and trivial instances, 3) selecting
the best model based on application requirements, 4) analyzing dataset
characteristics for guiding future data creation, 5) estimating Out-of-Domain
performance reliably. Comprehensive experiments for these applications result
in several interesting findings, such as evaluation using just 5% instances
(selected via ILDAE) achieves as high as 0.93 Kendall correlation with
evaluation using complete dataset and computing weighted accuracy using
difficulty scores leads to 5.2% higher correlation with Out-of-Domain
performance. We release the difficulty scores and hope our analyses and
findings will bring more attention to this important yet understudied field of
leveraging instance difficulty in evaluations.


title:
Virtual vs. Reality: External Validation of COVID-19 Classifiers using
  XCAT Phantoms for Chest Computed Tomography

abstract:
  Research studies of artificial intelligence models in medical imaging have
been hampered by poor generalization. This problem has been especially
concerning over the last year with numerous applications of deep learning for
COVID-19 diagnosis. Virtual imaging trials (VITs) could provide a solution for
objective evaluation of these models. In this work utilizing the VITs, we
created the CVIT-COVID dataset including 180 virtually imaged computed
tomography (CT) images from simulated COVID-19 and normal phantom models under
different COVID-19 morphology and imaging properties. We evaluated the
performance of an open-source, deep-learning model from the University of
Waterloo trained with multi-institutional data and an in-house model trained
with the open clinical dataset called MosMed. We further validated the model's
performance against open clinical data of 305 CT images to understand virtual
vs. real clinical data performance. The open-source model was published with
nearly perfect performance on the original Waterloo dataset but showed a
consistent performance drop in external testing on another clinical dataset
(AUC=0.77) and our simulated CVIT-COVID dataset (AUC=0.55). The in-house model
achieved an AUC of 0.87 while testing on the internal test set (MosMed test
set). However, performance dropped to an AUC of 0.65 and 0.69 when evaluated on
clinical and our simulated CVIT-COVID dataset. The VIT framework offered
control over imaging conditions, allowing us to show there was no change in
performance as CT exposure was changed from 28.5 to 57 mAs. The VIT framework
also provided voxel-level ground truth, revealing that performance of in-house
model was much higher at AUC=0.87 for diffuse COVID-19 infection size >2.65%
lung volume versus AUC=0.52 for focal disease with <2.65% volume. The virtual
imaging framework enabled these uniquely rigorous analyses of model
performance.


title:
Simultaneous perturbation stochastic approximation: towards
  one-measurement per iteration

abstract:
  When measuring the value of a function to be minimized is not only expensive
but also with noise, the popular simultaneous perturbation stochastic
approximation (SPSA) algorithm requires only two function values in each
iteration. In this paper, we propose a method requiring only one function
measurement value per iteration in the average sense. We prove the strong
convergence and asymptotic normality of the new algorithm. Experimental results
show the effectiveness and potential of our algorithm.


title:
Ergodicity of a nonlinear stochastic reaction-diffusion equation with
  memory

abstract:
  We consider a class of semi-linear differential Volterra equations with
memory terms, polynomial nonlinearities and random perturbation. For a broad
class of nonlinearities, we study statistically steady states of the system and
find that they possess regularities compatible with those of the weak
solutions. Moreover, if sufficiently many directions in the phase space are
stochastically forced, we employ the \emph{generalized coupling} approach to
establish the existence and uniqueness of the invariant probability measure to
which the system is exponentially attractive. This extends ergodicity results
previously established in [Bonaccorsi et al., SIAM J. Math. Anal., 44 (2012)].


title: A Study of Third-party Resources Loading on Web

abstract:
  This paper performs a large-scale study of dependency chains in the web, to
find that around 50% of first-party websites render content that they did not
directly load. Although the majority (84.91%) of websites have short dependency
chains (below 3 levels), we find websites with dependency chains exceeding 30.
Using VirusTotal, we show that 1.2% of these third-parties are classified as
suspicious -- although seemingly small, this limited set of suspicious
third-parties have remarkable reach into the wider ecosystem. We find that 73%
of websites under-study load resources from suspicious third-parties, and 24.8%
of first-party webpages contain at least three third-parties classified as
suspicious in their dependency chain. By running sandboxed experiments, we
observe a range of activities with the majority of suspicious JavaScript codes
downloading malware.


title:
Fast and Data Efficient Reinforcement Learning from Pixels via
  Non-Parametric Value Approximation

abstract:
  We present Nonparametric Approximation of Inter-Trace returns (NAIT), a
Reinforcement Learning algorithm for discrete action, pixel-based environments
that is both highly sample and computation efficient. NAIT is a lazy-learning
approach with an update that is equivalent to episodic Monte-Carlo on episode
completion, but that allows the stable incorporation of rewards while an
episode is ongoing. We make use of a fixed domain-agnostic representation,
simple distance based exploration and a proximity graph-based lookup to
facilitate extremely fast execution. We empirically evaluate NAIT on both the
26 and 57 game variants of ATARI100k where, despite its simplicity, it achieves
competitive performance in the online setting with greater than 100x speedup in
wall-time.


title:
GlideNet: Global, Local and Intrinsic based Dense Embedding NETwork for
  Multi-category Attributes Prediction

abstract:
  Attaching attributes (such as color, shape, state, action) to object
categories is an important computer vision problem. Attribute prediction has
seen exciting recent progress and is often formulated as a multi-label
classification problem. Yet significant challenges remain in: 1) predicting
diverse attributes over multiple categories, 2) modeling attributes-category
dependency, 3) capturing both global and local scene context, and 4) predicting
attributes of objects with low pixel-count. To address these issues, we propose
a novel multi-category attribute prediction deep architecture named GlideNet,
which contains three distinct feature extractors. A global feature extractor
recognizes what objects are present in a scene, whereas a local one focuses on
the area surrounding the object of interest. Meanwhile, an intrinsic feature
extractor uses an extension of standard convolution dubbed Informed Convolution
to retrieve features of objects with low pixel-count. GlideNet uses gating
mechanisms with binary masks and its self-learned category embedding to combine
the dense embeddings. Collectively, the Global-Local-Intrinsic blocks
comprehend the scene's global context while attending to the characteristics of
the local object of interest. Finally, using the combined features, an
interpreter predicts the attributes, and the length of the output is determined
by the category, thereby removing unnecessary attributes. GlideNet can achieve
compelling results on two recent and challenging datasets -- VAW and CAR -- for
large-scale attribute prediction. For instance, it obtains more than 5\% gain
over state of the art in the mean recall (mR) metric. GlideNet's advantages are
especially apparent when predicting attributes of objects with low pixel counts
as well as attributes that demand global context understanding. Finally, we
show that GlideNet excels in training starved real-world scenarios.


title:
Weighted composition operators on weak holomorphic spaces and
  application to weak Bloch-type spaces on the unit ball of a Hilbert space

abstract:
  Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a
Banach space $ X.$ In this work, we introduce a Banach structure associated to
$ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic
functions on $ B_X $ such that $ w \circ f \in E $ for every $ w \in W, $ a
separating subspace of the dual $ Y' $ of a Banach $ Y. $ We establish the
relation between the boundedness, the (weak) compactness of the weighted
composition operators $ W_{\psi,\varphi}: f\mapsto \psi\cdot(f \circ \varphi) $
on $ E $ and $ \widetilde{W}_{\psi,\varphi}: g\mapsto \psi\cdot(g \circ
\varphi) $ on $ WE(Y)$ via some characterizations of the separating subspace $
W. $ As an application, via the estimates for the restrictions of $ \psi $ and
$ \varphi $ to a $ m$-dimensional subspace of $ X $ for some $ m\ge2, $ we
characterize the properties mentioned above of $ W_{\psi,\varphi} $ on
Bloch-type spaces $ \mathcal B_\mu(B_X) $ of holomorphic functions on the unit
ball $ B_X $ of an infinite-dimensional Hilbert space as well as their the
associated spaces $W\mathcal B_\mu(B_X,Y), $ where $ \mu $ is a normal weight
on $ B_X. $


title:
Ellis drainhole solution in Einstein-{\AE}ther gravity and the axial
  gravitational quasinormal modes

abstract:
  In this work, the Ellis drainhole solution is derived in Einstein-{\AE}ther
gravity, and subsequently, the axial quasinormal modes of the resulting
drainhole are investigated. Owing to the presence of a minimally coupled scalar
field with antiorthodox coupling polarity, the resultant metric solution is
featured by a throat instead of a horizon, for which static {\ae}ther solution
becomes feasible. Moreover, the derived master equations for the axial
gravitational perturbations consist of two coupled vector degrees of freedom.
By utilizing the finite difference method, the temporal profiles of the
quasinormal oscillations are evaluated, and, subsequently, the complex
frequencies are extracted and compared against the specific values obtained by
the WKB method when the coupling is turned off. Besides, the effect of the
coupling on the low-lying quasinormal spectrum is explored, and its possible
physical relevance is discussed.


title:
Ferroelectric tuning of superconductivity and band topology in a
  two-dimensional heterobilayer

abstract:
  Realization of tunable superconductivity with concomitant nontrivial band
topology is conceptually intriguing and highly desirable for superconducting
devices and topological quantum computation. Based on first-principles
calculations, here we present the first prediction of simultaneously tunable
superconducting transition temperature (Tc) and band topology in a
superconducting IrTe2 overlayer on a ferroelectric In2Se3 monolayer. We first
demonstrate that the Tc is substantially enhanced from that of IrTe2 nanoflakes
(Tc ~3 K) due to significant charge repartitioning around the Fermi level. More
importantly, the Tc is shown to sensitively depend on the In2Se3 polarization,
with the higher Tc of ~(8-10) K attributed to enhanced interlayer
electron-phonon coupling when the polarization is downward. The band topology
is also switched from trivial to nontrivial as the polarization is reversed
from upward to downward. These findings provide physically realistic platforms
for simultaneously tuning superconductivity and band topology in
two-dimensional heterobilayers and related heterostructures using a reversible
and nonvolatile approach.


title:
Charge Transfer Simulations using Hamiltonian Elements and Forces from
  Neural Networks

abstract:
  The trajectory surface hopping method has been widely used in the simulation
of charge transport in organic semiconductors. In the present study, we employ
the machine learning (ML) based Hamiltonian to simulate the charge transport in
anthracene and pentacene. The neural network (NN) based models are able to
predict not just site energies and couplings but also the gradients of the site
energy as well as off-diagonal gradients necessary for forces. We train the
models on DFTB-quality data for both anthracene and pentacene. By using the
obtained models in propagation simulations, we evaluate their performance in
reproducing hole mobilities in these materials in terms of both quality and
computational cost. The results show that the charge mobilities obtained using
the NN-based Hamiltonian are in very good agreements with the charge mobilities
computed using the DFTB-based Hamiltonian.


title: Preparation of Metrological States in Dipolar-Interacting Spin Systems

abstract:
  Spin systems are an attractive candidate for quantum-enhanced metrology. Here
we develop a variational method to generate metrological states in small
dipolar-interacting ensembles with limited qubit controls and unknown spin
locations. The generated states enable sensing beyond the standard quantum
limit (SQL) and approaching the Heisenberg limit (HL). Depending on the circuit
depth and the level of readout noise, the resulting states resemble
Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing
beyond the SQL holds in the presence of finite spin polarization and a
non-Markovian noise environment.