title: Integrated optical-readout of a high-Q mechanical out-of-plane mode

abstract:
  The rapid development of high-Q macroscopic mechanical resonators has enabled
great advances in optomechanics. Further improvements could allow for
quantum-limited or quantum-enhanced applications at ambient temperature. Some
of the remaining challenges include the integration of high-Q structures on a
chip, while simultaneously achieving large coupling strengths through an
optical read-out. Here, we present a versatile fabrication method, which allows
us to build fully integrated optomechanical structures. We place a photonic
crystal cavity directly above a mechanical resonator with high-Q fundamental
out-of-plane mode, separated by a small gap. The highly confined optical field
has a large overlap with the mechanical mode, enabling strong optomechanical
interaction strengths. Furthermore, we implement a novel photonic crystal
design, which allows for a very large cavity photon number, a highly important
feature for optomechanical experiments and sensor applications. Our versatile
approach is not limited to our particular design but allows for integrating an
out-of-plane optical read-out into almost any device layout. Additionally, it
can be scaled to large arrays and paves the way to realizing quantum
experiments and applications with mechanical resonators based on high-Q
out-of-plane modes alike.


title: Learning to Rank from Relevance Judgments Distributions

abstract:
  Learning to Rank (LETOR) algorithms are usually trained on annotated corpora
where a single relevance label is assigned to each available document-topic
pair. Within the Cranfield framework, relevance labels result from merging
either multiple expertly curated or crowdsourced human assessments. In this
paper, we explore how to train LETOR models with relevance judgments
distributions (either real or synthetically generated) assigned to
document-topic pairs instead of single-valued relevance labels. We propose five
new probabilistic loss functions to deal with the higher expressive power
provided by relevance judgments distributions and show how they can be applied
both to neural and GBM architectures. Moreover, we show how training a LETOR
model on a sampled version of the relevance judgments from certain probability
distributions can improve its performance when relying either on traditional or
probabilistic loss functions. Finally, we validate our hypothesis on real-world
crowdsourced relevance judgments distributions. Overall, we observe that
relying on relevance judgments distributions to train different LETOR models
can boost their performance and even outperform strong baselines such as
LambdaMART on several test collections.


title:
DEEPCHORUS: A Hybrid Model of Multi-scale Convolution and Self-attention
  for Chorus Detection

abstract:
  Chorus detection is a challenging problem in musical signal processing as the
chorus often repeats more than once in popular songs, usually with rich
instruments and complex rhythm forms. Most of the existing works focus on the
receptiveness of chorus sections based on some explicit features such as
loudness and occurrence frequency. These pre-assumptions for chorus limit the
generalization capacity of these methods, causing misdetection on other
repeated sections such as verse. To solve the problem, in this paper we propose
an end-to-end chorus detection model DeepChorus, reducing the engineering
effort and the need for prior knowledge. The proposed model includes two main
structures: i) a Multi-Scale Network to derive preliminary representations of
chorus segments, and ii) a Self-Attention Convolution Network to further
process the features into probability curves representing chorus presence. To
obtain the final results, we apply an adaptive threshold to binarize the
original curve. The experimental results show that DeepChorus outperforms
existing state-of-the-art methods in most cases.


title: A simple model of radiating solitary waves

abstract:
  To understand an oft-observed but poorly understood phenomenon in which a
solitary wave in a dispersive equation slowly deteriorates due to a persistent
emission of radiation (i.e. a ``radiating solitary wave''), we propose a
bare-bones model which captures many essential features and which we are
capable of analyzing completely by way of the Laplace transform. We find that
wave amplitude decreases at an exponential rate but with a decay constant that
is (in many cases) small beyond all orders of the frequency.


title:
Well-posedness of classical solutions to the vacuum free boundary
  problem of the viscous Saint-Venant system for shallow waters

abstract:
  We establish the local-in-time well-posedness of classical solutions to the
vacuum free boundary problem of the viscous Saint-Venant system for shallow
waters derived rigorously from incompressible Navier-Stokes system with a
moving free surface by Gerbeau-Perthame. Our solutions (the height and
velocity) are smooth (the solutions satisfy the equations point-wisely) all the
way to the moving boundary, although the height degenerates as a singularity of
the distance to the vacuum boundary. The proof is built on some new
higher-order weighted energy functional and weighted estimates associated to
the degeneracy near the moving vacuum boundary.


title:
Amplifying quantum correlations with quench dynamics in a quantum spin
  chain: Steady-states versus ground-states

abstract:
  We analyze the behavior of steady-state quantum correlations (QCs) in the
spin-1/2 transverse field XY chains analytically, in terms of quench dynamics
at zero-temperature. We show that steady-state QCs are strikingly greater than
the equilibrium ones in its ground-state, where a single quench is performed
from ferro- into para-magnetic phases. Another framework to amplify the QCs
here is a feasible protocol called double quench dynamics. To fulfill this
purpose, we probe a middle quench point and spending time T (defined as the
time passing from the middle quench point before reaching a second quench). By
doing so, both single and double quenches act as practical tools to control the
enhancement of the steady-state QCs in the final quenched point. In particular,
and in parallel to expectations for some other quantities, we indicate that the
nonequilibrium quantum phase transitions also can be identified by
nonanalyticities in the steady-state QCs. Our work may be testable with the
current class of trapped-ion or ultracold-atom experiments, and encourage the
possible potential in the quantum information field.


title:
The water entry surface seal behavior of spheres at intermediate speed
  regimes

abstract:
  This research focuses on the water entry of spheres in the surface seal
regime. Herein, surface seal occurs in the wake of a sphere impact with the
water surface and is characterized by splash dome over and cavity pull-away
between the \emph{low-speed} ($U<30$~m/s) and \emph{high-speed} ($U>165$~m/s)
regimes for various sphere diameters $D$. The established empirical scaling
laws for pinch-off time $t_p$ hold well for both low and high speeds (i.e.,
respectively $ t_pUD^{-1}~C_d^{-1/2}=const$ and $ t_pUD^{-1}~C_d^{-1/2}\propto
Ca^{-1}$) but the transition deserves refinement. The intermediate regime in
particular scales as $t_pUD^{-1}~C_d^{-1/2}\propto Ca^{-1/2}$, which means that
the pressure reduction inside the cavity determines the surface seal dynamics
as speeds increase. We also report on the transition from deep to surface seal,
where the seal time is scaled more like a deep seal. The partial pull-away,
ripples on the cavity surface, and the secondary pinch-off are also reported.


title:
A characterization of Gabor Riesz bases with separable time-frequency
  shifts

abstract:
  A Gabor system generated by a window function $g\in L^2(\mathbb{R}^d)$ and a
separable set $\Lambda\times \Gamma \subset \mathbb{R}^{2d}$ is the collection
of time-frequency shifts of $g$ given by $\mathcal G(g, \Lambda\times \Gamma) =
\left\{ e^{2\pi i \xi\cdot t}g(t-x)\right\}_{ (x,\xi)\in \Lambda\times \Gamma
}$. One of the fundamental problems in Gabor analysis is to characterize all
windows and time-frequency sets that generate a Gabor frame or Gabor
orthonormal basis. The case of Gabor orthonormal bases generated by
characteristic functions $g=\chi_\Omega$ has been solved by Han and Wang. In
this paper, we build on these results and obtain a full characterization of
Riesz Gabor systems of the form $\mathcal G(\chi_\Omega, \Lambda\times \Gamma)$
when $\Omega$ is a tiling of $\mathbb{R}^d$ with respect to $\Lambda$.
Furthermore, for a certain class of lattices $\Lambda\times \Gamma$, we prove
that a necessary condition for the characteristic function of a multi-tiling
set to serve as a window function for a Riesz Gabor basis is that the set must
be a tiling set. To prove this, we develop new results on the zeros of the Zak
transform and connect these results to Gabor frames.


title: A Data Augmentation Method for Fully Automatic Brain Tumor Segmentation

abstract:
  Automatic segmentation of glioma and its subregions is of great significance
for diagnosis, treatment and monitoring of disease. In this paper, an
augmentation method, called TensorMixup, was proposed and applied to the three
dimensional U-Net architecture for brain tumor segmentation. The main ideas
included that first, two image patches with size of 128 in three dimensions
were selected according to glioma information of ground truth labels from the
magnetic resonance imaging data of any two patients with the same modality.
Next, a tensor in which all elements were independently sampled from Beta
distribution was used to mix the image patches. Then the tensor was mapped to a
matrix which was used to mix the one-hot encoded labels of the above image
patches. Therefore, a new image and its one-hot encoded label were synthesized.
Finally, the new data was used to train the model which could be used to
segment glioma. The experimental results show that the mean accuracy of Dice
scores are 91.32%, 85.67%, and 82.20% respectively on the whole tumor, tumor
core, and enhancing tumor segmentation, which proves that the proposed
TensorMixup is feasible and effective for brain tumor segmentation.


title:
Reinforcement Learning Based Power Control for Reliable Wireless
  Transmission

abstract:
  In this paper, we investigate a sequential power allocation problem over fast
varying channels, aiming to minimize the expected sum power while guaranteeing
the transmission success probability. In particular, a reinforcement learning
framework is constructed with appropriate reward design so that the optimal
policy maximizes the Lagrangian of the primal problem, where the maximizer of
the Lagrangian is shown to have several good properties. For the model-based
case, a fast converging algorithm is proposed to find the optimal Lagrange
multiplier and thus the corresponding optimal policy. For the model-free case,
we develop a three-stage strategy, composed in order of online sampling,
offline learning, and online operation, where a backward Q-learning with full
exploitation of sampled channel realizations is designed to accelerate the
learning process. According to our simulation, the proposed reinforcement
learning framework can solve the primal optimization problem from the dual
perspective. Moreover, the model-free strategy achieves a performance close to
that of the optimal model-based algorithm.


title: On subelliptic harmonic maps with potential

abstract:
  Let $(M,H,g_H;g)$ be a sub-Riemannian manifold and $(N,h)$ be a Riemannian
manifold. For a smooth map $u: M \to N$, we consider the energy functional
$E_G(u) = \frac{1}{2} \int_M[|\mathrm{d}u_H|^2-2G(u)] \mathrm{d}V_M$, where
$\mathrm{d}u_H$ is the horizontal differential of $u$, $G:N\to \mathbb{R}$ is a
smooth function on $N$. The critical maps of $E_G(u)$ are referred to as
subelliptic harmonic maps with potential $G$. In this paper, we investigate the
existence problem for subelliptic harmonic maps with potentials by a
subelliptic heat flow. Assuming that the target Riemannian manifold has
non-positive sectional curvature and the potential $G$ satisfies various
suitable conditions, we prove some Eells-Sampson type existence results when
the source manifold is either a step-$2$ sub-Riemannian manifold or a step-$r$
sub-Riemannian manifold whose sub-Riemannian structure comes from a tense
Riemannian foliation.


title: On equivariantly formal 2-torus manifolds

abstract:
  A 2-torus manifold is a closed connected smooth n-manifold with a non-free
effective smooth $\mathbb{Z}^n_2$-action. In this paper, we prove that a
2-torus manifold is equivariantly formal if and only if the
$\mathbb{Z}^n_2$-action is locally standard and every face of its orbit space
(including the whole orbit space) is mod 2 acyclic. Our study is parallel to
the study by M. Masuda and T. Panov on torus manifolds with vanishing
odd-degree cohomology. As an application, we determine what kind of locally
standard 2-torus manifolds can have regular m-involutions (i.e. involutions
with only isolated fixed points of the maximum possible number).


title: Understanding Paxos and other distributed consensus algorithms

abstract:
  Paxos is a widely used and notoriously hard to understand method for solving
one type of distributed consensus problem. This note provides a quick
explanation of Paxos, a novel proof of correctness that is intended to provide
insight into why the algorithm is as simple as the author has claimed, an
explanation of why it does and why it doesn't work, and has a brief discussion
of alternatives.


title:
Coupling matter and curvature in Weyl geometry: conformally invariant
  $f\left(R,L_m\right)$ gravity

abstract:
  We investigate the coupling of matter to geometry in conformal quadratic Weyl
gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$
is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The
coupling explicitly satisfies the conformal invariance of the theory. By
expressing $\tilde{R}^2$ with the help of an auxiliary scalar field and of the
Weyl scalar, the gravitational action can be linearized, leading in the Riemann
space to a conformally invariant $f\left(R,L_m\right)$ type theory, with the
matter Lagrangian nonminimally coupled to the Ricci scalar. We obtain the
gravitational field equations of the theory, as well as the energy-momentum
balance equations. The divergence of the matter energy-momentum tensor does not
vanish, and an extra force, depending on the Weyl vector, and matter Lagrangian
is generated. The thermodynamic interpretation of the theory is also discussed.
The generalized Poisson equation is derived, and the Newtonian limit of the
equations of motion is considered in detail. The perihelion precession of a
planet in the presence of an extra force is also considered, and constraints on
the magnitude of the Weyl vector in the Solar System are obtained from the
observational data of Mercury. The cosmological implications of the theory are
also considered for the case of a flat, homogeneous and isotropic
Friedmann-Lemaitre-Robertson-Walker geometry, and it is shown that the model
can give a good description of the observational data for the Hubble function
up to a redshift of the order of $z\approx 3$.


title: Numerical prescriptions of early-time divergences of the in-in formalism

abstract:
  In quantum field theory, the in and out states can be related to the full
Hamiltonian by the $i\epsilon$ prescription. A Wick rotation can further bring
the correlation functions to Euclidean spacetime where the integrals are better
defined. This setup is convenient for analytical calculations. However, for
numerical calculations, an infinitesimal $\epsilon$ or a Wick rotation of
numerical functions are difficult to implement. We propose two new numerical
methods to solve this problem, namely an Integral Basis method based on linear
regression and a Beta Regulator method based on Ces\`aro/Riesz summation.
Another class of partition-extrapolation methods previously used in
electromagnetic engineering is also introduced. We benchmark these methods with
existing methods using in-in formalism integrals, indicating advantages of
these new methods over the existing methods in computation time and accuracy.


title:
Comparing Flexible Skylines And Top-k Queries: Which Is the Best
  Alternative?

abstract:
  The question of how to get the best results out of the data we have is an
everlasting problem in data science. The two main approaches to tackle the
problem are top-k queries and skyline queries. Since their introduction, a new
paradigm called flexible skylines has emerged. The aim of this survey is to
provide a solid comparison between the new and the old approaches,
understanding and exploring their differences and similarities.


title: Emergence of scaling in dockless bike-sharing systems

abstract:
  Fundamental laws of human mobility have been extensively studied, yet we are
still lacking a comprehensive understanding of the mobility patterns of sharing
conveyances. Since travellers would highly probably no longer possess their own
conveyances in the near future, the interplay between travellers and sharing
bikes is a central question for developing more sustainable transportation.
Dockless bike-sharing systems that record detailed information of every trip
provide us a unique opportunity for revealing the hidden patterns behind riding
activities. By treating each bike as an individual entity, we reveal that
distributions of mobility indicators of bikes are quite different from humans;
and mobility patterns are even inconsistent across cities. All above
discrepancies can be well explained by a choice model that is characterized by
a universal scaling. Our model unveils that instead of choosing among the
newest bikes, the distribution of rank values of selected bikes on usage
condition manifests a truncated power-law and is quite stable across several
cities despite various diversities. Our framework would have broad implications
in sharing economy and contribute towards developing a greener, healthier, and
more sustainable future city.


title:
Power, Rate, and Decoding Order Optimization for NOMA-Based Vehicular
  Communications

abstract:
  This paper considers a two-user non-orthogonal multiple access (NOMA) based
infrastructure-to-vehicle (I2V) network, where one user requires reliable
safety-critical data transmission and the other pursues high-capacity services.
Leveraging only slow fading of channel state information, we aim to maximize
the expected sum throughput of the capacity hungry user subject to a constraint
on the payload delivery success probability of the reliability sensitive user,
by jointly optimizing the transmit powers, target rates, and decoding order. We
introduce a dual variable and formulate the optimization as an unconstrained
single-objective sequential decision problem. Then, we design a dynamic
programming based algorithm to derive the optimal policy that maximizes the
Lagrangian. Afterwards, a bisection search based method is proposed to find the
optimal dual variable. The proposed strategy is shown by numerical results to
be superior to the baseline approaches from the perspectives of expected
return, performance region, and objective value.


title: Non-fungible Tokens: Promise or Peril?

abstract:
  Non-fungible tokens or NFTs are the digital assets on a blockchain. NFTs are
unique and they cannot be divided like cryptocurrencies. NFTs could store
digital ownership of an artwork or collections or can be fan tokens or tickets
for clubs. NFTs are based on a smart contract on a blockchain network which
supports them, such as Ethereum, Cardano or Polkadot. Most of the NFTs are now
minted on Ethereum (ERC-20) network, but it has some main issues like high
transaction fees and low speed. There are lots of domains which can be
benefited from NFT technology such as art, music, gaming, sport and wildlife
conservation. NFTs could be also bought or sold on lots of NFT marketplaces
such as OpenSea and Chiliz. The trend is in a huge hype because the market cap
and popularity of NFTs are growing significantly.


title:
Geometric deep learning reveals the spatiotemporal fingerprint of
  microscopic motion

abstract:
  The characterization of dynamical processes in living systems provides
important clues for their mechanistic interpretation and link to biological
functions. Thanks to recent advances in microscopy techniques, it is now
possible to routinely record the motion of cells, organelles, and individual
molecules at multiple spatiotemporal scales in physiological conditions.
However, the automated analysis of dynamics occurring in crowded and complex
environments still lags behind the acquisition of microscopic image sequences.
Here, we present a framework based on geometric deep learning that achieves the
accurate estimation of dynamical properties in various biologically-relevant
scenarios. This deep-learning approach relies on a graph neural network
enhanced by attention-based components. By processing object features with
geometric priors, the network is capable of performing multiple tasks, from
linking coordinates into trajectories to inferring local and global dynamic
properties. We demonstrate the flexibility and reliability of this approach by
applying it to real and simulated data corresponding to a broad range of
biological experiments.

categories: physics.data-an eess.IV physics.bio-ph q-bio.QM


title: Goal Recognition as Reinforcement Learning

abstract:
  Most approaches for goal recognition rely on specifications of the possible
dynamics of the actor in the environment when pursuing a goal. These
specifications suffer from two key issues. First, encoding these dynamics
requires careful design by a domain expert, which is often not robust to noise
at recognition time. Second, existing approaches often need costly real-time
computations to reason about the likelihood of each potential goal. In this
paper, we develop a framework that combines model-free reinforcement learning
and goal recognition to alleviate the need for careful, manual domain design,
and the need for costly online executions. This framework consists of two main
stages: Offline learning of policies or utility functions for each potential
goal, and online inference. We provide a first instance of this framework using
tabular Q-learning for the learning stage, as well as three measures that can
be used to perform the inference stage. The resulting instantiation achieves
state-of-the-art performance against goal recognizers on standard evaluation
domains and superior performance in noisy environments.


title:
All even (unitary) perfect polynomials over $\F_2$ with only Mersenne
  primes as odd divisors

abstract:
  We address an arithmetic problem in the ring $\F_2[x]$ related to the fixed
points of the sum of divisors function. We study some binary polynomials $A$
such that $\sigma(A)/A $ is still a binary polynomial. Technically, we prove
that the only (unitary) perfect polynomials over $\F_2$ that are products of
$x$, $x+1$ and of Mersenne primes are precisely the nine (resp. nine "classes")
known ones. This follows from a new result about the factorization of $M^{2h+1}
+1$, for a Mersenne prime $M$ and for a positive integer $h$.


title: Diverse facial inpainting guided by exemplars

abstract:
  Facial image inpainting is a task of filling visually realistic and
semantically meaningful contents for missing or masked pixels in a face image.
Although existing methods have made significant progress in achieving high
visual quality, the controllable diversity of facial image inpainting remains
an open problem in this field. This paper introduces EXE-GAN, a novel diverse
and interactive facial inpainting framework, which can not only preserve the
high-quality visual effect of the whole image but also complete the face image
with exemplar-like facial attributes. The proposed facial inpainting is
achieved based on generative adversarial networks by leveraging the global
style of input image, the stochastic style, and the exemplar style of exemplar
image. A novel attribute similarity metric is introduced to encourage networks
to learn the style of facial attributes from the exemplar in a self-supervised
way. To guarantee the natural transition across the boundary of inpainted
regions, a novel spatial variant gradient backpropagation technique is designed
to adjust the loss gradients based on the spatial location. A variety of
experimental results and comparisons on public CelebA-HQ and FFHQ datasets are
presented to demonstrate the superiority of the proposed method in terms of
both the quality and diversity in facial inpainting.


title:
Quasistatic cohesive fracture with an alternating direction method of
  multipliers

abstract:
  A method for quasistatic cohesive fracture is introduced that uses an
alternating direction method of multipliers (ADMM) to implement an energy
approach to cohesive fracture. The ADMM algorithm minimizes a non-smooth,
non-convex potential functional at each strain increment to predict the
evolution of a cohesive-elastic system. The optimization problem bypasses the
explicit stress criterion of force-based (Newtonian) methods, which interferes
with Newton iterations impeding convergence. The model is extended with an
extrapolation method that significantly reduces the computation time of the
sequence of optimizations. The ADMM algorithm is experimentally shown to have
nearly linear time complexity and fast iteration times, allowing it to simulate
much larger problems than were previously feasible. The effectiveness, as well
as the insensitivity of the algorithm to its numerical parameters is
demonstrated through examples. It is shown that the Lagrange multiplier method
of ADMM is more effective than earlier Nitsche and continuation methods for
quasistatic problems. Close spaced minima are identified in complicated
microstructures and their effect discussed.


title: Dark User Experience: From Manipulation to Deception

abstract:
  Hassenzahl (2008) defines User Experience (UX) as "the momentary feeling
(good or bad) while interacting with a product or service" (p. 2). Even though
this definition, or any other UX definition for that matter, do not mention
that users' experiences need to be positive, the importance of experiencing
positive emotions while interacting with a device is widely acknowledged. The
equation "better UX = more business" is the motto that determined the industry
to embrace this field, and at the same time, opened the path for the UX to go
beyond usability guidelines and the human factors studies. It is clear that, by
facilitating tasks to the users and by addressing their needs, they will be
more satisfied, more engaged, and eventually, it will have positive
consequences on the business. Nonetheless, some companies are willing to reach
their economic goals at any cost, regardless of whether the customer's feels
satisfied after obtaining what she needed. They wonder: how can we design the
user interface in order to increase the possibilities of reaching our
objectives in a much more effective way? Metrics related to purchase
conversions, user retention and engagement become the main focus of design, and
any UX research conducted is aimed at understanding the user's needs or
preferences is used for this purpose. In these cases, design is mainly aimed at
increasing the company's revenue, and companies sometimes cross the ethical
line with this goal in mind. Such a phenomenon is called Dark UX.


title:
Quantum control of quasi-collisions in a maximally symmetric three-body
  Coulomb problem

abstract:
  Triple collisions in Coulomb three-body problems, which are unstable
classical configurations, may become quantum scar eigenstates in confined
environments. Control of such states by time changing electromagnetic fields is
discussed.


title: Castelnuovo-Mumford regularity and Schubert geometry

abstract:
  We study the Castelnuovo-Mumford regularity of tangent cones of Schubert
varieties. Conjectures about this statistic are presented; these are proved for
the covexillary case. This builds on work of L. Li and the author on these
tangent cones, as well as that of J. Rajchgot-Y. Ren-C. Robichaux-A. St.
Dizier-A. Weigandt and J. Rajchgot-C. Robichaux-A. Weigandt on tableau rules
for computing regularity of some matrix Schubert varieties.


title:
Carleson measure estimates, corona decompositions, and perturbation of
  elliptic operators without connectivity

abstract:
  Let $\Omega$ be an open set with Ahlfors-David regular boundary satisfying
the corkscrew condition. When $\Omega$ is connected in some quantitative form
one can establish that for any real elliptic operator with bounded
coefficients, the quantitative absolute continuity of elliptic measures is
equivalent to the fact that all bounded null solutions satisfy Carleson measure
estimates. In turn, in the same setting these equivalent properties are stable
under Fefferman-Kenig-Pipher perturbations. However, without connectivity,
there is no Fefferman-Kenig-Pipher perturbation result available. In this
paper, we work with a corona decomposition associated with the elliptic measure
and show that it is equivalent to the fact that bounded null solutions satisfy
partial/weak Carleson measure estimates, or to the fact that the Green function
is comparable to the distance to the boundary in the corona sense. This
characterization has profound consequences. We extend Fefferman-Kenig-Pipher's
perturbation to non-connected settings. For the Laplacian, these corona
decompositions or, equivalently, the partial/weak Carleson measure estimates
are meaningful enough to characterize the uniform rectifiability of the
boundary. As a consequence, we obtain that the boundary of the set is uniformly
rectifiable if bounded null solutions for any Fefferman-Kenig-Pipher
perturbation of the Laplacian satisfy Carleson measure estimates. For
Kenig-Pipher operators any of the properties of the characterization is stable
under transposition or symmetrization of the matrices of coefficients. As a
result, we obtain that Carleson measure estimates for bounded null-solutions of
non-symmetric variable operators satisfying an $L^1$-Kenig-Pipher condition
occur if and only if the boundary of the open set is uniformly rectifiable. Our
results generalize previous work in settings where quantitative connectivity.


title:
A conjecture strengthening the Zariski dense orbit problem for
  birational maps of dynamical degree one

abstract:
  We formulate a strengthening of the Zariski dense orbit conjecture for
birational maps of dynamical degree one. So, given a quasiprojective variety
$X$ defined over an algebraically closed field $K$ of characteristic $0$,
endowed with a birational self-map $\phi$ of dynamical degree $1$, we expect
that either there exists a non-constant rational function $f:X\dashrightarrow
\mathbb{P}^1$ such that $f\circ \phi=f$, or there exists a proper subvariety
$Y\subset X$ with the property that for any invariant proper subvariety
$Z\subset X$, we have that $Z\subseteq Y$. We prove our conjecture for
automorphisms $\phi$ of dynamical degree $1$ of semiabelian varieties $X$.
Also, we prove a related result for regular dominant self-maps $\phi$ of
semiabelian varieties $X$: assuming $\phi$ does not preserve a non-constant
rational function, we have that the dynamical degree of $\phi$ is larger than
$1$ if and only if the union of all $\phi$-invariant proper subvarieties of $X$
is Zariski dense. We give applications of our results to representation
theoretic questions about twisted homogeneous coordinate rings associated to
abelian varieties.


title: Unsourced Multiple Access With Random User Activity

abstract:
  To account for the massive uncoordinated random access scenario, which is
relevant for the Internet of Things, Polyanskiy (2017) proposed a novel
formulation of the multiple-access problem, commonly referred to as unsourced
multiple access, where all users employ a common codebook and the receiver
decodes up to a permutation of the messages. We extend this seminal work to the
case where the number of active users is random and unknown a priori. We define
a random-access code accounting for both misdetection (MD) and false alarm
(FA), and derive a random-coding achievability bound for the Gaussian multiple
access channel. Our bound captures the fundamental trade-off between MD and FA.
It suggests that the lack of knowledge of the number of active users entails a
small penalty in energy efficiency when the target MD and FA probabilities are
high. However, as the target MD and FA probabilities decrease, the energy
efficiency penalty becomes significant. For example, in a typical IoT scenario,
the required energy per bit to achieve both MD and FA probabilities below 0.1,
predicted by our bound, is only 0.5-0.7 dB higher than that predicted by the
bound in Polyanskiy (2017) for a known number of active users. This gap
increases to 3-4 dB when the target MD and/or FA probability is 0.001. Taking
both MD and FA into account, we use our bound to benchmark the energy
efficiency of slotted ALOHA with multi-packet reception, of a decoder that
treats interference as noise, and of some recently proposed coding schemes.
Numerical results suggest that, when the target MD and FA probabilities are
high, it is effective to estimate the number of active users, then treat this
estimate as the true value, and use a coding scheme that performs well for the
case of known number of active users. However, this approach becomes energy
inefficient when the requirements on MD and FA probabilities are stringent.


title: Learning Perspective Deformation in X-Ray Transmission Imaging

abstract:
  In cone-beam X-ray transmission imaging, due to the divergence of X-rays,
imaged structures with different depths have different magnification factors on
an X-ray detector, which results in perspective deformation. Perspective
deformation causes difficulty in direct, accurate geometric assessments of
anatomical structures. In this work, to reduce perspective deformation in X-ray
images acquired from regular cone-beam computed tomography (CBCT) systems, we
investigate on learning perspective deformation, i.e., converting perspective
projections into orthogonal projections. Directly converting a single
perspective projection image into an orthogonal projection image is extremely
challenging due to the lack of depth information. Therefore, we propose to
utilize one additional perspective projection, a complementary (180-degree) or
orthogonal (90-degree) view, to provide a certain degree of depth information.
Furthermore, learning perspective deformation in different spatial domains is
investigated. Our proposed method is evaluated on numerical spherical bead
phantoms as well as patients' chest and head X-ray data. The experiments on
numerical bead phantom data demonstrate that learning perspective deformation
in polar coordinates has significant advantages over learning in Cartesian
coordinates, as root-mean-square error (RMSE) decreases from 5.31 to 1.40,
while learning in log-polar coordinates has no further considerable improvement
(RMSE = 1.85). In addition, using a complementary view (RMSE = 1.40) is better
than an orthogonal view (RMSE = 3.87). The experiments on patients' chest and
head data demonstrate that learning perspective deformation using dual
complementary views is also applicable in anatomical X-ray data, allowing
accurate cardiothoracic ratio measurements in chest X-ray images and
cephalometric analysis in synthetic cephalograms from cone-beam X-ray
projections.


title: Information Density in Multi-Layer Resistive Memories

abstract:
  Resistive memories store information in a crossbar arrangement of
two-terminal devices that can be programmed to patterns of high or low
resistance. While extremely compact, this technology suffers from the
"sneak-path" problem: certain information patterns cannot be recovered, as
multiple low resistances in parallel make a high resistance indistinguishable
from a low resistance. In this paper, a multi-layer device is considered, and
the number of bits it can store is derived exactly and asymptotic bounds are
developed. The information density of a series of isolated arrays with extreme
aspect ratios is derived in the single- and multi-layer cases with and without
peripheral selection circuitry. This density is shown to be non-zero in the
limit, unlike that of the arrays with moderate aspect ratios previously
considered. A simple encoding scheme that achieves capacity asymptotically is
presented.


title:
Crossed homomorphisms and low dimensional representations of mapping
  class groups of surfaces

abstract:
  We continue the study of low dimensional linear representations of mapping
class groups of surfaces initiated by Franks--Handel and Korkmaz. We consider
$(2g+1)$-dimensional complex linear representations of the pure mapping class
groups of compact orientable surfaces of genus $g$. We give a complete
classification of such representations for $g \geq 7$ up to conjugation, in
terms of certain twisted $1$-cohomology groups of the mapping class groups. A
new ingredient is to use the computation of a related twisted $1$-cohomology
group by Morita. The classification result implies in particular that there are
no irreducible linear representations of dimension $2g+1$ for $g \geq 7$, which
marks a contrast with the case $g=2$.


title: Incremental user embedding modeling for personalized text classification

abstract:
  Individual user profiles and interaction histories play a significant role in
providing customized experiences in real-world applications such as chatbots,
social media, retail, and education. Adaptive user representation learning by
utilizing user personalized information has become increasingly challenging due
to ever-growing history data. In this work, we propose an incremental user
embedding modeling approach, in which embeddings of user's recent interaction
histories are dynamically integrated into the accumulated history vectors via a
transformer encoder. This modeling paradigm allows us to create generalized
user representations in a consecutive manner and also alleviate the challenges
of data management. We demonstrate the effectiveness of this approach by
applying it to a personalized multi-class classification task based on the
Reddit dataset, and achieve 9% and 30% relative improvement on prediction
accuracy over a baseline system for two experiment settings through appropriate
comment history encoding and task modeling.


title: Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems

abstract:
  We propose a new interconnection relation for infinite-dimensional
port-Hamiltonian systems that enables the coupling of ports with different
spatial dimensions by integrating over the the surplus dimensions. To show the
practical relevance, we apply this interconnection to a model system of an
actively cooled gas turbine blade. We also show that this interconnection
relation behaves well with respect to a discretization in finite element space,
ensuring its usability for practical applications.


title: Omnifont Persian OCR System Using Primitives

abstract:
  In this paper, we introduce a model-based omnifont Persian OCR system. The
system uses a set of 8 primitive elements as structural features for
recognition. First, the scanned document is preprocessed. After normalizing the
preprocessed image, text rows and sub-words are separated and then thinned.
After recognition of dots in sub-words, strokes are extracted and primitive
elements of each sub-word are recognized using the strokes. Finally, the
primitives are compared with a predefined set of character identification
vectors in order to identify sub-word characters. The separation and
recognition steps of the system are concurrent, eliminating unavoidable errors
of independent separation of letters. The system has been tested on documents
with 14 standard Persian fonts in 6 sizes. The achieved precision is 97.06%.


title:
A Survey of Deep Learning Techniques for the Analysis of COVID-19 and
  their usability for Detecting Omicron

abstract:
  The Coronavirus (COVID-19) outbreak in December 2019 has become an ongoing
threat to humans worldwide, creating a health crisis that infected millions of
lives, as well as devastating the global economy. Deep learning (DL) techniques
have proved helpful in analysis and delineation of infectious regions in
radiological images in a timely manner. This paper makes an in-depth survey of
DL techniques and draws a taxonomy based on diagnostic strategies and learning
approaches. DL techniques are systematically categorized into classification,
segmentation, and multi-stage approaches for COVID-19 diagnosis at image and
region level analysis. Each category includes pre-trained and custom-made
Convolutional Neural Network architectures for detecting COVID-19 infection in
radiographic imaging modalities; X-Ray, and Computer Tomography (CT).
Furthermore, a discussion is made on challenges in developing diagnostic
techniques such as cross-platform interoperability and examining imaging
modality. Similarly, a review of the various methodologies and performance
measures used in these techniques is also presented. This survey provides an
insight into the promising areas of research in DL for analyzing radiographic
images, and further accelerates the research in designing customized DL based
diagnostic tools for effectively dealing with new variants of COVID-19 and
emerging challenges.


title:
Scheduling Techniques for Liver Segmentation: ReduceLRonPlateau Vs
  OneCycleLR

abstract:
  Machine learning and computer vision techniques have influenced many fields
including the biomedical one. The aim of this paper is to investigate the
important concept of schedulers in manipulating the learning rate (LR), for the
liver segmentation task, throughout the training process, focusing on the newly
devised OneCycleLR against the ReduceLRonPlateau. A dataset, published in 2018
and produced by the Medical Segmentation Decathlon Challenge organizers, called
Task 8 Hepatic Vessel (MSDC-T8) has been used for testing and validation. The
reported results that have the same number of maximum epochs (75), and are the
average of 5-fold cross-validation, indicate that ReduceLRonPlateau converges
faster while maintaining a similar or even better loss score on the validation
set when compared to OneCycleLR. The epoch at which the peak LR occurs perhaps
should be made early for the OneCycleLR such that the super-convergence feature
can be observed. Moreover, the overall results outperform the state-of-the-art
results from the researchers who published the liver masks for this dataset. To
conclude, both schedulers are suitable for medical segmentation challenges,
especially the MSDC-T8 dataset, and can be used confidently in rapidly
converging the validation loss with a minimal number of epochs.


title: Optimal sizing of a holdout set for safe predictive model updating

abstract:
  Risk models in medical statistics and healthcare machine learning are
increasingly used to guide clinical or other interventions. Should a model be
updated after a guided intervention, it may lead to its own failure at making
accurate predictions. The use of a `holdout set' -- a subset of the population
that does not receive interventions guided by the model -- has been proposed to
prevent this. Since patients in the holdout set do not benefit from risk
predictions, the chosen size must trade off maximising model performance whilst
minimising the number of held out patients. By defining a general loss
function, we prove the existence and uniqueness of an optimal holdout set size,
and introduce parametric and semi-parametric algorithms for its estimation. We
demonstrate their use on a recent risk score for pre-eclampsia. Based on these
results, we argue that a holdout set is a safe, viable and easily implemented
solution to the model update problem.


title:
Exactly Optimal Deterministic Radio Broadcasting with Collision
  Detection

abstract:
  We consider the broadcast problem in synchronous radio broadcast models with
collision detection. One node of the network is given a message that must be
learned by all nodes in the network. We provide a deterministic algorithm that
works on the beeping model, which is a restricted version of the radio
broadcast model with collision detection. This algorithm improves on the round
complexity of previous algorithms. We prove an exactly matching lower bound in
the radio broadcast model with collision detection. This shows that the extra
power provided by the radio broadcast model with collision detection does not
help improve the round complexity.


title:
An Approach for Non-Convex Uniformly Concave Structured Saddle Point
  Problem

abstract:
  Recently, saddle point problems have received much attention due to their
powerful modeling capability for a lot of problems from diverse domains.
Applications of these problems occur in many applied areas, such as robust
optimization, distributed optimization, game theory, and many applications in
machine learning such as empirical risk minimization and generative adversarial
networks training. Therefore, many researchers have actively worked on
developing numerical methods for solving saddle point problems in many
different settings. This paper is devoted to developing a numerical method for
solving saddle point problems in the non-convex uniformly-concave setting. We
study a general class of saddle point problems with composite structure and
H\"older-continuous higher-order derivatives. To solve the problem under
consideration, we propose an approach in which we reduce the problem to a
combination of two auxiliary optimization problems separately for each group of
variables, outer minimization problem w.r.t. primal variables, and inner
maximization problem w.r.t the dual variables. For solving the outer
minimization problem, we use the \textit{Adaptive Gradient Method}, which is
applicable for non-convex problems and also works with an inexact oracle that
is generated by approximately solving the inner problem. For solving the inner
maximization problem, we use the \textit{Restarted Unified Acceleration
Framework}, which is a framework that unifies the high-order acceleration
methods for minimizing a convex function that has H\"older-continuous
higher-order derivatives. Separate complexity bounds are provided for the
number of calls to the first-order oracles for the outer minimization problem
and higher-order oracles for the inner maximization problem. Moreover, the
complexity of the whole proposed approach is then estimated.


title:
On limiting spectral distribution and joint convergence of some
  patterned random matrices

abstract:
  This article deals with the limiting spectral distribution and joint
convergence of reverse circulant and symmetric circulant matrices with
independent entries. These results are already proved in articles Bose and Sen
(2008) \cite{bose_sen_LSD_EJP}, and Bose, Hazra and Saha (2011)
\cite{bose_saha_patter_JC_annals}, respectively. But this article provides
alternate proofs of these results which are shorter than the existing proofs.
Our method is mainly based on moment method.


title: Superconducting vortex-charge measurement using cavity electromechanics

abstract:
  As the magnetic field penetrates the surface of a superconductor, it results
in the formation of flux-vortices. It has been predicted that the flux-vortices
will have a charged vortex core and create a dipolelike electric field. Such a
charge trapping in vortices is particularly enhanced in high-T$_c$
superconductors (HTS). Here, we integrate a mechanical resonator made of a thin
flake of HTS Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ into a microwave circuit to
realize a cavity-electromechanical device. Due to the exquisite sensitivity of
cavity-based devices to the external forces, we directly detect the charges in
the flux-vortices by measuring the electromechanical response of the mechanical
resonator. Our measurements reveal the strength of surface electric dipole
moment due to a single vortex core to be approximately 30~$|e|a_B$, equivalent
to a vortex charge per CuO$_2$ layer of $3.7\times 10^{-2}|e|$, where $a_B$ is
the Bohr radius and $e$ is the electronic charge.


title: GOE statistics on the moduli space of surfaces of large genus

abstract:
  For a compact hyperbolic surface, we define a smooth linear statistic,
mimicking the number of Laplace eigenvalues in a short energy window. We study
the variance of this statistic, when averaged over the moduli space $\mathcal
M_g$ of all genus $g$ surfaces with respect to the Weil-Petersson measure. We
show that in the double limit, first taking the large genus limit and then the
high energy limit, we recover GOE statistics. The proof makes essential use of
Mirzakhani's integration formula.

categories: math.SP math-ph math.GT math.MP math.NT nlin.CD


title: Central Limit Theorems for Semidiscrete Wasserstein Distances

abstract:
  We prove a Central Limit Theorem for the empirical optimal transport cost,
$\sqrt{\frac{nm}{n+m}}\{\mathcal{T}_c(P_n,Q_m)-\mathcal{T}_c(P,Q)\}$, in the
semi discrete case, i.e when the distribution $P$ is supported in $N$ points,
but without assumptions on $Q$. We show that the asymptotic distribution is the
supremun of a centered Gaussian process, which is Gaussian under some
additional conditions on the probability $Q$ and on the cost. Such results
imply the central limit theorem for the $p$-Wassertein distance, for $p\geq 1$.
This means that, for fixed $N$, the curse of dimensionality is avoided. To
better understand the influence of such $N$, we provide bounds of
$E|\mathcal{W}_1(P,Q_m)-\mathcal{W}_1(P,Q)|$ depending on $m$ and $N$. Finally,
the semidiscrete framework provides a control on the second derivative of the
dual formulation, which yields the first central limit theorem for the optimal
transport potentials. The results are supported by simulations that help to
visualize the given limits and bounds. We analyse also the cases where
classical bootstrap works.


title:
Pleasant behavior of swampland conjectures in the face of specific
  inflationary models

abstract:
  Recently researchers have been studying various conditions as swampland
criteria in cosmological implications. They have studied many inflation models
with different swampland conditions. Occasionally these conjectures are
modified and lead to fascinating points. The swampland conjecture is in
contradiction with the slow-roll single-field inflation model. So in this
paper, we will briefly describe resolving this contradiction with the special
method; we consider a small parameter {\lambda} with respect to a coupling
function in inflation and resolve this important antithesis. Then we will
discuss a new point of view in studying inflation models according to the
swampland criteria. Therefore we introduce some inflation models and challenge
the swampland criteria. We specify the allowable range of cosmological
parameters as the tensor-to-scalar ratio (r) the scalar spectral index (ns)
according to the latest observable data. Next, we study the new constraints to
determine the compatibility or incompatibility of the corresponding model with
the swampland conjectures. Finally, we express the results and compare them
with the latest observational data by plotting some figures.


title: Neural Network Trojans Analysis and Mitigation from the Input Domain

abstract:
  Deep Neural Networks (DNNs) can learn Trojans (or backdoors) from benign or
poisoned data, which raises security concerns of using them. By exploiting such
Trojans, the adversary can add a fixed input space perturbation to any given
input to mislead the model predicting certain outputs (i.e., target labels). In
this paper, we analyze such input space Trojans in DNNs, and propose a theory
to explain the relationship of a model's decision regions and Trojans: a
complete and accurate Trojan corresponds to a hyperplane decision region in the
input domain. We provide a formal proof of this theory, and provide empirical
evidence to support the theory and its relaxations. Based on our analysis, we
design a novel training method that removes Trojans during training even on
poisoned datasets, and evaluate our prototype on five datasets and five
different attacks. Results show that our method outperforms existing solutions.
Code: \url{https://anonymous.4open.science/r/NOLE-84C3}.


title:
Surgical Scheduling via Optimization and Machine Learning with
  Long-Tailed Data

abstract:
  Using data from cardiovascular surgery patients with long and highly variable
post-surgical lengths of stay (LOS), we develop a model to reduce recovery unit
congestion. We estimate LOS using a variety of machine learning models,
schedule procedures with a variety of online optimization models, and estimate
performance with simulation. The machine learning models achieved only modest
LOS prediction accuracy, despite access to a very rich set of patient
characteristics. Compared to the current paper-based system used in the
hospital, most optimization models failed to reduce congestion without
increasing wait times for surgery. A conservative stochastic optimization with
sufficient sampling to capture the long tail of the LOS distribution
outperformed the current manual process. These results highlight the perils of
using oversimplified distributional models of patient length of stay for
scheduling procedures and the importance of using stochastic optimization
well-suited to dealing with long-tailed behavior.


title: FairTraDEX: A Decentralised Exchange Preventing Value Extraction

abstract:
  An idealised decentralised exchange (DEX) provides a medium in which players
wishing to exchange one token for another can interact with other such players
and liquidity providers at a price which reflects the true exchange rate,
without the need for a trusted third-party. Unfortunately, extractable value is
an inherent flaw in existing blockchain-based DEX implementations. This
extractable value takes the form of monetizable opportunities that allow
blockchain participants to extract money from a DEX without adding demand or
liquidity to the DEX, the two functions for which DEXs are intended. This money
is taken directly from the intended DEX participants. As a result, the cost of
participation in existing DEXs is much larger than the upfront fees required to
post a transaction on a blockchain and/or into a smart contract.
  We present FairTraDEX, a decentralised variant of a frequent batch auction
(FBA), a DEX protocol which provides formal game-theoretic guarantees against
extractable value. FBAs when run by a trusted third-party provide unique
game-theoretic optimal strategies which ensure players are shown prices equal
to the liquidity provider's fair price, excluding explicit, pre-determined
fees. FairTraDEX replicates the key features of an FBA that provide these
game-theoretic guarantees using a combination of set-membership in
zero-knowledge protocols and an escrow-enforced commit-reveal protocol. We
extend the results of FBAs to handle monopolistic and/or malicious liquidity
providers, and provide a detailed pseudo-code implementation of FairTraDEX
based on existing mainstream blockchain protocols.


title: Sample-Efficient Reinforcement Learning with loglog(T) Switching Cost

abstract:
  We study the problem of reinforcement learning (RL) with low (policy)
switching cost - a problem well-motivated by real-life RL applications in which
deployments of new policies are costly and the number of policy updates must be
low. In this paper, we propose a new algorithm based on stage-wise exploration
and adaptive policy elimination that achieves a regret of
$\widetilde{O}(\sqrt{H^4S^2AT})$ while requiring a switching cost of $O(HSA
\log\log T)$. This is an exponential improvement over the best-known switching
cost $O(H^2SA\log T)$ among existing methods with
$\widetilde{O}(\mathrm{poly}(H,S,A)\sqrt{T})$ regret. In the above, $S,A$
denotes the number of states and actions in an $H$-horizon episodic Markov
Decision Process model with unknown transitions, and $T$ is the number of
steps. We also prove an information-theoretical lower bound which says that a
switching cost of $\Omega(HSA)$ is required for any no-regret algorithm. As a
byproduct, our new algorithmic techniques allow us to derive a
\emph{reward-free} exploration algorithm with an optimal switching cost of
$O(HSA)$.


title: Improved analysis for a proximal algorithm for sampling

abstract:
  We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new
convergence guarantees under weaker assumptions than strong log-concavity:
namely, our results hold for (1) weakly log-concave targets, and (2) targets
satisfying isoperimetric assumptions which allow for non-log-concavity. We
demonstrate our results by obtaining new state-of-the-art sampling guarantees
for several classes of target distributions. We also strengthen the connection
between the proximal sampler and the proximal method in optimization by
interpreting the proximal sampler as an entropically regularized Wasserstein
proximal method, and the proximal point method as the limit of the proximal
sampler with vanishing noise.


title:
Scaling Laws Under the Microscope: Predicting Transformer Performance
  from Small Scale Experiments

abstract:
  Neural scaling laws define a predictable relationship between a model's
parameter count and its performance after training in the form of a power law.
However, most research to date has not explicitly investigated whether scaling
laws can be used to accelerate model development. In this work, we perform such
an empirical investigation across a wide range of language understanding tasks,
starting from models with as few as 10K parameters, and evaluate downstream
performance across 9 language understanding tasks. We find that scaling laws
emerge at finetuning time in some NLP tasks, and that they can also be
exploited for debugging convergence when training large models. Moreover, for
tasks where scaling laws exist, they can be used to predict the performance of
larger models, which enables effective model selection. However, revealing
scaling laws requires careful hyperparameter tuning and multiple runs for the
purpose of uncertainty estimation, which incurs additional overhead, partially
offsetting the computational benefits.


title:
Ore- and P\'osa-type conditions for partitioning $2$-edge-coloured
  graphs into monochromatic cycles

abstract:
  In 2019, Letzter confirmed a conjecture of Balogh, Bar\'at, Gerbner,
Gy\'arf\'as and S\'ark\"ozy, proving that every large $2$-edge-coloured graph
$G$ on $n$ vertices with minimum degree at least $3n/4$ can be partitioned into
two monochromatic cycles of different colours. Here, we propose a weaker
condition on the degree sequence of $G$ to also guarantee such a partition and
prove an approximate version. Continuing work by Allen, B\"ottcher, Lang,
Skokan and Stein, we also show that if $\operatorname{deg}(u) +
\operatorname{deg}(v) \geq 4n/3 + o(n)$ holds for all non-adjacent vertices
$u,v \in V(G)$, then all but $o(n)$ vertices can be partitioned into three
monochromatic cycles.


title:
Optimal Embeddings for Triebel-Lizorkin and Besov Spaces on Quasi-Metric
  Measure Spaces

abstract:
  In this article, via certain lower bound conditions on the measures under
consideration, the authors fully characterize the Sobolev embeddings for the
scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the
general context of quasi-metric measure spaces for an optimal range of the
smoothness parameter $s$. An interesting facet of this work is how the range of
$s$ for which the above characterizations of these embeddings hold true is
intimately linked (in a quantitative manner) to the geometric makeup of the
underlying space. Moreover, although stated for Haj{\l}asz-Triebel-Lizorkin and
Haj{\l}asz-Besov spaces in the context of quasi-metric spaces, the main results
in this article improve known work even for Sobolev spaces in the metric
setting.


title:
Deep Learning based Coverage and Rate Manifold Estimation in Cellular
  Networks

abstract:
  This article proposes Convolutional Neural Network-based Auto Encoder
(CNN-AE) to predict location-dependent rate and coverage probability of a
network from its topology. We train the CNN utilising BS location data of
India, Brazil, Germany, and the USA and compare its performance with stochastic
geometry (SG) based analytical models. In comparison to the best-fitted
SG-based model, CNN-AE improves the coverage and rate prediction errors by a
margin of as large as $40\%$ and $25\%$ respectively. As an application, we
propose a low complexity, provably convergent algorithm that, using trained
CNN-AE, can compute locations of new BSs that need to be deployed in a network
in order to satisfy pre-defined spatially heterogeneous performance goals.


title: Checking volume-law entropy with HRT surfaces

abstract:
  We check formally that the HRT prescription for holographic entanglement
entropy - when applied to a static black brane spacetime and to a wide class of
subregions which do not lie on a constant timeslice - gives rise to volume-law
entropy in the limit of large subregion. By volume-law entropy, we mean that
the entanglement entropy scales with the volume of the projection of the
boundary subregion onto a constant timeslice (with the same coefficient as in
the volume-law on the static timeslice). Our result applies to subregions which
have reflection symmetry as well as strips, and we also present field-theoretic
arguments in support of our holographic findings.


title: Local approximation of operators

abstract:
  Many applications, such as system identification, classification of time
series, direct and inverse problems in partial differential equations, and
uncertainty quantification lead to the question of approximation of a
non-linear operator between metric spaces $\mathfrak{X}$ and $\mathfrak{Y}$. We
study the problem of determining the degree of approximation of a such
operators on a compact subset $K_\mathfrak{X}\subset \mathfrak{X}$ using a
finite amount of information. If $\mathcal{F}: K_\mathfrak{X}\to
K_\mathfrak{Y}$, a well established strategy to approximate $\mathcal{F}(F)$
for some $F\in K_\mathfrak{X}$ is to encode $F$ (respectively,
$\mathcal{F}(F)$) in terms of a finite number $d$ (repectively $m$) of real
numbers. Together with appropriate reconstruction algorithms (decoders), the
problem reduces to the approximation of $m$ functions on a compact subset of a
high dimensional Euclidean space $\mathbb{R}^d$, equivalently, the unit sphere
$\mathbb{S}^d$ embedded in $\mathbb{R}^{d+1}$. The problem is challenging
because $d$, $m$, as well as the complexity of the approximation on
$\mathbb{S}^d$ are all large, and it is necessary to estimate the accuracy
keeping track of the inter-dependence of all the approximations involved. In
this paper, we establish constructive methods to do this efficiently; i.e.,
with the constants involved in the estimates on the approximation on
$\\mathbb{S}^d$ being $\mathcal{O}(d^{1/6})$. We study different smoothness
classes for the operators, and also propose a method for approximation of
$\mathcal{F}(F)$ using only information in a small neighborhood of $F$,
resulting in an effective reduction in the number of parameters involved. To
further mitigate the problem of large number of parameters, we propose
prefabricated networks, resulting in a substantially smaller number of
effective parameters.


title:
Comparing the Perceived Legitimacy of Content Moderation Processes:
  Contractors, Algorithms, Expert Panels, and Digital Juries

abstract:
  While research continues to investigate and improve the accuracy, fairness,
and normative appropriateness of content moderation processes on large social
media platforms, even the best process cannot be effective if users reject its
authority as illegitimate. We present a survey experiment comparing the
perceived institutional legitimacy of four popular content moderation
processes. We conducted a within-subjects experiment in which we showed US
Facebook users moderation decisions and randomized the description of whether
those decisions were made by paid contractors, algorithms, expert panels, or
juries of users. Prior work suggests that juries will have the highest
perceived legitimacy due to the benefits of judicial independence and
democratic representation. However, expert panels had greater perceived
legitimacy than algorithms or juries. Moreover, outcome alignment - agreement
with the decision - played a larger role than process in determining perceived
legitimacy. These results suggest benefits to incorporating expert oversight in
content moderation and underscore that any process will face legitimacy
challenges derived from disagreement about outcomes.


title: The monotone-light factorization for 2-categories via 2-prorders

abstract:
  It is shown that the reflection 2Cat --> 2Preord of the category of all
2-categories into the category of 2-preorders determines a monotone-light
factorization system on 2Cat and that the light morphisms are precisely the
2-functors faithful on 2-cells with respect to the vertical structure. In order
to achieve such result it was also proved that the reflection 2Cat --> 2Preord
has stable units, a stronger condition than admissibility in categorical Galois
theory, and that the 2-functors surjective both on horizontally and on
vertically composable triples of 2-cells are effective descent morphisms in
2Cat.


title: Rank axioms and supersimplicity

abstract:
  Just as Lascar's notion of abstract rank axiomatizes the U-rank, we propose
axioms for the ranks $SU^d$ and $SU^f$, the foundation ranks of dividing and
forking. We study the relationships between these axioms. As with superstable,
we characterize supersimple types and theories based on the existence of these
ranks. We show that the U-rank is the foundation rank of the Lascar-splitting
independence relationship. We also provide an alternative definition of SUd
similar to the original definition of U. Finally, we check that if in the
standard characterizations of simple and supersimple we change the non-forking
independence for the non-lascar-splitting independence, we characterize stable
and superstable.


title: Topology of Singularities on Algebraic Loop Spaces

abstract:
  We study the topology of some simple infinite dimensional singularities
arising from spaces of \emph{algebraic formal loops}. We prove that in some
simple cases the natural analogue of nearby cycles cohomology for a function on
the loop space vanishes, and show further that a suitably renormalized version
of the above cohomology produces a simple (non-zero) result.


title: Transformer-based Approaches for Legal Text Processing

abstract:
  In this paper, we introduce our approaches using Transformer-based models for
different problems of the COLIEE 2021 automatic legal text processing
competition. Automated processing of legal documents is a challenging task
because of the characteristics of legal documents as well as the limitation of
the amount of data. With our detailed experiments, we found that
Transformer-based pretrained language models can perform well with automated
legal text processing problems with appropriate approaches. We describe in
detail the processing steps for each task such as problem formulation, data
processing and augmentation, pretraining, finetuning. In addition, we introduce
to the community two pretrained models that take advantage of parallel
translations in legal domain, NFSP and NMSP. In which, NFSP achieves the
state-of-the-art result in Task 5 of the competition. Although the paper
focuses on technical reporting, the novelty of its approaches can also be an
useful reference in automated legal document processing using Transformer-based
models.


title:
Derived Geometry and Non-Linear Differential Equations on the Punctured
  Disc

abstract:
  We study non-linear differential equations on the punctured formal disc by
considering the natural derived enhancements of their spaces of solutions. In
particular, by appealing to results of the inverse theory in the calculus of
variations, we show that a variational formulation of a differential equation
is \emph{equivalent} to the residue pairing inducing a (-1)-symplectic form on
the derived space of solutions equipped with a certain decoration of its
tangent complex.


title:
Action Principles and Conservation Laws for Chew-Goldberger-Low
  Anisotropic Plasmas

abstract:
  The ideal CGL plasma equations, including the double adiabatic conservation
laws for the parallel ($p_\parallel$) and perpendicular pressure ($p_\perp$),
are investigated using a Lagrangian variational principle. An Euler-Poincar\'e
variational principle is developed and the non-canonical Poisson bracket is
obtained, in which the non-canonical variables consist of the mass flux ${\bf
M}$, the density $\rho$, three entropy variables, $\sigma=\rho S$,
$\sigma_\parallel=\rho S_\parallel$, $\sigma_\perp=\rho S_\perp$ ($S_\parallel$
and $S_\perp$ are the two scalar entropy invariants), and the magnetic
induction ${\bf B}$. Conservation laws of the CGL plasma equations are derived
via Noether's theorem. The Galilean group leads to conservation of energy,
momentum, center of mass, and angular momentum. Cross helicity conservation
arises from a fluid relabeling symmetry, and is local or nonlocal depending on
whether the entropy gradients of $S_\parallel$, $S_\perp$ and $S$ are
perpendicular to ${\bf B}$ or otherwise. The point Lie symmetries of the CGL
system are shown to comprise the Galilean transformations and scalings.


title:
Misspecification Analysis of High-Dimensional Random Effects Models for
  Estimation of Signal-to-Noise Ratios

abstract:
  Estimation of signal-to-noise ratios and noise variances in high-dimensional
linear models have important applications in statistical inference,
hyperparameter selection, and heritability estimation in genomics. One common
approach in practice is maximum likelihood estimation under random effects
models. This paper aims to conduct model misspecification analysis on the
consistency of this method, in which the true model only has fixed effects.
Assume that the ratio between the number of samples and features converges to a
nonzero constant, our results provide conditions on the design matrices under
which random effects model based maximum likelihood estimation is
asymptotically consistent in estimating the SNR and noise variance. Our model
misspecification analysis also extends to the high-dimensional linear models
with feature groups, in which group SNR estimation has important applications
such as tuning parameter selection for group ridge regression.


title: Individual-Level Inverse Reinforcement Learning for Mean Field Games

abstract:
  The recent mean field game (MFG) formalism has enabled the application of
inverse reinforcement learning (IRL) methods in large-scale multi-agent
systems, with the goal of inferring reward signals that can explain
demonstrated behaviours of large populations. The existing IRL methods for MFGs
are built upon reducing an MFG to a Markov decision process (MDP) defined on
the collective behaviours and average rewards of the population. However, this
paper reveals that the reduction from MFG to MDP holds only for the fully
cooperative setting. This limitation invalidates existing IRL methods on MFGs
with non-cooperative environments. To measure more general behaviours in large
populations, we study the use of individual behaviours to infer ground-truth
reward functions for MFGs. We propose Mean Field IRL (MFIRL), the first
dedicated IRL framework for MFGs that can handle both cooperative and
non-cooperative environments. Based on this theoretically justified framework,
we develop a practical algorithm effective for MFGs with unknown dynamics. We
evaluate MFIRL on both cooperative and mixed cooperative-competitive scenarios
with many agents. Results demonstrate that MFIRL excels in reward recovery,
sample efficiency and robustness in the face of changing dynamics.


title: The Deformation Space of Delaunay Triangulations of the Sphere

abstract:
  In this paper, we determine the topology of the spaces of convex polyhedra
inscribed in the unit $2$-sphere and the spaces of strictly Delaunay geodesic
triangulations of the unit $2$-sphere. These spaces can be regarded as
discretized groups of diffeomorphisms of the unit $2$-sphere. Hence, it is
natural to conjecture that these spaces have the same homotopy types as those
of their smooth counterparts. The main result of this paper confirms this
conjecture for the unit $2$-sphere. It follows from an observation on the
variational principles on triangulated surfaces developed by I. Rivin.
  On the contrary, the similar conjecture does not hold in the cases of flat
tori and convex polygons. We will construct simple examples of flat tori and
convex polygons such that the corresponding spaces of Delaunay geodesic
triangulations are not connected.


title:
Evaluation of cosmogenic production of $^{39}Ar$ and $^{42}Ar$ for
  rare-event physics using underground argon

abstract:
  Underground argon (UAr) with lower cosmogenic activities of $^{39}Ar$ and
$^{42}Ar$ has been planned as a detector in detecting scintillation light and
charge collection using time projection chambers for dark matter searches and
as a veto detector in suppressing backgrounds for neutrinoless double beta
decay (0$\nu\beta\beta$) experiments. Long-lived radioactive isotopes,
$^{39}Ar$ and $^{42}Ar$, can also be produced on the surface when UAr is pumped
out from a deep well. Understanding the production of long-lived isotopes in Ar
is important for utilizing UAr for dark matter and 0$\nu\beta\beta$ experiments
in terms of its production, transportation, and storage. Ar exposure to cosmic
rays at sea-level is simulated using Geant4 for a given cosmic ray muon,
neutron, and proton energy spectrum. We report the simulated cosmogenic
production rates of $^{39}Ar$, $^{42}Ar$, and other long-lived isotopes at
sea-level from fast neutrons, high energy muons, and high energy protons. Total
production rates of 938.53/kg$_{Ar}\cdot$day and
5.81$\times$10$^{-3}$/kg$_{Ar}\cdot$day for $^{39}$Ar and $^{42}$Ar are found
from our simulation. Utilizing these production rates, we set a time limit of
954 days constrained by the production of $^{39}$Ar for UAr to be on the
surface before it compromises the sensitivity for a dark matter experiment.
Similarly, a time limit of 1702 days constrained by the production of $^{42}$Ar
is found for a 0$\nu\beta\beta$ experiment.


title: Friction and mobility of carbon nanoparticles on a graphene sheet

abstract:
  It is shown using the method of molecular dynamics that the motion of carbon
nanoparticles (rectangular graphene flakes, spherical fullerenes of size $L<10$
nm) on the surface of a thermalized graphene sheet lying on a flat substrate
can be described as the motion of particles in a viscous medium with a constant
coefficient of friction, the value of which depends on the temperature and
particle size. It has been shown that there are two types of effective
friction: diffusion and ballistic. In ballistic regime of motion (at velocities
$v>100$ m/s), deceleration occurs due to the interaction of moving
nanoparticles with thermal out-of-plane bending vibrations of a graphene sheet.
Because of this, with the increasing temperature, the coefficient of friction
monotonically increases. In the diffusion regime of motion (at $v<10$ m/s),
friction arises due to the need for the particle to overcome local energy
barriers, therefore it decreases with increasing emperature. The difference
between ballistic and diffusion friction is most pronounced at low
temperatures, since the mobility of nanoparticles in the ballistic regime of
motion decreases with increasing temperature, while in the diffusion regime it
monotonously increases. It is shown that the presence of a normal force
pressing the nanoparticle to the substrate leads to an increases in its
friction with the substrate.


title:
Difference operators and duality for trigonometric Gaudin and Dynamical
  Hamiltonians

abstract:
  We study the difference analog of the quotient differential operator from
arXiv:1907.02117. Starting with a space of quasi-exponentials $W=\langle
\alpha_{i}^{x}p_{ij}(x), i=1,\dots , n, j=1,\dots , n_{i}\rangle$, where
$\alpha_{i}\in\mathbb{C}^{*}$ and $p_{ij}(x)$ are polynomials, we consider the
formal conjugate $\check{S}^{\dagger}_{W}$ of the quotient difference operator
$\check{S}_{W}$ satisfying $\hat{S} =\check{S}_{W}S_{W}$. Here, $S_{W}$ is a
linear difference operator of order $\dim W$ annihilating $W$, and $\hat{S}$ is
a linear difference operator with constant coefficients depending on
$\alpha_{i}$ and $\operatorname{deg} p_{ij}(x)$ only. We show that $\ker
\check{S}^{\dagger}_{W}$ is also a space of quasi-exponentials, describe its
basis and discrete exponents. We also consider a similar construction for
differential operators associated with spaces of quasi-polynomials, which are
linear combinations of functions of the form $x^{z}q(x)$, where
$z\in\mathbb{C}$ and $q(x)$ is a polynomial. Combining our results with the
results on the bispectral duality obtained in arXiv:math/0605172, we relate the
construction of the quotient difference operator to the
$(\mathfrak{gl}_{k},\mathfrak{gl}_{n})$-duality of the trigonometric Gaudin
Hamiltonians and trigonometric Dynamical Hamiltonians acting on the space of
polynomials in $kn$ anticommuting variables.


title:
Visual Sound Localization in the Wild by Cross-Modal Interference
  Erasing

abstract:
  The task of audio-visual sound source localization has been well studied
under constrained scenes, where the audio recordings are clean. However, in
real-world scenarios, audios are usually contaminated by off-screen sound and
background noise. They will interfere with the procedure of identifying desired
sources and building visual-sound connections, making previous studies
non-applicable. In this work, we propose the Interference Eraser (IEr)
framework, which tackles the problem of audio-visual sound source localization
in the wild. The key idea is to eliminate the interference by redefining and
carving discriminative audio representations. Specifically, we observe that the
previous practice of learning only a single audio representation is
insufficient due to the additive nature of audio signals. We thus extend the
audio representation with our Audio-Instance-Identifier module, which clearly
distinguishes sounding instances when audio signals of different volumes are
unevenly mixed. Then we erase the influence of the audible but off-screen
sounds and the silent but visible objects by a Cross-modal Referrer module with
cross-modality distillation. Quantitative and qualitative evaluations
demonstrate that our proposed framework achieves superior results on sound
localization tasks, especially under real-world scenarios. Code is available at
https://github.com/alvinliu0/Visual-Sound-Localization-in-the-Wild.


title:
Hierarchical Point Cloud Encoding and Decoding with Lightweight
  Self-Attention based Model

abstract:
  In this paper we present SA-CNN, a hierarchical and lightweight
self-attention based encoding and decoding architecture for representation
learning of point cloud data. The proposed SA-CNN introduces convolution and
transposed convolution stacks to capture and generate contextual information
among unordered 3D points. Following conventional hierarchical pipeline, the
encoding process extracts feature in local-to-global manner, while the decoding
process generates feature and point cloud in coarse-to-fine, multi-resolution
stages. We demonstrate that SA-CNN is capable of a wide range of applications,
namely classification, part segmentation, reconstruction, shape retrieval, and
unsupervised classification. While achieving the state-of-the-art or comparable
performance in the benchmarks, SA-CNN maintains its model complexity several
order of magnitude lower than the others. In term of qualitative results, we
visualize the multi-stage point cloud reconstructions and latent walks on rigid
objects as well as deformable non-rigid human and robot models.


title:
Lorentzian spectral zeta functions on asymptotically Minkowski
  spacetimes

abstract:
  In this note, we consider perturbations of Minkowski space as well as more
general spacetimes on which the wave operator $\square_g$ is essentially
self-adjoint. We review a recent result which gives the meromorphic
continuation of the Lorentzian spectral zeta function density, i.e. of the
trace density of complex powers $\alpha \mapsto (\square_g-i
\varepsilon)^{-\alpha}$. In even dimension $n\geq 4$, the residue at
$\frac{n}{2}-1$ is shown to be a multiple of the scalar curvature in the limit
$\varepsilon\to 0^+$. This yields a spectral action for gravity in Lorentzian
signature.


title: Distribution augmentation for low-resource expressive text-to-speech

abstract:
  This paper presents a novel data augmentation technique for text-to-speech
(TTS), that allows to generate new (text, audio) training examples without
requiring any additional data. Our goal is to increase diversity of text
conditionings available during training. This helps to reduce overfitting,
especially in low-resource settings. Our method relies on substituting text and
audio fragments in a way that preserves syntactical correctness. We take
additional measures to ensure that synthesized speech does not contain
artifacts caused by combining inconsistent audio samples. The perceptual
evaluations show that our method improves speech quality over a number of
datasets, speakers, and TTS architectures. We also demonstrate that it greatly
improves robustness of attention-based TTS models.


title: Mechanics of micropillar confined thin film plasticity

abstract:
  Micropillar compression experiments probing size effects in confined
plasticity of metal thin films, including the indirect imposition of
'canonical' simple shearing boundary conditions, show dramatically different
responses in compression and shear of the film. The Mesoscale Field Dislocation
Mechanics (MFDM) model is confronted with this set of experimental observations
and shown to be capable of modeling such behavior, without any ad-hoc
modification to the basic structure of the theory (including boundary
conditions), or the use of extra fitting parameters. This is a required
theoretical advance in the current state-of-the art of strain gradient
plasticity models. It is also shown that significantly different inhomogeneous
fields can display qualitatively similar size effect trends in overall
agreement with the experimental results. The (plastic) Swift and (elastic)
Poynting finite deformation effects are also demonstrated.


title: How Likely A Coalition of Voters Can Influence A Large Election?

abstract:
  For centuries, it has been widely believed that the influence of a small
coalition of voters is negligible in a large election. Consequently, there is a
large body of literature on characterizing the asymptotic likelihood for an
election to be influence, especially by the manipulation of a single voter,
establishing an $O(\frac{1}{\sqrt n})$ upper bound and an
$\Omega(\frac{1}{n^{67}})$ lower bound for many commonly studied voting rules
under the i.i.d.~uniform distribution, known as Impartial Culture (IC) in
social choice, where $n$ is the number is voters.
  In this paper, we extend previous studies in three aspects: (1) we consider a
more general and realistic semi-random model that resembles the model in
smoothed analysis, (2) we consider many coalitional influence problems,
including coalitional manipulation, margin of victory, and various vote
controls and bribery, and (3) we consider arbitrary and variable coalition size
$B$. Our main theorem provides asymptotically tight bounds on the semi-random
likelihood of the existence of a size-$B$ coalition that can successfully
influence the election under a wide range of voting rules. Applications of the
main theorem and its proof techniques resolve long-standing open questions
about the likelihood of coalitional manipulability under IC, by showing that
the likelihood is $\Theta\left(\min\left\{\frac{B}{\sqrt n}, 1\right\}\right)$
for many commonly studied voting rules.
  The main technical contribution is a characterization of the semi-random
likelihood for a Poisson multinomial variable (PMV) to be unstable, which we
believe to be a general and useful technique with independent interest.


title:
Gravity Estimation at Small Bodies via Optical Tracking of Hopping
  Artificial Probes

abstract:
  Despite numerous successful missions to small celestial bodies, the gravity
field of such targets has been poorly characterized so far. Gravity estimates
can be used to infer the internal structure and composition of small bodies
and, as such, have strong implications in the fields of planetary science,
planetary defense, and in-situ resource utilization. Current gravimetry
techniques at small bodies mostly rely on tracking the spacecraft orbital
motion, where the gravity observability is low. To date, only lower-degree and
order spherical harmonics of small-body gravity fields could be resolved. In
this paper, we evaluate gravimetry performance for a novel mission architecture
where artificial probes repeatedly hop across the surface of the small body and
perform low-altitude, suborbital arcs. Such probes are tracked using optical
measurements from the mothership's onboard camera and orbit determination is
performed to estimate the probe trajectories, the small body's rotational
kinematics, and the gravity field. The suborbital motion of the probes provides
dense observations at low altitude, where the gravity signal is stronger. We
assess the impact of observation parameters and mission duration on gravity
observability. Results suggest that the gravitational spherical harmonics of a
small body with the same mass as the asteroid Bennu, can be observed at least
up to degree 40 within months of observations. Measurement precision and
frequency are key to achieve high-performance gravimetry.


title:
An Optimal Control Model of the transmission dynamics of COVID-19 in
  Ghana

abstract:
  The emergence of COVID-19 has led to the loss of lives of over 1300 people in
Ghana. In this paper, we propose a Susceptible, Exposed, Asymptomatic,
Symptomatic, Vaccinated, Recovered (SEAQVR) model to study the transmission
dynamics of COVID-19 in Ghana. We also introduce a compartment for the COVID-19
related deaths and we validate the model using COVID-19 data of Ghana. The
steady states and the stability analyses are examined. The disease free
equilibrium is both locally and globally stable. The reproductive number of the
model has been computed. The numerical simulation prediction is consistent with
COVID-19 situation in Ghana. Optimal controls were incorporated into the model
to determine the effectiveness of two preventive control measures which were
the use of a nose mask and vaccination. Both measures were very effective in
curbing the spread of the disease. However, the use of the mask increases
susceptibility, unlike vaccination.


title:
Defense Strategies Toward Model Poisoning Attacks in Federated Learning:
  A Survey

abstract:
  Advances in distributed machine learning can empower future communications
and networking. The emergence of federated learning (FL) has provided an
efficient framework for distributed machine learning, which, however, still
faces many security challenges. Among them, model poisoning attacks have a
significant impact on the security and performance of FL. Given that there have
been many studies focusing on defending against model poisoning attacks, it is
necessary to survey the existing work and provide insights to inspire future
research. In this paper, we first classify defense mechanisms for model
poisoning attacks into two categories: evaluation methods for local model
updates and aggregation methods for the global model. Then, we analyze some of
the existing defense strategies in detail. We also discuss some potential
challenges and future research directions. To the best of our knowledge, we are
the first to survey defense methods for model poisoning attacks in FL.


title:
Magneto-Optical Measurements of the Negatively Charged 2$s$ Exciton in
  WSe$_2$

abstract:
  Monolayer transition metal dichalcogenides host a variety of optically
excited quasiparticles species that stem from two-dimensional confinement
combined with relatively large carrier effective masses and reduced dielectric
screening. The magnetic response of these quasiparticles gives information on
their spin and valley configurations, nuanced carrier interactions, and insight
into the underlying band structure. Recently, there have been several reports
of 2$s$/3$s$ charged excitons in TMDs, but very little is still known about
their response to external magnetic fields. Using photoluminescence excitation
spectroscopy, we observe the presence of the 2$s$ charged exciton and report
for the first time its response to an applied magnetic field. We benchmark this
response against the neutral exciton and find that both the 2$s$ neutral and
charged excitons exhibit similar behavior with $g$-factors of
g$_{\rm{X_0^{2s}}}$=-5.20$\pm$0.11$\mu_{\rm{B}}$ and
g$_{\rm{X_-^{2s}}}$=-4.98$\pm$0.11$\mu_{\rm{B}}$, respectively.


title:
State-of-the-Art Review of Design of Experiments for Physics-Informed
  Deep Learning

abstract:
  This paper presents a comprehensive review of the design of experiments used
in the surrogate models. In particular, this study demonstrates the necessity
of the design of experiment schemes for the Physics-Informed Neural Network
(PINN), which belongs to the supervised learning class. Many complex partial
differential equations (PDEs) do not have any analytical solution; only
numerical methods are used to solve the equations, which is computationally
expensive. In recent decades, PINN has gained popularity as a replacement for
numerical methods to reduce the computational budget. PINN uses physical
information in the form of differential equations to enhance the performance of
the neural networks. Though it works efficiently, the choice of the design of
experiment scheme is important as the accuracy of the predicted responses using
PINN depends on the training data. In this study, five different PDEs are used
for numerical purposes, i.e., viscous Burger's equation, Shr\"{o}dinger
equation, heat equation, Allen-Cahn equation, and Korteweg-de Vries equation. A
comparative study is performed to establish the necessity of the selection of a
DoE scheme. It is seen that the Hammersley sampling-based PINN performs better
than other DoE sample strategies.


title: A Contrastive Framework for Neural Text Generation

abstract:
  Text generation is of great importance to many natural language processing
applications. However, maximization-based decoding methods (e.g. beam search)
of neural language models often lead to degenerate solutions -- the generated
text is unnatural and contains undesirable repetitions. Existing approaches
introduce stochasticity via sampling or modify training objectives to decrease
probabilities of certain tokens (e.g., unlikelihood training). However, they
often lead to solutions that lack coherence. In this work, we show that an
underlying reason for model degeneration is the anisotropic distribution of
token representations. We present a contrastive solution: (i) SimCTG, a
contrastive training objective to calibrate the model's representation space,
and (ii) a decoding method -- contrastive search -- to encourage diversity
while maintaining coherence in the generated text. Extensive experiments and
analyses on three benchmarks from two languages demonstrate that our proposed
approach outperforms state-of-the-art text generation methods as evaluated by
both human and automatic metrics.


title: On a Boundary Updating Method for the Scalar Stefan Problem

abstract:
  We report on a general purpose method for the scalar Stefan problem inspired
by the standard boundary updating method used in several existence proofs. By
suitably modifying it we can solve numerically any kind of Stefan problem. We
present a theoretical justification of the method and several computational
results.


title: Muon g-2, Neutralino Dark Matter and Stau NLSP

abstract:
  We explore the implications of resolving the muon g-2 anomaly in a SU(4)_c x
SU(2)_L x SU(2)_R model, where the soft supersymmetry breaking scalar and
gaugino masses break the left-right (LR) symmetry. A 2 sigma resolution of the
anomaly requires relatively light sleptons, chargino and LSP neutralino. The
stau turns out to be the NLSP of mass <~ 400 GeV, and the sleptons from the
first two families can be as heavy as about 800 GeV. The chargino is also
required to be lighter than about 600 GeV to accommodate the muon g-2 solutions
consistent with the dark matter relic density constraint. The dominant
right-handed nature of the light slepton states suppress the sensitivity of
possible signals which can be probed in Run3 experiments at the LHC. We also
discuss the impact of accomodating the Higgs boson mass and the vacuum
stability of the scalar potential for these solutions. The Higgsinos are
heavier than about 4 TeV, and the LSP neutralino has the correct relic density
if it is Bino-like. We identify stau-neutralino coannihilation as the dominant
mechanism for realizing the desired dark matter relic density, with
sneutrino-neutralino coannihiliation playing a minor role. These bino-like dark
matter solutions can yield a spin-independent scattering cross-section on the
order of 10^{-3} pb which hopefully, can be expected to be tested in the near
future.


title: Robust Statistical Inference for Cell Type Deconvolution

abstract:
  Cell type deconvolution is a computational approach to infer proportions of
individual cell types from bulk transcriptomics data. Though many new methods
have been developed for cell type deconvolution, most of them only provide
point estimation of the cell type proportions. On the other hand, estimates of
the cell type proportions can be very noisy due to various sources of bias and
randomness, and ignoring their uncertainty may greatly affect the validity of
downstream analyses. In this paper, we propose a comprehensive statistical
framework for cell type deconvolution and construct asymptotically valid
confidence intervals both for each individual's cell type proportion and for
quantifying how cell type proportions change across multiple bulk individuals
in downstream regression analyses. Our analysis takes into account various
factors including the biological randomness of gene expressions across cells
and individuals, gene-gene dependence, and the cross-platform biases and
sequencing errors, and avoids any parametric assumptions on the data
distributions. We also provide identification conditions of the cell type
proportions when there are arbitrary platforms-specific bias across sequencing
technologies.


title:
Exploring the Research Landscape of Pakistan: A Data-driven Analysis of
  Scopus Indexed Scientific Literature

abstract:
  Scientific contribution and research performance of a university, research
group, or institute needs to be evaluated all the more with the increasing
volume and fast-developing disciplines of research. The need of the time is to
develop tools for strategic planning and management that will help research
bodies to rank and benchmark themselves against international standards. This
will enable them to invest appropriately in research areas of promising
strength and gain maximally from them, thus fulfilling the ultimate purpose of
positive impact of research on society. Our tool is capable of rating and
benchmarking universities as well as research institutes in not only the major
disciplines and sub-disciplines, but at the finest level of niche areas of
science and technology too with the help of its innovative bibliometric
indicators based on publications and citation analysis. The tool accepts inputs
like discipline/subject area, university, and country and time window while
using data retrieved from bibliography database, Scopus, to benchmark and rate
the research body under consideration. We have evaluated that there are many
niche subject areas in which small or medium size universities are performing
good in comparison to the large universities. Most of these subject areas are
of more significance in the present day and the future. Government and funds
allocating bodies should take this factor in account that investing the right
money at right place will give far better results than we they are having right
now


title: Energy Conscious Dynamic Window Scheduling of Chip Multiprocessors

abstract:
  The need to develop systems that exploit multi and many-core architectures to
reduce wasteful heat generation is of utmost importance in compute-intensive
applications. We propose an energy-conscious approach to multicore scheduling
known as non-preemptive dynamic window (NPDW) scheduling that achieves
effective load and temperature balancing over chip multiprocessors. NPDW
utilizes the concept of dynamic time windows to accumulate tasks and find an
optimal stable matching between accumulated tasks and available processor cores
using a modified Gale-Shapely algorithm. The metrics of window and matching
performance are defined to create a dynamic window heuristic to determine the
next time window size based on the current and previous window sizes. Based on
derived formulation and experimental results, we show that our NPDW scheduler
is able to distribute the computational and thermal load throughout the
processors in a multicore environment better than baseline schedulers. We
believe that within multicore compute applications requiring temperature and
energy-conscious system design, our scheduler may be employed to effectively
disperse system load and prevent excess core heating.