title: Contextualize Me -- The Case for Context in Reinforcement Learning

abstract:
  While Reinforcement Learning (RL) has made great strides towards solving
increasingly complicated problems, many algorithms are still brittle to even
slight changes in environments. Contextual Reinforcement Learning (cRL)
provides a theoretical framework to model such changes in a principled manner,
thereby enabling flexible, precise and interpretable task specification and
generation. Thus, cRL is an important formalization for studying generalization
in RL. In this work, we reason about solving cRL in theory and practice. We
show that theoretically optimal behavior in contextual Markov Decision
Processes requires explicit context information. In addition, we empirically
explore context-based task generation, utilizing context information in
training and propose cGate, our state-modulating policy architecture. To this
end, we introduce the first benchmark library designed for generalization based
on cRL extensions of popular benchmarks, CARL. In short: Context matters!


title:
Counterintuitive properties of fixation probability and fixation time in
  population structures with spatially periodic resource distribution

abstract:
  Resource are often not uniformly distributed within a population. Spatial
variations of concentration of a resource, change the fitness of competing
strategies locally. The notion of fitness varying with respect to both genotype
and environment is important in modeling cancer initiation, microbial evolution
and evolution of drug resistance. Environmental interactions can be asymmetric,
that is, they affect the fitness of one type more than the other. The question
is how local environmental variations in network population structures change
the selection dynamics in a finite population setting. We consider
one-dimensional lattice population structures with spatial fitness
distributions with a periodic pattern. Heterogeneity is determined by standard
deviation of fitnesses and period. The model covers biologically relevant
limits of two-habitat subdivided populations and randomly-distributed resources
in high- and low-periods. We numerically calculate fixation probability and
fixation times for a constant population birth-death process as fitness
heterogeneity and period vary. We identify levels of heterogeneity for which a
previously deleterious mutant, in a uniform environment, becomes beneficial. In
other regimes of the problem we observe unexpected behavior where the fixation
probability of both types are larger than their neutral value at the same time.
This coincides with an exponential increase in time to fixation as a function
of population size, which points to significant slow-down in selection process
and the potential for coexistence between types in realistic time scales. We
also discuss `fitness shift' model where the fitness function of one type is
identical to the other up to a constant spatial shift. This leads to
significant increase (or decrease) in the fixation probability of the mutant
depending the value of the shift.


title: High-energy colliders as a probe of neutrino properties

abstract:
  The mediators of neutrino mass generation can provide a probe of neutrino
properties at the next round of high-energy hadron (FCC-hh) and lepton
colliders (FCC-ee/ILC/CEPC/CLIC). We show how the decays of the Higgs triplet
scalars mediating the simplest seesaw mechanism can shed light on the neutrino
mass scale and mass-ordering, as well as the atmospheric octant. Four-lepton
signatures at the high-energy frontier may provide the discovery-site for
charged lepton flavour non-conservation in nature, rather than low-energy
intensity frontier experiments.


title:
Plasma solitons in gated two-dimensional electron systems: exactly
  solvable analytical model for the regime beyond weak non-linearity

abstract:
  We analytically study plasma solitary waves, or solitons, in a
two-dimensional (2D) electron system (ES) placed in close proximity to and
between two ideal metallic gates. As a rule, solitons are described using a
perturbative approach applicable only in the weak non-linearity regime. In
contrast, we analyze solitons considering a non-perturbative model. This
framework enables an exact analytical description of the soliton shape.
Moreover, it can be achieved in the regime beyond weak non-linearity -- when
the concentration deviation due to the soliton is of the order of the
equilibrium concentration. We determine the conditions required for a soliton
to exist and derive the relationship between its amplitude, width, and
velocity. We believe that our results obtained for the given model can provide
valuable insight into the physics of non-linear waves.


title:
Prediction Sensitivity: Continual Audit of Counterfactual Fairness in
  Deployed Classifiers

abstract:
  As AI-based systems increasingly impact many areas of our lives, auditing
these systems for fairness is an increasingly high-stakes problem. Traditional
group fairness metrics can miss discrimination against individuals and are
difficult to apply after deployment. Counterfactual fairness describes an
individualized notion of fairness but is even more challenging to evaluate
after deployment. We present prediction sensitivity, an approach for continual
audit of counterfactual fairness in deployed classifiers. Prediction
sensitivity helps answer the question: would this prediction have been
different, if this individual had belonged to a different demographic group --
for every prediction made by the deployed model. Prediction sensitivity can
leverage correlations between protected status and other features and does not
require protected status information at prediction time. Our empirical results
demonstrate that prediction sensitivity is effective for detecting violations
of counterfactual fairness.


title: Growth of Sobolev norms in quasi integrable quantum systems

abstract:
  We prove an abstract result giving a $\langle t\rangle^{\epsilon}$ upper
bound on the growth of the Sobolev norms of a time dependent Schr\"odinger
equation of the form $i \dot \psi = H_0 \psi + V(t) \psi $. $H_0$ is assumed to
be the Hamiltonian of a steep quantum integrable system and to be a
pseudodifferential operator of order ${\tt d}>1$; $V(t)$ is a time dependent
family of pseudodifferential operators, unbounded, but of order ${\tt b}<{\tt
d}$. The abstract theorem is then applied to perturbations of the quantum
anharmonic oscillators in dimension 2 and to perturbations of the Laplacian on
a manifold with integrable geodesic flow, and in particular Zoll manifolds,
rotation invariant surfaces and Lie groups. We also cover the case of several
particles on a Zoll manifold or on a Lie group, possibly obeying some
restrictions due to the Fermionic or Bosonic nature of the particles. The proof
is based a on quantum version of the proof of the classical Nekhoroshev
theorem.


title: Optimising hadronic collider simulations using amplitude neural networks

abstract:
  Precision phenomenological studies of high-multiplicity scattering processes
at collider experiments present a substantial theoretical challenge and are
vitally important ingredients in experimental measurements. Machine learning
technology has the potential to dramatically optimise simulations for
complicated final states. We investigate the use of neural networks to
approximate matrix elements, studying the case of loop-induced diphoton
production through gluon fusion. We train neural network models on one-loop
amplitudes from the NJet C++ library and interface them with the Sherpa Monte
Carlo event generator to provide the matrix element within a realistic hadronic
collider simulation. Computing some standard observables with the models and
comparing to conventional techniques, we find excellent agreement in the
distributions and a reduced total simulation time by a factor of thirty.


title:
Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped
  $SU(5)$ Asymmetric $\mathbb{Z}_2 \times \mathbb{Z}_2$ Heterotic String
  Orbifolds

abstract:
  The free fermionic classification method provides a powerful tool to
investigate string vacua, which led to the discovery of spinor--vector duality
and exophobic string models. We extend the classification methodology to both
$\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ $\mathbb{Z}_2 \times
\mathbb{Z}_2$ heterotic string orbifolds with asymmetric shifts. The impact of
the asymmetric assignments on the phenomenological characteristics of these
models is investigated. Of particular interest is the analysis of untwisted
moduli fixing for various choices of asymmetric boundary conditions. Two
classes of vacua with different characteristics are systematically investigated
with help from SAT/SMT algorithms, which are shown to increase search
efficiency by up to two orders of magnitude, as well as providing useful tools
to find contradictions between various phenomenological criteria. The general
form of the partition function for the space of models is explained and given
for two specific example models for different choices of asymmetric boundary
conditions. Additionally, the distribution of one-loop cosmological constant
contributions for samples in the two different classes of models are depicted
and discussed.


title: Morse-Novikov cohomology on foliated manifolds

abstract:
  The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has
been utilized by many researchers to study important properties and invariants
of a manifold. Morse-Novikov cohomology is defined using the differential
$d_\omega=d+\omega\wedge$, where $\omega$ is a closed $1$-form. We study
Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy
invariance and then extend it to more general type of forms on a Riemannian
foliation. We study the Laplacian and Hodge decompositions for the
corresponding differential operators on reduced leafwise Morse-Novikov
complexes. In the case of Riemannian foliations, we prove that the reduced
leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and
Poincar{\'e} duality. The resulting isomorphisms yield a Hodge diamond
structure for leafwise Morse-Novikov cohomology.


title:
Optimal learning rate schedules in high-dimensional non-convex
  optimization problems

abstract:
  Learning rate schedules are ubiquitously used to speed up and improve
optimisation. Many different policies have been introduced on an empirical
basis, and theoretical analyses have been developed for convex settings.
However, in many realistic problems the loss-landscape is high-dimensional and
non convex -- a case for which results are scarce. In this paper we present a
first analytical study of the role of learning rate scheduling in this setting,
focusing on Langevin optimization with a learning rate decaying as
$\eta(t)=t^{-\beta}$. We begin by considering models where the loss is a
Gaussian random function on the $N$-dimensional sphere ($N\rightarrow \infty$),
featuring an extensive number of critical points. We find that to speed up
optimization without getting stuck in saddles, one must choose a decay rate
$\beta<1$, contrary to convex setups where $\beta=1$ is generally optimal. We
then add to the problem a signal to be recovered. In this setting, the dynamics
decompose into two phases: an \emph{exploration} phase where the dynamics
navigates through rough parts of the landscape, followed by a
\emph{convergence} phase where the signal is detected and the dynamics enter a
convex basin. In this case, it is optimal to keep a large learning rate during
the exploration phase to escape the non-convex region as quickly as possible,
then use the convex criterion $\beta=1$ to converge rapidly to the solution.
Finally, we demonstrate that our conclusions hold in a common regression task
involving neural networks.


title:
The crowding effect on the melting of short DNA: Comparison with
  experiments

abstract:
  We study the effect of crowders on the melting profile of homogeneous and
heterogeneous DNA molecules. We find out the melting profile of short DNA
molecules and compare our findings with the experiments. We consider some
random distribution of crowders along the chain, and by finding out the best
match with the experiments, we attempt to identify the location of crowders in
the experimental findings of Ghosh \cite{Ghosh_PNAS_2020}. We also study the
melting of homogeneous DNA molecules of different lengths (25, 50, 75) in the
presence of only one crowder in the chain. By varying the location of the
crowder from one end to the other, we find that the melting temperature is
susceptible to the location of the crowder at the ends. At the same time, there
is minimal effect on the melting temperature due to the location of the
crowder. {\it In vivo}, the strength of a crowders may vary along the chain. We
study the melting of long heterogeneous chain in presence of five crowders of
different strength. We find that there is a significant variation in the
melting process of DNA in presence of crowders of variable strength.


title: Geometric properties of disintegration of measures

abstract:
  In this paper we study the connection of disintegration of measures and some
geometric properties of probability spaces. We prove a disintegration theorem,
and then address disintegration from the perspective of an optimal transport
problem. In particular, we look at the disintegration of transport plans, which
are used to define and study disintegration maps. Using these objects we study
the relationship between disintegration of measures and absolute continuity. We
show a condition for disintegration of measures into absolutely continuous
measures.


title:
A vectorial binary Darboux transformation of the first member of the
  negative part of the AKNS hierarchy

abstract:
  Using bidifferential calculus, we derive a vectorial binary Darboux
transformation for the first member of the "negative" part of the AKNS
hierarchy. A reduction leads to the first "negative flow" of the NLS hierarchy.
This rather simple nonlinear PDE in two dimensions with a leading mixed third
order derivative, may be regarded as describing geometric dynamics of a complex
scalar field in one dimension, since it is invariant under coordinate
transformations in one of the two independent variables. We exploit the
correspondingly reduced binary Darboux transformation to generate multi-soliton
solutions of the PDE, also with additional rational dependence on the
independent variables, and on a plane wave background. This includes rogue
waves.


title: The no-free-lunch theorems of supervised learning

abstract:
  The no-free-lunch theorems promote a skeptical conclusion that all possible
machine learning algorithms equally lack justification. But how could this
leave room for a learning theory, that shows that some algorithms are better
than others? Drawing parallels to the philosophy of induction, we point out
that the no-free-lunch results presuppose a conception of learning algorithms
as purely data-driven. On this conception, every algorithm must have an
inherent inductive bias, that wants justification. We argue that many standard
learning algorithms should rather be understood as model-dependent: in each
application they also require for input a model, representing a bias. Generic
algorithms themselves, they can be given a model-relative justification.


title:
A Model-Agnostic Causal Learning Framework for Recommendation using
  Search Data

abstract:
  Machine-learning based recommender systems(RSs) has become an effective means
to help people automatically discover their interests. Existing models often
represent the rich information for recommendation, such as items, users, and
contexts, as embedding vectors and leverage them to predict users' feedback. In
the view of causal analysis, the associations between these embedding vectors
and users' feedback are a mixture of the causal part that describes why an item
is preferred by a user, and the non-causal part that merely reflects the
statistical dependencies between users and items, for example, the exposure
mechanism, public opinions, display position, etc. However, existing RSs mostly
ignored the striking differences between the causal parts and non-causal parts
when using these embedding vectors. In this paper, we propose a model-agnostic
framework named IV4Rec that can effectively decompose the embedding vectors
into these two parts, hence enhancing recommendation results. Specifically, we
jointly consider users' behaviors in search scenarios and recommendation
scenarios. Adopting the concepts in causal analysis, we embed users' search
behaviors as instrumental variables (IVs), to help decompose original embedding
vectors in recommendation, i.e., treatments. IV4Rec then combines the two parts
through deep neural networks and uses the combined results for recommendation.
IV4Rec is model-agnostic and can be applied to a number of existing RSs such as
DIN and NRHUB. Experimental results on both public and proprietary industrial
datasets demonstrate that IV4Rec consistently enhances RSs and outperforms a
framework that jointly considers search and recommendation.


title:
Leverage Score Sampling for Tensor Product Matrices in Input Sparsity
  Time

abstract:
  We give an input sparsity time sampling algorithm for spectrally
approximating the Gram matrix corresponding to the $q$-fold column-wise tensor
product of $q$ matrices using a nearly optimal number of samples, improving
upon all previously known methods by poly$(q)$ factors. Furthermore, for the
important special care of the $q$-fold self-tensoring of a dataset, which is
the feature matrix of the degree-$q$ polynomial kernel, the leading term of our
method's runtime is proportional to the size of the dataset and has no
dependence on $q$. Previous techniques either incur a poly$(q)$ factor slowdown
in their runtime or remove the dependence on $q$ at the expense of having
sub-optimal target dimension, and depend quadratically on the number of
data-points in their runtime. Our sampling technique relies on a collection of
$q$ partially correlated random projections which can be simultaneously applied
to a dataset $X$ in total time that only depends on the size of $X$, and at the
same time their $q$-fold Kronecker product acts as a near-isometry for any
fixed vector in the column span of $X^{\otimes q}$. We show that our sampling
methods generalize to other classes of kernels beyond polynomial, such as
Gaussian and Neural Tangent kernels.


title:
An approximate $C^1$ multi-patch space for isogeometric analysis with a
  comparison to Nitsche's method

abstract:
  We present an approximately $C^1$-smooth multi-patch spline construction
which can be used in isogeometric analysis (IGA). A key property of IGA is that
it is simple to achieve high order smoothness within a single patch. To
represent more complex geometries one often uses a multi-patch construction. In
this case, the global continuity for the basis functions is in general only
$C^0$. Therefore, to obtain $C^1$-smooth isogeometric functions, a special
construction for the basis is needed. Such spaces are of interest when solving
numerically fourth-order problems, such as the biharmonic equation or
Kirchhoff-Love plate/shell formulations, using an isogeometric Galerkin method.
  Isogeometric spaces that are globally $C^1$ over multi-patch domains can be
constructed as in (Collin, Sangalli, Takacs; CAGD, 2016) and (Kapl, Sangalli,
Takacs; CAGD, 2019). The constructions require so-called analysis-suitable
$G^1$ parametrizations. To allow $C^1$ spaces over more general multi-patch
parametrizations, we need to increase the polynomial degree and relax the $C^1$
conditions. We adopt the approximate $C^1$ construction for two-patch domains,
as developed in (Weinm\"uller, Takacs; CMAME, 2021), and extend it to more
general multi-patch domains.
  We employ the construction for a biharmonic model problem and compare the
results with Nitsche's method. We compare both methods over complex multi-patch
domains with non-trivial interfaces. The numerical tests indicate that the
proposed construction converges optimally under $h$-refinement, comparable to
the solution using Nitsche's method. In contrast to weakly imposing coupling
conditions, the approximate $C^1$ construction is explicit and no additional
terms need to be introduced to stabilize the method. Thus, the new proposed
method can be used more easily as no parameters need to be estimated.


title:
A Neural Network based Framework for Effective Laparoscopic Video
  Quality Assessment

abstract:
  Video quality assessment is a challenging problem having a critical
significance in the context of medical imaging. For instance, in laparoscopic
surgery, the acquired video data suffers from different kinds of distortion
that not only hinder surgery performance but also affect the execution of
subsequent tasks in surgical navigation and robotic surgeries. For this reason,
we propose in this paper neural network-based approaches for distortion
classification as well as quality prediction. More precisely, a Residual
Network (ResNet) based approach is firstly developed for simultaneous ranking
and classification task. Then, this architecture is extended to make it
appropriate for the quality prediction task by using an additional Fully
Connected Neural Network (FCNN). To train the overall architecture (ResNet and
FCNN models), transfer learning and end-to-end learning approaches are
investigated. Experimental results, carried out on a new laparoscopic video
quality database, have shown the efficiency of the proposed methods compared to
recent conventional and deep learning based approaches.


title: Protocol Insecurity with Assertions

abstract:
  In the study of symbolic verification of cryptographic protocols, a central
result due to Rusinowitch and Turuani [2003] is that the insecurity problem
(deciding whether a protocol admits an execution which leaks a designated
secret to the intruder) for security protocols with finitely many sessions is
NP-complete. Central to their proof strategy is the observation that any
execution of a protocol can be simulated by one where the intruder only
communicates terms of bounded size. They prove this by analyzing how variables
used in the protocol can be instantiated in different contexts by the intruder.
However, when we consider protocols where, in addition to terms, some logical
statements or "assertions" about the terms (as presented by Ramanujam,
Sundararajan, and Suresh [2017]) are also communicated, the analysis of the
insecurity problem becomes tricky. In this paper we consider the insecurity
problem for protocols with a class of assertions that includes equality on
terms and existential quantification. The intruder can potentially exploit the
fact that witnesses for existential quantifiers may be unbounded, and obtaining
small witness terms while maintaining equality proofs complicates the analysis
considerably. We use a notion of well-typed equality proofs that helps in
bounding the sizes of the terms involved, and show that the insecurity problem
for assertions is in NP.


title:
Relaxation of the parameter independence assumption in the `bootComb` R
  package

abstract:
  Background. The bootComb R package allows researchers to derive confidence
intervals with correct target coverage for arbitrary combinations of arbitrary
numbers of independently estimated parameters. Previous versions (< 1.1.0) of
bootComb used independent bootstrap sampling and required that the parameters
themselves are independent - an unrealistic assumption in some real-world
applications.
  Findings. Using Gaussian copulas to define the dependence between parameters,
the bootComb package has been extended to allow for dependent parameters.
  Implications. The updated bootComb package can now handle cases of dependent
parameters, with users specifying a correlation matrix defining the dependence
structure. While in practice it may be difficult to know the exact dependence
structure between parameters, `bootComb` allows running sensitivity analyses to
assess the impact of parameter dependence on the resulting confidence interval
for the combined parameter.
  Availability. bootComb is available from the Comprehensive R Archive Network
(https://CRAN.R-project.org/package=bootComb).


title: Obtaining Dyadic Fairness by Optimal Transport

abstract:
  Fairness has been taken as a critical metric on machine learning models. Many
works studying how to obtain fairness for different tasks emerge. This paper
considers obtaining fairness for link prediction tasks, which can be measured
by dyadic fairness. We aim to propose a pre-processing methodology to obtain
dyadic fairness through data repairing and optimal transport. To obtain dyadic
fairness with satisfying flexibility and unambiguity requirements, we transform
the dyadic repairing to the conditional distribution alignment problem based on
optimal transport and obtain theoretical results on the connection between the
proposed alignment and dyadic fairness. The optimal transport-based dyadic
fairness algorithm is proposed for graph link prediction. Our proposed
algorithm shows superior results on obtaining fairness compared with the other
pre-processing methods on two benchmark graph datasets.


title:
The Value of Recycling for Low-Carbon Energy Systems -- a Case Study of
  Germany's Energy Transition

abstract:
  To achieve climate neutrality, synergies between circular economy and
reduction of greenhouse gas emissions must be strengthened. Previously idle
emission reduction potentials of resource efficiency are to be exploited. Since
all potentially possible emission reduction measures are linked by
interactions, the evaluation of a single measure in terms of cost efficiency,
effectiveness, and compliance with climate protection targets is very complex
and requires a model-based analysis that takes the entire energy system into
account. This work advances an energy system model for Germany so that through
comprehensive modeling of industrial processes and implementation of recycling
options, the impact of recycling measures in the context of national greenhouse
gas mitigation strategies can be analyzed. The scenario evaluation shows that
different recycling strategies have large effects on the German energy system.
Without recycling energy demand in 2050 will increase by more than 300 TWh and
cost of transformation will rise by 85% compared to a reference scenario. On
the other hand, if maximum recycling rates can be achieved, costs of
transformation can be reduced by 26% until 2050. Recycling is an essential and
cost-efficient greenhouse gas reduction strategy for future low-carbon energy
system designs.


title:
Constructing and Analyzing the LSM Compaction Design Space (Updated
  Version)

abstract:
  Log-structured merge (LSM) trees offer efficient ingestion by appending
incoming data, and thus, are widely used as the storage layer of production
NoSQL data stores. To enable competitive read performance, LSM-trees
periodically re-organize data to form a tree with levels of exponentially
increasing capacity, through iterative compactions. Compactions fundamentally
influence the performance of an LSM-engine in terms of write amplification,
write throughput, point and range lookup performance, space amplification, and
delete performance. Hence, choosing the appropriate compaction strategy is
crucial and, at the same time, hard as the LSM-compaction design space is vast,
largely unexplored, and has not been formally defined in the literature. As a
result, most LSM-based engines use a fixed compaction strategy, typically
hand-picked by an engineer, which decides how and when to compact data.
  In this paper, we present the design space of LSM-compactions, and evaluate
state-of-the-art compaction strategies with respect to key performance metrics.
Toward this goal, our first contribution is to introduce a set of four design
primitives that can formally define any compaction strategy: (i) the compaction
trigger, (ii) the data layout, (iii) the compaction granularity, and (iv) the
data movement policy. Together, these primitives can synthesize both existing
and completely new compaction strategies. Our second contribution is to
experimentally analyze 10 compaction strategies. We present 12 observations and
7 high-level takeaway messages, which show how LSM systems can navigate the
compaction design space.


title:
Unified Grothendieck's and Kwapie\'{n}'s theorems for multilinear
  operators

abstract:
  Kwapie\'{n}'s theorem asserts that every continuous linear operator from
$\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for
$1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous
Grothendieck's theorem. In this paper investigate multilinear variants of these
theorems and related issues. Among other results we present a unified version
of Kwapie\'{n}'s and Grothendieck's results that encompasses the cases of
multiple summing and absolutely summing multilinear operators.


title:
Techtile -- Open 6G R&D Testbed for Communication, Positioning, Sensing,
  WPT and Federated Learning

abstract:
  New concepts for next-generation wireless systems are being developed. It is
expected that these 6G and beyond systems will incorporate more than only
communication, but also sensing, positioning, (deep) edge computing, and other
services. The discussed measurement facility and approach, named Techtile, is
an open, both in design and operation, and unique testbed to evaluate these
newly envisioned systems. Techtile is a multi-functional and versatile testbed,
providing fine-grained distributed resources for new communication, positioning
and sensing technologies. The facility enables experimental research on
hyper-connected interactive environments and validation of new algorithms and
topologies. The backbone connects 140~resource units equipped with edge
computing devices, software-defined radios, sensors, and LED sources. By doing
so, different network topologies and local-versus-central computing can be
assessed. The introduced diversity of i) the technologies (e.g., RF, acoustics
and light), ii) the distributed resources and iii) the interconnectivity allows
exploring more degrees and new types of diversity, which can be investigated in
this testbed.


title:
Electric field control of magnons in magnetic thin films: ab initio
  predictions for 2D metallic heterostructures

abstract:
  We explore possibilities for control of magnons in two-dimensional
heterostructures by an external electric field acting across a dielectric
barrier. By performing ab-initio calculations for a Fe monolayer and a Fe
bilayer, both suspended in vacuum and deposited on Cu(001), we demonstrate that
external electric field can significantly modify magnon lifetimes and that
these changes can be related to field-induced changes in the layer-resolved
Bloch spectral functions. For systems with more magnon dispersion branches, the
gap between high- and low-energy eigenmodes varies with the external field.
These effects are strongly influenced by the substrate. Considerable
variability in how the magnon spectra are sensitive to the external electric
field can be expected, depending on the substrate and on the thickness of the
magnetic layer.


title:
Soundiation: A multi-functional GUI-based software in evaluation of the
  acoustophoresis by the acoustic radiation force and torque on arbitrary
  axisymmetric objects

abstract:
  Acoustic radiation force and torque arising from wave scattering are commonly
used to manipulate micro-objects without contact. We applied the partial wave
expansion series and the conformal transformation approach to estimate the
radiation force and torque exerted on an axisymmetric particle. Meanwhile,
translational and rotational transformations are required to keep the
coordinate system consistent [1]. Although these theoretical derivations have
been well established, coding the required systems, including generation of the
wave function, implementation of the transformations, calculations between
modules, etc., is non-trivial and time-consuming. Here, a new open-source,
MATLAB-based software, called Soundiation, is provided to address the radiation
force and torque while supporting the dynamic prediction of non-spherical
particles. The implementation is basically generic, and its applicability is
demonstrated through the validation of numerical methods. Furthermore, a
graphical user interface is provided so that it can be used and extended
easily.


title: Explainable Predictive Modeling for Limited Spectral Data

abstract:
  Feature selection of high-dimensional labeled data with limited observations
is critical for making powerful predictive modeling accessible, scalable, and
interpretable for domain experts. Spectroscopy data, which records the
interaction between matter and electromagnetic radiation, particularly holds a
lot of information in a single sample. Since acquiring such high-dimensional
data is a complex task, it is crucial to exploit the best analytical tools to
extract necessary information. In this paper, we investigate the most commonly
used feature selection techniques and introduce applying recent explainable AI
techniques to interpret the prediction outcomes of high-dimensional and limited
spectral data. Interpretation of the prediction outcome is beneficial for the
domain experts as it ensures the transparency and faithfulness of the ML models
to the domain knowledge. Due to the instrument resolution limitations,
pinpointing important regions of the spectroscopy data creates a pathway to
optimize the data collection process through the miniaturization of the
spectrometer device. Reducing the device size and power and therefore cost is a
requirement for the real-world deployment of such a sensor-to-prediction system
as a whole. We specifically design three different scenarios to ensure that the
evaluation of ML models is robust for the real-time practice of the developed
methodologies and to uncover the hidden effect of noise sources on the final
outcome.


title:
A Multimodal Canonical-Correlated Graph Neural Network for
  Energy-Efficient Speech Enhancement

abstract:
  This paper proposes a novel multimodal self-supervised architecture for
energy-efficient AV speech enhancement by integrating graph neural networks
with canonical correlation analysis (CCA-GNN). This builds on a
state-of-the-art CCA-GNN that aims to learn representative embeddings by
maximizing the correlation between pairs of augmented views of the same input
while decorrelating disconnected features. The key idea of the conventional
CCA-GNN involves discarding augmentation-variant information and preserving
augmentation-invariant information whilst preventing capturing of redundant
information. Our proposed AV CCA-GNN model is designed to deal with the
challenging multimodal representation learning context. Specifically, our model
improves contextual AV speech processing by maximizing canonical correlation
from augmented views of the same channel, as well as canonical correlation from
audio and visual embeddings. In addition, we propose a positional encoding of
the nodes that considers a prior-frame sequence distance instead of a
feature-space representation while computing the node's nearest neighbors. This
serves to introduce temporal information in the embeddings through the
neighborhood's connectivity. Experiments conducted with the benchmark ChiME3
dataset show that our proposed prior frame-based AV CCA-GNN reinforces better
feature learning in the temporal context, leading to more energy-efficient
speech reconstruction compared to state-of-the-art CCA-GNN and multi-layer
perceptron models. The results demonstrate the potential of our proposed
approach for exploitation in future assistive technology and energy-efficient
multimodal devices.


title: Slope and concordance of links

abstract:
  The slope is an isotopy invariant of colored links with a distinguished
component, initially introduced by the authors to describe an extra correction
term in the computation of the signature of the splice. It appeared to be
closely related to several classical invariants, such as the Conway potential
function or the Kojima eta-function (defined for two-components links). In this
paper, we prove that the slope is invariant under colored concordance of links.
Besides, we present a formula to compute the slope in terms of C-complexes and
generalized Seifert forms.


title: An Exploration of Multicalibration Uniform Convergence Bounds

abstract:
  Recent works have investigated the sample complexity necessary for fair
machine learning. The most advanced of such sample complexity bounds are
developed by analyzing multicalibration uniform convergence for a given
predictor class. We present a framework which yields multicalibration error
uniform convergence bounds by reparametrizing sample complexities for Empirical
Risk Minimization (ERM) learning. From this framework, we demonstrate that
multicalibration error exhibits dependence on the classifier architecture as
well as the underlying data distribution. We perform an experimental evaluation
to investigate the behavior of multicalibration error for different families of
classifiers. We compare the results of this evaluation to multicalibration
error concentration bounds. Our investigation provides additional perspective
on both algorithmic fairness and multicalibration error convergence bounds.
Given the prevalence of ERM sample complexity bounds, our proposed framework
enables machine learning practitioners to easily understand the convergence
behavior of multicalibration error for a myriad of classifier architectures.


title:
Vortex Formation and Quantum Turbulence in a Binary Bose-Einstein
  Condensates

abstract:
  Motivated by the recent observation of a gigantic vortex cluster in a
two-dimensional Bose-Einstein condensate [Science 364, 1264 (2019)], we conduct
a theoretical study of the creation and dynamics of vortices in a binary
Bose-Einstein condensate with a mass imbalance between the species. To initiate
the dynamics, we use one or two rotating paddle potentials in one species,
while the other species is influenced only via the interspecies interaction. In
both species, the number as well as the dominant sign of the vortices are
determined by the rotation frequency of the paddle potential. Clusters of
positive and negative vortices form at low rotation frequency comparable to
that of the trap when using the single paddle potential. In contrast, vortices
of the same sign tend to dominate as rotation frequency increases. When the
rotation frequency is sufficiently high, the rapid annihilation of
vortex-antivortex pairs significantly reduces the number of vortices in the
system. For two paddle potentials rotating in the same direction, the vortex
dynamics phenomenon is similar to that of a single paddle. However, when the
paddle potentials are rotated in the opposite direction, both positive and
negative signed vortices occur at all rotational frequencies. At low rotational
frequencies, the cluster of like-signed vortices produces the $k^{-5/3}$ and
$k^{-3}$ power laws in the incompressible kinetic energy spectrum at low and
high wavenumbers, respectively, a hallmark property of the quantum turbulent
flows.


title: On a question of supports

abstract:
  We give a sufficient condition in order that $n$ closed connected subsets in
the $n$-dimensional real projective space admit a common multitangent
hyperplane.


title: NIMBLE: A Non-rigid Hand Model with Bones and Muscles

abstract:
  Emerging Metaverse applications demand reliable, accurate, and photorealistic
reproductions of human hands to perform sophisticated operations as if in the
physical world. While real human hand represents one of the most intricate
coordination between bones, muscle, tendon, and skin, state-of-the-art
techniques unanimously focus on modeling only the skeleton of the hand. In this
paper, we present NIMBLE, a novel parametric hand model that includes the
missing key components, bringing 3D hand model to a new level of realism. We
first annotate muscles, bones and skins on the recent Magnetic Resonance
Imaging hand (MRI-Hand) dataset and then register a volumetric template hand
onto individual poses and subjects within the dataset. NIMBLE consists of 20
bones as triangular meshes, 7 muscle groups as tetrahedral meshes, and a skin
mesh. Via iterative shape registration and parameter learning, it further
produces shape blend shapes, pose blend shapes, and a joint regressor. We
demonstrate applying NIMBLE to modeling, rendering, and visual inference tasks.
By enforcing the inner bones and muscles to match anatomic and kinematic rules,
NIMBLE can animate 3D hands to new poses at unprecedented realism. To model the
appearance of skin, we further construct a photometric HandStage to acquire
high-quality textures and normal maps to model wrinkles and palm print.
Finally, NIMBLE also benefits learning-based hand pose and shape estimation by
either synthesizing rich data or acting directly as a differentiable layer in
the inference network.


title:
Small ball probabilities for the stochastic heat equation with colored
  noise

abstract:
  We consider a stochastic heat equation on the 1-dimensional torus
$\mathbb{T}:=[-1,1]$ with periodic boundary conditions: $$\partial_t
u(t,x)=\partial^2_x u(t,x)+\sigma(t,x,u)\dot{F}(t,x),\quad x\in
\mathbb{T},t\in\mathbb{R}^+$$ and $\dot{F}(t,x)$ is 2-parameter 1-dimensional
white in time, colored in space noise. We assume that $\sigma$ is Lipschitz in
$u$ and uniformly elliptic. We prove small ball probabilities for the solution
$u$ when $u(0,x)\equiv 0$.


title: Partition regularity of affine algebraic plane curves

abstract:
  We completely characterize non-trivial partition regularity of systems of
affine algebraic plane curves over algebraically closed fields of
characteristic 0 using two different methods. The first uses a combination of
ultrafilters, nonstandard analysis and basic algebraic geometry; the second
uses a known result about colorings related to functions with no fixed points.
This provides one of the first examples of a large class of nonlinear equations
whose partition regularity is completely characterized. Finally, we provide an
explicit upper bound on the number of colors needed to disprove the partition
regularity of those systems that are not non-trivially partition regular.


title: Divergences of the scalar sector of quadratic gravity

abstract:
  The divergences coming from a particular sector of gravitational fluctuations
around a generic background in general theories of quadratic gravity are
analyzed. They can be summarized in a particular type of scalar model, whose
properties are analyzed.


title:
Time complexity analysis of quantum difference methods for linear high
  dimensional and multiscale partial differential equations

abstract:
  We investigate time complexities of finite difference methods for solving the
high-dimensional linear heat equation, the high-dimensional linear hyperbolic
equation and the multiscale hyperbolic heat system with quantum algorithms
(hence referred to as the "quantum difference methods"). Our detailed analyses
show that for the heat and linear hyperbolic equations the quantum difference
methods provide exponential speedup over the classical difference method with
respect to the spatial dimension. For the multiscale problem, the time
complexity of both the classical treatment and quantum treatment for the
explicit scheme scales as $O(1/\varepsilon)$, where $\varepsilon$ is the
scaling parameter, while the scaling for the Asymptotic-Preserving (AP) schemes
does not depend on $\varepsilon$. This indicates that it is still of great
importance to develop AP schemes for multiscale problems in quantum computing.


title:
Generating Training Data with Language Models: Towards Zero-Shot
  Language Understanding

abstract:
  Pretrained language models (PLMs) have demonstrated remarkable performance in
various natural language processing tasks: Unidirectional PLMs (e.g., GPT) are
well known for their superior text generation capabilities; bidirectional PLMs
(e.g., BERT) have been the prominent choice for natural language understanding
(NLU) tasks. While both types of models have achieved promising few-shot
learning performance, their potential for zero-shot learning has been
underexplored. In this paper, we present a simple approach that uses both types
of PLMs for fully zero-shot learning of NLU tasks without requiring any
task-specific data: A unidirectional PLM generates class-conditioned texts
guided by prompts, which are used as the training data for fine-tuning a
bidirectional PLM. With quality training data selected based on the generation
probability and regularization techniques (label smoothing and temporal
ensembling) applied to the fine-tuning stage for better generalization and
stability, our approach demonstrates strong performance across seven
classification tasks of the GLUE benchmark (e.g., 72.3/73.8 on MNLI-m/mm and
92.8 on SST-2), significantly outperforming zero-shot prompting methods and
achieving even comparable results to strong few-shot approaches using 32
training samples per class.


title: Dynamic self-triggered control for nonlinear systems with delays

abstract:
  Self-triggered control (STC) is a resource efficient approach to determine
sampling instants for Networked Control Systems (NCS). Recently, a dynamic STC
strategy based on hybrid Lyapunov functions for nonlinear NCS has been proposed
in Hertneck and Allg\"ower (2021b), however with the limitation to NCS without
transmission delays. In this paper, we extend this strategy for nonlinear NCS
with transmission delays. The capability to handle systems with delays makes it
possible to use the resulting dynamic STC mechanism in many practical scenarios
where instant transmissions without delays cannot be guaranteed. The proposed
dynamic STC mechanism guarantees stability despite bounded transmission delays.
The effectiveness of the mechanism is illustrated with a numerical example and
compared to state-of-the art literature.


title: Stringballs and Planckballs for Dark Matter

abstract:
  As a follow up of the seminal work by Guiot, Borquez, Deur, and Werner on
``Graviballs and Dark Matter'', we explicitly show that contrary to Einstein's
gravity, in string theory, local and nonlocal higher derivative theories, as
well as general asymptotically-free or finite theories, gravitationally
interacting bound states can form when the energy is larger than the Planck
energy. On the other hand, in higher derivative or nonlocal theories with
interaction governed by a dimensionless or a dimensionful coupling constant,
the bound states form when the energy is smaller than the Planck energy. Such
bound states are allowed because of the softness of the scattering amplitudes
in the ultraviolet region. Indeed, in such theories, the potential is finite
while the force is zero or constant in $r=0$. Finally, since the bound states
that form in the early Universe may have an energy that ranges from the Planck
mass to any arbitrarily large or small value, we argue that they can serve as
dark matter candidates and/or as the seeds for the structure's formation at
large scale in the Cosmos.


title:
Sparse superposition codes under VAMP decoding with generic rotational
  invariant coding matrices

abstract:
  Sparse superposition codes were originally proposed as a capacity-achieving
communication scheme over the gaussian channel, whose coding matrices were made
of i.i.d. gaussian entries.We extend this coding scheme to more generic
ensembles of rotational invariant coding matrices with arbitrary spectrum,
which include the gaussian ensemble as a special case. We further introduce and
analyse a decoder based on vector approximate message-passing (VAMP).Our main
findings, based on both a standard replica symmetric potential theory and state
evolution analysis, are the superiority of certain structured ensembles of
coding matrices (such as partial row-orthogonal) when compared to i.i.d.
matrices, as well as a spectrum-independent upper bound on VAMP's threshold.
Most importantly, we derive a simple "spectral criterion " for the scheme to be
at the same time capacity-achieving while having the best possible algorithmic
threshold, in the "large section size" asymptotic limit. Our results therefore
provide practical design principles for the coding matrices in this promising
communication scheme.


abstract:
  The method of Common Spatial Patterns (CSP) is widely used for feature
extraction of electroencephalography (EEG) data, such as in motor imagery
brain-computer interface (BCI) systems. It is a data-driven method estimating a
set of spatial filters so that the power of the filtered EEG signal is
maximized for one motor imagery class and minimized for the other. This method,
however, is prone to overfitting and is known to suffer from poor
generalization especially with limited calibration data. Additionally, due to
the high heterogeneity in brain data and the non-stationarity of brain
activity, CSP is usually trained for each user separately resulting in long
calibration sessions or frequent re-calibrations that are tiring for the user.
In this work, we propose a novel algorithm called Spectrally Adaptive Common
Spatial Patterns (SACSP) that improves CSP by learning a temporal/spectral
filter for each spatial filter so that the spatial filters are concentrated on
the most relevant temporal frequencies for each user. We show the efficacy of
SACSP in providing better generalizability and higher classification accuracy
from calibration to online control compared to existing methods. Furthermore,
we show that SACSP provides neurophysiologically relevant information about the
temporal frequencies of the filtered signals. Our results highlight the
differences in the motor imagery signal among BCI users as well as spectral
differences in the signals generated for each class, and show the importance of
learning robust user-specific features in a data-driven manner.


title: Locally Cartesian Closed Categories

abstract:
  This note explains how dependent sums and products are interpreted by
adjoints of the base change functor in a locally cartesian closed category. An
effort is made to unpack all the definitions so as to make the concepts more
transparent to new learners.


title: A blast from the infant Universe: the very high-z GRB 210905A

abstract:
  We present the discovery of the very energetic GRB 210905A at the high
redshift z=6.312 and its luminous X-ray and optical afterglow. We obtained
photometric and spectroscopic follow-up in the optical and near-infrared (NIR),
covering both the prompt and afterglow emission from a few minutes up to 7.5 Ms
after burst. With an isotropic gamma-ray energy of Eiso=1.27x10^54erg, GRB
210905A lies in the top ~7% GRBs in terms of energy released. Its afterglow is
among the most luminous ever observed and, in particular, it is one of the most
luminous in the optical at t<0.5 d, in the rest frame. The afterglow starts
with a shallow evolution that can be explained by energy injection, and is
followed by a steeper decay, while the spectral energy distribution is in
agreement with slow cooling in a constant-density environment within the
standard fireball theory. A jet break at 39+-21 d has been observed in the
X-ray light curve; however, it is hidden in the H-band, potentially due to a
constant contribution from an unknown component, most likely a foreground
intervening galaxy and/or the host galaxy. We derived a half-opening angle of
7.9+-1.6 degrees, the highest ever measured for a z>~6 burst but within the
range covered by closer events. The resulting collimation-corrected gamma-ray
energy of 10^52erg is also among the highest ever measured. The moderately
large half-opening angle argues against recent claims of an inverse dependence
of the half-opening angle on the redshift. The total jet energy is likely too
large for a standard magnetar, and suggests that the central engine of this
burst was a newly formed black hole. Despite the outstanding energetics and
luminosity of both GRB 210905A and its afterglow, we demonstrate that they are
consistent within 2swith those of less distant bursts, indicating that the
powering mechanisms and progenitors do not evolve significantly with redshift.


title: Lower Complexity Bounds for Minimizing Regularized Functions

abstract:
  In this paper, we establish lower bounds for the oracle complexity of the
first-order methods minimizing regularized convex functions. We consider the
composite representation of the objective. The smooth part has H\"older
continuous gradient of degree $\nu \in [0, 1]$ and is accessible by a black-box
local oracle. The composite part is a power of a norm. We prove that the best
possible rate for the first-order methods in the large-scale setting for
Euclidean norms is of the order $O(k^{- p(1 + 3\nu) / (2(p - 1 - \nu))})$ for
the functional residual, where $k$ is the iteration counter and $p$ is the
power of regularization. Our formulation covers several cases, including
computation of the Cubically regularized Newton step by the first-order
gradient methods, in which case the rate becomes $O(k^{-6})$. It can be
achieved by the Fast Gradient Method. Thus, our result proves the latter rate
to be optimal. We also discover lower complexity bounds for non-Euclidean
norms.


title:
Proving Non-Termination and Lower Runtime Bounds with LoAT (System
  Description)

abstract:
  We present the new version of the Loop Acceleration Tool (LoAT), a powerful
tool for proving non-termination and worst-case lower bounds for programs
operating on integers. It is based on a novel calculus for loop acceleration,
i.e., transforming loops into non-deterministic straight-line code, and for
finding non-terminating configurations. To implement it efficiently, LoAT uses
a new approach based on SMT solving and unsat cores. An extensive evaluation
shows that LoAT is highly competitive with other state-of-the-art tools for
proving non-termination. While no other tool is able to deduce worst-case lower
bounds for full integer programs, we also demonstrate that LoAT significantly
outperforms its predecessors.


title: Self-Sensing Hysteresis-Type Bearingless Motor

abstract:
  Bearingless motors use a single stator assembly to apply torque and magnetic
suspension forces on the rotor, making these machines compact with frictionless
operation and thus well suited to high-speed applications. One major challenge
that prevents wide usage of bearingless motors is the need for air-gap position
sensors, which are typically expensive. Here we present a method to estimate
the radial position of a hysteresis-type bearingless motor using the inductance
variation of the stator coils amplified by an injected high-frequency signal.
We have carried out finite element (FE) simulations to demonstrate its
feasibility, and have constructed a prototype self-sensing bearingless motor
for experimental validations.


title: Forward and Back: Kinematics of the Palomar 5 Tidal Tails

abstract:
  The tidal tails of Palomar 5 (Pal 5) have been the focus of many
spectroscopic studies in an attempt to identify individual stars lying along
the stream and characterise their kinematics. The well-studied trailing tail
has been explored out to a distance of 15^\text{o} from the cluster centre,
while less than four degrees have been examined along the leading tail. In this
paper, we present results of a spectroscopic study of two fields along the
leading tail that we have observed with the AAOmega spectrograph on the
Anglo-Australian telescope. One of these fields lies roughly 7^\text{o} along
the leading tail, beyond what has been previously been explored
spectroscopically. Combining our measurements of kinematics and line strengths
with Pan-STARRS1 photometric data and Gaia EDR3 astrometry, we adopt a
probabilistic approach to identify 16 stars with high probability of belonging
to the Pal 5 stream. Eight of these stars lie in the outermost field and their
sky positions confirm the presence of ``fanning'' in the leading arm. We also
revisit previously-published radial velocity studies and incorporate Gaia EDR3
astrometry to remove interloping field stars. With a final sample of 109 {\it
bona fide} Pal 5 cluster and tidal stream stars, we characterise the 3D
kinematics along the the full extent of the system. We provide this catalogue
for future modeling work.


title:
The two-sphere partition function from timelike Liouville theory at
  three-loop order

abstract:
  While the Euclidean two-dimensional gravitational path integral is in general
highly fluctuating, it admits a semiclassical two-sphere saddle if coupled to a
matter CFT with large and positive central charge. In Weyl gauge this gravity
theory is known as timelike Liouville theory, and is conjectured to be a
non-unitary two-dimensional CFT. We explore the semiclassical limit of timelike
Liouville theory by calculating the two-sphere partition function from the
perspective of the path integral to three-loop order, extending the work in
2106.01665. We also compare our result to the conjectured all-loop sphere
partition function obtained from the DOZZ formula. Since the two-sphere is the
geometry of Euclidean two-dimensional de Sitter space our discussion is tied to
the conjecture of Gibbons-Hawking, according to which the dS entropy is encoded
in the Euclidean gravitational path integral over compact manifolds.


title:
Integrated routing for a vehicle-robot pickup and delivery system with
  time constraints

abstract:
  This paper considers an unmanned vehicle-robot pickup and delivery system, in
which a self-driving vehicle carrying multiple unmanned robots in the form of
the mother ship travels from a depot to a number of stations distributed in a
neighborhood to perform multiple pickup and delivery services. First of all, we
present it as a Multi-modal Vehicle Routing Problem (MMVRP) with time
constraints, which are typical service requirements for grocery and food
delivery in practice. We then formulate it as a Mixed Integer Quadratically
Con-strained Program (MIQCP) model to determine the optimal integrated routing
plan (vehicle routing and robot routing) to minimize the total weighted
tardiness of all services. Finally, a small-size and a medium-size problem
instance are solved using the Gurobi solver in Python to demonstrate the
validity and the performance of the proposed MIQCP model.


title: Shortest Paths without a Map, but with an Entropic Regularizer

abstract:
  In a 1989 paper titled "shortest paths without a map", Papadimitriou and
Yannakakis introduced an online model of searching in a weighted layered graph
for a target node, while attempting to minimize the total length of the path
traversed by the searcher. This problem, later called layered graph traversal,
is parametrized by the maximum cardinality $k$ of a layer of the input graph.
It is an online setting for dynamic programming, and it is known to be a rather
general and fundamental model of online computing, which includes as special
cases other acclaimed models. The deterministic competitive ratio for this
problem was soon discovered to be exponential in $k$, and it is now nearly
resolved: it lies between $\Omega(2^k)$ and $O(k2^k)$. Regarding the randomized
competitive ratio, in 1993 Ramesh proved, surprisingly, that this ratio has to
be at least $\Omega(k^2 / \log^{1+\epsilon} k)$ (for any constant $\epsilon >
0$). In the same paper, Ramesh also gave an $O(k^{13})$-competitive randomized
online algorithm. Since 1993, no progress has been reported on the randomized
competitive ratio of layered graph traversal. In this work we show how to apply
the mirror descent framework on a carefully selected evolving metric space, and
obtain an $O(k^2)$-competitive randomized online algorithm, nearly matching the
known lower bound on the randomized competitive ratio.


title:
Benchmark problems for transcranial ultrasound simulation:
  Intercomparison of compressional wave models

abstract:
  Computational models of acoustic wave propagation are frequently used in
transcranial ultrasound therapy, for example, to calculate the intracranial
pressure field or to calculate phase delays to correct for skull distortions.
To allow intercomparison between the different modeling tools and techniques
used by the community, an international working group was convened to formulate
a set of numerical benchmarks. Here, these benchmarks are presented, along with
intercomparison results. Nine different benchmarks of increasing geometric
complexity are defined. These include a single-layer planar bone immersed in
water, a multi-layer bone, and a whole skull. Two transducer configurations are
considered (a focused bowl and a plane piston), giving a total of 18
permutations of the benchmarks. Eleven different modeling tools are used to
compute the benchmark results. The models span a wide range of numerical
techniques, including the finite-difference time-domain method,
angular-spectrum method, pseudospectral method, boundary-element method, and
spectral-element method. Good agreement is found between the models,
particularly for the position, size, and magnitude of the acoustic focus within
the skull. When comparing results for each model with every other model in a
cross comparison, the median values for each benchmark for the difference in
focal pressure and position are less than 10\% and 1 mm, respectively. The
benchmark definitions, model results, and intercomparison codes are freely
available to facilitate further comparisons.


title: Longitudinal regression of covariance matrix outcomes

abstract:
  In this study, a longitudinal regression model for covariance matrix outcomes
is introduced. The proposal considers a multilevel generalized linear model for
regressing covariance matrices on (time-varying) predictors. This model
simultaneously identifies covariate associated components from covariance
matrices, estimates regression coefficients, and estimates the within-subject
variation in the covariance matrices. Optimal estimators are proposed for both
low-dimensional and high-dimensional cases by maximizing the (approximated)
hierarchical likelihood function and are proved to be asymptotically
consistent, where the proposed estimator is the most efficient under the
low-dimensional case and achieves the uniformly minimum quadratic loss among
all linear combinations of the identity matrix and the sample covariance matrix
under the high-dimensional case. Through extensive simulation studies, the
proposed approach achieves good performance in identifying the covariate
related components and estimating the model parameters. Applying to a
longitudinal resting-state fMRI dataset from the Alzheimer's Disease
Neuroimaging Initiative (ADNI), the proposed approach identifies brain networks
that demonstrate the difference between males and females at different disease
stages. The findings are in line with existing knowledge of AD and the method
improves the statistical power over the analysis of cross-sectional data.


title: Real-time decision-making for autonomous vehicles under faults

abstract:
  This paper addresses the challenges of decision-making for autonomous
vehicles under faults during a transport mission. A real-time decision-making
problem of vehicle routing planning considering maintenance management is
formulated as an optimization problem. The goal is to minimize the total time
to finish the transport mission by selecting the optimal workshop to conduct
the maintenance and the corresponding routes. Two methods are proposed to solve
the optimization problem based on two methods of fundamental solutions: (1)
Mixed Integer Programming; (2) Dijkstra's algorithm. We adapt these methods to
solve the optimization problem and consider improving the computation
efficiency. Numerical studies of test cases of highway and urban scenarios are
presented to demonstrate the proposed methods, which show the feasibility and
high computational efficiency of both methods.


title: A Birman-Schwinger principle in galactic dynamics

abstract:
  These are the (somewhat extended) lecture notes for four lectures delivered
at the spring school during the thematic programme "Mathematical Perspectives
of Gravitation beyond the Vacuum Regime" at ESI Vienna in February 2022.


title: Modification of Convex Ends to Cylindrical and Symplectic Foliations

abstract:
  We show that the natural symplectic structure on the Milnor fiber of an
isolated singularity in complex three variables whose link fibers over the
circle can be modified into one which is cylindrical at the end. As a
consequence we see that the foliation of codimension one on S^5 which is
adapted to the Milnor open book of S^5 associated with such a singularity
admits a leafwise symplectic structure. The modification also enables us to
construct certain closed symplectic 4-manifolds.


title:
Universal Hopfield Networks: A General Framework for Single-Shot
  Associative Memory Models

abstract:
  A large number of neural network models of associative memory have been
proposed in the literature. These include the classical Hopfield networks
(HNs), sparse distributed memories (SDMs), and more recently the modern
continuous Hopfield networks (MCHNs), which possesses close links with
self-attention in machine learning. In this paper, we propose a general
framework for understanding the operation of such memory networks as a sequence
of three operations: similarity, separation, and projection. We derive all
these memory models as instances of our general framework with differing
similarity and separation functions. We extend the mathematical framework of
Krotov et al (2020) to express general associative memory models using neural
network dynamics with only second-order interactions between neurons, and
derive a general energy function that is a Lyapunov function of the dynamics.
Finally, using our framework, we empirically investigate the capacity of using
different similarity functions for these associative memory models, beyond the
dot product similarity measure, and demonstrate empirically that Euclidean or
Manhattan distance similarity metrics perform substantially better in practice
on many tasks, enabling a more robust retrieval and higher memory capacity than
existing models.


title: Diagonalization of the metric of a Lorentzian 3-manifold

abstract:
  We study the problem of diagonalization of the metric of 3-dimensional
Lorentzian manifold. Applying the technique of moving frames, we prove that
every smooth Lorentzian 3-manifold admits an atlas in which the metric assumes
a diagonal form.


title:
Manipulation of transverse emittances in circular accelerators by
  crossing non-linear 2D resonances

abstract:
  Controlling non-linear effects in the transverse dynamics of charged particle
beams in circular accelerators opens new possibilities for controlling some of
the beam properties. Beam splitting by crossing a stable 1D non-linear
resonance is part of the routine operation of the CERN Proton Synchrotron. The
beam undergoes trapping and transport inside stable islands created in the
horizontal plane to allow multi-turn extraction towards the Super Proton
Synchrotron, where the beam is used for fixed-target experiments. This process
acts only on the horizontal beam emittance, inducing a reduction of its initial
value. In this paper, we present a generalisation of this approach, in which
both transverse planes are affected by the proposed technique. We will discuss
in detail how to manipulate the transverse emittances by means of a controlled
crossing of a 2D non-linear resonance. The novel technique will be presented by
discussing the theoretical analysis of a Hamiltonian model, as well as
simulating the performance of the proposed manipulation using a more realistic
non-linear symplectic map.


title:
The craft and coordination of data curation: complicating "workflow"
  views of data science

abstract:
  Data curation is the process of making a dataset fit-for-use and archiveable.
It is critical to data-intensive science because it makes complex data
pipelines possible, makes studies reproducible, and makes data (re)usable. Yet
the complexities of the hands-on, technical and intellectual work of data
curation is frequently overlooked or downplayed. Obscuring the work of data
curation not only renders the labor and contributions of the data curators
invisible; it also makes it harder to tease out the impact curators' work has
on the later usability, reliability, and reproducibility of data. To better
understand the specific work of data curation -- and thereby, explore ways of
showing curators' impact -- we conducted a close examination of data curation
at a large social science data repository, the Inter-university Consortium of
Political and Social Research (ICPSR). We asked, What does curatorial work
entail at ICPSR, and what work is more or less visible to different
stakeholders and in different contexts? And, how is that curatorial work
coordinated across the organization? We triangulate accounts of data curation
from interviews and records of curation in Jira tickets to develop a rich and
detailed account of curatorial work. We find that curators describe a number of
craft practices needed to perform their work, which defies the rote sequence of
events implied by many lifecycle or workflow models. Further, we show how best
practices and craft practices are deeply intertwined.


title:
Erasing Labor with Labor: Dark Patterns and Lockstep Behaviors on the
  Google Play Store

abstract:
  Google Play Store's policy forbids the use of incentivized installs, ratings,
and reviews to manipulate the placement of apps. However, there still exist
apps that incentivize installs for other apps on the platform. To understand
how install-incentivizing apps affect their users, we examine their ecosystem
through a socio-technical lens and perform a longitudinal mixed-methods
analysis of their reviews. We shortlist 60 install-incentivizing apps which
collectively account for over 160.5M installs on the Google Play Store. We
collect 1,000 most relevant reviews on these apps every day for a period of 52
days. First, our qualitative analysis reveals various types of dark patterns
that developers incorporate in install-incentivizing apps to extort services
and build market at the expense of their users. Second, we highlight the
normative concerns of these dark patterns at both the individual and collective
levels, elaborating on their detrimental effects on the price transparency and
trust in the market of Google Play Store. Third, we uncover evidence of
install-incentivizing apps indulging in review and rating fraud. Building upon
our findings, we model apps and reviewers as networks and discover lockstep
behaviors in the reviewing patterns that are strong indicators of review fraud.
Fourth, we leverage the content information of reviews to find that reviewers
who co-review more apps also show greater similarity in the content of their
reviews, making them more suspicious. Finally, we conclude with a discussion on
how our future work will generate implications for Google Play Store to prevent
the exploitation of users while preserving transparency and trust in its
market.


title:
Assessing the potential for liquid solvents from X-ray sources:
  considerations on bodies orbiting AGN

abstract:
  Aims. We aim to establish a rough first prospect on the potential of certain
biorelevant solvents (water, ammonia and methane) to be present in liquid form
inside the uppermost few meters of several modelled surfaces (rocky and icy
crusts of various compositions) of hypothetical bodies orbiting active galactic
nuclei (AGN), and investigate under which constraints this might occur.
Methods. We adjust and average together X-ray spectra from a sample of 20 Type
1 Seyfert galaxies to calculate a mean snowline of the sample used. Based on
this, we introduce variation of a hypothetical body's orbit across distances
between 10% and 100% of the snowline radius, and calculate a sub-surface
attenuation within four different model surface compositions for each. Surface
compositions are based on lunar soil and solvent ices found in the milky way's
circumnuclear region. We then use this as a continuous source term for a
thermal model. Example bodies are systematically investigated with sizes
between 1/30 and 20 earth radii. Further outlier variations are also considered
(such as the case of bound rotation of the body) to end up with a perspective
of solvent phases under a wide slew of many different conditions. Results. We
find that liquid solvents are possible under a multitude of parameters, with
temperature being the main constraint to liquid water and body size as well as
pressure being the main constraint to liquid methane and ammonia. We further
find that these results, when adjusted for snowline distance, depend less on
the energy output of the central source within the Seyfert Type 1 AGN than on
other parameters, such as body sizes and solvent properties.


title: Symmetries in subatomic six-quark fermions

abstract:
  The evidence of the existence of tetra-quark meson and penta-quark fermion
systems has revived interest in the hunt of other multi-quark systems. We
explore the possibility of six-quark cluster configurations with the two
nucleon spin-isospin quantum numbers existing in the nuclear medium. The
investigation of such clusters is feasible if one exploits all the symmetries
involved, in particular orbital, color-spin $SU(6)_{cs}$ and isospin SU(2). We
investigate whether such clusters contribute to neutrinoless double-beta decay
mediated by heavy neutrinos or other exotic particles, since in conventional
nuclear physics the relevant nuclear matrix elements are suppressed due to the
presence of the nuclear hard core.


title: K\"ahler stability of symplectic forms

abstract:
  Using dynamical stability of symplectic curvature flow, we show that on a
compact Calabi-Yau manifold, any small symplectic deformation of a K\"ahler
form remains K\"ahler.


title:
Precision Radiotherapy via Information Integration of Expert Human
  Knowledge and AI Recommendation to Optimize Clinical Decision Making

abstract:
  In the precision medicine era, there is a growing need for precision
radiotherapy where the planned radiation dose needs to be optimally determined
by considering a myriad of patient-specific information in order to ensure
treatment efficacy. Existing artificial-intelligence (AI) methods can recommend
radiation dose prescriptions within the scope of this available information.
However, treating physicians may not fully entrust the AI's recommended
prescriptions due to known limitations or when the AI recommendation may go
beyond physicians' current knowledge. This paper lays out a systematic method
to integrate expert human knowledge with AI recommendations for optimizing
clinical decision making. Towards this goal, Gaussian process (GP) models are
integrated with deep neural networks (DNNs) to quantify the uncertainty of the
treatment outcomes given by physicians and AI recommendations, respectively,
which are further used as a guideline to educate clinical physicians and
improve AI models performance. The proposed method is demonstrated in a
comprehensive dataset where patient-specific information and treatment outcomes
are prospectively collected during radiotherapy of $67$ non-small cell lung
cancer patients and retrospectively analyzed.


title:
Scaling relations for globular cluster systems in early-type galaxies.
  II. Is there an environmental dependence?

abstract:
  The current properties of globular cluster systems (GCSs) are the result of
the evolution experienced by their host galaxies, which shape the richness of
the GCS as well as its spatial distribution, among other features. We carry out
an analysis of the projected radial distribution of globular clusters for a
sample of almost 30 early-type galaxies (ETGs) of intermediate and low
luminosity, located in cluster environments (Virgo, Fornax and Coma). We also
include in the study six ETGs, for which the parameters of their GCS radial
profiles are publicly available. The final analysis is performed on an enlarged
sample (~ 100 GCSs), by adding the GCSs of ETGs from our previous paper (Paper
I). Scaling relations involving different parameters of the GCSs are obtained
for the whole sample and complement those obtained in Paper I. Several of such
relations point to a second-order dependence on the environmental density.
Finally, the results are analysed in the literature context.


title:
Optimal Hyperparameters and Structure Setting of Multi-Objective Robust
  CNN Systems via Generalized Taguchi Method and Objective Vector Norm

abstract:
  Recently, Machine Learning (ML), Artificial Intelligence (AI), and
Convolutional Neural Network (CNN) have made huge progress with broad
applications, where their systems have deep learning structures and a large
number of hyperparameters that determine the quality and performance of the
CNNs and AI systems. These systems may have multi-objective ML and AI
performance needs. There is a key requirement to find the optimal
hyperparameters and structures for multi-objective robust optimal CNN systems.
This paper proposes a generalized Taguchi approach to effectively determine the
optimal hyperparameters and structure for the multi-objective robust optimal
CNN systems via their objective performance vector norm. The proposed approach
and methods are applied to a CNN classification system with the original ResNet
for CIFAR-10 dataset as a demonstration and validation, which shows the
proposed methods are highly effective to achieve an optimal accuracy rate of
the original ResNet on CIFAR-10.


title: A note on the conservation properties of the generalized-$\alpha$ method

abstract:
  We show that the second-order accurate generalized-$\alpha$ method on a
uniform temporal mesh may be viewed as an implicit midpoint method on a shifted
temporal mesh. With this insight, we demonstrate generalized-$\alpha$ time
integration of a finite element spatial discretization of a conservation law
system results in a fully-discrete method admitting discrete balance laws when
(i) the time integration is second-order accurate, (ii) a uniform temporal mesh
is employed, (iii) the spatial discretization is conservative, and (iv)
conservation variables are discretized.


title:
Flexible Bayesian Nowcasting with application to COVID-19 fatalities in
  Sweden

abstract:
  The real-time analysis of infectious disease surveillance data, e.g.
time-series of reported cases or fatalities, can help to provide situational
awareness about the current state of a pandemic. This task is challenged by
reporting delays that give rise to occurred-but-not-yet-reported events. If
these events are not taken into consideration, this can lead to an
under-estimation of the counts-to-be-reported and, hence, introduces
misconceptions by the interpreter, the media or the general public -- as has
been seen for example for reported fatalities during the COVID-19 pandemic.
Nowcasting methods provide close to real-time estimates of the complete number
of events using the incomplete time-series of currently reported events by
using information about the reporting delays from the past. In this report, we
consider nowcasting the number of COVID-19 related fatalities in Sweden. We
propose a flexible Bayesian approach that considers temporal changes in the
reporting delay distribution and, as an extension to existing nowcasting
methods, incorporates a regression component for the (lagged) time-series of
the number of ICU admissions. This results in a model considering both the past
behavior of the time-series of fatalities as well as additional data streams
that are in a time-lagged association with the number of fatalities.


title:
Influence of surfactant concentration on drop production by bubble
  bursting

abstract:
  Bubble bursting at the surface of the sea water produce drops and is the main
source of sea spay aerosol. The mechanisms underlying the drops production from
a single bubble bursting event have been intensively studied and the influence
of the bubble size and liquid parameters (density, viscosity and surface
tension) has been unified. However, despite the diversity of the surfactant
molecules present in the oceans, their influence has been overlooked. In this
paper we experimentally explore the influence of the surfactant concentration
(Sodium Dodecyl Surfate - SDS) in a water solution on a single bubble collapse
and subsequent drop production. We show that these surfactant molecules have an
astonishing effect. In particular, we quantitatively show that they modify the
bubble collapse, they induce less, smaller and faster drops and they can even
completely prevent the drop production for a particular concentration. These
results are presented in the existing dimensionless framework and they allow us
to affirme that these effects are mainly a consequence of the surface tension
gradients (Marangoni stresses) more than just the surface tension lowering.
Finally, this study shows that the role of water contamination by
surface-active agents is important and needs to be understood to improve the
prediction of the sea spray aerosol.


title: Harnack inequality for nonlocal problems with non-standard growth

abstract:
  We prove a full Harnack inequality for local minimizers, as well as weak
solutions to nonlocal problems with non-standard growth. The main auxiliary
results are local boundedness and a weak Harnack inequality for functions in a
corresponding De Giorgi class. This paper builds upon a recent work on
regularity estimates for such nonlocal problems by the same authors.


title:
Single top production via FCNC couplings at an $e^{-}e^{+}$ collider
  with center-of-mass energy $\sqrt{s}=240$ GeV

abstract:
  Aspects of top quark physics can be studied at a future Circular
Electron-Positron Collider (CEPC). In particular, Flavor-Changing Neutral
Current interactions (FCNC) of the top quark can be studied even with a
center-of-mass energy from $\sqrt{s}\gtrsim m_t$ to $\sqrt{s}=240$ GeV, through
the production a single top quark in association with a charm quark, which can
arise in several scenarios of new physics. We explore here this signal within
the Left-Right Mirror Model, which is a Left-Right model that includes mirror
fermions; this model is motivated as a possible solution to the strong CP
problem and by its rich phenomenology. We find that for particular scenarios of
the model parameters, which are in agreement with the most up-to-date
experimental constraints, the signal coming from the process $e^+e^-\to V \to
tc$ ($V=Z,\,Z^{\prime}$) provide a detectable signal and thus it can give
evidence for FCNC interactions; in these scenarios the mass of a new neutral
gauge boson can be as high as $m_{Z'}=7$ TeV.


title:
On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear
  Economies

abstract:
  In this paper, we show that if every consumer in an economy has a
quasi-linear utility function, then the normalized equilibrium price is unique,
and it is locally stable with respect to the t\^atonnement process. If the
dimension of the consumption space is two, then this result can be expressed by
the corresponding partial equilibrium model. Our study can be seen as that
extends the results in partial equilibrium theory to economies with more than
two dimensional consumption space.


title: Diffuse Galactic emission spectrum between 0.5 and 8.0 MeV

abstract:
  The last measurement of the diffuse emission spectrum of the Milky Way in the
megaelectronvolt (MeV) photon energy range was performed by CGRO/COMPTEL more
than 20 years ago. We report a new analysis with the spectrometer SPI aboard
INTEGRAL in the band 0.5-8.0 MeV, finally superseding the signal-to-noise ratio
of the historic observations. This is possible thanks to an elaborate
instrumental background model and careful considerations of the selected data,
which are strongly affected by solar activity. We base our analysis on
energy-dependent spatial template fitting in a region of $\Delta l \times
\Delta b = 95^\circ \times 95^\circ$ around the Galactic centre. Our flux
estimates are consistent with COMPTEL measurements and show no `MeV bump'. The
spectrum follows a power-law shape with index $-1.39 \pm 0.09_{\rm stat} \pm
0.10_{\rm syst}$ and an integrated flux of $(5.7 \pm 0.8_{\rm stat} \pm
1.7_{\rm syst}) \times 10^{-8}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$ between 0.5 and
8.0 MeV. We find that cosmic-ray electrons and propagation models consistent
with the latest Fermi/LAT, Voyager 1, and AMS-02 data are broadly in agreement
with the inferred inverse Compton spectral shape. However, a mismatch of a
factor of 2-3 in normalisation with respect to baseline expectations may point
to enhanced target photon densities and/or electron source spectra in the inner
Galaxy, slightly modified diffusion properties, or the presence of an
unresolved population of MeV $\gamma$-ray sources.


title:
Soft Robots Learn to Crawl: Jointly Optimizing Design and Control with
  Sim-to-Real Transfer

abstract:
  This work provides a complete framework for the simulation, co-optimization,
and sim-to-real transfer of the design and control of soft legged robots. The
compliance of soft robots provides a form of "mechanical intelligence" -- the
ability to passively exhibit behaviors that would otherwise be difficult to
program. Exploiting this capacity requires careful consideration of the
coupling between mechanical design and control. Co-optimization provides a
promising means to generate sophisticated soft robots by reasoning over this
coupling. However, the complex nature of soft robot dynamics makes it difficult
to provide a simulation environment that is both sufficiently accurate to allow
for sim-to-real transfer, while also being fast enough for contemporary
co-optimization algorithms. In this work, we show that finite element
simulation combined with recent model order reduction techniques provide both
the efficiency and the accuracy required to successfully learn effective soft
robot design-control pairs that transfer to reality. We propose a reinforcement
learning-based framework for co-optimization and demonstrate successful
optimization, construction, and zero-shot sim-to-real transfer of several soft
crawling robots. Our learned robot outperforms an expert-designed crawling
robot, showing that our approach can generate novel, high-performing designs
even in well-understood domains.


title:
Every metric space of weight $\lambda=\lambda^{\aleph_0}$ admits a
  condensation onto a Banach space

abstract:
  In this paper, we have proved that for each cardinal number $\lambda$ such
that $\lambda=\lambda^{\aleph_0}$ a metric space of weight $\lambda$ admits a
bijective continuous mapping onto a Banach space of weight $\lambda$. Then, we
get that every metric space of weight continuum admits a bijective continuous
mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when
does a metric (possibly Banach) space $X$ admit a bijective continuous mapping
onto a compact metric space?) in the class of metric spaces of weight
continuum. Also we get that every metric space of weight
$\lambda=\lambda^{\aleph_0}$ admits a bijective continuous mapping onto a
Hausdorff compact space. This resolves the Alexandroff Problem (when does a
Hausdorff space $X$ admit a bijective continuous mapping onto a Hausdorff
compact space?) in the class of metric spaces of weight
$\lambda=\lambda^{\aleph_0}$.


title: Effect of initial infection size on network SIR model

abstract:
  We consider the effect of a nonvanishing fraction of initially infected nodes
(seeds) on the SIR epidemic model on random networks. This is relevant when,
for example, the number of arriving infected individuals is large, but also to
the modeling of a large number of infected individuals, but also to more
general situations such as the spread of ideas in the presence of publicity
campaigns. This model is frequently studied by mapping to a bond percolation
problem, in which edges in the network are occupied with the probability, $p$,
of eventual infection along an edge connecting an infected individual to a
susceptible neighbor. This approach allows one to calculate the total final
size of the infection and epidemic threshold in the limit of a vanishingly
small seed fraction. We show, however, that when the initial infection occupies
a nonvanishing fraction $f$ of the network, this method yields ambiguous
results, as the correspondence between edge occupation and contagion
transmission no longer holds. We propose instead to measure the giant component
of recovered individuals within the original contact network. This has an
unambiguous interpretation and correctly captures the dependence of the
epidemic size on $f$. We give exact equations for the size of the epidemic and
the epidemic threshold in the infinite size limit. We observe a second order
phase transition as in the original formulation, however with an epidemic
threshold which decreases with increasing $f$. When the seed fraction $f$ tends
to zero we recover the standard results.


title: Gauge reduction in covariant field theory

abstract:
  In this work we develop a Lagrangian reduction theory for covariant field
theories with local symmetries and, more specifically, with gauge symmetries.
We model these symmetries by using a Lie group fiber bundle acting fiberwisely
on the corresponding configuration bundle. In order to reduce the variational
principle, we utilize generalized principal connections, a type of Ehresmann
connections that are equivariant by the fiberwise action. After obtaining the
reduced equations, we give the reconstruction condition and we relate the
vertical reduced equation with the Noether theorem. Lastly, we illustrate the
theory by applying it to several examples, including the classical case
(Lagrange-Poincar\'e reduction) and electromagnetism.


title:
Neural Sheaf Diffusion: A Topological Perspective on Heterophily and
  Oversmoothing in GNNs

abstract:
  Cellular sheaves equip graphs with "geometrical" structure by assigning
vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs)
implicitly assume a graph with a trivial underlying sheaf. This choice is
reflected in the structure of the graph Laplacian operator, the properties of
the associated diffusion equation, and the characteristics of the convolutional
models that discretise this equation. In this paper, we use cellular sheaf
theory to show that the underlying geometry of the graph is deeply linked with
the performance of GNNs in heterophilic settings and their oversmoothing
behaviour. By considering a hierarchy of increasingly general sheaves, we study
how the ability of the sheaf diffusion process to achieve linear separation of
the classes in the infinite time limit expands. At the same time, we prove that
when the sheaf is non-trivial, discretised parametric diffusion processes have
greater control than GNNs over their asymptotic behaviour. On the practical
side, we study how sheaves can be learned from data. The resulting sheaf
diffusion models have many desirable properties that address the limitations of
classical graph diffusion equations (and corresponding GNN models) and obtain
state-of-the-art results in heterophilic settings. Overall, our work provides
new connections between GNNs and algebraic topology and would be of interest to
both fields.


title:
Stratospheric balloons as a platform for the next large far infrared
  observatory

abstract:
  Observations that require large physical instrument dimensions and/or a
considerable amount of cryogens, as it is the case for high spatial resolution
far infrared (FIR) astronomy, currently still face technological limits for
their execution from space. Angular resolution and available observational
capabilities are particularly affected. Balloon-based platforms promise to
complement the existing observational capabilities by offering means to deploy
comparatively large telescopes with comparatively little effort, including
other advantages such as the possibility to regularly refill cryogens and to
change and/or update instruments. The planned European Stratospheric Balloon
Observatory (ESBO) aims at providing these additional large aperture FIR
capabilities, exceeding the spatial resolution of Herschel, in the long term.
The plans focus on reusable platforms performing regular flights and an
operations concept that provides researchers with proposal-based access to
observations. It thereby aims at offering a complement to other airborne,
ground-based and space-based observatories in terms of access to wavelength
regions, spatial resolution capability, and photometric stability. While the
FIR capabilities are a main long-term objective, ESBO will offer benefits in
other wavelength regimes along the way. Within the ESBO Design Study (ESBO DS),
a prototype platform carrying a 0.5 m telescope for ultraviolet and visible
light observations is being built and a platform concept for a next-generation
FIR telescope is being studied. A flight of the UV/VIS prototype platform is
estimated for 2021. In this paper we will outline the scientific and technical
motivation for a large aperture balloon-based FIR observatory and the ESBO DS
approach towards such an infrastructure. Secondly, we will present the
technical motivation, science case, and instrumentation of the 0.5 m UV/VIS
platform.


title: Noise fingerprints in quantum computers: Machine learning software tools

abstract:
  In this paper we present the high-level functionalities of a
quantum-classical machine learning software, whose purpose is to learn the main
features (the fingerprint) of quantum noise sources affecting a quantum device,
as a quantum computer. Specifically, the software architecture is designed to
classify successfully (more than 99% of accuracy) the noise fingerprints in
different quantum devices with similar technical specifications, or distinct
time-dependences of a noise fingerprint in single quantum machines.


title:
Topic Discovery via Latent Space Clustering of Pretrained Language Model
  Representations

abstract:
  Topic models have been the prominent tools for automatic topic discovery from
text corpora. Despite their effectiveness, topic models suffer from several
limitations including the inability of modeling word ordering information in
documents, the difficulty of incorporating external linguistic knowledge, and
the lack of both accurate and efficient inference methods for approximating the
intractable posterior. Recently, pretrained language models (PLMs) have brought
astonishing performance improvements to a wide variety of tasks due to their
superior representations of text. Interestingly, there have not been standard
approaches to deploy PLMs for topic discovery as better alternatives to topic
models. In this paper, we begin by analyzing the challenges of using PLM
representations for topic discovery, and then propose a joint latent space
learning and clustering framework built upon PLM embeddings. In the latent
space, topic-word and document-topic distributions are jointly modeled so that
the discovered topics can be interpreted by coherent and distinctive terms and
meanwhile serve as meaningful summaries of the documents. Our model effectively
leverages the strong representation power and superb linguistic features
brought by PLMs for topic discovery, and is conceptually simpler than topic
models. On two benchmark datasets in different domains, our model generates
significantly more coherent and diverse topics than strong topic models, and
offers better topic-wise document representations, based on both automatic and
human evaluations.


title:
Controlled-NOT gates for fluxonium qubits via selective darkening of
  transitions

abstract:
  We analyze the cross-resonance effect for fluxonium circuits and investigate
a two-qubit gate scheme based on selective darkening of a transition. In this
approach, two microwave pulses at the frequency of the target qubit are applied
simultaneously with a proper ratio between their amplitudes to achieve a
controlled-NOT operation. We study in detail coherent gate dynamics and
calculate gate error. With nonunitary effects accounted for, we demonstrate
that gate error below $10^{-4}$ is possible for realistic hardware parameters.
This number is facilitated by long coherence times of computational transitions
and strong anharmonicity of fluxoniums, which easily prevents excitation to
higher excited states during the gate microwave drive.


title:
Cosmic Birefringence: Cross-Spectra and Cross-Bispectra with CMB
  Anisotropies

abstract:
  Parity-violating extensions of Maxwell electromagnetism induce a rotation of
the linear polarization plane of photons during propagation. This effect, known
as cosmic birefringence, impacts on the Cosmic Microwave Background (CMB)
observations producing a mixing of $E$ and $B$ polarization modes which is
otherwise null in the standard scenario. Such an effect is naturally
parametrized by a rotation angle which can be written as the sum of an
isotropic component $\alpha_0$ and an anisotropic one
$\delta\alpha(\hat{\mathbf{n}})$. In this paper we compute angular power
spectra and bispectra involving $\delta\alpha$ and the CMB temperature and
polarization maps. In particular, contrarily to what happens for the
cross-spectra, we show that even in absence of primordial cross-correlations
between the anisotropic birefringence angle and the CMB maps, there exist
non-vanishing three-point correlation functions carrying signatures of
parity-breaking physics. Furthermore, we find that such angular bispectra still
survive in a regime of purely anisotropic cosmic birefringence, which
corresponds to the conservative case of having $\alpha_0=0$. These bispectra
represent an additional observable aimed at studying cosmic birefringence and
its parity-violating nature beyond power spectrum analyses. They provide also a
way to perform consistency checks for specific models of cosmic birefringence.
Moreover, we estimate that among all the possible birefringent bispectra,
$\langle\delta\alpha\, TB\rangle$ and $\langle\delta\alpha\,EB\rangle$ are the
ones which contain the largest signal-to-noise ratio. Once the cosmic
birefringence signal is taken to be at the level of current constraints, we
show that these bispectra are within reach of future CMB experiments, as
LiteBIRD.