title:
A New Virtual Oscillator based Grid-forming Controller with Decoupled
  Control Over Individual Phases and Improved Performance of Unbalanced Fault
  Ride-through

abstract:
  Virtual Oscillator (VO) control is the latest and promising control technique
for grid-forming and grid-supporting inverters. VO Controllers (VOCs) provide
time-domain synchronization with a connected electrical network. At the same
time, a VOC can incorporate additional nested control loops to meet the
system-level requirements such as fault ride-through capability. However,
existing VOCs have two limitations. Firstly, the existing VOCs do not have
decoupled control over individual phases. As a result, the performance of the
existing VOCs is not satisfactory in presence of unbalanced grid voltages.
Secondly, the fault ride-through performance of the existing VOCs under
unbalanced faults is not satisfactory. The power operation at a healthy phase
is badly affected by a faulty phase. This paper has introduced a modified VO
based system-level grid-forming controller to overcome the limitations
mentioned above. Systematic development of the proposed control architecture
with analytical reasoning is presented. Simulation studies and hardware
experiments are conducted for validation.


title:
Vector-valued statistics of binomial processes: Berry-Esseen bounds in
  the convex distance

abstract:
  We study the discrepancy between the distribution of a vector-valued
functional of i.i.d. random elements and that of a Gaussian vector. Our main
contribution is an explicit bound on the convex distance between the two
distributions, holding in every dimension. Such a finding constitutes a
substantial extension of the one-dimensional bounds deduced in Chatterjee
(2007) and Lachi\`eze-Rey and Peccati (2017), as well as of the
multidimensional bounds for smooth test functions and indicators of rectangles
derived, respectively, in Dung (2019), and Fang and Koike (2021). Our
techniques involve the use of Stein's method, combined with a suitable
adaptation of the recursive approach inaugurated by Schulte and Yukich (2017):
this yields rates of converge that have a presumably optimal dependence on the
sample size. We develop several applications of a geometric nature, among which
is a new collection of multidimensional quantitative limit theorems for the
intrinsic volumes associated with coverage processes in Euclidean spaces.


title:
Lagrangian Formalism in Biology: I. Standard Lagrangians and their Role
  in Population Dynamics

abstract:
  The Lagrangian formalism is developed for the population dynamics of
interacting species that are described by several well-known models. The
formalism is based on standard Lagrangians, which represent differences between
the physical kinetic and potential energy-like terms. A method to derive these
Lagrangians is presented and applied to selected theoretical models of the
population dynamics. The role of the derived Lagrangians and the energy-like
terms in the population dynamics is investigated and discussed. It is suggested
that the obtained standard Lagrangians can be used to identify physical
similarities between different population models.


title: Mobile Wireless Rechargeable UAV Networks: Challenges and Solutions

abstract:
  Unmanned aerial vehicles (UAVs) can help facilitate cost-effective and
flexible service provisioning in future smart cities. Nevertheless, UAV
applications generally suffer severe flight time limitations due to constrained
onboard battery capacity, causing a necessity of frequent battery recharging or
replacement when performing persistent missions. Utilizing wireless mobile
chargers, such as vehicles with wireless charging equipment for on-demand
self-recharging has been envisioned as a promising solution to address this
issue. In this article, we present a comprehensive study of
\underline{v}ehicle-assisted \underline{w}ireless rechargeable \underline{U}AV
\underline{n}etworks (VWUNs) to promote on-demand, secure, and efficient UAV
recharging services. Specifically, we first discuss the opportunities and
challenges of deploying VWUNs and review state-of-the-art solutions in this
field. We then propose a secure and privacy-preserving VWUN framework for UAVs
and ground vehicles based on differential privacy (DP). Within this framework,
an online double auction mechanism is developed for optimal charging
scheduling, and a two-phase DP algorithm is devised to preserve the sensitive
bidding and energy trading information of participants. Experimental results
demonstrate that the proposed framework can effectively enhance charging
efficiency and security. Finally, we outline promising directions for future
research in this emerging field.


title: Online Bipartite Matching via Smoothness

abstract:
  The analysis of online bipartite matching of Eden et al. (2021) is a
smoothness proof (Syrgkanis and Tardos, 2013). Moreover, it can be interpreted
as combining a $\lambda = 1-1/e$ value covering (which holds for
single-dimensional agents and randomized auctions) and $\mu = 1$ revenue
covering (Hartline et al., 2014). Note that value covering is a fact about
single-dimensional agents and has nothing to do with the underlying feasibility
setting. Thus, the essential new result from Eden et al. (2021) is that online
bipartite matching is $\mu=1$ revenue covered.


title: Quantitative uniqueness for fractional heat type operators

abstract:
  In this paper we obtain quantitative bounds on the maximal order of vanishing
for solutions to $(\partial_t - \Delta)^s u =Vu$ for $s\in [1/2, 1)$ via new
Carleman estimates. Our main result Theorem 1.1 and Theorem 1.3 can be thought
of as a parabolic generalization of the corresponding quantitative uniqueness
result in the time independent case due to R\"uland and it can also be regarded
as a nonlocal generalization of a similar result due to Zhu for solutions to
local parabolic equations.


title:
Infinite-dimensional Dubrovin-Frobenius manifolds and the Stokes
  phenomenon

abstract:
  We study the Dubrovin equation of the infinite-dimensional 2D Toda
Dubrovin-Frobenius manifold at its irregular singularity. We first revisit the
definition of the canonical coordinates, proving that they emerge naturally as
generalized eigenvalues of the operator of multiplication by the Euler vector
field. We then show that the formal solutions to the Dubrovin equation with
exponential type behaviour at the irregular singular point are not uniquely
determined by their leading order, but instead depend on an infinite number of
parameters, contrary to what happens in the finite-dimensional case. Next, we
obtain a large family of solutions to the Dubrovin equation given by integrals
along the unit circle of certain combinations of the superpotentials. Observing
that such a family is not complete and has trivial monodromy, we study a larger
family of weak solutions obtained via Borel resummation of some distinguished
formal solutions. These resummed solutions naturally appear in
monodromy-related pairs, finally allowing us to compute the
infinite-dimensional analogue of the Stokes matrices.


title:
New determination of the production cross section for secondary
  positrons and electrons in the Galaxy

abstract:
  The cosmic-ray fluxes of electrons and positrons ($e^{\pm}$) are measured
with high precision by the space-borne particle spectrometer AMS-02. To infer a
precise interpretation of the production processes for $e^{\pm}$ in our Galaxy,
it is necessary to have an accurate description of the secondary component,
produced by the interaction of cosmic-ray proton and helium with the
interstellar medium atoms. We determine new analytical functions of the Lorentz
invariant cross section for the production of $\pi^\pm$ and $K^\pm$ by fitting
data from collider experiments. We also evaluate the invariant cross sections
for several other channels, involving for example hyperon decays, contributing
at the few \% level on the total cross section. For all these particles, the
relevant 2 and 3 body decay channels are implemented, with the polarized
$\mu^\pm$ decay computed with next-to-leading order corrections. The cross
section for scattering of nuclei heavier than protons is modeled by fitting
data on $p+C$ collisions. The total differential cross section
$d\sigma/dT_{e^\pm}(p+p\rightarrow e^\pm+X)$ is predicted from 10 MeV up to 10
TeV of $e^\pm$ energy with an uncertainty of about 5-7\% in the energies
relevant for AMS-02 positron flux, thus dramatically reducing the precision of
the theoretical model with respect to the state of the art. Finally, we provide
a prediction for the secondary Galactic $e^\pm$ source spectrum with an
uncertainty of the same level. As a service for the scientific community, we
provide numerical tables and a script to calculate energy-differential cross
sections.


title: QCD equation of state via the complex Langevin method

abstract:
  We present lattice simulations on the phase diagram of Quantum Chromodynamics
(QCD) with two light quark flavours at finite chemical potential $\mu$. To
circumvent the sign problem we use the complex Langevin method. In this study,
we have carried out finite density lattice computations for a pion mass of
$\sim 480$ MeV. We report on the pressure, energy and entropy equations of
state in ab-initio lattice QCD calculations, as well as the observation of the
Silver Blaze phenomenon.


title: Emergence of periodic in magnetic moment effective QED action

abstract:
  We evaluate for the inhomogeneous static electric Sauter step potential the
imaginary part of the emerging homogeneous in electric field effective
Euler-Heisenberg-Schwinger action sourced by vacuum fluctuations of a charged
particle with magnetic moment of arbitrary strength. The result is convergent
for all values of gyromagnetic ratio $g$, periodic in $g$, with a cusp at
$g=2$. We consider the relation to the QED beta-function which is also found to
be periodic in $g$. We confirm presence of asymptotic freedom conditions using
this novel method and document a wider range of $g$-values for which asymptotic
freedom is present.


title:
Approximate Parametric Computation of Minimum-Cost Flows with Convex
  Costs

abstract:
  This paper studies a variant of the minimum-cost flow problem in a graph with
convex cost function where the demands at the vertices are functions depending
on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches
for the approximate computation of parametric solutions for this problem. The
first approach transforms an instance of the parametric problem into an
instance with piecewise quadratic cost functions by interpolating the marginal
cost functions. The new instance can be solved exactly with an algorithm we
developed in prior work. In the second approach, we compute a fixed number of
non-parametric solutions and interpolate the resulting flows yielding an
approximate solution for the original, parametric problem. For both methods we
formulate explicit bounds on the step sizes used in the respective
interpolations that guarantee relative and absolute error margins. Finally, we
test our approaches on real-world traffic and gas instances in an empirical
study.


title:
Self-Triggered Coordination Control of Connected Automated Vehicles in
  Traffic Networks

abstract:
  In this paper, a self-triggered scheme is proposed to optimally control the
traffic flow of Connected and Automated Vehicles (CAVs) at conflict areas of a
traffic network with the main aim of reducing the data exchange among CAVs in
the control zone and at the same to minimize the travel time and energy
consumption. The safety constraints and the vehicle limitations are considered
using the Control Barrier Function (CBF) framework and a self-triggered scheme
is proposed using the CBF constraints. Moreover, modified CBF constraints are
developed to ensure a minimum inter-event interval for the proposed
self-triggered schemes. Finally, it is shown through a simulation study that
the number of data exchanges among CAVs is significantly reduced using the
proposed self-triggered schemes in comparison with the standard time-triggered
framework.


title:
Physics-based Learning of Parameterized Thermodynamics from Real-time
  Thermography

abstract:
  Progress in automatic control of thermal processes has long been limited by
the difficulty of obtaining high-fidelity thermodynamic models. Traditionally,
in complex thermodynamic systems, it is often infeasible to estimate the
thermophysical parameters of spatiotemporally varying processes, forcing the
adoption of model-free control architectures. This comes at the cost of losing
any robustness guarantees, and implies a need for extensive real-life testing.
In recent years, however, infrared cameras and other thermographic equipment
have become readily applicable to these processes, allowing for a real-time,
non-invasive means of sensing the thermal state of a process. In this work, we
present a novel physics-based approach to learning a thermal process's dynamics
directly from such real-time thermographic data, while focusing attention on
regions with high thermal activity. We call this process, which applies to any
higher-dimensional scalar field, attention-based noise robust averaging (ANRA).
Given a partial-differential equation model structure, we show that our
approach is robust against noise, and can be used to initialize optimization
routines to further refine parameter estimates. We demonstrate our method on
several simulation examples, as well as by applying it to electrosurgical
thermal response data on in vivo porcine skin tissue.


title:
Observation of Dual-band Topological Corner Modes in Acoustic Kagome
  Lattice with Long-range Interactions

abstract:
  The recent exotic topological corner modes (CMs) in photonic higher-order
topological insulators with long-distance interactions have attracted numerous
attentions and enriched the physics than their condensed-matter counterparts.
While the next-nearest-neighbour (NNN) coupling appears between NNN lattice
sites unselectively, and the NNN coupling and their associated dynamics remains
elusive in acoustics due to the waveguide-resonator model, an analogy of
tight-binding model (TBM), drastically hinders its NNN coupling. Here, in
acoustics, we demonstrate selective NNN coupling-induced CMs in split-ring
resonators-based kagome crystal and observe dual-band CMs. Three types of CMs
are demonstrated in the first bulk gap which can be explained by TBM
considering NNN coupling and one type of CMs is observed in the second. All of
these findings are verified theoretically and experimentally which reveals rich
physics in acoustics, opening a new way towards tunable or multi-band
metamaterials design, and offering opportunities for intriguing acoustic
manipulation and energy localization.


title: Infinitesimal deformations of some Quot schemes

abstract:
  Let $E$ be a vector bundle on a smooth complex projective curve $C$ of genus
at least two. Let $\mathcal{Q}(E,d)$ be the Quot scheme parameterizing the
torsion quotients of $E$ of degree $d$. We compute the cohomologies of the
tangent bundle $T_{\mathcal{Q}(E,d)}$. In particular, the space of
infinitesimal deformations of $\mathcal{Q}(E,d)$ is computed. Kempf and
Fantechi computed the space of infinitesimal deformations of
$\mathcal{Q}(\mathcal{O}_C,d)\,=\, C^{(d)}$. We also explicitly describe the
infinitesimal deformations of $\mathcal{Q}(E,d)$.


title:
Multi-armed bandits for online optimization of language model
  pre-training: the use case of dynamic masking

abstract:
  Transformer-based language models (TLMs) provide state-of-the-art performance
in many modern natural language processing applications. TLM training is
conducted in two phases. First, the model is pre-trained over large volumes of
text to minimize a generic objective function, such as the Masked Language
Model (MLM). Second, the model is fine-tuned in specific downstream tasks.
Pre-training requires large volumes of data and high computational resources,
while introducing many still unresolved design choices. For instance, selecting
hyperparameters for language model pre-training is often carried out based on
heuristics or grid-based searches. In this work, we propose a multi-armed
bandit-based online optimization framework for the sequential selection of
pre-training hyperparameters to optimize language model performance. We pose
the pre-training procedure as a sequential decision-making task, where at each
pre-training step, an agent must determine what hyperparameters to use towards
optimizing the pre-training objective. We propose a Thompson sampling bandit
algorithm, based on a surrogate Gaussian process reward model of the MLM
pre-training objective, for its sequential minimization. We empirically show
how the proposed Gaussian process based Thompson sampling pre-trains robust and
well-performing language models. Namely, by sequentially selecting masking
hyperparameters of the TLM, we achieve satisfactory performance in less epochs,
not only in terms of the pre-training MLM objective, but in diverse downstream
fine-tuning tasks. The proposed bandit-based technique provides an automated
hyperparameter selection method for pre-training TLMs of interest to
practitioners. In addition, our results indicate that, instead of MLM
pre-training with fixed masking probabilities, sequentially adapting the
masking hyperparameters improves both pre-training loss and downstream task
metrics.


title: Polynomial description for the T-Orbit Spaces of Multiplicative Actions

abstract:
  A finite group with an integer representation has a multiplicative action on
the ring of Laurent polynomials, which is induced by a nonlinear action on the
complex torus. We study the structure of the associated orbit space as the
image of the fundamental invariants. For the Weyl groups of types A, B, C and
D, this image is a compact basic semi--algebraic set and we present the
defining polynomial inequalities explicitly. We show how orbits correspond to
solutions in the complex torus of symmetric polynomial systems and give a
characterization of the orbit space as the positivity--locus of a real
symmetric matrix polynomial. The resulting domain is the region of
orthogonality for a family of generalized Chebyshev polynomials, which have
connections to topics such as Fourier analysis and representations of Lie
algebras.


title:
Wideband precision stabilization of the -18.6 kV retarding voltage for
  the KATRIN spectrometer

abstract:
  The Karlsruhe Tritium Neutrino Experiment (KATRIN) measures the effective
electron anti-neutrino mass with an unprecedented design sensitivity of 0.2 eV
(90 % C.L.). In this experiment, the energy spectrum of beta electrons near the
tritium decay endpoint is analyzed with a highly accurate spectrometer. To
reach the KATRIN sensitivity target, the retarding voltage of this spectrometer
must be stable to the ppm level and well known on various time scales ($\mu s$
up to months), for values around -18.6 kV. A custom-designed high-voltage
regulation system mitigates the impact of interference sources in the absence
of a closed electric shield around the large spectrometer vessel. In this
article, we describe the regulation system and its integration into the KATRIN
setup. Independent monitoring methods demonstrate a stability within 2 ppm,
exceeding KATRIN's specifications.


title: Addressing Missing Sources with Adversarial Support-Matching

abstract:
  When trained on diverse labeled data, machine learning models have proven
themselves to be a powerful tool in all facets of society. However, due to
budget limitations, deliberate or non-deliberate censorship, and other problems
during data collection and curation, the labeled training set might exhibit a
systematic shortage of data for certain groups. We investigate a scenario in
which the absence of certain data is linked to the second level of a two-level
hierarchy in the data. Inspired by the idea of protected groups from
algorithmic fairness, we refer to the partitions carved by this second level as
"subgroups"; we refer to combinations of subgroups and classes, or leaves of
the hierarchy, as "sources". To characterize the problem, we introduce the
concept of classes with incomplete subgroup support. The representational bias
in the training set can give rise to spurious correlations between the classes
and the subgroups which render standard classification models ungeneralizable
to unseen sources. To overcome this bias, we make use of an additional, diverse
but unlabeled dataset, called the "deployment set", to learn a representation
that is invariant to subgroup. This is done by adversarially matching the
support of the training and deployment sets in representation space. In order
to learn the desired invariance, it is paramount that the sets of samples
observed by the discriminator are balanced by class; this is easily achieved
for the training set, but requires using semi-supervised clustering for the
deployment set. We demonstrate the effectiveness of our method with experiments
on several datasets and variants of the problem.


title: If $R^m \cong R^n$ must $m=n$?

abstract:
  A fundamental theorem of linear algebra asserts that every basis for the
vector space $\mathbb{R}^n$ has $n$ elements. In this expository note we
present a theorem of W. G. Leavitt describing one way in which this invariant
basis number property can fail when one does linear algebra over rings, rather
than over fields. We give a proof of Leavitt's theorem that combines ideas of
P. M. Cohn and A. L. S. Corner into an elementary form requiring only a nodding
acquaintance with matrices and modular arithmetic.


title:
Four-fermion deformations of the massless Schwinger model and
  confinement

abstract:
  We consider the massless charge-$N$ Schwinger model and its deformation with
two four-fermion operators. Without the deformations, this model exhibits
chiral symmetry breaking without confinement. It is usually asserted that the
massless Schwinger model is always deconfined and a string tension emerges only
when a mass for the fermion field is turned on. We show that in the presence of
these four-fermion operators, the massless theory can in fact confine. One of
the four-fermion deformations is chirally neutral, and is a marginal
deformation. The other operator can be relevant or irrelevant, and respects a
$\mathbb{Z}_2$ subgroup of chiral symmetry for even $N$, hence forbidding a
mass term. When it is relevant, even the exactly massless theory exhibits both
confinement and spontaneous chiral symmetry breaking. The construction is
analogous to QCD(adj) in 2d. While the theory without four-fermion deformations
is deconfined, the theory with these deformations is generically in a confining
phase. We study the model on $\mathbb{R}^2$ using bosonization, and also
analyze the mechanism of confinement on $\mathbb{R}\times S^1$, where we find
that confinement is driven by fractional instantons.


title:
Tuning rules for passivity-based integral control for a class of
  mechanical systems

abstract:
  This manuscript introduces a passivity-based integral control approach for
fully-actuated mechanical systems. The novelty of our methodology is that we
exploit the gyroscopic forces of the mechanical systems to exponentially
stabilize the mechanical system at the desired equilibrium even in the presence
of matched disturbances; additionally, we show that our approach is robust
against unmatched disturbances. Furthermore, we provide tuning rules to
prescribe the performance of the closed-loop system. We conclude this
manuscript with experimental results obtained from a robotic arm.


title: midiVERTO: A Web Application to Visualize Tonality in Real Time

abstract:
  This paper presents a web application for visualizing the tonality of a piece
of music -- the organization of its chords and scales -- at a high level of
abstraction and with coordinated playback. The application applies the discrete
Fourier transform to the pitch-class domain of a user-specified segmentation of
a MIDI file and visualizes the Fourier coefficients' trajectories. Since the
coefficients indicate different musical properties, such as harmonic function,
triadicity, and diatonicity, the application isolates aspects of a piece's
tonality and shows their development in time. The aim of the application is to
bridge a gap between mathematical music theory, musicology, and the general
public by making the discrete Fourier transform as applied to the pitch-class
domain accessible without requiring advanced mathematical knowledge or
programming skills up front.


title:
Bidding and Scheduling in Energy Markets: Which Probabilistic Forecast
  Do We Need?

abstract:
  Probabilistic forecasting in combination with stochastic programming is a key
tool for handling the growing uncertainties in future energy systems. Derived
from a general stochastic programming formulation for the optimal scheduling
and bidding in energy markets we examine several common special instances
containing uncertain loads, energy prices, and variable renewable energies. We
analyze for each setup whether only an expected value forecast, marginal or
bivariate predictive distributions, or the full joint predictive distribution
is required. For market schedule optimization, we find that expected price
forecasts are sufficient in almost all cases, while the marginal distributions
of renewable energy production and demand are often required. For bidding curve
optimization, pairwise or full joint distributions are necessary except for
specific cases. This work helps practitioners choose the simplest type of
forecast that can still achieve the best theoretically possible result for
their problem and researchers to focus on the most relevant instances.


title:
Topological properties of subsystem-symmetry-protected edge states in an
  extended quasi-one-dimensional dimerized lattice

abstract:
  We investigate theoretically the topological properties of dimerized
quasi-one-dimensional (1D) lattice comprising of multi legs $(L)$ as well as
multi sublattices $(R)$. The system has main and subsidiary exchange
symmetries. In the basis of latter one, the system can be divided into $L$ 1D
subsystems each of which corresponds to a generalized $SSH_R$ model having $R$
sublattices and on-site potentials. Chiral symmetry is absent in all subsystems
except when the axis of main exchange symmetry coincides on the central chain.
We find that the system may host zero- and finite-energy topological edge
states. The existence of zero-energy edge state requires a certain relation
between the number of legs and sublattices. As such, different topological
phases, protected by subsystem symmetry, including zero-energy edge states in
the main gap, no zero-energy edge states, and zero-energy edge states in the
bulk states are characterized. Despite the classification symmetry of the
system belongs to $BDI$ but each subsystem falls in either $AI$ or $BDI$
symmetry class.


title:
Learning Hierarchical Cross-Modal Association for Co-Speech Gesture
  Generation

abstract:
  Generating speech-consistent body and gesture movements is a long-standing
problem in virtual avatar creation. Previous studies often synthesize pose
movement in a holistic manner, where poses of all joints are generated
simultaneously. Such a straightforward pipeline fails to generate fine-grained
co-speech gestures. One observation is that the hierarchical semantics in
speech and the hierarchical structures of human gestures can be naturally
described into multiple granularities and associated together. To fully utilize
the rich connections between speech audio and human gestures, we propose a
novel framework named Hierarchical Audio-to-Gesture (HA2G) for co-speech
gesture generation. In HA2G, a Hierarchical Audio Learner extracts audio
representations across semantic granularities. A Hierarchical Pose Inferer
subsequently renders the entire human pose gradually in a hierarchical manner.
To enhance the quality of synthesized gestures, we develop a contrastive
learning strategy based on audio-text alignment for better audio
representations. Extensive experiments and human evaluation demonstrate that
the proposed method renders realistic co-speech gestures and outperforms
previous methods in a clear margin. Project page:
https://alvinliu0.github.io/projects/HA2G


title: Conjugate Plateau constructions in product spaces

abstract:
  This survey paper investigates, from a purely geometric point of view,
Daniel's isometric conjugation between minimal and constant mean curvature
surfaces immersed in homogeneous Riemannian three-manifolds with isometry group
of dimension four. On the one hand, we collect the results and strategies in
the literature that have been developed so far to deal with the analysis of
conjugate surfaces and their embeddedness. On the other hand, we revisit some
constructions of constant mean curvature surfaces in the homogeneous product
spaces $\mathbb{S}^2\times\mathbb{R}$, $\mathbb{H}^2\times\mathbb{R}$ and
$\mathbb{R}^3$ having different topologies and geometric properties depending
on the value of the mean curvature. Finally, we also provide some numerical
pictures using Surface Evolver.


title:
Scattering Matrices for Close Singular Selfadjoint Perturbations of
  Unbounded Selfadjoint Operators

abstract:
  In this paper, we consider an unbounded selfadjoint operator $A$ and its
selfadjoint perturbations in the same Hilbert space $\mathcal{H}$. As
S.Albeverio and P. Kurosov (2000), we call a selfadjoint operator $A_{1}$ the
singular perturbation of $A$ if $A_{1}$ and {A} have different domains
$\mathcal{D}(A),\mathcal{D}(A_{1})$ but $A=A_{1}$ on
$\mathcal{D}(A)\cap\mathcal{D}(A_{1})$. Assuming that $A$ has absolutely
continuous spectrum and the difference of resolvents $R_{z}(A_{1}) -R_{z}(A)$
of $A_{1}$ and $A$ for non-real $z$ is a trace class operator we find the
explicit expression for the scattering matrix for the pair $A, A_{1}$ through
the constituent elements of the Krein formula for the resolvents of this pair.
As an illustration, we find the scattering matrix for the standardly defined
Laplace operator in $L_{2}\left(\mathbf{R}_{3}\right)$ and its singular
perturbation in the form of an infinite sum of zero-range potentials.


title:
On the Kullback-Leibler divergence between pairwise isotropic
  Gaussian-Markov random fields

abstract:
  The Kullback-Leibler divergence or relative entropy is an
information-theoretic measure between statistical models that play an important
role in measuring a distance between random variables. In the study of complex
systems, random fields are mathematical structures that models the interaction
between these variables by means of an inverse temperature parameter,
responsible for controlling the spatial dependence structure along the field.
In this paper, we derive closed-form expressions for the Kullback-Leibler
divergence between two pairwise isotropic Gaussian-Markov random fields in both
univariate and multivariate cases. The proposed equation allows the development
of novel similarity measures in image processing and machine learning
applications, such as image denoising and unsupervised metric learning.

categories: cs.IT math.IT nlin.AO physics.data-an stat.ML


title: Unjamming strongly compressed particle rafts

abstract:
  We experimentally study the unjamming dynamics of strongly compressed
particle rafts confined between two fixed walls and two movable barriers. The
back barrier is made of an elastic band, whose deflection indicates the local
stress. The front barrier is pierced by a gate, whose opening triggers local
unjamming. The rafts are compressed by moving only one of the two barriers in
the vicinity of which folds form. Using high speed imaging, we follow the
folded, jammed, and unjammed raft areas and measure the velocity fields inside
and outside of the initially confined domain. Two very different behaviors
develop. For rafts compressed by the back barrier, only partial unjamming
occurs. At the end of the process, many folds remain and the back stress does
not relax. The flow develops only along the compression axis and the particles
passing the gate form a dense raft whose width is the gate width. For rafts
compressed at the front, quasi-total unjamming is observed. No folds persist
and only minimal stress remains, if any. The particles flow along the
compression axis but also normally to it and form, after the gate, a rather
circular and not dense assembly. We attribute this difference to the opposite
orientation of the force chain network that builds up from the compressed side
and branchs. For rafts compressed at the gate side, keystone particles are
immediately removed which enhances local disentanglement and leads to large
scale unjamming. In contrast, for back compressed rafts, the force chain
network redirects the stress laterally forming arches around the gate and
resulting in a limited unjamming process.


title: Self-supervised Video-centralised Transformer for Video Face Clustering

abstract:
  This paper presents a novel method for face clustering in videos using a
video-centralised transformer. Previous works often employed contrastive
learning to learn frame-level representation and used average pooling to
aggregate the features along the temporal dimension. This approach may not
fully capture the complicated video dynamics. In addition, despite the recent
progress in video-based contrastive learning, few have attempted to learn a
self-supervised clustering-friendly face representation that benefits the video
face clustering task. To overcome these limitations, our method employs a
transformer to directly learn video-level representations that can better
reflect the temporally-varying property of faces in videos, while we also
propose a video-centralised self-supervised framework to train the transformer
model. We also investigate face clustering in egocentric videos, a
fast-emerging field that has not been studied yet in works related to face
clustering. To this end, we present and release the first large-scale
egocentric video face clustering dataset named EasyCom-Clustering. We evaluate
our proposed method on both the widely used Big Bang Theory (BBT) dataset and
the new EasyCom-Clustering dataset. Results show the performance of our
video-centralised transformer has surpassed all previous state-of-the-art
methods on both benchmarks, exhibiting a self-attentive understanding of face
videos.


title:
Towards Exemplar-Free Continual Learning in Vision Transformers: an
  Account of Attention, Functional and Weight Regularization

abstract:
  In this paper, we investigate the continual learning of Vision Transformers
(ViT) for the challenging exemplar-free scenario, with special focus on how to
efficiently distill the knowledge of its crucial self-attention mechanism
(SAM). Our work takes an initial step towards a surgical investigation of SAM
for designing coherent continual learning methods in ViTs. We first carry out
an evaluation of established continual learning regularization techniques. We
then examine the effect of regularization when applied to two key enablers of
SAM: (a) the contextualized embedding layers, for their ability to capture
well-scaled representations with respect to the values, and (b) the prescaled
attention maps, for carrying value-independent global contextual information.
We depict the perks of each distilling strategy on two image recognition
benchmarks (CIFAR100 and ImageNet-32) -- while (a) leads to a better overall
accuracy, (b) helps enhance the rigidity by maintaining competitive
performances. Furthermore, we identify the limitation imposed by the symmetric
nature of regularization losses. To alleviate this, we propose an asymmetric
variant and apply it to the pooled output distillation (POD) loss adapted for
ViTs. Our experiments confirm that introducing asymmetry to POD boosts its
plasticity while retaining stability across (a) and (b). Moreover, we
acknowledge low forgetting measures for all the compared methods, indicating
that ViTs might be naturally inclined continual learner


title: Model-Agnostic Multi-Agent Perception Framework

abstract:
  Existing multi-agent perception systems assume that every agent utilizes the
same models with identical parameters and architecture, which is often
impractical in the real world. The significant performance boost brought by the
multi-agent system can be degraded dramatically when the perception models are
noticeably different. In this work, we propose a model-agnostic multi-agent
framework to reduce the negative effect caused by model discrepancies and
maintain confidentiality. Specifically, we consider the perception
heterogeneity between agents by integrating a novel uncertainty calibrator
which can eliminate the bias among agents' predicted confidence scores. Each
agent performs such calibration independently on a standard public database,
and therefore the intellectual property can be protected. To further refine the
detection accuracy, we also propose a new algorithm called
Promotion-Suppression Aggregation (PSA) that considers not only the confidence
score of proposals but also the spatial agreement of their neighbors. Our
experiments emphasize the necessity of model calibration across different
agents, and the results show that our proposed approach outperforms the
state-of-the-art baseline methods for 3D object detection on the open OPV2V
dataset.


title: An Evolutionary Note on Smart City Development in China

abstract:
  In response to challenges posed by urbanization, David Bollier from the
University of Southern California raised a new idea for city planning: a
comprehensive network and applications of information technologies. IBM later
echoed the idea and initiated its Smart Planet vision in 2008. After that, the
smart city concept was quickly adopted by major cities throughout the world,
and it has gradually evolved into a strategic choice by ambitious cities. This
paper looks into the smart city trend by reviewing how the concept of smart
city was proposed and what the essence of a smart city is. More specifically,
the driving forces of the smart city development in China are investigated, and
the key differences of smart cities between China and other countries are
summarized. Finally, four big challenges to build future smart cities are
discussed.


title: Geometric Dominating Sets

abstract:
  We consider a minimizing variant of the well-known \emph{No-Three-In-Line
Problem}, the \emph{Geometric Dominating Set Problem}: What is the smallest
number of points in an $n\times n$~grid such that every grid point lies on a
common line with two of the points in the set? We show a lower bound of
$\Omega(n^{2/3})$ points and provide a constructive upper bound of size $2
\lceil n/2 \rceil$. If the points of the dominating sets are required to be in
general position we provide optimal solutions for grids of size up to $12
\times 12$. For arbitrary $n$ the currently best upper bound for points in
general position remains the obvious $2n$. Finally, we discuss the problem on
the discrete torus where we prove an upper bound of $O((n \log n)^{1/2})$. For
$n$ even or a multiple of 3, we can even show a constant upper bound of 4. We
also mention a number of open questions and some further variations of the
problem.


title: Self-testing nonlocality without entanglement

abstract:
  Quantum theory allows for nonlocality without entanglement. Notably, there
exist bipartite quantum measurements consisting of only product eigenstates,
yet they cannot be implemented via local quantum operations and classical
communication. In the present work, we show that a measurement exhibiting
nonlocality without entanglement can be certified in a device-independent
manner. Specifically, we consider a simple quantum network and construct a
self-testing procedure. This result also demonstrates that genuine network
quantum nonlocality can be obtained using only non-entangled measurements. From
a more general perspective, our work establishes a connection between the
effect of nonlocality without entanglement and the area of Bell nonlocality.


title: Inverse reduction inequalities for spectral numbers and applications

abstract:
  Our main result is the proof of an inequality between the spectral numbers of
a Lagrangian and the spectral numbers of its reductions, in the opposite
direction to the classical inequality (see e.g [Vit92]). This has applications
to the "Geometrically bounded Lagrangians are spectrally bounded" conjecture
from [Vit08], to the structure of elements in the $\gamma$-completion of the
set of exact Lagrangians. We also investigate the local path-connectedness of
the set of Hamiltonian diffeomorphisms with the spectral metric.


title: Zone extrapolations in parametric timed automata

abstract:
  Timed automata (TAs) are an efficient formalism to model and verify systems
with hard timing constraints, and concurrency. While TAs assume exact timing
constants with infinite precision, parametric TAs (PTAs) leverage this
limitation and increase their expressiveness, at the cost of undecidability. A
practical explanation for the efficiency of TAs is zone extrapolation, where
clock valuations beyond a given constant are considered equivalent. This
concept cannot be easily extended to PTAs, due to the fact that parameters can
be unbounded. In this work, we propose several definitions of extrapolation for
PTAs based on the M-extrapolation, and we study their correctness. Our
experiments show an overall decrease of the computation time and, most
importantly, allow termination of some previously unsolvable benchmarks.


title: Finding large additive and multiplicative Sidon sets in sets of integers

abstract:
  Given $h,g \in \mathbb{N}$, we write a set $X \subseteq \mathbb{Z}$ to be a
$B_{h}^{+}[g]$ set if for any $n \in \mathbb{R}$, the number of solutions to
the additive equation $n = x_1 + \dots + x_h$ with $x_1, \dots, x_h \in X$ is
at most $g$, where we consider two such solutions to be the same if they differ
only in the ordering of the summands. We define a multiplicative
$B_{h}^{\times}[g]$ set analogously. In this paper, we prove, amongst other
results, that there exists some absolute constant $g \in \mathbb{N}$ such that
for any $h \in \mathbb{N}$ and for any finite set $A$ of integers, either $A$
contains a $B_{h}^{+}[g]$ set $B$ or a $B_{h}^{\times}[g]$ set $C$ satisfying
\[ \max \{ |B| , |C| \} \gg_{h} |A|^{(1+ \delta_h)/h }, \] for some $\delta_h >
0$. In fact, for $h$ sufficiently large, we may set $g = 1$ and $\delta_h \gg
(\log \log h)^{1/2 - o(1)}$.


title: The gravitational imprint of an interior-orbital resonance in Jupiter-Io

abstract:
  At mid-mission perijove 17, NASA's Juno mission has revealed a $7\sigma$
discrepancy between Jupiter's observed high-degree tidal response and the
theoretical equilibrium tidal response, namely the Love number $k_{42}$. Here,
we propose an interpretation for this puzzling disagreement based on an
interior-orbital resonance between internal gravity waves trapped in Jupiter's
dilute core and the orbital motion of Io. We use simple Jupiter models to
calculate a fractional correction $\Delta k_{42}$ to the equilibrium tidal
response that comes from the dynamical tidal response of a $g$-mode trapped in
Jupiter's dilute core. Our results suggest that an extended dilute core
($r\gtrsim0.7R_J$) produces an interior-orbital resonance with Io that modifies
Jupiter's tidal response in $\Delta k_{42}\sim-11\%$, allowing us to fit Juno's
$k_{42}$. In our proposed self-consistent scenario, Jupiter's dilute core
evolves in resonant locking with Io's orbital migration, which allows the
interior-orbital resonance to persist over geological timescales. This scenario
requires a dilute core that becomes smoother or shrinks over time, together
with a $_4^2g_1$ mode ($\ell,m,n=4,2,1$) with resonant tidal dissipation
reaching $Q_4\sim1000$. Jupiter's dilute core evolution path and the
dissipation mechanism for the resonant $_4^2g_1$ mode are uncertain and
motivate future analysis. No other alternative exists so far to explain the
$7\sigma$ discrepancy in Juno $k_{42}$. Our proposed interior-orbital resonance
can be tested by Juno observations of $k_{42}$ tides raised on Jupiter by
Europa as obtained at the end of the extended mission (mid 2025), and by future
seismological observations of Jupiter's $_4^2g_1$ mode oscillation frequency.


title: Emergence of hierarchical reference systems in multi-agent communication

abstract:
  In natural language, referencing objects at different levels of specificity
is a fundamental pragmatic mechanism for efficient communication in context. We
develop a novel communication game, the hierarchical reference game, to study
the emergence of such reference systems in artificial agents. We consider a
simplified world, in which concepts are abstractions over a set of primitive
attributes (e.g., color, style, shape). Depending on how many attributes are
combined, concepts are more general ("circle") or more specific ("red dotted
circle"). Based on the context, the agents have to communicate at different
levels of this hierarchy. Our results show, that the agents learn to play the
game successfully and can even generalize to novel concepts. To achieve
abstraction, they use implicit (omitting irrelevant information) and explicit
(indicating that attributes are irrelevant) strategies. In addition, the
compositional structure underlying the concept hierarchy is reflected in the
emergent protocols, indicating that the need to develop hierarchical reference
systems supports the emergence of compositionality.


title:
A monotonicity formula for minimizers of the Mumford-Shah functional in
  2d and a sharp lower bound on the energy density

abstract:
  We establish a new monotonicity formula for minimizers of the Mumford-Shah
functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus,
but works with the David-L\'eger entropy instead of the energy. Interestingly,
this allows for a sharp truncation threshold. In particular, our monotonicity
formula is able to discriminate between points at a $C^1$ interface and any
other type of singularity in terms of a finite gap in the entropy. As a
corollary, we prove an optimal lower bound on the energy density around any
nonsmooth point for minimizers of the Mumford-Shah functional.


title:
Complete gradient expanding Ricci solitons with finite asymptotic scalar
  curvature ratio

abstract:
  Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton
with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the
asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $
\limsup_{r\to \infty} R r^2< \infty $), then the Riemann curvature tensor must
have at least sub-quadratic decay, namely, $\limsup_{r\to \infty} |Rm| \ \!
r^{\alpha}< \infty$ for any $0<\alpha<2$.


title: Automatic User Profiling in Darknet Markets: a Scalability Study

abstract:
  In this study, we investigate the scalability of state-of-the-art user
profiling technologies across different online domains. More specifically, this
work aims to understand the reliability and limitations of current
computational stylometry approaches when these are applied to underground fora
in which user populations potentially differ from other online platforms
(predominantly male, younger age and greater computer use) and cyber offenders
who attempt to hide their identity. Because no ground truth is available and no
validated criminal data from historic investigations is available for
validation purposes, we have collected new data from clearweb forums that do
include user demographics and could be more closely related to underground fora
in terms of user population (e.g., tech communities) than commonly used social
media benchmark datasets showing a more balanced user population.


title: Mounting evidence for a 95 GeV Higgs boson

abstract:
  In 2018 CMS reported an excess in the light Higgs-boson search in the
diphoton decay mode at about 95GeV based on Run 1 and first year Run 2 data.
The combined local significance of the excess was $2.8\,\sigma$. The excess is
compatible with the limits obtained in the ATLAS searches from the diphoton
search channel. Recently, CMS reported another local excess with a significance
of $3.1\,\sigma$ in the light Higgs-boson search in the di-tau final state,
which is compatible with the interpretation of a Higgs boson with a mass of
about 95GeV. We show that the observed results can be interpreted as
manifestations of a Higgs boson in the Two-Higgs Doublet Model with an
additional real singlet (N2HDM). We find that the lightest Higgs boson of the
N2HDM can fit both excesses simultaneously, while the second-lightest state is
such that it satisfies the Higgs-boson measurements at 125GeV, and the full
Higgs-boson sector is compatible with all Higgs exclusion bounds from the
searches at LEP, the Tevatron and the LHC as well as with other theoretical and
experimental constraints. Finally, we demonstrate that it is furthermore
possible to accommodate the excesses observed by CMS in the two search channels
together with a local $2.3\,\sigma$ excess in the $b \bar b$ final state
observed at LEP in the same mass range.


title: The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks

abstract:
  The term `surrogate modeling' in computational science and engineering refers
to the development of computationally efficient approximations for expensive
simulations, such as those arising from numerical solution of partial
differential equations (PDEs). Surrogate modeling is an enabling methodology
for many-query computations in science and engineering, which include iterative
methods in optimization and sampling methods in uncertainty quantification.
Over the last few years, several approaches to surrogate modeling for PDEs
using neural networks have emerged, motivated by successes in using neural
networks to approximate nonlinear maps in other areas. In principle, the
relative merits of these different approaches can be evaluated by
understanding, for each one, the cost required to achieve a given level of
accuracy. However, the absence of a complete theory of approximation error for
these approaches makes it difficult to assess this cost-accuracy trade-off. The
purpose of the paper is to provide a careful numerical study of this issue,
comparing a variety of different neural network architectures for operator
approximation across a range of problems arising from PDE models in continuum
mechanics.


title: Deep Bidirectional Transformers for SoC Flow Specification Mining

abstract:
  High-quality system-level message flow specifications can lead to
comprehensive validation of system-on-chip (SoC) designs. We propose a
disruptive method that utilizes an attention mechanism to produce accurate flow
specifications from SoC IP communication traces. The proposed method can
overcome the inherent complexity of SoC traces induced by the concurrency and
parallelism of multicore designs that existing flow specification mining tools
often find extremely challenging. Experiments on highly interleaved traces show
promising flow reconstruction compared to several tools dedicated to the flow
specification mining problem.


title:
Molecular gas properties of Planck-selected protocluster candidates at
  z~1.3-3

abstract:
  We report on IRAM-30m/EMIR observations of 38 red Herschel sources in 18
Planck-selected protocluster candidates (PHz). We detect 40 CO lines on a total
of 24 bright Herschel sources in 14 of the 18 PHz fields. The measured average
redshift is <z>=2.25. We measure redshifts for multiple Herschel sources in
eight PHz fields. In half of those fields we detect from two to three objects
at similar redshifts, supporting the idea that they contain high-z
protoclusters. The detection of sources at different redshifts demonstrates
that foreground and background sources also contribute to the total sub-mm
emission. We compare the properties of the molecular gas, and of the star
formation activity of our sources with samples of normal star-forming galaxies
(SFGs), sub-mm galaxies, and CO-detected cluster and protocluster galaxies at
similar redshifts. We find that the PHz-IRAM sources are mainly normal SFGs,
with only ~20% undergoing a starburst phase. The PHz-IRAM sources are
characterized by star formation rates and gas masses that are, on average,
eight and five times higher than those typical of normal SFGs at similar
redshifts. Their dust temperatures, and depletion timescales are instead
consistent with those of normal SFGs. The analysis of the CO spectral line
energy distribution, available for ten sources, peaks at Jup=3 in most of the
cases, implying low gas excitation. These properties imply that a significant
fraction of the PHz-IRAM sources contains extended, and cold molecular gas
reservoirs at low excitation, and that their star-formation is driven by
secular processes. Multiplicity and moderate gravitational lensing might also
play a role in producing the observed properties. We find that the highest
star-forming protoclusters drawn from the large volume simulations, have
similar SFRs as the PHz protoclusters, but separate out into a larger number of
SFGs. (Abridged)


title: Nuclear spin polarization and control in a van der Waals material

abstract:
  Van der Waals layered materials are a focus of materials research as they
support strong quantum effects and can easily form heterostructures. Electron
spins in van der Waals materials played crucial roles in many recent
breakthroughs, including topological insulators, two-dimensional (2D) magnets,
and spin liquids. However, nuclear spins in van der Waals materials remain an
unexplored quantum resource. Here we report the first demonstration of optical
polarization and coherent control of nuclear spins in a van der Waals material
at room temperature. We use negatively-charged boron vacancy ($V_B^-$) spin
defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins.
Remarkably, we observe the Rabi frequency of nuclear spins at the excited-state
level anti-crossing of $V_B^-$ defects to be 350 times larger than that of an
isolated nucleus, and demonstrate fast coherent control of nuclear spins. We
also detect strong electron-mediated nuclear-nuclear spin coupling that is 5
orders of magnitude larger than the direct nuclear spin dipolar coupling,
enabling multi-qubit operations. Nitrogen nuclear spins in a triangle lattice
will be suitable for large-scale quantum simulation. Our work opens a new
frontier with nuclear spins in van der Waals materials for quantum information
science and technology.


title: Quantum Motion Segmentation

abstract:
  Motion segmentation is a challenging problem that seeks to identify
independent motions in two or several input images. This paper introduces the
first algorithm for motion segmentation that relies on adiabatic quantum
optimization of the objective function. The proposed method achieves on-par
performance with the state of the art on problem instances which can be mapped
to modern quantum annealers.


title:
Improving Maximum Likelihood Difference Scaling method to measure inter
  content scale

abstract:
  The goal of most subjective studies is to place a set of stimuli on a
perceptual scale. This is mostly done directly by rating, e.g. using single or
double stimulus methodologies, or indirectly by ranking or pairwise comparison.
All these methods estimate the perceptual magnitudes of the stimuli on a scale.
However, procedures such as Maximum Likelihood Difference Scaling (MLDS) have
shown that considering perceptual distances can bring benefits in terms of
discriminatory power, observers' cognitive load, and the number of trials
required. One of the disadvantages of the MLDS method is that the perceptual
scales obtained for stimuli created from different source content are generally
not comparable. In this paper, we propose an extension of the MLDS method that
ensures inter-content comparability of the results and shows its usefulness
especially in the presence of observer errors.


title: Effect of relativity and vacuum fluctuations on quantum measurement

abstract:
  Vacuum fluctuations can obscure the detection signal of the measurement of
the smallest quantum objects like single particles seemingly implying a
fundamental limit to measurement accuracy. However, as we show relativistic
invariance implies the disappearance of fluctuations for the space-like
%frequency-wavevector spectrum of an observable at zero temperature. This
complete absence of noise can be harnessed to perform noiseless measurement of
single particles, as we illustrate for electrons or photons. We outline a
general scheme to illustrate the noiseless measurement involving the space-like
spectrum of observables based on the self-interference of counter-propagating
paths of a single particle in a triangular Sagnac interferometer.


title:
Derivation of an Inverse Spatial Autoregressive Model for Estimating
  Moran's Index

abstract:
  Spatial autocorrelation measures such as Moran's index can be expressed as a
pair of equations based on a standardized size variable and a globally
normalized weight matrix. One is based on inner product, and the other is based
on outer product of the size variable. The inner product equation is actually a
spatial autocorrelation model. However, the theoretical basis of the inner
product equation for Moran's index is not clear. This paper is devoted to
revealing the antecedents and consequences of the inner product equation of
Moran's index. The method is mathematical derivation and empirical analysis.
The main results are as follows. First, the inner product equation is derived
from a simple spatial autoregressive model, and thus the relation between
Moran's index and spatial autoregressive coefficient is clarified. Second, the
least squares regression is proved to be one of effective approaches for
estimating Moran's index and spatial autoregressive coefficient. Third, the
value ranges of the Moran's index and spatial autoregressive coefficient can be
identified from three angles of view. A conclusion can be drawn that spatial
autocorrelation model is actually an inverse spatial autoregressive model, and
Moran's index, spatial autoregressive models, and canonical Moran's scatterplot
can be integrated into the same framework through inner product and outer
product equations. This work may be helpful for understanding the connections
and differences between spatial autocorrelation measurements and spatial
autoregressive modeling.


title: A remark on a proof of $[G, L]=0$ for a Lie group $G$

abstract:
  In this note we give an improvement of our proof of $[G, L]=0$ for a compact
framed Lie group $(G, L)$, which depends heavily on the choice of a circle
subgroup $S\subset G$. We attempt here to make a more suitable choice of this
circle subgroup.


title: GEMA: An open-source Python library for self-organizing-maps

abstract:
  Organizations have realized the importance of data analysis and its benefits.
This in combination with Machine Learning algorithms has allowed to solve
problems more easily, making these processes less time-consuming. Neural
networks are the Machine Learning technique that is recently obtaining very
good best results. This paper describes an open-source Python library called
GEMA developed to work with a type of neural network model called
Self-Organizing-Maps. GEMA is freely available under GNU General Public License
at GitHub (https://github.com/ufvceiec/GEMA). The library has been evaluated in
different a particular use case obtaining accurate results.


title: The Lorentz factor in a reverse coordinate system

abstract:
  In the present study, we have derived the Lorentz factor using a coordinate
system with antiparallel X-axes. Using a thought experiment, common in
relativistic literature, we have used the case of a pulse of light moving along
the X-axis. Next, we have argued that, consequently with the isotropy of space,
the result must be the same if the trajectory of the light pulse is any angle
$\alpha>0^{\circ}$, thus obtaining an alternative transformation factor that
generates the same results as the Lorenz factor at any angle of the trajectory
of the light pulse, therefore confirming the relativistic isotropy of space in
the context of the Minkowski spacetime. Nevertheless, a particularly important
novelty is that the derived alternative transformation factor allows the
reference frames involved to move at speeds greater than that of light.


title: Impact of Delay on Predator-Prey Models

abstract:
  Mathematical modeling based on time-delay differential equations is an
important tool to study the role of delay in biological systems and to evaluate
its impact on the asymptotic behavior of their dynamics. Delays are indeed
found in many biological, physical, and engineering systems and are a
consequence of the limited speed at which physiological, chemical, or
biological processes are transmitted from one place to another. Since real
biological systems are always subject to perturbations that are not fully
understood or cannot be explicitly modeled, stochastic delay differential
systems (SDDEs) provide a more realistic approximation to these models. In this
work, we study the predator-prey system considering three time delay models:
one deterministic and two types of stochastic models. Our numerical results
show relevant differences in their respective asymptotic behaviors.


title:
Modeling-informed policy, policy evaluated by modeling: Evolution of
  mathematical epidemiology in the context of society and economy

abstract:
  The COronaVIrus Disease 2019 (COVID-19) pandemic that has had the world in
its grip from the beginning of 2020, has resulted in an unprecedented level of
public interest and media attention on the field of mathematical epidemiology.
Ever since the disease came to worldwide attention, numerous models with
varying levels of sophistication have been proposed; many of these have tried
to predict the course of the disease over different time-scales. Other models
have examined the efficacy of various policy measures that have been adopted
(including the unparalleled use of "lockdowns") to contain and combat the
disease. This multiplicity of models may have led to bewilderment in many
quarters about the true capabilities and utility of mathematical modeling. Here
we provide a brief guide to epidemiological modeling, focusing on how it has
emerged as a tool for informed public-health policy-making and has in turn,
influenced the design of interventions aimed at preventing disease outbreaks
from turning into raging epidemics. We show that the diversity of models is
somewhat illusory, as the bulk of them are rooted in the compartmental modeling
framework that we describe here. While their basic structure may appear to be a
highly idealized description of the processes at work, we show that features
that provide more realism, such as the community organization of populations or
strategic decision-making by individuals, can be incorporated into such models.
We conclude with the argument that the true value of models lies in their
ability to test in silico the consequences of different policy choices in the
course of an epidemic, a much superior alternative to trial-and-error
approaches that are highly costly in terms of both lives and socio-economic
disruption.


title:
Temporal Heterogeneity Improves Speed and Convergence in Genetic
  Algorithms

abstract:
  Genetic algorithms have been used in recent decades to solve a broad variety
of search problems. These algorithms simulate natural selection to explore a
parameter space in search of solutions for a broad variety of problems. In this
paper, we explore the effects of introducing temporal heterogeneity in genetic
algorithms. In particular, we set the crossover probability to be inversely
proportional to the individual's fitness, i.e., better solutions change slower
than those with a lower fitness. As case studies, we apply heterogeneity to
solve the $N$-Queens and Traveling Salesperson problems. We find that temporal
heterogeneity consistently improves search without having prior knowledge of
the parameter space.


title:
Novel Metric based on Walsh Coefficients for measuring problem
  difficulty in Estimation of Distribution Algorithms

abstract:
  Estimation of distribution algorithms are evolutionary algorithms that use
extracted information from the population instead of traditional genetic
operators to generate new solutions. This information is represented as a
probabilistic model and the effectiveness of these algorithms is dependent on
the quality of these models. However, some studies have shown that even
multivariate EDAs fail to build a proper model in some problems. Usually, in
these problems, there is intrinsic pairwise independence between variables. In
the literature, there are few studies that investigate the difficulty and the
nature of problems that can not be solved by EDAs easily. This paper proposes a
new metric for measuring problem difficulty by examining the properties of
model-building mechanisms in EDAs. For this purpose, we use the estimated Walsh
coefficients of dependent and independent variables. The proposed metric is
used to evaluate the difficulty of some well-known benchmark problems in EDAs.
Different metrics like Fitness Distance Correlation (FDC) are used to compare
how well the proposed metric measures problem difficulty for EDAs. Results
indicate that the proposed metric can accurately predict the EDA's performance
in different problems.


title: Does Time exist? -- catchphrases and concepts

abstract:
  This paper lends perspective to the media catchphrase that <time does not
exist>. To show how phrases such as this should be interpreted, we formulate
some of the most important questions that arise in discussions about time in
physics. We start by analyzing Newton's objective view on time and explain how
entropy gives it a direction. After that, we discuss how relativity distances
us from Newton's views, while quantum theory brings us closer to the Newtonian
view. The arguments are presented in such a way that they can be followed and
checked by anyone who studies the theories involved - be they undergraduate
physics students or otherwise.


title: Carroll covariant scalar fields in two dimensions

abstract:
  Conformal Carroll symmetry generically arises on null manifolds and is
important for holography of asymptotically flat spacetimes, generic black hole
horizons and tensionless strings. In this paper, we focus on two dimensional
(2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the
3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the
most general free massless Carroll scalar field theory and discover three
inequivalent actions. Of these, two viz. the time-like and space-like actions,
have made their appearance in literature before. We uncover a third that we
call the mixed-derivative theory. As expected, all three theories enjoy
off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of
mixed derivative theory is a single Virasoro algebra instead of the full BMS.
We discuss potential applications to tensionless strings and flat holography.


title: Dynamical properties of neuromorphic Josephson junctions

abstract:
  Neuromorphic computing exploits the dynamical analogy between many physical
systems and neuron biophysics. Superconductor systems, in particular, are
excellent candidates for neuromorphic devices due to their capacity to operate
in great speeds and with low energy dissipation compared to their silicon
counterparts. In this study we revisit a prior work on Josephson Junction-based
"neurons" in order to identify the exact dynamical mechanisms underlying the
system's neuron-like properties and reveal new complex behaviors which are
relevant for neurocomputation. Our work lies at the intersection of
superconducting physics and theoretical neuroscience, both viewed under a
common framework, that of nonlinear dynamics theory.


title: Snowmass 2021 White Paper: Electron Ion Collider for High Energy Physics

abstract:
  Electron Ion Collider (EIC) is a particle accelerator facility planned for
construction at Brookhaven National Laboratory on Long Island, New York by the
United States Department of Energy. EIC will provide capabilities of colliding
beams of polarized electrons with polarized beams of proton and light ions. EIC
will be one of the largest and most sophisticated new accelerator facilities
worldwide, and the only new large-scale accelerator facility planned for
construction in the United States in the next few decades. The versatility,
resolving power and intensity of EIC will present many new opportunities to
address some of the crucial and fundamental open scientific questions in
particle physics. This document provides an overview of the science case of EIC
from the perspective of the high energy physics community.


title:
Modified Hamiltonian for a particle in an infinite box that includes
  wall effects

abstract:
  We give a modified Hamiltonian for a particle in a box with infinite
potential walls that takes into account wall effects. The Hamiltonian is
expressed in both the position and momentum representation. In the momentum
representation the eigenvalue problem for energy is an integral equation.


title: Effective Medium Perspective on Topological Transitions in Metamaterials

abstract:
  Many properties of photonic structures rely on band topology characterized by
the integer invariants that can change during the topological transitions and
give rise to the disorder-robust topological edge, corner, or interface states.
Typically the periods of such structures are comparable to the wavelength.
However, in many cases, the unit cell becomes deeply subwavelength and hence
the entire metamaterial can be described in terms of the effective material
parameters. Here, focusing on subwavelength topological metamaterials, we
identify the behavior of permittivity and permeability accompanying the
topological transition on the example of the two structures possessing $D_6$
symmetry.


title: Multi Expression Programming for solving classification problems

abstract:
  Multi Expression Programming (MEP) is a Genetic Programming variant which
encodes multiple solutions in a single chromosome. This paper introduces and
deeply describes several strategies for solving binary and multi-class
classification problems within the \textit{multi solutions per chromosome}
paradigm of MEP. Extensive experiments on various classification problems are
performed. MEP shows similar or better performances than other methods used for
comparison (namely Artificial Neural Networks and Linear Genetic Programming).


title: Constrained Parameter Inference as a Principle for Learning

abstract:
  Learning in biological and artificial neural networks is often framed as a
problem in which targeted error signals guide parameter updating for more
optimal network behaviour. Backpropagation of error (BP) is an example of such
an approach and has proven to be a highly successful application of stochastic
gradient descent to deep neural networks. However, BP relies on the global
transmission of gradient information and has therefore been criticised for its
biological implausibility. We propose constrained parameter inference (COPI) as
a new principle for learning. COPI allows for the estimation of network
parameters under the constraints of decorrelated neural inputs and top-down
perturbations of neural states. We show that COPI is not only more biologically
plausible but also provides distinct advantages for fast learning, compared
with the backpropagation algorithm.


title:
Decouple-and-Sample: Protecting sensitive information in task agnostic
  data release

abstract:
  We propose sanitizer, a framework for secure and task-agnostic data release.
While releasing datasets continues to make a big impact in various applications
of computer vision, its impact is mostly realized when data sharing is not
inhibited by privacy concerns. We alleviate these concerns by sanitizing
datasets in a two-stage process. First, we introduce a global decoupling stage
for decomposing raw data into sensitive and non-sensitive latent
representations. Secondly, we design a local sampling stage to synthetically
generate sensitive information with differential privacy and merge it with
non-sensitive latent features to create a useful representation while
preserving the privacy. This newly formed latent information is a task-agnostic
representation of the original dataset with anonymized sensitive information.
While most algorithms sanitize data in a task-dependent manner, a few
task-agnostic sanitization techniques sanitize data by censoring sensitive
information. In this work, we show that a better privacy-utility trade-off is
achieved if sensitive information can be synthesized privately. We validate the
effectiveness of the sanitizer by outperforming state-of-the-art baselines on
the existing benchmark tasks and demonstrating tasks that are not possible
using existing techniques.


title: Honeycombs in the Pascal triangle and beyond

abstract:
  In this paper we present a geometric approach to discovering some known and
some new identities using triangular arrays. Our main aim is to demonstrate how
to use the geometric patterns (by Carlitz), in the Pascal and Hosoya triangles
to rediscover some classical identities and integer sequences. Therefore, we
use new techniques in classical settings which then provide a new perspective
in undergraduate research.


title: Introduction to Quantum Optics

abstract:
  These are the lecture notes for a course that I am teaching at Zhiyuan
College of Shanghai Jiao Tong University (available at
https://www.youtube.com/derekkorg), though the first draft was created for a
previous course I taught at the University of Erlangen-Nuremberg in Germany. It
has been designed for students who have only had basic training on quantum
mechanics, and hence, the course is suited for people at all levels. The notes
are a work in progress, meaning that some proofs and many figures are still
missing. However, I've tried my best to write everything in such a way that a
reader can follow naturally all arguments and derivations even with these
missing bits. Quantum optics treats the interaction between light and matter.
We may think of light as the optical part of the electromagnetic spectrum, and
matter as atoms. However, modern quantum optics covers a wild variety of
systems, including superconducting circuits, confined electrons, excitons in
semiconductors, defects in solid state, or the center-of-mass motion of micro-,
meso-, and macroscopic systems. Moreover, quantum optics is at the heart of the
field of quantum information. The ideas and experiments developed in quantum
optics have also allowed us to take a fresh look at many-body problems and even
high-energy physics. In addition, quantum optics holds the promise of testing
foundational problems in quantum mechanics as well as physics beyond the
standard model in table-sized experiments. Quantum optics is therefore a topic
that no future researcher in quantum physics should miss.


title:
Supervised Training of Siamese Spiking Neural Networks with Earth's
  Mover Distance

abstract:
  This study adapts the highly-versatile siamese neural network model to the
event data domain. We introduce a supervised training framework for optimizing
Earth's Mover Distance (EMD) between spike trains with spiking neural networks
(SNN). We train this model on images of the MNIST dataset converted into
spiking domain with novel conversion schemes. The quality of the siamese
embeddings of input images was evaluated by measuring the classifier
performance for different dataset coding types. The models achieved performance
similar to existing SNN-based approaches (F1-score of up to 0.9386) while using
only about 15% of hidden layer neurons to classify each example. Furthermore,
models which did not employ a sparse neural code were about 45% slower than
their sparse counterparts. These properties make the model suitable for low
energy consumption and low prediction latency applications.


title:
Direct Photons in Hydrodynamic Modeling of Relativistic Nuclear
  Collisions

abstract:
  We review direct photons in the phenomenology of nuclear collisions at
relativistic energies. Direct photons carry information about the space-time
evolution of nuclear collisions because the QCD medium is transparent against
colorless particles. After a status summary of theoretical and experimental
studies, transverse momentum spectra and azimuthal momentum anisotropies of
direct photons are studied in the context of the hydrodynamic modeling of
relativistic nuclear collisions with emphasis on pre-equilibrium photons. It is
implied that pre-equilibrium photons can be as important as thermal and prompt
photons for comprehensive understanding of direct photon production.


title: Direct parsing to sentiment graphs

abstract:
  This paper demonstrates how a graph-based semantic parser can be applied to
the task of structured sentiment analysis, directly predicting sentiment graphs
from text. We advance the state of the art on 4 out of 5 standard benchmark
sets. We release the source code, models and predictions.


title:
A comparison of two frameworks for multi-state modelling, applied to
  outcomes after hospital admissions with COVID-19

abstract:
  We compare two multi-state modelling frameworks that can be used to represent
dates of events following hospital admission for people infected during an
epidemic. The methods are applied to data from people admitted to hospital with
COVID-19, to estimate the probability of admission to ICU, the probability of
death in hospital for patients before and after ICU admission, the lengths of
stay in hospital, and how all these vary with age and gender. One modelling
framework is based on defining transition-specific hazard functions for
competing risks. A less commonly used framework defines partially-latent
subpopulations who will experience each subsequent event, and uses a mixture
model to estimate the probability that an individual will experience each
event, and the distribution of the time to the event given that it occurs. We
compare the advantages and disadvantages of these two frameworks, in the
context of the COVID-19 example. The issues include the interpretation of the
model parameters, the computational efficiency of estimating the quantities of
interest, implementation in software and assessing goodness of fit. In the
example, we find that some groups appear to be at very low risk of some events,
in particular ICU admission, and these are best represented by using
"cure-rate" models to define transition-specific hazards. We provide
general-purpose software to implement all the models we describe in the
"flexsurv" R package, which allows arbitrarily-flexible distributions to be
used to represent the cause-specific hazards or times to events.


title:
The normal bundle of a general canonical curve of genus at least 7 is
  semistable

abstract:
  Let $C$ be a general canonical curve of genus $g$ defined over an
algebraically closed field of arbitrary characteristic. We prove that if $g
\notin \{4,6\}$, then the normal bundle of $C$ is semistable. In particular, if
$g \equiv 1$ or $3$ mod $6$, then the normal bundle is stable.


title:
The partial uniform ellipticity and prescribed problems on the conformal
  classes of complete metrics

abstract:
  We clarify how close a second order fully nonlinear equation can come to
uniform ellipticity, through showing an inequality for the linearized operator.
As applications, we study prescribed problems for complete conformal metrics,
where a sufficient and necessary condition is derived for existence of complete
noncompact conformal metrics with prescribed curvature functions. Our method is
delicate as shown by a topological obstruction.


title:
Localization of Pairs in One-Dimensional Quasicrystals with Power-Law
  Hopping

abstract:
  Pair localization in one-dimensional quasicrystals with nearest-neighbor
hopping is independent of whether short-range interactions are repulsive or
attractive. We numerically demonstrate that this symmetry is broken when the
hopping follows a power law $1/r^{\alpha}$. In particular, for repulsively
bound states, we find that the critical quasiperiodicity that signals the
transition to localization is always bounded by the standard Aubry-Andr\'e
critical point, whereas attractively bound dimers get localized at larger
quasiperiodic modulations when the range of the hopping increases. Extensive
numerical calculations establish the contrasting nature of the pair energy gap
for repulsive and attractive interactions, as well as the behavior of the
algebraic localization of the pairs as a function of quasiperiodicity,
interaction strength, and power-law hops. The results here discussed are of
direct relevance to the study of the quantum dynamics of systems with power-law
couplings.


title:
A Perturbation Constrained Adversarial Attack for Evaluating the
  Robustness of Optical Flow

abstract:
  Recent optical flow methods are almost exclusively judged in terms of
accuracy, while analyzing their robustness is often neglected. Although
adversarial attacks offer a useful tool to perform such an analysis, current
attacks on optical flow methods rather focus on real-world attacking scenarios
than on a worst case robustness assessment. Hence, in this work, we propose a
novel adversarial attack - the Perturbation Constrained Flow Attack (PCFA) -
that emphasizes destructivity over applicability as a real-world attack. More
precisely, PCFA is a global attack that optimizes adversarial perturbations to
shift the predicted flow towards a specified target flow, while keeping the L2
norm of the perturbation below a chosen bound. Our experiments not only
demonstrate PCFA's applicability in white- and black-box settings, but also
show that it finds stronger adversarial samples for optical flow than previous
attacking frameworks. Moreover, based on these strong samples, we provide the
first common ranking of optical flow methods in the literature considering both
prediction quality and adversarial robustness, indicating that high quality
methods are not necessarily robust. Our source code will be publicly available.


title: Neural Neighbor Style Transfer

abstract:
  We propose Neural Neighbor Style Transfer (NNST), a pipeline that offers
state-of-the-art quality, generalization, and competitive efficiency for
artistic style transfer. Our approach is based on explicitly replacing neural
features extracted from the content input (to be stylized) with those from a
style exemplar, then synthesizing the final output based on these rearranged
features. While the spirit of our approach is similar to prior work, we show
that our design decisions dramatically improve the final visual quality.


title:
Complex Frequency Domain Linear Prediction: A Tool to Compute Modulation
  Spectrum of Speech

abstract:
  Conventional Frequency Domain Linear Prediction (FDLP) technique models the
squared Hilbert envelope of speech with varied degrees of approximation which
can be sampled at the required frame rate and used as features for Automatic
Speech Recognition (ASR). Although previously the complex cepstrum of the
conventional FDLP model has been used as compact frame-wise speech features, it
has lacked interpretability in the context of the Hilbert envelope. In this
paper, we propose a modification of the conventional FDLP model that allows
easy interpretability of the complex cepstrum as temporal modulations in an
all-pole model approximation of the power of the speech signal. Additionally,
our "complex" FDLP yields significant speed-ups in comparison to conventional
FDLP for the same degree of approximation.


title:
A global analysis of $b \to s \ell \ell$ data in heavy and light $Z'$
  models

abstract:
  We perform a model-independent global fit to all $b \to s \ell \ell$ data in
the light of recent measurements of the lepton flavour universality violating
(LFUV) observables $R_{K_S^0}$ and $R_{K^{*+}}$ as well as the updated
measurements of observables in $B_s \to \phi \mu^+ \mu^-$ decay, by the LHCb
collaboration. We obtain new physics (NP) solutions to the current anomalies in
the data, assuming NP in the muon sector only. We find that the 1D NP scenarios
$C_9^{\rm NP} <0 $ and $C_{9}^{\rm NP}=-C_{10}^{\rm NP}$ continue to be the
most favoured ones. However, the significance of the then favoured scenario
$C_{9}^{\rm NP}=-C'_{9}$ has reduced and the updated data now marginally
prefers $C_{10}^{\rm NP}$ scenario over $C_{9}^{\rm NP}=-C'_{9}$. The 2D
scenarios $(C_9^{\rm NP}, C_{10}^{\prime} )$, $(C_9^{\rm NP}, C_{9}^{\prime} )$
and $(C_9^{\rm NP}, C_{10}^{\rm NP} )$, continue to be favoured by the data in
the listed order. We also analyse generic TeV scale $Z'$ models which can
generate the favored 1D scenarios, $C_9^{\rm NP} $ and $C_9^{\rm NP} =
-C_{10}^{\rm NP}$ along with the 2D NP scenarios $(C_9^{\rm NP}, C_{9}^{\prime}
)$ and $(C_9^{\rm NP}, C_{10}^{\rm NP} )$. Using the additional constraints
from $B_s -\bar{B_s}$ mixing and neutrino trident data, we find that all four
models provide an equally good fit to the data. Further, we consider a model
with a 25 MeV $Z'$ that couples to muons and has a $q^2$ dependent $b - s$
coupling. We also study the implications of the current data on the LFUV
observable $R_{\phi}$, $Q_{4,5}$ along with $R_{K^{(*)}}$ in the high $q^2$. We
find that a precise measurements of these observables can provide a good
discrimination between a few favored model-independent solutions, and have a
potential to disentangle different heavy and light $Z'$ scenarios considered in
this work.


title: Fermi Bubbles in Scalar Field Dark Matter halos

abstract:
  In recent times, the Scalar Field Dark Matter (SFDM) model (also called
Fuzzy, Wave, Ultralight dark matter model) has received much attention due to
its success in describing dark matter on both cosmological and galactic scales.
Several challenges of the Cold Dark Matter (CDM) model can be explained very
easily and naturally by the SFDM model. Two of these challenges are to describe
the anomalous trajectories of satellite galaxies called the Vast Polar
Structure (VPOS) and to explain the Fermi Bubbles (FB) observed in our galaxy.
In Phys.Rev.D103(2021)083535 an alternative explanation for VPOS was shown
using the SFDM excited states, explaining the anomalous trajectories in a
natural and simple way. In this work we use the same dark matter structure to
show that these excited states of the SFDM can provide a very simple and
natural explanation for the FB, assuming that the SFDM is a kind of dark boson.
If this assumption is correct, we should see FB in several more galaxies and
continue to see gamma-ray events at higher energies, these observations would
take place in the near future and could be crucial to the ultimate answer to
the nature of dark matter.


title:
Amphiphilic co-polymer network gel films based on tetra-poly(ethylene
  glycol) and tetra-poly({\epsilon}-caprolactone)

abstract:
  In order to allow the simultaneous transport of hydrophilic and hydrophobic
substances, polymeric networks with finely distributed hydrophilic and
hydrophobic components are very suitable. When designing new soft materials
like coatings, in addition to the structure in the volume phase, the structure
at the interface plays a critical role. In this study, two alternating
tetra-arm star polymers poly({\epsilon}-caprolactone) (tetra-PCL-Ox) and
amino-terminated poly(ethylene glycol) (tetra-PEG-NH2) form an amphiphilic
co-polymer network. They serve as a model system for controlling and
understanding the structure-property relationship at the interface of ACN gels.
The correlation between different synthesis strategies for gel films and their
resulting properties will be described. Through various spin coating
techniques, control over film thickness and roughness is achievable and
highlights differences to macroscopic gel samples. Atomic force microscopy
(AFM) measurements reveal the effect of solvents of different polarities on the
swelling ability and surface structure. This correlates with AFM investigations
of the mechanical properties on ACN gel films, demonstrating a strong effect on
the resulting elastic modulus E, depending on the presence or absence of a good
solvent during synthesis. Furthermore, a higher E modulus is obtained in the
presence of the selective solvent water, compared to the non-selective solvent
toluene. This observation is explained through selective swelling of the
tetra-arm star polymers displaying a different hydrophobicity.


title: Quantum Melting in a Polariton Lattice

abstract:
  Inspired by the recent experimental observation of strongly coupled
polaritons in a Moir\'e heterobilayer, we study a model of dipole-interacting
excitons localized on sites of a lattice and coupled to planar cavity photons.
We calculate the phase diagram of this system by computing fluctuations around
the mean field and determining the stability of the excitation spectrum. We
find that the transition from the normal state to a polariton condensate is
intermediated by a series of ordered states at partial fillings of the exciton
lattice, stabilized by the exciton interactions. In particular we predict a
supersolid phase in which a polariton condensate coexists with spatial order.


title:
The Promise and Limitations of Precision Gravity: Application to the
  Interior Structure of Uranus and Neptune

abstract:
  We study the constraining power of a high-precision measurement of the
gravity field for Uranus and Neptune, as could be delivered by a low periapse
orbiter. Our study is practical, assessing the possible deliverables and
limitations of such a mission with respect to the structure of the planets. Our
study is also academic, assessing in a general way the relative importance of
the low order gravity, high order gravity, rotation rate, and moment of inertia
(MOI) in constraining planetary structure. We attempt to explore all possible
interior density structures of a planet that are consistent with hypothetical
gravity data, via MCMC sampling of parameterized density profiles. When the
gravity field is poorly known, as it is today, uncertainties in the rotation
rate on the order of 10 minutes are unimportant, as they are interchangeable
with uncertainties in the gravity coefficients. By the same token, when the
gravity field is precisely determined the rotation rate must be known to
comparable precision. When gravity and rotation are well known the MOI becomes
well-constrained, limiting the usefulness of independent MOI determinations
unless they are extraordinarily precise. For Uranus and Neptune, density
profiles can be well-constrained. However, the non-uniqueness of the relative
roles of H/He, watery volatiles, and rock in the deep interior will still
persist with high-precision gravity data. Nevertheless, the locations and
magnitudes (in pressure-space) of any large-scale composition gradient regions
can likely be identified, offering a crucially better picture of the interiors
of Uranus or Neptune.


title:
Stability analysis of hybrid systems with higher order transverse
  discontinuity mapping

abstract:
  This article generalizes the implementation of higher order corrections to
state transition matrices during instantaneous reversals in hybrid dynamical
systems impacting a discontinuity boundary transversally. A closed form
expression for saltation terms in systems possessing a degree of smoothness
zero is derived. The difference in flight times of two closely initiated
trajectories in state space to the impacting surface has been estimated up to
$\mathcal{O}(2)$. A comparison of the times of impact estimated with the first
order approximation reveals that higher order corrections lead to a significant
improvement of estimates. Next, two new algorithms to estimate the Lyapunov
spectrum and Floquet multipliers for piecewise-smooth systems have been
presented using the derived second order corrections. Stability analyses are
subsequently carried out using the proposed framework for two representative
cases {\it i.e.,} of a hard impact oscillator and a pair impact oscillator. It
is established that the obtained Floquet multipliers and Lyapunov spectrum
accurately predict the stability of the dynamical states, as validated by their
corresponding bifurcation diagrams.


title:
Inverse Nodal Problems for Dirac Type Integro Differential System with a
  Nonlocal Boundary Condition

abstract:
  In this work, the Dirac-type integro di{\S}erential system with one classical
boundary condition and another nonlocal integral boundary condition is
considered. We obtain the asymptotic formulae for the solutions, eigenvalues
and nodal points. We also investigate the inverse nodal problem and prove that
given a dense subset of nodal points uniquely determines the boundary condition
parameter and the potential function of the considered di{\S}erential system.
We also provide an e{\S}ective procedure for solving the inverse nodal problem.


title:
Language Models that Seek for Knowledge: Modular Search & Generation for
  Dialogue and Prompt Completion

abstract:
  Language models (LMs) have recently been shown to generate more factual
responses by employing modularity (Zhou et al., 2021) in combination with
retrieval (Adolphs et al., 2021). We extend the recent approach of Adolphs et
al. (2021) to include internet search as a module. Our SeeKeR (Search
engine->Knowledge->Response) method thus applies a single LM to three modular
tasks in succession: search, generating knowledge, and generating a final
response. We show that, when using SeeKeR as a dialogue model, it outperforms
the state-of-the-art model BlenderBot 2 (Chen et al., 2021) on open-domain
knowledge-grounded conversations for the same number of parameters, in terms of
consistency, knowledge and per-turn engagingness. SeeKeR applied to topical
prompt completions as a standard language model outperforms GPT2 (Radford et
al., 2019) and GPT3 (Brown et al., 2020) in terms of factuality and topicality,
despite GPT3 being a vastly larger model. Our code and models are made publicly
available.


title: Distributionally Robust Optimization via Ball Oracle Acceleration

abstract:
  We develop and analyze algorithms for distributionally robust optimization
(DRO) of convex losses. In particular, we consider group-structured and bounded
$f$-divergence uncertainty sets. Our approach relies on an accelerated method
that queries a ball optimization oracle, i.e., a subroutine that minimizes the
objective within a small ball around the query point. Our main contribution is
efficient implementations of this oracle for DRO objectives. For DRO with $N$
non-smooth loss functions, the resulting algorithms find an $\epsilon$-accurate
solution with $\widetilde{O}\left(N\epsilon^{-2/3} + \epsilon^{-2}\right)$
first-order oracle queries to individual loss functions. Compared to existing
algorithms for this problem, we improve complexity by a factor of up to
$\epsilon^{-4/3}$.


title: SMARAGD: Synthesized sMatch for Accurate and Rapid AMR Graph Distance

abstract:
  The semantic similarity of graph-based meaning representations, such as
Abstract Meaning Representation (AMR), is typically assessed using graph
matching algorithms, such as SMATCH (Cai and Knight, 2013). However, SMATCH
suffers from NP-completeness, making its large-scale application, e.g., for AMR
clustering or semantic search, infeasible. To mitigate this issue, we propose
SMARAGD (Synthesized sMatch for accurate and rapid AMR graph distance). We show
the potential of neural networks to approximate the SMATCH scores and graph
alignments, i) in linear time using a machine translation framework to predict
the alignments, or ii) in constant time using a Siamese CNN to directly predict
SMATCH scores. We show that the approximation error can be substantially
reduced by applying data augmentation and AMR graph anonymization.


title:
Influence of implantation induced defects on the thermoelectric
  properties of ScN

abstract:
  Epitaxial 111 oriented ScN thin films deposited by magnetron sputtering were
implanted with argon ions at high fluences to introduce defects in order to
reduce the thermal conductivity and thus increase the thermoelectric figure of
merit. The films were investigated by structural, electrical, optical and
thermoelectric characterisation methods. The results show that argon
implantation leads to the formation of stable defects (up to 750 K operating
temperature) which are identified as interstitial type defect clusters and
argon-vacancy complexes. These defects induce acceptor-type deep levels in the
bandgap and reduce the free carrier mobility. The effect on the power factor
remains low due to the large drop in resistivity induced by the implantation
which is compensated by an increase of the absolute value of the Seebeck
coefficient. However, the thermal conductivity is strongly reduced by a factor
of 4 (3 W.m-1.K-1 at 300 K). Subsequent high temperature annealing, at 1573 K,
leads to the progressive evolution of defects: the clusters of interstitials
grow to the benefit of smaller ones and bubbles are formed. Thus, the number of
free carriers, the resistivity and the Seebeck coefficient are almost restored
but the mobility of the carriers remains low and a 30% drop in thermal
conductivity is still effective (8.5 W.m-1.K-1). In a more general way, this
study shows that the controlled introduction of defects as the
implantation-defect engineering can be an attractive method to enhance the
figure of merit of thermoelectric materials.