title: Discrete Optimal Transport with Independent Marginals is #P-Hard

abstract:
  We study the computational complexity of the optimal transport problem that
evaluates the Wasserstein distance between the distributions of two
K-dimensional discrete random vectors. The best known algorithms for this
problem run in polynomial time in the maximum of the number of atoms of the two
distributions. However, if the components of either random vector are
independent, then this number can be exponential in K even though the size of
the problem description scales linearly with K. We prove that the described
optimal transport problem is #P-hard even if all components of the first random
vector are independent uniform Bernoulli random variables, while the second
random vector has merely two atoms, and even if only approximate solutions are
sought. We also develop a dynamic programming-type algorithm that approximates
the Wasserstein distance in pseudo-polynomial time when the components of the
first random vector follow arbitrary independent discrete distributions, and we
identify special problem instances that can be solved exactly in strongly
polynomial time.


title:
Gyrokinetic modelling of the Alfv\'en mode activity in ASDEX Upgrade
  with an isotropic slowing-down fast-particle distribution

abstract:
  In the present paper, the evolution of the Alfv\'en modes is studied in a
realistic ASDEX Upgrade equilibrium by analysing the results of simulations
with the global, electromagnetic, gyrokinetic particle-in-cell code ORB5. The
energetic particles are modelled both via the newly implemented isotropic
slowing-down and with Maxwellian distribution functions. The comparison of the
numerical results shows that modelling the energetic particles with the
equivalent Maxwellian rather than with the slowing-down, does not affect the
frequency of the driven Alfv\'en mode, while its growth rate appears to be
underestimated with a quantitative difference as large as almost 30 %.
Additionally the choice of the isotropic slowing-down allows a better
description of the nonlinear modification of the dominant Alfv\'en mode
frequency, while an equivalent Maxwellian underestimates it. A good comparison
with the experimental spectrogram is found.


title: Conformal and chiral phase transitions in Rydberg chains

abstract:
  Using density matrix renormalization group simulations on open chains, we map
out the wave-vector in the incommensurate disordered phase of a realistic model
of Rydberg chains with $1/r^6$ interactions, and we locate and characterize the
points along the commensurate lines where the transition out of the period 3
and 4 phases is conformal. We confirm that it is 3-state Potts for the period-3
phase, and we show that it is Ashkin-Teller with $\nu\simeq 0.80$ for the
period-4 phase. We further show that close to these points the transition is
still continuous, but with a completely different scaling of the wave-vector,
in agreement with a chiral transition. Finally, we propose to use the conformal
points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a
conclusive identification of the chiral universality class.


title: Speaker recognition improvement using blind inversion of distortions

abstract:
  In this paper we propose the inversion of nonlinear distortions in order to
improve the recognition rates of a speaker recognizer system. We study the
effect of saturations on the test signals, trying to take into account real
situations where the training material has been recorded in a controlled
situation but the testing signals present some mismatch with the input signal
level (saturations). The experimental results shows that a combination of data
fusion with and without nonlinear distortion compensation can improve the
recognition rates with saturated test sentences from 80% to 88.57%, while the
results with clean speech (without saturation) is 87.76% for one microphone.


title: Renault's $j$-map for Fell bundle $C^*$-algebras

abstract:
  If $p \colon \mathcal B\to G$ is a Fell bundle over an \'etale groupoid, then
we show that there is an norm reducing injective linear map $j \colon
C^*_r(G;\mathcal B)\to \Gamma_{0}(G;\mathcal B)$ generalizing the well know map
$j \colon C^*_{r}(G)\to C_{0}(G)$ in the case of an \'etale groupoid.


title:
Hecke algebras and the Schlichting completion for discrete quantum
  groups

abstract:
  We introduce Hecke algebras associated to discrete quantum groups with
commensurated quantum subgroups. We study their modular properties and the
associated Hecke operators. In order to investigate their analytic properties
we adapt the construction of the Schlichting completion to the quantum setting,
thus obtaining locally compact quantum groups with compact open quantum
subgroups. We study in detail a class of examples arising from quantum HNN
extensions.


title:
Optimal protocol for spin-orbit torque switching of a perpendicular
  nanomagnet

abstract:
  It is demonstrated by means of the optimal control theory that the energy
cost of the spin-orbit torque induced reversal of a nanomagnet with
perpendicular anisotropy can be strongly reduced by proper shaping of both
in-plane components of the current pulse. The time-dependence of the optimal
switching pulse that minimizes the energy cost associated with Joule heating is
derived analytically in terms of the required reversal time and material
properties. The optimal reversal time providing a tradeoff between the
switching speed and energy efficiency is obtained. A sweet-spot balance between
the field-like and damping-like components of the spin-orbit torque is
discovered; it permits for a particularly efficient switching by a down-chirped
rotating current pulse whose duration does not need to be adjusted precisely.


title: Bi- and tetracritical phase diagrams in three dimensions

abstract:
  The critical behavior of many physical systems involves two competing
$n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf
S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control
parameter $g$, %(e.g. uniaxial stress or magnetic field), one encounters
ordering of ${\bf S}^{}_1$ below a critical (second-order) line for $g<0$ and
of ${\bf S}^{}_2$ below another critical line for $g>0$. These two ordered
phases are separated by a first-order line, which meets the above critical
lines at a bicritical point, or by an intermediate (mixed) phase, bounded by
two critical lines, which meet the above critical lines at a tetracritical
point. For $n=1+2=3$, the critical behavior around the (bi- or tetra-)
multicritical point either belongs to the universality class of a
non-rotationally invariant (cubic or biconical) fixed point, or it has a
fluctuation driven first-order transition. These asymptotic behaviors arise
only very close to the transitions. We present accurate renormalization-group
flow trajectories yielding the effective crossover exponents near
multicriticality.


title: Applying multi-angled parallelism to Spanish topographical maps

abstract:
  Multi-Angled Parallelism (MAP) is a method to recognize lines in binary
images. It is suitable to be implemented in parallel processing and image
processing hardware. The binary image is transformed into directional planes,
upon which, directional operators of erosion-dilation are iteratively applyed.
From a set of basic operators, more complex ones are created, which let to
extract the several types of lines. Each type is extracted with a different set
of operations and so the lines are identified when extracted. In this paper, an
overview of MAP is made, and it is adapted to line recognition in Spanish
topographical maps, with the double purpose of testing the method in a real
case and studying the process of adapting it to a custom application.


title:
Efficient Online Linear Control with Stochastic Convex Costs and Unknown
  Dynamics

abstract:
  We consider the problem of controlling an unknown linear dynamical system
under a stochastic convex cost and full feedback of both the state and cost
function. We present a computationally efficient algorithm that attains an
optimal $\sqrt{T}$ regret-rate against the best stabilizing linear controller.
In contrast to previous work, our algorithm is based on the Optimism in the
Face of Uncertainty paradigm. This results in a substantially improved
computational complexity and a simpler analysis.


title: Imitation of Manipulation Skills Using Multiple Geometries

abstract:
  Daily manipulation tasks are characterized by regular characteristics
associated with the task structure, which can be described by multiple
geometric primitives related to actions and object shapes. Such geometric
descriptors can not be expressed only in Cartesian coordinate systems. In this
paper, we propose a learning approach to extract the optimal representation
from a dictionary of coordinate systems to represent an observed movement. This
is achieved by using an extension of Gaussian distributions on Riemannian
manifolds, which is used to analyse a set of user demonstrations statistically,
by considering multiple geometries as candidate representations of the task. We
formulate the reproduction problem as a general optimal control problem based
on an iterative linear quadratic regulator (iLQR), where the Gaussian
distribution in the extracted coordinate systems are used to define the cost
function. We apply our approach to grasping and box opening tasks in simulation
and on a 7-axis Franka Emika robot. The results show that the robot can exploit
several geometries to execute the manipulation task and generalize it to new
situations, by maintaining the invariant features of the skill in the
coordinate system(s) of interest.


title: Thermodynamical and topological properties of metastable Fe3Sn

abstract:
  Combining experimental data, first-principles calculations, and Calphad
assessment, thermodynamic and topological transport properties of the Fe-Sn
system were investigated. Density functional theory (DFT) calculations were
performed to evaluate the intermetallics' finite-temperature heat capacity
(Cp). A consistent thermodynamic assessment of the Fe-Sn phase diagram was
achieved by using the experimental and DFT results, together with all available
data from previous publications. Hence, the metastable phase Fe3Sn was firstly
introduced into the current metastable phase diagram, and corrected phase
locations of Fe5Sn3 and Fe3Sn2 under the newly measured corrected temperature
ranges. Furthermore, the anomalous Hall conductivity and anomalous Nernst
conductivity of Fe3Sn were calculated, with magnetization directions and doping
considered as perturbations to tune such transport properties. It was observed
that the enhanced anomalous Hall and Nernst conductivities originate from the
combination of nodal lines and small gap areas that can be tuned by doping Mn
at Fe sites and varying magnetization direction


title: Characteristics of de Bruijn's early proof checker Automath

abstract:
  The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968,
was the first theorem prover actually working and was used for checking many
specimina of mathematical content. Its goals and syntactic ideas inspired Th.
Coquand and G. Huet to develop the calculus of constructions, CC, which was one
of the first widely used interactive theorem provers and forms the basis for
the widely used Coq system. The original syntax of Automath is not easy to
grasp. Yet, it is essentially based on a derivation system that is similar to
the Calculus of Constructions (`CC'). The relation between the Automath syntax
and CC has not yet been sufficiently described, although there are many
references in the type theory community to Automath. In this paper we focus on
the backgrounds and on some uncommon aspects of the syntax of Automath. We
expose the fundamental aspects of a `generic' Automath system, encapsulating
the most common versions of Automath. We present this generic Automath system
in a modern syntactic frame. The obtained system makes use of {\lambda}D, a
direct extension of CC with definitions.


title:
Spherical accretion of collisional gas in modified gravity I:
  self-similar solutions and a new cosmological hydrodynamical code

abstract:
  The spherical collapse scenario has great importance in cosmology since it
captures several crucial aspects of structure formation. The presence of
self-similar solutions in the Einstein-de Sitter (EdS) model greatly simplifies
its analysis, making it a powerful tool to gain valuable insights into the real
and more complicated physical processes involved in galaxy formation. While
there has been a large body of research to incorporate various additional
physical processes into spherical collapse, the effect of modified gravity (MG)
models, which are popular alternatives to the $\Lambda CDM$ paradigm to explain
the cosmic acceleration, is still not well understood in this scenario. In this
paper, we study the spherical accretion of collisional gas in a particular MG
model, which is a rare case that also admits self-similar solutions. The model
displays interesting behaviours caused by the enhanced gravity and a screening
mechanism. Despite the strong effects of MG, we find that its self-similar
solution agrees well with that of the EdS model. These results are used to
assess a new cosmological hydrodynamical code for spherical collapse
simulations introduced here, which is based on the hyperbolic partial
differential equation engine ExaHyPE 2. Its good agreement with the theoretical
predictions confirms the reliability of this code in modelling astrophysical
processes in spherical collapse. We will use this code to study the evolution
of gas in more realistic MG models in future work.


title:
libRoadRunner 2.0: A High-Performance SBML Simulation and Analysis
  Library

abstract:
  Motivation: This paper presents libRoadRunner 2.0, an extensible,
high-performance, cross-platform, open-source software library for the
simulation and analysis of models expressed using Systems Biology Markup
Language SBML).
  Results: libRoadRunner is a self-contained library, able to run both as a
component inside other tools via its C++ and C bindings, and interactively
through its Python or Julia interface. libRoadRunner uses a custom Just-In-Time
JIT compiler built on the widely-used LLVM JIT compiler framework. It compiles
SBML-specified models directly into native machine code for a large variety of
processors, making it appropriate for solving extremely large models or
repeated runs. libRoadRunner is flexible, supporting the bulk of the SBML
specification (except for delay and nonlinear algebraic equations) and
including several SBML extensions such as composition and distributions. It
offers multiple deterministic and stochastic integrators, as well as tools for
steady-state, sensitivity, stability analysis, and structural analysis of the
stoichiometric matrix.
  Availability: libRoadRunner binary distributions are available for Mac OS X,
Linux, and Windows. The library is licensed under the Apache License Version
2.0. libRoadRunner is also available for ARM-based computers such as the
Raspberry Pi and can in principle be compiled on any system supported by
LLVM-13. http://sys-bio.github.io/roadrunner/index.html provides online
documentation, full build instructions, binaries, and a git source repository.


title:
Avant-Satie! Using ERIK to encode task-relevant expressivity into the
  animation of autonomous social robots

abstract:
  ERIK is an expressive inverse kinematics technique that has been previously
presented and evaluated both algorithmically and in a limited user-interaction
scenario. It allows autonomous social robots to convey posture-based expressive
information while gaze-tracking users. We have developed a new scenario aimed
at further validating some of the unsupported claims from the previous
scenario. Our experiment features a fully autonomous Adelino robot, and
concludes that ERIK can be used to direct a user's choice of actions during
execution of a given task, fully through its non-verbal expressive queues.


title: Detecting Adversarial Perturbations in Multi-Task Perception

abstract:
  While deep neural networks (DNNs) achieve impressive performance on
environment perception tasks, their sensitivity to adversarial perturbations
limits their use in practical applications. In this paper, we (i) propose a
novel adversarial perturbation detection scheme based on multi-task perception
of complex vision tasks (i.e., depth estimation and semantic segmentation).
Specifically, adversarial perturbations are detected by inconsistencies between
extracted edges of the input image, the depth output, and the segmentation
output. To further improve this technique, we (ii) develop a novel edge
consistency loss between all three modalities, thereby improving their initial
consistency which in turn supports our detection scheme. We verify our
detection scheme's effectiveness by employing various known attacks and image
noises. In addition, we (iii) develop a multi-task adversarial attack, aiming
at fooling both tasks as well as our detection scheme. Experimental evaluation
on the Cityscapes and KITTI datasets shows that under an assumption of a 5%
false positive rate up to 100% of images are correctly detected as
adversarially perturbed, depending on the strength of the perturbation. Code
will be available on github. A short video at https://youtu.be/KKa6gOyWmH4
provides qualitative results.


title: DCT-Former: Efficient Self-Attention with Discrete Cosine Transform

abstract:
  Since their introduction the Trasformer architectures emerged as the
dominating architectures for both natural language processing and, more
recently, computer vision applications. An intrinsic limitation of this family
of "fully-attentive" architectures arises from the computation of the
dot-product attention, which grows both in memory consumption and number of
operations as $O(n^2)$ where $n$ stands for the input sequence length, thus
limiting the applications that require modeling very long sequences. Several
approaches have been proposed so far in the literature to mitigate this issue,
with varying degrees of success. Our idea takes inspiration from the world of
lossy data compression (such as the JPEG algorithm) to derive an approximation
of the attention module by leveraging the properties of the Discrete Cosine
Transform. An extensive section of experiments shows that our method takes up
less memory for the same performance, while also drastically reducing inference
time. This makes it particularly suitable in real-time contexts on embedded
platforms. Moreover, we assume that the results of our research might serve as
a starting point for a broader family of deep neural models with reduced memory
footprint. The implementation will be made publicly available at
https://github.com/cscribano/DCT-Former-Public


title:
Achieving Heisenberg Scaling on Measurement of A Three-Qubit System via
  Quantum Error Correction

abstract:
  In many-body quantum systems, the quantum Fisher information an observer can
obtain is susceptible to decoherence. Consequently, quantum enhanced metrology,
such as Heisenberg scaling, cannot usually be achieved. We show, via two
distinct methods, that by applying periodic quantum error corrections, we can
achieve the Heisenberg scaling for an extended period of time on a three-qubit
Tavis-Cumming Model, where three two-level atoms interact with a single cavity
mode, under certain approximations. The generalization to arbitrary number of
atoms case is also discussed.


title:
Fast and Robust Ground Surface Estimation from LIDAR Measurements using
  Uniform B-Splines

abstract:
  We propose a fast and robust method to estimate the ground surface from LIDAR
measurements on an automated vehicle. The ground surface is modeled as a UBS
which is robust towards varying measurement densities and with a single
parameter controlling the smoothness prior. We model the estimation process as
a robust LS optimization problem which can be reformulated as a linear problem
and thus solved efficiently. Using the SemanticKITTI data set, we conduct a
quantitative evaluation by classifying the point-wise semantic annotations into
ground and non-ground points. Finally, we validate the approach on our research
vehicle in real-world scenarios.


title:
Polar flocks with discretized directions: the active clock model
  approaching the Vicsek model

abstract:
  We consider the two-dimensional $q$-state active clock model (ACM) as a
natural discretization of the Vicsek model (VM) describing flocking. The ACM
consists of particles able to move in the plane in a discrete set of $q$
equidistant angular directions, as in the active Potts model (APM), with an
alignment interaction inspired by the ferromagnetic equilibrium clock model. We
find that for a small number of directions $2<q\le q_c=5$ the flocking
transition of the ACM has the same phenomenology as the APM, including
macro-phase separation and reorientation transition. For a larger number of
directions, $q>q_c$, the flocking transition in the ACM becomes equivalent to
the one of the VM and displays micro-phase separation and only transverse
bands, i.e. no re-orientation transition. Concomitantly also the transition of
the $q\to\infty$ limit of the ACM, the active XY model (AXYM), is in the same
universality class as the VM. The main difference between the VM and the AXYM
is the presence of a long range order at zero activity. We also construct an
extensive coarse-grained hydrodynamic description for the ACM and AXYM akin to
the VM.


title: Using Products of Exponentials to Define (Draw) Orbits and More

abstract:
  The Product of Exponentials (PoE) formula is a mathematical tool that is used
extensively in robotics. The virtue of using the exponential mapping, Lie
Algebra and screw theory is that it allows an elegant and concise way of
describing the orientation and position of a body with respect to another body
in a multi-body system. Although the PoE formula is mainly used in robotics,
this work aims to demonstrate the utility of the PoE formula as an alternative
method for defining and drawing orbits given an orbital elements set. The work
also explores the first derivative of the adapted PoE formula in the framework
of orbital mechanics, which allows obtaining the state of the satellite
(position and velocity) from the orbital elements set using the developed
formulation.


title:
Omnidirectional MediA Format (OMAF): Toolbox for Virtual Reality
  Services

abstract:
  This paper provides an overview of the Omnidirectional Media Format (OMAF)
standard, second edition, which has been recently finalized. OMAF specifies the
media format for coding, storage, delivery, and rendering of omnidirectional
media, including video, audio, images, and timed text. Additionally, OMAF
supports multiple viewpoints corresponding to omnidirectional cameras and
overlay images or video rendered over the omnidirectional background image or
video. Many examples of usage scenarios for multiple viewpoints and overlays
are described in the paper. OMAF provides a toolbox of features, which can be
selectively used in virtual reality services. Consequently, the paper presents
the interoperability points specified in the OMAF standard, which enable
signaling which OMAF features are in use or required to be supported in
implementations. Finally, the paper summarizes which OMAF interoperability
points have been taken into use in virtual reality service specifications by
the 3rd Generation Partnership Project (3GPP) and the Virtual Reality Industry
Forum (VRIF).


title:
Deep-SWIM: A few-shot learning approach to classify Solar WInd Magnetic
  field structures

abstract:
  The solar wind consists of charged particles ejected from the Sun into
interplanetary space and towards Earth. Understanding the magnetic field of the
solar wind is crucial for predicting future space weather and planetary
atmospheric loss. Compared to large-scale magnetic events, smaller-scale
structures like magnetic discontinuities are hard to detect but entail
important information on the evolution of the solar wind. A lack of labeled
data makes an automated detection of these discontinuities challenging. We
propose Deep-SWIM, an approach leveraging advances in contrastive learning,
pseudo-labeling and online hard example mining to robustly identify
discontinuities in solar wind magnetic field data. Through a systematic
ablation study, we show that we can accurately classify discontinuities despite
learning from only limited labeled data. Additionally, we show that our
approach generalizes well and produces results that agree with expert
hand-labeling.


title:
Probabilistic rough paths II Lions-Taylor expansions and Random
  controlled rough paths

abstract:
  In line with the notion of probabilistic rough paths introduced in the
previous contribution \cite{salkeld2021Probabilistic}, we address corresponding
random controlled rough paths (first introduced in
\cite{2019arXiv180205882.2B}), the structure of which is indexed by Lions
forests. These are statistical distributions over the space of paths described
by the combination of a jet on the underlying probabilistic rough path and a
remainder term. The regularity of the latter facilitates the definition of a
rough integral.
  We establish closedness and stability of two key operators on random
controlled rough paths: rough integration and composition by a smooth function
on the Wasserstein space. These are important results towards a complete theory
of rough McKean-Vlasov equations that is still in gestation. The proof goes
through a higher-order Taylor expansion for the Lions derivative which we
rigorously expound.
  The coupled Hopf algebra structure (see \cite{salkeld2021Probabilistic}) and
the Lions-Taylor expansion (established in Section
\ref{section:TaylorExpansions}) introduce a number of additional challenges
which mean these results are not simply a natural extension of classical
theory. We dedicate this work to pursuing these details.


title: Hybrid Model-based / Data-driven Graph Transform for Image Coding

abstract:
  Transform coding to sparsify signal representations remains crucial in an
image compression pipeline. While the Karhunen-Lo\`{e}ve transform (KLT)
computed from an empirical covariance matrix $\bar{C}$ is theoretically optimal
for a stationary process, in practice, collecting sufficient statistics from a
non-stationary image to reliably estimate $\bar{C}$ can be difficult. In this
paper, to encode an intra-prediction residual block, we pursue a hybrid
model-based / data-driven approach: the first $K$ eigenvectors of a transform
matrix are derived from a statistical model, e.g., the asymmetric discrete sine
transform (ADST), for stability, while the remaining $N-K$ are computed from
$\bar{C}$ for performance. The transform computation is posed as a graph
learning problem, where we seek a graph Laplacian matrix minimizing a graphical
lasso objective inside a convex cone sharing the first $K$ eigenvectors in a
Hilbert space of real symmetric matrices. We efficiently solve the problem via
augmented Lagrangian relaxation and proximal gradient (PG). Using WebP as a
baseline image codec, experimental results show that our hybrid graph transform
achieved better energy compaction than default discrete cosine transform (DCT)
and better stability than KLT.


title: Visual Feature Encoding for GNNs on Road Networks

abstract:
  In this work, we present a novel approach to learning an encoding of visual
features into graph neural networks with the application on road network data.
We propose an architecture that combines state-of-the-art vision backbone
networks with graph neural networks. More specifically, we perform a road type
classification task on an Open Street Map road network through encoding of
satellite imagery using various ResNet architectures. Our architecture further
enables fine-tuning and a transfer-learning approach is evaluated by
pretraining on the NWPU-RESISC45 image classification dataset for remote
sensing and comparing them to purely ImageNet-pretrained ResNet models as
visual feature encoders. The results show not only that the visual feature
encoders are superior to low-level visual features, but also that the
fine-tuning of the visual feature encoder to a general remote sensing dataset
such as NWPU-RESISC45 can further improve the performance of a GNN on a machine
learning task like road type classification.


title: EnDSUM: Entropy and Diversity based Disaster Tweet Summarization

abstract:
  The huge amount of information shared in Twitter during disaster events are
utilized by government agencies and humanitarian organizations to ensure quick
crisis response and provide situational updates. However, the huge number of
tweets posted makes manual identification of the relevant tweets impossible. To
address the information overload, there is a need to automatically generate
summary of all the tweets which can highlight the important aspects of the
disaster. In this paper, we propose an entropy and diversity based summarizer,
termed as EnDSUM, specifically for disaster tweet summarization. Our
comprehensive analysis on 6 datasets indicates the effectiveness of EnDSUM and
additionally, highlights the scope of improvement of EnDSUM.


title:
GNN-based end-to-end reconstruction in the CMS Phase 2 High-Granularity
  Calorimeter

abstract:
  We present the current stage of research progress towards a one-pass,
completely Machine Learning (ML) based imaging calorimeter reconstruction. The
model used is based on Graph Neural Networks (GNNs) and directly analyzes the
hits in each HGCAL endcap. The ML algorithm is trained to predict clusters of
hits originating from the same incident particle by labeling the hits with the
same cluster index. We impose simple criteria to assess whether the hits
associated as a cluster by the prediction are matched to those hits resulting
from any particular individual incident particles. The algorithm is studied by
simulating two tau leptons in each of the two HGCAL endcaps, where each tau may
decay according to its measured standard model branching probabilities. The
simulation includes the material interaction of the tau decay products which
may create additional particles incident upon the calorimeter. Using this
varied multiparticle environment we can investigate the application of this
reconstruction technique and begin to characterize energy containment and
performance.


title: Model-free Neural Lyapunov Control for Safe Robot Navigation

abstract:
  Model-free Deep Reinforcement Learning (DRL) controllers have demonstrated
promising results on various challenging non-linear control tasks. While a
model-free DRL algorithm can solve unknown dynamics and high-dimensional
problems, it lacks safety assurance. Although safety constraints can be encoded
as part of a reward function, there still exists a large gap between an RL
controller trained with this modified reward and a safe controller. In
contrast, instead of implicitly encoding safety constraints with rewards, we
explicitly co-learn a Twin Neural Lyapunov Function (TNLF) with the control
policy in the DRL training loop and use the learned TNLF to build a runtime
monitor. Combined with the path generated from a planner, the monitor chooses
appropriate waypoints that guide the learned controller to provide
collision-free control trajectories. Our approach inherits the scalability
advantages from DRL while enhancing safety guarantees. Our experimental
evaluation demonstrates the effectiveness of our approach compared to DRL with
augmented rewards and constrained DRL methods over a range of high-dimensional
safety-sensitive navigation tasks.


title:
Larmor frequency shift from magnetized cylinders with arbitrary
  orientation distribution

abstract:
  We present a theoretical framework for the NMR and MRI measured Larmor
frequency in media with magnetized microstructure using the mesoscopic Lorentz
sphere and the principle of coarse graining. We obtain an analytical expression
for infinite cylinders with arbitrary orientation dispersion and show how it
depends on the fiber orientation distribution, measurable using diffusion MRI.
Through simulations, we scrutinize the framework including the effect of the
shape and size of the Lorentz cavity and validate our result for cylinders.


title:
Improving Generalization of Deep Networks for Estimating Physical
  Properties of Containers and Fillings

abstract:
  We present methods to estimate the physical properties of household
containers and their fillings manipulated by humans. We use a lightweight,
pre-trained convolutional neural network with coordinate attention as a
backbone model of the pipelines to accurately locate the object of interest and
estimate the physical properties in the CORSMAL Containers Manipulation (CCM)
dataset. We address the filling type classification with audio data and then
combine this information from audio with video modalities to address the
filling level classification. For the container capacity, dimension, and mass
estimation, we present a data augmentation and consistency measurement to
alleviate the over-fitting issue in the CCM dataset caused by the limited
number of containers. We augment the training data using an
object-of-interest-based re-scaling that increases the variety of physical
values of the containers. We then perform the consistency measurement to choose
a model with low prediction variance in the same containers under different
scenes, which ensures the generalization ability of the model. Our method
improves the generalization ability of the models to estimate the property of
the containers that were not previously seen in the training.


title:
VAE-iForest: Auto-encoding Reconstruction and Isolation-based Anomalies
  Detecting Fallen Objects on Road Surface

abstract:
  In road monitoring, it is an important issue to detect changes in the road
surface at an early stage to prevent damage to third parties. The target of the
falling object may be a fallen tree due to the external force of a flood or an
earthquake, and falling rocks from a slope. Generative deep learning is
possible to flexibly detect anomalies of the falling objects on the road
surface. We prototype a method that combines auto-encoding reconstruction and
isolation-based anomaly detector in application for road surface monitoring.
Actually, we apply our method to a set of test images that fallen objects is
located on the raw inputs added with fallen stone and plywood, and that snow is
covered on the winter road. Finally we mention the future works for practical
purpose application.


title:
Theoretical Foundation of Colored Petri Net through an Analysis of their
  Markings as Multi-classification

abstract:
  Barwise and Seligman stated the first principle of information flow:
"Information flow results from regularities in the distributed system." They
represent a distributed system in terms of a classification consisting of a set
of objects or tokens to be classified, a set of types used to classify tokens,
and a binary relation between tokens and types that tells one which tokens are
classified as being of which types. We aim to further this investigation and
proceed with a dynamic or evolving system instead of a static system. We claim
that a classification is a snapshot of a distributed system at a given moment
or context. We then aim to answer the question posed by an evolving context. As
the context or configuration changes, how to regularities evolve. This paper is
a continuation of an investigation we started in \cite{esterlin}, where we
initiated how to capture a dynamism of information flow with a Kripke
structure. Here we develop the same procedure with colored Petri net(CPN). We
first extend the classification concept to multiclassification by replacing its
binary relation between tokens and types with a multi relation: a function from
tok(A) x typ(A) to N, the set of natural numbers. The multiclassification will
unfold into binary classification in order to compute its theory. It turns out
that markings of a CPN are multiclassification; Amalgamating the theories of
those classifications obtained as markings of CPN results in a CPN's knowledge
base.


title: Properties of the linearised functional renormalization group

abstract:
  Interactions growing slower than a certain exponential of the square of a
scalar field, are well behaved when evolved under the functional
renormalization group linearised around the Gaussian fixed point. They satisfy
properties usually taken for granted, and reproduce standard perturbative
quantisation. However, ever more challenging effects appear the more
interactions grow faster than this. We show explicitly that firstly the flow no
longer splits uniquely into operators of definite scaling dimension; then
(linearised) flows to the infrared can end prematurely in a singularity; and
finally new interactions can spontaneously appear at any scale.

categories: hep-th cond-mat.stat-mech gr-qc math-ph math.MP


title:
Quantum oscillations of the nonlinear planar effects signifying chiral
  anomaly in Weyl Semimetals

abstract:
  In view of searching the signature of the celebrated chiral anomaly (CA) in
Weyl semimetals (WSMs) in ongoing experiments, quantum oscillation in linear
response regime has been considered as an important signature in the magneto
transports in WSMs, due to its unique relation to CA. Investigating the
nonlinear planar effects (NPEs) starting from the semiclassical regime to the
ultra-quantum limit within the framework of Boltzmann transport theory
incorporating Landau quantization, we here propose the quantum oscillations in
NPEs can serve as a robust signature of CA in WSMs. By obtaining analytical
expressions, we show that the quantum oscillations of the nonlinear effects
exhibit two different period scales in 1/B (B is the magnetic field) compared
to the linear responses where only one period scale exists. We find that these
quantum oscillations in NPEs are attributed to the deviation of chiral chemical
potential (CCP), which is proportional to the finite band tilt as well as
transverse electric field and therefore, directly linked to CA in WSMs. In
addition, we also show that the CA-induced nonlinear magneto conductivity is
linear and independent in the magnetic field in the semiclassical and
ultraquantum regimes, respectively. We conclude that the proposed behaviors of
NPEs in different regimes uniquely signify the existence of CA and therefore,
can serve as a probe of identifying CA in WSMs in experiments.


title: DextAIRity: Deformable Manipulation Can be a Breeze

abstract:
  This paper introduces DextAIRity, an approach to manipulate deformable
objects using active airflow. In contrast to conventional contact-based
quasi-static manipulations, DextAIRity allows the system to apply dense forces
on out-of-contact surfaces, expands the system's reach range, and provides safe
high-speed interactions. These properties are particularly advantageous when
manipulating under-actuated deformable objects with large surface areas or
volumes. We demonstrate the effectiveness of DextAIRity through two challenging
deformable object manipulation tasks: cloth unfolding and bag opening. We
present a self-supervised learning framework that learns to effectively perform
a target task through a sequence of grasping or air-based blowing actions. By
using a closed-loop formulation for blowing, the system continuously adjusts
its blowing direction based on visual feedback in a way that is robust to the
highly stochastic dynamics. We deploy our algorithm on a real-world three-arm
system and present evidence suggesting that DextAIRity can improve system
efficiency for challenging deformable manipulation tasks, such as cloth
unfolding, and enable new applications that are impractical to solve with
quasi-static contact-based manipulations (e.g., bag opening). Video is
available at https://youtu.be/_B0TpAa5tVo


title: Linear Stochastic Bandits over a Bit-Constrained Channel

abstract:
  One of the primary challenges in large-scale distributed learning stems from
stringent communication constraints. While several recent works address this
challenge for static optimization problems, sequential decision-making under
uncertainty has remained much less explored in this regard. Motivated by this
gap, we introduce a new linear stochastic bandit formulation over a
bit-constrained channel. Specifically, in our setup, an agent interacting with
an environment transmits encoded estimates of an unknown model parameter to a
server over a communication channel of finite capacity. The goal of the server
is to take actions based on these estimates to minimize cumulative regret. To
this end, we develop a novel and general algorithmic framework that hinges on
two main components: (i) an adaptive encoding mechanism that exploits
statistical concentration bounds, and (ii) a decision-making principle based on
confidence sets that account for encoding errors. As our main result, we prove
that when the unknown model is $d$-dimensional, a channel capacity of $O(d)$
bits suffices to achieve order-optimal regret. To demonstrate the generality of
our approach, we then show that the same result continues to hold for
non-linear observation models satisfying standard regularity conditions.
Finally, we establish that for the simpler unstructured multi-armed bandit
problem, $1$ bit channel-capacity is sufficient for achieving optimal regret
bounds. Overall, our work takes a significant first step towards paving the way
for statistical decision-making over finite-capacity channels.

categories: cs.LG cs.IT cs.SY eess.SY math.IT math.OC


title:
Global solution of the 3D Relativistic Vlasov-Maxwell system for large
  data with cylindrical symmetry

abstract:
  We show that the $3D$ relativistic Vlasov-Maxwell system admits global
solution for a class of arbitrarily large cylindrically symmetric initial data.


title: Observation of microcavity fine structure

abstract:
  We observe fine structure in the resonance spectra of optical microcavities.
We identify the polarization-resolved modes in the spectrum and find that
resonance frequencies split in accordance with the theoretical prediction. The
observed fine structure is dominantly caused by an optical spin-orbit coupling
and non-paraxial propagation and reflection. Both effects are intrinsic, i.e.
present in an ideal rotation-symmetric system, and scale inversely proportional
to the mirror radius of curvature. For cavities with a small radius of
curvature, the influence of fine structure on the resonance spectrum is
important and unavoidable and should thus be taken into account.


title: Analytical Solutions for the Inverse Problem within Gradual Semantics

abstract:
  Gradual semantics within abstract argumentation associate a numeric score
with every argument in a system, which represents the level of acceptability of
this argument, and from which a preference ordering over arguments can be
derived. While some semantics operate over standard argumentation frameworks,
many utilise a weighted framework, where a numeric initial weight is associated
with each argument. Recent work has examined the inverse problem within gradual
semantics. Rather than determining a preference ordering given an argumentation
framework and a semantics, the inverse problem takes an argumentation
framework, a gradual semantics, and a preference ordering as inputs, and
identifies what weights are needed to over arguments in the framework to obtain
the desired preference ordering. Existing work has attacked the inverse problem
numerically, using a root finding algorithm (the bisection method) to identify
appropriate initial weights. In this paper we demonstrate that for a class of
gradual semantics, an analytical approach can be used to solve the inverse
problem. Unlike the current state-of-the-art, such an analytic approach can
rapidly find a solution, and is guaranteed to do so. In obtaining this result,
we are able to prove several important properties which previous work had posed
as conjectures.


title:
Remarks on the Large data global solutions of $3D$ RVP system and $3D$
  RVM system

abstract:
  We show that the simplified $3D$ relativistic Vlasov-Maxwell (sRVM) system,
in which there is no magnetic field, poses a global solution for a class of
arbitrarily large cylindrically symmetric initial data. In particular, a
vanishing order condition imposed on the initial data for the relativistic
Vlasov-Poisson system (RVP) in Wang(2022) is not imposed for the sRVM system.


title: Manipulation of unknown objects via contact configuration regulation

abstract:
  We present an approach to robotic manipulation of unknown objects through
regulation of the object's contact configuration: the location, geometry, and
mode of all contacts between the object, robot, and environment. A contact
configuration constrains the forces and motions that can be applied to the
object; however, synthesizing these constraints generally requires knowledge of
the object's pose and geometry. We develop an object-agnostic approach for
estimation and control that circumvents this need. Our framework directly
estimates a set of wrench and motion constraints which it uses to regulate the
contact configuration. We use this to reactively manipulate unknown planar
objects in the gravity plane. A video describing our work can be found on our
project page: http://mcube.mit.edu/research/contactConfig.html.


title: Generalised symmetries and bases for Dunkl monogenics

abstract:
  We introduce a family of commuting generalised symmetries of the Dunkl--Dirac
operator inspired by the Maxwell construction in harmonic analysis. We use
these generalised symmetries to construct bases of the polynomial
null-solutions of the Dunkl--Dirac operator. These polynomial spaces form
representation spaces of the Dunkl--Dirac symmetry algebra. For the
$\mathbb{Z}_2^d$ case, the results are compared with previous investigations.


title: Audio Self-supervised Learning: A Survey

abstract:
  Inspired by the humans' cognitive ability to generalise knowledge and skills,
Self-Supervised Learning (SSL) targets at discovering general representations
from large-scale data without requiring human annotations, which is an
expensive and time consuming task. Its success in the fields of computer vision
and natural language processing have prompted its recent adoption into the
field of audio and speech processing. Comprehensive reviews summarising the
knowledge in audio SSL are currently missing. To fill this gap, in the present
work, we provide an overview of the SSL methods used for audio and speech
processing applications. Herein, we also summarise the empirical works that
exploit the audio modality in multi-modal SSL frameworks, and the existing
suitable benchmarks to evaluate the power of SSL in the computer audition
domain. Finally, we discuss some open problems and point out the future
directions on the development of audio SSL.


title: The Green function of p-Laplace operators and applications

abstract:
  On a bounded domain $\Omega \subset \mathbb{R}^N$, $N\geq 2$, we consider
existence, uniqueness and "regularity" issues for the Green function
$G_\lambda$ of the quasi-linear operator $u \to -\Delta_p u-\lambda |u|^{p-2}u$
with $1<p \leq N$, homogeneous Dirichlet boundary condition and
$\lambda<\lambda_1$, where $\lambda_1>0$ is the first eigenvalue of
$-\Delta_p$. Of independent interest, these properties represent a fundamental
tool to discuss, as a non-trivial application, existence results for a
quasi-linear elliptic equation of critical Sobolev growth [H. Brezis, L.
Nirenberg, Positive solutions of nonlinear elliptic equations involving
critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437--477; M.
Guedda, L. Veron, Quasilinear elliptic equations involving critical Sobolev
exponents, Nonlinear Anal. 13 (1989), no. 8, 879--902] in the low-dimensional
case, where the problem has a global character which is encoded in the regular
part of $G_\lambda$ as in [O. Druet, Elliptic equations with critical Sobolev
exponents in dimension $3$, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 19
(2002), no. 2, 125--142; P. Esposito, On some conjectures proposed by Ha\"{i}m
Brezis, Nonlinear Anal. 54 (2004), no. 5, 751--759].


title: Container Localisation and Mass Estimation with an RGB-D Camera

abstract:
  In the research area of human-robot interactions, the automatic estimation of
the mass of a container manipulated by a person leveraging only visual
information is a challenging task. The main challenges consist of occlusions,
different filling materials and lighting conditions. The mass of an object
constitutes key information for the robot to correctly regulate the force
required to grasp the container. We propose a single RGB-D camera-based method
to locate a manipulated container and estimate its empty mass i.e.,
independently of the presence of the content. The method first automatically
selects a number of candidate containers based on the distance with the fixed
frontal view, then averages the mass predictions of a lightweight model to
provide the final estimation. Results on the CORSMAL Containers Manipulation
dataset show that the proposed method estimates empty container mass obtaining
a score of 71.08% under different lighting or filling conditions.


title:
Improvements in $L^2$ Restriction bounds for Neumann Data along
  Hypersurfaces

abstract:
  We seek to improve the restriction bounds of Neumann data of semiclassical
Schr\"{o}dinger eigenfunctions $u_h$ considered by Christianson-Hassell-Toth
\cite{CHT} and Tacy \cite{Tacy2} by studying the $L^2$ restriction bounds of
eigenfunctions and their $L^2$ concentration as measured by defect measures.
Let $\Gamma$ be a smooth hypersurface with unit exterior normal $\nu$. Our main
result says that $\| h \partial_\nu u_{h} \|_{L^2(\Gamma)}=o(1)$ when $\{u_h\}$
is admissible.


title: End-to-End Simulation of 5G Networks Assisted by IRS and AF Relays

abstract:
  The high propagation and penetration loss experienced at millimeter wave
(mmWave) frequencies requires ultra-dense deployments of 5th generation (5G)
base stations, which may be infeasible and costly for network operators.
Integrated Access and Backhaul (IAB) has been proposed to partially address
this issue, even though raising concerns in terms of power consumption and
scalability. Recently, the research community has been investigating
Intelligent Reflective Surfaces (IRSs) and Amplify-and-Forward (AF) relays as
more energy-efficient alternatives to solve coverage issues in 5G scenarios.
Along these lines, this paper relies on a new simulation framework, based on
ns-3, to simulate IRS/AF systems with a full-stack, end-to-end perspective,
with considerations on to the impact of the channel model and the protocol
stack of 5G NR networks. Our goal is to demonstrate whether these technologies
can be used to relay 5G traffic requests and, if so, how to dimension IRS/AF
nodes as a function of the number of end users.


title: Commensurability of lattices in right-angled buildings

abstract:
  Let $\Gamma$ be a graph product of finite groups, with finite underlying
graph, and let $\Delta$ be the associated right-angled building. We prove that
a uniform lattice $\Lambda$ in the cubical automorphism group Aut$(\Delta)$ is
weakly commensurable to $\Gamma$ if and only if all convex subgroups of
$\Lambda$ are separable. As a corollary, any two finite special cube complexes
with universal cover $\Delta$ have a common finite cover. An important special
case of our theorem is where $\Gamma$ is a right-angled Coxeter group and
$\Delta$ is the associated Davis complex. We also obtain an analogous result
for right-angled Artin groups. In addition, we deduce quasi-isometric rigidity
for the group $\Gamma$ when $\Delta$ has the structure of a Fuchsian building.


title: Multi-Quantum Dark Solitons in One-Dimensional Bose Gas

abstract:
  Quantum and classical integrable systems share common mathematical
structures, and the phenomena appearing in them are interrelated. Solitons,
which universally appear in classical integrable systems, also appear in
quantum integrable systems. Here, we consider quantum-classical correspondence
in a one-dimensional Bose gas with repulsive delta-function interaction and
present quantum states corresponding to multi-dark solitons. Using an exact
method, we compute the time evolution of the density profile in the
multi-quantum dark soliton states. Localized solitary waves that behave like
classical dark solitons are observed in the density profile. We observe
collisions of quantum dark solitons and show that they exhibit the properties
of classical solitons: stability against scatterings and position shifts due to
interactions.

categories: cond-mat.quant-gas cond-mat.stat-mech math-ph math.MP


title: A Quantitative Geometric Approach to Neural Network Smoothness

abstract:
  Fast and precise Lipschitz constant estimation of neural networks is an
important task for deep learning. Researchers have recently found an intrinsic
trade-off between the accuracy and smoothness of neural networks, so training a
network with a loose Lipschitz constant estimation imposes a strong
regularization and can hurt the model accuracy significantly. In this work, we
provide a unified theoretical framework, a quantitative geometric approach, to
address the Lipschitz constant estimation. By adopting this framework, we can
immediately obtain several theoretical results, including the computational
hardness of Lipschitz constant estimation and its approximability. Furthermore,
the quantitative geometric perspective can also provide some insights into
recent empirical observations that techniques for one norm do not usually
transfer to another one.
  We also implement the algorithms induced from this quantitative geometric
approach in a tool GeoLIP. These algorithms are based on semidefinite
programming (SDP). Our empirical evaluation demonstrates that GeoLIP is more
scalable and precise than existing tools on Lipschitz constant estimation for
$\ell_\infty$-perturbations. Furthermore, we also show its intricate relations
with other recent SDP-based techniques, both theoretically and empirically. We
believe that this unified quantitative geometric perspective can bring new
insights and theoretical tools to the investigation of neural-network
smoothness and robustness.


title: Truthful Online Scheduling of Cloud Workloads under Uncertainty

abstract:
  Cloud computing customers often submit repeating jobs and computation
pipelines on \emph{approximately} regular schedules, with arrival and running
times that exhibit variance. This pattern, typical of training tasks in machine
learning, allows customers to partially predict future job requirements. We
develop a model of cloud computing platforms that receive statements of work
(SoWs) in an online fashion. The SoWs describe future jobs whose arrival times
and durations are probabilistic, and whose utility to the submitting agents
declines with completion time. The arrival and duration distributions, as well
as the utility functions, are considered private customer information and are
reported by strategic agents to a scheduler that is optimizing for social
welfare.
  We design pricing, scheduling, and eviction mechanisms that incentivize
truthful reporting of SoWs. An important challenge is maintaining incentives
despite the possibility of the platform becoming saturated. We introduce a
framework to reduce scheduling under uncertainty to a relaxed scheduling
problem without uncertainty. Using this framework, we tackle both adversarial
and stochastic submissions of statements of work, and obtain logarithmic and
constant competitive mechanisms, respectively.


title:
Towards Efficient and Stable K-Asynchronous Federated Learning with
  Unbounded Stale Gradients on Non-IID Data

abstract:
  Federated learning (FL) is an emerging privacy-preserving paradigm that
enables multiple participants collaboratively to train a global model without
uploading raw data. Considering heterogeneous computing and communication
capabilities of different participants, asynchronous FL can avoid the
stragglers effect in synchronous FL and adapts to scenarios with vast
participants. Both staleness and non-IID data in asynchronous FL would reduce
the model utility. However, there exists an inherent contradiction between the
solutions to the two problems. That is, mitigating the staleness requires to
select less but consistent gradients while coping with non-IID data demands
more comprehensive gradients. To address the dilemma, this paper proposes a
two-stage weighted $K$ asynchronous FL with adaptive learning rate (WKAFL). By
selecting consistent gradients and adjusting learning rate adaptively, WKAFL
utilizes stale gradients and mitigates the impact of non-IID data, which can
achieve multifaceted enhancement in training speed, prediction accuracy and
training stability. We also present the convergence analysis for WKAFL under
the assumption of unbounded staleness to understand the impact of staleness and
non-IID data. Experiments implemented on both benchmark and synthetic FL
datasets show that WKAFL has better overall performance compared to existing
algorithms.


title: Mukayese: Turkish NLP Strikes Back

abstract:
  Having sufficient resources for language X lifts it from the under-resourced
languages class, but not necessarily from the under-researched class. In this
paper, we address the problem of the absence of organized benchmarks in the
Turkish language. We demonstrate that languages such as Turkish are left behind
the state-of-the-art in NLP applications. As a solution, we present Mukayese, a
set of NLP benchmarks for the Turkish language that contains several NLP tasks.
We work on one or more datasets for each benchmark and present two or more
baselines. Moreover, we present four new benchmarking datasets in Turkish for
language modeling, sentence segmentation, and spell checking. All datasets and
baselines are available under: https://github.com/alisafaya/mukayese


title: A Simple and Universal Rotation Equivariant Point-cloud Network

abstract:
  Equivariance to permutations and rigid motions is an important inductive bias
for various 3D learning problems. Recently it has been shown that the
equivariant Tensor Field Network architecture is universal -- it can
approximate any equivariant function. In this paper we suggest a much simpler
architecture, prove that it enjoys the same universality guarantees and
evaluate its performance on Modelnet40. The code to reproduce our experiments
is available at \url{https://github.com/simpleinvariance/UniversalNetwork}


title: Hybrid Tracker with Pixel and Instance for Video Panoptic Segmentation

abstract:
  Video Panoptic Segmentation (VPS) requires generating consistent panoptic
segmentation and tracking identities to all pixels across video frames.
Existing methods are mainly based on the trained instance embedding to maintain
consistent panoptic segmentation. However, they inevitably struggle to cope
with the challenges of small objects, similar appearance but inconsistent
identities, occlusion, and strong instance contour deformations. To address
these problems, we present HybridTracker, a lightweight and joint tracking
model attempting to eliminate the limitations of the single tracker.
HybridTracker performs pixel tracker and instance tracker in parallel to obtain
the association matrices, which are fused into a matching matrix. In the
instance tracker, we design a differentiable matching layer, ensuring the
stability of inter-frame matching. In the pixel tracker, we compute the dice
coefficient of the same instance of different frames given the estimated
optical flow, forming the Intersection Over Union (IoU) matrix. We additionally
propose mutual check and temporal consistency constraints during inference to
settle the occlusion and contour deformation challenges. Extensive experiments
demonstrate that HybridTracker outperforms state-of-the-art methods on
Cityscapes-VPS and VIPER datasets.


title: Learning Conditional Variational Autoencoders with Missing Covariates

abstract:
  Conditional variational autoencoders (CVAEs) are versatile deep generative
models that extend the standard VAE framework by conditioning the generative
model with auxiliary covariates. The original CVAE model assumes that the data
samples are independent, whereas more recent conditional VAE models, such as
the Gaussian process (GP) prior VAEs, can account for complex correlation
structures across all data samples. While several methods have been proposed to
learn standard VAEs from partially observed datasets, these methods fall short
for conditional VAEs. In this work, we propose a method to learn conditional
VAEs from datasets in which auxiliary covariates can contain missing values as
well. The proposed method augments the conditional VAEs with a prior
distribution for the missing covariates and estimates their posterior using
amortised variational inference. At training time, our method marginalises the
uncertainty associated with the missing covariates while simultaneously
maximising the evidence lower bound. We develop computationally efficient
methods to learn CVAEs and GP prior VAEs that are compatible with
mini-batching. Our experiments on simulated datasets as well as on a clinical
trial study show that the proposed method outperforms previous methods in
learning conditional VAEs from non-temporal, temporal, and longitudinal
datasets.


title: Are Latent Factor Regression and Sparse Regression Adequate?

abstract:
  We propose the Factor Augmented sparse linear Regression Model (FARM) that
not only encompasses both the latent factor regression and sparse linear
regression as special cases but also bridges dimension reduction and sparse
regression together. We provide theoretical guarantees for the estimation of
our model under the existence of sub-Gaussian and heavy-tailed noises (with
bounded (1+x)-th moment, for all x>0), respectively. In addition, the existing
works on supervised learning often assume the latent factor regression or the
sparse linear regression is the true underlying model without justifying its
adequacy. To fill in such an important gap, we also leverage our model as the
alternative model to test the sufficiency of the latent factor regression and
the sparse linear regression models. To accomplish these goals, we propose the
Factor-Adjusted de-Biased Test (FabTest) and a two-stage ANOVA type test
respectively. We also conduct large-scale numerical experiments including both
synthetic and FRED macroeconomics data to corroborate the theoretical
properties of our methods. Numerical results illustrate the robustness and
effectiveness of our model against latent factor regression and sparse linear
regression models.


title: Time-frequency as quantum continuous variables

abstract:
  We present a second quantization description of frequency-based continuous
variables quantum computation in the subspace of single photons. For this, we
define frequency and time operators using the free field Hamiltonian and its
Fourier transform, and show that these observables, when restricted to the one
photon per mode subspace, reproduce the canonical position-momentum commutation
relations. As a consequence, frequency and time operators can be used to define
a universal set of gates in this particular subspace. We discuss the physical
implementation of these gates as well as their effect on single photon states,
and show that frequency and time variables can also be used to implement
continuous variables quantum information protocols, in the same way than
polarization is currently used as a two-dimensional quantum variable.


title: The importance of horizontal Poynting flux in the solar photosphere

abstract:
  The electromagnetic energy flux in the lower atmosphere of the Sun is a key
tool to describe the energy balance of the solar atmosphere. Current
investigations on energy flux in the solar atmosphere focus primarily on the
vertical electromagnetic flux through the photosphere, ignoring the Poynting
flux in other directions and its possible contributions to local heating. Based
on a realistic Bifrost simulation of a quiet-Sun (coronal hole) atmosphere, we
find that the total electromagnetic energy flux in the photosphere occurs
mainly parallel to the photosphere, concentrating in small regions along
intergranular lanes. Thereby, it was possible to define a proxy for this energy
flux based on only variables that can be promptly retrieved from observations,
namely, horizontal velocities of the small-scale magnetic elements and their
longitudinal magnetic flux. Our proxy accurately describes the actual Poynting
flux distribution in the simulations, with the electromagnetic energy flux
reaching $10^{10}$ erg\,cm$^{-2}$\,s$^{-1}$. To validate our findings, we
extended the analysis to SUNRISE/IMaX data. First, we show that Bifrost
realistically describes photospheric quiet-Sun regions, as the simulation
presents similar distributions for line-of-sight magnetic flux and horizontal
velocity field. Second, we found very similar horizontal Poynting flux proxy
distributions for the simulated photosphere and observational data. Our results
also indicate that the horizontal Poynting flux in the observations is
considerably larger than the vertical electromagnetic flux from previous
observational estimates. Therefore, our analysis confirms that the
electromagnetic energy flux in the photosphere is mainly horizontal and is most
intense in localized regions along intergranular lanes.


title: Chance-Constrained Iterative Linear-Quadratic Stochastic Games

abstract:
  Dynamic game arises as a powerful paradigm for multi-robot planning, for
which the safety constraints satisfaction is crucial. Constrained stochastic
games are of particular interest, as real-world robots need to operate and
satisfy constraints under uncertainty. Existing methods for solving stochastic
games handle constraints using soft penalties with hand-tuned weights. However,
finding a suitable penalty weight is non-trivial and requires trial and error.
In this paper, we propose the chance-constrained iterative linear-quadratic
stochastic games (CCILQGames) algorithm. CCILQGames solves chance-constrained
stochastic games using the augmented Lagrangian method, with the merit of
automatically finding a suitable penalty weight. We evaluate our algorithm in
three autonomous driving scenarios, including merge, intersection, and
roundabout. Experimental results and Monte Carlo tests show that CCILQGames
could generate safe and interactive strategies in stochastic environments.


title: Metric limits of manifolds with positive scalar curvature

abstract:
  We show that any Riemannian metric conformal to the round metric on $S^n$,
for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of
positive scalar curvature on $S^n$ in the sense of uniform convergence of
Riemannian distance. In particular, non-negativity of scalar curvature is not
preserved under such limits.


title:
Hydrogen-bonded aggregates in the mixtures of piperidine with water:
  thermodynamic, SANS and theoretical studies

abstract:
  Structures resembling semiclathrates probably arise in liquid aqueous
solutions of piperidine at the amine mole fraction below 0.03. With the
increasing concentration, the structures gradually decay, but the 1:1 complexes
of piperidine with water remain linked one to another through the O-H...O bonds
between the hydration water molecules. A periodic order of the bicontinuous
microemulsion type occurs in the range of the mole fractions from 0.08 to 0.5.
In the piperidine-rich mixtures, the 1:1 complexes are dispersed uniformly in
the amine. Relatively low stabilization energy of these complexes probably
causes that piperidine is totally miscible with water.


title: Video Question Answering: Datasets, Algorithms and Challenges

abstract:
  Video Question Answering (VideoQA) aims to answer natural language questions
according to the given videos. It has earned increasing attention with recent
research trends in joint vision and language understanding. Yet, compared with
ImageQA, VideoQA is largely underexplored and progresses slowly. Although
different algorithms have continually been proposed and shown success on
different VideoQA datasets, we find that there lacks a meaningful survey to
categorize them, which seriously impedes its advancements. This paper thus
provides a clear taxonomy and comprehensive analyses to VideoQA, focusing on
the datasets, algorithms, and unique challenges. We then point out the research
trend of studying beyond factoid QA to inference QA towards the cognition of
video contents, Finally, we conclude some promising directions for future
exploration.


title:
Competing instabilities of the extended Hubbard model on the triangular
  lattice: Truncated-unity functional renormalization group and application to
  moir\'e materials

abstract:
  A simple yet paradigmatic model for the interplay of strong electronic
correlations and geometric frustration is the triangular lattice Hubbard model.
Recently it was proposed that moir\'e structures of transition metal
dichalcogenides can be used to simulate extended versions that include
non-local density-density interactions. We study competing instabilities of
interacting electrons in such an extended Hubbard model on the triangular
lattice near a filling where the density of states has a Van Hove singularity.
We employ a truncated-unity functional renormalization group approach to
investigate two cases: a paradigmatic minimally extended Hubbard model and a
specific model with parameters that are applicable to hetero-bilayers of
transition metal dichalcogenides. We unravel rich phase diagrams, including
tendencies to spin-density-wave order and unconventional pairing, which can
give rise to topological superconductivity. We classify the symmetry of the
superconducting instabilities according to their irreducible representations
and show that higher lattice harmonics are dominant when the nearest-neighbor
interaction is sizable indicating pair formation between second-nearest
neighbors. The phenomenological consequences can be enhanced spin and thermal
quantum Hall responses in a topological superconductor.


title: Understanding the Sources of Error in MBAR through Asymptotic Analysis

abstract:
  Multiple sampling strategies commonly used in molecular dynamics, such as
umbrella sampling and alchemical free energy methods, involve sampling from
multiple thermodynamic states. Commonly, the data are then recombined to
construct estimates of free energies and ensemble averages using the Multistate
Bennett Acceptance Ratio (MBAR) formalism. However, the error of the MBAR
estimator is not well-understood: previous error analysis of MBAR assumed
independent samples and did not permit attributing contributions to the total
error to individual thermodynamic states. In this work, we derive a novel
central limit theorem for MBAR estimates. This central limit theorem yields an
error estimator which can be decomposed into contributions from the individual
Markov chains used to sample the states. We demonstrate the error estimator for
an umbrella sampling calculation of the alanine dipeptide in two dimensions and
an alchemical calculation of the hydration free energy of methane. In both
cases, the states' individual contributions to the error provide insight into
the sources of error of the simulations. Our numerical results demonstrate that
the time required for the Markov chain to decorrelate in individual
thermodynamic states contributes considerably to the total MBAR error.
Moreover, they indicate that it may be possible to use the contributions to
tune the sampling and improve the accuracy of MBAR calculations.


title: Estimating average causal effects from patient trajectories

abstract:
  In medical practice, treatments are selected based on the expected causal
effects on patient outcomes. Here, the gold standard for estimating causal
effects are randomized controlled trials; however, such trials are costly and
sometimes even unethical. Instead, medical practice is increasingly interested
in estimating causal effects among patient subgroups from electronic health
records, that is, observational data. In this paper, we aim at estimating the
average causal effect (ACE) from observational data (patient trajectories) that
are collected over time. For this, we propose DeepACE: an end-to-end deep
learning model. DeepACE leverages the iterative G-computation formula to adjust
for the bias induced by time-varying confounders. Moreover, we develop a novel
sequential targeting procedure which ensures that DeepACE has favorable
theoretical properties, i.e., is doubly robust and asymptotically efficient. To
the best of our knowledge, this is the first work that proposes an end-to-end
deep learning model for estimating time-varying ACEs. We compare DeepACE in an
extensive number of experiments, confirming that it achieves state-of-the-art
performance. We further provide a case study for patients suffering from low
back pain to demonstrate that DeepACE generates important and meaningful
findings for clinical practice. Our work enables medical practitioners to
develop effective treatment recommendations tailored to patient subgroups.


title:
On the application of generative adversarial networks for nonlinear
  modal analysis

abstract:
  Linear modal analysis is a useful and effective tool for the design and
analysis of structures. However, a comprehensive basis for nonlinear modal
analysis remains to be developed. In the current work, a machine learning
scheme is proposed with a view to performing nonlinear modal analysis. The
scheme is focussed on defining a one-to-one mapping from a latent `modal' space
to the natural coordinate space, whilst also imposing orthogonality of the mode
shapes. The mapping is achieved via the use of the recently-developed
cycle-consistent generative adversarial network (cycle-GAN) and an assembly of
neural networks targeted on maintaining the desired orthogonality. The method
is tested on simulated data from structures with cubic nonlinearities and
different numbers of degrees of freedom, and also on data from an experimental
three-degree-of-freedom set-up with a column-bumper nonlinearity. The results
reveal the method's efficiency in separating the `modes'. The method also
provides a nonlinear superposition function, which in most cases has very good
accuracy.


title:
Pattern-Selective Feedback Stabilization of Ginzburg--Landau Spiral
  Waves

abstract:
  The complex Ginzburg--Landau equation serves as a paradigm of pattern
formation and the existence and stability properties of Ginzburg--Landau
$m$-armed spiral waves have been investigated extensively. However, most spiral
waves are unstable and thereby rarely visible in experiments and numerical
simulations. In this article we selectively stabilize certain significant
classes of unstable spiral waves within circular and spherical geometries. As a
result, stable spiral waves with an arbitrary number of arms are obtained for
the first time. Our tool for stabilization is the symmetry-breaking control
triple method, which is an equivariant generalization of the widely applied
Pyragas control to the setting of PDEs.


title: Differentiable IFS Fractals

abstract:
  I present my explorations in rendering Iterated Function System (IFS)
fractals using a differentiable rendering pipeline. Differentiable rendering is
a recent innovation at the intersection of graphics and machine learning. This
opens up many possibilities for generating fractals that meet particular
criteria. In this paper I show how my method can be used to generate an IFS
fractal that resembles a target image.


title:
Real structures on complex algebraic varieties with a reductive group
  action

abstract:
  This is a survey article devoted to the study of real structures on complex
algebraic varieties endowed with a reductive group action.


title: Bilateral Contracts and Social Welfare

abstract:
  This paper defines and analyzes default delegation, an indirect mechanism
that describes how the government influences bilateral contracts to maximize
social welfare. In default delegation, the government chooses the default
contract and a possibly-limited set of contract terms it is willing to enforce.
Our analysis of this mechanism provides a theoretical foundation for immutable
and default rules in contract law: immutable rules mitigate externalities,
while default rules achieve particular distributions of surplus in
non-contractible states of the world. We derive conditions under which default
delegation implements the entire set of first-best contracts. We then
characterize how optimal default delegation responds to changes in the
underlying contracting environment and in the social welfare function's
weighting of efficiency, externalities and distributional concerns.


title: Dynamical analysis of logarithmic energy-momentum squared gravity

abstract:
  We perform the dynamical system analysis of a cosmological model in the
energy-momentum squared gravity (EMSG) of the form
$f(T_{\mu\nu}T^{\mu\nu})=\alpha\ln({\lambda}T_{\mu\nu} T^{\mu\nu})$, which is
known as energy-momentum log gravity (EMLG). In particular, we show that the
analytical cosmological solution of EMLG presented by Akarsu {\it et al.} (Eur.
Phys. J. C 79:846, 2019) is a future attractor. It includes new terms in the
right-hand side of the Einstein field equations, which yield constant inertial
mass density and provide a dynamical dark energy with a density passing below
zero at large redshifts, accommodating a mechanism for screening $\Lambda$ in
the past, suggested for alleviating some cosmological tensions. We show that
the model gives rise to an entire class of new stable late-time solutions with
$H\rightarrow\sqrt{(\Lambda+2\alpha)/3}$ as $a\rightarrow\infty$, where the new
term is due to the constant effective inertial mass density that arises from
EMLG contribution of dust, whereas $H\rightarrow\sqrt{\Lambda/3}$ as
$a\rightarrow\infty$ in the $\Lambda$CDM model. We also show existence of new
interesting features and trajectories that are absent in the $\Lambda$CDM
model.


title:
Is Our Research Productivity In Decline? A New Approach in Resolving the
  Controversy

abstract:
  This contribution examines the current controversy over research
productivity. There are two sides in this controversy. Using extensive data
from several industries and areas of research, one side argues that research
productivity is currently in decline. The other side disputes this conclusion.
It contends that the data used in making this argument are selective and
limited; they do not reflect the overall state of research. The conclusion that
follows from this critique is that the indicators of research productivity we
currently use are not reliable and do not warrant a definitive answer to the
problem.
  The article agrees that we need a new set of indicators in assessing research
productivity. It proposes that we should look at global indicators related to
knowledge production in general, rather than look at selective data that are
inevitably limited in their scope. The article argues that the process of
creation plays the essential role in knowledge production. Therefore, the
perspective that uses the process of creation as its central organizing
principle offers a unique and global view on the production of knowledge and
makes a definitive resolution of the controversy possible. The article also
outlines some steps for improving research productivity and realizing the full
potential of the human capacity to produce knowledge.
  Key words: Research productivity, knowledge growth, the process of creation,
levels of organization, equilibration and the production of disequilibrium.


title: Convolutional neural networks as an alternative to Bayesian retrievals

abstract:
  Exoplanet observations are currently analysed with Bayesian retrieval
techniques. Due to the computational load of the models used, a compromise is
needed between model complexity and computing time. Analysis of data from
future facilities, will need more complex models which will increase the
computational load of retrievals, prompting the search for a faster approach
for interpreting exoplanet observations. Our goal is to compare machine
learning retrievals of exoplanet transmission spectra with nested sampling, and
understand if machine learning can be as reliable as Bayesian retrievals for a
statistically significant sample of spectra while being orders of magnitude
faster. We generate grids of synthetic transmission spectra and their
corresponding planetary and atmospheric parameters, one using free chemistry
models, and the other using equilibrium chemistry models. Each grid is
subsequently rebinned to simulate both HST/WFC3 and JWST/NIRSpec observations,
yielding four datasets in total. Convolutional neural networks (CNNs) are
trained with each of the datasets. We perform retrievals on a 1,000 simulated
observations for each combination of model type and instrument with nested
sampling and machine learning. We also use both methods to perform retrievals
on real WFC3 transmission spectra. Finally, we test how robust machine learning
and nested sampling are against incorrect assumptions in our models. CNNs reach
a lower coefficient of determination between predicted and true values of the
parameters. Nested sampling underestimates the uncertainty in ~8% of
retrievals, whereas CNNs estimate them correctly. For real WFC3 observations,
nested sampling and machine learning agree within $2\sigma$ for ~86% of
spectra. When doing retrievals with incorrect assumptions, nested sampling
underestimates the uncertainty in ~12% to ~41% of cases, whereas this is always
below ~10% for the CNN.


title: Paraconsistent G\"{o}del modal logic

abstract:
  We introduce a~paraconsistent modal logic $\mathbf{K}\mathsf{G}^2$, based on
G\"{o}del logic with coimplication (bi-G\"{o}del logic) expanded with a De
Morgan negation $\neg$. We use the logic to formalise reasoning with graded,
incomplete and inconsistent information. Semantics of $\mathbf{K}\mathsf{G}^2$
is two-dimensional: we interpret $\mathbf{K}\mathsf{G}^2$ on crisp frames with
two valuations $v_1$ and $v_2$, connected via $\neg$, that assign to each
formula two values from the real-valued interval $[0,1]$. The first (resp.,
second) valuation encodes the positive (resp., negative) information the state
gives to a~statement. We obtain that $\mathbf{K}\mathsf{G}^2$ is strictly more
expressive than the classical modal logic $\mathbf{K}$ by proving that finitely
branching frames are definable and by establishing a faithful embedding of
$\mathbf{K}$ into $\mathbf{K}\mathsf{G}^2$. We also construct a~constraint
tableau calculus for $\mathbf{K}\mathsf{G}^2$ over finitely branching frames,
establish its decidability and provide a~complexity evaluation.


title:
On the Optimization Landscape of Neural Collapse under MSE Loss: Global
  Optimality with Unconstrained Features

abstract:
  When training deep neural networks for classification tasks, an intriguing
empirical phenomenon has been widely observed in the last-layer classifiers and
features, where (i) the class means and the last-layer classifiers all collapse
to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and
(ii) cross-example within-class variability of last-layer activations collapses
to zero. This phenomenon is called Neural Collapse (NC), which seems to take
place regardless of the choice of loss functions. In this work, we justify NC
under the mean squared error (MSE) loss, where recent empirical evidence shows
that it performs comparably or even better than the de-facto cross-entropy
loss. Under a simplified unconstrained feature model, we provide the first
global landscape analysis for vanilla nonconvex MSE loss and show that the
(only!) global minimizers are neural collapse solutions, while all other
critical points are strict saddles whose Hessian exhibit negative curvature
directions. Furthermore, we justify the usage of rescaled MSE loss by probing
the optimization landscape around the NC solutions, showing that the landscape
can be improved by tuning the rescaling hyperparameters. Finally, our
theoretical findings are experimentally verified on practical network
architectures.

categories: cs.LG cs.AI cs.IT math.IT math.OC stat.ML


title:
Electron driven reactive processes involving H$^+_2$ and HD$^+$
  molecular cations in the Early Universe

abstract:
  We describe the major low-energy electron-impact processes involving H$^+_2$
and HD$^+$, relevant for the astrochemistry of the early Universe: Dissociative
recombination, elastic, inelastic and superelastic scattering. We report cross
sections and Maxwellian rate coefficients of both rotational and vibrational
transitions, and outline several important features, like isotopic, rotational
and resonant effects.


title: Suppression of bacterial rheotaxis in wavy channels

abstract:
  Controlling the swimming behavior of bacteria is crucial, for example, to
prevent contamination of ducts and catheters. We show the bacteria modeled by
deformable microswimmers can accumulate in flows through straight microchannels
either in their center or on previously unknown attractors near the channel
walls. We predict a novel resonance effect for semiflexible microswimmers in
flows through wavy microchannels. As a result, microswimmers can be deflected
in a controlled manner so that they swim in modulated channels distributed over
the channel cross-section rather than localized near the wall or the channel
center.
  Thus, depending on the flow amplitude, both upstream orientation of swimmers
and their accumulation at the boundaries which can lead to surface rheotaxis
are suppressed. Our results suggest new strategies for controlling the behavior
of live and synthetic swimmers in microchannels.


title: Optimal deletion-robust coreset for submodular maximization

abstract:
  In recent years we have witnessed an increase on the development of methods
for submodular optimization, which have been motivated by the wide
applicability of submodular functions in real-world data-science problems. In
this paper, we contribute to this line of work by considering the problem of
robust submodular maximization against unexpected deletions, which may occur
due to privacy issues or user preferences. Specifically, we study and derive
bounds for the minimum number of items a streaming algorithm has to remember,
in order to achieve a non-trivial approximation guarantee against adversarial
deletions up to $d$ items. We call the set of items that are kept by the
algorithm before adversarial deletions a deletion-robust coreset. We propose a
single-pass streaming algorithm that yields a
$(1-2\epsilon)/(4p)$-approximation for maximizing a non-decreasing submodular
function under a general $p$-matroid constraint and requires a coreset size $k
+ d/\epsilon$, where $k$ is the maximum size of a feasible solution. To the
best of our knowledge, this is the first work to achieve an (asymptotically)
optimal coreset size, as no constant approximation is possible with a coreset
of size sublinear in $d$.


title: Quench-drive spectroscopy of cuprates

abstract:
  Cuprates are d-wave superconductors which exhibit a rich phase diagram: they
are characterized by superconducting fluctuations even above the critical
temperature, and thermal disorder can reduce or suppress the phase coherence.
However, photoexcitation can have the opposite effect: recent experiments have
shown an increasing phase coherence in optimally doped BSCCO with mid-infrared
driving. Time-resolved terahertz spectroscopies are powerful techniques to
excite and probe non-equilibrium states of superconductors, directly addressing
collective modes, such as amplitude (Higgs) oscillations. In this work, we
calculate the full time evolution of the current generated by a cuprate with a
quench-drive spectroscopy setup. Analyzing the response in Fourier space with
respect to both the real time and the quench-drive delay time, we look for the
signature of a transient modulation of higher harmonics as well as the Higgs
mode, in order to characterize the ground state phase. In particular, this
approach can provide a smoking gun for induced or increased phase coherence
when applied to the pseudogap phase. These results can pave the way for future
experimental schemes to characterize and study superconductors alongside
incoherent phases and phase transitions, including induced and transient
superconductivity.


title: Flow-based density of states for complex actions

abstract:
  Emerging sampling algorithms based on normalizing flows have the potential to
solve ergodicity problems in lattice calculations. Furthermore, it has been
noted that flows can be used to compute thermodynamic quantities which are
difficult to access with traditional methods. This suggests that they are also
applicable to the density-of-states approach to complex action problems. In
particular, flow-based sampling may be used to compute the density directly, in
contradistinction to the conventional strategy of reconstructing it via
measuring and integrating the derivative of its logarithm. By circumventing
this procedure, the accumulation of errors from the numerical integration is
avoided completely and the overall normalization factor can be determined
explicitly. In this proof-of-principle study, we demonstrate our method in the
context of two-component scalar field theory where the $O(2)$ symmetry is
explicitly broken by an imaginary external field. First, we concentrate on the
zero-dimensional case which can be solved exactly. We show that with our
method, the Lee-Yang zeroes of the associated partition function can be
successfully located. Subsequently, we confirm that the flow-based approach
correctly reproduces the density computed with conventional methods in one- and
two-dimensional models.


title: The Physical Significance of Imaginary Phonon Modes in Crystals

abstract:
  The lattice vibrations (phonon modes) of crystals underpin a large number of
material properties. The harmonic phonon spectrum of a solid is the simplest
description of its structural dynamics and can be straightforwardly derived
from the Hellman-Feynman forces obtained in a ground-state electronic structure
calculation. The presence of imaginary harmonic modes in the spectrum indicates
that a structure is a local maximum on the athermal structural potential-energy
surface and can yield important insight into the fundamental nature and
physical properties of a material. In this review article, we discuss the
physical significance of imaginary harmonic modes and distinguish between cases
where imaginary modes are indicative of such phenomena, and those where they
reflect technical problems in the calculations. We outline basic approaches for
exploring and renormalising imaginary modes, and demonstrate their utility
through a set of three case studies in the materials sciences.


title: QED and Lasers: A Tutorial

abstract:
  This is a write-up of a short tutorial talk on high-intensity QED,
video-presented at the 2021 annual Christmas meeting of the Central Laser
Facility at Rutherford-Appleton Lab, UK. The first half consists of a largely
historical introduction to (quantum) electrodynamics focussing on a few key
concepts. This well-established theory is then compared to its strong-field
generalisation when a high-intensity laser is present. Some supplementary
material and a fair amount of references have been added.


title:
Estimating Elliptic Flow Coefficient in Heavy Ion Collisions using Deep
  Learning

abstract:
  Machine Learning (ML) techniques have been employed for the high energy
physics (HEP) community since the early 80s to deal with a broad spectrum of
problems. This work explores the prospects of using Deep Learning techniques to
estimate elliptic flow ($v_2$) in heavy-ion collisions at the RHIC and LHC
energies. A novel method is developed to process the input observables from
track-level information. The proposed DNN model is trained with Pb-Pb
collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events simulated with
AMPT model. The predictions from the ML technique are compared to both
simulation and experiment. The Deep Learning model seems to preserve the
centrality and energy dependence of $v_2$ for the LHC and RHIC energies. The
DNN model is also quite successful in predicting the $p_{\rm T}$ dependence of
$v_2$. When subjected to event simulation with additional noise, the proposed
DNN model still keeps the robustness and prediction accuracy intact up to a
reasonable extent.


title: H4D: Human 4D Modeling by Learning Neural Compositional Representation

abstract:
  Despite the impressive results achieved by deep learning based 3D
reconstruction, the techniques of directly learning to model 4D human captures
with detailed geometry have been less studied. This work presents a novel
framework that can effectively learn a compact and compositional representation
for dynamic human by exploiting the human body prior from the widely used SMPL
parametric model. Particularly, our representation, named H4D, represents a
dynamic 3D human over a temporal span with the SMPL parameters of shape and
initial pose, and latent codes encoding motion and auxiliary information. A
simple yet effective linear motion model is proposed to provide a rough and
regularized motion estimation, followed by per-frame compensation for pose and
geometry details with the residual encoded in the auxiliary code. Technically,
we introduce novel GRU-based architectures to facilitate learning and improve
the representation capability. Extensive experiments demonstrate our method is
not only efficacy in recovering dynamic human with accurate motion and detailed
geometry, but also amenable to various 4D human related tasks, including motion
retargeting, motion completion and future prediction. Please check out the
project page for video and code: https://boyanjiang.github.io/H4D/.


title:
WaveY-Net: Physics-augmented deep learning for high-speed
  electromagnetic simulation and optimization

abstract:
  The calculation of electromagnetic field distributions within structured
media is central to the optimization and validation of photonic devices. We
introduce WaveY-Net, a hybrid data- and physics-augmented convolutional neural
network that can predict electromagnetic field distributions with ultra fast
speeds and high accuracy for entire classes of dielectric photonic structures.
This accuracy is achieved by training the neural network to learn only the
magnetic near-field distributions of a system and to use a discrete formalism
of Maxwell's equations in two ways: as physical constraints in the loss
function and as a means to calculate the electric fields from the magnetic
fields. As a model system, we construct a surrogate simulator for periodic
silicon nanostructure arrays and show that the high speed simulator can be
directly and effectively used in the local and global freeform optimization of
metagratings. We anticipate that physics-augmented networks will serve as a
viable Maxwell simulator replacement for many classes of photonic systems,
transforming the way they are designed.


title: Periodic striped states in Ising models with dipolar interactions

abstract:
  We review the problem of determining the ground states of 2D Ising models
with nearest neighbor ferromagnetic and dipolar interactions, and prove a new
result supporting the conjecture that, if the nearest neighbor coupling $J$ is
sufficiently large, the ground states are periodic and `striped'. More
precisely, we prove a restricted version of the conjecture, by constructing the
minimizers within the variational class of states whose domain walls are
arbitrary collections of horizontal and/or vertical straight lines.


title: Mass concentration in rescaled first order integral functionals

abstract:
  We consider first order local minimization problems of the form $\min
\int_{\mathbb{R}^N}f(u,\nabla u)$ under a mass constraint
$\int_{\mathbb{R}^N}u=m\in\mathbb{R}$. We prove that the minimal energy
function $H(m)$ is always concave on $(-\infty,0)$ and $(0,+\infty)$, and that
relevant rescalings of the energy, depending on a small parameter
$\varepsilon$, $\Gamma$-converge in the weak topology of measures towards the
$H$-mass, defined for atomic measures $\sum_i m_i\delta_{x_i}$ as $\sum_i
H(m_i)$. We also consider space dependent Lagrangians $f(x,u,\nabla u)$, which
cover the case of space dependent $H$-masses $\sum_i H(x_i,m_i)$, and also the
case of a family of Lagrangians $(f_\varepsilon)_\varepsilon$ converging as
$\varepsilon\to 0$. The $\Gamma$-convergence result holds under mild
assumptions on $f$, and covers several situations including homogeneous
\(H\)-masses in any dimension $N\geq 2$ for exponents above a critical
threshold, and all concave $H$-masses in dimension $N=1$. Our result yields in
particular the concentration of Cahn-Hilliard fluids into droplets, and is
related to the approximation of branched transport by elliptic energies.


title: Sharp phase transition for Cox percolation

abstract:
  We prove the sharpness of the percolation phase transition for a class of Cox
percolation models, i.e., models of continuum percolation in a random
environment. The key requirements are that the environment has a finite range
of dependence and satisfies a local boundedness condition, however the FKG
inequality need not hold. The proof combines the OSSS inequality with a
coarse-graining construction.


title: A Unified Query-based Paradigm for Point Cloud Understanding

abstract:
  3D point cloud understanding is an important component in autonomous driving
and robotics. In this paper, we present a novel Embedding-Querying paradigm
(EQ-Paradigm) for 3D understanding tasks including detection, segmentation and
classification. EQ-Paradigm is a unified paradigm that enables the combination
of any existing 3D backbone architectures with different task heads. Under the
EQ-Paradigm, the input is firstly encoded in the embedding stage with an
arbitrary feature extraction architecture, which is independent of tasks and
heads. Then, the querying stage enables the encoded features to be applicable
for diverse task heads. This is achieved by introducing an intermediate
representation, i.e., Q-representation, in the querying stage to serve as a
bridge between the embedding stage and task heads. We design a novel Q-Net as
the querying stage network. Extensive experimental results on various 3D tasks
including semantic segmentation, object detection and shape classification show
that EQ-Paradigm in tandem with Q-Net is a general and effective pipeline,
which enables a flexible collaboration of backbones and heads, and further
boosts the performance of the state-of-the-art methods. All codes and models
will be published soon.