title: Scalable single-mode Berkeley Surface Emitting Lasers

abstract:
  The scaling of electromagnetic apertures is a long-standing question that has
been investigated for at least six decades but has still not been resolved
[1-5]. The size of single aperture cavities, bounded by the existence of
higher-order transverse modes, fundamentally limits the power emitted by
single-mode lasers or the brightness of quantum light sources. The
free-spectral range of existing electromagnetic apertures goes to zero when the
size of the aperture increases, and the demonstration of scale-invariant
apertures or lasers has remained elusive. Here, we report open-Dirac
electromagnetic apertures that exploit a subtle cavity-mode-dependent scaling
of losses in reciprocal space. For cavities with a quadratic dispersion, the
complex frequencies of modes converge towards each other with the size of
cavities, making cavities invariably multimode. Surprisingly, for a class of
cavities with linear dispersion, we discover that, while the convergence of the
real parts of cavity modes towards each other is delayed (it still quickly goes
to zero), the normalized complex free-spectral range converge towards a
constant governed by the loss rate of distinct Bloch bands. We show that this
unconventional scaling of the complex frequency of cavity modes in open-Dirac
electromagnetic apertures guarantees single-mode operation of large cavities.
We experimentally demonstrate that single-mode lasing of such cavities is
maintained when the cavity is scale up in size. We name such sources Berkeley
Surface Emitting Lasers (BerkSELs). We further show that the far-field emitted
by the proposed single-mode BerkSELs corresponds to a topological singularity
of charge two, in full agreement with our theory. Open-Dirac apertures open new
avenues for light-matter interaction and basic science in open-wave systems
with applications in classical and quantum communications, sensing, and
imaging.


title:
Ultrahigh reversible hydrogen storage in K and Ca decorated 4-6-8
  biphenylene sheet

abstract:
  By applying density functional theory (DFT) and ab-initio molecular dynamics
(AIMD) simulations, we predict the ultrahigh hydrogen storage capacity of K and
Ca decorated single-layer biphenylene sheet (BPS). We have kept various alkali
and alkali earth metals, including Na, Be, Mg, K, Ca, at different sites of BPS
and found that K and Ca atoms prefer to bind individually on the BPS instead of
forming clusters. It was found that 2x2x1 supercell of biphenylene sheet can
adsorb eight K, or eight Ca atoms, and each K or Ca atom can adsorb 5 H$_2$,
leading to 11.90 % or 11.63 % of hydrogen uptake, respectively, which is
significantly higher than the DOE-US demands of 6.5 %. The average adsorption
energy of H$_2$ for K and Ca decorated BPS is -0.24 eV and -0.33 eV,
respectively, in the suitable range for reversible H$_2$ storage. Hydrogen
molecules get polarized in the vicinity of ionized metal atoms hence get
attached to the metal atoms through electrostatic and van der Waals
interactions. We have estimated the desorption temperatures of H$_2$ and found
that the adsorbed H$_2$ can be utilized for reversible use. We have found that
a sufficient energy barrier of 2.52 eV exists for the movement of Ca atoms,
calculated using the climbing-image nudged elastic band (CI-NEB) method. This
energy barrier can prevent the clustering issue of Ca atoms. The solidity of K
and Ca decorated BPS structures were investigated using AIMD simulations.


title:
Lattice Boltzmann simulations of two linear microswimmers using the
  immersed boundary method

abstract:
  The performance of a single or the collection of microswimmers strongly
depends on the hydrodynamic coupling among their constituents and themselves.
We present a numerical study for a single and a pair of microswimmers based on
lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of
two separable parts. Lagrange polynomials provide a discretization of the
microswimmers and the lattice Boltzmann method captures the dynamics of the
surrounding fluid. The two components couple via an immersed boundary method.
We present data for a single swimmer system and our data also show the onset of
collective effects and, in particular, an overall velocity increment of
clusters of swimmers.


title:
A novel unsupervised covid lung lesion segmentation based on the lung
  tissue identification

abstract:
  This study aimed to evaluate the performance of a novel unsupervised deep
learning-based framework for automated infections lesion segmentation from CT
images of Covid patients. In the first step, two residual networks were
independently trained to identify the lung tissue for normal and Covid patients
in a supervised manner. These two models, referred to as DL-Covid and DL-Norm
for Covid-19 and normal patients, respectively, generate the voxel-wise
probability maps for lung tissue identification. To detect Covid lesions, the
CT image of the Covid patient is processed by the DL-Covid and DL-Norm models
to obtain two lung probability maps. Since the DL-Norm model is not familiar
with Covid infections within the lung, this model would assign lower
probabilities to the lesions than the DL-Covid. Hence, the probability maps of
the Covid infections could be generated through the subtraction of the two lung
probability maps obtained from the DL-Covid and DL-Norm models. Manual lesion
segmentation of 50 Covid-19 CT images was used to assess the accuracy of the
unsupervised lesion segmentation approach. The Dice coefficients of 0.985 and
0.978 were achieved for the lung segmentation of normal and Covid patients in
the external validation dataset, respectively. Quantitative results of
infection segmentation by the proposed unsupervised method showed the Dice
coefficient and Jaccard index of 0.67 and 0.60, respectively. Quantitative
evaluation of the proposed unsupervised approach for Covid-19 infectious lesion
segmentation showed relatively satisfactory results. Since this framework does
not require any annotated dataset, it could be used to generate very large
training samples for the supervised machine learning algorithms dedicated to
noisy and/or weakly annotated datasets.


title: Phonon thermal Hall effect in a metallic spin ice

abstract:
  It has become common knowledge that phonons can generate thermal Hall effect
in a wide variety of materials, although the underlying mechanism is still
controversial. We study longitudinal $\kappa_{xx}$ and transverse $\kappa_{xy}$
thermal conductivity in Pr$_2$Ir$_2$O$_7$, which is a metallic analogue of spin
ice. Despite the presence of mobile charge carriers, we find that both
$\kappa_{xx}$ and $\kappa_{xy}$ are dominated by phonons. A $T/H$ scaling of
$\kappa_{xx}$ unambiguously reveals that longitudinal heat current is
substantially impeded by resonant scattering of phonons on paramagnetic spins.
Upon cooling, the resonant scattering is strongly affected by a development of
spin ice correlation and $\kappa_{xx}$ deviates from the scaling in an
anisotropic way with respect to field directions. Strikingly, a set of the
$\kappa_{xx}$ and $\kappa_{xy}$ data clearly shows that $\kappa_{xy}$
correlates with $\kappa_{xx}$ in its response to magnetic field including a
success of the $T/H$ scaling and its failure at low temperature. This
remarkable correlation provides solid evidence that an indispensable role is
played by spin-phonon scattering not only for hindering the longitudinal heat
conduction, but also for generating the transverse response.


title:
Tighter Expected Generalization Error Bounds via Convexity of
  Information Measures

abstract:
  Generalization error bounds are essential to understanding machine learning
algorithms. This paper presents novel expected generalization error upper
bounds based on the average joint distribution between the output hypothesis
and each input training sample. Multiple generalization error upper bounds
based on different information measures are provided, including Wasserstein
distance, total variation distance, KL divergence, and Jensen-Shannon
divergence. Due to the convexity of the information measures, the proposed
bounds in terms of Wasserstein distance and total variation distance are shown
to be tighter than their counterparts based on individual samples in the
literature. An example is provided to demonstrate the tightness of the proposed
generalization error bounds.


title: Magnon corner states in twisted bilayer honeycomb magnets

abstract:
  Search for higher-order topological insulators, characterized by
topologically protected gapless boundary states of codimension higher than one,
in bosonic systems has attracted growing interest. Here, we establish twisted
bilayer honeycomb magnets as a new platform for hosting second-order
topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple,
minimal Heisenberg spin model to describe misaligned bilayer sheets of
honeycomb ferromagnetic magnets with a large commensurate twist angle. We found
that the higher-order topology in this bilayer system shows a significant
dependence on the interlayer exchange coupling. The SOTMI, featuring
topologically protected magnon corner states, appears for ferromagnetic
interlayer couplings, while the twisted bilayer exhibits a nodal phase in the
case of antiferromagnetic interlayer coupling.


title:
Discrete approximation of the Griffith functional by adaptative finite
  elements

abstract:
  This paper is devoted to show a discrete adaptative finite element
approximation result for the isotropic two-dimensional Griffith energy arising
in fracture mechanics. The problem is addressed in the geometric measure
theoretic framework of generalized special functions of bounded deformation
which corresponds to the natural energy space for this functional. It is proved
to be approximated in the sense of $\Gamma$-convergence by a sequence of
discrete integral functionals defined on continuous piecewise affine functions.
The main feature of this result is that the mesh is part of the unknown of the
problem, and it gives enough flexibility to recover isotropic surface energies.


title:
Estimates of Lebesgue Constants for Lagrange Interpolation Processes by
  Rational Functions under Mild Restrictions to their Fixed Poles

abstract:
  We estimate the Lebesgue constants for Lagrange interpolation processes on
one or several intervals by rational functions with fixed poles. We admit that
the poles have accumulation points on the intervals.
  To prove it we use an analog of the inverse polynomial image method for
rational functions with fixed poles.


title: Towards Effective and Robust Neural Trojan Defenses via Input Filtering

abstract:
  Trojan attacks on deep neural networks are both dangerous and surreptitious.
Over the past few years, Trojan attacks have advanced from using only a single
input-agnostic trigger and targeting only one class to using multiple,
input-specific triggers and targeting multiple classes. However, Trojan
defenses have not caught up with this development. Most defense methods still
make out-of-date assumptions about Trojan triggers and target classes, thus,
can be easily circumvented by modern Trojan attacks. To deal with this problem,
we propose two novel "filtering" defenses called Variational Input Filtering
(VIF) and Adversarial Input Filtering (AIF) which leverage lossy data
compression and adversarial learning respectively to effectively purify all
potential Trojan triggers in the input at run time without making assumptions
about the number of triggers/target classes or the input dependence property of
triggers. In addition, we introduce a new defense mechanism called
"Filtering-then-Contrasting" (FtC) which helps avoid the drop in classification
accuracy on clean data caused by "filtering", and combine it with VIF/AIF to
derive new defenses of this kind. Extensive experimental results and ablation
studies show that our proposed defenses significantly outperform well-known
baseline defenses in mitigating five advanced Trojan attacks including two
recent state-of-the-art while being quite robust to small amounts of training
data and large-norm triggers.


title:
Cyclicity of Rigid Centers on Center Manifolds of Three-dimensional
  systems

abstract:
  We work with polynomial three-dimensional rigid differential systems. Using
the Lyapunov constants, we obtain lower bounds for the cyclicity of the known
rigid centers on their center manifolds. Moreover, we obtain an example of a
quadratic rigid center from which is possible to bifurcate 13 limit cycles,
which is a new lower bound for three-dimensional quadratic systems.


title: A Monte Carlo Method for Rayleigh Scattering in Liquid Detectors

abstract:
  A new Monte Carlo method has been implemented to describe the angular and
polarization distributions of anisotropic liquids, like water and linear
alkylbenzene, by considering orientational fluctuations of polarizability
tensors. The scattered light of anisotropic liquids is depolarized with an
angular distribution of $1+(1-\rho_v)/(1+3\rho_v)\cos^2\theta$, which is
modified by the depolarization ratio $\rho_v$. A standalone experiment has
validated the simulation results of LAB. The new method can provide more
accurate knowledge on light propagation in large liquid detectors, which is
beneficial to the developments of reconstruction for detectors.


title:
Gluon Fusion Production at NLO: Merging the Transverse Momentum and the
  High-Energy Expansions

abstract:
  The virtual corrections to $gg\to HH$ and $gg\to ZH$ are analytically
evaluated combining an expansion in the small transverse momentum of the final
particles with an expansion valid at high energies. The two expansion methods
describe complementary regions of the phase space and we merge their results,
extending the range of validity of both expansions using Pad\'e approximants.
We show that this approach can reproduce the available numerical results
retaining the exact top quark mass dependence with an accuracy well below the
1% level. Our results allow a fast and flexible evaluation of the virtual
corrections of the considered processes. Furthermore, they are available in
different renormalisation schemes of the top quark mass.


title:
Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory
  Optimization Problems

abstract:
  Recent low-thrust space missions have highlighted the importance of designing
trajectories that are robust against uncertainties. In its complete form, this
process is formulated as a nonlinear constrained stochastic optimal control
problem. This problem is among the most complex in control theory, and no
practically applicable method to low-thrust trajectory optimization problems
has been proposed to date. This paper presents a new algorithm to solve
stochastic optimal control problems with nonlinear systems and constraints. The
proposed algorithm uses the unscented transform to convert a stochastic optimal
control problem into a deterministic problem, which is then solved by
trajectory optimization methods such as differential dynamic programming. Two
numerical examples, one of which applies the proposed method to low-thrust
trajectory design, illustrate that it automatically introduces margins that
improve robustness. Finally, Monte Carlo simulations are used to evaluate the
robustness and optimality of the solution.


title:
An NLP Solution to Foster the Use of Information in Electronic Health
  Records for Efficiency in Decision-Making in Hospital Care

abstract:
  The project aimed to define the rules and develop a technological solution to
automatically identify a set of attributes within free-text clinical records
written in Portuguese. The first application developed and implemented on this
basis was a structured summary of a patient's clinical history, including
previous diagnoses and procedures, usual medication, and relevant
characteristics or conditions for clinical decisions, such as allergies, being
under anticoagulant therapy, etc. The project's goal was achieved by a
multidisciplinary team that included clinicians, epidemiologists, computational
linguists, machine learning researchers and software engineers, bringing
together the expertise and perspectives of a public hospital, the university
and the private sector. Relevant benefits to users and patients are related
with facilitated access to the patient's history, which translates into
exhaustiveness in apprehending the patient's clinical past and efficiency due
to time saving.


title: Self-Attention for Incomplete Utterance Rewriting

abstract:
  Incomplete utterance rewriting (IUR) has recently become an essential task in
NLP, aiming to complement the incomplete utterance with sufficient context
information for comprehension. In this paper, we propose a novel method by
directly extracting the coreference and omission relationship from the
self-attention weight matrix of the transformer instead of word embeddings and
edit the original text accordingly to generate the complete utterance.
Benefiting from the rich information in the self-attention weight matrix, our
method achieved competitive results on public IUR datasets.


title: Line-field Coherent Sensing with LED Illumination

abstract:
  We describe a method of low-coherence interferometry based optical
profilometry using standard light-emitting diode (LED) illumination and
complementary metal-oxide-semiconductor (CMOS) image sensors. A line-field
illumination strategy allows for the simultaneous measurement of many points in
space. Micron scale accuracy and resolution are achieved and demonstrated using
a variety of targets.


title: Measuring CLEVRness: Blackbox testing of Visual Reasoning Models

abstract:
  How can we measure the reasoning capabilities of intelligence systems? Visual
question answering provides a convenient framework for testing the model's
abilities by interrogating the model through questions about the scene.
However, despite scores of various visual QA datasets and architectures, which
sometimes yield even a super-human performance, the question of whether those
architectures can actually reason remains open to debate. To answer this, we
extend the visual question answering framework and propose the following
behavioral test in the form of a two-player game. We consider black-box neural
models of CLEVR. These models are trained on a diagnostic dataset benchmarking
reasoning. Next, we train an adversarial player that re-configures the scene to
fool the CLEVR model. We show that CLEVR models, which otherwise could perform
at a human level, can easily be fooled by our agent. Our results put in doubt
whether data-driven approaches can do reasoning without exploiting the numerous
biases that are often present in those datasets. Finally, we also propose a
controlled experiment measuring the efficiency of such models to learn and
perform reasoning.


title:
Attentive Temporal Pooling for Conformer-based Streaming Language
  Identification in Long-form Speech

abstract:
  In this paper, we introduce a novel language identification system based on
conformer layers. We propose an attentive temporal pooling mechanism to allow
the model to carry information in long-form audio via a recurrent form, such
that the inference can be performed in a streaming fashion. Additionally, we
investigate two domain adaptation approaches to allow adapting an existing
language identification model without retraining the model parameters for a new
domain. We perform a comparative study of different model topologies under
different constraints of model size, and find that conformer-based models
significantly outperform LSTM and transformer based models. Our experiments
also show that attentive temporal pooling and domain adaptation improve model
accuracy.


title: The Dunkl-Laplace transform and Macdonald's hypergeometric series

abstract:
  We continue a program generalizing classical results from the analysis on
symmetric cones to the Dunkl setting for root systems of type A. In particular,
we prove a Dunkl-Laplace transform identity for Heckman-Opdam hypergeometric
functions of type A and more generally, for the associated Cherednik kernel.
This is achieved by analytic continuation from a Laplace transform identity for
non-symmetric Jack polynomials which was stated, for the symmetric case, as a
key conjecture in an unpublished manuscript of Macdonald (2013). Our proof for
the Jack polynomials is based on Dunkl operator techniques and the raising
operator of Knop and Sahi. Moreover, we use these results to establish Laplace
transform identities between hypergeometric series in terms of Jack
polynomials. Finally, we conclude with a Post-Widder inversion formula for the
Dunkl-Laplace transform.


title: Transformers in Medical Image Analysis: A Review

abstract:
  Transformers have dominated the field of natural language processing, and
recently impacted the computer vision area. In the field of medical image
analysis, Transformers have also been successfully applied to full-stack
clinical applications, including image synthesis/reconstruction, registration,
segmentation, detection, and diagnosis. Our paper presents both a position
paper and a primer, promoting awareness and application of Transformers in the
field of medical image analysis. Specifically, we first overview the core
concepts of the attention mechanism built into Transformers and other basic
components. Second, we give a new taxonomy of various Transformer architectures
tailored for medical image applications and discuss their limitations. Within
this review, we investigate key challenges revolving around the use of
Transformers in different learning paradigms, improving the model efficiency,
and their coupling with other techniques. We hope this review can give a
comprehensive picture of Transformers to the readers in the field of medical
image analysis.


title: Attention Enables Zero Approximation Error

abstract:
  Deep learning models have been widely applied in various aspects of daily
life. Many variant models based on deep learning structures have achieved even
better performances. Attention-based architectures have become almost
ubiquitous in deep learning structures. Especially, the transformer model has
now defeated the convolutional neural network in image classification tasks to
become the most widely used tool. However, the theoretical properties of
attention-based models are seldom considered. In this work, we show that with
suitable adaptations, the single-head self-attention transformer with a fixed
number of transformer encoder blocks and free parameters is able to generate
any desired polynomial of the input with no error. The number of transformer
encoder blocks is the same as the degree of the target polynomial. Even more
exciting, we find that these transformer encoder blocks in this model do not
need to be trained. As a direct consequence, we show that the single-head
self-attention transformer with increasing numbers of free parameters is
universal. These surprising theoretical results clearly explain the outstanding
performances of the transformer model and may shed light on future
modifications in real applications. We also provide some experiments to verify
our theoretical result.


title:
Role of surfactant-induced Marangoni stresses in retracting liquid
  sheets

abstract:
  In this work, we study the effect of insoluble surfactants on the
three-dimensional rim-driven retraction dynamics of thin water sheets in air.
We employ an interface-tracking/level-set method to ensure the full coupling
between the surfactant-induced Marangoni-stresses, interfacial diffusion, and
inertia. Our findings are contrasted with the (Newtonian) dynamics of a liquid
sheet edge finding that the surfactant concentration can prevent, or delay, the
breakup of the rim. Our simulations use the fastest growing Rayleigh-Plateau
instability to drive droplet detachment from the fluid sheet (rim). The results
of this work unravel the significant role of Marangoni stresses in the
retracting sheet dynamics at large elasticity numbers. We study the sensitivity
of the dynamics to the elasticity number and the rigidification of the
interface.


title:
Entropies in $\mu$-framework of canonical metrics and K-stability, II --
  Non-archimedean aspect: non-archimedean $\mu$-entropy and
  $\mu$K-semistability

abstract:
  This is the second in a series of two papers studying $\mu$-cscK metrics and
$\mu$K-stability from a new perspective, inspired by observations on
$\mu$-character in arXiv:2004.06393 and on Perelman's $W$-entropy in the first
paper arXiv:2101.11197.
  This second paper is devoted to studying a non-archimedean counterpart of
Perelman's $\mu$-entropy. The concept originally appeared as $\mu$-character of
polarized family in the previous research arXiv:2004.06393, where we used it to
introduce an analogue of CM line bundle adapted to $\mu$K-stability.
  We firstly show some differential of the characteristic $\mu$-entropy
$\mathbf{\check{\mu}}^\lambda$ is the minus of $\mu^\lambda$-Futaki invariant,
which connects $\mu^\lambda$K-semistability to the maximization of
characteristic $\mu^\lambda$-entropy. It in particular provides us a criterion
for $\mu^\lambda$K-semistability working without detecting the vector $\xi$
involved in the $\mu^\lambda_\xi$-Futaki invariant.
  In the latter part, we propose a non-archimedean pluripotential approach to
the maximization problem. In order to adjust the characteristic $\mu$-entropy
$\mathbf{\check{\mu}}^\lambda$ to Boucksom--Jonsson's non-archimedean
framework, we introduce a natural modification
$\mathbf{\check{\mu}}^\lambda_{\mathrm{NA}}$ which we call non-archimedean
$\mu$-entropy. We extend the non-archimedean $\mu$-entropy from the set of test
configurations to a space $\mathcal{E}^{\exp} (X, L)$ of non-archimedean psh
metrics on the Berkovich space $X^{\mathrm{NA}}$, which is endowed with a
complete metric structure. We introduce a measure $\int \chi
\mathcal{D}_\varphi$ on Berkovich space called moment measure for this sake,
which can be considered as a hybrid of Monge--Amp\`ere measure and
Duistermaat--Heckman measure.


title: Closing the Gap between Single-User and Multi-User VoiceFilter-Lite

abstract:
  VoiceFilter-Lite is a speaker-conditioned voice separation model that plays a
crucial role in improving speech recognition and speaker verification by
suppressing overlapping speech from non-target speakers. However, one
limitation of VoiceFilter-Lite, and other speaker-conditioned speech models in
general, is that these models are usually limited to a single target speaker.
This is undesirable as most smart home devices now support multiple enrolled
users. In order to extend the benefits of personalization to multiple users, we
previously developed an attention-based speaker selection mechanism and applied
it to VoiceFilter-Lite. However, the original multi-user VoiceFilter-Lite model
suffers from significant performance degradation compared with single-user
models. In this paper, we devised a series of experiments to improve the
multi-user VoiceFilter-Lite model. By incorporating a dual learning rate
schedule and by using feature-wise linear modulation (FiLM) to condition the
model with the attended speaker embedding, we successfully closed the
performance gap between multi-user and single-user VoiceFilter-Lite models on
single-speaker evaluations. At the same time, the new model can also be easily
extended to support any number of users, and significantly outperforms our
previously published model on multi-speaker evaluations.


title: A pathway to peptides in space through the condensation of atomic carbon

abstract:
  Organic molecules are widely present in the dense interstellar medium, and
many have been synthesized in the laboratory on Earth under the conditions
typical for an interstellar environment. Until now, however, only relatively
small molecules of biological interest have been demonstrated to form
experimentally under typical space conditions. Here we prove experimentally
that the condensation of carbon atoms on the surface of cold solid particles
(cosmic dust) leads to the formation of isomeric polyglycine monomers
(aminoketene molecules). Following encounters between aminoketene molecules,
they polymerize to produce peptides of different lengths. The chemistry
involves three of the most abundant species (CO, C and NH$_3$) present in
star-forming molecular clouds, and proceeds via a novel pathway that skips the
stage of amino acid formation in protein synthesis. The process is efficient,
even at low temperatures, without irradiation or the presence of water. The
delivery of biopolymers formed by this chemistry to rocky planets in the
habitable zone might be an important element in the origins of life.


title: Exact mediation analysis for ordinal outcome and binary mediator

abstract:
  With reference to a single mediator context, this brief report presents a
model-based strategy to estimate counterfactual direct and indirect effects
when the response variable is ordinal and the mediator is binary. Postulating a
logistic regression model for the mediator and a cumulative logit model for the
outcome, the exact parametric formulation of the causal effects is presented,
thereby extending previous work that only contained approximated results. The
identification conditions are equivalent to the ones already established in the
literature. The effects can be estimated by making use of standard statistical
software and standard errors can be computed via a bootstrap algorithm. To make
the methodology accessible, routines to implement the proposal in R are
presented in the Appendix. A natural effect model coherent with the postulated
data generating mechanism is also derived.


title: Overcoming a Theoretical Limitation of Self-Attention

abstract:
  Although transformers are remarkably effective for many tasks, there are some
surprisingly easy-looking regular languages that they struggle with. Hahn shows
that for languages where acceptance depends on a single input symbol, a
transformer's classification decisions become less and less confident (that is,
with cross-entropy approaching 1 bit per string) as input strings get longer
and longer. We examine this limitation using two languages: PARITY, the
language of bit strings with an odd number of 1s, and FIRST, the language of
bit strings starting with a 1. We demonstrate three ways of overcoming the
limitation suggested by Hahn's lemma. First, we settle an open question by
constructing a transformer that recognizes PARITY with perfect accuracy, and
similarly for FIRST. Second, we use layer normalization to bring the
cross-entropy of both models arbitrarily close to zero. Third, when
transformers need to focus on a single position, as for FIRST, we find that
they can fail to generalize to longer strings; we offer a simple remedy to this
problem that also improves length generalization in machine translation.


title: The Impact of Selfish Behavior in Load Balancing Games

abstract:
  To what extent does the structure of the players' strategy space influence
the efficiency of decentralized solutions in congestion games? In this work, we
investigate whether better performance are possible when restricting to load
balancing games in which players can only choose among single resources. We
consider three different solutions concepts, namely, approximate pure Nash
equilibria, approximate one-round walks generated by selfish players aiming at
minimizing their personal cost and approximate one-round walks generated by
cooperative players aiming at minimizing the marginal increase in the sum of
the players' personal costs. The last two concepts can be interpreted as
solutions of greedy online algorithms for the related resource selection
problem. We show that, under fairly general latency functions on the resources,
better bounds cannot be achieved if players are either weighted or asymmetric.
On the positive side, we prove that, under mild assumptions on the latency
functions, improvements on the performance of approximate pure Nash equilibria
are possible for load balancing games with weighted and symmetric players in
the case of identical resources. We also design lower bounds on the performance
of one-round walks in load balancing games with unweighted players and
identical resources.


title:
Collaborative Training of Heterogeneous Reinforcement Learning Agents in
  Environments with Sparse Rewards: What and When to Share?

abstract:
  In the early stages of human life, babies develop their skills by exploring
different scenarios motivated by their inherent satisfaction rather than by
extrinsic rewards from the environment. This behavior, referred to as intrinsic
motivation, has emerged as one solution to address the exploration challenge
derived from reinforcement learning environments with sparse rewards. Diverse
exploration approaches have been proposed to accelerate the learning process
over single- and multi-agent problems with homogeneous agents. However, scarce
studies have elaborated on collaborative learning frameworks between
heterogeneous agents deployed into the same environment, but interacting with
different instances of the latter without any prior knowledge. Beyond the
heterogeneity, each agent's characteristics grant access only to a subset of
the full state space, which may hide different exploration strategies and
optimal solutions. In this work we combine ideas from intrinsic motivation and
transfer learning. Specifically, we focus on sharing parameters in actor-critic
model architectures and on combining information obtained through intrinsic
motivation with the aim of having a more efficient exploration and faster
learning. We test our strategies through experiments performed over a modified
ViZDooM's My Way Home scenario, which is more challenging than its original
version and allows evaluating the heterogeneity between agents. Our results
reveal different ways in which a collaborative framework with little additional
computational cost can outperform an independent learning process without
knowledge sharing. Additionally, we depict the need for modulating correctly
the importance between the extrinsic and intrinsic rewards to avoid undesired
agent behaviors.


title: Removing Popular Faces in Curve Arrangements

abstract:
  A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate popular faces in an
arrangement by inserting a single additional curve. This turns out to be
already NP-hard; however, we present a probabilistic FPT-approach in the number
of such faces.


title:
Clarifying MCMC-based training of modern EBMs : Contrastive Divergence
  versus Maximum Likelihood

abstract:
  The Energy-Based Model (EBM) framework is a very general approach to
generative modeling that tries to learn and exploit probability distributions
only defined though unnormalized scores. It has risen in popularity recently
thanks to the impressive results obtained in image generation by parameterizing
the distribution with Convolutional Neural Networks (CNN). However, the
motivation and theoretical foundations behind modern EBMs are often absent from
recent papers and this sometimes results in some confusion. In particular, the
theoretical justifications behind the popular MCMC-based learning algorithm
Contrastive Divergence (CD) are often glossed over and we find that this leads
to theoretical errors in recent influential papers (Du & Mordatch, 2019; Du et
al., 2020). After offering a first-principles introduction of MCMC-based
training, we argue that the learning algorithm they use can in fact not be
described as CD and reinterpret theirs methods in light of a new
interpretation. Finally, we discuss the implications of our new interpretation
and provide some illustrative experiments.


title:
Bubble Planner: Planning High-speed Smooth Quadrotor Trajectories using
  Receding Corridors

abstract:
  Quadrotors are agile platforms. With human experts, they can perform
extremely high-speed flights in cluttered environments. However, fully
autonomous flight at high speed remains a significant challenge. In this work,
we propose a motion planning algorithm based on the corridor-constrained
minimum control effort trajectory optimization (MINCO) framework. Specifically,
we use a series of overlapping spheres to represent the free space of the
environment and propose two novel designs that enable the algorithm to plan
high-speed quadrotor trajectories in real-time. One is a sampling-based
corridor generation method that generates spheres with large overlapped areas
(hence overall corridor size) between two neighboring spheres. The second is a
Receding Horizon Corridors (RHC) strategy, where part of the previously
generated corridor is reused in each replan. Together, these two designs
enlarge the corridor spaces in accordance with the quadrotor's current state
and hence allow the quadrotor to maneuver at high speeds. We benchmark our
algorithm against other state-of-the-art planning methods to show its
superiority in simulation. Comprehensive ablation studies are also conducted to
show the necessity of the two designs. The proposed method is finally evaluated
on an autonomous LiDAR-navigated quadrotor UAV in woods environments, achieving
flight speeds over 13.7 m/s without any prior map of the environment or
external localization facility.


title: Nonunitary Superconductivity in Complex Quantum Materials

abstract:
  We present a comprehensive discussion on nonunitary superconductivity in
complex quantum materials. Starting with a brief review of the notion of
nonunitary superconductivity, we discuss its spectral signatures in simple
models with only the spin as an internal degree of freedom. In complex
materials with multiple internal degrees of freedom, there are many more
possibilities for the development of nonunitary order parameters. We provide
examples focusing on d-electron systems with two orbitals, applicable to a
variety of materials. We discuss the consequences for the superconducting
spectra, highlighting that gap openings of band crossings at finite energies
can be attributed to a nonunitary order parameter if this is associated with a
finite superconducting fitness matrix $\hat{F}_C(\mathbf{k})$. We speculate
that nonunitary superconductivity in complex quantum materials is in fact very
common and can be associated with multiple cases of time-reversal symmetry
breaking superconductors.


title:
Cybersecurity Challenges in the Offshore Oil and Gas Industry: An
  Industrial Cyber-Physical Systems (ICPS) Perspective

abstract:
  The offshore oil and gas industry has recently been going through a
digitalisation drive, with use of `smart' equipment using technologies like the
Industrial Internet of Things (IIoT) and Industrial Cyber-Physical Systems
(ICPS). There has also been a corresponding increase in cyber attacks targeted
at oil and gas companies. Oil production offshore is usually in remote
locations, requiring remote access and control. This is achieved by integrating
ICPS, Supervisory, Control and Data Acquisition (SCADA) systems, and IIoT
technologies. A successful cyber attack against an oil and gas offshore asset
could have a devastating impact on the environment, marine ecosystem and safety
of personnel. Any disruption to the world's supply of oil and gas (O\&G) can
also have an effect on oil prices and in turn, the global economy. This makes
it important to secure the industry against cyber threats. We describe the
potential cyberattack surface within the oil and gas industry, discussing
emerging trends in the offshore sub-sector, and provide a timeline of known
cyberattacks. We also present a case study of a subsea control system
architecture typically used in offshore oil and gas operations and highlight
potential vulnerabilities affecting the components of the system. This study is
the first to provide a detailed analysis on the attack vectors in a subsea
control system and is crucial to understanding key vulnerabilities, primarily
to implement efficient mitigation methods that safeguard the safety of
personnel and the environment when using such systems.


title: Quantum Deep Reinforcement Learning for Robot Navigation Tasks

abstract:
  In this work, we utilize Quantum Deep Reinforcement Learning as method to
learn navigation tasks for a simple, wheeled robot in three simulated
environments of increasing complexity. We show similar performance of a
parameterized quantum circuit trained with well established deep reinforcement
learning techniques in a hybrid quantum-classical setup compared to a classical
baseline. To our knowledge this is the first demonstration of quantum machine
learning (QML) for robotic behaviors. Thus, we establish robotics as a viable
field of study for QML algorithms and henceforth quantum computing and quantum
machine learning as potential techniques for future advancements in autonomous
robotics. Beyond that, we discuss current limitations of the presented approach
as well as future research directions in the field of quantum machine learning
for autonomous robots.


title: FreeSOLO: Learning to Segment Objects without Annotations

abstract:
  Instance segmentation is a fundamental vision task that aims to recognize and
segment each object in an image. However, it requires costly annotations such
as bounding boxes and segmentation masks for learning. In this work, we propose
a fully unsupervised learning method that learns class-agnostic instance
segmentation without any annotations. We present FreeSOLO, a self-supervised
instance segmentation framework built on top of the simple instance
segmentation method SOLO. Our method also presents a novel localization-aware
pre-training framework, where objects can be discovered from complicated scenes
in an unsupervised manner. FreeSOLO achieves 9.8% AP_{50} on the challenging
COCO dataset, which even outperforms several segmentation proposal methods that
use manual annotations. For the first time, we demonstrate unsupervised
class-agnostic instance segmentation successfully. FreeSOLO's box localization
significantly outperforms state-of-the-art unsupervised object
detection/discovery methods, with about 100% relative improvements in COCO AP.
FreeSOLO further demonstrates superiority as a strong pre-training method,
outperforming state-of-the-art self-supervised pre-training methods by +9.8% AP
when fine-tuning instance segmentation with only 5% COCO masks. Code is
available at: github.com/NVlabs/FreeSOLO


title: Cavity induced bifurcation in classical rate theory

abstract:
  We show how coupling an ensemble of bistable systems to a common cavity field
affects the collective stochastic behavior of this ensemble. In particular, the
cavity provides an effective interaction between the systems, and
parametrically modifies the transition rates between the metastable states. We
predict that for a coupling strength exceeding a certain threshold, the cavity
induces a spontaneous symmetry breaking where the stationary states of the
bistable system bifurcate and the systems coalesce preferentially in one of the
states. The effect crucially depends on the distribution of system-cavity
coupling strengths. In the case of alternating signs of the couplings, the
bifurcation shows up as a phase separation. Our results are of particular
relevance in polaritonic chemistry where the presence of a cavity has been
suggested to affect chemical reactions.


title:
Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning
  with Provable Convergence

abstract:
  NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking
metric in information retrieval and machine learning. However, efficient and
provable stochastic methods for maximizing NDCG are still lacking, especially
for deep models. In this paper, we propose a principled approach to optimize
NDCG and its top-$K$ variant. First, we formulate a novel compositional
optimization problem for optimizing the NDCG surrogate, and a novel bilevel
compositional optimization problem for optimizing the top-$K$ NDCG surrogate.
Then, we develop efficient stochastic algorithms with provable convergence
guarantees for the non-convex objectives. Different from existing NDCG
optimization methods, the per-iteration complexity of our algorithms scales
with the mini-batch size instead of the number of total items. To improve the
effectiveness for deep learning, we further propose practical strategies by
using initial warm-up and stop gradient operator. Experimental results on
multiple datasets demonstrate that our methods outperform prior ranking
approaches in terms of NDCG. To the best of our knowledge, this is the first
time that stochastic algorithms are proposed to optimize NDCG with a provable
convergence guarantee.


title: Consistent data fusion with Parker

abstract:
  When combining data from multiple sources, inconsistent data complicates the
production of a coherent result. In this paper, we introduce a new type of
constraints called edit rules under a partial key (EPKs). These constraints can
model inconsistencies both within and between sources, but in a loosely-coupled
matter. We show that we can adapt the well-known set cover methodology to the
setting of EPKs and this yields an efficient algorithm to find minimal cost
repairs of sources. This algorithm is implemented in a repair engine called
Parker. Empirical results show that Parker is several orders of magnitude
faster than state-of-the-art repair tools. At the same time, the quality of the
repairs in terms of $F_1$-score ranges from comparable to better compared to
these tools.


title: Competition among alliances of different sizes

abstract:
  To understand the biodiversity of an ecosystem cannot be understood by solely
analyzing the pair relations of competing species. Instead, we should consider
multi-point interactions because the presence of a third party could change the
original microscopic outcome significantly. In this way an alliance may emerge
where species, who may have biased relations otherwise, can protect each other
from an external invader. Such an alliance can be formed by two, three or even
more species. By introducing a minimal model where six species compete for
space we here study how the size of an alliance determines the vitality of a
formation. We show that in the majority of parameter space the group of the
smallest size prevails and other solutions can only be observed in a limited
parameter range. These phases are separated by discontinuous phase transitions
which can only be identified by intensive numerical efforts due to serious
finite size effects and long relaxation processes.

categories: q-bio.PE cond-mat.stat-mech physics.bio-ph physics.soc-ph


title: Sequential Asset Ranking within Nonstationary Time Series

abstract:
  Financial time series are both autocorrelated and nonstationary, presenting
modelling challenges that violate the independent and identically distributed
random variables assumption of most regression and classification models. The
prediction with expert advice framework makes no assumptions on the
data-generating mechanism yet generates predictions that work well for all
sequences, with performance nearly as good as the best expert with hindsight.
We conduct research using S&P 250 daily sampled data, extending the academic
research into cross-sectional momentum trading strategies. We introduce a novel
ranking algorithm from the prediction with expert advice framework, the naive
Bayes asset ranker, to select subsets of assets to hold in either long-only or
long/short portfolios. Our algorithm generates the best total returns and
risk-adjusted returns, net of transaction costs, outperforming the long-only
holding of the S&P 250 with hindsight. Furthermore, our ranking algorithm
outperforms a proxy for the regress-then-rank cross-sectional momentum trader,
a sequentially fitted curds and whey multivariate regression procedure.


title: SonOpt: Sonifying Bi-objective Population-Based Optimization Algorithms

abstract:
  We propose SonOpt, the first (open source) data sonification application for
monitoring the progress of bi-objective population-based optimization
algorithms during search, to facilitate algorithm understanding. SonOpt
provides insights into convergence/stagnation of search, the evolution of the
approximation set shape, location of recurring points in the approximation set,
and population diversity. The benefits of data sonification have been shown for
various non-optimization related monitoring tasks. However, very few attempts
have been made in the context of optimization and their focus has been
exclusively on single-objective problems. In comparison, SonOpt is designed for
bi-objective optimization problems, relies on objective function values of
non-dominated solutions only, and is designed with the user (listener) in mind;
avoiding convolution of multiple sounds and prioritising ease of familiarizing
with the system. This is achieved using two sonification paths relying on the
concepts of wavetable and additive synthesis. This paper motivates and
describes the architecture of SonOpt, and then validates SonOpt for two popular
multi-objective optimization algorithms (NSGA-II and MOEA/D). Experience SonOpt
yourself via https://github.com/tasos-a/SonOpt-1.0 .


title: Euler integral as a source of chaos in the three-body problem

abstract:
  In this paper we address, from a purely numerical point of view, the
question, raised in [20, 21], and partly considered in [22, 9, 3], whether a
certain function, referred to as "Euler Integral", is a quasi-integral along
the trajectories of the three-body problem. Differently from our previous
investigations, here we focus on the region of the "unperturbed separatrix",
which turns to be complicated by a collision singularity. Concretely, we reduce
the Hamiltonian to two degrees of freedom and, after fixing some energy level,
we discuss in detail the resulting three-dimensional phase space around an
elliptic and an hyperbolic periodic orbit. After measuring the strength of
variation of the Euler Integral (which are in fact small), we detect the
existence of chaos closely to the unperturbed separatrix. The latter result is
obtained through a careful use of the machinery of covering relations,
developed in [13, 24, 23].


title:
Finite-size effects in the diffusion dynamics of a glass-forming binary
  mixture with large size ratio

abstract:
  Extensive molecular dynamics (MD) computer simulations of an equimolar
glass-forming AB mixture with large size ratio are presented. While the large A
particles show a glass transition around the critical density of mode coupling
theory $\rho_c$, the small B particles remain mobile with a relatively weak
decrease of their self diffusion coefficient $D_{\rm B}$ with increasing
density. Surprisingly, around $\rho_c$, the self-diffusion coefficient of the A
particles, $D_{\rm A}$, also starts to follow a rather weak dependence on
density. We show that this is due to finite-size effects that can be understood
from the analysis of the collective interdiffusion dynamics.


title:
Improved Hausdorff dimension estimate of the singular set of the
  supercritical surface quasigeostrophic equation

abstract:
  We prove that the spacetime singular set of any suitable Leray-Hopf solution
of the surface quasigeostrophic equation with fractional dissipation of order
$0< \alpha < \frac{1}{2}$ has Hausdorff dimension at most
$\frac{1}{2\alpha^2}\,.$ This result improves previously known dimension
estimate established in [6] and builds on the excess decay result and the
control on the particle flow already developed there. The improvement lies in
the initial iteration of the local energy inequality in analogy with the
celebrated result of Caffarelli-Kohn-Nirenberg [2] for the Navier-Stokes
equations.


title: Finding Inverse Document Frequency Information in BERT

abstract:
  For many decades, BM25 and its variants have been the dominant document
retrieval approach, where their two underlying features are Term Frequency (TF)
and Inverse Document Frequency (IDF). The traditional approach, however, is
being rapidly replaced by Neural Ranking Models (NRMs) that can exploit
semantic features. In this work, we consider BERT-based NRMs and study if IDF
information is present in the NRMs. This simple question is interesting because
IDF has been indispensable for the traditional lexical matching, but global
features like IDF are not explicitly learned by neural language models
including BERT. We adopt linear probing as the main analysis tool because
typical BERT based NRMs utilize linear or inner-product based score
aggregators. We analyze input embeddings, representations of all BERT layers,
and the self-attention weights of CLS. By studying MS-MARCO dataset with three
BERT-based models, we show that all of them contain information that is
strongly dependent on IDF.


title:
A decreasing upper bound of energy for time-fractional phase-field
  equations

abstract:
  In this article, we study the energy dissipation property of time-fractional
Allen-Cahn equation. We propose a decreasing upper bound of energy that
decreases with respect to time and coincides with the original energy at $t =
0$ and as $t$ tends to $\infty$. This upper bound can also be viewed as a
nonlocal-in-time modified energy, the summation of the original energy and an
accumulation term due to the memory effect of time fractional derivative. In
particular, this indicates that the original energy indeed decays w.r.t. time
in a small neighborhood at $t=0$. We illustrate the theory mainly with the
time-fractional Allen-Cahn equation, but it could be applied to other
time-fractional phase-field models such as the Cahn-Hilliard equation.
  On the discrete level, the first-order L1 and second-order L2 schemes for
time-fractional Allen-Cahn equation have similar decreasing modified energies,
so that the stability can be established. Some numerical results are provided
to illustrate the behavior of this modified energy and to verify our
theoretical results.


title: Black-Box Algorithm Synthesis -- Divide-and-Conquer and More

abstract:
  Algorithm synthesis is a newly emerging branch of program synthesis,
targeting to automatically apply a predefined class of algorithms to a
user-provided program. In algorithm synthesis, one popular topic is to
synthesize divide-and-conquer-style parallel programs. Existing approaches on
this topic rely on the syntax of the user-provided program and require it to
follow a specific format, namely single-pass.
  In many cases, implementing such a program is still difficult for the user.
Therefore, in this paper, we study the black-box synthesis for
divide-and-conquer which removes the requirement on the syntax and propose a
novel algorithm synthesizer AutoLifter. Besides, we show that AutoLifter can be
generalized to other algorithms beyond divide-and-conquer. We propose a novel
type of synthesis tasks, namely lifting problems, and show that AutoLifter can
be applied to those algorithms where the synthesis task is an instance of
lifting problems. To our knowledge, AutoLifter is the first algorithm
synthesizer that generalizes across algorithm types. We evaluate AutoLifter on
two datasets containing 57 tasks covering five different algorithms. The
results demonstrate the effectiveness of AutoLifter for solving lifting
problems and show that though AutoLifter does not access the syntax of the
user-provided program, it still achieves competitive performance compared with
white-box approaches for divide-and-conquer.


title:
Towards a Heterogeneous Smart Electromagnetic Environment for
  Millimeter-Wave Communications: An Industrial Viewpoint

abstract:
  Fifth generation (5G) and beyond communication systems open the door to
millimeter Wave (mmWave) frequency bands to leverage the extremely large
operating bandwidths and deliver unprecedented network capacity. These
frequency bands are affected by high propagation losses that severely limit the
achievable coverage. The simplest way to address this problem would be to
increase the number of installed mmWave base stations (BSs), at the same time
augmenting the overall network cost, power consumption and ElectroMagnetic
Field (EMF) levels. As alternative direction, here we propose to complement the
macro-layer of mmWave BSs with a heterogeneous deployment of Smart
Electromagnetic (Smart EM) Entities - namely IAB nodes, Smart Repeaters,
Reconfigurable Intelligent Surfaces (RISs) and passive surfaces - that is
judiciously planned to minimize the total installation costs while at the same
time optimizing the network spectral efficiency. Initial network planning
results underline the effectiveness of the proposed approach. The available
technologies and the key research directions for achieving this view are
thoroughly discussed by accounting for issues ranging from system-level design
to the development of new materials.


title: LAGC Semantics of Concurrent Programming Languages

abstract:
  Formal, mathematically rigorous programming language semantics are the
essential prerequisite for the design of logics and calculi that permit
automated reasoning about concurrent programs. We propose a novel modular
semantics designed to align smoothly with program logics used in deductive
verification and formal specification of concurrent programs. Our semantics
separates local evaluation of expressions and statements performed in an
abstract, symbolic environment from their composition into global computations,
at which point they are concretised. This makes incremental addition of new
language concepts possible, without the need to revise the framework. The basis
is a generalisation of the notion of a program trace as a sequence of evolving
states that we enrich with event descriptors and trailing continuation markers.
This allows to postpone scheduling constraints from the level of local
evaluation to the global composition stage, where well-formedness predicates
over the event structure declaratively characterise a wide range of concurrency
models. We also illustrate how a sound program logic and calculus can be
defined for this semantics.


title:
Electromagnetic quasinormal modes of Schwarzschild-anti-de Sitter black
  holes: bifurcations, spectral similarity, and exact solutions in the large
  black hole limit

abstract:
  We revisit the peculiar electromagnetic quasinormal mode spectrum of an
asymptotically anti-de Sitter Schwarzschild black hole. Recent numerical
calculations have shown that some quasinormal mode frequencies become purely
overdamped at some critical black hole sizes, where the spectrum also
bifurcates. In this paper, we shed light on unnoticed and unexplained
properties of this spectrum by exploiting some novel analytic results for the
large black hole limit. We demonstrate, both numerically and analytically, that
the quasinormal mode spectra of large black holes become approximately
isospectral, and refer to this new symmetry property as spectral similarity. We
take advantage of this spectral similarity to derive a precise analytic
expression for the locations of the bifurcations, in which a surprising
Feigenbaum-like constant appears. Also in this large black hole limit, we show
that the differential operator is of Sturm-Liouville type and thus
self-adjoint. We derive an exact solution for its spectrum and eigenfunctions,
and find that large black holes cannot be made to vibrate with electromagnetic
perturbations, independently of the boundary conditions imposed at spatial
infinity. Finally, we characterize the insensitivity of the spectrum to
different boundary conditions by analyzing the expansion of the quasinormal
mode spectrum around the large black hole limit.


title:
Situational Graphs for Robot Navigation in Structured Indoor
  Environments

abstract:
  Autonomous mobile robots should be aware of their situation, understood as a
comprehensive understanding of the environment along with the estimation of its
own state, to successfully make decisions and execute tasks in natural
environments. 3D scene graphs are an emerging field of research with great
potential to represent these situations in a joint model comprising geometric,
semantic and relational/topological dimensions. Although 3D scene graphs have
already been utilized for this, further research is still required to
effectively deploy them on-board mobile robots.
  To this end, we present in this paper a real-time online built Situational
Graphs (S-Graphs), composed of a single graph representing the environment,
while simultaneously improving the robot pose estimation. Our method utilizes
odometry readings and planar surfaces extracted from 3D LiDAR scans, to
construct and optimize in real-time a three layered S-Graph that includes a
robot tracking layer where the robot poses are registered, a metric-semantic
layer with features such as planar walls and our novel topological layer
constraining higher-level features such as corridors and rooms. Our proposal
does not only demonstrate state-of-the-art results for pose estimation of the
robot, but also contributes with a metric-semantic-topological model of the
environment


title: The $M_d$-Approximation Property and Unitarisability

abstract:
  We define a strengthening of the Haagerup-Kraus approximation property by
means of the algebras of generalised Herz-Schur multipliers $M_d(G)$ ($d\geq
1$) introduced by Pisier. We show that unitarisable groups satisfying this
property for all $d\geq 1$ are amenable. Moreover, we show that groups acting
properly on finite-dimensional CAT(0) cube complexes satisfy $M_d$-AP for all
$d\geq 1$. We also give examples of non-weakly amenable groups satisfying
$M_d$-AP for all $d\geq 1$.


title: Detection by Sampling: Massive MIMO Detector based on Langevin Dynamics

abstract:
  Optimal symbol detection in multiple-input multiple-output (MIMO) systems is
known to be an NP-hard problem. Hence, the objective of any detector of
practical relevance is to get reasonably close to the optimal solution while
keeping the computational complexity in check. In this work, we propose a MIMO
detector based on an annealed version of Langevin (stochastic) dynamics. More
precisely, we define a stochastic dynamical process whose stationary
distribution coincides with the posterior distribution of the symbols given our
observations. In essence, this allows us to approximate the maximum a
posteriori estimator of the transmitted symbols by sampling from the proposed
Langevin dynamic. Furthermore, we carefully craft this stochastic dynamic by
gradually adding a sequence of noise with decreasing variance to the
trajectories, which ensures that the estimated symbols belong to a
pre-specified discrete constellation. Through numerical experiments, we show
that our proposed detector yields state-of-the-art symbol error rate
performance.


title:
Coherent $J/ \psi$ electroproduction on $^4$He and $^3$He at the
  Electron-Ion Collider: probing nuclear shadowing one nucleon at a time

abstract:
  While the phenomenon of gluon nuclear shadowing at small $x$ has been getting
confirmation in QCD analyses of various LHC measurements involving heavy
nuclei, it has not been possible so far to establish experimentally the number
of target nucleons responsible for nuclear shadowing in a given process. To
address this issue, we study coherent $J/\psi$ electroproduction on $^4$He and
$^3$He in the kinematics of a future electron-ion collider (EIC). Using an
accurate treatment of the wave functions of $^4$He and $^3$He, we show that
this process has the power to disentangle the contributions of the interaction
with a specific number of nucleons, in particular, the contribution of two
nucleons at the momentum transfer $t \neq 0$. This challenging, first ever
calculation of coherent vector meson production on light nuclei, using
realistic nuclear wave functions, provides an additional test of models of
nuclear shadowing and a novel probe of the gluon distribution in impact
parameter representation, allowing for a 3D imaging of gluons in light nuclei.
Besides, thanks to this analysis, unique information on the real part of the
corresponding scattering amplitude could be accessed.


title:
Energy-Efficient Transmission Range and Duration for Cognitive Radio
  Sensor Networks

abstract:
  Cognitive Radio (CR) promises an efficient utilization of radio spectrum
resources by enabling dynamic spectrum access to overcome the spectrum scarcity
problem. Cognitive Radio Sensor Networks (CRSNs) are one type of Wireless
Sensor Networks (WSNs) equipped with CR capabilities. CRSN nodes need to
operate energy-efficiently to extend network lifetime due to their limited
battery capacity. In this paper, for the first time in literature, we formulate
the problem of finding a common energy-efficient transmission range and
transmission duration for all CRSN nodes and network deployment that would
minimize the energy consumed per goodput per meter toward the sink in a greedy
forwarding scenario. Results reveal non-trivial relations for energy-efficient
CRSN transmission range and duration as a function of nine critical network
parameters such as primary user activity levels. These relations provide
valuable insights for detailed CRSN designs prior to deployment.


title: Hydrodynamics of a single filament moving in a fluid spherical membrane

abstract:
  Dynamic organization of the cytoskeletal filaments and rod-like proteins in
the cell membrane and other biological interfaces occurs in many cellular
processes. Previous modeling studies have considered the dynamics of a single
rod on fluid planar membranes. We extend these studies to the more
physiologically relevant case of a single filament moving in a spherical
membrane. Specifically, we use a slender-body formulation to compute the
translational and rotational resistance of a single filament of length $L$
moving in a membrane of radius $R$ and 2D viscosity $\eta_m$, and surrounded on
its interior and exterior with Newtonian fluids of viscosities $\eta^{-}$ and
$\eta^{+}$. We first discuss the case where the filament's curvature is at its
minimum $\kappa=1/R$. We show that the boundedness of spherical geometry gives
rise to flow confinement effects that increase in strength with increasing the
ratio of filament's length to membrane radius $L/R$. These confinement flows
only result in a mild increase in filament's resistance along its axis,
$\xi_{\parallel}$, and its rotational resistance, $\xi_{\Omega}$. As a result,
our predictions of $\xi_\parallel$ and $\xi_{\Omega}$ can be quantitatively
mapped to the results on a planar membrane. In contrast, we find that the drag
in perpendicular direction, $\xi_\perp$, increases superlinearly with the
filament's length, when $L/R >1$ and ultimately $\xi_\perp \to \infty$ as $L/R
\to \pi$. Next, we consider the effect of the filament's curvature, $\kappa$,
on its parallel motion, while fixing the membrane's radius. We show that the
flow around the filament becomes increasingly more asymmetric with increasing
its curvature. These flow asymmetries induce a net torque on the filament,
coupling its parallel and rotational dynamics. This coupling becomes stronger
with increasing $L/R$ and $\kappa$.


title: Unconventional mechanism of virtual-state population through dissipation

abstract:
  Virtual states are a central concept in quantum mechanics. By definition, the
probability of finding a quantum system in a virtual state should be
vanishingly small at all times. In contrast to this notion, we report a
phenomenon occurring in open quantum systems by which virtual states can
acquire a sizable population in the long time limit, even if they are not
directly coupled to any dissipative channel. This means that the situation
where the virtual state remains unpopulated can be metastable. We describe this
effect by introducing a two-step adiabiatic elimination method, that we termed
hierarchical adiabatic elimination, which allows one to obtain analytical
expressions of the timescale of metastability in general open quantum systems.
We show how these results can be relevant for practical questions such as the
generation of stable and metastable entangled states in dissipative systems of
interacting qubits.


title: Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast}$ Theory

abstract:
  We use massive spinor helicity formalism to study scattering amplitudes in
$\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the
amplitudes at an arbitrary point in the Coulomb branch of this theory. We
compute amplitudes using projection from $\mathcal{N}=4$ theory and write three
point amplitudes in a convenient form using special kinematics. We then compute
four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We
find some of the shifted amplitudes have a pole at $z=\infty$. Taking the
residue at $z=\infty$ into account ensures little group covariance of the final
result.


title:
Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing?
  A Structured Review

abstract:
  Advocates for Neuro-Symbolic AI (NeSy) assert that combining deep learning
with symbolic reasoning will lead to stronger AI than either paradigm on its
own. As successful as deep learning has been, it is generally accepted that
even our best deep learning systems are not very good at abstract reasoning.
And since reasoning is inextricably linked to language, it makes intuitive
sense that Natural Language Processing (NLP), would be a particularly
well-suited candidate for NeSy. We conduct a structured review of studies
implementing NeSy for NLP, challenges and future directions, and aim to answer
the question of whether NeSy is indeed meeting its promises: reasoning,
out-of-distribution generalization, interpretability, learning and reasoning
from small data, and transferability to new domains. We examine the impact of
knowledge representation, such as rules and semantic networks, language
structure and relational structure, and whether implicit or explicit reasoning
contributes to higher promise scores. We find that knowledge encoded in
relational structures and explicit reasoning tend to lead to more NeSy goals
being satisfied. We also advocate for a more methodical approach to the
application of theories of reasoning, which we hope can reduce some of the
friction between the symbolic and sub-symbolic schools of AI.


title:
The evolution of the Si IV content in the Universe from the epoch of
  reionization to cosmic noon

abstract:
  We investigate the abundance and distribution of metals in the high-redshift
intergalactic medium and circum-galactic medium through the analysis of a
sample of almost 600 SiIV absorption lines detected in high and intermediate
resolution spectra of 147 quasars. The evolution of the number density of SiIV
lines, the column density distribution function and the cosmic mass density are
studied in the redshift interval 1.7 <= z <= 6.2 and for log N(SiIV) >= 12.5.
All quantities show a rapid increase between z~6 and z< 5 and then an almost
constant behaviour to z~2 in very good agreement with what is already observed
for CIV absorption lines. The present results are challenging for numerical
simulations: when simulations reproduce our SiIV results, they tend to
underpredict the properties of CIV, and when the properties of CIV are
reproduced, the number of strong SiIV lines (log N(SiIV) > 14) is
overpredicted.


title:
A real-space many-body marker for correlated ${\mathbb Z}_2$ topological
  insulators

abstract:
  Taking the clue from the modern theory of the polarization [R. Resta, Rev.
Mod. Phys. 66, 899 (1994)], we identify an operator to distinguish between
${\mathbb Z}_2$-even (trivial) and ${\mathbb Z}_2$-odd (topological) insulators
in two spatial dimensions. Its definition extends the position operator [R.
Resta and S. Sorella, Phys. Rev. Lett. 82, 370 (1999)], which was introduced in
one-dimensional systems. We illustrate a few examples of non-interacting
models, where single-particle wave functions are defined and allow for a direct
comparison with standard techniques. However, its formulation in the Fock space
opens the possibility to investigate interacting systems by a direct
computation of an expectation value over the ground-state wave function (or any
approximation of it).


title: Synthesizing Efficient Dynamic Programming Algorithms

abstract:
  Dynamic programming is an important optimization technique, but designing
efficient dynamic programming algorithms can be difficult even for professional
programmers. Motivated by this point, we propose a synthesizer namely MetHyl,
which automatically synthesizes efficient dynamic programming algorithms from a
possibly inefficient program in the form of relational hylomorphism. MetHyl
consists of a transformation system and efficient synthesis algorithms, where
the former transforms a hylomorphism to an efficient dynamic programming
algorithm via four synthesis tasks, and the latter solves these tasks
efficiently. We evaluate MetHyl on 37 tasks related to 16 optimization problems
collected from Introduction to Algorithm. The results show that MetHyl achieves
exponential speed-ups on 97.3% tasks and the time complexity of the standard
solutions on 70.3% tasks with an average time cost of less than one minute.


title:
Engineering symmetry-selective couplings of a superconducting artificial
  molecule to microwave waveguides

abstract:
  Tailoring the decay rate of structured quantum emitters into their
environment opens new avenues for nonlinear quantum optics, collective
phenomena, and quantum communications. Here we demonstrate a novel coupling
scheme between an artificial molecule comprising two identical, strongly
coupled transmon qubits, and two microwave waveguides. In our scheme, the
coupling is engineered so that transitions between states of the same
(opposite) symmetry, with respect to the permutation operator, are
predominantly coupled to one (the other) waveguide. The symmetry-based coupling
selectivity, as quantified by the ratio of the coupling strengths, exceeds a
factor of 30 for both the waveguides in our device. In addition, we implement a
two-photon Raman process activated by simultaneously driving both waveguides,
and show that it can be used to coherently couple states of different symmetry
in the single-excitation manifold of the molecule. Using that process, we
implement frequency conversion across the waveguides, mediated by the molecule,
with efficiency of about 95%. Finally, we show that this coupling arrangement
makes it possible to straightforwardly generate spatially-separated Bell states
propagating across the waveguides. We envisage further applications to quantum
thermodynamics, microwave photodetection, and photon-photon gates.


title: BERTVision -- A Parameter-Efficient Approach for Question Answering

abstract:
  We present a highly parameter efficient approach for Question Answering that
significantly reduces the need for extended BERT fine-tuning. Our method uses
information from the hidden state activations of each BERT transformer layer,
which is discarded during typical BERT inference. Our best model achieves
maximal BERT performance at a fraction of the training time and GPU or TPU
expense. Performance is further improved by ensembling our model with BERTs
predictions. Furthermore, we find that near optimal performance can be achieved
for QA span annotation using less training data. Our experiments show that this
approach works well not only for span annotation, but also for classification,
suggesting that it may be extensible to a wider range of tasks.


title: Self-Distilled StyleGAN: Towards Generation from Internet Photos

abstract:
  StyleGAN is known to produce high-fidelity images, while also offering
unprecedented semantic editing. However, these fascinating abilities have been
demonstrated only on a limited set of datasets, which are usually structurally
aligned and well curated. In this paper, we show how StyleGAN can be adapted to
work on raw uncurated images collected from the Internet. Such image
collections impose two main challenges to StyleGAN: they contain many outlier
images, and are characterized by a multi-modal distribution. Training StyleGAN
on such raw image collections results in degraded image synthesis quality. To
meet these challenges, we proposed a StyleGAN-based self-distillation approach,
which consists of two main components: (i) A generative-based self-filtering of
the dataset to eliminate outlier images, in order to generate an adequate
training set, and (ii) Perceptual clustering of the generated images to detect
the inherent data modalities, which are then employed to improve StyleGAN's
"truncation trick" in the image synthesis process. The presented technique
enables the generation of high-quality images, while minimizing the loss in
diversity of the data. Through qualitative and quantitative evaluation, we
demonstrate the power of our approach to new challenging and diverse domains
collected from the Internet. New datasets and pre-trained models are available
at https://self-distilled-stylegan.github.io/ .


title:
Impact of metastable defect structures on carrier recombination in solar
  cells

abstract:
  The efficiency of a solar cell is often limited by electron-hole
recombination mediated by defect states within the band gap of the photovoltaic
(PV) semiconductor. The Shockley-Read-Hall (SRH) model considers a static trap
that can successively capture electrons and holes. In reality however, true
trap levels vary with both the defect charge state and local structure. Here we
consider the role of metastable structural configurations in capturing
electrons and holes, taking the tellurium interstitial in CdTe as an
illustrative example. Consideration of the defect dynamics, and
symmetry-breaking, changes the qualitative behaviour and activates new pathways
for carrier capture. Our results reveal the potential importance of metastable
defect structures in non-radiative recombination, in particular for
semiconductors with anharmonic/ionic-covalent bonding, multinary compositions,
low crystal symmetries or highly-mobile defects.


title:
Geometric decomposition of geodesics and null phase curves using
  Majorana star representation

abstract:
  Geodesics are the shortest curves between any two points on a given surface.
Geodesics in the state space of quantum systems play an important role in the
theory of geometric phases, as these are also the curves along which the
acquired geometric phase is zero. Null phase curves (NPCs) are the
generalization of the geodesics, which are defined as the curves along which
the acquired geometric phase is zero even though they need not be the shortest
curves between two points. Here we present a geometric decomposition of
geodesics and NPCs in higher-dimensional state space, which allows
understanding the intrinsic symmetries of these curves. We use Majorana star
representation to decompose a geodesic in the $n$-dimensional Hilbert space to
$n-1$ curves on the Bloch sphere and show that all the $n-1$ curves are
circular segments with specific properties that are determined by the inner
product of the end states connected by the given geodesic. We also propose a
method to construct infinitely many NPCs between any two arbitrary states for
$(n>2)$-dimensional Hilbert space using our geometric decomposition.


title: No-go guide for the Hubble tension : matter perturbations

abstract:
  The Hubble tension seems to be a crisis with $\sim5\sigma$ discrepancy
between the most recent local distance ladder measurement from Type Ia
supernovae calibrated by Cepheids and the global fitting constraint from the
cosmic microwave background data. To narrow down the possible late-time
solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D
105 (2022) L021301] an improved inverse distance ladder method calibrated by
the absolute measurements of the Hubble expansion rate at high redshifts from
the cosmic chronometer data, and found no appealing evidence for new physics at
the late time beyond the $\Lambda$CDM model characterized by a parametrization
based on the cosmic age. In this paper, we further investigate the perspective
of this improved inverse distance ladder method by including the late-time
matter perturbation growth data. Independent of the dataset choices, model
parametrizations, and diagnostic quantities ($S_8$ and $S_{12}$), the new
physics at the late time beyond the $\Lambda$CDM model is strongly disfavoured
so that the previous late-time no-go guide for the Hubble tension is further
strengthened.


title: Solutions of Yang-Mills theory in four-dimensional de Sitter space

abstract:
  This doctoral work deals with the analysis of some Yang-Mills solutions on
4-dimensional de Sitter space d$S_4$. The conformal equivalence of this space
with a finite Lorentzian cylinder over the 3-sphere and also with parts of
Minkowski space has recently led to the discovery of a family of rational
knotted electromagnetic field configurations. These "basis-knot" solutions of
the Maxwell equations, aka $U(1)$ Yang-Mills theory, are labelled with the
hyperspherical harmonics of the 3-sphere and have nice properties such as
finite-energy, finite-action and presence of a conserved topological quantity
called helicity. We study their symmetry properties, compute their conserved
Noether charges for the conformal group and study behaviour of charged
particles in their presence.
  Moreover, in the non-Abelian case of the gauge group $SU(2)$ there exist
time-dependent solutions of Yang-Mills equation on d$S_4$ in terms of Jacobi
elliptic functions that are of cosmological significance. These could play a
role in early-time cosmology where an $SO(4)$-symmetric Higgs vacuum is
stabilized due to rapid fluctuations of these gauge fields. We analyze the
linear stability of such $SU(2)$ "cosmic gauge fields" against arbitrary
perturbations of the Yang-Mills equation, while keeping the FLRW metric frozen.
The stablity analysis of the time-dependent normal modes that arise from the
diagonalization of the Yang-Mills fluctuation operator is carried out using
Floquet theory.


title:
Observations of Bell Inequality Violations with causal isolation between
  source and detectors

abstract:
  We report the experimental observations of Bell Inequality Violations (BIV)
in entangled photons causally separated by a rotating mirror. A Foucault mirror
gating geometry is used to causally isolate the entangled photon source and
detectors. We report an observed BIV of CHSH-$S = 2.30 \pm 0.07 > 2.00$. This
result rules out theories that explain correlations with traveling
communication between source and detectors.


title: Bounds on multiplicities of symmetric pairs of finite groups

abstract:
  Let $\Gamma$ be a finite group, let $\theta$ be an involution of $\Gamma$,
and let $\rho$ be an irreducible complex representation of $\Gamma$. We bound
$\dim \rho^{\Gamma^{\theta}}$ in terms of the smallest dimension of a faithful
$\mathbb{F}_p$-representation of $\Gamma/Rad_p(\Gamma)$, where $p$ is any odd
prime and $Rad_p(\Gamma)$ is the maximal normal $p$-subgroup of $\Gamma$.
  This implies, in particular, that if $\mathbf{G}$ is a group scheme over
$\mathbb{Z}$ and $\theta$ is an involution of $\mathbf{G}$, then the
multiplicity of any irreducible representation in $C^\infty \left(
\mathbf{G}(\mathbb{Z}_p)/ \mathbf{G} ^{\theta}(\mathbb{Z}_p) \right)$ is
bounded, uniformly in $p$.


title: Robust spin relaxometry with fast adaptive Bayesian estimation

abstract:
  Spin relaxometry with nitrogen-vacancy (NV) centers in diamond offers a
spectrally selective, atomically localized, and calibrated measurement of
microwave-frequency magnetic noise, presenting a versatile probe for condensed
matter and biological systems. Typically, relaxation rates are estimated with
curve-fitting techniques that do not provide optimal sensitivity, often leading
to long acquisition times that are particularly detrimental in systems prone to
drift or other dynamics of interest. Here we show that adaptive Bayesian
estimation is well suited to this problem, producing dynamic relaxometry pulse
sequences that rapidly find an optimal operating regime. In many situations
(including the system we employ), this approach can speed the acquisition by an
order of magnitude. We also present a four-signal measurement protocol that is
robust to drifts in spin readout contrast, polarization, and microwave pulse
fidelity while still achieving near-optimal sensitivity. The combined technique
offers a practical, hardware-agnostic approach for a wide range of NV
relaxometry applications.


title: Debugging Differential Privacy: A Case Study for Privacy Auditing

abstract:
  Differential Privacy can provide provable privacy guarantees for training
data in machine learning. However, the presence of proofs does not preclude the
presence of errors. Inspired by recent advances in auditing which have been
used for estimating lower bounds on differentially private algorithms, here we
show that auditing can also be used to find flaws in (purportedly)
differentially private schemes. In this case study, we audit a recent open
source implementation of a differentially private deep learning algorithm and
find, with 99.99999999% confidence, that the implementation does not satisfy
the claimed differential privacy guarantee.


title: Thermodynamic Uncertainty Relation in Interacting Many-Body Systems

abstract:
  The thermodynamic uncertainty relation (TUR) has been well studied for
systems with few degrees of freedom. While, in principle, the TUR holds for
more complex systems with many interacting degrees of freedom as well, little
is known so far about its behavior in such systems. We analyze the TUR in the
thermodynamic limit for mixtures of driven particles with short-range
interactions. Our main result is an explicit expression for the optimal
estimate of the total entropy production in terms of single-particle currents
and correlations between two-particle currents. Quantitative results for
various versions of a driven lattice gas demonstrate the practical
implementation of this approach.


title: Geometric energy transport and refrigeration with driven quantum dots

abstract:
  We study geometric energy transport in a slowly driven single-level quantum
dot weakly coupled to electronic contacts and with strong onsite interaction,
which can be either repulsive or attractive. Exploiting a recently discovered
fermionic duality for the evolution operator of the master equation, we provide
compact and insightful analytic expressions of energy pumping curvatures for
any pair of driving parameters. This enables us to systematically identify and
explain the pumping mechanisms for different driving schemes, thereby also
comparing energy and charge pumping. We determine the concrete impact of
many-body interactions and show how particle-hole symmetry and fermionic
duality manifest, both individually and in combination, as system-parameter
symmetries of the energy pumping curvatures. Building on this transport
analysis, we study the driven dot acting as a heat pump or refrigerator, where
we find that the sign of the onsite interaction plays a crucial role in the
performance of these thermal machines.


title:
Oscillating magnetised hybrid stars under the magnifying glass of
  multi-messenger observations

abstract:
  We model neutron stars as magnetised hybrid stars with an abrupt hadron-quark
phase transition in their cores, taking into account current constraints from
nuclear experiments and multi-messenger observations. We include magnetic field
effects considering the Landau level quantisation of charged particles and the
anomalous magnetic moment of neutral particles. We construct the magnetised
hybrid equation of state, and we compute the particle population, the matter
magnetisation and the transverse and parallel pressure components. We integrate
the stable stellar models, considering the dynamical stability for \emph{rapid}
or \emph{slow} hadron-quark phase conversion. Finally, we calculate the
frequencies and damping times of the fundamental and $g$ non-radial oscillation
modes. The latter, a key mode to learn about phase transitions in compact
objects, is only obtained for stars with slow conversions. For low magnetic
fields, we find that one of the objects of the GW170817 binary system might be
a hybrid star belonging to the slow extended stability branch. For magnetars,
we find that a stronger magnetic field always softens the hadronic equation of
state. Besides, only for some parameter combinations a stronger magnetic field
implies a higher hybrid star maximum mass. Contrary to previous results, the
incorporation of anomalous magnetic moment does not affect the studied
astrophysical quantities. We discuss possible imprints of the microphysics of
the equation of state that could be tested observationally in the future, and
that might help infer the nature of dense matter and hybrid stars.


title: From evolution to folding of repeat proteins

abstract:
  Repeat proteins are made with tandem copies of similar amino acid stretches
that fold into elongated architectures. Due to their symmetry, these proteins
constitute excellent model systems to investigate how evolution relates to
structure, folding and function. Here, we propose a scheme to map evolutionary
information at the sequence level to a coarse-grained model for repeat-protein
folding and use it to investigate the folding of thousands of repeat-proteins.
We model the energetics by a combination of an inverse Potts model scheme with
an explicit mechanistic model of duplications and deletions of repeats to
calculate the evolutionary parameters of the system at single residue level.
This is used to inform an Ising-like model that allows for the generation of
folding curves, apparent domain emergence and occupation of intermediate states
that are highly compatible with experimental data in specific case studies. We
analyzed the folding of thousands of natural Ankyrin-repeat proteins and found
that a multiplicity of folding mechanisms are possible. Fully cooperative
all-or-none transition are obtained for arrays with enough sequence-similar
elements and strong interactions between them, while non-cooperative
element-by-element intermittent folding arose if the elements are dissimilar
and the interactions between them are energetically weak. In between, we
characterised nucleation-propagation and multi-domain folding mechanisms.
Finally, we showed that stability and cooperativity of a repeat-array can be
quantitatively predicted from a simple energy score, paving the way for guiding
protein folding design with a co-evolutionary model.


title: An optimal scheduled learning rate for a randomized Kaczmarz algorithm

abstract:
  We study how the learning rate affects the performance of a relaxed
randomized Kaczmarz algorithm for solving $A x \approx b + \varepsilon$, where
$A x =b$ is a consistent linear system and $\varepsilon$ has independent mean
zero random entries. We derive a learning rate schedule which optimizes a bound
on the expected error that is sharp in certain cases; in contrast to the
exponential convergence of the standard randomized Kaczmarz algorithm, our
optimized bound involves the reciprocal of the Lambert-$W$ function of an
exponential.


title: New approaches to $\mathfrak{gl}_N$ weight system

abstract:
  The present paper has been motivated by an aspiration for understanding the
weight system corresponding to the Lie algebra $\mathfrak{gl}_N$. The
straightforward approach to computing the values of a Lie algebra weight system
on a general chord diagram amounts to elaborating calculations in the
noncommutative universal enveloping algebra, in spite of the fact that the
result belongs to the center of the latter. The first approach is based on a
suggestion due to M. Kazarian to define an invariant of permutations taking
values in the center of the universal enveloping algebra of $\mathfrak{gl}_N$.
The restriction of this invariant to involutions without fixed points (such an
involution determines a chord diagram) coincides with the value of the
$\mathfrak{gl}_N$ -weight system on this chord diagram. We describe the
recursion allowing one to compute the $\mathfrak{gl}_N$ -invariant of
permutations and demonstrate how it works in a number of examples. The second
approach is based on the Harish-Chandra isomorphism for the Lie algebras
$\mathfrak{gl}_N$. This isomorphism identifies the center of the universal
enveloping algebra $\mathfrak{gl}_N$ with the ring $\Lambda^*(N)$ of shifted
symmetric polynomials in $N$ variables. The Harish-Chandra projection can be
applied separately for each monomial in the defining polynomial of the weight
system; as a result, the main body of computations can be done in a commutative
algebra, rather than noncommutative one.


title: Probing BERT's priors with serial reproduction chains

abstract:
  Sampling is a promising bottom-up method for exposing what generative models
have learned about language, but it remains unclear how to generate
representative samples from popular masked language models (MLMs) like BERT.
The MLM objective yields a dependency network with no guarantee of consistent
conditional distributions, posing a problem for naive approaches. Drawing from
theories of iterated learning in cognitive science, we explore the use of
serial reproduction chains to sample from BERT's priors. In particular, we
observe that a unique and consistent estimator of the ground-truth joint
distribution is given by a Generative Stochastic Network (GSN) sampler, which
randomly selects which token to mask and reconstruct on each step. We show that
the lexical and syntactic statistics of sentences from GSN chains closely match
the ground-truth corpus distribution and perform better than other methods in a
large corpus of naturalness judgments. Our findings establish a firmer
theoretical foundation for bottom-up probing and highlight richer deviations
from human priors.


title:
Inclusive production of a $J/\psi$ or a $\Upsilon$ from single-parton
  fragmentation plus a jet in hybrid factorization

abstract:
  We investigate the inclusive hadroproduction of a heavy quarkonium ($J/\psi$
or $\Upsilon$), in association with a light-flavored jet, as a testing ground
for the semi-hard regime of QCD. Our theoretical setup is the hybrid
high-energy and collinear factorization, where the standard collinear approach
is supplemented by the $t$-channel resummation of leading and next-to-leading
energy logarithms \`a la BFKL. We present predictions for rapidity and
azimuthal-angle differential distributions, hunting for stabilizing effects of
the high-energy series under higher-order corrections. Our reaction represents
an additional channel to test the production mechanisms of quarkonia at high
energies and large transverse momenta and to possibly shed light on the
transition region from heavy-quark pair production to single-parton
fragmentation of $J/\psi$ and $\Upsilon$ states.


title:
Examining quasar absorption-line analysis methods: the tension between
  simulations and observational assumptions key to modelling clouds

abstract:
  A key assumption in quasar absorption line studies of the circumgalactic
medium (CGM) is that each absorption component maps to a spatially isolated
"cloud" structure that has single valued properties (e.g. density, temperature,
metallicity). We aim to assess and quantify the degree of accuracy underlying
this assumption. We used adaptive mesh refinement hydrodynamic cosmological
simulations of two $z=1$ dwarf galaxies and generated synthetic quasar
absorption-line spectra of their CGM. For the SiII $\lambda 1260$ transition,
and the CIV $\lambda\lambda1548, 1550$ and OVI $\lambda\lambda1031, 1037$
fine-structure doublets, we objectively determined which gas cells along a
line-of-sight (LOS) contribute to detected absorption. We implemented a fast,
efficient, and objective method to define individual absorption components in
each absorption profile. For each absorption component, we quantified the
spatial distribution of the absorbing gas. We studied a total of 1,302
absorption systems containing a total of 7,755 absorption components. 48% of
SiII, 68% of CIV, and 72% of OVI absorption components arise from two or more
spatially isolated "cloud" structures along the LOS. Spatially isolated "cloud"
structures were most likely to have cloud-cloud LOS separations of
0.03$R_{vir}$, 0.11$R_{vir}$, and 0.13$R_{vir}$ for SiII, CIV, and OVI,
respectively. There can be very little overlap between multi-phase gas
structures giving rise to absorption components. If our results reflect the
underlying reality of how absorption lines record CGM gas, they place tension
on current observational analysis methods as they suggest that
component-by-component absorption line formation is more complex than is
assumed and applied for chemical-ionisation modelling.


title:
The Linear Capacity of Single-Server Individually-Private Information
  Retrieval with Side Information

abstract:
  This paper considers the problem of single-server Individually-Private
Information Retrieval with side information (IPIR). In this problem, there is a
remote server that stores a dataset of $K$ messages, and there is a user that
initially knows $M$ of these messages, and wants to retrieve $D$ other messages
belonging to the dataset. The goal of the user is to retrieve the $D$ desired
messages by downloading the minimum amount of information from the server while
revealing no information about whether an individual message is one of the $D$
desired messages. In this work, we focus on linear IPIR schemes, i.e., the IPIR
schemes in which the user downloads only linear combinations of the original
messages from the server. We prove a converse bound on the download rate of any
linear IPIR scheme for all $K,D,M$, and show the achievability of this bound
for all $K,D,M$ satisfying a certain divisibility condition. Our results
characterize the linear capacity of IPIR, which is defined as the maximum
achievable download rate over all linear IPIR schemes, for a wide range of
values of $K,D,M$.