  Prompt-based knowledge probing for 1-hop relations has been used to measure
how much world knowledge is stored in pretrained language models. Existing work
uses considerable amounts of data to tune the prompts for better performance.
In this work, we compare a variety of approaches under a few-shot knowledge
probing setting, where only a small number (e.g., 10 or 20) of example triples
are available. In addition, we create a new dataset named TREx-2p, which
contains 2-hop relations. We report that few-shot examples can strongly boost
the probing performance for both 1-hop and 2-hop relations. In particular, we
find that a simple-yet-effective approach of finetuning the bias vectors in the
model outperforms existing prompt-engineering methods. Our dataset and code are
available at \url{https://github.com/cloudygoose/fewshot_lama}.


  Here we introduce and study a photonic analogue of the Kondo model. The model
is defined as a far detuned regime of photonic scattering off a three-level
emitter in a $\Lambda$-type configuration coupled to a one-dimensional
transmission line with linear dispersion. We characterize this system by
studying the dynamics of a local system (emitter) driven by a coherent field
pulse as well as the first- and second-order correlation functions of the
scattered light. Various polarization-dependent correlation effects including
entanglement between the emitter and transmitted photons are quantified by the
purity of the emitter's state. We also show that statistical properties of the
scattered light are very sensitive to the polarization of the incoming coherent
pulse.


  Given a real curve, we study special linear systems called "very special" for
which the dimension does not satisfy a Clifford type inequality. We classify
all these very special linear systems when the gonality of the curve is small.


  Given two finite words $u$ and $v$ of equal length, define the \emph{overlap
gap between $u$ and $v$}, denoted $og(u,v)$, as the least integer $m$ for which
there exist words $x$ and $x'$ of length $m$ such that $xu=vx'$ or $ux=x'v$.
Informally, the overlap gap measures the outside parts of the greatest overlap
of the given words.
  For a left-infinite word $\lambda$ and a right-infinite word $\rho$, let
$og_{\lambda,\rho}$ be the function defined, for each non-negative integer $n$,
by $og_{\lambda,\rho}(n)=og(\lambda_n,\rho_n)$, where $\lambda_n$ and $\rho_n$
are, respectively, the suffix of $\lambda$ and the prefix of $\rho$ of length
$n$. Also, denote by $OG_{\lambda,\rho}$ the image of the function
$og_{\lambda,\rho}$.
  In this paper, we show that $OG_{\lambda,\rho}$ is a finite set if and only
if $\lambda$ and $\rho$ are ultimately periodic infinite words of the form
$\lambda=u^{-\infty}w_1=\cdots uuuw_1$ and $\rho=w_2u^\infty=w_2uuu\cdots$ for
some finite words $u$, $w_1$ and $w_2$.


  We calculate the abundances of electrons and ions in the hot (> 500 K), dusty
parts of protoplanetary disks, treating for the first time the effects of
thermionic and ion emission from the dust grains. High-temperature ionization
modeling has involved simply assuming that alkali elements such as potassium
occur as gas-phase atoms and are collisionally ionized following the Saha
equation. We show that the Saha equation often does not hold, because free
charges are produced by thermionic and ion emission and destroyed when they
stick to grain surfaces. This means the ionization state depends not on the
first ionization potential of the alkali atoms, but rather on the grains' work
functions. The charged species' abundances typically rise abruptly above about
800 K, with little qualitative dependence on the work function, gas density, or
dust-to-gas mass ratio. Applying our results, we find that protoplanetary
disks' dead zone, where high diffusivities stifle magnetorotational turbulence,
has its inner edge located where the temperature exceeds a threshold value
~1000 K. The threshold is set by ambipolar diffusion except at the highest
densities, where it is set by Ohmic resistivity. We find that the disk gas can
be diffusively loaded onto the stellar magnetosphere at temperatures below a
similar threshold. We investigate whether the "short-circuit" instability of
current sheets can operate in disks and find that it cannot, or works only in a
narrow range of conditions; it appears not to be the chondrule formation
mechanism. We also suggest that thermionic emission is important for
determining the rate of Ohmic heating in hot Jupiters.


  The electronic structure of two vertically coupled quantum dots containing
two electrons is investigated in the presence of interdot tunneling. Our
approach also includes the interdot exchange and we find that the tunneling is
affected by the Coulomb interaction. There is an interplay between direct
tunneling, the interdot exchange and the Coulomb interaction influence on the
tunneling, which can lead to a zero angular momentum spin-singlet -
spin-triplet transition of the ground state, even in the absence of a magnetic
field.


  We present a successful inflation model based on $\lambda \phi^4$ potential
in which a Standard Model (SM) singlet inflaton $\phi$, with mass of around a
TeV or less, also plays the role of a weakly interacting scalar dark matter
particle (WIMP). The WIMP relic abundance generated after inflation is in
accord with the current observations. The spectral index $n_s$ lies within the
WMAP 1-$\sigma$ bounds, while the Planck satellite may observe the
tensor-to-scalar ratio, a canonical measure of gravity waves, which we estimate
lies between 0.003 and 0.007.An unbroken $Z_2$ parity ensures that the scalar
WIMP is absolutely stable.


  Many commercial products are sold with warranties and indirectly through
dealers. The manufacturer-retailer distribution mechanism results in serious
missing data problems in field return data, as the sales date for an unreturned
unit is generally unknown to the manufacturer. This study considers a general
setting for field failure data with unknown sales dates and a warranty limit. A
stochastic expectation-maximization (SEM) algorithm is developed to estimate
the distributions of the sales lag (time between shipment to a retailer and
sale to a customer) and the lifetime of the product under study. Extensive
simulations are used to evaluate the performance of the SEM algorithm and to
compare with the imputation method proposed by Ghosh [Ann. Appl. Stat. 4 (2010)
1976-1999]. Three real examples illustrate the methodology proposed in this
paper.


  Insider threat detection is getting an increased concern from academia,
industry, and governments due to the growing number of malicious insider
incidents. The existing approaches proposed for detecting insider threats still
have a common shortcoming, which is the high number of false alarms (false
positives). The challenge in these approaches is that it is essential to detect
all anomalous behaviours which belong to a particular threat. To address this
shortcoming, we propose an opportunistic knowledge discovery system, namely
AnyThreat, with the aim to detect any anomalous behaviour in all malicious
insider threats. We design the AnyThreat system with four components. (1) A
feature engineering component, which constructs community data sets from the
activity logs of a group of users having the same role. (2) An oversampling
component, where we propose a novel oversampling technique named Artificial
Minority Oversampling and Trapper REmoval (AMOTRE). AMOTRE first removes the
minority (anomalous) instances that have a high resemblance with normal
(majority) instances to reduce the number of false alarms, then it
synthetically oversamples the minority class by shielding the border of the
majority class. (3) A class decomposition component, which is introduced to
cluster the instances of the majority class into subclasses to weaken the
effect of the majority class without information loss. (4) A classification
component, which applies a classification method on the subclasses to achieve a
better separation between the majority class(es) and the minority class(es).
AnyThreat is evaluated on synthetic data sets generated by Carnegie Mellon
University. It detects approximately 87.5% of malicious insider threats, and
achieves the minimum of false positives=3.36%.


  A list of forty third-order exactly integrable two-field evolutionary systems
is presented. Differential substitutions connecting various systems from the
list are found. It is proved that all the systems can be obtained from only two
of them. Examples of zero curvature representations with $4 \times 4$ matrices
are presented.


  We develop a simple stock selection model to explain why active equity
managers tend to underperform a benchmark index. We motivate our model with the
empirical observation that the best performing stocks in a broad market index
often perform much better than the other stocks in the index. Randomly
selecting a subset of securities from the index may dramatically increase the
chance of underperforming the index. The relative likelihood of
underperformance by investors choosing active management likely is much more
important than the loss to those same investors from the higher fees for active
management relative to passive index investing. Thus, active management may be
even more challenging than previously believed, and the stakes for finding the
best active managers may be larger than previously assumed.


  We study symmetry restoration at finite temperature in the standard model
during the electroweak phase transition in the presence of a weak magnetic
field. We compute the finite temperature effective potential up to the
contribution of ring diagrams, using the broken phase degrees of freedom, and
keep track of the gauge parameter dependence of the results. We show that under
these conditions, the phase transition becomes stronger first order.


  For the incompressible Euler equations the pressure formally scales as a
quadratic function of velocity. We provide several optimal regularity estimates
on the pressure by using regularity of velocity in various Sobolev, Besov and
Hardy spaces. Our proof exploits the incompressibility condition in an
essential way and is deeply connected with the classic Div-Curl lemma which we
also generalise as a fractional Leibniz rule in Hardy spaces. To showcase the
sharpness of results, we construct a class of counterexamples at several
end-points.


  Universal Drinfeld twists are inner automorphisms which relate the coproduct
of a quantum enveloping algebra to the coproduct of the undeformed enveloping
algebra. Even though they govern the deformation theory of classical symmetries
and have appeared in numerous applications, no twist for a semi-simple quantum
enveloping algebra has ever been computed. It is argued that universal twists
can be reconstructed from their well known representations. A method to
reconstruct an arbitrary element of the enveloping algebra from its irreducible
representations is developed. For the twist this yields an algebra valued
generating function to all orders in the deformation parameter, expressed by a
combination of basic and ordinary hypergeometric functions. An explicit
expression for the universal twist of su(2) is given up to third order.


  Partial Split Supersymmetry with violation of R-parity as a model for
neutrino masses is explored. It is shown that at the one-loop level the model
can give predictions that are in agreement with all present experimental values
for the neutrino sector. An analytical result is that the small solar neutrino
mass difference can be naturally explained in the decoupling limit for the
heavy Higgs mass eigenstates.


  We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson
initiated the study of families $\\mathcal F$ of graphs with the property that
if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some
fixed $p\in(0,1]$ for every $F\in \mathcal F$, then $G$ is quasirandom with
density $p$. Such families $\mathcal F$ are said to be forcing. Several forcing
families were found over the last three decades and characterising all
bipartite graphs $F$ such that $(K_2,F)$ is a forcing pair is a well-known open
problem in the area of quasirandom graphs, which is closely related to
Sidorenko's conjecture. In fact, most of the known forcing families involve
bipartite graphs only.
  We consider forcing pairs containing the triangle $K_3$. In particular, we
show that if $(K_2,F)$ is a forcing pair, then so is $(K_3,F')$, where $F'$ is
obtained from $F$ by replacing every edge of $F$ by a triangle (each of which
introduces a new vertex). For the proof we first show that $(K_3,C'_4)$ is a
forcing pair, which strengthens related results of Simonovits and S\'os and of
Conlon et al.


  Planar superconducting microwave resonators are key elements in a variety of
technical applications and also act as sensitive probes for microwave
spectroscopy of various materials of interest. Here superconducting Pb is a
suitable material as a basis for microwave stripline resonators.
  To utilize Pb stripline resonators in a variable magnetic field (e.g. in
ESR), the electrodynamics of such resonators in finite magnetic field has to be
well understood. Therefore we performed microwave transmission measurements on
superconducting Pb stripline resonators in a variable, parallel magnetic field.
We determined surface resistance, penetration depth as well as real and
imaginary parts, \sigma$_1$ and \sigma$_2$, of the complex conductivity of
superconducting Pb as a function of magnetic field. Here we find features
reminiscent of those in temperature-dependent measurements, such as a maximum
in \sigma$_1$ (coherence peak). At magnetic fields above the critical field of
this type-I superconductor we still find low-loss microwave response, which we
assign to remaining superconductivity in the form of filaments within the Pb.
Hysteresis effects are found in the quality factor of resonances once the swept
magnetic field has exceeded the critical magnetic field. This is due to normal
conducting areas that are pinned and can therefore persist in the
superconducting phase. Besides zero-field-cooling we show an alternative way to
eliminate these even at T<T$_c$. Based on our microwave data, we determine the
critical magnetic field and the critical temperature of Pb in a temperature
range between 1.6K and 6.5K and magnetic fields up to 140mT, showing good
agreement with BCS predictions. We study a Sn sample in a Pb resonator to
demonstrate the applicability of superconducting Pb stripline resonators in the
experimental study of other (super-)conducting materials in a variable magnetic
field.


  Starting from noncommutative quantum mechanics algebra, we investigate the
variances of the deformed two-mode quadrature operators under the evolution of
three types of two-mode squeezed states in noncommutative space. A novel
conclusion can be found and it may associate the checking of the variances in
noncommutative space with homodyne detecting technology. Moreover, we analyze
the influence of the scaling parameter on the degree of squeezing for the
deformed level and the corresponding consequences.


  Filter pruning has been widely used for compressing convolutional neural
networks to reduce computation costs during the deployment stage. Recent
studies have shown that filter pruning techniques can achieve lossless
compression of deep neural networks, reducing redundant filters (kernels)
without sacrificing accuracy performance. However, the evaluation is done when
the training and testing data are from similar environmental conditions
(independent and identically distributed), and how the filter pruning
techniques would affect the cross-domain generalization (out-of-distribution)
performance is largely ignored. We conduct extensive empirical experiments and
reveal that although the intra-domain performance could be maintained after
filter pruning, the cross-domain performance will decay to a large extent. As
scoring a filter's importance is one of the central problems for pruning, we
design the importance scoring estimation by using the variance of domain-level
risks to consider the pruning risk in the unseen distribution. As such, we can
remain more domain generalized filters. The experiments show that under the
same pruning ratio, our method can achieve significantly better cross-domain
generalization performance than the baseline filter pruning method. For the
first attempt, our work sheds light on the joint problem of domain
generalization and filter pruning research.


  The paper of Arovas, Schrieffer and Wilczek is corrected. It is found that
the Berry's phase is vanishingly small. Accordingly, the statistical vector
potential becomes negligibly small.


  We introduce NATURAL PLAN, a realistic planning benchmark in natural language
containing 3 key tasks: Trip Planning, Meeting Planning, and Calendar
Scheduling. We focus our evaluation on the planning capabilities of LLMs with
full information on the task, by providing outputs from tools such as Google
Flights, Google Maps, and Google Calendar as contexts to the models. This
eliminates the need for a tool-use environment for evaluating LLMs on Planning.
We observe that NATURAL PLAN is a challenging benchmark for state of the art
models. For example, in Trip Planning, GPT-4 and Gemini 1.5 Pro could only
achieve 31.1% and 34.8% solve rate respectively. We find that model performance
drops drastically as the complexity of the problem increases: all models
perform below 5% when there are 10 cities, highlighting a significant gap in
planning in natural language for SoTA LLMs. We also conduct extensive ablation
studies on NATURAL PLAN to further shed light on the (in)effectiveness of
approaches such as self-correction, few-shot generalization, and in-context
planning with long-contexts on improving LLM planning.


  In this work, we focus on effectively leveraging and integrating information
from concept-level as well as word-level via projecting concepts and words into
a lower dimensional space while retaining most critical semantics. In a broad
context of opinion understanding system, we investigate the use of the fused
embedding for several core NLP tasks: named entity detection and
classification, automatic speech recognition reranking, and targeted sentiment
analysis.


  The question of pseudovector versus pseudoscalar coupling schemes for the
kaon-hyperon-nucleon interaction is re-examined for the reaction $\gamma p\to
K^+ \Lambda$ in several isobaric models. These models typically include Born
terms, $K^*$- and $K_1$-exchange in the t-channel, and a few different
combinations of spin-1/2 baryon resonances in the $s$- and $u$-channels. The
coupling constants are obtained by fitting to a large data set. We find that
both pseudoscalar and pseudovector couplings can allow for a satisfactory
description of the present database. The resulting coupling constants,
$g_{K\Lambda N}$ and $g_{K\Sigma N}$, in the pseudovector coupling scheme are
smaller than those predicted using flavor SU(3) symmetry, but consistent with
the values obtained in a QCD sum rule calculation.


  To constrain the large-scale magnetic field strengths in cosmologically
distant galax- ies, we derive the probability distribution function of Faraday
rotation measure (RM) when random lines of sight pass through a sample of disc
galaxies, with axisymmetric large-scale magnetic fields. We find that the width
of the RM distribution of the galaxy sample is directly related to the mean
large-scale field strength of the galaxy population, provided the dispersion
within the sample is lower than the mean value. In the absence of additional
constraints on parameters describing the magneto-ionic medium of the
intervening galaxies, and in the situation where RMs produced in the
intervening galaxies have already been statistically isolated from other RM
contributions along the lines of sight, our simple model of the magneto-ionic
medium in disc galaxies suggests that the mean large-scale magnetic field of
the population can be measured to within ~ 50% accuracy.


  In dynamic quantum circuits, classical information from mid-circuit
measurements is fed forward during circuit execution. This emerging capability
of quantum computers confers numerous advantages that can enable more efficient
and powerful protocols by drastically reducing the resource requirements for
certain core algorithmic primitives. In particular, in the case of the
$n$-qubit quantum Fourier transform followed immediately by measurement, the
scaling of resource requirements is reduced from $O(n^2)$ two-qubit gates in an
all-to-all connectivity in the standard unitary formulation to $O(n)$
mid-circuit measurements in its dynamic counterpart without any connectivity
constraints. Here, we demonstrate the advantage of dynamic quantum circuits for
the quantum Fourier transform on IBM's superconducting quantum hardware with
certified process fidelities of $>50\%$ on up to $16$ qubits and $>1\%$ on up
to $37$ qubits, exceeding previous reports across all quantum computing
platforms. These results are enabled by our contribution of an efficient method
for certifying the process fidelity, as well as of a dynamical decoupling
protocol for error suppression during mid-circuit measurements and feed-forward
within a dynamic quantum circuit that we call ``feed-forward-compensated
dynamical decoupling" (FC-DD). Our results demonstrate the advantages of
leveraging dynamic circuits in optimizing the compilation of quantum
algorithms.


  We present a study of the intra-cluster population of low-mass X-ray binaries
(LMXB) residing in globular clusters (GC) in the central 1 $deg^2$ of the
Fornax galaxy cluster. Differently from previous studies, which were restricted
to the innermost regions of individual galaxies, this work is aimed at
comparing the properties of the intra-cluster population of GC-LMXBs with those
of the host galaxy. We use VLT Survey Telescope (VST) and Chandra observations.
We identify 168 LMXBs residing in GCs and divide it into host-galaxy and
intra-cluster objects based on their distance from the nearest galaxy in terms
of effective radius. We found 82 intra-cluster GC-LMXBs and 86 objects that are
hosted in galaxies. We perform a Gaussian mixture model to divide the
population into red and blue GCs. As has been found for the innermost regions
of galaxies, LMXBs tend to form in red and bright GCs in intra-cluster space as
well. We find, however, that the likelihood of a red GC to host an LMXB
decreases with galactocentric distance, but it remains approximately constant
for the blue GC population. Investigating the X-ray properties of the LMXBs
residing in GCs, we find a difference in the X-ray luminosity function between
the intra-cluster and host-galaxy sample: both follow a power-law down to $\sim
8.5\times 10^{37}$ erg s$^{-1}$, which is consistent with field LMXBs for the
intra-cluster sample, while the latter agree with previous estimates for LMXBs
in GCs. We detect a tentative difference in the hardness ratio of two
populations, where the intra-cluster GC-LMXBs appear to have harder spectra
than the host-galaxy objects. We find the same trend when we compare red and
blue GC-LMXBs: the spectra of the blue sample are harder spectra than those of
the red sample. This result could suggest a relation between the spectral
properties of LMXBs and the host GC colour and therefore its metallicity.


  Using the Tibet-III air shower array, we search for TeV gamma-rays from 27
potential Galactic sources in the early list of bright sources obtained by the
Fermi Large Area Telescope at energies above 100 MeV. Among them, we observe 7
sources instead of the expected 0.61 sources at a significance of 2 sigma or
more excess. The chance probability from Poisson statistics would be estimated
to be 3.8 x 10^-6. If the excess distribution observed by the Tibet-III array
has a density gradient toward the Galactic plane, the expected number of
sources may be enhanced in chance association. Then, the chance probability
rises slightly, to 1.2 x 10^-5, based on a simple Monte Carlo simulation. These
low chance probabilities clearly show that the Fermi bright Galactic sources
have statistically significant correlations with TeV gamma-ray excesses. We
also find that all 7 sources are associated with pulsars, and 6 of them are
coincident with sources detected by the Milagro experiment at a significance of
3 sigma or more at the representative energy of 35 TeV. The significance maps
observed by the Tibet-III air shower array around the Fermi sources, which are
coincident with the Milagro >=3sigma sources, are consistent with the Milagro
observations. This is the first result of the northern sky survey of the Fermi
bright Galactic sources in the TeV region.


  This article offers sharp spatial and temporal mean-square regularity results
for a class of semi-linear parabolic stochastic partial differential equations
(SPDEs) driven by infinite dimensional fractional Brownian motion with the
Hurst parameter greater than one-half. In addition, mean-square numerical
approximation of such problem are investigated, performed by the spectral
Galerkin method in space and the linear implicit Euler method in time. The
obtained sharp regularity properties of the problems enable us to identify
optimal mean-square convergence rates of the full discrete scheme. These
theoretical findings are accompanied by several numerical examples.


  In this paper, we study certain critical Schr\"{o}dinger-Kirchhoff type
systems involving the fractional $p$-Laplace operator on a bounded domain. More
precisely, using the properties of the associated functional energy on the
Nehari manifold sets and exploiting the analysis of the fibering map, we
establish the multiplicity of solutions for such systems.


  An action principle for the generalized harmonic formulation of general
relativity is presented. The action is a functional of the spacetime metric and
the gauge source vector. An action principle for the Z4 formulation of general
relativity has been proposed recently by Bona, Bona--Casas and Palenzuela
(BBP). The relationship between the generalized harmonic action and the BBP
action is discussed in detail.


  It is shown that Bogoliubov quasi-averages select the pure or ergodic states
in the ergodic decomposition of the thermal (Gibbs) state. Our examples include
quantum spin systems and many-body boson systems. As a consequence, we
elucidate the problem of equivalence between Bose-Einstein condensation and the
quasi-average spontaneous symmetry breaking (SSB) discussed for continuous
boson systems. The multi-mode extended van den Berg-Lewis-Pul\'{e} condensation
of type III demonstrates that the only physically reliable quantities are those
that defined by Bogoliubov quasi-averages.


  We propose a new semi-parametric approach to the joint segmentation of
multiple series corrupted by a functional part. This problem appears in
particular in geodesy where GPS permanent station coordinate series are
affected by undocumented artificial abrupt changes and additionally show
prominent periodic variations. Detecting and estimating them are crucial, since
those series are used to determine averaged reference coordinates in
geosciences and to infer small tectonic motions induced by climate change. We
propose an iterative procedure based on Dynamic Programming for the
segmentation part and Lasso estimators for the functional part. Our Lasso
procedure, based on the dictionary approach, allows us to both estimate smooth
functions and functions with local irregularity, which permits more flexibility
than previous proposed methods. This yields to a better estimation of the bias
part and improvements in the segmentation. The performance of our method is
assessed using simulated and real data. In particular, we apply our method to
data from four GPS stations in Yarragadee, Australia. Our estimation procedure
results to be a reliable tool to assess series in terms of change detection and
periodic variations estimation giving an interpretable estimation of the
functional part of the model in terms of known functions.


  Aims. We provide an in-depth analysis of the COSMOS-Web ring, an Einstein
ring at z=2 that we serendipitously discovered in the COSMOS-Web survey and
possibly the most distant lens discovered to date.
  Methods. We extract the visible and NIR photometry from more than 25 bands
and we derive the photometric redshifts and physical properties of both the
lens and the source with three different SED fitting codes. Using JWST/NIRCam
images, we also produce two lens models to (i) recover the total mass of the
lens, (ii) derive the magnification of the system, (iii) reconstruct the
morphology of the lensed source, and (iv) measure the slope of the total mass
density profile of the lens.
  Results. The lens is a very massive and quiescent (sSFR < 10^(-13) yr-1)
elliptical galaxy at z = 2.02 \pm 0.02 with a total mass Mtot(<thetaE) = (3.66
\pm 0.36) x 10^11 Msun and a stellar mass M* = (1.37 \pm 0.14) x 10^11 Msun.
Compared to SHMRs from the literature, we find that the total mass is
consistent with the presence of a DM halo of mass Mh = 1.09^(+1.46)_(-0.57) x
10^13 Msun. In addition, the background source is a M* = (1.26 \pm 0.17) x
10^10 Msun star-forming galaxy (SFR=(78 \pm 15) Msun/yr) at z = 5.48 \pm 0.06.
Its reconstructed morphology shows two components with different colors. Dust
attenuation values from SED fitting and nearby detections in the FIR also
suggest it could be partially dust-obscured.
  Conclusions. We find the lens at z=2. Its total, stellar, and DM halo masses
are consistent within the Einstein ring, so we do not need any unexpected
changes in our description of the lens (e.g. change its IMF or include a
non-negligible gas contribution). The most likely solution for the lensed
source is at z = 5.5. Its reconstructed morphology is complex and highly
wavelength dependent, possibly because it is a merger or a main sequence galaxy
with a heterogeneous dust distribution.


  We investigate the dependence of the GRB jet structure and its evolution on
the properties of the accreting torus in the central engine. Our models
numerically evolve the accretion disk around a Kerr black hole using 3D general
relativistic magnetohydrodynamic simulations. We use two different analytical
hydrodynamical models of the accretion disk, based on the Fishbone-Moncrief and
Chakrabarti solutions, as our initial states for the structure of the collapsar
disk and the remnant after a binary neutron star merger, respectively. We
impose poloidal magnetic fields of two different geometries upon the initial
stable solutions. We study the formation and evolution of the magnetically
arrested disk state and its effect on the properties of the emitted jet. The
jets produced in our models are structured and have a relatively hollow core
and reach higher Lorentz factors at an angle $\gtrsim 9{^\circ}$ from the axis.
The jet in our short GRB model has an opening angle of up to $\sim 25^{\circ}$
while our long GRB engine produces a narrower jet, of up to $\sim 11^{\circ}$.
We also study the time variability of the jets and provide an estimate of the
minimum variability timescale in our models. The application of our models to
the GRB jets in the binary neutron star post-merger system and to the
ultra-relativistic jets launched from collapsing stars are briefly discussed.


  Gibbs sampling is the de facto Markov chain Monte Carlo method used for
inference and learning on large scale graphical models. For complicated factor
graphs with lots of factors, the performance of Gibbs sampling can be limited
by the computational cost of executing a single update step of the Markov
chain. This cost is proportional to the degree of the graph, the number of
factors adjacent to each variable. In this paper, we show how this cost can be
reduced by using minibatching: subsampling the factors to form an estimate of
their sum. We introduce several minibatched variants of Gibbs, show that they
can be made unbiased, prove bounds on their convergence rates, and show that
under some conditions they can result in asymptotic single-update-run-time
speedups over plain Gibbs sampling.


  In this paper, we study the existence of infinite dimensional closed linear
subspaces of a rearrangement invariant space on [0,1] every nonzero element of
which does not belong to any included rearrangement invariant space of the same
class such that the inclusion operator is disjointly strictly singular. We
consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative
for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the
same problem is studied for Nakano spaces assuming different hypothesis.


  Agent-based modeling (ABM) is a powerful paradigm to gain insight into social
phenomena. One area that ABM has rarely been applied is coalition formation.
Traditionally, coalition formation is modeled using cooperative game theory. In
this paper, a heuristic algorithm is developed that can be embedded into an ABM
to allow the agents to find coalition. The resultant coalition structures are
comparable to those found by cooperative game theory solution approaches,
specifically, the core. A heuristic approach is required due to the
computational complexity of finding a cooperative game theory solution which
limits its application to about only a score of agents. The ABM paradigm
provides a platform in which simple rules and interactions between agents can
produce a macro-level effect without the large computational requirements. As
such, it can be an effective means for approximating cooperative game solutions
for large numbers of agents. Our heuristic algorithm combines agent-based
modeling and cooperative game theory to help find agent partitions that are
members of a games' core solution. The accuracy of our heuristic algorithm can
be determined by comparing its outcomes to the actual core solutions. This
comparison achieved by developing an experiment that uses a specific example of
a cooperative game called the glove game. The glove game is a type of exchange
economy game. Finding the traditional cooperative game theory solutions is
computationally intensive for large numbers of players because each possible
partition must be compared to each possible coalition to determine the core
set; hence our experiment only considers games of up to nine players. The
results indicate that our heuristic approach achieves a core solution over 90%
of the time for the games considered in our experiment.


  We study the eigenvectors of generalized Wigner matrices with subexponential
entries and prove that they delocalize at the optimal rate with overwhelming
probability. We also prove high probability delocalization bounds with sharp
constants. Our proof uses an analysis of the eigenvector moment flow introduced
by Bourgade and Yau (2017) to bound logarithmic moments of eigenvector entries
for random matrices with small Gaussian components. We then extend this control
to all generalized Wigner matrices by comparison arguments based on a framework
of regularized eigenvectors, level repulsion, and the observable employed by
Landon, Lopatto, and Marcinek (2018) to compare extremal eigenvalue statistics.
Additionally, we prove level repulsion and eigenvalue overcrowding estimates
for the entire spectrum, which may be of independent interest.


  We present a version of ten-dimensional IIA supergravity containing a 9-form
potential for which the field equations are equivalent to those of the
standard, massless, IIA theory for vanishing 10-form field strength, $F_{10}$,
and to those of the `massive' IIA theory for non-vanishing $F_{10}$. We present
a multi 8-brane solution of these equations that generalizes the 8-brane of
Polchinski and Witten. We show that this solution is T-dual to a new multi
7-brane solution of $S^1$ compactified IIB supergravity, and that the latter is
T-dual to the IIA 6-brane. When combined with the $Sl(2;\Z)$ U-duality of the
type IIB superstring, the T-duality between type II 7-branes and 8-branes
implies a quantization of the cosmological constant of type IIA superstring
theory. These results are made possible by the construction of a new {\it
massive} N=2 D=9 supergravity theory. We also discuss the 11-dimensional
interpretation of these type II p-branes.


  G4.8+6.2 was proposed as a possible kilonova remnant associated with the
Korean guest star of AD 1163 in our Milky Way galaxy. Its age is about 860
years according to the historical record. If a neutron star was left in the
center of G4.8+6.2, this young neutron star may radiate strong continuous
gravitational waves, which could beat the indirect age-based upper limit with
current LIGO sensitivity. In this work, we searched such continuous
gravitational waves in the frequency band $20-1500 \mathrm{~Hz}$. This search
used two days of LIGO O3b data from the Hanford and Livingston detectors. While
no signal was found, we placed upper limits on the gravitational wave strain.
For comparison, we also showed the latest results of all-sky searches obtained
with various search pipelines. With upgrading of the gravitational wave
detectors, it will provide the opportunity to see whether a black hole or a
neutron star is harbored inside G4.8+6.2.


  The PYTHIA Monte Carlo (PMC) has been applied broadly to simulations of
high-energy $p$-$p$ and $p$-$\bar p$ collisions. The PMC is based on several
assumptions, such as that most hadrons result from jet production (multiple
parton interactions or MPIs), that $p$-$p$ centrality is relevant and that
color reconnection (CR) strongly influences fragmentation to jets. An
alternative description is provided by the two-component (soft + hard) model
(TCM) of hadron production. TCM analysis of $p$-Pb ensemble-mean-$p_t$ data
reveals centrality trends quite different from those estimated via a geometric
Glauber model based on the eikonal approximation. Glauber estimates of
binary-collision number are three times TCM estimates. Detailed study of $p$-Pb
data conflicts with a basic Glauber assumption -- that a projectile proton may
interact simultaneously with multiple target nucleons. Instead, in both $p$-$p$
and $p$-A collisions, a $p$-N collision once initiated is exclusive of other
possible interactions (during that collision), and within the collision any
pair of participant partons may interact -- a $p$-N collision is thus "all or
nothing." In this presentation the PMC is challenged by an assortment of
contradictory data, and evidence for $p$-N exclusivity is reviewed to make a
case for the "preoccupied proton" of the title.


  We study the irreversible growth of magnetic thin films under the influence
of spatially periodic fields by means of extensive Monte Carlo simulations. We
find first-order pseudo-phase transitions that separate a dynamically
disordered phase from a dynamically ordered phase. By analogy with
time-dependent oscillating fields applied to Ising-type models, we
qualitatively associate this dynamic transition with the
localization/delocalization transition of "spatial hysteresis" loops. Depending
on the relative width of the magnetic film, $L$, compared to the wavelength of
the external field, $\lambda$, different transition regimes are observed. For
small systems ($L<\lambda$), the transition is associated with the Standard
Stochastic Resonance regime, while, for large systems ($L>\lambda$), the
transition is driven by Anomalous Stochastic Resonance. The origin of the
latter is identified as due to the emergence of an additional relevant
lengthscale, namely the roughness of the spin domain switching interface. The
distinction between different stochastic resonance regimes is discussed at
length, both qualitatively by means of snapshot configurations, as well as
quantitatively via residence-length and order-parameter probability
distributions.


  Lepton-flavour violating processes, such as $\mu \to e\gamma$, are studied in
ordinary (non-SUSY) SU(5) and SUSY SU(5) grand unified theories. First given
are some introductory argument on the mechanism of U.V. divergence cancellation
in flavour changing neutral current processes and on the decoupling of
particles with GUT scale masses . We next see that such general argument is
confirmed by an explicit calculation of the amplitude of $\mu \to e\gamma$ in
ordinary SU(5), which shows that logarithmic divergence really cancels among
diagrams and remaining finite part are suppressed by at least $1/M_{GUT}^2$. In
SUSY SU(5), flavour changing slepton mass-squared term get a logarithmic
correction, as recently claimed. However, when the effect of flavour changing
wave function renormalization is also taken into account such logarithmic
correction turns out to disappear, provided a condition is met among SUSY
breaking soft masses. In SUGRA-inspired SUSY GUT, such condition is not
satisfied. But the remaining logarithmic effect is argued not to be taken as a
prediction of the theory associated with an irrelevant operator. We find that
the log-correction should not exist in models with gauge mediated SUSY
breaking.


  We show that the exact ground state for a class of extended Hubbard models
including bond-charge, exchange, and pair-hopping terms, is the Yang
"eta-paired" state for any non-vanishing value of the pair-hopping amplitude,
at least when the on-site Coulomb interaction is attractive enough and the
remaining physical parameters satisfy a single constraint. The ground state is
thus rigorously superconducting. Our result holds on a bipartite lattice in any
dimension, at any band filling, and for arbitrary electron hopping.


  This is a preliminary report on the work aimed at making CR-Prolog -- a
version of ASP with consistency restoring rules -- more suitable for use in
teaching and large applications. First we describe a sorted version of
CR-Prolog called SPARC. Second, we translate a basic version of the CR-Prolog
into the language of DLV and compare the performance with the state of the art
CR-Prolog solver. The results form the foundation for future more efficient and
user friendly implementation of SPARC and shed some light on the relationship
between two useful knowledge representation constructs: consistency restoring
rules and weak constraints of DLV.


  A new system, Bee Cluster 3D, allowing the study of the time evolution of the
3D temperature distribution in a bee hive is presented. This system can be used
to evaluate the cluster size and the location of the queen during winter. In
summer, the device can be used to quantify the size of the brood nest and the
breeding activity of the queen. The system does not disturb the activity of the
colony and can be used on any hive. This electronic system was developed to be
non-intrusive, miniaturized, and energy autonomous.


  We calculate modified Urca neutrino emission rates in the dense nuclear
matter in neutron star cores. We find that these rates are strongly enhanced in
the beta-stable matter in regions of the core close to the direct Urca process
threshold. This enhancement can be tracked to the use of the in-medium nucleon
spectrum in the virtual nucleon propagator. We describe the in-medium nucleon
scattering in the non-relativistic Bruckner-Hartree-Fock framework taking into
account two-body as well as the effective three-body forces, although the
proposed enhancement does not rely on a particular way of the nucleon
interaction treatment. Finally we suggest a simple approximate expression for
the emissivity of the n-branch of the modified Urca process that can be used in
the neutron stars cooling simulations with any nucleon equation of state of
dense matter.


  This work aims at identifying and quantifying uncertainties related to
elastic and viscoelastic parameters, which characterize the arterial wall
behavior, in one-dimensional modeling of the human arterial hemodynamics. The
chosen uncertain parameters are modeled as random Gaussian-distributed
variables, making stochastic the system of governing equations. The proposed
methodology is initially validated on a model equation, presenting a thorough
convergence study which confirms the spectral accuracy of the stochastic
collocation method and the second-order accuracy of the IMEX finite volume
scheme chosen to solve the mathematical model. Then, univariate and
multivariate uncertain quantification analyses are applied to the a-FSI blood
flow model, concerning baseline and patient-specific single-artery test cases.
A different sensitivity is depicted when comparing the variability of flow rate
and velocity waveforms to the variability of pressure and area, the latter ones
resulting much more sensitive to the parametric uncertainties underlying the
mechanical characterization of vessel walls. Simulations performed considering
both the simple elastic and the more realistic viscoelastic constitutive law
show that the great uncertainty of the viscosity parameter plays a major role
in the prediction of pressure waveforms, enlarging the confidence interval of
this variable. In-vivo recorded patient-specific pressure data falls within the
confidence interval of the output obtained with the proposed methodology and
expectations of the computed pressures are comparable to the recorded
waveforms.


  This paper focuses on the use of knowledge possessed by designers. Data
collection was based on observations (by the cognitive ergonomics researcher)
and simultaneous verbalisations (by the designers) in empirical studies
conducted in the context of industrial design projects. The contribution of
this research is typical of cognitive ergonomics, in that it provides data on
actual activities implemented by designers in their actual work situation
(rather than on prescribed and/or idealised processes and methods). Data
presented concern global strategies (the way in which designers actually
organise their activity) and local strategies (reuse in design). Results from
cognitive ergonomics and other research that challenges the way in which people
are supposed to work with existing systems are generally not received warmly.
Abundant corroboration of such results is required before industry may consider
taking them into account. The opportunistic organisation of design activity is
taken here as an example of this reluctance. The results concerning this aspect
of design have been verified repeatedly, but only prototypes and experimental
systems implementing some of the requirements formulated on their basis, are
under development.


  In Part I, we study a special case of the unweighted Tree Augmentation
Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we
forbid so-called stems; these are a particular type of subtree configuration.
For stemless TAP, we prove that the integrality ratio of an SDP relaxation (the
Lasserre tightening of an LP relaxation) is $\leq \frac{3}{2}+\epsilon$, where
$\epsilon>0$ can be any small constant. We obtain this result by designing a
polynomial-time algorithm for stemless TAP that achieves an approximation
guarantee of ($\frac32+\epsilon$) relative to the SDP relaxation. The algorithm
is combinatorial and does not solve the SDP relaxation, but our analysis relies
on the SDP relaxation.
  We generalize the combinatorial analysis of integral solutions from the
previous literature to fractional solutions by identifying some properties of
fractional solutions of the Lasserre system via the decomposition result of
Karlin, Mathieu and Nguyen (IPCO 2011).
  Also, we present an example of stemless TAP such that the approximation
guarantee of $\frac32$ is tight for the algorithm.
  In Part II of this paper, we extend the methods of Part I to prove the same
results relative to the same SDP relaxation for TAP.


  By accumulating all available radial velocity data and combining it with our
own spectroscopy we present a new and improved ephemeris for Cygnus X-1 (V1357
Cygni/HDE226868). We initially calculate an orbital period of
5.599847+/-0.000018.days and then, by including the more recent radial
velocities of LaSala et al. (1998) and Sowers et al.(1998) we refine this to
5.599829+/-0.000016 days. Using 27 years' worth of photometry, we also
calculate a photometric period of 5.599836+/-0.000024 - remarkably similar to
the spectroscopic one.


  Motivated by works on extension sets in standard domains we introduce a
notion of the Carath\'eodory set that seems better suited for the methods used
in proofs of results on characterization of extension sets. A special stress is
put on a class of two dimensional submanifolds in the tridisc which not only
turns out to be Carath\'eodory but also provides examples of two dimensional
domains for which the celebrated Lempert Theorem holds. Additionally, a
recently introduced notion of universal sets for the Carath\'eodory extremal
problem is studied and new results on domains admitting (no) finite universal
sets are given.


  We present an approach to model time series data from resting state fMRI for
autism spectrum disorder (ASD) severity classification. We propose to adopt
kernel machines and employ graph kernels that define a kernel dot product
between two graphs. This enables us to take advantage of spatio-temporal
information to capture the dynamics of the brain network, as opposed to
aggregating them in the spatial or temporal dimension. In addition to the
conventional similarity graphs, we explore the use of L1 graph using sparse
coding, and the persistent homology of time delay embeddings, in the proposed
pipeline for ASD classification. In our experiments on two datasets from the
ABIDE collection, we demonstrate a consistent and significant advantage in
using graph kernels over traditional linear or non linear kernels for a variety
of time series features.


  The new data on k_t distributions obtained at RHIC are analysed by means of
selected models of statistical and stochastic origin in order to estimate their
importance in providing new information on hadronization process, in particular
on the value of the temperature at freeze-out to hadronic phase.


  We use results on Virasoro conformal blocks to study chaotic dynamics in
CFT$_2$ at large central charge c. The Lyapunov exponent $\lambda_L$, which is
a diagnostic for the early onset of chaos, receives $1/c$ corrections that may
be interpreted as $\lambda_L = \frac{2 \pi}{\beta} \left( 1 + \frac{12}{c}
\right)$. However, out of time order correlators receive other equally
important $1/c$ suppressed contributions that do not have such a simple
interpretation. We revisit the proof of a bound on $\lambda_L$ that emerges at
large $c$, focusing on CFT$_2$ and explaining why our results do not conflict
with the analysis leading to the bound. We also comment on relationships
between chaos, scattering, causality, and bulk locality.


  Wide neural networks with linear output layer have been shown to be
near-linear, and to have near-constant neural tangent kernel (NTK), in a region
containing the optimization path of gradient descent. These findings seem
counter-intuitive since in general neural networks are highly complex models.
Why does a linear structure emerge when the networks become wide? In this work,
we provide a new perspective on this "transition to linearity" by considering a
neural network as an assembly model recursively built from a set of sub-models
corresponding to individual neurons. In this view, we show that the linearity
of wide neural networks is, in fact, an emerging property of assembling a large
number of diverse "weak" sub-models, none of which dominate the assembly.


  We present a dynamical analysis of the galaxy cluster Abell 376 based on a
set of 73 velocities, most of them measured at Pic du Midi and Haute-Provence
observatories and completed with data from the literature. Data on individual
galaxies are presented and the accuracy of the determined velocities is
discussed as well as some properties of the cluster. We obtained an improved
mean redshift value z=0.0478^{+0.005}_{-0.006} and velocity dispersion
sigma=852^{+120}_{-76}km/s. Our analysis indicates that inside a radius of
900h_{70}^{-1}kpc (15 arcmin) the cluster is well relaxed without any
remarkable feature and the X-ray emission traces fairly well the galaxy
distribution. A possible substructure is seen at 20 arcmin from the centre
towards the Southwest direction, but is not confirmed by the velocity field.
This SW clump is, however, kinematically bound to the main structure of Abell
376. A dense condensation of galaxies is detected at 46 arcmin (projected
distance 2.6h_{70}^{-1}Mpc) from the centre towards the Northwest and analysis
of the apparent luminosity distribution of its galaxies suggests that this
clump is part of the large scale structure of Abell 376. X-ray spectroscopic
analysis of ASCA data resulted in a temperature kT = 4.3+/-0.4 keV and metal
abundance Z = 0.32+/-0.08 Z_solar. The velocity dispersion corresponding to
this temperature using the T_X-sigma scaling relation is in agreement with the
measured galaxies velocities.


  In this paper, we discuss the evolution operator and the transition
probabilities expressed as functions of the vacuum mass squared differences,
the vacuum mixing angles, and the matter density parameter for three flavor
neutrino oscillations in matter of varying density in the plane wave
approximation. The applications of this to neutrino oscillations in a model of
the Earth's matter density profile, step function matter density profiles,
constant matter density profiles, linear matter density profiles, and finally
in a model of the Sun's matter density profile are discussed. We show that for
matter density profiles, which do not fluctuate too much, the total evolution
operator consisting of $n$ operators can be replaced by one single evolution
operator in the semi-classical approximation.


  If h is a ring-valued function on a simplicial complex G we can define two
matrices L and g, where the matrix entries are the h energy of homoclinic
intersections. We know that the sum over all h values on G is equal to the sum
of the Green matrix entries g(x,y). We also have already seen that that the
determinants of L or g are both the product of the h(x). In the case where h(x)
is the parity of dimension, the sum of the energy values was the standard Euler
characteristic and the determinant was a unit. If h(x) was the unit in the ring
then L,g are integral quadratic forms which are isospectral and inverse
matrices of each other. We prove here that the quadratic energy expression
summing over all pairs h(x)^* h(y) of intersecting sets is a signed sum of
squares of Green function entries. The quadratic energy expression is Wu
characteristic in the case when h is dimension parity. For general h, the
quadratic energy expression resembles an Ising Heisenberg type interaction. The
conjugate of g is the inverse of L if h takes unit values in a normed ring or
in the group of unitary operators in an operator algebra.


  This paper proposes a method for uncertainty quantification of an
autoencoder-based Koopman operator. The main challenge of using the Koopman
operator is to design the basis functions for lifting the state. To this end,
this paper builds an autoencoder to automatically search the optimal lifting
basis functions with a given loss function. We approximate the Koopman operator
in a finite-dimensional space with the autoencoder, while the approximated
Koopman has an approximation uncertainty. To resolve the problem, we compute a
robust positively invariant set for the approximated Koopman operator to
consider the approximation error. Then, the decoder of the autoencoder is
analyzed by robustness certification against approximation error using the
Lipschitz constant in the reconstruction phase. The forced Van der Pol model is
used to show the validity of the proposed method. From the numerical simulation
results, we confirmed that the trajectory of the true state stays in the
uncertainty set centered by the reconstructed state.


  First principles electronic structure calculations have been carried out on
ordered double perovskites Sr_2B'B"O_6 (for B' = Cr or Fe and B" 4d and 5d
transition metal elements) with increasing number of valence electrons at the
B-sites, and on Ba_2MnReO_6 as well as Ba_2FeMoO_6. The Curie temperatures are
estimated ab initio from the electronic structures obtained with the local
spin-density functional approximation, full-potential generalized gradient
approximation and/or the LDA+U method (U - Hubbard parameter). Frozen
spin-spirals are used to model the excited states needed to evaluate the
spherical approximation for the Curie temperatures. In cases, where the induced
moments on the oxygen was found to be large, the determination of the Curie
temperature is improved by additional exchange functions between the oxygen
atoms and between oxygen and B' and B" atoms.
  A pronounced systematics can be found among the experimental and/or
calculated Curie temperatures and the total valence electrons of the transition
metal elements.


  Starting from a recent result expressing the Lerch zeta function as a
fractional derivative, we consider further fractional derivatives of the Lerch
zeta function with respect to different variables. We establish a partial
differential equation, involving an infinite series of fractional derivatives,
which is satisfied by the Lerch zeta function.


  In addition to novel surface states, topological insulators can also exhibit
robust gapless states at crystalline defects. Step edges constitute a class of
common defects on the surface of crystals. In this work we establish the
topological nature of one-dimensional (1D) bound states localized at step edges
of the [001] surface of a topological crystalline insulator (TCI)
Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the
topological stability of the step edge states arises from an emergent
particle-hole symmetry of the surface low-energy physics, and demonstrate the
experimental signatures of the particle-hole symmetry breaking. We also reveal
the effects of an external magnetic field on the 1D bound states. Our work
suggests the possibility of similar topological step edge modes in other
topological materials with a rocks-salt structure.


  Trying to dope graphite flakes we found that the magnetization of pure,
several tens of micrometers grain size graphite powder and after a simple
treatment with pure water shows clear and reproducible granular superconducting
behavior with a critical temperature above 300K. The observed magnetic
characteristics as a function of temperature, magnetic field and time, provide
evidence for weakly coupled grains through Josephson interaction, revealing the
existence of superconducting vortices.


  We study the capacity of Bayesian Neural Networks (BNNs) to detect new
physics in the dark matter power spectrum. As in previous studies, the Bayesian
Cosmological Network (BaCoN) classifies spectra into one of 5 classes:
$\Lambda$CDM, $f(R)$, $w$CDM, Dvali-Gabadaze-Porrati (DGP) gravity and a
'random' class, with this work extending it to include the effects of massive
neutrinos and baryonic feedback. We further develop the treatment of
theoretical errors in BaCoN-II, investigating several approaches and
identifying the one that best allows the trained network to generalise to other
power spectrum modelling prescriptions. In particular, we compare power spectra
data produced by EuclidEmulator2, HMcode and halofit, all supplemented with the
halo model reaction to model beyond-$\Lambda$CDM physics. We investigate
BNN-classifiers trained on these sets of spectra, adding in Stage-IV survey
noise and various theoretical error models. Using our optimal theoretical error
model, our fiducial classifier achieves a total classification accuracy of
$\sim$ 95% when it is trained on EuclidEmulator2-based spectra with
modification parameters drawn from a Gaussian distribution centred around
$\Lambda$CDM ($f(R)$: $\sigma_{fR0} = 10^{-5.5}$, DGP: $\sigma_{r\mathrm{c}} =
0.173$, $w$CDM: $\sigma_{w0} = 0.097$, $\sigma_{wa}=0.32$). This strengthens
the promise of this method to glean the maximal amount of unbiased
gravitational and cosmological information from forthcoming Stage-IV galaxy
surveys.


  We investigate the laws of thermodynamics in an accelerating universe driven
by dark energy with a time-dependent equation of state. In the case we consider
that the physically relevant part of the Universe is that envelopped by the
dynamical apparent horizon, we have shown that both the first law and second
law of thermodynamics are satisfied. On the other hand, if the boundary of the
Universe is considered to be the cosmological event horizon the thermodynamical
description based on the definitions of boundary entropy and temperature breaks
down. No parameter redefinition can rescue the thermodynamics laws from such a
fate, rendering the cosmological event horizon unphysical from the point of
view of the laws of thermodynamics.


  The Nakayama conjecture is one of the most important conjectures in ring
theory. The Auslander-Reiten conjecture is closely related to it. The purpose
of this note is to show that if the Auslander-Reiten conjecture holds in
codimension one for a commutative Gorenstein ring $R$, then it holds for $R$.


  We define, in a consistent way, non-local pseudo-differential operators
acting on a space of analytic functionals. These operators include the
fractional derivative case. In this context we show how to solve homogeneous
and inhomogeneous equations associated with these operators. We also extend the
formalism to d-dimensional space-time solving, in particular, the fractional
Wave and Klein-Gordon equations.


  We consider the ultradiscretization of a solvable one-dimensional chaotic map
which arises from the duplication formula of the elliptic functions. It is
shown that ultradiscrete limit of the map and its solution yield the tent map
and its solution simultaneously. A geometric interpretation of the dynamics of
the tent map is given in terms of the tropical Jacobian of a certain tropical
curve. Generalization to the maps corresponding to the $m$-th multiplication
formula of the elliptic functions is also discussed.


  We study the finite quark mass effects of the low-energy QCD using the
improved ladder Schwinger-Dyson and Bethe-Salpeter equations which are derived
in the manner consistent with the vector and axial-vector Ward-Takahashi
identities. The non-perturbative mass-independent renormalization allows us to
calculate the quark condensate for a non-zero quark mass. We explicitly show
that the PCAC relation holds. The key ingredients are the
Cornwall-Jackiw-Tomboulis effective action, the generalized Noether current and
the introduction of the regularization function to the Lagrangian. The
reasonable values of the pion mass, the pion decay constant and the quark
condensate are obtained with a rather large $\Lambda_{QCD}$. The pion mass
square and the pion decay constant are almost proportional to the current quark
mass up to the strange quark mass region. It suggests that the chiral
perturbation is applicable up to the strange quark mass region.
  We study the validity of the approximation often used in solving the
Bethe-Salpeter equations too.


  A prototype of a dual-readout calorimeter using brass capillary tubes
surrounding scintillating and clear plastic optical fibres was tested using
beams of particles with energies between 10 and 100 GeV produced by the CERN
SPS. The scope of the test was to characterise the performance of the
tube-based detector response to positrons in terms of linearity, energy
resolution, and lateral granularity. After calibrating the detector and
processing the output signal to correct for the energy dependency on the
particle impact point, the linearity of the measurement was found to be better
than 1\%. The positron response was compared to that predicted by a
Geant4-based simulation, finding good agreement both in terms of energy
resolution and shower profile. The detector resolution was estimated to be well
described by a stochastic term of 14.5\% with a negligible constant term.


  Given a linear equation $\mathcal{L}$, a set $A \subseteq [n]$ is
$\mathcal{L}$-free if $A$ does not contain any `non-trivial' solutions to
$\mathcal{L}$. In this paper we consider the following three general questions:
  (i) What is the size of the largest $\mathcal{L}$-free subset of $[n]$?
  (ii) How many $\mathcal{L}$-free subsets of $[n]$ are there?
  (iii) How many maximal $\mathcal{L}$-free subsets of $[n]$ are there?
  We completely resolve (i) in the case when $\mathcal{L}$ is the equation
$px+qy=z$ for fixed $p,q\in \mathbb N$ where $p\geq 2$. Further, up to a
multiplicative constant, we answer (ii) for a wide class of such equations
$\mathcal{L}$, thereby refining a special case of a result of Green. We also
give various bounds on the number of maximal $\mathcal{L}$-free subsets of
$[n]$ for three-variable homogeneous linear equations $\mathcal{L}$. For this,
we make use of container and removal lemmas of Green.


  Inflation has the potential to seed the galactic magnetic fields observed
today. However, there is an obstacle to the amplification of the quantum
fluctuations of the electromagnetic field during inflation: namely the
conformal invariance of electromagnetic theory on a conformally flat underlying
geometry. As the existence of a preferred minimal length breaks the conformal
invariance of the background geometry, it is plausible that this effect could
generate some electromagnetic field amplification. We show that this scenario
is equivalent to endowing the photon with a large negative mass during
inflation. This effective mass is negligibly small in a radiation and matter
dominated universe. Depending on the value of the free parameter of the theory,
we show that the seed required by the dynamo mechanism can be generated. We
also show that this mechanism can produce the requisite galactic magnetic field
without resorting to a dynamo mechanism.


  We extend a factorization theorem by Gwo\'zdziewicz and Hejmej from the ring
of formal power series to any complete regular local ring $ R $. More
precisely, let $ f \in R $ and assume that its Newton polyhedron has a loose
edge such that the initial formal of $ f $ along the latter is a product of two
coprime polynomials, where one of them is not divided by any variable. Then
this provides a factorization of $ f $ in $ R $. As a consequence we obtain a
factorization theorem for Weierstra{\ss} polynomials with coefficients in $ R
$, which generalizes an earlier result by Rond and the author.


  The nonlinear Hall effect has recently attracted significant interest due to
its potential as a promising spectral tool and device applications. A theory of
the nonlinear Hall effect on a disordered lattice is a crucial step towards
explorations in realistic devices, but has not been addressed. We study the
nonlinear Hall response on a lattice, which allows us to introduce strong
disorder numerically. We reveal a disorder-induced fluctuation of the Berry
curvature that was not discovered in the previous perturbation theories. The
fluctuating Berry curvature induces a fluctuation of the nonlinear Hall
conductivity, which anomalously increases as the Fermi energy moves from the
band edges to higher energies. More importantly, the fluctuation may explain
those observations in the recent experiments. We also discover an "Anderson
localization" of the nonlinear Hall effect. This work shows a territory of the
nonlinear Hall effect yet to be explored.


  It is shown how states of a quantum mechanical particle in the Schroedinger
representation can be approximated by states in the so-called polymer
representation. The result may shed some light on the semiclassical limit of
loop quantum gravity.


  The motivation of this work is the use of non-invasive and low cost
techniques to obtain a faster and more accurate diagnosis of systemic sclerosis
(SSc), rheumatic, autoimmune, chronic and rare disease. The technique in
question is Near Infrared Spectroscopy (NIRS). Spectra were acquired from three
different regions of hand's volunteers. Machine learning algorithms are used to
classify and search for the best optical wavelength. The results demonstrate
that it is easy to obtain wavelength bands more important for the diagnosis. We
use the algorithm RFECV and SVC. The results suggests that the most important
wavelength band is at 1270 nm, referring to the luminescence of Singlet Oxygen.
The results indicates that the Proximal Interphalangeal Joints region returns
better accuracy's scores. Optical spectrometers can be found at low prices and
can be easily used in clinical evaluations, while the algorithms used are
completely diffused on open source platforms.


  Attosecond angular streaking measurements have revealed deep insights into
the timing of tunnel ionization processes of atoms in intense laser fields. So
far experiments of this type have been performed only with a cold-target
recoil-ion momentum spectrometer (COLTRIMS). Here, we present a way to apply
attosecond angular streaking experiments to a velocity map imaging spectrometer
(VMIS) with few-cycle pulses at a repetition rate of 10 kHz and a high
ionization yield per pulse. Three-dimensional photoelectron momentum
distributions from strong-field ionization of helium with an elliptically
polarized, sub-10-fs pulse were retrieved by tomographic reconstruction from
the momentum space electron images and used for the analysis in the
polarization plane.


  This is a non-perturbative treatment of correlation functions for the weakly
coupled massless Gross-Neveu model in a finite volume. The main result is that
all correlation functions, treated as distributions, are uniformly bounded in
the ultraviolet cutoff.


  We associate to each nilpotent orbit of a real semisimple Lie algebra $g_o$ a
weighted Vogan diagram, that is a Dynkin diagram with an involution of the
diagram, a subset of painted nodes and a weight for each node. Every nilpotent
element of $g_o$ is noticed in some subalgebra of $g_o$. In this paper we
characterize the weighted Vogan diagrams associated to orbits of noticed
nilpotent elements.


  In recent years, the emergence of the first quantum computers at a time when
AI is undergoing a fruitful era has led many AI researchers to be tempted into
adapting their algorithms to run on a quantum computer. However, in many cases
the initial enthusiasm has ended in frustration, since the features and
principles underlying quantum computing are very different from traditional
computers. In this paper, we present a discussion of the difficulties arising
when designing a quantum version of an evolutionary algorithm based on Darwin's
evolutionary mechanism, the so-called genetic algorithms. The paper includes
the code in both Python and QISKIT of the quantum version of one of these
evolutionary algorithms allowing the reader to experience the setbacks arising
when translating a classical algorithm to its quantum version. The algorithm
studied in this paper, termed RQGA (Reduced Quantum Genetic Algorithm), has
been chosen as an example that clearly shows these difficulties, which are
common to other AI algorithms.


  A systematic procedure for generating cubic multisections of Eisenstein
series is given. The relevant series are determined from Fourier expansions for
Eisenstein series by restricting the congruence class of the summation index
modulo three. We prove that the resulting series are rational functions of
\eta(\tau) and \eta(3\tau), where \eta is the Dedekind eta function. A more
general treatment of cubic dissection formulas is given by describing the
dissection operators in terms of linear transformations. These operators
exhibit properties that mirror those of similarly defined quintic operators.


  We consider a system where multiple sensors communicate timely information
about various random processes to a sink. The sensors share orthogonal
sub-channels to transmit such information in the form of status update packets.
A central controller can control the sampling actions of the sensors to
trade-off between the transmit power consumption and information freshness
which is quantified by the Age of Information (AoI). We jointly optimize the
sampling action of each sensor, the transmit power allocation, and the
sub-channel assignment to minimize the average total transmit power of all
sensors subject to a maximum average AoI constraint for each sensor. To solve
the problem, we develop a dynamic control algorithm using the Lyapunov
drift-plus-penalty method and provide optimality analysis of the algorithm.
According to the Lyapunov drift-plus-penalty method, to solve the main problem
we need to solve an optimization problem in each time slot which is a mixed
integer non-convex optimization problem. We propose a low-complexity
sub-optimal solution for this per-slot optimization problem that provides
near-optimal performance and we evaluate the computational complexity of the
solution. Numerical results illustrate the performance of the proposed dynamic
control algorithm and the performance of the sub-optimal solution for the
per-slot optimization problems versus the different parameters of the system.
The results show that the proposed dynamic control algorithm achieves more than
$60~\%$ saving in the average total transmit power compared to a baseline
policy.


  The motion of a nonlinearly oscilating partical under the influence of a
periodic sequence of short impulses is investigated. We analyze the Schrodinger
equation for the universal Hamiltonian. The idea about the emerging of quantum
chaos due to the adiabatic motion along the curves of Mathieu characteristics
at multiple passages through the points of branching is advanced


  In this work, we introduce new combinatorial objects called Dyck tableaux,
which present a natural insertion algorithm. These tools may be useful to
describe statistics which are relevant in the study of the physical model named
PASEP.


  Pneumonia is one of the foremost lung diseases and untreated pneumonia will
lead to serious threats for all age groups. The proposed work aims to extract
and evaluate the Coronavirus disease (COVID-19) caused pneumonia infection in
lung using CT scans. We propose an image-assisted system to extract COVID-19
infected sections from lung CT scans (coronal view). It includes following
steps: (i) Threshold filter to extract the lung region by eliminating possible
artifacts; (ii) Image enhancement using Harmony-Search-Optimization and Otsu
thresholding; (iii) Image segmentation to extract infected region(s); and (iv)
Region-of-interest (ROI) extraction (features) from binary image to compute
level of severity. The features that are extracted from ROI are then employed
to identify the pixel ratio between the lung and infection sections to identify
infection level of severity. The primary objective of the tool is to assist the
pulmonologist not only to detect but also to help plan treatment process. As a
consequence, for mass screening processing, it will help prevent diagnostic
burden.


  The two-dimensional electron gas (2DEG) at the non-isostructural interface
between spinel gamma-Al2O3 and perovskite SrTiO3 is featured by a record
electron mobility among complex oxide interfaces in addition to a high carrier
density up to the order of 1E15 cm-2. Herein, we report on the patterning of
2DEG at the gamma-Al2O3/SrTiO3 interface grown at 650 {\deg}C by pulsed laser
deposition using a hard mask of LaMnO3. The patterned 2DEG exhibits a critical
thickness of 2 unit cells of gamma-Al2O3 for the occurrence of interface
conductivity, similar to the unpatterned sample. However, its maximum carrier
density is found to be approximately 3E13 cm-2, much lower than that of the
unpatterned sample (1E15 cm-2). Remarkably, a high electron mobility of
approximately 3,600 cm2V-1s-1 was obtained at low temperatures for the
patterned 2DEG at a carrier density of 7E12 cm-2, which exhibits clear
Shubnikov-de Hass quantum oscillations. The patterned high-mobility 2DEG at the
gamma-Al2O3/SrTiO3 interface paves the way for the design and application of
spinel/perovskite interfaces for high-mobility all-oxide electronic devices.


  The Grothendieck group of the tower of symmetric group algebras has a
self-dual graded Hopf algebra structure. Inspired by this, we introduce by way
of axioms, a general notion of a tower of algebras and study two Grothendieck
groups on this tower linked by a natural paring. Using representation theory,
we show that our axioms give a structure of graded Hopf algebras on each
Grothendieck groups and these structures are dual to each other. We give some
examples to indicate why these axioms are necessary. We also give auxiliary
results that are helpful to verify the axioms. We conclude with some remarks on
generalized towers of algebras leading to a structure of generalized bialgebras
(in the sense of Loday) on their Grothendieck groups.


  We chart the expected Galactic distribution of neutron stars and black holes.
These compact remnants of dead stars -- the Galactic underworld -- are found to
exhibit a fundamentally different distribution and structure to the visible
Galaxy. Compared to the visible Galaxy, concentration into a thin flattened
disk structure is much less evident with the scale height more than tripling to
1260 +- 30 pc. This difference arises from two primary causes. Firstly, the
distribution is in part inherited from the integration over the evolving
structure of the Galaxy itself (and hence the changing distribution of the
parent stars). Secondly, an even larger effect arises from the natal kick
received by the remnant at the event of its supernova birth. Due to this kick
we find 30% of remnants have sufficient kinetic energy to entirely escape the
Galactic potential (40% of neutron stars and 2% of black holes) leading to a
Galactic mass loss integrated to the present day of ~ 0.4% of the stellar mass
of the Galaxy. The black hole -- neutron star fraction increases near the
Galactic centre: a consequence of smaller kick velocities in the former (the
assumption made is that kick velocity is inversely proportional to mass). Our
simulated remnant distribution yields probable distances of 19 pc and 21 pc to
the nearest neutron star and black hole respectively, while our nearest
probable magnetar lies at 4.2 kpc. Although the underworld only contains of
order ~ 1% of the Galaxy's mass, observational signatures and physical traces
of its population, such as microlensing, will become increasingly present in
data ranging from gravitational wave detectors to high precision surveys from
space missions such as Gaia.


  We consider the gelation of particles which are permanently connected by
random crosslinks, drawn from an ensemble of finite-dimensional continuum
percolation. To average over the randomness, we apply the replica trick, and
interpret the replicated and crosslink-averaged model as an effective molecular
fluid. A Mayer-cluster expansion for moments of the local static density
fluctuations is set up. The simplest non-trivial contribution to this series
leads back to mean-field theory. The central quantity of mean-field theory is
the distribution of localization lengths, which we compute for all
connectivities. The highly crosslinked gel is characterized by a one-to-one
correspondence of connectivity and localization length. Taking into account
higher contributions in the Mayer-cluster expansion, systematic corrections to
mean-field can be included. The sol-gel transition shifts to a higher number of
crosslinks per particle, as more compact structures are favored. The critical
behavior of the model remains unchanged as long as finite truncations of the
cluster expansion are considered. To complete the picture, we also discuss
various geometrical properties of the crosslink network, e.g. connectivity
correlations, and relate the studied crosslink ensemble to a wider class of
ensembles, including the Deam-Edwards distribution.


  We construct a collision model description of the thermalization of a finite
many-body system by using careful derivation of the corresponding Lindblad-type
master equation in the weak coupling regime. Using the example of two level
target system, we show that collision model thermalization is crucially
dependent on the various relevant system and bath timescales and on ensuring
that the environment is composed of ancillae which are resonant with the system
transition frequencies. Using this we extend our analysis to show that our
collision model can lead to thermalisation for certain classes of many-body
systems. We establish that for classically correlated systems our approach is
effective, while we also highlight its shortcomings, in particular with regards
to reaching entangled thermal states.


  We demonstrate a novel method to ionize molecules or molecular clusters by
proton transfer at temperatures below 1 K. The method yields nascent ions and
largely eliminates secondary reactions, even for notoriously "delicate"
molecules. Protonation is achieved inside liquid helium nanodroplets (HNDs) and
begins with the formation of (H$_{2}$)$_{m}$H$^{+}$ ions as the proton donors.
In a separate and subsequent step the HNDs are doped with a proton acceptor
molecule, X. Proton transfer occurs between X and the cold proton donor ions
inside a helium droplet, an approach that avoids the large excess energy that
is released if HNDs are first doped and then ionized. Mass spectra, recorded
after stripping excess helium and hydrogen in a collision cell, show that this
method offers a new way to determine proton affinities of molecules and
clusters by proton-transfer bracketing, to investigate astrochemically relevant
ion-molecule reactions at sub-kelvin temperatures, and to prepare XH$^{+}$ ions
that are suitable for messenger-tagging action spectroscopy.


  The sensitivity of aLIGO detectors is adversely affected by the presence of
noise caused by light scattering. Low frequency seismic disturbances can create
higher frequency scattering noise adversely impacting the frequency band in
which we detect gravitational waves. In this paper, we analyze instances of a
type of scattered light noise we call "Fast Scatter" that is produced by motion
at frequencies greater than 1 Hz, to locate surfaces in the detector that may
be responsible for the noise. We model the phase noise to better understand the
relationship between increases in seismic noise near the site and the resulting
Fast Scatter observed. We find that mechanical damping of the Arm Cavity
Baffles (ACBs) led to a significant reduction of this noise in recent data. For
a similar degree of seismic motion in the 1-3 Hz range, the rate of noise
transients is reduced by a factor of ~ 50.


  Neural network approaches are machine learning methods that are widely used
in various domains, such as healthcare and cybersecurity. Neural networks are
especially renowned for their ability to deal with image datasets. During the
training process with images, various fundamental mathematical operations are
performed in the neural network. These operations include several algebraic and
mathematical functions, such as derivatives, convolutions, and matrix
inversions and transpositions. Such operations demand higher processing power
than what is typically required for regular computer usage. Since CPUs are
built with serial processing, they are not appropriate for handling large image
datasets. On the other hand, GPUs have parallel processing capabilities and can
provide higher speed. This paper utilizes advanced neural network techniques,
such as VGG16, Resnet50, Densenet, Inceptionv3, Xception, Mobilenet, XGBOOST
VGG16, and our proposed models, to compare CPU and GPU resources. We
implemented a system for classifying Autism disease using face images of
autistic and non-autistic children to compare performance during testing. We
used evaluation matrices such as Accuracy, F1 score, Precision, Recall, and
Execution time. It was observed that GPU outperformed CPU in all tests
conducted. Moreover, the performance of the neural network models in terms of
accuracy increased on GPU compared to CPU.


  We present the discovery of a long-period, rapidly oscillating Ap star,
HD177765. Using high-resolution time-series observations obtained with UVES at
the ESO VLT telescope, we found radial velocity variations with amplitudes
7-150 m/s and a period of 23.6 min, exceeding that of any previously known roAp
star. The largest pulsation amplitudes are observed for Eu III, Ce III and for
the narrow core of Halpha. We derived the atmospheric parameters and chemical
composition of HD177765, showing this star to be similar to other long-period
roAp stars. Comparison with theoretical pulsational models indicates an
advanced evolutionary state for HD177765. Abundance analyses of this and other
roAp stars suggest a systematic variation with age of the rare-earth line
anomalies seen in cool Ap stars.


  Unmanned Aerial Vehicle (UAV) swarms are often required in off-grid
scenarios, such as disaster-struck, war-torn or rural areas, where the UAVs
have no access to the power grid and instead rely on renewable energy.
Considering a main battery fed from two renewable sources, wind and solar, we
scale such a system based on the financial budget, environmental
characteristics, and seasonal variations. Interestingly, the source of energy
is correlated with the energy expenditure of the UAVs, since strong winds cause
UAV hovering to become increasingly energy-hungry. The aim is to maximize the
cost efficiency of coverage at a particular location, which is a combinatorial
optimization problem for dimensioning of the multivariate energy generation
system under non-convex criteria. We have devised a customized algorithm by
lowering the processing complexity and reducing the solution space through
sampling. Evaluation is done with condensed real-world data on wind, solar
energy, and traffic load per unit area, driven by vendor-provided prices. The
implementation was tested in four locations, with varying wind or solar
intensity. The best results were achieved in locations with mild wind presence
and strong solar irradiation, while locations with strong winds and low solar
intensity require higher Capital Expenditure (CAPEX) allocation.


  Light storage in an atomic Bose-Einstein condensate is one of the most
practical usage of these coherent atom-optical systems. In order to make them
even more practical, it is necessary to enhance our ability to inject multiple
pulses into the condensate. In this paper, we report that dispersion of pulses
injected into the condensate can be compensated by optical nonlinearity. In
addition, we will present a brief review of our earlier results in which
enhancement of light storage capacity is accomplished by utilizing multi-mode
light propagation or choosing an optimal set of experimental parameters.


  We compute the vacuum expectation values of $1/6$ supersymmetric Wilson loops
in higher dimensional representations of the gauge group in ABJM theory. We
present results for the $m$-symmetric and $m$-antisymmetric representations by
exploiting standard matrix model techniques. At leading order, in the saddle
point approximation, our expressions reproduce holographic results from both D6
and D2 branes corresponding to the antisymmetric and symmetric representations,
respectively. We also compute 1/N corrections to the leading saddle point
results.


  In this note we observe, answering a question of Eliashberg and Thurston,
that all contact structures on a closed oriented 3-manifold are
$C^\infty$-deformations of foliations.


  We answer a question posed by Carlson, Peng, and Wheeler, and demonstrate
that in general Rickard modules in relatively stable categories are not
idempotent modules even if one localizes with respect to a tensor ideal
subcategory. We also show that there is a modification one can make so as to
recover the idempotent behaviour.


  In this talk, we present the first, numerically stable, results for the
one-loop amplitudes needed for computing W,Z + 3 jet cross sections at the LHC
to next-to-leading order in the QCD coupling. We implemented these processes in
BlackHat, an automated program based on on-shell methods. These methods scale
very well with increasing numbers of external partons, and are applicable to a
wide variety of problems of phenomenological interest at the LHC.


  This study focuses on Pristine$\_180956.78$$-$$294759.8$ (hereafter P180956,
$[Fe/H] =-1.95\pm0.02$), a star selected from the Pristine Inner Galaxy Survey
(PIGS), and followed-up with the recently commissioned Gemini High-resolution
Optical SpecTrograph (GHOST) at the Gemini South telescope. The GHOST
spectrograph's high efficiency in the blue spectral region ($3700-4800$~\AA)
enables the detection of elemental tracers of early supernovae (\eg Al, Mn, Sr,
Eu). The star exhibits chemical signatures resembling those found in
ultra-faint dwarf systems, characterised by very low abundances of
neutron-capture elements (Sr, Ba, Eu), which are uncommon among stars in the
Milky Way halo. Our analysis suggests that P180956 bears the chemical imprints
of a small number (2 or 4) of low-mass hypernovae ($\sim10-15 M_{\odot}$),
which are needed to mostly reproduce the abundance pattern of the
light-elements (\eg [Si, Ti/Mg, Ca] $\sim0.6$), and one fast-rotating
intermediate-mass supernova ($\sim300\kms$, $\sim80-120 M_{\odot}$), which is
the main channel contributing to the high [Sr/Ba] ($\sim +1.2$). The small
pericentric ($\sim0.7$ kpc) and apocentric ($\sim13$ kpc) distances and its
orbit confined to the plane ($\lesssim 2$ kpc), indicate that this star was
likely accreted during the early Galactic assembly phase. Its chemo-dynamical
properties suggest that P180956 formed in a system similar to an ultra-faint
dwarf galaxy accreted either alone, as one of the low-mass building blocks of
the proto-Galaxy, or as a satellite of Gaia-Sausage-Enceladus. The combination
of Gemini's large aperture with GHOST's high efficiency and broad spectral
coverage makes this new spectrograph one of the leading instruments for
near-field cosmology investigations.


  We study limit models in the class of abelian groups with the subgroup
relation and in the class of torsion-free abelian groups with the pure subgroup
relation. We show:
  $\textbf{Theorem}$
  (1) If $G$ is a limit model of cardinality $\lambda$ in the class of abelian
groups with the subgroup relation, then $G \cong (\oplus_{\lambda}\mathbb{Q})
\oplus \oplus_{p \text{ prime}} (\oplus_{\lambda} \mathbb{Z}(p^\infty))$.
  (2) If $G$ is a limit model of cardinality $\lambda$ in the class of
torsion-free abelian groups with the pure subgroup relation, then:
  * If the length of the chain has uncountable cofinality, then $ G \cong
(\oplus_{\lambda} \mathbb{Q} ) \oplus \Pi_{p\text{ prime}}
\overline{(\oplus_{\lambda} \mathbb{Z}_{(p)})}$.
  * If the length of the chain has countable cofinality, then $G$ is not
algebraically compact.
  We also study the class of finitely Butler groups with the pure subgroup
relation, we show that it is an AEC, Galois-stable and $(<\aleph_0)$-tame and
short.


  It is well known that integrable hierarchies in (1+1) dimensions are local
while the recursion operators that generate them usually contain nonlocal
terms. We resolve this apparent discrepancy by providing simple and universal
sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions
to generate a hierarchy of local symmetries. These conditions are satisfied by
virtually all known today recursion operators and are much easier to verify
than those found in earlier work.
  We also give explicit formulas for the nonlocal parts of higher recursion
operators, Poisson and symplectic structures of integrable systems in (1+1)
dimensions.
  Using these two results we prove, under some natural assumptions, the
Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and
recursion operators of integrable systems in (1+1) dimensions are weakly
nonlocal, i.e., the coefficients of these operators are local and these
operators contain at most one integration operator in each term.


  Recent applications of machine learning and statistical inference provide
case studies demonstrating how such approaches can accelerate the discovery
process in physical chemistry and related fields. Examples discussed in this
review include the introduction of automated approaches to systematically
improve experimental design, increase the efficiency of computationally
expensive molecular simulations, facilitate construction of predictive models
for complex biological processes, and discover interparticle potentials that
lead to materials which meet specified design goals. A common theme is the
synergy between experiment and computation enabled by such approaches.


  Robust travel time predictions are of prime importance in managing any
transportation infrastructure, and particularly in rail networks where they
have major impacts both on traffic regulation and passenger satisfaction. We
aim at predicting the travel time of trains on rail sections at the scale of an
entire rail network in real-time, by estimating trains' delays relative to a
theoretical circulation plan.
  Predicting the evolution of a given train's delay is a uniquely hard problem,
distinct from mainstream road traffic forecasting problems, since it involves
several hard-to-model phenomena: train spacing, station congestion and
heterogeneous rolling stock among others. We first offer empirical evidence of
the previously unexplored phenomenon of delay propagation at the scale of a
railway network, leading to delays being amplified by interactions between
trains and the network's physical limitations.
  We then contribute a novel technique using the transformer architecture and
pre-trained embeddings to make real-time massively parallel predictions for
train delays at the scale of the whole rail network (over 3000 trains at peak
hours, making predictions at an average horizon of 70 minutes). Our approach
yields very positive results on real-world data when compared to currently-used
and experimental prediction techniques.


  Kondo lattices are ideal testbeds for the exploration of heavy-fermion
quantum phases of matter. While our understanding of Kondo lattices has
traditionally relied on complex bulk f-electron systems, transition metal
dichalcogenide heterobilayers have recently emerged as simple, accessible and
tunable 2D Kondo lattice platforms where, however, their ground state remains
to be established. Here we present evidence of a coherent ground state in the
1T/1H-TaSe2 heterobilayer by means of scanning tunneling
microscopy/spectroscopy at 340 mK. Our measurements reveal the existence of two
symmetric electronic resonances around the Fermi energy, a hallmark of
coherence in the spin lattice. Spectroscopic imaging locates both resonances at
the central Ta atom of the charge density wave of the 1T phase, where the
localized magnetic moment is held. Furthermore, the evolution of the electronic
structure with the magnetic field reveals a non-linear increase of the energy
separation between the electronic resonances. Aided by ab initio and
auxiliary-fermion mean-field calculations, we demonstrate that this behavior is
inconsistent with a fully screened Kondo lattice, and suggests a ground state
with magnetic order mediated by conduction electrons. The manifestation of
magnetic coherence in TMD-based 2D Kondo lattices enables the exploration of
magnetic quantum criticality, Kondo breakdown transitions and unconventional
superconductivity in the strict two-dimensional limit.


  The Mu3e experiment aims to find or exclude the lepton flavour violating
decay $\mu^+\to e^+e^-e^+$ with a sensitivity of one in 10$^{16}$ muon decays.
The first phase of the experiment is currently under construction at the Paul
Scherrer Institute (PSI, Switzerland), where beams with up to 10$^8$ muons per
second are available. The detector will consist of an ultra-thin pixel tracker
made from High-Voltage Monolithic Active Pixel Sensors (HV-MAPS), complemented
by scintillating tiles and fibres for precise timing measurements. The
experiment produces about 100 Gbit/s of zero-suppressed data which are
transported to a filter farm using a network of FPGAs and fast optical links.
On the filter farm, tracks and three-particle vertices are reconstructed using
highly parallel algorithms running on graphics processing units, leading to a
reduction of the data to 100 Mbyte/s for mass storage and offline analysis. The
paper introduces the system design and hardware implementation of the Mu3e data
acquisition and filter farm.


  After two major outbursts in 2006 and 2011, on 2017 May 16 the magnetar CXOU
J164710.2-455216, hosted within the massive star cluster Westerlund I, emitted
a short (20 ms) burst, which marked the onset of a new active phase. We started
a long-term monitoring campaign with Swift (45 observations), Chandra (5
observations) and NuSTAR (4 observations) from the activation until 2018 April.
During the campaign, Swift BAT registered the occurrence of multiple bursts,
accompanied by two other enhancements of the X-ray persistent flux. The long
time span covered by our observations allowed us to study the spectral as well
as the timing evolution of the source. After 11 months since the 2017 May
outburst onset, the observed flux was about 15 times higher than its historical
minimum level and a factor of 3 higher than the level reached after the 2006
outburst. This suggests that the crust has not fully relaxed to the quiescent
level, or that the source quiescent level has changed following the multiple
outburst activities in the past 10 years or so. This is another case of
multiple outbursts from the same source on a yearly time scale, a somehow
recently discovered behaviour in magnetars.


  Rates of binomial processes are modeled using beta-binomial distributions
(for example, from Beta Regression). We treat the offline optimization scenario
and then the online one, where we optimize the exploration-exploitation
problem. The rates given by two processes are compared through their
distributions, but we would like to optimize the net payout (given a constant
value per successful event, unique for each of the processes). The result is an
analytically-closed, probabilistic, hypergeometric expression for comparing the
payout distributions of two processes. To conclude, we contrast this Bayesian
result with an alternative frequentist approach and find 4.5 orders of
magnitude improvement in performance, for a numerical accuracy level of 0.01%.


  We study the dynamics of co-evolution of producers and customers described by
bit-strings representing individual traits. Individual ''size-like'' properties
are controlled by binary encounters which outcome depends upon a recognition
process. Depending upon the parameter set-up, mutual selection of producers and
customers results in different types of attractors, either an exclusive niches
regime or a competition regime.