  The concept of image similarity is ambiguous, and images can be similar in
one context and not in another. This ambiguity motivates the creation of
metrics for specific contexts. This work explores the ability of deep
perceptual similarity (DPS) metrics to adapt to a given context. DPS metrics
use the deep features of neural networks for comparing images. These metrics
have been successful on datasets that leverage the average human perception in
limited settings. But the question remains if they could be adapted to specific
similarity contexts. No single metric can suit all similarity contexts, and
previous rule-based metrics are labor-intensive to rewrite for new contexts. On
the other hand, DPS metrics use neural networks that might be retrained for
each context. However, retraining networks takes resources and might ruin
performance on previous tasks. This work examines the adaptability of DPS
metrics by training ImageNet pretrained CNNs to measure similarity according to
given contexts. Contexts are created by randomly ranking six image distortions.
Distortions later in the ranking are considered more disruptive to similarity
when applied to an image for that context. This also gives insight into whether
the pretrained features capture different similarity contexts. The adapted
metrics are evaluated on a perceptual similarity dataset to evaluate if
adapting to a ranking affects their prior performance. The findings show that
DPS metrics can be adapted with high performance. While the adapted metrics
have difficulties with the same contexts as baselines, performance is improved
in 99% of cases. Finally, it is shown that the adaption is not significantly
detrimental to prior performance on perceptual similarity. The implementation
of this work is available online:
https://github.com/LTU-Machine-Learning/Analysis-of-Deep-Perceptual-Loss-Networks


  The nature of transverse momentum dependence of the inclusive cross-sections
for secondary pions produced in high energy hadronic($PP$), hadronuclear($PA$)
and nuclear($AA$) collisions has here been exhaustively investigated for a
varied range of interactions in a unified way with the help of a master
formula. This formula evolved from a new combination of the basic Hagedorn's
model for particle(pion) production in PP scattering at ISR range of energies,
a phenomenological approach proposed by Peitzmann for converting the results of
$NN(PP)$ reactions to those for either $PA$ or $AA$ collisions, and a specific
form of parametrization for mass number-dependence of the nuclear cross
sections. This grand combination of models(GCM) is then applied to analyse the
assorted extensive data on various high energy collisions. The nature of
qualitative agreement between measurements and calculations on both the
inclusive cross-sections for production of pions, and some ratios of them as
well, is quite satisfactory. The modest successes that we achieve here in
dealing with the massive data-sets are somewhat encouraging in view of the
diversity of the reactions and the very wide range of interaction energies.


  Objective. Many electroencephalogram (EEG)-based brain-computer interface
(BCI) systems use a large amount of channels for higher performance, which is
time-consuming to set up and inconvenient for practical applications. Finding
an optimal subset of channels without compromising the performance is a
necessary and challenging task. Approach. In this article, we proposed a
cross-correlation based discriminant criterion (XCDC) which assesses the
importance of a channel for discriminating the mental states of different motor
imagery (MI) tasks. Channels are ranked and selected according to the proposed
criterion. The efficacy of XCDC is evaluated on two motor imagery EEG datasets.
Main results. In both datasets, XCDC significantly reduces the amount of
channels without compromising classification accuracy compared to the
all-channel setups. Under the same constraint of accuracy, the proposed method
requires fewer channels than existing channel selection methods based on
Pearson's correlation coefficient and common spatial pattern. Visualization of
XCDC shows consistent results with neurophysiological principles. Significance.
This work proposes a quantitative criterion for assessing and ranking the
importance of EEG channels in MI tasks and provides a practical method for
selecting the ranked channels in the calibration phase of MI BCI systems, which
alleviates the computational complexity and configuration difficulty in the
subsequent steps, leading to real-time and more convenient BCI systems.


  We investigate the dynamics of test particles undergoing friction forces in a
Friedmann-Robertson-Walker (FRW) spacetime. The interaction with the background
fluid is modeled by introducing a Poynting-Robertson-like friction force in the
equations of motion, leading to measurable (at least in principle) deviations
of the particle trajectories from geodesic motion. The effect on the peculiar
velocities of the particles is investigated for various equations of state of
the background fluid and different standard cosmological models. The friction
force is found to have major effects on particle motion in closed FRW
universes, where it turns the time-asymptotic value (approaching the
recollapse) of the peculiar particle velocity from ultra-relativistic (close to
light speed) to a co-moving one, i.e., zero peculiar speed. On the other hand,
for open or flat universes the effect of the friction is not so significant,
because the time-asymptotic peculiar particle speed is largely non-relativistic
also in the geodesic case.


  Starting from the well-known light-clock thought experiment to derive time
dilation and length contraction, it is shown that finding the Lorentz
Transformation requires nothing more than the most trivial vector addition
formula. The form which is obtaine for the L.T. allows an easy derivation of
the velocity and acceleration transformations which are also given.


  The prime number problem falls within the realm of number theory,
specifically elementary number theory. Current research approaches have
unnecessarily complicated this matter. In contrast to more advanced
mathematical tools, the methods of elementary number theory can effectively
address the twin prime problem. The primary contribution of this article lies
in establishing a set that systematically includes all twin prime pairs without
omissions. This set's distribution is governed by a precise general solution
formula. Furthermore, an analysis of the distribution set reveals
characteristics of parity balance, enabling us to determine whether twin prime
pairs are finite. Finally, our method can be extended to the general case of
twin primes, such as the Polignac's conjecture.


  We present a frequency domain reduced order model (ROM) for the aligned-spin
effective-one-body (EOB) model for binary black holes (BBHs) SEOBNRv4HM that
includes the spherical harmonics modes $(\ell, |m|) = (2,1),(3,3),(4,4),(5,5)$
beyond the dominant $(\ell, |m|) = (2,2)$ mode. These higher modes are crucial
to accurately represent the waveform emitted from asymmetric BBHs. We discuss a
decomposition of the waveform, extending other methods in the literature, that
allows us to accurately and efficiently capture the morphology of higher mode
waveforms. We show that the ROM is very accurate with median (maximum) values
of the unfaithfulness against SEOBNRv4HM lower than $0.001\% (0.03\%)$ for
total masses in $[2.8,100] M_\odot$. For a total mass of $M = 300 M_\odot$ the
median (maximum) value of the unfaithfulness increases up to $0.004\%
(0.17\%)$. This is still at least an order of magnitude lower than the
estimated accuracy of SEOBNRv4HM compared to numerical relativity simulations.
The ROM is two orders of magnitude faster in generating a waveform compared to
SEOBNRv4HM. Data analysis applications typically require
$\mathcal{O}(10^6-10^8)$ waveform evaluations for which SEOBNRv4HM is in
general too slow. The ROM is therefore crucial to allow the SEOBNRv4HM waveform
to be used in searches and Bayesian parameter inference. We present a targeted
parameter estimation study that shows the improvements in measuring binary
parameters when using waveforms that includes higher modes and compare against
three other waveform models.


  The recently proposed SNLI-VE corpus for recognising visual-textual
entailment is a large, real-world dataset for fine-grained multimodal
reasoning. However, the automatic way in which SNLI-VE has been assembled (via
combining parts of two related datasets) gives rise to a large number of errors
in the labels of this corpus. In this paper, we first present a data collection
effort to correct the class with the highest error rate in SNLI-VE. Secondly,
we re-evaluate an existing model on the corrected corpus, which we call
SNLI-VE-2.0, and provide a quantitative comparison with its performance on the
non-corrected corpus. Thirdly, we introduce e-SNLI-VE, which appends
human-written natural language explanations to SNLI-VE-2.0. Finally, we train
models that learn from these explanations at training time, and output such
explanations at testing time.


  Shear viscosity of the classical $\Phi^4$ theory is measured using classical
microcanonical simulation. To calculate the Kubo formula, we measure the
energy-momentum tensor correlation function, and apply the Green-Kubo relation.
Being a classical theory, the results depend on the cutoff which should be
chosen in the range of the temperature. Comparison with experimentally
accessible systems is also performed.


  Using a description of defects in solids in terms of three-dimensional
gravity, we study the propagation of electrons in the background of
disclinations and screw dislocations. We study the situations where there are
bound states that are effectively localized on the defect and hence can be
described in terms of an effective 1+1 dimensional field theory for the low
energy excitations. In the case of screw dislocations, we find that these
excitations are chiral and can be described by an effective field theory of
chiral fermions. Fermions of both chirality occur even for a given direction of
the magnetic field. The ``net'' chirality of the system however is not always
the same for a given direction of the magnetic field, but changes from one sign
of the chirality through zero to the other sign as the Fermi momentum or the
magnitude of the magnetic flux is varied. On coupling to an external
electromagnetic field, the latter becomes anomalous, and predicts novel
conduction properties for these materials.


  Misaligned Active Galactic Nuclei (MAGNs), i.e., radio galaxies and quasars
with the jet not directly pointing at the observer, are a new class of GeV
emitters. In low power radio galaxies (i.e., FRIs), gamma-rays are mainly
produced in compact jet regions, although in at least one case, Centaurus A,
high energy photons from the radio lobes have been also observed. The first
localization of the gamma-ray dissipation zone in a high power radio galaxy
(i.e., FRII) excludes major contributions from extended regions. The study of
the FRII source 3C111 indicates that gamma-ray photons are produced in the jet.
The site, coincident with the radio core, is estimated to be at a distance
<~0.3 pc from the black hole. Although the place where high energy photons are
produced is probably similar in FRIs and FRIIs, high power radio galaxies are
rarer in the GeV sky. Our study of all the radio sources belonging to four
complete radio catalogs (3CR, 3CRR, MS4, 2Jy) disfavors the idea that the
paucity of FRIIs is due to their larger distance (and therefore to their
faintness) and supports other possibilities, pointing to beaming/jet structural
differences between FRIs and FRIIs.


  We show that the local period at position n in a characteristic Sturmian word
can be given in terms of the Ostrowski representation for n + 1.


  We study the analogue of polynomials (solutions to $\Delta^{n+1} u =0$ for
some $n$) on the Sierpinski gasket ($SG$) with respect to a family of
symmetric, self-similar Laplacians constructed by Fang, King, Lee, and
Strichartz, extending the work of Needleman, Strichartz, Teplyaev, and Yung on
the polynomials with respect to the standard Kigami Laplacian. We define a
basis for the space of polynomials, the monomials, characterized by the
property that a certain "derivative" is 1 at one of the boundary points, while
all other "derivatives" vanish, and we compute the values of the monomials at
the boundary points of $SG$. We then present some data which suggest surprising
relationships between the values of the monomials at the boundary and certain
Neumann eigenvalues of the family of symmetric self-similar Laplacians.
Surprisingly, the results for the general case are quite different from the
results for the Kigami Laplacian.


  Many gravitational wave (GW) sources are expected to have non-negligible
eccentricity in the millihertz band. These highly eccentric compact object
binaries may commonly serve as a progenitor stage of GW mergers, particularly
in dynamical channels where environmental perturbations bring a binary with
large initial orbital separation into a close pericenter passage, leading to
efficient GW emission and a final merger. This work examines the stochastic GW
background from highly eccentric ($e\gtrsim 0.9$), stellar-mass sources in the
mHz band. Our findings suggest that these binaries can contribute a substantial
GW power spectrum, potentially exceeding the LISA instrumental noise at $\sim
3-7$~mHz. This stochastic background is likely to be dominated by eccentric
sources within the Milky Way, thus introducing anisotropy and time dependence
in LISA's detection. However, given efficient search strategies to identify GW
transients from highly eccentric binaries, the unresolvable noise level can be
substantially lower, approaching $\sim 2$ orders of magnitude below the LISA
noise curve. Therefore, we highlight the importance of characterizing
stellar-mass GW sources with extreme eccentricity, especially their transient
GW signals in the millihertz band.


  CABLE is a land surface model (LSM) that can be applied stand-alone, as well
as providing for land surface-atmosphere exchange within the Australian
Community Climate and Earth System Simulator (ACCESS). We describe critical new
developments that extend the applicability of CABLE for regional and global
carbon-climate simulations, accounting for vegetation response to biophysical
and anthropogenic forcings. A land-use and land-cover change module, driven by
gross land-use transitions and wood harvest area was implemented, tailored to
the needs of the Coupled Model Intercomparison Project-6 (CMIP6). Novel aspects
include the treatment of secondary woody vegetation, which benefits from a
tight coupling between the land-use module and the Population Orders Physiology
(POP) module for woody demography and disturbance-mediated landscape
heterogeneity. Land-use transitions and harvest associated with secondary
forest tiles modify the annually-resolved patch age distribution within
secondary-vegetated tiles, in turn affecting biomass accumulation and turnover
rates and hence the magnitude of the secondary forest sink. Additionally, we
implemented a novel approach to constrain modelled GPP consistent with the
Co-ordination Hypothesis, predicted by evolutionary theory, which suggests that
electron transport and Rubisco-limited rates adjust seasonally and across
biomes to be co-limiting. We show that the default prior assumption - common to
CABLE and other LSMs - of a fixed ratio of electron transport to carboxylation
capacity is at odds with this hypothesis, and implement an alternative
algorithm for dynamic optimisation of this ratio, such that co-ordination is
achieved as an outcome of fitness maximisation. Results have significant
implications the magnitude of the simulated CO2 fertilisation effect on
photosynthesis in comparison to alternative estimates and observational
proxies.


  This paper looks into the problem of pedestrian tracking using a monocular,
potentially moving, uncalibrated camera. The pedestrians are located in each
frame using a standard human detector, which are then tracked in subsequent
frames. This is a challenging problem as one has to deal with complex
situations like changing background, partial or full occlusion and camera
motion. In order to carry out successful tracking, it is necessary to resolve
associations between the detected windows in the current frame with those
obtained from the previous frame. Compared to methods that use temporal windows
incorporating past as well as future information, we attempt to make decision
on a frame-by-frame basis. An occlusion reasoning scheme is proposed to resolve
the association problem between a pair of consecutive frames by using an
affinity matrix that defines the closeness between a pair of windows and then,
uses a binary integer programming to obtain unique association between them. A
second stage of verification based on SURF matching is used to deal with those
cases where the above optimization scheme might yield wrong associations. The
efficacy of the approach is demonstrated through experiments on several
standard pedestrian datasets.


  The Higgs low-energy theorem gives a simple and elegant way to estimate the
couplings of the Higgs boson to massless gluons and photons induced by loops of
heavy particles. We extend this theorem to take into account possible nonlinear
Higgs interactions resulting from a strong dynamics at the origin of the
breaking of the electroweak symmetry. We show that, while it approximates with
an accuracy of order a few percents single Higgs production, it receives
corrections of order 50% for double Higgs production. A full one-loop
computation of the gg->hh cross section is explicitly performed in MCHM5, the
minimal composite Higgs model based on the SO(5)/SO(4) coset with the Standard
Model fermions embedded into the fundamental representation of SO(5). In
particular we take into account the contributions of all fermionic resonances,
which give sizeable (negative) corrections to the result obtained considering
only the Higgs nonlinearities. Constraints from electroweak precision and
flavor data on the top partners are analyzed in detail, as well as direct
searches at the LHC for these new fermions called to play a crucial role in the
electroweak symmetry breaking dynamics.


  The success of Deep Neural Networks (DNNs) highly depends on data quality.
Moreover, predictive uncertainty makes high performing DNNs risky for
real-world deployment. In this paper, we aim to address these two issues by
proposing a unified filtering framework leveraging underlying data density,
that can effectively denoise training data as well as avoid predicting
uncertain test data points. Our proposed framework leverages underlying data
distribution to differentiate between noise and clean data samples without
requiring any modification to existing DNN architectures or loss functions.
Extensive experiments on multiple image classification datasets and multiple
CNN architectures demonstrate that our simple yet effective framework can
outperform the state-of-the-art techniques in denoising training data and
abstaining uncertain test data.


  In this paper we consider some aspects of tridiagonal, non self-adjoint,
Hamiltonians and of their supersymmetric counterparts. In particular, the
problem of factorization is discussed, and it is shown how the analysis of the
eigenstates of these Hamiltonians produce interesting recursion formulas giving
rise to biorthogonal families of vectors. Some examples are proposed, and a
connection with bi-squeezed states is analyzed.


  We introduce a new stochastic verification algorithm that formally quantifies
the behavioral robustness of any time-continuous process formulated as a
continuous-depth model. Our algorithm solves a set of global optimization (Go)
problems over a given time horizon to construct a tight enclosure (Tube) of the
set of all process executions starting from a ball of initial states. We call
our algorithm GoTube. Through its construction, GoTube ensures that the
bounding tube is conservative up to a desired probability and up to a desired
tightness. GoTube is implemented in JAX and optimized to scale to complex
continuous-depth neural network models. Compared to advanced reachability
analysis tools for time-continuous neural networks, GoTube does not accumulate
overapproximation errors between time steps and avoids the infamous wrapping
effect inherent in symbolic techniques. We show that GoTube substantially
outperforms state-of-the-art verification tools in terms of the size of the
initial ball, speed, time-horizon, task completion, and scalability on a large
set of experiments. GoTube is stable and sets the state-of-the-art in terms of
its ability to scale to time horizons well beyond what has been previously
possible.


  We consider two dimensional QCD with the spatial dimension compactified to a
circle. We show that the states in the theory consist of interacting strings
that wind around the circle and derive the Hamiltonian for this theory in the
large $N$ limit, complete with interactions. Mapping the winding states into
momentum states, we express this Hamiltonian in terms of a continuous field.
For a $U(N)$ gauge group with a background source of Wilson loops, we recover
the collective field Hamiltonian found by Das and Jevicki for the $c=1$ matrix
model, except the spatial coordinate is on a circle. We then proceed to show
that two dimensional QCD with a $U(N)$ gauge group can be reduced to a one-
dimensional unitary matrix model and is hence equivalent to a theory of $N$
free nonrelativistic fermions on a circle. A similar result is true for the
group $SU(N)$, but the fermions must be modded out by the center of mass
coordinate.


  We study the effect of a background flux string on the vacuum energy of
massive Dirac fermions in 3+1 dimensions confined to a finite spatial region
through MIT boundary conditions. We treat two admissible self-adjoint
extensions of the Hamiltonian. The external sector is also studied and
unambiguous results for the Casimir energy of massive fermions in the whole
space are obtained.


  In this paper, we try to realize the unbounded derived category of an abelian
category as the homotopy category of a Quillen model structure on the category
of unbounded chain complexes. We construct such a model structure based on
injective resolutions for an arbitrary Grothendieck category, as has apparently
also been done by Morel. In particular, this works for sheaves on a ringed
space, and for quasi-coherent sheaves on a quasi-compact, quasi-separated
scheme. However, this injective model structure is not well suited to studying
the derived tensor product, so we investigate other model structures. The most
successful of these is the flat model structure on complexes of sheaves over a
ringed space. This is based on flat resolutions, and is compatible with the
tensor product. As a corollary, we get model categories of differential graded
algebras of sheaves and differential graded modules over a given differential
graded algebra of sheaves.
  This is the author's first attempt to understand sheaves, so comments from
those more experienced with the subject are welcome.


  The Comisso-Asenjo mechanism is a novel mechanism proposed recently to
extract energy from black holes through magnetic reconnection of the
surrounding charged plasma, in which the magnetic field plays a crucial role.
In this work, we revisit this process by taking into account the backreaction
of the magnetic field on the black hole's geometry. We employ the Kerr-Melvin
metric to describe the local near-horizon geometry of the magnetized black
hole. By analyzing the circular orbits in the equatorial plane, energy
extraction conditions, power and efficiency of the energy extraction, we found
that while a stronger magnetic field can enhance plasma magnetization and aid
energy extraction, its backreaction on the spacetime may hinder the process,
with a larger magnetic field posing a greater obstacle. Balancing these
effects, an optimal moderate magnetic field strength is found to be most
conducive to energy extraction. Moreover, there is a maximum limit to the
magnetic field strength associated with the black hole's spin, beyond which
circular orbits in the equatorial plane are prohibited, thereby impeding energy
extraction in the current scenario.


  We introduce a novel superconducting qubit architecture utilizing parallel
arrays of Josephson junctions. This design offers a substantialy improved
relative anharmonicity, typically within the range of $|\alpha_r| \approx 0.1 -
0.3$, while maintaining transition matrix elements in both the charge and flux
channels that are on par with those of transmon qubits. Our proposed device
also features exceptional tunability and includes a parameter regime akin to an
enhanced version of the fluxonium qubit. Notably, it enables an additional
order of magnitude reduction in matrix elements influenced by flux noise, thus
further enhancing its suitability for quantum information processing
applications.


  A new combined next to leading order QCD analysis of the polarized inclusive
and semi-inclusive deep inelastic lepton-hadron scattering (DIS) data is
presented. In contrast to previous combined analyses, the $1/Q^2$ terms
(kinematic - target mass corrections, and dynamic - higher twist corrections)
in the expression for the nucleon spin structure function $g_1$ are taken into
account. The new COMPASS data are included in the analysis. The impact of the
semi-inclusive data on the polarized parton densities (PDFs) and on the higher
twist corrections is discussed. The new results for the PDFs are compared to
our (Leader, Sidorov, Stamenov) LSS'06 PDFs, obtained from the fit to the
inclusive DIS data alone, and to those obtained from the de Florian, Sassot,
Stratmann, and Vogelsang global analysis.


  While there is universal agreement that agents ought to act ethically, there
is no agreement as to what constitutes ethical behaviour. To address this
problem, recent philosophical approaches to `moral uncertainty' propose
aggregation of multiple ethical theories to guide agent behaviour. However, one
of the foundational proposals for aggregation - Maximising Expected
Choiceworthiness (MEC) - has been criticised as being vulnerable to fanaticism;
the problem of an ethical theory dominating agent behaviour despite low
credence (confidence) in said theory. Fanaticism thus undermines the
`democratic' motivation for accommodating multiple ethical perspectives. The
problem of fanaticism has not yet been mathematically defined. Representing
moral uncertainty as an instance of social welfare aggregation, this paper
contributes to the field of moral uncertainty by 1) formalising the problem of
fanaticism as a property of social welfare functionals and 2) providing
non-fanatical alternatives to MEC, i.e. Highest k-trimmed Mean and Highest
Median.


  This work is concerned with the estimation of the intensity parameter of a
stationary determinantal point process. We consider the standard estimator,
corresponding to the number of observed points per unit volume and a recently
introduced median-based estimator more robust to outliers. The consistency and
asymptotic normality of estimators are obtained under mild assumptions on the
determinantal point process. We illustrate the efficiency of the procedures in
a simulation study.


  In this paper, we study the half-supersymmetric time-dependent configurations
in M-theory and their matrix models. We find a large class of 11D supergravity
solutions, which keeps sixteen supersymmetries. Furthermore, we investigate the
isometries of these configurations and show that in general these
configurations have no supernumerary supersymmetries. And also we define the
Matrix models in these backgrounds following Discrete Light-Cone Quantization
(DLCQ) prescription.


  In this work, we present the first-ever calculation of the isovector flavor
combination of the twist-3 parton distribution function $g_T(x)$ for the proton
from lattice QCD. We use an ensemble of gauge configurations with two
degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally
twisted mass fermions with a clover improvement. The lattice has a spatial
extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of
$260$ MeV. We use the quasi-distribution approach and employ three values of
the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a
source-sink separation of 1.12~fm to suppress excited-states contamination. The
lattice data are renormalized non-perturbatively. We calculate the matching
equation within Large Momentum Effective Theory, which is applied to the
lattice data in order to obtain $g_T$. The final distribution is presented in
the $\overline{\rm MS}$ scheme at a scale of 2 GeV. We also calculate the
helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for
$g_T$. We find that the approximation works well for a broad range of $x$. This
work demonstrates the feasibility of accessing twist-3 parton distribution
functions from novel methods within lattice QCD and can provide essential
insights into the structure of hadrons.


  Multilingual pretrained language models (MPLMs) have demonstrated substantial
performance improvements in zero-shot cross-lingual transfer across various
natural language understanding tasks by finetuning MPLMs on task-specific
labelled data of a source language (e.g. English) and evaluating on a wide
range of target languages. Recent studies show that prompt-based finetuning
surpasses regular finetuning in few-shot scenarios. However, the exploration of
prompt-based learning in multilingual tasks remains limited. In this study, we
propose the ProFiT pipeline to investigate the cross-lingual capabilities of
Prompt-based Finetuning. We conduct comprehensive experiments on diverse
cross-lingual language understanding tasks (sentiment classification,
paraphrase identification, and natural language inference) and empirically
analyze the variation trends of prompt-based finetuning performance in
cross-lingual transfer across different few-shot and full-data settings. Our
results reveal the effectiveness and versatility of prompt-based finetuning in
cross-lingual language understanding. Our findings indicate that prompt-based
finetuning outperforms vanilla finetuning in full-data scenarios and exhibits
greater advantages in few-shot scenarios, with different performance patterns
dependent on task types. Additionally, we analyze underlying factors such as
language similarity and pretraining data size that impact the cross-lingual
performance of prompt-based finetuning. Overall, our work provides valuable
insights into the cross-lingual prowess of prompt-based finetuning.


  The construction of gauge invariant states of SU(3) lattice gauge theories
has garnered new interest in recent years, but implementing them is complicated
by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron
(LSH) approach to lattice gauge theories, the elementary excitations are
strictly gauge invariant, and constructing the basis requires no knowledge of
Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH
formulation was recently generalized to SU(3), but limited to one spatial
dimension. In this work, we generalize the LSH approach to constructing the
basis of SU(3) gauge invariant states at a trivalent vertex - the essential
building block to multidimensional space. A direct generalization from the
SU(2) vertex yields a legitimate basis; however, in certain sectors of the
Hilbert space, the naive LSH basis vectors so defined suffer from being
nonorthogonal. The issues with orthogonality are directly related to the
`missing label' or `outer multiplicity' problem associated with SU(3) tensor
products, and may also be phrased in terms of Littlewood-Richardson
coefficients or the need for a `seventh Casimir' operator. The states that are
unaffected by the problem are orthonormalized in closed form. For the sectors
that are afflicted, we discuss the nonorthogonal bases and their
orthogonalization. A few candidates for seventh Casimir operators are readily
constructed from the suite of LSH gauge-singlet operators. The diagonalization
of a seventh Casimir represents one prescriptive solution towards obtaining a
complete orthonormal basis, but a closed-form general solution remains to be
found.


  It is well known that correlations predicted by quantum mechanics cannot be
explained by any classical (local-realistic) theory. The relative strength of
quantum and classical correlations is usually studied in the context of Bell
inequalities, but this tells us little about the geometry of the quantum set of
correlations. In other words, we do not have good intuition about what the
quantum set actually looks like. In this paper we study the geometry of the
quantum set using standard tools from convex geometry. We find explicit
examples of rather counter-intuitive features in the simplest non-trivial Bell
scenario (two parties, two inputs and two outputs) and illustrate them using
2-dimensional slice plots. We also show that even more complex features appear
in Bell scenarios with more inputs or more parties. Finally, we discuss the
limitations that the geometry of the quantum set imposes on the task of
self-testing.


  We prove that under certain conditions, the quantum cohomology of a
positively monotone compact symplectic manifold is a deformation of the
symplectic cohomology of the complement of a simple crossings symplectic
divisor. We also prove rigidity results for the skeleton of the divisor
complement.


  We report calculations of energy levels, radiative rates, and electron impact
excitation rates for transitions in Li-like ions with 12 <= Z <= 20. The GRASP
(general-purpose relativistic atomic structure package) is adopted for
calculating energy levels and radiative rates, while for determining the
collision strengths and subsequently the excitation rates, the Dirac atomic
R-matrix code DARC is used. Oscillator strengths, radiative rates, and line
strengths are reported for all E1, E2, M1, and M2 transitions among the lowest
24 levels of the Li-like ions considered. Collision strengths have been
averaged over a Maxwellian velocity distribution, and the effective collision
strengths obtained are reported over a wide temperature range up to 10$^{7.4}$
K. Additionally, lifetimes are also listed for all calculated levels of the
above ions. Finally, extensive comparisons are made with available results in
the literature, as well as with our parallel calculations for all parameters
with the Flexible Atomic Code FAC in order to assess the accuracy of the
reported results.


  We study aqueous xanthan solutions at shear rates up to about 105 s-1. At
these shear rates, the salt-free solutions show a second Newtonian branch.
Depending on the xanthan concentration, we find two different regimes with
scaling laws well-known for the zero viscosity of dilute and semidilute
particle solutions: The crossover concentration is considerably higher than in
the first Newtonian branch, which can be related to the orientation of the
polyelectrolytes. In the second regime, the normal stress differences increase
with an exponent of about 1, indicating that the polymer solution behaves like
nematic liquid crystals or rigid fiber suspensions. In the first regime, the
exponent is smaller suggesting that the polyelectrolytes behave more flexible


  Ravishankar et al. claimed the drive-level capacitance profiling (DLCP)
method cannot resolve trap density along depth direction in perovskites with
given thickness, and explained the measured charges to be a consequence of
geometrical capacitance and diffusion capacitance. We point out that the trap
densities in DLCP method are derived from the differential capacitance at
different frequencies, and thus the background charges caused by diffusion and
geometry capacitance has been subtracted. Even for the non-differential doping
analysis by DLCP, the contribution from diffusion capacitance is shown to be
negligible and contribution from geometry capacitance is excluded. Additional
experiment results further support the measured trap density represents the
actual trap distribution in perovskite solar cells.


  One of the most fundamental concepts in statistics is the concept of sample
mean. Properties of the sample mean that are well-defined in Euclidean spaces
become unwieldy or even unclear in graph spaces. Open problems related to the
sample mean of graphs include: non-existence, non-uniqueness, statistical
inconsistency, lack of convergence results of mean algorithms, non-existence of
midpoints, and disparity to midpoints. We present conditions to resolve all six
problems and propose a Majorize-Minimize-Mean (MMM) Algorithm. Experiments on
graph datasets representing images and molecules show that the MMM-Algorithm
best approximates a sample mean of graphs compared to six other mean
algorithms.


  Given a star-shaped bounded Lipschitz domain $\Omega\subset{\mathbb R}^d$, we
consider the Schr\"odinger operator $L_{\mathcal G}=-\Delta+V$ on $\Omega$ and
its restrictions $L^{\Omega_t}_{\mathcal G}$ on the subdomains $\Omega_t$,
$t\in[0,1]$, obtained by shrinking $\Omega$ towards its center. We impose
either the Dirichlet or quite general Robin-type boundary conditions determined
by a subspace ${\mathcal G}$ of the boundary space
$H^{1/2}(\partial\Omega)\times H^{-1/2}(\partial\Omega)$, and assume that the
potential is smooth and takes values in the set of symmetric $(N\times N)$
matrices. Two main results are proved: First, for any $t_0\in(0,1]$ we give an
asymptotic formula for the eigenvalues $\lambda(t)$ of the operator
$L^{\Omega_t}_{\mathcal G}$ as $t\to t_0$ up to quadratic terms, that is, we
explicitly compute the first and second $t$-derivatives of the eigenvalues.
This includes the case of the eigenvalues with arbitrary multiplicities.
Second, we compute the first derivative of the eigenvalues via the (Maslov)
crossing form utilized in symplectic topology to define the
Arnold-Maslov-Keller index of a path in the set of Lagrangian subspaces of the
boundary space. The path is obtained by taking the Dirichlet and Neumann traces
of the weak solutions of the eigenvalue problems for $L^{\Omega_t}_{\mathcal
G}$.


  Many neuronal systems and models display a certain class of mixed mode
oscillations (MMOs) consisting of periods of small amplitude oscillations
interspersed with spikes. Various models with different underlying mechanisms
have been proposed to generate this type of behavior. Stochastic versions of
these models can produce similarly looking time series, often with noise-driven
mechanisms different from those of the deterministic models. We present a suite
of measures which, when applied to the time series, serves to distinguish
models and classify routes to producing MMOs, such as noise-induced
oscillations or delay bifurcation. By focusing on the subthreshold
oscillations, we analyze the interspike interval density, trends in the
amplitude and a coherence measure. We develop these measures on a biophysical
model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and
apply them on related models. The analysis highlights the influence of model
parameters and reset and return mechanisms in the context of a novel approach
using noise level to distinguish model types and MMO mechanisms. Ultimately, we
indicate how the suite of measures can be applied to experimental time series
to reveal the underlying dynamical structure, while exploiting either the
intrinsic noise of the system or tunable extrinsic noise.


  This paper investigates whether observations of seismic anisotropy are
compatible with a cubic structure of the inner core Fe alloy. We assume that
anisotropy is the result of plastic deformation within a large scale flow
induced by preferred growth at the inner core equator. Based on elastic moduli
from the literature, bcc- or fcc-Fe produce seismic anisotropy well below
seismic observations ($\textless{}0.4\%$). A Monte-Carlo approach allows us to
generalize this result to any form of elastic anisotropy in a cubic system.
Within our model, inner core global anisotropy is not compatible with a cubic
structure of Fe alloy. Hence, if the inner core material is indeed cubic, large
scale coherent anisotropic structures, incompatible with plastic deformation
induced by large scale flow, must be present.


  Recently, the reference functions for the synthesis and analysis of the
autostereoscopic multiview and integral images in three-dimensional displays we
introduced. In the current paper, we propose the wavelets to analyze such
images. The wavelets are built on the reference functions as on the scaling
functions of the wavelet analysis. The continuous wavelet transform was
successfully applied to the testing wireframe binary objects. The restored
locations correspond to the structure of the testing wireframe binary objects.


  The paper presents the solutions for the zonal electrophoresis equations are
obtained by analytical and numerical methods. The method proposed by the
authors is used. This method allows to reduce the Cauchy problem for two
hyperbolic quasilinear PDE's to the Cauchy problem for ODE's. In some respect,
this method is analogous to the method of characteristics for two hyperbolic
equations. The method is effectively applicable in all cases when the explicit
expression for the Riemann-Green function of some linear second order PDE,
resulting from the use of the hodograph method for the original equations, is
known. One of the method advantages is the possibility of constructing a
multi-valued solutions. Compared with the previous authors paper, in which, in
particular, the shallow water equations are studied, here we investigate the
case when the Riemann-Green function can be represent as the sum of the terms
each of them is a product of two multipliers depended on different variables.
The numerical results for zonal electrophoresis equations are presented. For
computing the different initial data (periodic, wave packet, the Gaussian
distribution) are used.


  The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.


  We investigate homogeneity in the special Colombeau algebra. It is shown that
strongly scaling invariant functions on the d-dimensional space are simply the
constants. On the pierced space, strongly homogeneous functions admit tempered
representatives, whereas on the whole space, such functions are polynomials
with generalized coefficients. We also introduce weak notions of homogeneity
and show that these are consistent with the classical notion on the
distributional level. Moreover, we investigate the relation between generalized
solutions of the Euler differential equation and homogeneity.


  In this paper, we study the initial boundary value problem for the nonlinear
wave equation with combined power-type nonlinearities with variable
coefficients. The global behavior of the solutions with non-positive and
sub-critical energy is completely investigated. The threshold between the
nonexistence of global in time weak solutions and non-blowing up solutions is
found. For super-critical energy, two new sufficient conditions guaranteeing
nonexistence of global in time solutions are given. One of them is proved for
arbitrary sign of the scalar product of the initial data, while the other one
is derived only for positive sign. Uniqueness and existence of local weak
solutions are proved.


  The theory of gravitational structure formation in astrophysics and cosmology
is revised based on real fluid behavior and turbulent mixing theory. Gibson's
1996-1998 theory balances fluid mechanical forces with gravitational forces and
density diffusivity with gravitational diffusivity at critical viscous,
turbulent, magnetic, and diffusion length scales termed Schwarz scales L_SX.
Condensation and void formation occurs on non-acoustic density nuclei produced
by turbulent mixing for scales L>=L_SXmax rather than on sound wave crests and
troughs for L>=L_J as required by Jeans's 1902 linear acoustic theory. Schwarz
scales L_SX = L_SV, L_ST, L_SM, or L_SD may be smaller or larger than Jeans's
scale L_J. Thus, a very different "nonlinear" cosmology emerges to replace the
currently accepted "linear" cosmology. According to the new theory, most of the
inner halo dark matter of galaxies consists of planetary mass objects that
formed soon after the plasma to neutral gas transition 300,000 years after the
Big Bang. These objects are termed primordial fog particles (PFPs) and provide
an explanation for Schild's 1996 "rogue planets ... likely to be the missing
mass" of his observed quasar-lens galaxy, inferred from the twinkling
frequencies of both quasar images and their phased difference.


  We study structural transitions in a system of interacting particles arranged
as a crystalline bilayer, as a function of the density $\rho$ and the distance
$d$ between the layers. As $d$ is decreased a sequence of transitions involving
triangular, rhombic, square and centered rectangular lattices is observed. The
sequence of phases and the order of transitions depends on the nature of
interactions.


  We prove global well-posedness for the microscopic FENE model under a sharp
boundary requirement. The well-posedness of the FENE model that consists of the
incompressible Navier-Stokes equation and the Fokker-Planck equation has been
studied intensively, mostly with the zero flux boundary condition. Recently it
was illustrated by C. Liu and H. Liu [2008, SIAM J. Appl. Math.,
68(5):1304--1315] that any preassigned boundary value of a weighted
distribution will become redundant once the non-dimensional parameter $b>2$. In
this article, we show that for the well-posedness of the microscopic FENE model
($b>2$) the least boundary requirement is that the distribution near boundary
needs to approach zero faster than the distance function. Under this condition,
it is shown that there exists a unique weak solution in a weighted Sobolev
space. Moreover, such a condition still ensures that the distribution is a
probability density. The sharpness of this boundary requirement is shown by a
construction of infinitely many solutions when the distribution approaches zero
as fast as the distance function.


  The present work is a generalisation of the dynamical screening factor
presented in [1] to consider an atom located at an arbitrary position within
the fullerene. A more elaborated investigation into the case where the atom is
located at the centre is performed and compared with quantum mechanical
calculations for dynamical screening factor of Ar@C$_{60}$ [2] and Mg@C$_{60}$
[3]. The $\pi$ and $\sigma$ plasmons of the fullerene are accounted for in a
modified screening factor to improve correspondence with the quantum
calculations. The spatial dependence of the screening factor was explored with
Ar@C$_{60}$ and Ar@C$_{240}$ and found to depend significantly on the radial
distance of the atom from the centre of the fullerene. A spatial averaging of
the screening factor is presented.


  The Jones polynomial of a knot in 3-space is a Laurent polynomial in $q$,
with integer coefficients. Many people have pondered why is this so, and what
is a proper generalization of the Jones polynomial for knots in other closed
3-manifolds. Our paper centers around this question. After reviewing several
existing definitions of the Jones polynomial, we show that the Jones polynomial
is really an analytic function, in the sense of Habiro. Using this, we extend
the holonomicity properties of the colored Jones function of a knot in 3-space
to the case of a knot in an integer homology sphere, and we formulate an
analogue of the AJ Conjecture. Our main tools are various integrality
properties of topological quantum field theory invariants of links in
3-manifolds, manifested in Habiro's work on the colored Jones function.Revised
version updating references on Witten-Reshetikhin-Turaev invariants.


  The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a
dynamical group possesses a rich algebraic structure of physical interesting
subgroups that define its distinct exactly solvable dynamical limits. The
classical images corresponding to different dynamical symmetries are obtained
by means of the coherent state method. The phase structure of the IVBM is
investigated and the following basic phase shapes, connected to a specific
geometric configurations of the ground state, are determined: spherical,
$U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed
shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions
between different phase shapes, corresponding to the different dynamical
symmetries and mixed symmetry case, are investigated.


  A measurement of the inclusive b-jet production cross section is presented in
pp and p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV, using data collected
with the ALICE detector at the LHC. The jets were reconstructed in the central
rapidity region $|\eta|<0.5$ from charged particles using the anti-$k_{\rm T}$
algorithm with resolution parameter $R=0.4$. Identification of b jets exploits
the long lifetime of b hadrons, using the properties of secondary vertices and
impact parameter distributions. The $p_{\rm T}$-differential inclusive
production cross section of b jets, as well as the corresponding inclusive
b-jet fraction, are reported for pp and p-Pb collisions in the jet transverse
momentum range $10 \le p_{\text{T, ch jet}} \le 100$ GeV/$c$, together with the
nuclear modification factor, $R_{\rm pPb}^{\text{b-jet}}$. The analysis thus
extends the lower $p_{\rm T}$ limit of b-jet measurements at the LHC. The
nuclear modification factor is found to be consistent with unity, indicating
that the production of b jets in p-Pb at $\sqrt{s_{\rm NN}} = 5.02$ TeV is not
affected by cold nuclear matter effects within the current precision. The
measurements are well reproduced by POWHEG NLO pQCD calculations with PYTHIA
fragmentation.


  We study factorizations of HOMFLY polynomials of certain knots and oriented
links. We begin with a computer analysis of knots with at most 12 crossings,
finding 17 non-trivial factorizations. Next, we give an irreducibility
criterion for HOMFLY polynomials of oriented links associated to 2-connected
plane graphs.


  We study the dynamics of a system of hard-core particles sliding downwards on
a one dimensional fluctuating interface, which in a special case can be mapped
to the problem of a passive scalar advected by a Burgers fluid. Driven by the
surface fluctuations, the particles show a tendency to cluster, but the
hard-core interaction prevents collapse. We use numerical simulations to
measure the auto-correlation function in steady state and in the aging regime,
and space-time correlation functions in steady state. We have also calculated
these quantities analytically in a related surface model. The steady state
auto-correlation is a scaling function of t/L^z, where L is the system size and
z the dynamic exponent. Starting from a finite intercept, the scaling function
decays with a cusp, in the small argument limit. The finite value of the
intercept indicates the existence of long range order in the system. The
space-time correlation, which is a function of r/L and t/L^z, is non-monotonic
in t for fixed r. The aging auto-correlation is a scaling function of t_1 and
t_2 where t_1 is the waiting time and t_2 the time difference. This scaling
function decays as a power law for t_2 \gg t_1; for t_1 \gg t_2, it decays with
a cusp as in steady state. To reconcile the occurrence of strong fluctuations
in the steady state with the fact of an ordered state, we measured the
distribution function of the length of the largest cluster. This shows that
fluctuations never destroy ordering, but rather the system meanders from one
ordered configuration to another on a relatively rapid time scale.


  Extending the approach of Grillakis-Shatah-Strauss, Bronski-Johnson-Kapitula,
and others for Hamiltonian systems, we explore relations between the
constrained variational problem $\min_{X:C(X)=c_0} \mathcal{E}(X)$, $c_0\in
\RM^r$, and stability of solutions of a class of degenerate "quasi-gradient"
systems $dX/dt=-M(X)\nabla \mathcal{E}(X)$ admitting constraints, including
Cahn-Hilliard equations, one- and multi-dimensional viscoelasticity, and
coupled conservation law-reaction diffusion systems arising in chemotaxis and
related settings. Using the relation between variational stability and the
signature of $\partial c/\partial \omega \in \R^{r\times r}$, where
$c(\omega)=C(X^*_\omega)\in \RM^r$ denote the values of the imposed constraints
and $\omega\in \RM^r$ the associated Lagrange multipliers at a critical point
$X^*_\omega$, we obtain as in the Hamiltonian case a general criterion for
co-periodic stability of periodic waves, illuminating and extending a number of
previous results obtained by direct Evans function techniques. More
interestingly, comparing the form of the Jacobian arising in the co-periodic
theory to Jacobians arising in the formal Whitham equations associated with
modulation, we recover and substantially generalize a previously mysterious
"modulational dichotomy" observed in special cases by Oh-Zumbrun and Howard,
showing that co-periodic and sideband stability are incompatible. In
particular, we both illuminate and extend to general viscosity/strain-gradient
effects and multidimensional deformations the result of Oh-Zumbrun of universal
modulational instability of periodic solutions of the equations of
viscoelasticity with strain-gradient effects, considered as functions on the
whole line. Likewise, we generalize to multi-dimensions corresponding results
of Howard on periodic solutions of Cahn-Hilliard equations.


  We present $\texttt{ENIGMA}$, a time domain, inspiral-merger-ringdown
waveform model that describes non-spinning binary black holes systems that
evolve on moderately eccentric orbits. The inspiral evolution is described
using a consistent combination of post-Newtonian theory, self-force and black
hole perturbation theory. Assuming eccentric binaries that circularize prior to
coalescence, we smoothly match the eccentric inspiral with a stand-alone,
quasi-circular merger, which is constructed using machine learning algorithms
that are trained with quasi-circular numerical relativity waveforms. We show
that $\texttt{ENIGMA}$ reproduces with excellent accuracy the dynamics of
quasi-circular compact binaries. We validate $\texttt{ENIGMA}$ using a set of
$\texttt{Einstein Toolkit}$ eccentric numerical relativity waveforms, which
describe eccentric binary black hole mergers with mass-ratios between $1 \leq q
\leq 5.5$, and eccentricities $e_0 \lesssim 0.2$ ten orbits before merger. We
use this model to explore in detail the physics that can be extracted with
moderately eccentric, non-spinning binary black hole mergers. We use
$\texttt{ENIGMA}$ to show that GW150914, GW151226, GW170104, GW170814 and
GW170608 can be effectively recovered with spinning, quasi-circular templates
if the eccentricity of these events at a gravitational wave frequency of 10Hz
satisfies $e_0\leq \{0.175,\, 0.125,\,0.175,\,0.175,\, 0.125\}$, respectively.
We show that if these systems have eccentricities $e_0\sim 0.1$ at a
gravitational wave frequency of 10Hz, they can be misclassified as
quasi-circular binaries due to parameter space degeneracies between
eccentricity and spin corrections. Using our catalog of eccentric numerical
relativity simulations, we discuss the importance of including higher-order
waveform multipoles in gravitational wave searches of eccentric binary black
hole mergers.


  Gauge models with massive vector leptoquarks at the TeV scale provide a
successful framework for addressing the B-physics anomalies. Among them, the
4321 model has been considered as the low-energy limit of some complete
theories of flavor. In this work, we study the renormalization group evolution
of this model, laying particular emphasis on the scalar sector. We find that,
despite the asymptotic freedom of the gauge couplings, Landau poles can arise
at relatively low scale due to the fast running of quartic couplings. Moreover,
we discuss the possibility of radiative electroweak symmetry breaking, and
characterize the fine-tuning associated with the hierarchy between the
electroweak scale and the additional TeV-scale scalars. Finally, the idea of
scalar fields unification is explored, motivated by ultraviolet embeddings of
the 4321 model.


  This paper considers a strongly connected network of agents, each capable of
partially observing and controlling a discrete-time linear time-invariant (LTI)
system that is jointly observable and controllable. Additionally, agents
collaborate to achieve a shared estimated state, computed as the average of
their local state estimates. Recent studies suggest that increasing the number
of average consensus steps between state estimation updates allows agents to
choose from a wider range of state feedback controllers, thereby potentially
enhancing control performance. However, such approaches require that agents
know the input matrices of all other nodes, and the selection of control gains
is, in general, centralized. Motivated by the limitations of such approaches,
we propose a new technique where: (i) estimation and control gain design is
fully distributed and finite-time, and (ii) agent coordination involves a
finite-time exact average consensus algorithm, allowing arbitrary selection of
estimation convergence rate despite the estimator's distributed nature. We
verify our methodology's effectiveness using illustrative numerical
simulations.


  Artificial audition aims at providing hearing capabilities to machines,
computers and robots. Existing frameworks in robot audition offer interesting
sound source localization, tracking and separation performance, although
involve a significant amount of computations that limit their use on robots
with embedded computing capabilities. This paper presents ODAS, the Open
embeddeD Audition System framework, which includes strategies to reduce the
computational load and perform robot audition tasks on low-cost embedded
computing systems. It presents key features of ODAS, along with cases
illustrating its uses in different robots and artificial audition applications.


  The Magellanic Stream (MS) is a massive and extended tail of multi-phase gas
stripped out of the Magellanic Clouds and interacting with the Galactic halo.
In this first paper of an ongoing program to study the Stream in absorption, we
present a chemical abundance analysis based on HST/COS and VLT/UVES spectra of
four AGN (RBS 144, NGC 7714, PHL 2525, and HE 0056-3622) lying behind the MS.
Two of these sightlines yield good MS metallicity measurements: toward RBS 144
we measure a low MS metallicity of [S/H]=[S II/H I]=-1.13+/-0.16 while toward
NGC 7714 we measure [O/H]=[O I/H I]=-1.24+/-0.20. Taken together with the
published MS metallicity toward NGC 7469, these measurements indicate a uniform
abundance of ~0.1 solar along the main body of the Stream. This provides strong
support to a scenario in which most of the Stream was tidally stripped from the
SMC ~1.5--2.5 Gyr ago (a time at which the SMC had a metallicity of ~0.1
solar), as predicted by several N-body simulations. However, in Paper II of
this series (Richter et al. 2013), we report a much higher metallicity (S/H=0.5
solar) in the inner Stream toward Fairall 9, a direction sampling a filament of
the MS that Nidever et al. (2008) claim can be traced kinematically to the LMC,
not the SMC. This shows that the bifurcation of the Stream is evident in its
metal enrichment. Finally we measure a similar low metallicity [O/H]=[O I/H
I]=-1.03+/-0.18 in the v_LSR=150 km/s cloud toward HE 0056--3622, which belongs
to a population of anomalous velocity clouds near the South Galactic Pole. This
suggests these clouds are associated with the Stream or more distant structures
(possibly the Sculptor Group, which lies in this direction at the same
velocity), rather than tracing foreground Galactic material.


  We compare low velocity impacts that ricochet with the same impact velocity
and impact angle into granular media with similar bulk density, porosity and
friction coefficient but different mean grain size. The ratio of projectile
diameter to mean grain length ranges from 4 in our coarsest medium to 50 in our
finest sand. Using high speed video and fluorescent markers, we measure the
ratio of pre- to post-impact horizontal and vertical velocity components, which
we refer to as coefficients of restitution, and the angle of deflection caused
by the impact in the horizontal plane. Coefficients of restitution are
sensitive to mean grain size with the ratio associated with the horizontal
velocity component about twice as large for our coarsest gravel as that for our
finest sand. This implies that coefficients for hydro-static-like, drag-like
and lift-like forces, used in empirical force laws, are sensitive to mean grain
size. The coefficient that is most strongly sensitive to grain size is the lift
coefficient which decreases by a factor of 3 between our coarsest and finest
media. The deflection angles are largest in the coarser media and their size
approximately depends on grain size to the 3/2 power. This scaling is matched
with a model where momentum transfer takes place via collisions with individual
grains. The dependence of impact mechanics on substrate size distribution
should be considered in future models for populations of objects that impact
granular asteroid surfaces.


  We have used the Keck I Telescope to measure K-band surface brightness
fluctuations (SBFs) of NGC 4874, the dominant elliptical galaxy in the Coma
cluster. We use deep HST WFPC2 optical imaging to account for the contamination
due to faint globular clusters and improved analysis techniques to derive
measurements of the SBF apparent magnitude. Using a new SBF calibration which
accounts for the dependence of K-band SBFs on the integrated color of the
stellar population, we measure a distance modulus of 34.99+/-0.21 mag (100+/-10
Mpc) for the Coma cluster. The resulting value of the Hubble constant is 71+/-8
km/s/Mpc, not including any systematic error in the HST Cepheid distance scale.


  We give a detailed proof that, for any natural number n, each algebraic two
complex over C_n \times C_\infty is realised up to congruence by a geometric
complex arising from a presentation for the group.


  The dynamics of many natural systems is dominated by non-linear waves
propagating through the medium. We show that the dynamics of non-linear wave
fronts with positive surface tension can be formulated as a gradient system.
The variational potential is simply given by a linear combination of the
occupied volume and surface area of the wave front, and changes monotonically
in time. Finally, we demonstrate that vortex filaments can be written as a
gradient system only if their binormal velocity component vanishes, which
occurs in chemical system with equal diffusion of reactants.


  Within the context of the banking-related literature on contingent
convertible bonds, we comprehensively formalise the design and features of a
relatively new type of insurance-linked security, called a contingent
convertible catastrophe bond (CocoCat). We begin with a discussion of its
design and compare its relative merits to catastrophe bonds and
catastrophe-equity puts. Subsequently, we derive analytical valuation formulae
for index-linked CocoCats under the assumption of independence between natural
catastrophe and financial markets risks. We model natural catastrophe losses by
a time-inhomogeneous compound Poisson process, with the interest-rate process
governed by the Longstaff model. By using an exponential change of measure on
the loss process, as well as a Girsanov-like transformation to synthetically
remove the correlation between the share and interest-rate processes, we obtain
these analytical formulae. Using selected parameter values in line with earlier
research, we empirically analyse our valuation formulae for index-linked
CocoCats. An analysis of the results reveals that the CocoCat prices are most
sensitive to changing interest-rates, conversion fractions and the threshold
levels defining the trigger times.


  Explosions near ground generate multiple geophysical waveforms in the
radiation-dominated range of their signature fields. Multi-phenomological
explosion monitoring (MultiPEM) at these ranges requires the predictive
capability to forecast trigger rates of digital detectors that process such
waveform data, and thereby accurately anticipate the probability that
hypothetical explosions can be identified in operations. To confront this
challenge, we derive and compare the predicted and observed performance of
three digital detectors that process radio, acoustic and seismic waveform data
that record a small, aboveground explosion. We measure this comparison with the
peak range in magnitude (magnitude discrepancy) over which different
performance curves report the same probability of detection, within an interval
of moderate detection probability, and thereby quantify solutions to three
topical monitoring questions. In particular, our solutions (1) demonstrate how
empirically parameterized detectors that operate in a variable noisy
environments provide fair-to-very good forecasting capability to detect small
explosions, (2) show that the observed performance of a particular waveform
detector can better forecast performance curves constructed from different
observations, when compared to theoretical performance curves, and (3) provide
an upper bound on detection uncertainty, in terms of a physical source
attribute (magnitude)


  The conductivity of concentrated salt solutions has posed a real puzzle for
theories of electrolytes. Despite a quantitative understanding of highly dilute
solutions, an analytical theory for concentrated ones remains a challenge
almost a century, although a number of parameters and effects incorporated into
theories increases with time. Here we show that the conductivity of univalent
salt solutions can be perfectly interpreted using an extremely simple model
that relies just on a mean-field description of electrostatic effects and on an
adapted for salt ions classical approach to calculating colloid
electrophoresis. We derive a compact equation, which predicts that the ratio of
conductivity at a finite concentration to that at an infinite dilution is the
same for all salt, if it is plotted against a product of the harmonic mean of
ion hydrodynamic radii and the square root of concentration. Our equation fits
very well the experimental data for inorganic salts up to 3 mol/l.


  We reobtain the Kondo-Doublet interaction by means of the Brillouin-Wigner
Perturbation theory. By applying the same method to the single impurity case we
show that the Kondo-Doublet interaction is a direct consequence of the Kondo
screening cloud. We fully confirm our previous results on this novel
interaction. In particular, we found that for values of the system parameters
typical of semiconductor Quantum Dots heterostructures, the ferromagnetic
Kondo-Doublet interaction dominates over the RKKY one.


  In this paper we use display calculus to show the decidability for normal
modal logic K and some of its extensions.


  The development of adaptive optics (AO) played a major role in modern
astronomy over the last three decades. By compensating for the atmospheric
turbulence, these systems enable to reach the diffraction limit on large
telescopes. In this review, we will focus on high contrast applications of
adaptive optics, namely, imaging the close vicinity of bright stellar objects
and revealing regions otherwise hidden within the turbulent halo of the
atmosphere to look for objects with a contrast ratio lower than 10^-4 with
respect to the central star. Such high-contrast AO-corrected observations have
led to fundamental results in our current understanding of planetary formation
and evolution as well as stellar evolution. AO systems equipped three
generations of instruments, from the first pioneering experiments in the
nineties, to the first wave of instruments on 8m-class telescopes in the years
2000, and finally to the extreme AO systems that have recently started
operations. Along with high-contrast techniques, AO enables to reveal the
circumstellar environment: massive protoplanetary disks featuring spiral arms,
gaps or other asymmetries hinting at on-going planet formation, young giant
planets shining in thermal emission, or tenuous debris disks and micron-sized
dust leftover from collisions in massive asteroid-belt analogs. After
introducing the science case and technical requirements, we will review the
architecture of standard and extreme AO systems, before presenting a few
selected science highlights obtained with recent AO instruments.


  Traditional approaches to mathematically describe spontaneous imbibition are
usually based on either macro-scale models, such as Richards equation, or
simplified pore-scale models, such as the bundle of capillary tubes (BCTM) or
pore-network modeling (PNM). It is well known that such models cannot provide
full microscopic details of the multiphase flow processes and that many
pore-scale mechanisms still lack proper mathematical descriptions. To improve
the predictive capabilities of traditional models, a fundamental understanding
of pore-scale dynamics is needed. The focus of this paper is obtaining detailed
insight and consistent explanation of particular processes during
capillary-controlled water imbibition into dry porous media. We use
two-dimensional model geometries and perform fully dynamic volume-of-fluid
based direct numerical simulations of air-water multiphase flow at the
pore-scale, to study processes that generally are not considered in traditional
models. More specifically, we investigate differences between converging and
diverging geometries, dynamic pressure and meniscus reconfiguration during
pore-filling events, and the influence of inertia and pore size on imbibition
dynamics and the occurrence of capillary barriers. Furthermore, we perform a
detailed comparison between non-interacting and interacting BCTM and study the
impact of the narrow contractions on imbibition dynamics and the trapping of
the non-wetting phase. Obtained knowledge can be used to improve predictive
models, which are broadly relevant considering the importance of spontaneous
imbibition in many different natural and industrial processes.


  Neural machine translation (NMT) models are usually trained with the
word-level loss using the teacher forcing algorithm, which not only evaluates
the translation improperly but also suffers from exposure bias. Sequence-level
training under the reinforcement framework can mitigate the problems of the
word-level loss, but its performance is unstable due to the high variance of
the gradient estimation. On these grounds, we present a method with a
differentiable sequence-level training objective based on probabilistic n-gram
matching which can avoid the reinforcement framework. In addition, this method
performs greedy search in the training which uses the predicted words as
context just as at inference to alleviate the problem of exposure bias.
Experiment results on the NIST Chinese-to-English translation tasks show that
our method significantly outperforms the reinforcement-based algorithms and
achieves an improvement of 1.5 BLEU points on average over a strong baseline
system.


  In this paper we define and study the "ghost loop orbifold" of an orbifold
$X$ consisting of those loops that remain constant in the coarse moduli space
of $X$. We construct a configuration space model for the ghost loop orbifold
using an idea of G. Segal. From this we exhibit the relation between the
Hochschild and cyclic homologies of the inertia orbifold of $X$ (that generate
the so-called twisted sectors in string theory) and the ordinary and
equivariant homologies of the ghost loop orbifold. We also show how this
clarifies the relation between orbifold K-theory, Chen-Ruan orbifold
cohomology, Hochschild homology, and periodic cyclic homology.


  The optimum distance profiles of linear block codes were studied for
increasing or decreasing message length while keeping the minimum distances as
large as possible, especially for Golay codes and the second-order Reed-Muller
codes, etc. Cyclic codes have more efficient encoding and decoding algorithms.
In this paper, we investigate the optimum distance profiles with respect to the
cyclic subcode chains (ODPCs) of the punctured generalized second-order
Reed-Muller codes $\mathcal{GRM}(2,m)^*$ which were applied in Power Control in
OFDM Modulations in channels with synchronization, and so on. For this, two
standards are considered in the inverse dictionary order, i.e., for increasing
message length. Four lower bounds and upper bounds on ODPC are presented, where
the lower bounds almost achieve the corresponding upper bounds in some sense.
The discussions are over nonbinary prime field.


  We propose quantum engines powered entirely by the quantum measurement
process. Our theoretical construction of the engine requires no work from the
system Hamiltonian, and takes energy only from the process of observation to
move a particle against a force. We present results for the work done and the
efficiency for different values of the engine parameters. Feedback is required
for optimal performance. We find that unit efficiency can be approached when
one measurement outcome prepares the initial state of the next engine cycle,
while the other outcomes leave the original state nearly unchanged.


  Products and tensor products are linked by a universal property. Imposing the
invariance of the laws of Nature under tensor composition along with Leibniz
identity determines quantum and classical mechanics algebraic structure through
the interplay between products, coproducts, and the tensor product. Violations
of Bell's inequalities distinguishes quantum from classical mechanics.


  During its first two years, the SARS-CoV-2 pandemic manifested as multiple
waves shaped by complex interactions between variants of concern,
non-pharmaceutical interventions, and the immunological landscape of the
population. Understanding how the age-specific epidemiology of SARS-CoV-2 has
evolved throughout the pandemic is crucial for informing policy decisions. We
developed an inference-based modelling approach to reconstruct the burden of
true infections and hospital admissions in children, adolescents and adults
over the seven waves of four variants (wild-type, Alpha, Delta, Omicron BA.1)
during the first two years of the pandemic, using the Netherlands as the
motivating example. We find that reported cases are a considerable
underestimate and a generally poor predictor of true infection burden,
especially because case reporting differs by age. The contribution of children
and adolescents to total infection and hospitalization burden increased with
successive variants and was largest during the Omicron BA.1 period. Before the
Delta period, almost all infections were primary infections occurring in naive
individuals. During the Delta and Omicron BA.1 periods, primary infections were
common in children but relatively rare in adults who experienced either
re-infections or breakthrough infections. Our approach can be used to
understand age-specific epidemiology through successive waves in other
countries where random community surveys uncovering true SARS-CoV-2 dynamics
are absent but basic surveillance and statistics data are available.


  The phase diagram of surface structures for the model catalyst RuO2(110) in
contact with a gas environment of O2 and CO is calculated by density-functional
theory and atomistic thermodynamics. Adsorption of the reactants is found to
depend crucially on temperature and partial pressures in the gas phase.
Assuming that a catalyst surface under steady-state operation conditions is
close to a constrained thermodynamic equilibrium, we are able to rationalize a
number of experimental findings on the CO oxidation over RuO2(110). We also
calculated reaction pathways and energy barriers. Based on the various results
the importance of phase coexistence conditions is emphasized as these will lead
to an enhanced dynamics at the catalyst surface. Such conditions may actuate an
additional, kinetically controlled reaction mechanism on RuO2(110).


  We present a bijective proof of the hook-length formula for shifted standard
tableaux of a fixed shape based on a modified jeu de taquin and the ideas of
the bijective proof of the hook-length formula for ordinary standard tableaux
by Novelli, Pak and Stoyanovskii. In their proof Novelli, Pak and Stoyanovskii
define a bijection between arbitrary fillings of the Ferrers diagram with the
integers $1,2,...,n$ and pairs of standard tableaux and hook tabloids. In our
shifted version of their algorithm the map from the set of arbitrary fillings
of the shifted Ferrers diagram onto the set of shifted standard tableaux is
analog to the construction of Novelli, Pak and Stoyanovskii, however, unlike to
their algorithm, we are forced to use the 'rowwise' total order of the cells in
the shifted Ferrers diagram rather than the 'columnwise' total order as the
underlying order in the algorithm. Unfortunately the construction of the
shifted hook tabloid is more complicated in the shifted case. As a side-result
we obtain a simple random algorithm for generating shifted standard tableaux of
a given shape, which produces every such tableau equally likely.


  Decentralized coordination is one of the fundamental challenges for societies
and organizations. While extensively explored from a variety of perspectives,
one issue which has received limited attention is human coordination in the
presence of adversarial agents. We study this problem by situating human
subjects as nodes on a network, and endowing each with a role, either regular
(with the goal of achieving consensus among all regular players), or
adversarial (aiming to prevent consensus among regular players). We show that
adversarial nodes are, indeed, quite successful in preventing consensus.
However, we demonstrate that having the ability to communicate among network
neighbors can considerably improve coordination success, as well as resilience
to adversarial nodes. Our analysis of communication suggests that adversarial
nodes attempt to exploit this capability for their ends, but do so in a
somewhat limited way, perhaps to prevent regular nodes from recognizing their
intent. In addition, we show that the presence of trusted nodes generally has
limited value, but does help when many adversarial nodes are present and
players can communicate. Finally, we use experimental data to develop a
computational model of human behavior, and explore a number of additional
parametric variations, such as features of network topologies, using the
resulting data-driven agent-based model.


  We construct uncertainty intervals for weak Poisson signals in the presence
of background. We consider the case where a primary experiment yields a
realization of the signal plus background, and a second experiment yields a
realization of the background. The data acquisitions times for the
background-only experiment,T_bg, and the primary experiment,T, are selected so
that their ratio varies from 1 to 25. The expected number of background counts
in the primary experiment varies from 0.2 to 2. We construct 90 and 95 percent
confidence intervals based on a propagation-of-errors method as well as two
implementations of a Neyman procedure where acceptance regions are constructed
based on a likelihood-ratio criterion that automatically determines whether the
resulting confidence interval is one-sided or two-sided. The first Neyman
procedure (due to Feldman and Cousins) neglects uncertainty in the background.
In the other Neyman procedure, we account for uncertainty in the background
with a parametric bootstrap method. We also construct minimum length Bayesian
credibility intervals. For each method, we test for the presence of a signal
based on the value of the lower endpoint of the uncertainty interval. When
T_bg/T is 5 or more and the expected background is 2 or less, the Feldman
Cousins method outperforms the other methods considered.


  We report on the small scale (0.5<r<40h^-1 Mpc) clustering of 78895 massive
(M*~10^11.3M_sun) galaxies at 0.2<z<0.4 from the first two years of data from
the Baryon Oscillation Spectroscopic Survey (BOSS), to be released as part of
SDSS Data Release 9 (DR9). We describe the sample selection, basic properties
of the galaxies, and caveats for working with the data. We calculate the real-
and redshift-space two-point correlation functions of these galaxies, fit these
measurements using Halo Occupation Distribution (HOD) modeling within dark
matter cosmological simulations, and estimate the errors using mock catalogs.
These galaxies lie in massive halos, with a mean halo mass of 5.2x10^13 h^-1
M_sun, a large scale bias of ~2.0, and a satellite fraction of 12+/-2%. Thus,
these galaxies occupy halos with average masses in between those of the higher
redshift BOSS CMASS sample and the original SDSS I/II LRG sample.


  We describe geometric algorithms that generalize the classical continued
fraction algorithm for the torus to all translation surfaces in hyperelliptic
components of translation surfaces. We show that these algorithms produce all
saddle connections which are best approximations in a geometric sense, which
generalizes the notion of best approximation for the classical continued
fraction. In addition, they allow to list all systoles along a Teichmueller
geodesic and all bispecial words which appear in the symbolic coding of linear
flows. The elementary moves of the described algorithms provide a geometric
invertible extension of the renormalization moves introduced by S. Ferenczi and
L. Zamboni for the corresponding interval exchange transformations.


  The XENON1T experiment uses a time projection chamber (TPC) with liquid Xenon
to search for Weakly Interacting Massive Particles (WIMPs), a proposed Dark
Matter particle, via direct detection. As this experiment relies on capturing
rare events, the focus is on achieving a high recall of WIMP events. Hence the
ability to distinguish between WIMP and the background is extremely important.
To accomplish this, we suggest using Convolutional Neural Networks (CNNs); a
Machine Learning procedure mainly used in image recognition tasks. To explore
this technique we use XENON collaboration open-source software to simulate the
TPC graphical output of Dark Matter signals and main backgrounds. A CNN turns
out to be a suitable tool for this purpose, as it can identify features in the
images that differentiate the two types of events without the need to
manipulate or remove data in order to focus on a particular region of the
detector. We find that the CNN can distinguish between the dominant background
events (ER) and 500 GeV WIMP events with a recall of 93.4\%, precision of
81.2\% and an accuracy of 87.2\%.


  An almost brief, though lengthy, review introduction about the long history
of higher order gravities and their applications, as employed in the
literature, is provided. We review the analogous procedure between higher order
gravities and GR, as described in our previous works, in order to highlight its
important achievements. Amongst which are presentation of an easy
classification of higher order Lagrangians and its employment as a
\emph{criteria} in order to distinguish correct metric theories of gravity. For
example, it does not permit the inclusion of only one of the second order
Lagrangians in \emph{isolation}. But, it does allow the inclusion of the
cosmological term. We also discuss on the compatibility of our procedure and
the Mach idea. We derive a dimensional dependent version of Duff's trace
anomaly relation, which in \emph{four}-dimension is the same as the usual Duff
relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}
dimension. The square of the Weyl tensor identically satisfies it independent
of dimension, however, this Lagrangian satisfies the previous relation only in
three and four dimensions.


  We present a new method for solving parametrized linear systems. Under
certain assumptions on the parametrization, solutions to the linear systems for
all parameters can be accurately approximated by linear combinations of
solutions to linear systems for a small set of fixed parameters. Combined with
either direct solvers or preconditioned iterative solvers for each linear
system with a fixed parameter, the method is particularly suitable for
situations when solutions to a large number of distinct parameters or a large
number of right hand sides are required. The method is also simple to
parallelize. We demonstrate the applicability of the method to the calculation
of the response functions in electronic structure theory. We demonstrate the
numerical performance of the method using a benzene molecule and a DNA
molecule.


  We construct the space of valuations on a quasi-Polish space in terms of the
characterization of quasi-Polish spaces as spaces of ideals of a countable
transitive relation. Our construction is closely related to domain theoretical
work on the probabilistic powerdomain, and helps illustrate the connections
between domain theory and quasi-Polish spaces. Our approach is consistent with
previous work on computable measures, and can be formalized within weak formal
systems, such as subsystems of second order arithmetic.


  It has been speculated that the recently detected ultra-high energy cosmic
rays may originate from the decays of relic particles with mass of order
$10^{12}$ GeV clustered in the halo of our Galaxy. This hypothesis can be
tested through forthcoming measurements of the spectra of both high energy
cosmic nucleons and neutrinos, which are determined in this model by the
physics of QCD fragmentation, with no astrophysical uncertainties. We evolve
fragmentation spectra measured at LEP energies up to the scale of the decaying
particle mass by numerical solution of the DGLAP equations. This enables
incorporation of the effects of supersymmetry on the development of the cascade
and we also allow for decays into many-particle states. The calculated spectral
shape agrees well with present cosmic ray data beyond the
Greisen-Zatsepin-Kuzmin energy.


  Neuromorphic computing implementing spiking neural networks (SNN) is a
promising technology for reducing the footprint of optical transceivers, as
required by the fast-paced growth of data center traffic. In this work, an SNN
nonlinear demapper is designed and evaluated on a simulated
intensity-modulation direct-detection link with chromatic dispersion. The SNN
demapper is implemented in software and on the analog neuromorphic hardware
system BrainScaleS-2 (BSS-2). For comparison, linear equalization (LE),
Volterra nonlinear equalization (VNLE), and nonlinear demapping by an
artificial neural network (ANN) implemented in software are considered. At a
pre-forward error correction bit error rate of 2e-3, the software SNN
outperforms LE by 1.5 dB, VNLE by 0.3 dB and the ANN by 0.5 dB. The hardware
penalty of the SNN on BSS-2 is only 0.2 dB, i.e., also on hardware, the SNN
performs better than all software implementations of the reference approaches.
Hence, this work demonstrates that SNN demappers implemented on electrical
analog hardware can realize powerful and accurate signal processing fulfilling
the strict requirements of optical communications.


  Decision Trees (DTs) are commonly used for many machine learning tasks due to
their high degree of interpretability. However, learning a DT from data is a
difficult optimization problem, as it is non-convex and non-differentiable.
Therefore, common approaches learn DTs using a greedy growth algorithm that
minimizes the impurity locally at each internal node. Unfortunately, this
greedy procedure can lead to inaccurate trees. In this paper, we present a
novel approach for learning hard, axis-aligned DTs with gradient descent. The
proposed method uses backpropagation with a straight-through operator on a
dense DT representation, to jointly optimize all tree parameters. Our approach
outperforms existing methods on binary classification benchmarks and achieves
competitive results for multi-class tasks. The method is available under:
https://github.com/s-marton/GradTree


  The interaction of the visible and ultraviolet electromagnetic P-wave with
the thin flat metallic film localized between two dielectric media is studied
numerically in the framework of the quantum degenerate electron plasma
approach. The reflectance, transmittance and absorptance power coefficients are
chosen for investigation. It is shown that for the frequencies in the visible
and ultraviolet ranges, the quantum power coefficients differ from the ones
evaluated in framework of both the classical spatial dispersion and the Drude -
Lorentz approaches.


  This paper describes the organization and findings of AXOLOTL'24, the first
multilingual explainable semantic change modeling shared task. We present new
sense-annotated diachronic semantic change datasets for Finnish and Russian
which were employed in the shared task, along with a surprise test-only German
dataset borrowed from an existing source. The setup of AXOLOTL'24 is new to the
semantic change modeling field, and involves subtasks of identifying unknown
(novel) senses and providing dictionary-like definitions to these senses. The
methods of the winning teams are described and compared, thus paving a path
towards explainability in computational approaches to historical change of
meaning.


  In this paper, we deal with the problem of monogenity of number fields
defined by monic irreducible trinomials $F(x)=x^{12}+ax^m+b\in \mathbb{Z}[x]$
with $1\leq m\leq11$. We give sufficient conditions on $a$, $b$, and $m$ so
that the number field $K$ is not monogenic. In particular, for $m=1$ and for
every rational prime $p$, we characterize when $p$ divides the index of $K$ and
we provide a partial answer to the Problem $22$ of Narkiewicz \cite{Nar} for
these number fields. Our results are illustrated by computational examples.


  We report the first detection of the intrinsic velocity dispersion of the
Arches cluster - a young (~2 Myr), massive (~10,000 Solar Mass) starburst
cluster located near the Galactic center. This was accomplished using proper
motion measurements within the central region of the cluster, obtained with the
laser guide star adaptive optics system at Keck Observatory over a 3 year time
baseline (2006-2009). This uniform dataset results in proper motion
measurements that are improved by a factor ~5 over previous measurements from
heterogeneous instruments, yielding internal velocity dispersion estimates 0.15
+/- 0.01 mas/yr, which corresponds to 5.4 +/- 0.4 km/s at a distance of 8.4
kpc.
  Projecting a simple model for the cluster onto the sky to compare with our
proper motion dataset, in conjunction with surface density data, we estimate
the total present-day mass of the cluster to be 15,000 (+7400 -6000) Solar
masses. The mass in stars observed within a cylinder of radius R=0.4 pc is
found to be 9000 (+4000 -3500) Solar Masses at formal 3-sigma confidence. This
mass measurement is free from assumptions about the mass function of the
cluster, and thus may be used to check mass estimates from photometry and
simulation. When we conduct this check, we find that the present-day mass
function of the Arches cluster is likely either top-heavy or truncated at
low-mass, or both.
  Collateral benefits of our data and analysis include: 1. cluster membership
probabilities, which may be used to extract a clean cluster sample for future
photometric work; 2. a refined estimate of the bulk motion of the Arches
cluster with respect to the field, which we find to be 172 +/- 15 km/s, which
is slightly slower than suggested by previous VLT-Keck measurements; and 3. a
velocity dispersion estimate for the field itself, which is likely dominated by
the inner galactic bulge and the nuclear disk.


  We study by extensive Monte Carlo (MC) simulations and analytical Green
function (GF) method effects of frustrated surfaces on the properties of thin
films made of stacked triangular layers of atoms bearing Heisenberg spins with
an Ising-like interaction anisotropy. We suppose that the in-plane surface
interaction $J_s$ can be antiferromagnetic or ferromagnetic while all other
interactions are ferromagnetic. We show that the ground-state spin
configuration is non linear when $J_s$ is lower than a critical value $J_s^c$.
The film surfaces are then frustrated. In the frustrated case, there are two
phase transitions related to disorderings of surface and interior layers. There
is a good agreement between MC and GF results. In addition, we show from MC
histogram calculation that the value of the ratio of critical exponents
$\gamma/\nu$ of the observed transitions is deviated from the values of two and
three Ising universality classes. The origin of this deviation is discussed
with general physical arguments.


  The \textit{Spitzer} SAGE survey has allowed the identification and analysis
of significant samples of Young Stellar Object (YSO) candidates in the Large
Magellanic Cloud (LMC). However the angular resolution of \textit{Spitzer} is
relatively poor meaning that at the distance of the LMC, it is likely that many
of the \textit{Spitzer} YSO candidates in fact contain multiple components. We
present high resolution \textit{K}-band integral field spectroscopic
observations of the three most prominent massive YSO candidates in the N113
H\,{\sc ii} region using VLT/SINFONI. We have identified six \textit{K}-band
continuum sources within the three \textit{Spitzer} sources and we have mapped
the morphology and velocity fields of extended line emission around these
sources. Br$\gamma$, He\,{\sc i} and H$_2$ emission is found at the position of
all six \textit{K}-band sources; we discuss whether the emission is associated
with the continuum sources or whether it is ambient emission. H$_2$ emission
appears to be mostly ambient emission and no evidence of CO emission arising in
the discs of YSOs has been found. We have mapped the centroid velocities of
extended Br$\gamma$ emission and He {\sc i} emission and found evidence of two
expanding compact H\,{\sc ii} regions. One source shows compact and strong
H$_2$ emission suggestive of a molecular outflow. The diversity of
spectroscopic properties observed is interpreted in the context of a range of
evolutionary stages associated with massive star formation.


  In this paper, we study the task of enumerating (and counting) locally and
globally minimal defensive alliances in graphs. We consider general graphs as
well as special graph classes. From an input-sensitive perspective, our
presented algorithms are mostly optimal.


  A ground state path integral quantum Monte Carlo algorithm is introduced that
allows for the study of entanglement in lattice bosons at zero temperature. The
R\'enyi entanglement entropy between spatial subregions is explored across the
phase diagram of the one dimensional Bose-Hubbard model for systems consisting
of up to $L=256$ sites at unit-filling without any restrictions on site
occupancy, far beyond the reach of exact diagonalization. The favorable scaling
of the algorithm is demonstrated through a further measurement of the R\'enyi
entanglement entropy at the two dimensional superfluid-insulator critical point
for large system sizes, confirming the existence of the expected entanglement
boundary law in the ground state. The R\'enyi estimator is extended to measure
the symmetry resolved entanglement that is operationally accessible as a
resource for experimentally relevant lattice gases with fixed total particle
number.


  The synthesis and physical properties of two new and one known Ir-Sn-Se
compound are reported. Their crystal structures are elucidated with
transmission electron microscopy and powder X-ray diffraction. IrSn0.45Se1.55
is a pyrite phase which consists of tilted corner-sharing IrX6 octahedra with
randomly distributed (Sn-Se)4- and (Se-Se)2- dimers. Ir2Sn3Se3 is a trigonally
distorted skutterudite that consists of cooperatively tilted corner-sharing
IrSn3Se3 octahedra with ordered (Sn-Se)24- tetramers. Ir2SnSe5 is a layered,
distorted \b{eta}-MnO2 (pyrolusite) structure consisting of a double IrSe6
octrahedral row, corner-sharing in the a direction and edge-sharing in the b
direction. This distorted pyrolusite contains (Se-Se)2- dimers, Se2- anions,
and each double row is "capped" with a (Sn-Se)n polymeric chain. Resistivity,
specific heat, and magnetization measurements show that all three have
insulating and diamagnetic behavior, indicative of low spin 5d6 Ir3+.
Electronic structure calculations on Ir2Sn3Se3 show a single, spherical,
non-spin-orbit split valence band, and suggest that Ir2Sn3Se3 is topologically
non-trivial under tensile strain, due to inversion of Ir-d and Se-p states.