title:
Highly efficient water purification by WO3-based homo/heterojunction
  photocatalyst under visible light

abstract:
  Bandgap engineering has attracted increasing interest in the field of
semiconductive materials with specific electrical and optical characteristics
for various applications, such as solar energy harvesting, energy-related
applications, and photocatalysts. Here, we propose a novel and facile method to
obtain a combination of type-II structure and Ohmic contact by the fabrication
of WO3/Ti-WOx/TiHyOz homo/heterojunction on a WO3 photocatalyst using ball
milling. The morphology and structural characterizations of the material are
obtained using UV-vis, SEM/EDS, XRD, Raman spectroscopy, and XPS. It is
revealed that titanium hydride (TiH2) facilitates simultaneous WO3 reduction
and cation doping, which generates intervalent W ions (W5+, W4+) with oxygen
deficiency, leading to the formation of new band structures at the
WO3/Ti-WOx/TiHyOz interface. As a result, the homo/heterojunction significantly
extends light absorption above 400 nm and facilitates the spatial separation of
photoexcited carriers, which significantly enhances the photocatalytic
performance to degrade azo-dye water pollutants under visible light
irradiation.


title:
Stochastic aspects of crack deflection and crack path prediction in
  short fiber reinforced polymer matrix composites

abstract:
  Owing to the production process, short fiber reinforced composites exhibit a
pronounced anisotropy of both elastic properties and crack growth resistance.
In particular the latter issue has a major impact on crack deflection and
inevitably has to be taken into account for the sake of an accurate prediction
of crack paths. The perpendicular axes of transverse isotropy are associated
with the fiber orientations, whereupon a crack in transverse direction
encounters the largest fracture toughness. While the local mean fiber
orientations in polymer matrix composites are determined by the injection
molding process, their statistical fluctuations can approximately be described
in terms of Gaussian random field models. Furthermore, statistical variations
of the volume fraction of fibers and the fiber-matrix adhesion give rise to
stochasticity of the local ratio of fracture toughness anisotropy. Influencing
factors of prediction regions of crack paths obtained from finite element
simulations with an adapted J-integral deflection criterion are investigated,
just as stochastic aspects of bifurcation phenomena of crack deflection
observed under mode-I loading.


title: Information Flow in Deep Neural Networks

abstract:
  Although deep neural networks have been immensely successful, there is no
comprehensive theoretical understanding of how they work or are structured. As
a result, deep networks are often seen as black boxes with unclear
interpretations and reliability. Understanding the performance of deep neural
networks is one of the greatest scientific challenges. This work aims to apply
principles and techniques from information theory to deep learning models to
increase our theoretical understanding and design better algorithms. We first
describe our information-theoretic approach to deep learning. Then, we propose
using the Information Bottleneck (IB) theory to explain deep learning systems.
The novel paradigm for analyzing networks sheds light on their layered
structure, generalization abilities, and learning dynamics. We later discuss
one of the most challenging problems of applying the IB to deep neural networks
- estimating mutual information. Recent theoretical developments, such as the
neural tangent kernel (NTK) framework, are used to investigate generalization
signals. In our study, we obtained tractable computations of many
information-theoretic quantities and their bounds for infinite ensembles of
infinitely wide neural networks. With these derivations, we can determine how
compression, generalization, and sample size pertain to the network and how
they are related. At the end, we present the dual Information Bottleneck
(dualIB). This new information-theoretic framework resolves some of the IB's
shortcomings by merely switching terms in the distortion function. The dualIB
can account for known data features and use them to make better predictions
over unseen examples. An analytical framework reveals the underlying structure
and optimal representations, and a variational framework using deep neural
network optimization validates the results.


title: On the role of the microstructure in the deformation of porous solids

abstract:
  This study explores the role that the microstructure plays in determining the
macroscopic static response of porous elastic continua and exposes the
occurrence of position-dependent nonlocal effects that are strictly correlated
to the configuration of the microstructure. Then, a nonlocal continuum theory
based on variable-order fractional calculus is developed in order to accurately
capture the complex spatially distributed nonlocal response. The remarkable
potential of the fractional approach is illustrated by simulating the nonlinear
thermoelastic response of porous beams. The performance, evaluated both in
terms of accuracy and computational efficiency, is directly contrasted with
high-fidelity finite element models that fully resolve the pores' geometry.
Results indicate that the reduced-order representation of the porous
microstructure, captured by the synthetic variable-order parameter, offers a
robust and accurate representation of the multiscale material architecture that
largely outperforms classical approaches based on the concept of average
porosity.


title:
Ge-Ge$_{0.92}$Sn$_{0.08}$ core-shell single nanowire infrared
  photodetector with superior characteristics for on-chip optical communication

abstract:
  Recent development on Ge$_{1-x}$Sn$_x$ nanowires with high Sn content, beyond
its solid solubility limit, make them attractive for all group-IV Si-integrated
infrared photonics at nanoscale. Herein, we report a chemical vapour
deposition-grown high Sn-content Ge-Ge$_{0.92}$Sn$_{0.08}$ core-shell based
single nanowire photodetector operating at the optical communication wavelength
of 1.55 $\mu$m. The atomic concentration of Sn in nanowires has been studied
using X-ray photoelectron and Raman spectroscopy data. A
metal-semiconductor-metal based single nanowire photodetector, fabricated via
electron beam lithography process, exhibits significant room-temperature
photoresponse even at zero bias. In addition to the high-crystalline quality
and identical shell composition of the nanowire, the efficient collection of
photogenerated carriers under an external electric field result in the superior
responsivity and photoconductive gain as high as ~70.8 A/W and ~57,
respectively at an applied bias of -1.0 V. The extra-ordinary performance of
the fabricated photodetector demonstrates the potential of GeSn nanowires for
future Si CMOS compatible on-chip optical communication device applications.


title:
$Ab$ $initio$ study of magnetic tunnel junctions based on half-metallic
  and spin-gapless semiconducting Heusler compounds: Reconfigurable diode and
  inverse TMR effect for magnetic memory and logic applications

abstract:
  Magnetic tunnel junctions (MTJs) have attracted strong research interest
within the last decades due to their potential use as non-volatile memory such
as MRAM as well as for magnetic logic applications. Half-metallic magnets
(HMMs) have been suggested as ideal electrode materials for MTJs to achieve an
extremely large tunnel magnetoresistance (TMR) effect. Despite their high TMR
ratios, MTJs based on HMMs do not exhibit current rectification, i.e., a diode
effect, which was achieved in a novel MTJ concept based on HMMs and type-II
spin-gapless semiconductors (SGSs). The proposed concept has been recently
experimentally demonstrated using Heusler compounds. In the present work, we
investigate from first-principles MTJs based on type-II SGS and HMM quaternary
Heusler compounds FeVTaAl, FeVTiSi, MnVTiAl, and CoVTiSb. Our $ab$ $initio$
quantum transport calculations based on a non-equilibrium Green's function
method have demonstrated that the MTJs exhibit current rectification with
relatively high on/off ratios. We show that, in contrast to conventional
semiconductor diodes, the rectification bias voltage window (or breakdown
voltage) of the MTJs is limited by the spin gap of the HMM and SGS Heusler
compounds, which can be tuned by doping the electrode materials. A unique
feature of the present MTJs is that the diode effect can be configured
dynamically, i.e., depending on the relative orientation of the magnetization
of the electrodes, the MTJ allows the electrical current to pass either in one
or the other direction, which leads to an inverse TMR effect. The combination
of nonvolatility, reconfigurable diode functionality, tunable rectification
voltage window, and high Curie temperature of the electrode materials make the
proposed MTJs very promising for room temperature spintronic applications and
opens new ways to magnetic memory and logic concepts as well as logic-in-memory
computing.


title:
Stability of line-node semimetals with strong Coulomb interactions and
  properties of the symmetry-broken state

abstract:
  We employ diagrammatic Monte Carlo simulations to establish criteria for the
stability of line-node semimetals in the presence of Coulomb interactions. Our
results indicate a phase transition to a chiral insulating state that occurs at
a finite interaction threshold which we determine. We also compute the Landau
levels for out-of-plane and in-plane magnetic fields in the symmetric and
symmetry-broken phases. We find that the magnetic field couples to the chiral
order parameter, implying that this degree of freedom can be manipulated in
situ in experiments. Finally, we check the existence of edge states in the
symmetry-broken phase. On the system's boundary, we note that the metallic
"drum-head" states that exist in the symmetric phase are gapped out. However,
the symmetry-broken phase permits topological defects in the macroscopic order
parameter in the form of domain walls, which host metallic "interface states."
These consist of line-like gap-closings that occur on the two-dimensional
interfaces.


title:
Enhanced light collection from a gallium nitride color center using a
  near index-matched solid immersion lens

abstract:
  Among the wide-bandgap compound semiconductors, gallium nitride is the most
widely available material due to its prevalence in the solid state lighting and
high-speed/high-power electronics industries. It is now known that GaN is one
of only a handful of materials to host color centers that emit quantum light at
room temperature. In this paper, we report on a bright color center in a
semi-polar gallium nitride substrate, emitting at room temperature in the
near-infrared. We show that a hemispherical solid immersion lens, near index
matched to the semiconductor, can be used to enhance the photon collection
efficiency by a factor of $4.3\pm0.1$, whilst improving the lateral resolution
by a factor equal to the refractive index of the lens.

categories: physics.optics cond-mat.mtrl-sci physics.app-ph quant-ph


title:
Energy Tank-Based Policies for Robust Aerial Physical Interaction with
  Moving Objects

abstract:
  Although manipulation capabilities of aerial robots greatly improved in the
last decade, only few works addressed the problem of aerial physical
interaction with dynamic environments, proposing strongly model-based
approaches. However, in real scenarios, modeling the environment with high
accuracy is often impossible. In this work we aim at developing a control
framework for OMAVs for reliable physical interaction tasks with articulated
and movable objects in the presence of possibly unforeseen disturbances, and
without relying on an accurate model of the environment. Inspired by previous
applications of energy-based controllers for physical interaction, we propose a
passivity-based impedance and wrench tracking controller in combination with a
momentum-based wrench estimator. This is combined with an energy-tank framework
to guarantee the stability of the system, while energy and power flow-based
adaptation policies are deployed to enable safe interaction with any type of
passive environment. The control framework provides formal guarantees of
stability, which is validated in practice considering the challenging task of
pushing a cart of unknown mass, moving on a surface of unknown friction, as
well as subjected to unknown disturbances. For this scenario, we present,
evaluate and discuss three different policies.


title:
Long-range electron-electron interactions in quantum dot systems and
  applications in quantum chemistry

abstract:
  Long-range interactions play a key role in several phenomena of quantum
physics and chemistry. To study these phenomena, analog quantum simulators
provide an appealing alternative to classical numerical methods. Gate-defined
quantum dots have been established as a platform for quantum simulation, but
for those experiments the effect of long-range interactions between the
electrons did not play a crucial role. Here we present the first detailed
experimental characterization of long-range electron-electron interactions in
an array of gate-defined semiconductor quantum dots. We demonstrate significant
interaction strength among electrons that are separated by up to four sites,
and show that our theoretical prediction of the screening effects matches well
the experimental results. Based on these findings, we investigate how
long-range interactions in quantum-dot arrays may be utilized for analog
simulations of artificial quantum matter. We numerically show that about ten
quantum dots are sufficient to observe binding for a one-dimensional $H_2$-like
molecule. These combined experimental and theoretical results pave the way for
future quantum simulations with quantum dot arrays and benchmarks of numerical
methods in quantum chemistry.


title: Variational quantum solutions to the Shortest Vector Problem

abstract:
  A fundamental computational problem is to find a shortest non-zero vector in
Euclidean lattices, a problem known as the Shortest Vector Problem (SVP). This
problem is believed to be hard even on quantum computers and thus plays a
pivotal role in post-quantum cryptography. In this work we explore how
(efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may be used to
solve SVP. Specifically, we map the problem to that of finding the ground state
of a suitable Hamiltonian. In particular, (i) we establish new bounds for
lattice enumeration, this allows us to obtain new bounds (resp.~estimates) for
the number of qubits required per dimension for any lattices (resp.~random
q-ary lattices) to solve SVP; (ii) we exclude the zero vector from the
optimization space by proposing (a) a different classical optimisation loop or
alternatively (b) a new mapping to the Hamiltonian. These improvements allow us
to solve SVP in dimension up to 28 in a quantum emulation, significantly more
than what was previously achieved, even for special cases. Finally, we
extrapolate the size of NISQ devices that is required to be able to solve
instances of lattices that are hard even for the best classical algorithms and
find that with approximately $10^3$ noisy qubits such instances can be tackled.


title:
Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank
  Metric

abstract:
  Codes in the sum-rank metric have various applications in error control for
multishot network coding, distributed storage and code-based cryptography.
Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as
subclasses and fulfill the Singleton-like bound in the sum-rank metric with
equality. We propose the first known error-erasure decoder for LRS codes to
unleash their full potential for multishot network coding. The presented
syndrome-based Berlekamp-Massey-like error-erasure decoder can correct $t_F$
full errors, $t_R$ row erasures and $t_C$ column erasures up to $2t_F + t_R +
t_C \leq n-k$ in the sum-rank metric requiring at most $\mathcal{O}(n^2)$
operations in $\mathbb{F}_{q^m}$, where $n$ is the code's length and $k$ its
dimension. We show how the proposed decoder can be used to correct errors in
the sum-subspace metric that occur in (noncoherent) multishot network coding.


title:
Asymptotic behavior of small solutions of quadratic congruences in three
  variables modulo prime powers

abstract:
  Let $p>5$ be a fixed prime and assume that $\alpha_1,\alpha_2,\alpha_3$ are
coprime to $p$. We study the asymptotic behavior of small solutions of
congruences of the form $\alpha_1x_1^2+\alpha_2x_2^2+\alpha_3x_3^2\equiv
0\bmod{q}$ with $q=p^n$, where $\max\{|x_1|,|x_2|,|x_3|\}\le N$ and
$(x_1x_2x_3,p)=1$. (In fact, we consider a smoothed version of this problem.)
If $\alpha_1,\alpha_2,\alpha_3$ are fixed and $n\rightarrow \infty$, we
establish an asymptotic formula (and thereby the existence of such solutions)
under the condition $N\gg q^{1/2+\varepsilon}$. If these coefficients are
allowed to vary with $n$, we show that this formula holds if $N\gg
q^{11/18+\varepsilon}$. The latter should be compared with a result by
Heath-Brown who established the existence of non-zero solutions under the
condition $N \gg q^{3/5+\varepsilon}$ for odd square-free moduli $q$.


title: Stability and causality of Carter's multifluid theory

abstract:
  Stability and causality are studied for linear perturbations about
equilibrium in Carter's multifluid theory. Our stability analysis is grounded
on the requirement that the entropy of the multifluid, plus that of the
environment, must be maximised at equilibrium. This allows us to compute a
quadratic Lyapunov functional, whose positive definiteness implies stability.
Furthermore, we verify explicitly that, also for multifluids, thermodynamic
stability implies linear causality. As a notable stability condition, we find
that the entrainment matrix must always be positive definite, confirming a
widespread intuition.


title: Radonification of a cylindrical L\'evy process

abstract:
  In this work we present a direct proof about radonification of a cylindrical
L\'evy process. The radonification technique has been very useful to define an
genuine stochastic process starting from a cylindrical process, this is
possible thanks to the Hilbert-Schmidt operators. With this work we want to
propose a self-contained simple proofs who those who are not familiar with this
method, and also present our result which it is apply the radonification method
to the case of a cylindrical L\'evy process.


title:
Temporal Properties of Vaccine Effectiveness Measures in Presence of
  Multiple Pathogen Variants and Multiple Vaccines

abstract:
  Vaccine effectiveness (VE) is typically defined as incidence rate ratio,
cumulative-risk ratio, or odds ratio. The VE based on incidence rate ratio is
known to be time-invariant over the study period for leaky action vaccines and,
the VE based on cumulative-risk ratio is time-invariant for all-or-none action
vaccines. Consequently, these VE measures are recommended as appropriate
measures of VE for leaky and all-or-none vaccines, respectively. However, in
diseases with multiple pathogen variants and multiple vaccines, investigators
may also be interested in variant-specific VE of a vaccine, the relative VE of
a vaccine against two variants, or the relative VE of different vaccines
against a given variant. In this multi-variant and multi-vaccine scenario, the
temporal properties of the aforementioned VE measures have not been studied
entirely yet. Furthermore, no general-purpose sample size calculator is
available for either studies that intend to estimate variant-specific VE or
relative VE. As a solution, we define variant-specific and relative VE measures
while accounting for multiple competing pathogen variants. We then propose a
generic mode of action for all-or-none vaccines in a multi-variant setting.
Subsequently, we evaluate the conditions and the extent to which various VE
measures can be time-varying. We show that every VE measure is time-varying for
all-or-none action vaccines in a multi-variant and multi-vaccine scenario. For
leaky vaccines, we show that all measures other than those based on incidence
rate ratios are time-varying. We discuss the practical implications of these
results on VE studies in the context of the commonly used cohort, cumulative
case-control, and test-negative study designs. Lastly, for the multi-variant
and multi-vaccine scenario, we implement sample size calculations for both
variant-specific and relative VE in an R package and an online calculator.


title:
Machine Learning-Aided Discovery of Superionic Solid-State Electrolyte
  for Li-Ion Batteries

abstract:
  Li-Ion Solid-State Electrolytes (Li-SSEs) are a promising solution that
resolves the critical issues of conventional Li-Ion Batteries (LIBs) such as
poor ionic conductivity, interfacial instability, and dendrites growth. In this
study, a platform consisting of a high-throughput screening and a
machine-learning surrogate model for discovering superionic Li-SSEs among
20,237 Li-containing materials is developed. For the training database, the
ionic conductivity of Na SuperIonic CONductor (NASICON) and Li SuperIonic
CONductor (LISICON) type SSEs are obtained from the previous literature. Then,
the chemical descriptor (CD) and additional structural properties are used as
machine-readable features. Li-SSE candidates are selected through the screening
criteria, and the prediction on the ionic conductivity of those is followed.
Then, to reduce uncertainty in the surrogate model, the ensemble method by
considering the best-performing two models is employed, whose mean prediction
accuracy is 0.843 and 0.829, respectively. Furthermore, first-principles
calculations are conducted for confirming the ionic conductivity of the strong
candidates. Finally, six potential superionic Li-SSEs that have not previously
been investigated are proposed. We believe that the constructed platform can
accelerate the search for Li-SSEs with high ionic conductivity at minimum cost.


title: Low-latency Monaural Speech Enhancement with Deep Filter-bank Equalizer

abstract:
  It is highly desirable that speech enhancement algorithms can achieve good
performance while keeping low latency for many applications, such as digital
hearing aids, acoustically transparent hearing devices, and public address
systems. To improve the performance of traditional low-latency speech
enhancement algorithms, a deep filter-bank equalizer (FBE) framework was
proposed, which integrated a deep learning-based subband noise reduction
network with a deep learning-based shortened digital filter mapping network. In
the first network, a deep learning model was trained with a controllable small
frame shift to satisfy the low-latency demand, i.e., $\le$ 4 ms, so as to
obtain (complex) subband gains, which could be regarded as an adaptive digital
filter in each frame. In the second network, to reduce the latency, this
adaptive digital filter was implicitly shortened by a deep learning-based
framework, and was then applied to noisy speech to reconstruct the enhanced
speech without the overlap-add method. Experimental results on the WSJ0-SI84
corpus indicated that the proposed deep FBE with only 4-ms latency achieved
much better performance than traditional low-latency speech enhancement
algorithms in terms of the indices such as PESQ, STOI, and the amount of noise
reduction.


title: Quantitative Strongest Post

abstract:
  We present a novel strongest-postcondition-style calculus for quantitative
reasoning about non-deterministic programs with loops. Whereas existing
quantitative weakest pre allows reasoning about the value of a quantity after a
program terminates on a given initial state, quantitative strongest post allows
reasoning about the value that a quantity had before the program was executed
and reached a given final state. We show how strongest post enables reasoning
about the flow of quantitative information through programs. Similarly to
weakest liberal preconditions, we also develop a quantitative strongest liberal
post. As a byproduct, we obtain the entirely unexplored notion of strongest
liberal postconditions and show how these foreshadow a potential new program
logic - partial incorrectness logic - which would be a more liberal version of
O'Hearn's recent incorrectness logic.


title: Speech Analysis for Automatic Mania Assessment in Bipolar Disorder

abstract:
  Bipolar disorder is a mental disorder that causes periods of manic and
depressive episodes. In this work, we classify recordings from Bipolar Disorder
corpus that contain 7 different tasks, into hypomania, mania, and remission
classes using only speech features. We perform our experiments on splitted
tasks from the interviews. Best results achieved on the model trained with 6th
and 7th tasks together gives 0.53 UAR (unweighted average recall) result which
is higher than the baseline results of the corpus.


title:
Wukong: 100 Million Large-scale Chinese Cross-modal Pre-training Dataset
  and A Foundation Framework

abstract:
  Vision-Language Pre-training (VLP) models have shown remarkable performance
on various downstream tasks. Their success heavily relies on the scale of
pre-trained cross-modal datasets. However, the lack of large-scale datasets and
benchmarks in Chinese hinders the development of Chinese VLP models and broader
multilingual applications. In this work, we release a large-scale Chinese
cross-modal dataset named Wukong, containing 100 million Chinese image-text
pairs from the web. Wukong aims to benchmark different multi-modal pre-training
methods to facilitate the VLP research and community development. Furthermore,
we release a group of models pre-trained with various image encoders
(ViT-B/ViT-L/SwinT) and also apply advanced pre-training techniques into VLP
such as locked-image text tuning, token-wise similarity in contrastive
learning, and reduced-token interaction. Extensive experiments and a deep
benchmarking of different downstream tasks are also provided. Experiments show
that Wukong can serve as a promising Chinese pre-training dataset and benchmark
for different cross-modal learning methods. For the zero-shot image
classification task on 10 datasets, our model achieves an average accuracy of
73.03%. For the image-text retrieval task,our model achieves a mean recall of
71.6% on AIC-ICC which is 12.9% higher than the result of WenLan 2.0. More
information can refer to https://wukong-dataset.github.io/wukong-dataset/.


title: Probabilistic Embeddings Revisited

abstract:
  In recent years, deep metric learning and its probabilistic extensions
achieved state-of-the-art results in a face verification task. However, despite
improvements in face verification, probabilistic methods received little
attention in the community. It is still unclear whether they can improve image
retrieval quality. In this paper, we present an extensive comparison of
probabilistic methods in verification and retrieval tasks. Following the
suggested methodology, we outperform metric learning baselines using
probabilistic methods and propose several directions for future work and
improvements.


title: Punctuation restoration in Swedish through fine-tuned KB-BERT

abstract:
  Presented here is a method for automatic punctuation restoration in Swedish
using a BERT model. The method is based on KB-BERT, a publicly available,
neural network language model pre-trained on a Swedish corpus by National
Library of Sweden. This model has then been fine-tuned for this specific task
using a corpus of government texts. With a lower-case and unpunctuated Swedish
text as input, the model is supposed to return a grammatically correct
punctuated copy of the text as output. A successful solution to this problem
brings benefits for an array of NLP domains, such as speech-to-text and
automated text. Only the punctuation marks period, comma and question marks
were considered for the project, due to a lack of data for more rare marks such
as semicolon. Additionally, some marks are somewhat interchangeable with the
more common, such as exclamation points and periods. Thus, the data set had all
exclamation points replaced with periods. The fine-tuned Swedish BERT model,
dubbed prestoBERT, achieved an overall F1-score of 78.9. The proposed model
scored similarly to international counterparts, with Hungarian and Chinese
models obtaining F1-scores of 82.2 and 75.6 respectively. As further
comparison, a human evaluation case study was carried out. The human test group
achieved an overall F1-score of 81.7, but scored substantially worse than
prestoBERT on both period and comma. Inspecting output sentences from the model
and humans show satisfactory results, despite the difference in F1-score. The
disconnect seems to stem from an unnecessary focus on replicating the exact
same punctuation used in the test set, rather than providing any of the number
of correct interpretations. If the loss function could be rewritten to reward
all grammatically correct outputs, rather than only the one original example,
the performance could improve significantly for both prestoBERT and the human
group.


title:
Adiabatic conversion between gigahertz quasi-Rayleigh and quasi-Love
  modes for phononic integrated circuits

abstract:
  Unsuspended phononic integrated circuits have been proposed for on-chip
acoustic information processing. Limited by the operation mechanism of a
conventional interdigital transducer, the excitation of the quasi-Love mode in
GaN-on-Sapphire is inefficient and thus a high-efficiency Rayleigh-to-Love mode
converter is of great significance for future integrated phononic devices.
Here, we propose a high-efficiency and robust phononic mode converter based on
an adiabatic conversion mechanism. Utilizing the anisotropic elastic property
of the substrate, the adiabatic mode converter is realized by a simple tapered
phononic waveguide. A conversion efficiency exceeds $98\%$ with a
$3\,\mathrm{dB}$ bandwidth of $1.7\,\mathrm{GHz}$ can be realized for phononic
waveguides working at GHz frequency band, and excellent tolerance to the
fabrication errors is also numerically validated. The device that we proposed
can be useful in both classical and quantum phononic information processing,
and the adiabatic mechanism could be generalized to other phononic device
designs.


title:
DS4DH at TREC Health Misinformation 2021: Multi-Dimensional Ranking
  Models with Transfer Learning and Rank Fusion

abstract:
  This paper describes the work of the Data Science for Digital Health (DS4DH)
group at the TREC Health Misinformation Track 2021. The TREC Health
Misinformation track focused on the development of retrieval methods that
provide relevant, correct and credible information for health related searches
on the Web. In our methodology, we used a two-step ranking approach that
includes i) a standard retrieval phase, based on BM25 model, and ii) a
re-ranking phase, with a pipeline of models focused on the usefulness,
supportiveness and credibility dimensions of the retrieved documents. To
estimate the usefulness, we classified the initial rank list using pre-trained
language models based on the transformers architecture fine-tuned on the MS
MARCO corpus. To assess the supportiveness, we utilized BERT-based models
fine-tuned on scientific and Wikipedia corpora. Finally, to evaluate the
credibility of the documents, we employed a random forest model trained on the
Microsoft Credibility dataset combined with a list of credible sites. The
resulting ranked lists were then combined using the Reciprocal Rank Fusion
algorithm to obtain the final list of useful, supporting and credible
documents. Our approach achieved competitive results, being top-2 in the
compatibility measurement for the automatic runs. Our findings suggest that
integrating automatic ranking models created for each information quality
dimension with transfer learning can increase the effectiveness of
health-related information retrieval.


title:
Study on the Kinetics of Rayleigh Particle Jets Converging by Laser
  Beams

abstract:
  This paper discusses laser-induced flow stabilizing of Rayleigh particle
jets. Laser technology, has important applications in micro/nano-scale static
monomer particle operations, such as optical tweezers, or is used for the
passive measurement of macroscopic physical features of particle groups.
However, it is relatively rare for the laser beam to directly interfere with
the behavior of particle populations dynamically, so as to achieve the purpose
of instant group manipulations. Based on the theoretical analysis of particle
dynamics and hydrodynamic stability theory, the effects of light induced
convergence on rarified jets (as a point source emitting particle off a nozzle)
and denser jets consists of Rayleigh sized particles have been considered. For
rarified particle jet's analysis, compared with the classical vacuum
evaporation deposition theory, we found that the laser positively guided the
movement of particles, leading their pathes into more concentrated targets.
Such convergence effect also happens in the case of denser Rayleigh particle
jets. Particle dynamics simulations and hydrodynamic stability analysis
mutually authenticated that the optical field forces suppress the instability
both of long-wave and short-wave on particle jet interfaces, and have
broad-spectrum stabilization characteristics. Therefor, diffusive particles in
vacuum evaporation can also have very good targeted aggregations by laser.


title: Funnel control of linear systems under output measurement losses

abstract:
  We consider tracking control of linear minimum phase systems with known
arbitrary relative degree which are subject to possible output measurement
losses. We provide a control law which guarantees the evolution of the tracking
error within a (shifted) prescribed performance funnel whenever the output
signal is available. The result requires a maximal duration of measurement
losses and a minimal time of measurement availability, which both strongly
depend on the internal dynamics of the system, and are derived explicitly. The
controller is illustrated by a simulation of a mass-on-car system.


title: Random zonotopes and valuations

abstract:
  We define a random zonotope in Euclidean space, by adding finitely many
random segments, which are independently and identically distributed. For this
random polytope, we determine, under a mild assumption on the distribution, the
expectations of the intrinsic volumes, more generally, the expectations of
suitable valuations. We also prove a central limit theorem for a valuation
evaluated at these random zonotopes.


title:
A structure-preserving finite element approximation of surface diffusion
  for curve networks and surface clusters

abstract:
  We consider the evolution of curve networks in two dimensions (2d) and
surface clusters in three dimensions (3d). The motion of the interfaces is
described by surface diffusion, with boundary conditions at the triple junction
points/lines, where three interfaces meet, and at the boundary points/lines,
where an interface meets a fixed planar boundary. We propose a parametric
finite element method based on a suitable variational formulation. The
constructed method is semi-implicit and can be shown to satisfy the volume
conservation of each enclosed bubble and the unconditional energy-stability,
thus preserving the two fundamental geometric structures of the flow. Besides,
the method has very good properties with respect to the distribution of mesh
points, thus no mesh smoothing or regularization technique is required. A
generalization of the introduced scheme to the case of anisotropic surface
energies and non-neutral external boundaries is also considered. Numerical
results are presented for the evolution of two-dimensional curve networks and
three-dimensional surface clusters in the cases of both isotropic and
anisotropic surface energies.


title:
Aspect Based Sentiment Analysis Using Spectral Temporal Graph Neural
  Network

abstract:
  The objective of Aspect Based Sentiment Analysis is to capture the sentiment
of reviewers associated with different aspects. However, complexity of the
review sentences, presence of double negation and specific usage of words found
in different domains make it difficult to predict the sentiment accurately and
overall a challenging natural language understanding task. While recurrent
neural network, attention mechanism and more recently, graph attention based
models are prevalent, in this paper we propose graph Fourier transform based
network with features created in the spectral domain. While this approach has
found considerable success in the forecasting domain, it has not been explored
earlier for any natural language processing task. The method relies on creating
and learning an underlying graph from the raw data and thereby using the
adjacency matrix to shift to the graph Fourier domain. Subsequently, Fourier
transform is used to switch to the frequency (spectral) domain where new
features are created. These series of transformation proved to be extremely
efficient in learning the right representation as we have found that our model
achieves the best result on both the SemEval-2014 datasets, i.e., "Laptop" and
"Restaurants" domain. Our proposed model also found competitive results on the
two other recently proposed datasets from the e-commerce domain.


title: Multi-scale Attention Guided Pose Transfer

abstract:
  Pose transfer refers to the probabilistic image generation of a person with a
previously unseen novel pose from another image of that person having a
different pose. Due to potential academic and commercial applications, this
problem is extensively studied in recent years. Among the various approaches to
the problem, attention guided progressive generation is shown to produce
state-of-the-art results in most cases. In this paper, we present an improved
network architecture for pose transfer by introducing attention links at every
resolution level of the encoder and decoder. By utilizing such dense
multi-scale attention guided approach, we are able to achieve significant
improvement over the existing methods both visually and analytically. We
conclude our findings with extensive qualitative and quantitative comparisons
against several existing methods on the DeepFashion dataset.


title: Gravitational electron-positron scattering

abstract:
  A scattering process with gravitons as an intermediate state is investigated.
To study such a scattering, the Gravitoelectromagnetism theory is considered.
It is a gravitational theory built on the analogy between gravity and
electromagnetism. The complete Lagrangian formulation of the
gravitoelectromagnetic theory includes interactions of gravitons with fermions
and photons that leads us to calculate their scattering amplitudes and
cross-sections. In this context, the gravitational cross-section of the
$e^{-}+e^{+}\longrightarrow\mu^{-}+\mu^{+}$ scattering process is obtained. A
comparison between the electromagnetic and gravitational cross-sections is
made.


title:
Modelling and forecasting patient recruitment in clinical trials with
  patients' dropout

abstract:
  This paper focuses on statistical modelling and prediction of patient
recruitment in clinical trials accounting for patients dropout. The recruitment
model is based on a Poisson-gamma model introduced by Anisimov and Fedorov
(2007), where the patients arrive at different centres according to Poisson
processes with rates viewed as gamma-distributed random variables. Each patient
can drop the study during some screening period. Managing the dropout process
is of a major importance but data related to dropout are rarely correctly
collected. In this paper, a few models of dropout are proposed. The technique
for estimating parameters and predicting the number of recruited patients over
time and the recruitment time is developed. Simulation results confirm the
applicability of the technique and thus, the necessity to account for patients
dropout at the stage of forecasting recruitment in clinical trials.


title: Galactic halo magnetic fields and UHECR deflections

abstract:
  In the first part of our study, we consider synchrotron emission from
electrons in the Galactic halo region. Utilising a simple analytical expression
for the non-thermal electron distribution and a toy magnetic field model, we
simulate polarised synchrotron emission maps at 30~GHz. By comparing these maps
with observational data, we obtain constraints on the parameters of our toy
magnetic field model. In the second half of our study, we use the range of
parameter values obtained for our toy magnetic field model, and determine the
arrival directions and suppression factors of ultra high energy cosmic rays
(UHECRs) from potential sources at different locations. Our model predicts high
suppression levels for UHECRs up to 5% and large spread angles for parameter
sets obtained from 1{\sigma} constraints. These deductions form a convincing
argument for incorporating Galactic halo bubbles in Galactic magnetic field
modelling.


title:
Design of Explainability Module with Experts in the Loop for
  Visualization and Dynamic Adjustment of Continual Learning

abstract:
  Continual learning can enable neural networks to evolve by learning new tasks
sequentially in task-changing scenarios. However, two general and related
challenges should be overcome in further research before we apply this
technique to real-world applications. Firstly, newly collected novelties from
the data stream in applications could contain anomalies that are meaningless
for continual learning. Instead of viewing them as a new task for updating, we
have to filter out such anomalies to reduce the disturbance of extremely
high-entropy data for the progression of convergence. Secondly, fewer efforts
have been put into research regarding the explainability of continual learning,
which leads to a lack of transparency and credibility of the updated neural
networks. Elaborated explanations about the process and result of continual
learning can help experts in judgment and making decisions. Therefore, we
propose the conceptual design of an explainability module with experts in the
loop based on techniques, such as dimension reduction, visualization, and
evaluation strategies. This work aims to overcome the mentioned challenges by
sufficiently explaining and visualizing the identified anomalies and the
updated neural network. With the help of this module, experts can be more
confident in decision-making regarding anomaly filtering, dynamic adjustment of
hyperparameters, data backup, etc.


title:
Wasserstein Solution Quality and the Quantum Approximate Optimization
  Algorithm: A Portfolio Optimization Case Study

abstract:
  Optimizing of a portfolio of financial assets is a critical industrial
problem which can be approximately solved using algorithms suitable for quantum
processing units (QPUs). We benchmark the success of this approach using the
Quantum Approximate Optimization Algorithm (QAOA); an algorithm targeting
gate-model QPUs. Our focus is on the quality of solutions achieved as
determined by the Normalized and Complementary Wasserstein Distance, $\eta$,
which we present in a manner to expose the QAOA as a transporter of
probability. Using $\eta$ as an application specific benchmark of performance,
we measure it on selection of QPUs as a function of QAOA circuit depth $p$. At
$n = 2$ (2 qubits) we find peak solution quality at $p=5$ for most systems and
for $n = 3$ this peak is at $p=4$ on a trapped ion QPU. Increasing solution
quality with $p$ is also observed using variants of the more general Quantum
Alternating Operator Ans\"{a}tz at $p=2$ for $n = 2$ and $3$ which has not been
previously reported. In identical measurements, $\eta$ is observed to be
variable at a level exceeding the noise produced from the finite number of
shots. This suggests that variability itself should be regarded as a QPU
performance benchmark for given applications. While studying the ideal
execution of QAOA, we find that $p=1$ solution quality degrades when the
portfolio budget $B$ approaches $n/2$ and increases when $B \approx 1$ or
$n-1$. This trend directly corresponds to the binomial coefficient $nCB$ and is
connected with the recently reported phenomenon of reachability deficits.
Derivative-requiring and derivative-free classical optimizers are benchmarked
on the basis of the achieved $\eta$ beyond $p=1$ to find that derivative-free
optimizers are generally more effective for the given computational resources,
problem sizes and circuit depths.


title:
Monge solutions and uniqueness in multi-marginal optimal transport:
  weaker conditions on the cost, stronger conditions on the marginals

abstract:
  We establish a general condition on the cost function to obtain uniqueness
and Monge solutions in the multi-marginal optimal transport problem, under the
assumption that a given collection of the marginals are absolutely continuous
with respect to local coordinates. When only the first marginal is assumed to
be absolutely continuous, our condition is equivalent to the twist on splitting
sets condition found in [23]. In addition, it is satisfied by the special cost
functions in our earlier work [32, 33], when absolute continuity is imposed on
certain other collections of marginals. We also present several new examples of
cost functions which violate the twist on splitting sets condition but satisfy
the new condition introduced here; we therefore obtain Monge solution and
uniqueness results for these cost functions, under regularity conditions on an
appropriate subset of the marginals.


title:
A model for the canonical algebras of bimodules type (1, 4) over
  truncated polynomial rings

abstract:
  Let $k=\mathbb{C}(\!(\epsilon)\!)$ be the field of complex Laurent series. We
use Galois descent techniques to show that the simple regular representations
of the species of type $(1,\, 4)$ over $k$ are naturally parametrized by the
closed points of $\mathrm{Spec}(k[x])\dot{\cup}\{1,\,2\}$. Moreover we provide
weak normal forms for those representations. We use our representatives of the
simple regular representations to describe the canonical algebras associated to
the species of type (1, 4) over k. This suggest a model of those algebras in
the sense of the work of Geiss, Leclerc and Sch\"oer [GLS17] and [GLS20].


title: Beyond symmetry in generalized Petersen graphs

abstract:
  A graph is a core or unretractive if all its endomorphisms are automorphisms.
Well-known examples of cores include the Petersen graph and the graph of the
dodecahedron -- both generalized Petersen graphs. We characterize the
generalized Petersen graphs that are cores. A simple characterization of
endomorphism-transitive generalized Petersen graphs follows. This extends the
characterization of vertex-transitive generalized Petersen graphs due to
Frucht, Graver, and Watkins and solves a problem of Fan and Xie.
  Moreover, we study generalized Petersen graphs that are (underlying graphs
of) Cayley graphs of monoids. We show that this is the case for the Petersen
graph, answering a recent mathoverflow question, for the Desargues graphs, and
for the dodecahedron -- answering a question of Knauer and Knauer. Moreover, we
characterize the infinite family of generalized Petersen graphs that are Cayley
graph of a monoid with generating connection set of size two. This extends
Nedela and \v{S}koviera's characterization of generalized Petersen graphs that
are group Cayley graphs and complements results of Hao, Gao, and Luo.


title: Molecular origin of driving-dependent friction in fluids

abstract:
  The friction coefficient of fluids may become a function of the velocity at
increased external driving. This non-Newtonian behavior is of general
theoretical interest as well as of great practical importance, e.g., for the
design of lubricants. While the effect has been observed in large-scale
atomistic simulations of bulk liquids, its theoretical formulation and
microscopic origin is not well understood. Here we use dissipation-corrected
targeted molecular dynamics, which pulls apart two tagged liquid molecules in
the presence of surrounding molecules and analyzes this nonequilibrium process
via a generalized Langevin equation. The approach is based on a second-order
cumulant expansion of Jarzynski's identity, which is shown to be valid for
fluids and therefore allows for an exact computation of the friction profile as
well of the underlying memory kernel. We show that velocity-dependent friction
in fluids results from an intricate interplay of near-order structural effects
and the non-Markovian behavior of the friction memory kernel. For complex
fluids such as the model lubricant \alkane, the memory kernel exhibits a
stretched-exponential long-time decay, which reflects the multitude of
timescales of the system.


title: Solving Large-Scale Security Constrained AC Optimal Power Flow Problems

abstract:
  In this paper, we study efficient and robust computational methods for
solving the security-constrained alternating current optimal power flow
(SC-ACOPF) problem, a two-stage nonlinear mixed-integer optimization problem
central to the operation of electric power grids. The first-stage problem in
SC-ACOPF determines the operation of the power grid in normal condition, while
the second-stage problem responds to various contingencies of losing
generators, transmission lines, and transformers. The two stages are coupled
through disjunctive constraints, which model generators' active and reactive
power output changes responding to system-wide active power imbalance and
voltage deviations after contingencies. Real-world SC-ACOPF problems may
involve power grids with more than $30$k buses and $22$k contingencies and need
to be solved within 10-45 minutes to get a base case solution with high
feasibility and reasonably good generation cost.
  We develop a comprehensive algorithmic framework to solve SC-ACOPF that meets
the challenge of speed, solution quality, and computation robustness. In
particular, we develop a smoothing technique to approximate disjunctive
constraints into a smooth structure which can be handled by interior-point
solvers; we design a distributed optimization algorithm with convergence
guarantee to solve the two-stage SC-ACOPF model; we propose a screening
procedure to prioritize contingencies; and finally, we develop a reliable and
parallel architecture that integrates all algorithmic components. Extensive
tests on industry-scale systems demonstrate the superior performance of the
proposed algorithms.


title:
Spatially resolved evidence of the impact of quasar driven outflows on
  recent star formation : The case of Mrk 34

abstract:
  We present the results of our spatially resolved investigation into the
interplay between the ages of the stellar populations and the kinematics of the
warm ionised outflows in the well-studied type II quasar Markarian 34.
Utilising IFS data, we determine the spatial distribution of the young stellar
population (YSP; $t_{ysp} < 100 \mbox{ Myr}$) using spectral synthesis
modelling. We also employ the $\mbox{[OIII]}\lambda 5007$ emission line as a
tracer of the warm ionised gas kinematics. We demonstrate a spatial correlation
between the outer edges of the blue-side of the outflow and an enhancement in
the proportion of the YSP flux, suggesting that the outflow is responsible for
triggering star formation in this region. In regions with more highly disrupted
gas kinematics, we find that the proportion of YSP flux is consistent with that
found outside the outflow region, suggesting that the increased disruption is
preventing a similar enhancement in star formation from occurring. Our analysis
suggests that Mrk 34 is an example of quasar driven outflows simultaneously
producing both `positive' and `preventive' feedback, further demonstrating the
complex nature of the relationship between quasars and their host galaxies.


title: On the refined Kaneko-Zagier conjecture for general integer indices

abstract:
  The refined Kaneko-Zagier conjecture claims that the algebras spanned by two
kinds of "completed" finite multiple zeta values, called $\hat{A}$- and
$\hat{S}$-MZVs, are isomorphic. Recently, Komori defined $\hat{S}$-MZVs of
general integer (i.e., not necessarily positive) indices, extending the
existing definition for positive indices. In view of the refined Kaneko-Zagier
conjecture, Komori's work suggests that these extended values are closely
connected to $\hat{A}$-MZVs of general indices, which can be defined in an
obvious way. In this paper, we show that the generalization of the refined
Kaneko-Zagier conjecture for general integer indices is actually deduced from
the conjecture for positive indices. The key ingredient is an inductive formula
for $\hat{A}$-MZVs or $\hat{S}$-MZVs of indices which contain at least one
non-positive entry.


title: Quantum Walks with Indefinite Causal Order

abstract:
  In all existing quantum walk models, the assumption about a pre-existing
fixed background causal structure is always made and has been taken for
granted. Nevertheless, in this work we will get rid of this tacit assumption
especially by introducing indefinite causal order ways of coin tossing and
investigate this modern scenario. We find that an ideal-shape and
fast-spreading uniform distribution can be prepared with our new model. First
we will show how an always-symmetrical instantaneous distribution appears in an
indefinite causal order quantum walk, which then paves the way for deriving
conditions that enables one to interpret an evolved state as a superposition of
its definite causal order counterparts which is however in general prohibited.
This property of temporal superposition of states can be generalized from
two-process scenarios to cases where arbitrary many $\mathcal{N}$ processes are
involved. Finally, we demonstrate how a genuine uniform distribution emerges
from an indefinite causal order quantum walk. Remarkably, besides the ideal
shape of the distribution, our protocol has another powerful advantage, that is
the speed of spatial spreading reaches exactly the theoretical limit in
contrast to conventional cases where one may encounter the well-known issue of
a $1/\sqrt{2}$ degeneration.


title:
Output feedback control with prescribed performance via funnel
  pre-compensator

abstract:
  We study output reference tracking of systems with high relative degree via
output feedback only; this is, tracking where the output derivatives are
unknown. To this end, we prove that the conjunction of the funnel
pre-compensator with a minimum phase system of arbitrary relative degree yields
a system of the same relative degree which is minimum phase as well. The error
between the original system's output and the pre-compensator's output evolves
within a prescribed performance funnel; and moreover, the derivatives of the
funnel pre-compensator's output are known explicitly. Therefore, output
reference tracking with prescribed transient behaviour of the tracking error is
possible without knowledge of the derivatives of the original system's output;
via funnel control schemes for instance.


title:
Solutions of Gross-Pitaevskii Equation with Periodic Potential in
  Dimension Three

abstract:
  Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic
potential in dimension three are studied. It is proven that there is an
extensive "non-resonant" set ${\mathcal G} \subset \mathbb{R}^3$ such that for
every $\vec k\in \mathcal G$ there is a solution asymptotically close to a
plane wave $Ae^{i\langle{ \vec{k}, \vec{x} }\rangle}$ as $|\vec k|\to \infty $,
given $A$ is sufficiently small.


title:
Deep eROSITA observations of the "magnificent seven" isolated neutron
  stars

abstract:
  We report the initial results of deep eROSITA monitoring of the "magnificent
seven" isolated neutron stars (INSs). Thanks to a combination of high count
statistics and good energy resolution, the eROSITA datasets unveil the
increasingly complex energy distribution of these presumably simple thermal
emitters. For three targets, we report the detection of multiple (in some
cases, phase-dependent) spectral absorption features and deviations from the
dominant thermal continuum. Unexpected long-term changes of spectral state and
timing behaviour have additionally been observed for two INSs. The results pose
challenging theoretical questions on the nature of the variations and
absorption features and ultimately impact the modeling of the atmosphere and
cooling of highly magnetised neutron stars.


title: Disentangle VAE for Molecular Generation

abstract:
  Automatic molecule generation plays an important role on drug discovery and
has received a great deal of attention in recent years thanks to deep learning
successful use. Graph-based neural network represents state of the art methods
on automatic molecule generation. However, it is still challenging to generate
molecule with desired properties, which is a core task in drug discovery. In
this paper, we focus on this task and propose a Controllable Junction Tree
Variational Autoencoder (C JTVAE), adding an extractor module into VAE
framework to describe some properties of molecule. Our method is able to
generate similar molecular with desired property given an input molecule.
Experimental results is encouraging.


title:
Chambers in the symplectic cone and stability of symplectomorphism group
  for ruled surface

abstract:
  We continue our previous work to prove that for any non-minimal ruled surface
$(M,\omega)$, the stability under symplectic deformations of $\pi_0, \pi_1$ of
$Symp(M,\omega)$ is guided by embedded $J$-holomorphic curves. Further, we
prove that for any fixed sizes blowups, when the area ratio $\mu$ between the
section and fiber goes to infinity, there is a topological colimit of
$Symp(M,\omega_{\mu}).$ Moreover, when the blowup sizes are all equal to half
the area of the fiber class, we give a topological model of the colimit which
induces non-trivial symplectic mapping classes in $Symp(M,\omega) \cap \rm
Diff_0(M),$ where $\rm Diff_0(M)$ is the identity component of the
diffeomorphism group. These mapping classes are not Dehn twists along
Lagrangian spheres.


title:
Classical superdense coding and communication advantage of a single
  quantum

abstract:
  We analyze the communication utility of a single quantum system when the
sender and receiver share neither any entanglement nor any classical shared
randomness. To this aim, we propose a class of two-party communication games
that cannot be won with a noiseless $1$-bit classical channel, whereas the goal
can be perfectly achieved if the channel is assisted by classical shared
randomness. This resembles an advantage similar to the quantum superdense
coding phenomenon where pre-shared entanglement can enhance communication
utility of a perfect quantum communication line. Quite surprisingly, we show
that a qubit communication without any assistance of classical shared
randomness can achieve the goal, and hence establishes a novel quantum
advantage in the simplest communication scenario. In pursuit of a deeper origin
of this advantage we show that an advantageous quantum strategy must invoke
quantum interference both at the encoding step by the sender and at the
decoding step by the receiver. A subclass of these games can be won
deterministically if the sender communicates some non-classical toy systems
described by symmetric polygonal state spaces. We then proceed to design a
variant of the game that can be won neither with $1$-bit communication nor with
a polygon system, but $1$-qubit communication yields a perfect strategy,
establishing a strict quantum nature of the advantage. To this end, we show
that the quantum advantages are robust against imperfect encodings-decodings,
making the protocols implementable with presently available quantum
technologies.


title: Mapping Interstellar Dust with Gaussian Processes

abstract:
  Interstellar dust corrupts nearly every stellar observation, and accounting
for it is crucial to measuring physical properties of stars. We model the dust
distribution as a spatially varying latent field with a Gaussian process (GP)
and develop a likelihood model and inference method that scales to millions of
astronomical observations. Modeling interstellar dust is complicated by two
factors. The first is integrated observations. The data come from a vantage
point on Earth and each observation is an integral of the unobserved function
along our line of sight, resulting in a complex likelihood and a more difficult
inference problem than in classical GP inference. The second complication is
scale; stellar catalogs have millions of observations. To address these
challenges we develop ziggy, a scalable approach to GP inference with
integrated observations based on stochastic variational inference. We study
ziggy on synthetic data and the Ananke dataset, a high-fidelity mechanistic
model of the Milky Way with millions of stars. ziggy reliably infers the
spatial dust map with well-calibrated posterior uncertainties.


title: Continuous variable quantum state tomography of photoelectrons

abstract:
  We propose a continuous variable quantum state tomography protocol of
electrons which result from the ionization of atoms or molecules by the
absorption of extreme ultraviolet light pulses. Our protocol is benchmarked
against a direct calculation of the quantum state of photoelectrons ejected
from helium and argon in the vicinity of a Fano resonance. In the latter case,
we furthermore distill ion-photoelectron entanglement due to spin-orbit
splitting. This opens new routes towards the investigation of quantum coherence
and entanglement properties on the ultrafast timescale.


title:
Large Deviation Estimates of Selberg's Central Limit Theorem and
  Applications

abstract:
  For $V\sim \alpha \log\log T$ with $0<\alpha<2$, we prove \[
\frac{1}{T}\text{meas}\{t\in [T,2T]: \log|\zeta(1/2+ {\rm i} t)|>V\}\ll
\frac{1}{\sqrt{\log\log T}} e^{-V^2/\log\log T}. \] This improves prior results
of Soundararajan and of Harper on the large deviations of Selberg's Central
Limit Theorem in that range, without the use of the Riemann hypothesis. The
result implies the sharp upper bound for the fractional moments of the Riemann
zeta function proved by Heap, Radziwi{\l}{\l} and Soundararajan. It also shows
a new upper bound for the maximum of the zeta function on short intervals of
length $(\log T)^\theta$, $0<\theta <3$, that is expected to be sharp for
$\theta > 0$. Finally, it yields a sharp upper bound (to order one) for the
moments on short intervals, below and above the freezing transition. The proof
is an adaptation of the recursive scheme introduced by Bourgade,
Radziwi{\l}{\l} and one of the authors to prove fine asymptotics for the
maximum on intervals of length $1$.


title:
Construction of coronal hole and active region magnetohydrostatic
  solutions in two dimensions: Force and energy balance

abstract:
  Coronal holes and active regions are typical magnetic structures found in the
solar atmosphere. We propose several magnetohydrostatic equilibrium solutions
that are representative of these structures in two dimensions. Our models
include the effect of a finite plasma-$\beta$ and gravity, but the distinctive
feature is that we incorporate a thermal structure with properties similar to
those reported by observations. We developed a semi-analytical method to
compute the equilibrium configuration. Using this method, we obtain cold and
under-dense plasma structures in open magnetic fields representing coronal
holes, while in closed magnetic configurations, we achieve the characteristic
hot and over-dense plasma arrangements of active regions. Although coronal
holes and active regions seem to be antagonistic structures, we find that they
can be described using a common thermal structure that depends on the flux
function. In addition to the force balance, the energy balance is included in
the constructed models using an a posteriori approach. From the two-dimensional
computation of thermal conduction and radiative losses in our models, we infer
the required heating function to achieve energy equilibrium. We find that the
temperature dependence on height is an important parameter that may prevent the
system from accomplishing thermal balance at certain spatial locations. The
implications of these results are discussed in detail.


title: Numerical non-integrability of Hexagonal string billiard

abstract:
  We consider a remarkable $C^2$-smooth billiard table introduced by Hans
L.Fetter. It is obtained by the string construction from a regular hexagon for
a special value of the length of the string. It was suggested as a possible
counter-example to the Birkhoff-Poritsky conjecture. In this paper, we
investigate numerically the behavior of this billiard and find chaotic regions
near hyperbolic periodic orbits. They are very small since the billiard table
is nearly circular.


title: Gibbs measures on compact ultra metric spaces

abstract:
  One proves the equivalence of a Gibbs measure and a Gibbs conformal measure
for a dynamical system (G,X) when G is a countably infinite discrete group
acting expansively on a compact ultrametric space X. As an application one
proves for any beta-shift, that the unique equilibrium measure for a function
of summable variation is a Gibbs measure.


title:
Completing the Protostellar Luminosity Function in Cygnus-X with
  SOFIA/FORCAST Imaging

abstract:
  We present a new SOFIA/FORCAST mid-IR survey of luminous protostars and
crowded star-forming environments in Cygnus X, the nearest million-solar mass
molecular cloud complex. We derive bolometric luminosities for over 1000
sources in the region with these new data in combination with extant Spitzer
and UKIDSS photometry, with 63 new luminous protostar candidates identified by
way of the high quality SOFIA/FORCAST data. By including FORCAST data, we
construct protostellar luminosity functions (PLFs) with improved completeness
at the high luminosity end. The PLFs are well described by a power law function
with an index of ~-0.5. Based on the Herschel temperature and column density
measurements, we find no obvious dependence of the PLFs on the local gas
temperature, but PLFs in regions of high stellar density or gas column density
exhibit some excess at higher luminosities. Through the comparison between our
observed PLFs and existing accretion models, both the turbulent core (TC) and
the competitive accretion (CA) models are consistent with our results, while
the isothermal sphere (IS) model is disfavored. The implications of these
results on the star formation process are discussed.


title:
Flexible learning of quantum states with generative query neural
  networks

abstract:
  Deep neural networks are a powerful tool for characterizing quantum states.
In this task, neural networks are typically trained with measurement data
gathered from the quantum state to be characterized. But is it possible to
train a neural network in a general-purpose way, which makes it applicable to
multiple unknown quantum states? Here we show that learning across multiple
quantum states and different measurement settings can be achieved by a
generative query neural network, a type of neural network originally used in
the classical domain for learning 3D scenes from 2D pictures. Our network can
be trained offline with classically simulated data, and later be used to
characterize unknown quantum states from real experimental data. With little
guidance of quantum physics, the network builds its own data-driven
representation of quantum states, and then uses it to predict the outcome
probabilities of requested quantum measurements on the states of interest. This
approach can be applied to state learning scenarios where quantum measurement
settings are not informationally complete and predictions must be given in real
time, as experimental data become available, as well as to adversarial
scenarios where measurement choices and prediction requests are designed to
expose learning inaccuracies. The internal representation produced by the
network can be used for other tasks beyond state characterization, including
clustering of states and prediction of physical properties. The features of our
method are illustrated on many-qubit ground states of Ising model and
continuous-variable non-Gaussian states.


title: On presheaf submonads of quantale enriched categories

abstract:
  This paper focus on the presheaf monad and its submonads on the realm of
$V$-categories, for a quantale $V$. First we present two characterisations of
presheaf submonads, both using $V$-distributors: one based on admissible
classes of $V$-distributors, and other using Beck-Chevalley conditions on
$V$-distributors. Then we focus on the study of the corresponding
Eilenberg-Moore categories of algebras, having as main examples the formal ball
monad and the so-called Lawvere monad.


title: Captivate! Contextual Language Guidance for Parent-Child Interaction

abstract:
  To acquire language, children need rich language input. However, many parents
find it difficult to provide children with sufficient language input, which
risks delaying their language development. To aid these parents, we design
Captivate!, the first system that provides contextual language guidance to
parents during play. Our system tracks both visual and spoken language cues to
infer targets of joint attention, enabling the real-time suggestion of
situation-relevant phrases for the parent. We design our system through a
user-centered process with immigrant families--a highly vulnerable yet
understudied population--as well as professional speech language therapists.
Next, we evaluate Captivate! on parents with children aged 1-3 to observe
improvements in responsive language use. We share insights into developing
contextual guidance technology for linguistically diverse families.


title:
Sequential Doppler Shift based Optimal Localization and Synchronization
  with TOA

abstract:
  Doppler shift is an important measurement for localization and
synchronization (LAS), and is available in various practical systems. Existing
studies on LAS techniques in a time division broadcast LAS system (TDBS) only
use sequential time-of-arrival (TOA) measurements from the broadcast signals.
In this paper, we develop a new optimal LAS method in the TDBS, namely LAS-SDT,
by taking advantage of the sequential Doppler shift and TOA measurements. It
achieves higher accuracy compared with the conventional TOA-only method for
user devices (UDs) with motion and clock drift. Another two variant methods,
LAS-SDT-v for the case with UD velocity aiding, and LAS-SDT-k for the case with
UD clock drift aiding, are developed. We derive the Cramer-Rao lower bound
(CRLB) for these different cases. We show analytically that the accuracies of
the estimated UD position, clock offset, velocity and clock drift are all
significantly higher than those of the conventional LAS method using TOAs only.
Numerical results corroborate the theoretical analysis and show the optimal
estimation performance of the LAS-SDT.


title: Suslin homology via cycles with modulus and applications

abstract:
  We show that for a smooth projective variety $X$ over a field $k$ and a
reduced effective Cartier divisor $D \subset X$, the Chow group of 0-cycles
with modulus $\mathrm{CH}_0(X|D)$ coincides with the Suslin homology $H^S_0(X
\setminus D)$ under some necessary conditions on $k$ and $D$. Several
consequences are derived.


title:
The Metal-Silicate Partitioning of Carbon During Earth's Accretion and
  its Distribution in the Early Solar System

abstract:
  Carbon is an essential element for the existence and evolution of life on
Earth. Its abundance in Earth's crust and mantle (the Bulk Silicate Earth, BSE)
is surprisingly high given that carbon is strongly siderophile (metal-loving)
at low pressures and temperatures, and hence should have segregated almost
completely into Earth's core during accretion. Estimates of the concentration
of carbon in the BSE lie in the range 100-260 ppm and are much higher than
expected based on simple models of core-mantle differentiation. Here we show
through experiments at the putative conditions of Earth's core formation (49-71
GPa and 3600-4000 K) that carbon is significantly less siderophile at these
conditions than at the low pressures ($\leq$13 GPa) and temperatures
($\leq$2500 K) of previous large volume press studies, but at least an order of
magnitude more siderophile than proposed recently based on an experimental
approach that is similar to ours. Using our new data along with previously
published results, we derive a new parameterization of the pressure-temperature
dependence of the metal-silicate partitioning of carbon. We apply this
parameterization in a model that combines planet formation and core-mantle
differentiation that is based on astrophysical N-body accretion simulations.
Because differentiated planetesimals were almost completely depleted in carbon
due to sublimation at high temperatures, almost all carbon in the BSE was added
by the accretion of fully-oxidized carbonaceous chondrite material from the
outer solar system. Carbon is added to the mantle continuously throughout
accretion and its concentration reaches values within the BSE range (e.g.
140$\pm$40 ppm) at the end of accretion. The corresponding final core and bulk
Earth carbon concentrations are 1270$\pm$300 ppm and 495$\pm$125 ppm
respectively.


title: Structured Codes of Graphs

abstract:
  We investigate the maximum size of graph families on a common vertex set of
cardinality $n$ such that the symmetric difference of the edge sets of any two
members of the family satisfies some prescribed condition. We solve the problem
completely for infinitely many values of $n$ when the prescribed condition is
connectivity or $2$-connectivity, Hamiltonicity or the containment of a
spanning star. We also investigate local conditions that can be certified by
looking at only a subset of the vertex set. In these cases a capacity-type
asymptotic invariant is defined and when the condition is to contain a certain
subgraph this invariant is shown to be a simple function of the chromatic
number of this required subgraph. This is proven using classical results from
extremal graph theory. Several variants are considered and the paper ends with
a collection of open problems.


title:
Generalized quaternionic free rotational Dirac equation and spinor
  solutions in the electromagnetic field

abstract:
  Starting with the quaternionic Minkowski space-time and its four-vector
representation, a rotational analogue of the quaternionic Dirac equation in the
electromagnetic field is developed, which includes not only the energy
solutions but also the angular momentum solutions for rotating Dirac fermions.
The striking feature of the quaternionic approach is that it depicts a unified
representation of energy-momentum in a single framework as the space-time.
Furthermore, we establish the generalized Schrodinger-Pauli-like equation
associated with generalized electric and magnetic dipole energies that
corresponding to their dipole moments. As such, the present analysis deals with
the invariant behavior of the extended quaternionic rotational Dirac equation
under Lorentz, gauge, duality, and CPT invariance.


title:
On the generators of quantum dynamical semigroups with invariant
  subalgebras

abstract:
  The problem of characterizing GKLS-generators and CP-maps with an invariant
von Neumann subalgebra $\mathcal{A}$ appeared in different guises in the
literature. We prove two unifying results: First, we show how to construct a
normal form for $\mathcal{A}$-invariant GKLS-generators, if a normal form for
$\mathcal{A}$-invariant CP-maps is known - rendering the two problems
essentially equivalent. Second, we provide a normal form for
$\mathcal{A}$-invariant CP-maps if $\mathcal{A}$ is atomic (which includes the
finite-dimensional case). As an application we reproduce several results from
the literature as direct consequences of our characterizations and thereby
point out connections between different fields.


title:
Interacting and Non-interacting Re\'{n}yi Holographic Dark Energy Models
  in DGP Braneworld

abstract:
  We investigate both the interacting and non-interacting Re\'{n}yi Holographic
Dark Energy (RHDE) models in DGP brane world framework. Cosmological parameters
and their evolutions are probed to obtain realistic cosmological models. We
note that both the models accommodate the present accelerating phase of
expansion with the observed dark energy density. Classical stability of the
cosmological model and $Om$- diagnostic are also studied to test the
suitability of the cosmological models obtained in the presence of RHDE in DGP
braneworld.


title:
Enhancing Next-Generation Extended Reality Applications with Coded
  Caching

abstract:
  The next evolutionary step in human-computer interfaces will bring forward
immersive digital experiences that submerge users in a 3D world while allowing
them to interact with virtual or twin objects. Accordingly, various
collaborative extended reality (XR) applications are expected to emerge,
imposing stringent performance requirements on the underlying wireless
connectivity infrastructure. In this paper, we examine how novel multi-antenna
coded caching (CC) techniques can facilitate high-rate low-latency
communications and improve users' quality of experience (QoE) in our envisioned
multi-user XR scenario. Specifically, we discuss how these techniques make it
possible to prioritize the content relevant to wireless bottleneck areas while
enabling the cumulative cache memory of the users to be utilized as an
additional communication resource. In this regard, we first explore recent
advancements in multi-antenna CC that facilitate the efficient use of
distributed in-device memory resources. Then, we review how XR application
requirements are addressed within the third-generation partnership project
(3GPP) framework and how our envisioned XR scenario relates to the foreseen use
cases. Finally, we identify new challenges arising from integrating CC
techniques into multi-user XR scenarios and propose novel solutions to address
them in practice.


title:
Violation of the fluctuation-dissipation theorem and effective
  temperatures in spin ice

abstract:
  We present numerical tests of the fluctuation-dissipation theorem (FDT) in
the dumbbell model of spin ice with parameters suitable for dysprosium
titanate. The tests are made for local spin variables, magnetic monopole
density, and energy. We are able to achieve local equilibrium in which the FDT
is satisfied down to $T=0.4$ K below which the system completely freezes.
Non-equilibrium dynamics, together with violation of the FDT, are nonetheless
observed following a thermal quench into the non-contractable monopole pair
regime. Despite FDT violation, an approximate linear response regime allows for
the identification of effective non-equilibrium temperatures which are
different for each variable. The spin variable appears hotter than the heat
reservoir, the monopole concentration responds with a lower effective
temperature while the energy has a negative effective temperature. Results are
discussed in the context of the monopole picture of spin ice and compared to
the structure of FDT violations in other glassy materials. Prospectives for
future experiments are reviewed.


title: Quantum phase with coexisting localized, extended, and critical zones

abstract:
  Conventionally a mobility edge (ME) marks the critical energy that separates
two different transport zones where all states are extended and localized,
respectively. Here we propose a novel quasiperiodic lattice model with
experimental feasibility to realize a fundamentally new quantum phase with
three coexisting energy-dependent zones, i.e., the extended, critical and
localized zones. Accordingly, this phase exhibits new types of MEs which
separate the extended states from critical ones, and the localized states from
critical ones, respectively. We introduce the diagnostic quantities to
characterize and distinguish the different zones, and show that the predicted
phase can be detected by measuring the fractal dimension and a scaling index
obtained from the momentum distribution. The experimental realization is also
proposed and studied. This work extends the concept of ME and enriches the
quantum phases in disordered systems,which sheds light on searching for new
localization and critical phenomena with novel transport and thermoelectric
effects.


title: CATs++: Boosting Cost Aggregation with Convolutions and Transformers

abstract:
  Cost aggregation is a highly important process in image matching tasks, which
aims to disambiguate the noisy matching scores. Existing methods generally
tackle this by hand-crafted or CNN-based methods, which either lack robustness
to severe deformations or inherit the limitation of CNNs that fail to
discriminate incorrect matches due to limited receptive fields and
inadaptability. In this paper, we introduce Cost Aggregation with Transformers
(CATs) to tackle this by exploring global consensus among initial correlation
map with the help of some architectural designs that allow us to fully enjoy
global receptive fields of self-attention mechanism. Also, to alleviate some of
the limitations that CATs may face, i.e., high computational costs induced by
the use of a standard transformer that its complexity grows with the size of
spatial and feature dimensions, which restrict its applicability only at
limited resolution and result in rather limited performance, we propose CATs++,
an extension of CATs. Our proposed methods outperform the previous
state-of-the-art methods by large margins, setting a new state-of-the-art for
all the benchmarks, including PF-WILLOW, PF-PASCAL, and SPair-71k. We further
provide extensive ablation studies and analyses.


title:
Frequencies of astrophysical jets and gravitational strengths in the
  octonion spaces

abstract:
  The paper focuses on applying the octonions to explore the electromagnetic
and gravitational equations in the presence of some material media, exploring
the frequencies of astrophysical jets. Maxwell was the first to use the algebra
of quaternions to describe the electromagnetic equations. This method
encourages scholars in adopting the quaternions and octonions to study the
physical properties of electromagnetic and gravitational fields, including the
field strength, field source, linear momentum, and angular momentum and so
forth. In the paper, the field strength and angular momentum in the vacuum can
be combined together to become one new physical quantity, that is, the
composite field strength within the material media. Substituting the latter for
the field strength in the vacuum will deduce the field equations within
material media, including the electromagnetic and gravitational equations in
the presence of some material media. In terms of the electromagnetic fields,
the electromagnetic equations in the presence of some electromagnetic media are
able to explore a few new physical properties of electromagnetic media.
Especially, in case the magnetic flux density and magnetization intensity both
fluctuate at a single-frequency, their frequencies must be identical to each
other within electromagnetic media. In some extreme cases, the electromagnetic
equations within electromagnetic media will be degenerated into the Maxwell's
equations in the vacuum. The above reveals that the electromagnetic equations
within electromagnetic media are capable of extending the scope of application
of electromagnetic theory. For the gravitational fields, there are some similar
inferences and conclusions within gravitational media. Further they can be
utilized to research the frequencies of astrophysical jets.


title:
Learning from distinctive candidates to optimize reduced-precision
  convolution program on tensor cores

abstract:
  Convolution is one of the fundamental operations of deep neural networks with
demanding matrix computation. In a graphic processing unit (GPU), Tensor Core
is a specialized matrix processing hardware equipped with reduced-precision
matrix-multiply-accumulate (MMA) instructions to increase throughput. However,
it is challenging to achieve optimal performance since the best scheduling of
MMA instructions varies for different convolution sizes. In particular,
reduced-precision MMA requires many elements grouped as a matrix operand,
seriously limiting data reuse and imposing packing and layout overhead on the
schedule. This work proposes an automatic scheduling method of
reduced-precision MMA for convolution operation. In this method, we devise a
search space that explores the thread tile and warp sizes to increase the data
reuse despite a large matrix operand of reduced-precision MMA. The search space
also includes options of register-level packing and layout optimization to
lesson overhead of handling reduced-precision data. Finally, we propose a
search algorithm to find the best schedule by learning from the distinctive
candidates. This reduced-precision MMA optimization method is evaluated on
convolution operations of popular neural networks to demonstrate substantial
speedup on Tensor Core compared to the state of the arts with shortened search
time.


title: Experimental realization of a universal RF photonic integrated circuit

abstract:
  This paper demonstrates the operation of a universal RF photonic circuit that
consists of a generalized Mach Zehnder Interferometer architecture with its Nx1
combiner replaced by a NxN optical DFT network. The proposed circuit
architecture can be used for SSB modulation, frequency
up-conversion/down-conversion, frequency multiplication and phase correlated
subcarrier generation based on the choice of output ports and dimension (N) of
the circuit. An alternative representation of the circuit is also reported with
the aim of a systematic demultiplexing. A transfer matrix approach is used to
develop the theoretical predictions which are verified by simulation using
industry standard software tool. An integrated circuit based on silicon
photonics technology readily available in the laboratory is used for
experimental confirmation.


title:
Motif-topology and Reward-learning improved Spiking Neural Network for
  Efficient Multi-sensory Integration

abstract:
  Network architectures and learning principles are key in forming complex
functions in artificial neural networks (ANNs) and spiking neural networks
(SNNs). SNNs are considered the new-generation artificial networks by
incorporating more biological features than ANNs, including dynamic spiking
neurons, functionally specified architectures, and efficient learning
paradigms. In this paper, we propose a Motif-topology and Reward-learning
improved SNN (MR-SNN) for efficient multi-sensory integration. MR-SNN contains
13 types of 3-node Motif topologies which are first extracted from independent
single-sensory learning paradigms and then integrated for multi-sensory
classification. The experimental results showed higher accuracy and stronger
robustness of the proposed MR-SNN than other conventional SNNs without using
Motifs. Furthermore, the proposed reward learning paradigm was biologically
plausible and can better explain the cognitive McGurk effect caused by
incongruent visual and auditory sensory signals.


title: New examples of radical join-meet ideals

abstract:
  In this paper, we give new examples of a finite lattice $L$ such that the
join-meet ideal $I_L$ is radical.


title: Development and Comparison of Scoring Functions in Curriculum Learning

abstract:
  Curriculum Learning is the presentation of samples to the machine learning
model in a meaningful order instead of a random order. The main challenge of
Curriculum Learning is determining how to rank these samples. The ranking of
the samples is expressed by the scoring function. In this study, scoring
functions were compared using data set features, using the model to be trained,
and using another model and their ensemble versions. Experiments were performed
for 4 images and 4 text datasets. No significant differences were found between
scoring functions for text datasets, but significant improvements were obtained
in scoring functions created using transfer learning compared to classical
model training and other scoring functions for image datasets. It shows that
different new scoring functions are waiting to be found for text classification
tasks.


title: String integrability of the ABJM defect

abstract:
  ABJM theory in the presence of a half-BPS domain wall is dual to the D2-D4
probe brane system with nonzero worldvolume flux. The ABJM domain wall was
recently shown to be integrable to lowest order in perturbation theory and bond
dimension. In the present paper we show that the string theory dual of this
system is integrable, namely that the string boundary conditions on the probe
D4-brane preserve the integrability of the Green-Schwarz sigma model. Our
result suggests that the ABJM domain wall is integrable to all loop orders and
for any value of the bond dimension.


title:
Robust Estimation of Discrete Distributions under Local Differential
  Privacy

abstract:
  Although robust learning and local differential privacy are both widely
studied fields of research, combining the two settings is just starting to be
explored. We consider the problem of estimating a discrete distribution in
total variation from $n$ contaminated data batches under a local differential
privacy constraint. A fraction $1-\epsilon$ of the batches contain $k$ i.i.d.
samples drawn from a discrete distribution $p$ over $d$ elements. To protect
the users' privacy, each of the samples is privatized using an $\alpha$-locally
differentially private mechanism. The remaining $\epsilon n $ batches are an
adversarial contamination. The minimax rate of estimation under contamination
alone, with no privacy, is known to be $\epsilon/\sqrt{k}+\sqrt{d/kn}$, up to a
$\sqrt{\log(1/\epsilon)}$ factor. Under the privacy constraint alone, the
minimax rate of estimation is $\sqrt{d^2/\alpha^2 kn}$. We show that combining
the two constraints leads to a minimax estimation rate of
$\epsilon\sqrt{d/\alpha^2 k}+\sqrt{d^2/\alpha^2 kn}$ up to a
$\sqrt{\log(1/\epsilon)}$ factor, larger than the sum of the two separate
rates. We provide a polynomial-time algorithm achieving this bound, as well as
a matching information theoretic lower bound.


title: Parallel Repetition For All 3-Player Games Over Binary Alphabet

abstract:
  We prove that for every 3-player game with binary questions and answers and
value $<1$, the value of the $n$-fold parallel repetition of the game decays
polynomially fast to 0. That is, for every such game, there exists a constant
$c>0$, such that the value of the $n$-fold parallel repetition of the game is
at most $n^{-c}$. Along the way to proving this theorem, we prove two
additional parallel repetition theorems for multiplayer games, that may be of
independent interest:
  Playerwise Connected Games (with any number of players and any Alphabet
size): We identify a large class of multiplayer games and prove that for every
game with value $<1$ in that class, the value of the $n$-fold parallel
repetition of the game decays polynomially fast to 0. More precisely, our
result applies for playerwise connected games, with any number of players and
any alphabet size. The class of playerwise connected games is strictly larger
than the class of connected games that was defined in [DHVY17] and for which
exponentially fast decay bounds are known [DHVY17]. For playerwise connected
games that are not connected, only inverse Ackermann decay bounds were
previously known [Ver96].
  Exponential Bounds for the Anti-Correlation Game: In the 3-player
anti-correlation game, two out of three players are given $1$ as input, and the
remaining player is given $0$. The two players who were given $1$ must produce
different outputs in $\{0,1\}$. We prove that the value of the $n$-fold
parallel repetition of that game decays exponentially fast to 0. Only inverse
Ackermann decay bounds were previously known [Ver96]. This game was studied and
motivated in several previous works. In particular, Holmgren and Yang gave it
as an example for a 3-player game whose non-signaling value (is smaller than 1
and yet) does not decrease at all under parallel repetition [HY19].


title:
A Subpolynomial Approximation Algorithm for Graph Crossing Number in
  Low-Degree Graphs

abstract:
  We consider the classical Minimum Crossing Number problem: given an
$n$-vertex graph $G$, compute a drawing of $G$ in the plane, while minimizing
the number of crossings between the images of its edges. This is a fundamental
and extensively studied problem, whose approximability status is widely open.
In all currently known approximation algorithms, the approximation factor
depends polynomially on $\Delta$ -- the maximum vertex degree in $G$. The best
current approximation algorithm achieves an $O(n^{1/2-\varepsilon}\cdot
\text{poly}(\Delta\cdot\log n))$-approximation, for a small fixed constant
$\epsilon$, while the best negative result is APX-hardness, leaving a large gap
in our understanding of this basic problem. In this paper we design a
randomized $O\left(2^{O((\log n)^{7/8}\log\log
n)}\cdot\text{poly}(\Delta)\right )$-approximation algorithm for Minimum
Crossing Number. This is the first approximation algorithm for the problem that
achieves a subpolynomial in $n$ approximation factor (albeit only in graphs
whose maximum vertex degree is subpolynomial in $n$).
  In order to achieve this approximation factor, we design a new algorithm for
a closely related problem called Crossing Number with Rotation System, in
which, for every vertex $v\in V(G)$, the circular ordering, in which the images
of the edges incident to $v$ must enter the image of $v$ in the drawing is
fixed as part of the input. Combining this result with the recent reduction of
[Chuzhoy, Mahabadi, Tan '20] immediately yields the improved approximation
algorithm for Minimum Crossing Number. We introduce several new technical
tools, that we hope will be helpful in obtaining better algorithms for the
problem in the future.


title: On the Chattering of SARSA with Linear Function Approximation

abstract:
  SARSA, a classical on-policy control algorithm for reinforcement learning, is
known to chatter when combined with linear function approximation: SARSA does
not diverge but oscillates in a bounded region. However, little is know about
how fast SARSA converges to that region and how large the region is. In this
paper, we make progress towards solving this open problem by showing the
convergence rate of projected SARSA to a bounded region. Importantly, the
region is much smaller than the ball used for projection provided that the the
magnitude of the reward is not too large. Our analysis applies to expected
SARSA as well as SARSA($\lambda$). Existing works regarding the convergence of
linear SARSA to a fixed point all require the Lipschitz constant of SARSA's
policy improvement operator to be sufficiently small; our analysis instead
applies to arbitrary Lipschitz constants and thus characterizes the behavior of
linear SARSA for a new regime.


title: Permutation invariant matrix statistics and computational language tasks

abstract:
  The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam
and Sadrzadeh is an approach to the statistics of matrices that are generated
in type-driven distributional semantics, based on permutation invariant
polynomial functions which are regarded as the key observables encoding the
significant statistics. In this paper we generalize the previous results on the
approximate Gaussianity of matrix distributions arising from compositional
distributional semantics. We also introduce a geometry of observable vectors
for words, defined by exploiting the graph-theoretic basis for the permutation
invariants and the statistical characteristics of the ensemble of matrices
associated with the words. We describe successful applications of this unified
framework to a number of tasks in computational linguistics, associated with
the distinctions between synonyms, antonyms, hypernyms and hyponyms.


title: Online Approval Committee Elections

abstract:
  Assume $k$ candidates need to be selected. The candidates appear over time.
Each time one appears, it must be immediately selected or rejected -- a
decision that is made by a group of individuals through voting. Assume the
voters use approval ballots, i.e., for each candidate they only specify whether
they consider it acceptable or not. This setting can be seen as a voting
variant of choosing $k$ secretaries. Our contribution is twofold. (1) We assess
to what extent the committees that are computed online can proportionally
represent the voters. (2) If a prior probability over candidate approvals is
available, we show how to compute committees with maximal expected score.


title: Fault-tolerance in qudit circuit design

abstract:
  The efficient decomposition of multi-controlled gates is a significant factor
in quantum compiling, both in circuit depth and T-gate count. Recent work has
demonstrated that qudits have the potential to reduce resource requirements
from linear to logarithmic depth and to avoid fractional phase rotations. Here
we argue, based on the scaling of decoherence in high-index states, that
circuit depth is not the primary factor, and that both the choice of entangling
gate and interaction network topology act together to determine the spread of
errors and ultimate failure rate in a circuit. We further show that for certain
linear-depth circuits, additional error mitigation is possible via selective
application of resources.


title: Emergence of Objectivity for Quantum Many-Body Systems

abstract:
  We examine the emergence of objectivity for quantum many-body systems in a
setting without an environment to decohere the system's state, but where
observers can only access small fragments of the whole system. We extend the
result of Reidel (2017) to the case where the system is in a mixed state,
measurements are performed through POVMs, and imprints of the outcomes are
imperfect. We introduce a new condition on states and measurements to recover
full classicality for any number of observers. We further show that evolutions
of quantum many-body systems can be expected to yield states that satisfy this
condition whenever the corresponding measurement outcomes are redundant.