  We study the non-equilibrium steady-state phase transition from probe brane
holography in $z=2$ Schr\"odinger spacetime. Concerning differential
conductivity, a phase transition could occur in the conductor state.
Considering constant current operator as the external field and the
conductivity as an order parameter, we derive scaling behavior of order
parameter near the critical point. We explore the critical exponents of the
non-equilibrium phase transition in two different Schr\"odinger spacetimes,
which originated $1)$ from supergravity, and $2)$ from AdS blackhole in the
light-cone coordinates. Interestingly, we will see that even at the zero charge
density, in our first geometry, the dynamical critical exponent of $z=2$ has a
major effect on the critical exponents.


  Delta smelt is an endangered fish species in the San Francisco estuary that
have shown an overall population decline over the past 30 years. Researchers
have developed a stochastic, agent-based simulator to virtualize the system,
with the goal of understanding the relative contribution of natural and
anthropogenic factors suggested as playing a role in their decline. However,
the input configuration space is high-dimensional, running the simulator is
time-consuming, and its noisy outputs change nonlinearly in both mean and
variance. Getting enough runs to effectively learn input--output dynamics
requires both a nimble modeling strategy and parallel supercomputer evaluation.
Recent advances in heteroskedastic Gaussian process (HetGP) surrogate modeling
helps, but little is known about how to appropriately plan experiments for
highly distributed simulator evaluation. We propose a batch sequential design
scheme, generalizing one-at-a-time variance-based active learning for HetGP
surrogates, as a means of keeping multi-core cluster nodes fully engaged with
expensive runs. Our acquisition strategy is carefully engineered to favor
selection of replicates which boost statistical and computational efficiencies
when training surrogates to isolate signal in high noise regions. Design and
modeling performance is illustrated on a range of toy examples before embarking
on a large-scale smelt simulation campaign and downstream high-fidelity input
sensitivity analysis.


  An ultralow lattice thermal conductivity of 0.14 W$\cdot$ m$^{-1} \cdot$
K$^{-1}$ along the $\vec b$ axis of As$_2$Se$_3$ single crystals was obtained
at 300 K by first-principles calculations involving the density functional
theory and the resolution of the Boltzmann transport equation. This ultralow
lattice thermal conductivity arises from the combination of two mechanisms: 1)
a cascade-like fall of the low-lying optical modes, which results in avoided
crossings of these with the acoustic modes, low sound velocities and increased
scattering rates of the acoustic phonons; and 2) the repulsion between the
lone-pair electrons of the As cations and the valence $p$ orbitals of the Se
anions, which leads to an increase in the anharmonicity of the bonds. The
physical origins of these mechanisms lie on the nature of the chemical bonding
in the material and its strong anisotropy. These results, whose validity has
been addressed by comparison with SnSe, for which excellent agreement between
the theoretical predictions and the experiments is achieved, point out that
As$_2$Se$_3$ could exhibit improved thermoelectric properties.


  This paper considers a distributed stochastic optimization problem where the
goal is to minimize the time average of a cost function subject to a set of
constraints on the time averages of a related stochastic processes called
penalties. We assume that a delayed information about an event in the system is
available as a common information at every user, and the state of the system is
evolving in an independent and non-stationary fashion. We show that an
approximate Drift-plus-penalty (DPP) algorithm that we propose achieves a time
average cost that is within some positive constant epsilon of the optimal cost
with high probability. Further, we provide a condition on the waiting time for
this result to hold. The condition is shown to be a function of the mixing
coefficient, the number of samples (w) used to compute an estimate of the
distribution of the state, and the delay. Unlike the existing work, the method
used in the paper can be adapted to prove high probability results when the
state is evolving in a non-i.i.d and non-stationary fashion. Under mild
conditions, we show that the dependency of the error bound on w is exponential,
which is a significant improvement compared to the exiting work.


  We analyze the symmetry group of massive Yang-Mills theories and their
quantization strongly motivated by an already proposed alternative to the
Standard Model of electroweak interactions without Higgs. In these models the
mass generation of the intermediate vector bosons is based on a non-Abelian
Stueckelberg mechanism where the dynamics of the Goldstone-like bosons is
addressed by a partial-trace Non-Linear-Sigma piece of the Lagrangian. In spite
of the high non-linearity of the scalar sector, the existence of an infinite
number of symmetries, extending the traditional gauge group, allows us to
sketch a group-theoretical quantization algorithm specially suited to
non-linear systems, which departs from usual canonical quantization. On the
quantum representation space of this extended symmetry group, a quantum
Hamiltonian preserving the representation is given, whose classical analog
reproduces the equations of motion.


  This work explores Boltzmann's time hypothesis, which associates the
perceived direction of "time flow" with the second law of thermodynamics. We
discuss mechanisms that can be responsible for the action of the second law,
for directional properties of time and, ultimately, for the perception that
past events cause future events. Special attention is paid to possibility of
testing these mechanisms in experiments. It is argued that CP-violations known
in particle physics may offer such an opportunity. A time-symmetric version of
Everett's many-worlds interpretation (which is based on a thermodynamic
interpretation of quantum collapses) is given in the Appendix.


  The notion of signal sparsity has been gaining increasing interest in
information theory and signal processing communities. As a consequence, a
plethora of sparsity metrics has been presented in the literature. The
appropriateness of these metrics is typically evaluated against a set of
objective criteria that has been proposed for assessing the credibility of any
sparsity metric. In this paper, we propose a Generalised Differential Sparsity
(GDS) framework for generating novel sparsity metrics whose functionality is
based on the concept that sparsity is encoded in the differences among the
signal coefficients. We rigorously prove that every metric generated using GDS
satisfies all the aforementioned criteria and we provide a computationally
efficient formula that makes GDS suitable for high-dimensional signals. The
great advantage of GDS is its flexibility to offer sparsity metrics that can be
well-tailored to certain requirements stemming from the nature of the data and
the problem to be solved. This is in contrast to current state-of-the-art
sparsity metrics like Gini Index (GI), which is actually proven to be only a
specific instance of GDS, demonstrating the generalisation power of our
framework. In verifying our claims, we have incorporated GDS in a stochastic
signal recovery algorithm and experimentally investigated its efficacy in
reconstructing randomly projected sparse signals. As a result, it is proven
that GDS, in comparison to GI, both loosens the bounds of the assumed sparsity
of the original signals and reduces the minimum number of projected dimensions,
required to guarantee an almost perfect reconstruction of heavily compressed
signals. The superiority of GDS over GI in conjunction with the fact that the
latter is considered as a standard in numerous scientific domains, prove the
great potential of GDS as a general purpose framework for measuring sparsity.


  There are two main approaches to the distributed representation of words:
low-dimensional deep learning embeddings and high-dimensional distributional
models, in which each dimension corresponds to a context word. In this paper,
we combine these two approaches by learning embeddings based on
distributional-model vectors - as opposed to one-hot vectors as is standardly
done in deep learning. We show that the combined approach has better
performance on a word relatedness judgment task.


  The project aims to investigate most important weak interaction nuclei in the
presupernova evolution of massive stars. To achieve the goal, an ensemble
containing 728 nuclei in the mass range A = 1--100 was considered. We computed
the mass fractions of these nuclei using Saha's equation for predetermined
values of \textit{$T$}, \textit{$\rho$} and \textit{$Y_e$} and assuming nuclear
statistical equilibrium. The nuclear partition functions were obtained using a
newly introduced recipe where excited states, up to 10 $MeV$, were treated as
discrete. The weak interaction rates (electron capture (\textit{ec}) and
$\beta$-decay (\textit{bd})) were calculated in a \textit{totally} microscopic
fashion using the proton-neutron quasiparticle random phase approximation
(pn-QRPA) model and without assuming the Brink-Axel hypothesis. The calculated
rates were coupled with the computed mass fractions to investigate the time
rate of change of lepton to baryon fraction of the stellar matter. We compare
our results with the previous calculations reported in the literature.
Noticeable differences up to orders of magnitude are reported with previous
calculations. These differences may influence the evolution of the star in the
later stages of presupernova. We present a list of top 50 \textit{ec} and
\textit{bd} nuclei which have the largest effect on $Y_e$ for conditions after
silicon core burning. The competition between the \textit{ec} and \textit{bd}
rates in stellar core was investigated and it was found that $Y_e$ =
0.424--0.455 is the interval where the \textit{bd} results are bigger than the
\textit{ec} rates.


  It follows from our analysis of CeRhSb that the formation of Kondo insulator
state due to the presence of the collective spin singlet state is strongly
reduced by its doping with various dopants when their amount exceeds 8--10\%,
regardless of whether they are substituted for Ce, Rh or Sb. A wide variety of
experimental results (electrical resistivity $\rho$, magnetic susceptibility
$\chi$, specific heat $C$, x-ray photoelectron spectroscopy) and theoretical
investigations have convincingly demonstrated the proposed earlier scaling law
$\chi\times\rho=const.$ in the Kondo insulator regime, which is universal for
all known Kondo insulators. We also analyze the properties of the
Griffiths--phase for CeRhSb when Pd substitutes Rh, or Sb is fractionally
replaced by Te and Sn, whereas doping of Ce with La leads to the formation of
magnetic cluster structure as a result of the Kondo hole effect.
Magnetoresistance of CeRhSb and CeRhSb$_{0.98}$Te$_{0.02}$ as a function of the
field $B$ shows a $-B^2$ behavior, which provides evidence for the
topologically nontrivial nature of these compounds, as was previously predicted
theoretically for CeRhSb on the basis on the band structure calculations.


  We explain 90 degree reorientation in the vortex lattice of borocarbide
superconductors on the basis of a phenomenological extension of the nonlocal
London model that takes full account of the symmetry of the system. We propose
microscopic mechanisms that could generate the correction terms and point out
the important role of the superconducting gap anisotropy.


  Understanding the relation between deep and shallow neural networks is
extremely important for the theoretical study of deep learning. In this work,
we discover an embedding principle in depth that loss landscape of an NN
"contains" all critical points of the loss landscapes for shallower NNs. The
key tool for our discovery is the critical lifting operator proposed in this
work that maps any critical point of a network to critical manifolds of any
deeper network while preserving the outputs. This principle provides new
insights to many widely observed behaviors of DNNs. Regarding the easy training
of deep networks, we show that local minimum of an NN can be lifted to strict
saddle points of a deeper NN. Regarding the acceleration effect of batch
normalization, we demonstrate that batch normalization helps avoid the critical
manifolds lifted from shallower NNs by suppressing layer linearization. We also
prove that increasing training data shrinks the lifted critical manifolds,
which can result in acceleration of training as demonstrated in experiments.
Overall, our discovery of the embedding principle in depth uncovers the
depth-wise hierarchical structure of deep learning loss landscape, which serves
as a solid foundation for the further study about the role of depth for DNNs.


  For two-dimensional last-passage time models of weakly increasing paths,
interesting scaling limits have been proved for points close the axis (the hard
edge). For strictly increasing paths of Bernoulli($p$) marked sites, the
relevant boundary is the line $y=px$. We call this the soft edge to contrast it
with the hard edge. We prove laws of large numbers for the maximal cardinality
of a strictly increasing path in the rectangle $[\fl{p^{-1}n -xn^a}]\times[n]$
as the parameters $a$ and $x$ vary. The results change qualitatively as $a$
passes through the value 1/2.


  An open question in the Deep Learning community is why neural networks
trained with Gradient Descent generalize well on real datasets even though they
are capable of fitting random data. We propose an approach to answering this
question based on a hypothesis about the dynamics of gradient descent that we
call Coherent Gradients: Gradients from similar examples are similar and so the
overall gradient is stronger in certain directions where these reinforce each
other. Thus changes to the network parameters during training are biased
towards those that (locally) simultaneously benefit many examples when such
similarity exists. We support this hypothesis with heuristic arguments and
perturbative experiments and outline how this can explain several common
empirical observations about Deep Learning. Furthermore, our analysis is not
just descriptive, but prescriptive. It suggests a natural modification to
gradient descent that can greatly reduce overfitting.


  The relativistic KMS condition introduced by Bros and Buchholz provides a
link between quantum statistical mechanics and quantum field theory. We show
that for the $P(\phi)_2$ model at positive temperature, the two point function
for fields satisfies the relativistic KMS condition.


  Predicting structural and energetic properties of a molecular system is one
of the fundamental tasks in molecular simulations, and it has use cases in
chemistry, biology, and medicine. In the past decade, the advent of machine
learning algorithms has impacted on molecular simulations for various tasks,
including property prediction of atomistic systems. In this paper, we propose a
novel methodology for transferring knowledge obtained from simple molecular
systems to a more complex one, possessing a significantly larger number of
atoms and degrees of freedom. In particular, we focus on the classification of
high and low free-energy states. Our approach relies on utilizing (i) a novel
hypergraph representation of molecules, encoding all relevant information for
characterizing the potential energy of a conformation, and (ii) novel message
passing and pooling layers for processing and making predictions on such
hypergraph-structured data. Despite the complexity of the problem, our results
show a remarkable AUC of 0.92 for transfer learning from tri-alanine to the
deca-alanine system. Moreover, we show that the very same transfer learning
approach can be used to group, in an unsupervised way, various secondary
structures of deca-alanine in clusters having similar free-energy values. Our
study represents a proof of concept that reliable transfer learning models for
molecular systems can be designed paving the way to unexplored routes in
prediction of structural and energetic properties of biologically relevant
systems.


  In double field theory, the physical space has been understood as a subspace
of the doubled space. Recently, the doubled space is defined as the
para-Hermitian manifold and the physical space is realized as a leaf of a
foliation of the doubled space. This construction naturally introduces the
fundamental 2-form, which plays an important role in a reformulation of string
theory known as the Born sigma model. In this paper, we present the Born sigma
model for $p$-branes in M-theory and type IIB theory by extending the
fundamental 2-form into U-duality-covariant $(p+1)$-forms.


  In late 2017, the ALICE experiment recorded a data sample of Xe--Xe
collisions at the unprecedented energy in A--A systems of $\sqrt{s_{\rm{NN}}} =
5.44\text{ TeV}$. The $p_{\rm T}$ spectra at mid-rapidity ($|y| < 0.5$) of
pions, kaons and protons are presented. The preliminary $p_{\rm T}$ spectra are
obtained by combining independent analyses with the Inner Tracking System
(ITS), the Time Projection Chamber (TPC), and the Time-Of-Flight (TOF)
detectors. This paper focuses on the details of the analysis performed with TOF
and in particular on the performance implications of the special Xe--Xe run
conditions. The peculiarity of this data set comes from the experimental
conditions: because of the lower magnetic field of the ALICE solenoid ($B =
0.2\text{ T}$, lower than the nominal $0.5\text{ T}$) we expect to explore a
$p_{\rm T}$ region unattainable before. A comparison between the yields at
different centrality bins will also be provided.


  Topic sparsity refers to the observation that individual documents usually
focus on several salient topics instead of covering a wide variety of topics,
and a real topic adopts a narrow range of terms instead of a wide coverage of
the vocabulary. Understanding this topic sparsity is especially important for
analyzing user-generated web content and social media, which are featured in
the form of extremely short posts and discussions. As topic sparsity of
individual documents in online social media increases, so does the difficulty
of analyzing the online text sources using traditional methods.
  In this paper, we propose two novel neural models by providing sparse
posterior distributions over topics based on the Gaussian sparsemax
construction, enabling efficient training by stochastic backpropagation. We
construct an inference network conditioned on the input data and infer the
variational distribution with the relaxed Wasserstein (RW) divergence. Unlike
existing works based on Gaussian softmax construction and Kullback-Leibler (KL)
divergence, our approaches can identify latent topic sparsity with training
stability, predictive performance, and topic coherence. Experiments on
different genres of large text corpora have demonstrated the effectiveness of
our models as they outperform both probabilistic and neural methods.


  Recovery of society after a large scale disaster generally consists of two
phases, short- and long-term recoveries. The main goal of the short-term
recovery is to bounce the damaged system back to the operating standards
enabling residents in damaged cities to survive, and fast supply with vital
resources to them is one of its important elements. We propose a general
principle by which the required redistribution of vital resources between the
affected and neighbouring cities can be efficiently implemented. The short-term
recovery is a rescuer operation where uncertainty in evaluating the state of
damaged region is highly probable. To allow for such an operation the developed
principle involves two basic components. The first one of ethic nature is the
triage concept determining the current city priority in the resource delivery.
The second one is the minimization of the delivery time subjected to this
priority. Finally a certain plan of the resource redistribution is generated
according to this principle. Several specific examples are studied numerically.
It elucidates, in particular, the effects of system characteristics such as the
city limit capacity in resource delivery, the type of initial resource
allocation among the cities, the number of cities able to participate in the
resource redistribution, and the damage level in the affected cities. As far as
the uncertainty in evaluating the state of damaged region is concerned, some
specific cases were studied. It assumes the initial communication system has
crashed and formation of a new one and the resource redistribution proceed
synchronously. The obtained results enable us to consider the resource
redistribution plan governed by the proposed method semi-optimal and rather
efficient especially under uncertainty.


  It has long been an ill-posed problem to predict absolute depth maps from
single images in real (unseen) indoor scenes. We observe that it is essentially
due to not only the scale-ambiguous problem but also the focal-ambiguous
problem that decreases the generalization ability of monocular depth
estimation. That is, images may be captured by cameras of different focal
lengths in scenes of different scales. In this paper, we develop a
focal-and-scale depth estimation model to well learn absolute depth maps from
single images in unseen indoor scenes. First, a relative depth estimation
network is adopted to learn relative depths from single images with diverse
scales/semantics. Second, multi-scale features are generated by mapping a
single focal length value to focal length features and concatenating them with
intermediate features of different scales in relative depth estimation.
Finally, relative depths and multi-scale features are jointly fed into an
absolute depth estimation network. In addition, a new pipeline is developed to
augment the diversity of focal lengths of public datasets, which are often
captured with cameras of the same or similar focal lengths. Our model is
trained on augmented NYUDv2 and tested on three unseen datasets. Our model
considerably improves the generalization ability of depth estimation by 41%/13%
(RMSE) with/without data augmentation compared with five recent SOTAs and well
alleviates the deformation problem in 3D reconstruction. Notably, our model
well maintains the accuracy of depth estimation on original NYUDv2.


  We studied the proximity effect between a superconductor (Nb) and a diluted
ferromagnetic alloy (CuNi) in a bilayer geometry. We measured the local density
of states on top of the ferromagnetic layer, which thickness varies on each
sample, with a very low temperature Scanning Tunneling Microscope. The measured
spectra display a very high homogeneity. The analysis of the experimental data
shows the need to take into account an additional scattering mechanism. By
including in the Usadel equations the effect of the spin relaxation in the
ferromagnetic alloy, we obtain a good description of the experimental data.


  This technical report summarizes the preliminary findings of a project that
has been developed in 2007 by an Italian company (Datanet, based in Siracusa,
Italy) togheter with two Italian research institutions: Universita' degli Studi
di Milano and Universita' Bocconi. The main aim of the OS4E (Open Source for
Enterprises) project, has been to investigate if and how open source solutions
could be profitabily and effectively exploited by an IT company based in the
South of Italy, whose core business is IT systems integration and which
operates in the market of Italian SMEs (Small and Medium Enterprises). Beside
this goal, the project also aimed at developing effective tools and
methodologies to support decision making processes while evaluating different
alternative software applications based on OSS (open source software).


  We prove Faltings Finiteness Theorem using Rieffel's classification of the
noncommutative tori.


  We show that there is no real conflict between the two determinations of the
strange sea density from the opposite--sign dimuon production and from the
difference of the $F_2$ structure functions measured in neutrino and muon deep
inelastic scattering. Once non universal sea parton densities are introduced,
which take into account the effects of different mass thresholds and different
longitudinal contributions, the discrepancy is shown to disappear and both sets
of data are simultaneously well reproduced. No need for a large strange sea
content of the nucleon emerges.


  Orbital degeneracy of the electronic conduction band edge in silicon is a
potential roadblock to the storage and manipulation of quantum information
involving the electronic spin degree of freedom in this host material. This
difficulty may be mitigated near an interface between Si and a barrier
material, where intervalley scattering may couple states in the conduction
ground state, leading to nondegenerate orbital ground and first excited states.
The level splitting is experimentally found to have a strong sample dependence,
varying by orders of magnitude for different interfaces and samples. The basic
physical mechanisms leading to such coupling in different systems are
addressed. We expand our recent study based on an effective mass approach,
incorporating the full plane-wave expansions of the Bloch functions at the
conduction band minima. Physical insights emerge naturally from a simple
Si/barrier model. In particular, we present a clear comparison between ours and
different approximations and formalisms adopted in the literature and establish
the applicability of these approximations in different physical scenarios.


  Axions are increasingly favoured as a candidate particle for the dark matter
in galaxies, since they satisfy the observational requirements for cold dark
matter and are theoretically well motivated. Fluctuations in the axion field
give rise to stable localised overdensities known as axion stars, which, for
the most massive, compact cases, are potential neutron star mimickers. In
principle, there are no fundamental arguments against the multi-messenger
observations of GW170817/GRB170817A/AT2017gfo arising from the merger of a
neutron star with a neutron star mimicker, rather than from a binary neutron
star. To constrain this possibility and better understand the astrophysical
signatures of a neutron star--axion star (NSAS) merger, we present in this work
a detailed example case of a NSAS merger based on full 3D numerical relativity
simulations, and give an overview of the many potential observables - ranging
from gravitational waves, to optical and near-infrared electromagnetic signals,
radio flares, fast radio bursts, gamma ray bursts, and neutrino emission. We
discuss the individual channels and estimate to which distances current and
future observatories might be able to detect such a NSAS merger. Such signals
could constrain the unknown axion mass and its couplings to standard baryonic
matter,thus enhancing our understanding of the dark matter sector of the
Universe.


  We say that a class of finite structures for a finite first-order signature
is $r$-compressible if each structure $G$ in the class has a first-order
description of size at most $O(r(|G|))$. We show that the class of finite
simple groups is $\log$-compressible, and the class of all finite groups is
$\log^3$-compressible. As a corollary we obtain that the class of all finite
transitive permutation groups is $\log^3$-compressible.
  The result relies on the classification of finite simple groups, the
bi-interpretability of the twisted Ree groups with finite difference fields,
the existence of profinite presentations with few relators, and group
cohomology.
  We also indicate why the results are close to optimal.


  This paper concerns with a class of elliptic equations on fractal domains
depending on a real parameter. Our approach is based on variational methods.
More precisely, the existence of at least two non-trivial weak (strong)
solutions for the treated problem is obtained exploiting a local minimum
theorem for differentiable functionals defined on reflexive Banach spaces. A
special case of the main result improves a classical application of the
Mountain Pass Theorem in the fractal setting, given by Falconer and Hu (1999).


  Training offline reinforcement learning (RL) models using visual inputs poses
two significant challenges, i.e., the overfitting problem in representation
learning and the overestimation bias for expected future rewards. Recent work
has attempted to alleviate the overestimation bias by encouraging conservative
behaviors. This paper, in contrast, tries to build more flexible constraints
for value estimation without impeding the exploration of potential advantages.
The key idea is to leverage off-the-shelf RL simulators, which can be easily
interacted with in an online manner, as the "test bed" for offline policies. To
enable effective online-to-offline knowledge transfer, we introduce CoWorld, a
model-based RL approach that mitigates cross-domain discrepancies in state and
reward spaces. Experimental results demonstrate the effectiveness of CoWorld,
outperforming existing RL approaches by large margins.


  This is an introductory review of the connection between homotopy theory and
path integrals, mainly focus on works done by Schulman [23] that he compared
path integral on SO(3) and its universal covering space SU(2), DeWitt and
Laidlaw [15] that they proved the theorem to the case of path integrals on the
multiply-connected topological spaces. Also, we discuss the application of the
theorem in Aharonov-Bohm effect given by [20,24]. An informal introduction to
homotopy theory is provided for readers who are not familiar with the theory.


  In this study, we applied a stochastic spread pairs trading strategy on the
Indian commodity market. The complete set of commodities were taken whose spot
price was available for the period of January 1st 2010 to December 31st 2018
including energy, metals and the agricultural commodity sector. Spot data was
taken from the MCX pooled spot prices for 17 commodities. The data was split
into training period (January 1st 2010 to 14th March 2017) and testing
period(15th Match 2017 to 31st December 2018). The splitting was done using a
80:20 split.Johanssen Cointegration tests were done on training data for pairs
of commodities to check for long-run relationship and the cointegrated
commodities were selected for formation of the trading process. We found a
total of 12 cointegrated pairs out of 136 possible pairs. Cointegration was
assumed for the testing period. A single-factor stochastic trading approach was
applied on the logarithmic spread of the cointegrated pairs for both the
training and testing period.The parameters of stochastic spread model were
estimated using differential evolution algorithm. Also parameters for the
trading rule were optimized by backtesting on the training period and assumed
for the testing period. The results show a sharpe ratio of above 1.4 for all
the commodity cointegrated pairs in the backtesing period.


  We define a closure operation for rings of mixed characteristic and verify
that the closure is a ring. We then show that this closure produces a ring with
good properties with respect to its Fontaine ring and give an example to show
that rings that are not closed in this sense do not satisfy these properties.


  Vision transformers (ViT) have made substantial progress for classification
tasks in computer vision. Recently, Gong et. al. '21, introduced
attention-based modeling for several audio tasks. However, relatively
unexplored is the use of a ViT for audio spoof detection task. We bridge this
gap and introduce ViTs for this task. A vanilla baseline built on fine-tuning
the SSAST (Gong et. al. '22) audio ViT model achieves sub-optimal equal error
rates (EERs). To improve performance, we propose a novel attention-based
contrastive learning framework (SSAST-CL) that uses cross-attention to aid the
representation learning. Experiments show that our framework successfully
disentangles the bonafide and spoof classes and helps learn better classifiers
for the task. With appropriate data augmentations policy, a model trained on
our framework achieves competitive performance on the ASVSpoof 2021 challenge.
We provide comparisons and ablation studies to justify our claim.


  We investigate neutrino-driven convection in core collapse supernovae and its
ramifications for the explosion mechanism, for a 15 solar mass model. Our
two-dimensional simulation begins at 12 ms after bounce and proceeds for 500
ms. We couple two-dimensional PPM hydrodynamics to precalculated
one-dimensional MGFLD neutrino transport. (The accuracy of this approximation
is assessed.) For the moment we sacrifice dimensionality for realism in other
aspects of our neutrino transport. MGFLD is an implementation of neutrino
transport that simultaneously (a) is multigroup and (b) simulates with greater
realism the transport of neutrinos in opaque, semitransparent, and transparent
regions. Both are crucial to the accurate determination of postshock neutrino
heating, which sensitively depends on the luminosities, spectra, and flux
factors of the electron neutrinos and antineutrinos emerging from their
respective neutrinospheres. By 212 ms after bounce, we see large-scale,
neutrino-driven convection beneath the shock, characterized by higher-entropy,
expanding upflows and denser, lower-entropy, finger-like downflows. The radial
convection velocities at this time become supersonic just below the shock,
reaching magnitudes in excess of 10^{9} cm/sec. Eventually, however, the shock
recedes to smaller radii, and at 500 ms after bounce there is no evidence in
our simulation of an explosion. While vigorous, neutrino-driven convection in
our model does not have a significant impact on the overall shock dynamics. The
differences between our results and those of other groups are considered. These
most likely result from differences in (1) numerical hydrodynamics methods, (2)
initial postbounce models, and most important, (3) neutrino transport
approximations.


  Mono-static sensing operations in ISAC perform joint beamforming between
transmitter and receiver. However, in contrast to pure radar systems, ISAC
requires to fulfill communications tasks and to retain the corresponding design
constraints for at least one half-duplex antenna array. This shifts the
available degrees of freedom to the design of the second half-duplex array,
that completes the mono-static sensing setup of the 6G ISAC system.
Consequently, although it is still possible to achieve the gains foreseen by
the radar sparse array literature, it is necessary to adapt these
considerations to the new ISAC paradigm.
  In this work, we propose a model to evaluate the angular capabilities of a
mono-static setup, constrained to the shape of the communications array and its
topology requirements in wireless networks. Accordingly, we enhance the joint
angular capabilities by utilizing a sparse element topology of the sensing
array with the same number of elements. Our analysis is validated by simulation
experiments, confirming the value of our model in providing system designers
with a tool to drastically improve the trade-off between angular capabilities
for sensing and the cost of the deployed hardware.


  In this article, inferences about the multicomponent stress strength
reliability are drawn under the assumption that strength and stress follow
independent Pareto distribution with different shapes $(\alpha_1,\alpha_2)$ and
common scale parameter $\theta$. The maximum likelihood estimator, Bayes
estimator under squared error and Linear exponential loss function, of
multicomponent stress-strength reliability are constructed with corresponding
highest posterior density interval for unknown $\theta.$ For known $\theta,$
uniformly minimum variance unbiased estimator and asymptotic distribution of
multicomponent stress-strength reliability with asymptotic confidence interval
is discussed. Also, various Bootstrap confidence intervals are constructed. A
simulation study is conducted to numerically compare the performances of
various estimators of multicomponent stress-strength reliability. Finally, a
real life example is presented to show the applications of derived results in
real life scenarios.


  Ranking models lie at the heart of research on information retrieval (IR).
During the past decades, different techniques have been proposed for
constructing ranking models, from traditional heuristic methods, probabilistic
methods, to modern machine learning methods. Recently, with the advance of deep
learning technology, we have witnessed a growing body of work in applying
shallow or deep neural networks to the ranking problem in IR, referred to as
neural ranking models in this paper. The power of neural ranking models lies in
the ability to learn from the raw text inputs for the ranking problem to avoid
many limitations of hand-crafted features. Neural networks have sufficient
capacity to model complicated tasks, which is needed to handle the complexity
of relevance estimation in ranking. Since there have been a large variety of
neural ranking models proposed, we believe it is the right time to summarize
the current status, learn from existing methodologies, and gain some insights
for future development. In contrast to existing reviews, in this survey, we
will take a deep look into the neural ranking models from different dimensions
to analyze their underlying assumptions, major design principles, and learning
strategies. We compare these models through benchmark tasks to obtain a
comprehensive empirical understanding of the existing techniques. We will also
discuss what is missing in the current literature and what are the promising
and desired future directions.


  We study quasilinear elliptic equations of the type $-\Delta_{p} u = \sigma
u^{q} + \mu \; \; \text{in} \;\; \bf{R}^n$ in the case $0<q< p-1$, where $\mu$
and $\sigma$ are nonnegative measurable functions, or locally finite measures,
and $\Delta_{p}u= \text{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian.
Similar equations with more general local and nonlocal operators in place of
$\Delta_{p}$ are treated as well.
  We obtain existence criteria and global bilateral pointwise estimates for all
positive solutions $u$: $$ u(x) \approx (\bf{W}_p
\sigma(x))^{\frac{p-q}{p-q-1}} + \bf{K}_{p,q} \sigma(x) + \bf{W}_p \mu (x),
\quad x \in \bf{R}^n,$$ where $\bf{W}_p$ and $\bf{K}_{p, q}$ are, respectively,
the Wolff potential and the intrinsic Wolff potential, with the constants of
equivalence depending only on $p$, $q$ and $n$.
  The contributions of $\mu$ and $\sigma$ in these pointwise estimates are
totally separated, which is a new phenomenon even when $p=2$. In the
homogeneous case $\mu=0$, such estimates were obtained earlier by a different
method only for minimal positive solutions.


  For a non-cyclic finite group $X$ let $\sigma(X)$ be the least number of
proper subgroups of $X$ whose union is $X$. Precise formulas or estimates are
given for $\sigma(S \wr C_{m})$ for certain nonabelian finite simple groups $S$
where $C_m$ is a cyclic group of order $m$.


  Knitted sensors frequently suffer from inconsistencies due to innate effects
such as offset, relaxation, and drift. These properties, in combination, make
it challenging to reliably map from sensor data to physical actuation. In this
paper, we demonstrate a method for counteracting this by applying processing
using a minimal artificial neural network (ANN) in combination with
straightforward pre-processing. We apply a number of exponential smoothing
filters on a re-sampled sensor signal, to produce features that preserve
different levels of historical sensor data and, in combination, represent an
adequate state of previous sensor actuation. By training a three-layer ANN with
a total of 8 neurons, we manage to significantly improve the mapping between
sensor reading and actuation force. Our findings also show that our technique
translates to sensors of reasonably different composition in terms of material
and structure, and it can furthermore be applied to related physical features
such as strain.


  Recent experimental limits for the direct CP asymmetries in $B^0 \to K^+
\pi^-$, $B^+ \to K^+ \pi^0$, $B^+ \to K^0 \pi^+$, and $B^0 \to \pi^+ \pi^-$,
and for the indirect CP asymmetry in $B^0 \to \pi^+ \pi^-$, are combined with
information on CP-averaged branching ratios to shed light on weak and strong
phases. At present such bounds favor $\gamma \ge 60^\circ$ at the $1 \sigma$
level. The prospects for further improvements are discussed.


  We study the Marangoni instability in a thin polymeric liquid film heated
from the free surface. Polymeric solutions are usually the binary mixture of a
Newtonian solvent with polymeric solute and exhibit viscoelastic behaviour. In
the presence of a temperature gradient, stratification of these polymeric
solutes can take place via the Soret effect, which may give rise to the
solutocapillary effect at the free surface. Considering the Soret effect and
incorporating the effects of gravity, here we analyse the stability
characteristics of this polymeric thin film bounded between its deformable free
surface and a poorly conductive rigid substrate from below. A linear stability
analysis around the quiescent base state reveals that under the combined
influences of thermo-solutocapillarity, apart from the monotonic disturbance,
two different oscillatory instabilities can emerge in the system. The
characteristics of each instability mode are discussed, and a complete
stability picture is perceived in terms of the phase diagrams, identifying the
model parameter space wherein a particular instability mode can get dominant.


  Quantum gravity, the initial low entropy state of the Universe, and the
problem of time are interlocking puzzles. In this article, we address the
origin of the arrow of time from a cosmological perspective motivated by a
novel approach to quantum gravitation. Our proposal is based on a quantum
counterpart of the equivalence principle, a general covariance of the dynamical
phase space. We discuss how the nonlinear dynamics of such a system provides a
natural description for cosmological evolution in the early Universe. We also
underscore connections between the proposed non-perturbative quantum gravity
model and fundamental questions in non-equilibrium statistical physics.


  We analyse the asymptotic behavior for kinetic models describing the
collective behavior of animal populations. We focus on models for
self-propelled individuals, whose velocity relaxes toward the mean orientation
of the neighbors. The self-propelling and friction forces together with the
alignment and the noise are interpreted as a collision/interaction mechanism
acting with equal strength. We show that the set of generalized collision
invariants, introduced in \cite{DM08}, is equivalent in our setting to the more
classical notion of collision invariants, i.e., the kernel of a suitably
linearized collision operator. After identifying these collision invariants, we
derive the fluid model, by appealing to the balances for the particle
concentration and orientation. We investigate the main properties of the
macroscopic model for a general potential with radial symmetry.


  Analyzing a Gross-Pitaevskii equation with cubic, quartic, and quintic
nonlinearities through analytical and numerical methods, we examine the
stability of two-dimensional (2D) trapless Bose-Einstein condensates (BECs)
with two-, three-body interactions and quantum fluctuations. Applying a
variational approach, we derive the equation of motion and effective potential
to discuss in detail the stability of the BECs in 2D free space. We show that
with the aid of quantum fluctuations it is possible to stabilize 2D trapless
BEC without any oscillatory nonlinearities. Also, there is an enhancement of
the stability of the system, due to the inclusion of the three-body interaction
and quantum fluctuations in addition to the two-body interaction. We further
study the stability of 2D trapless BECs with rapid periodic temporal modulation
of scattering length by using a Feshbach resonance. We discuss all possible
ways of stabilization of trapless BECs in 2D by three-body interaction and
quantum fluctuations. Finally, we verify our analytical results with numerical
simulation using split-step Crank-Nicholson method. These match well with the
analytical predictions.


  We introduce a numerical method for general coupled Korteweg-de Vries
systems. The scheme is valid for solving Cauchy problems for arbitrary number
of equations with arbitrary constant coefficients. The numerical scheme takes
its legality by proving its stability and convergence which gives the
conditions and the appropriate choice of the grid sizes. The method is applied
to Hirota-Satsuma (HS) system and compared with its known explicit solution
investigating the influence of initial conditions and grid sizes on accuracy.
We also illustrate the method to show the effects of constants with a
transition to non-integrable cases.


  Teleoperation is a widely adopted strategy to control robotic manipulators
executing complex tasks that require highly dexterous movements and critical
high-level intelligence. Classical teleoperation schemes are based on either
joystick control, or on more intuitive interfaces which map directly the user
arm motions into one robot arm's motions. These approaches have limits when the
execution of a given task requires reconfigurable multiple robotic arm systems.
Indeed, the simultaneous teleoperation of two or more robot arms could extend
the workspace of the manipulation cell, or increase its total payload, or
afford other advantages. In different phases of a reconfigurable multi-arm
system, each robot could act as an independent arm, or as one of a pair of
cooperating arms, or as one of the fingers of a virtual, large robot hand. This
manuscript proposes a novel telemanipulation framework that enables both the
individual and combined control of any number of robotic arms. Thanks to the
designed control architecture, the human operator can intuitively choose the
proposed control modalities and the manipulators that make the task convenient
to execute through the user interface. Moreover, through the tele-impedance
paradigm, the system can address complex tasks that require physical
interaction by letting the robot mimic the arm impedance and position
references of the human operator. The proposed framework is validated with 8
subjects controlling 4 Franka Emika Panda robots with 7-DoFs to execute a
telemanipulation task. Qualitative results of the experiments show us the
promising applicability of our framework.


  We report long-term laser frequency stabilization using only the target laser
and a pair of 5 m fiber interferometers, one as a frequency reference and the
second as a sensitive thermometer to stabilize the frequency reference. When
used to stabilize a distributed feedback laser at 795 nm, the frequency Allan
deviation at 1000 s drops from 5.6*10^{-8} to 6.9*10^{-10}. The performance
equals that of an offset lock employing a second, atom-stabilized laser in the
temperature control.


  Emergency service vehicles like ambulance, fire, police etc. should respond
to emergencies on time. Existing barriers like increased congestion, multiple
signalized intersections, queued vehicles, traffic phase timing etc. can
prevent emergency vehicles (EVs) achieving desired response times. Existing
solutions to route EVs have not been successful because they do not use dynamic
traffic parameters. Real time information on increased congestion, halts on
road, pedestrian flow, queued vehicles, real and adaptive speed, can be used to
properly actuate pre-emption and minimise the impact that EV movement can have
on other traffic. Smart cities provide the necessary infrastructure to enable
two critical factors in EV routing: real-time traffic data and connectivity. In
addition, using autonomous vehicles (AVs) in place of normal emergency service
vehicles can have further advantages in terms of safety and adaptability in
smart city environments. AVs feature several sensors and connectivity that can
help them make real-time decisions. We propose a novel idea of using autonomous
emergency vehicles (AEVs) that can meet the critical response time and drive
through a complex road network in smart cities efficiently and safely. This is
achieved by considering traffic network analogous to real-time systems (RTS)
where we use mixed-criticality real-time system (MCRTS) task scheduling to
schedule AEVs for meeting response time.


  The formalism for a linear-response many-body treatment of the electronic
contributions to thermal transport is developed for multilayered
nanostructures. By properly determining the local heat-current operator, it is
possible to show that the Jonson-Mahan theorem for the bulk can be extended to
inhomogeneous problems, so the various thermal-transport coefficient integrands
are related by powers of frequency (including all effects of vertex corrections
when appropriate). We illustrate how to use this formalism by showing how it
applies to measurements of the Peltier effect, the Seebeck effect, and the
thermal conductance.


  We consider the tails of probability density functions (PDF) for different
characteristics of velocity that satisfies Burgers equation driven by a
large-scale force. The saddle-point approximation is employed in the path
integral so that the calculation of the PDF tails boils down to finding the
special field-force configuration (instanton) that realizes the extremum of
probability. We calculate high moments of the velocity gradient $\partial_xu$
and find out that they correspond to the PDF with $\ln[{\cal
P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where ${\rm Re}$ is the
Reynolds number. That stretched exponential form is valid for negative
$\partial_xu$ with the modulus much larger than its root-mean-square (rms)
value. The respective tail of PDF for negative velocity differences $w$ is
steeper than Gaussian, $\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as
single-point velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$. For high
velocity derivatives $u^{(k)}=\partial_x^ku$, the general formula is found:
$\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.


  Qubit Models which aim to resolve the information paradox must not redefine
entanglement entropy as a redefinition does not address the correct issue of
the information paradox. The purpose of this letter is to understand why any
redefinition of entanglement entropy is not relevant to the paradox. Also,
conditions required for a bit model to resolve the information paradox are
listed, motivating the community to look for such conditions as a consistency
check in their qubit models.


  Let $M$ be a smooth finite-dimensional manifold, $G$ be a Lie group, and
$\Phi:G \times M \to M$ be a smooth action. Consider the following mapping
$\phi: C^{\infty}(M,G) \to C^{\infty}(M,M)$, defined by $\phi(\alpha)(x) =
\alpha(x)\cdot x$, for $\alpha\in C^{\infty}(M,G)$ and $x\in M$. In this paper
we describe the structure of inverse images of elements of $C^{\infty}(M,M)$
under $\phi$ for $\dim G=1$, i.e. when $G$ is either $\mathbb{R}$ or $S^1$. As
an application we obtain a new proof of the well-known theorem by M. Newman
concerning the interior of the fixed point set of a Lie group action.


  In this paper, we construct a geometric model for the bounded derived
category of a gentle algebra. The construction is based on the ribbon graph
associated to a gentle algebra by the third author, and is linked to partially
wrapped Fukaya categories by the work of Haiden, Katzarkov and Kontsevich and
to derived categories of coherent sheaves on nodal stacky curves by the work of
Lekili and Polishchuk. The ribbon graph gives rise to an oriented surface with
boundary and marked points in the boundary. We show that the homotopy classes
of curves connecting marked points and of closed curves are in bijection with
the isomorphism classes of indecomposable objects in the bounded derived
category of the gentle algebra. Intersections of curves correspond to morphisms
and resolving the crossings of curves gives rise to mapping cones. The
Auslander-Reiten translate corresponds to rotating endpoints of curves along
the boundary. Furthermore, we show that the surface encodes the derived
invariant of Avella-Alaminos and Geiss.


  In a previous paper we proposed a model to describe a gas of pyramidal
molecules interacting via dipole-dipole interactions. The interaction modifies
the tunneling properties between the classical equilibrium configurations of
the single molecule and, for sufficiently high pressure, the molecules become
localized in these classical configurations. The model explains quantitatively
the shift to zero-frequency of the inversion line observed upon increase of the
pressure in a gas of ammonia or deuterated ammonia. Here we analyze further the
model especially with respect to stability questions.


  We investigate the resurgence and asymptotic resurgence numbers of fiber
products of projective schemes. Particularly, we show that while the asymptotic
resurgence number of the k-fold fiber product of a projective scheme remains
unchanged, its resurgence number could strictly increase.


  Imitation plays an important role in development, being one of the precursors
of social cognition. Even though some children with autism imitate
spontaneously and other children with autism can learn to imitate, the dynamics
of imitation is affected in the large majority of cases. Existing studies from
the literature suggest that robots can be used to teach children with autism
basic interaction skills like imitation. Based on these findings, in this
study, we investigate if children with autism show more social engagement when
interacting with an imitative robot (Fig 1) compared to a human partner in a
motor imitation task.


  We present a new brane solution in the (1+5)-dimensional space-time with an
increasing warp factor, which localizes the zero modes of all kinds of matter
fields and Newtonian gravity. The interesting features of this solution are: 1)
In contrast to the Gogberashvili-Singleton case the effective wave function of
the zero mode spinor field confined on the brane is finite at a position of
brane; 2) There is exactly one zero mode for each matter field and the
gravitational field confined on the brane with a finite probability and
infinitely many zero modes (labelled by the angular momentum corresponding to
extra space) are located in the bulk at different localization radii.


  We introduce simplicial persistence, a measure of time evolution of network
motifs in subsequent temporal layers. We observe long memory in the evolution
of structures from correlation filtering, with a two regime power law decay in
the number of persistent simplicial complexes. Null models of the underlying
time series are tested to investigate properties of the generative process and
its evolutional constraints. Networks are generated with both TMFG filtering
technique and thresholding showing that embedding-based filtering methods
(TMFG) are able to identify higher order structures throughout the market
sample, where thresholding methods fail. The decay exponents of these long
memory processes are used to characterise financial markets based on their
stage of development and liquidity. We find that more liquid markets tend to
have a slower persistence decay. This is in contrast with the common
understanding that developed markets are more random. We find that they are
indeed less predictable for what concerns the dynamics of each single variable
but they are more predictable for what concerns the collective evolution of the
variables. This could imply higher fragility to systemic shocks.


  In this paper we show how it is possible to obtain mass generation in the
context of non Abelian gauge field theory, using a non commutative spacetime.
This is further confirmed by the modified dispersion relation that results from
such a geometry.


  For a Whitney stratification S of a space X (or more generally a topological
stratification in the sense of Goresky and MacPherson) we introduce the notion
of an S-constructible stack of categories on X. The motivating example is the
stack of S-constructible perverse sheaves. We introduce a 2-category $EP_{\leq
2}(X,S)$, called the exit-path 2-category, which is a natural stratified
version of the fundamental 2-groupoid. Our main result is that the 2-category
of S-constructible stacks on X is equivalent to the 2-category of 2-functors
from $EP_{\leq 2}(X,S)$ to the 2-category of small categories.


  Two-nucleon parity nonconserving (PNC) interaction induced by the
single-particle PNC weak potential and the two-nucleon residual strong
interaction is considered. An approximate analytical formula for this Induced
PNC Interaction (IPNCI) between proton and neutron is derived ($Q({\bf r} {\bf
\sigma}_{p} \times {\bf \sigma}_{n}) \delta({\bf r}_{p}-{\bf r}_{n})$), and the
interaction constant is estimated. As a result of coherent contributions from
the nucleons to the PNC potential, IPNCI is an order of magnitude stronger
($\sim A^{1/3}$) than the residual weak two-nucleon interaction and has a
different coordinate and isotopic structure (e.g., the strongest part of IPNCI
does not contribute to the PNC mean field). IPNCI plays an important role in
the formation of PNC effects, e.g., in neutron-nucleus reactions. In that case,
it is a technical way to take into account the contribution of the distant
(small) components of a compound state which dominates the result. The absence
of such enhancement ($\sim A^{1/3}$) in the case of T- and P-odd interaction
completes the picture.


  A \emph{Golomb ruler} is a sequence of distinct integers (the \emph{markings}
of the ruler) whose pairwise differences are distinct. Golomb rulers can be
traced back to additive number theory in the 1930s and have attracted recent
research activities on existence problems, such as the search for
\emph{optimal} Golomb rulers (those of minimal length given a fixed number of
markings). Our goal is to enumerate Golomb rulers in a systematic way: we study
[g_m(t) := # {\x \in \Z^{m+1} : \, 0 = x_0 < x_1 < ... < x_{m-1} < x_m = t,
\text{all} x_j - x_k \text{distinct}},] the number of Golomb rulers with $m+1$
markings and length $t$. Our main result is that $g_m(t)$ is a quasipolynomial
in $t$ which satisfies a combinatorial reciprocity theorem: $(-1)^{m-1}
g_m(-t)$ equals the number of rulers $\x$ of length $t$ with $m+1$ markings,
each counted with its \emph{Golomb multiplicity}, which measures how many
combinatorially different Golomb rulers are in a small neighborhood of $\x$.
Our reciprocity theorem can be interpreted in terms of certain mixed graphs
associated to Golomb rulers; in this language, it is reminiscent of Stanley's
reciprocity theorem for chromatic polynomials. Thus in the second part of the
paper we develop an analogue of Stanley's theorem to mixed graphs, which
connects their chromatic polynomials to acyclic orientations.


  The thermoelectric effects in semiconducting single-walled carbon nanotubes
(SWCNTs) are investigated based on the linear response theory combined with the
thermal Green's function method. It is shown that the electronic states near
the lowest conduction band minimum and the highest valence band maximum can be
effectively described in terms of one-dimensional (1D) Dirac electrons to which
a theoretical scheme is developed to describe the thermoelectric responses
making it possible to study the effects of inter-band impurity scattering and
in-gap states. Using the proposed scheme, the bipolar thermoelectric effects
(i.e., the sign inversion of the Seebeck coefficient) in semiconducting SWCNTs
observed in recent experiments are explained. Moreover, the temperature
dependence of the Seebeck coefficient of semiconducting SWCNTs at low
temperature is clarified.


  Code completion, one of the most useful features in the Integrated
Development Environments (IDEs), can accelerate software development by
suggesting the libraries, APIs, and method names in real-time. Recent studies
have shown that statistical language models can improve the performance of code
completion tools through learning from large-scale software repositories.
However, these models suffer from three major drawbacks: a) The hierarchical
structural information of the programs is not fully utilized in the program's
representation; b) In programs, the semantic relationships can be very long.
Existing recurrent neural networks based language models are not sufficient to
model the long-term dependency. c) Existing approaches perform a specific task
in one model, which leads to the underuse of the information from related
tasks. To address these challenges, in this paper, we propose a
self-attentional neural architecture for code completion with multi-task
learning. To utilize the hierarchical structural information of the programs,
we present a novel method that considers the path from the predicting node to
the root node. To capture the long-term dependency in the input programs, we
adopt a self-attentional architecture based network as the base language model.
To enable the knowledge sharing between related tasks, we creatively propose a
Multi-Task Learning (MTL) framework to learn two related tasks in code
completion jointly. Experiments on three real-world datasets demonstrate the
effectiveness of our model when compared with state-of-the-art methods.


  NASA's Double Asteroid Redirection Test (DART) mission will kinetically
impact Dimorphos, the secondary component of the Didymos binary asteroid
system, which will excite Dimorphos's dynamical state and lead to significant
libration about the synchronous state and possibly chaotic non-principal axis
rotation. Although this particular outcome is human caused, many other
secondary components of binary systems are also prone to such exotic spin
states. For a satellite in an excited spin state, the time-varying tidal and
rotational environment can lead to significant surface accelerations. Depending
on the circumstances, this mechanism may drive granular motion on the surface
of the secondary. We modeled the dynamical evolution of a Didymos-like binary
asteroid system using a fully coupled, three-dimensional simulation code. Then,
we computed the time-varying gravitational and rotational accelerations felt
over the entire surface resulting from the secondary's perturbed dynamical
state. We find that an excited spin and orbit can induce large changes in the
effective surface slope, potentially triggering granular motion and surface
refreshment. However, for the case of the DART impact, this effect is highly
dependent on many unknowns, such as Dimorphos's detailed shape, bulk density,
surface geology, and the momentum transferred. Aside from the Didymos system
and the DART mission, this effect also has important implications for binary
systems in general.


  We perform a semi-classical analysis of the Emergent Universe scenario for
inflation. Fixing the background, and taking the inflaton to be homogenous, we
cast the inflaton's evolution as a one-dimensional quantum mechanics problem.
We find that the tuning required over a long time scale for this inflationary
scenario is unstable quantum mechanically. Considering the inflaton field value
as a wavepacket, the spreading of the wavepacket destroys any chance of both
starting and ending with a well-formed state. Thus, one cannot have an Einstein
static universe to begin with that evolves into a well-defined beginning to
inflation a long time later.


  The explicit Verlinde formula for the dimension of conformal blocks, attached
to a marked projective curve $\Sigma$, a simple Lie algebra $\mathfrak{g}$ over
$\mathbb{C}$ and integrable highest weight modules of a fixed central charge of
the corresponding affine Lie algebra $\hat{L}(\mathfrak{g})$ attached to the
marked points, requires (among several other important ingredients) a Lie
algebra cohomology vanishing result due to C. Teleman for the positive part
$\hat{L}^+(\mathfrak{g})$ with coefficients in the tensor product of an
integrable highest weight module with copies of finite dimensional evaluation
modules. The aim of this paper is to extend this result of Teleman to a twisted
setting where $\mathfrak{g}$ is endowed with a special automorphism $\sigma$
and the curve $\Sigma$ is endowed with the action of $\sigma$. In this general
setting, the affine Lie algebra gets replaced by twisted affine Lie algebras.
The crucial ingredient (as in Teleman) is to prove a certain Nakano Identity.


  Mortality risk is a major concern to patients have just been discharged from
the intensive care unit (ICU). Many studies have been directed to construct
machine learning models to predict such risk. Although these models are highly
accurate, they are less amenable to interpretation and clinicians are typically
unable to gain further insights into the patients' health conditions and the
underlying factors that influence their mortality risk. In this paper, we use
patients' profiles extracted from the MIMIC-III clinical database to construct
risk calculators based on different machine learning techniques such as
logistic regression, decision trees, random forests and multilayer perceptrons.
We perform an extensive benchmarking study that compares the most salient
features as predicted by various methods. We observe a high degree of agreement
across the considered machine learning methods; in particular, the cardiac
surgery recovery unit, age, and blood urea nitrogen levels are commonly
predicted to be the most salient features for determining patients' mortality
risks. Our work has the potential for clinicians to interpret risk predictions.


  In this paper we extend the eliminant construction of Burchnall and Chaundy
for commuting differential operators in the Heisenberg algebra to the
q-deformed Heisenberg algebra and show that it again provides annihilating
curves for commuting elements, provided q satisfies a natural condition. As a
side result we obtain estimates on the dimensions of the eigenspaces of
elements of this algebra in its faithful module of Laurent series.


  Artists, using an empirical knowledge, manage to generate and play with giant
soap films and bubbles. Until now, scientific studies of soap films generated
at a controlled velocity and without any feeding from the top, studied films of
a few square centimeters. The present work aims to present a new setup to
generate and characterize giant soap films (2~m $\times$ 0.7~m). Our setup is
enclosed in a humidity-controlled box of 2.2~m high, 1~m long and 0.75~m large.
Soap films are entrained by a fishing line withdrawn out of a bubbling solution
at various velocities. We measure the maximum height of the generated soap
films, as well as their lifetime, thanks to an automatic detection. This is
allowed by light-sensitive resistors collecting the light reflected on the soap
films and ensures robust statistical measurements. In the meantime, thickness
measurements are performed with a UV-VIS-spectrometer, allowing us to map the
soap films thickness over time.


  Using CGRO/BATSE hard X-ray (HXR) data and GHz radio monitoring data from the
Green Bank Interferometer (GBI), we have performed a long term study ($\sim$
1800 days) of the unusual X-ray binary Cyg X-3 resulting in the discovery of a
remarkable relationship between these two wavelength bands. We find that,
during quiescent radio states, the radio flux is strongly anticorrelated with
the intensity of the HXR emission. The relationship switches to a correlation
with the onset of major radio flaring activity. During major radio flaring
activity the HXR drops to a very low intensity during quenching in the radio
and recovers during the radio flare. Injection of plasma into the radio jets of
Cyg X-3 occurs during changes in the HXR emission and suggests that
disk-related and jet-related components are responsible for the high energy
emission.


  We show that locally homogeneous $\mathcal{C}^0$-Riemannian manifolds are
smooth.


  In many data-driven applications, collecting data from different sources is
increasingly desirable for enhancing performance. In this paper, we are
interested in the problem of probabilistic forecasting with multi-source time
series. We propose a neural mixture structure-based probability model for
learning different predictive relations and their adaptive combinations from
multi-source time series. We present the prediction and uncertainty
quantification methods that apply to different distributions of target
variables. Additionally, given the imbalanced and unstable behaviors observed
during the direct training of the proposed mixture model, we develop a phased
learning method and provide a theoretical analysis. In experimental
evaluations, the mixture model trained by the phased learning exhibits
competitive performance on both point and probabilistic prediction metrics.
Meanwhile, the proposed uncertainty conditioned error suggests the potential of
the mixture model's uncertainty score as a reliability indicator of
predictions.


  The strong CP problem can be solved in Parity symmetric theories with
electroweak gauge group containing $SU(2)_L \times SU(2)_R$ broken by the
minimal Higgs content. Neutrino masses may be explained by adding the same
number of gauge singlet fermions as the number of generations. The neutrino
masses vanish at tree-level and are only radiatively generated, leading to
larger couplings of right-handed neutrinos to Standard Model particles than
with the tree-level seesaw mechanism. We compute these radiative corrections
and the mixing angles between left- and right-handed neutrinos. We discuss
sensitivities to these right-handed neutrinos from a variety of future
experiments that search for heavy neutral leptons with masses from tens of MeV
to the multi-TeV scale.


  Low dimensional structures comprised of ferroelectric (FE) PbTiO$_3$ (PTO)
and quantum paraelectric SrTiO$_3$ (STO) are hosts to complex polarization
textures such as polar waves, flux-closure domains and polar skyrmion phases.
Density functional theory (DFT) simulations can provide insight into this
order, but, are limited by the computational effort needed to simulate the
thousands of required atoms. To relieve this issue, we use the novel multi-site
support function (MSSF) method within DFT to reduce the solution time for the
electronic groundstate whilst preserving high accuracy. Using MSSFs, we
simulate thin PTO films on STO substrates with system sizes $>2000$ atoms. In
the ultrathin limit, the polar wave texture with cylindrical chiral bubbles
emerges as an intermediate phase between full flux closure domains and in-plane
polarization. This is driven by an internal bias field born of the
compositionally broken inversion symmetry in the [001] direction. Since the
exact nature of this bias field depends sensitively on the film boundary
conditions, this informs a new principle of design for manipulating chiral
order on the nanoscale through the careful choice of substrate, surface
termination or use of overlayers. Antiferrodistortive (AFD) order locally
interacts with these polar textures giving rise to strong FE/AFD coupling at
the PbO terminated surface driving a $p(2 \times \Lambda)$ surface
reconstruction. This offers another pathway for the local control of
ferroelectricity.


  We study machine learning formulations of inductive program synthesis; given
input-output examples, we try to synthesize source code that maps inputs to
corresponding outputs. Our aims are to develop new machine learning approaches
based on neural networks and graphical models, and to understand the
capabilities of machine learning techniques relative to traditional
alternatives, such as those based on constraint solving from the programming
languages community.
  Our key contribution is the proposal of TerpreT, a domain-specific language
for expressing program synthesis problems. TerpreT is similar to a
probabilistic programming language: a model is composed of a specification of a
program representation (declarations of random variables) and an interpreter
describing how programs map inputs to outputs (a model connecting unknowns to
observations). The inference task is to observe a set of input-output examples
and infer the underlying program. TerpreT has two main benefits. First, it
enables rapid exploration of a range of domains, program representations, and
interpreter models. Second, it separates the model specification from the
inference algorithm, allowing like-to-like comparisons between different
approaches to inference. From a single TerpreT specification we automatically
perform inference using four different back-ends. These are based on gradient
descent, linear program (LP) relaxations for graphical models, discrete
satisfiability solving, and the Sketch program synthesis system.
  We illustrate the value of TerpreT by developing several interpreter models
and performing an empirical comparison between alternative inference
algorithms. Our key empirical finding is that constraint solvers dominate the
gradient descent and LP-based formulations. We conclude with suggestions for
the machine learning community to make progress on program synthesis.


  With the recent advances in the development of devices capable of performing
quantum computations, a growing interest in finding near-term applications has
emerged in many areas of science. In the era of non-fault tolerant quantum
devices, algorithms that only require comparably short circuits accompanied by
high repetition rates are considered to be a promising approach for assisting
classical machines with finding solution on computationally hard problems. The
ADAPT approach previously introduced in Nat. Commun. 10, 3007 (2019) extends
the class of variational quantum eigensolver (VQE) algorithms with dynamically
growing ans\"atze in order to find approximations to ground and excited state
energies of molecules. In this work, the ADAPT algorithm has been combined with
a first-quantized formulation for the hydrogen molecule in the Born-Oppenheimer
approximation, employing the explicitly correlated basis functions introduced
in J. Chem. Phys. 43, 2429 (1965). By the virtue of their explicit electronic
correlation properties, it is shown in classically performed simulations that
relatively short circuits yield chemical accuracy ($< 1.6$ mHa) for ground and
excited state potential curves that can compete with second quantized
approaches such as Unitary Coupled Cluster.


  Topological Data Analysis (TDA) allows us to extract powerful topological and
higher-order information on the global shape of a data set or point cloud.
Tools like Persistent Homology or the Euler Transform give a single complex
description of the global structure of the point cloud. However, common machine
learning applications like classification require point-level information and
features to be available. In this paper, we bridge this gap and propose a novel
method to extract node-level topological features from complex point clouds
using discrete variants of concepts from algebraic topology and differential
geometry. We verify the effectiveness of these topological point features
(TOPF) on both synthetic and real-world data and study their robustness under
noise.


  In this paper, the starting point of our analysis is \ a coupled system of
linear elasticity and Stokes equation. We consider two small parameters: the
thickness $h$ of the thin plate and the pore scale $\varepsilon(h)$ which
depends on $h$. We will focus specifically on the case when the pore size is
comparatively small relative to the thickness of the plate. The main goal here
is derive a model of a poroelastic plate, starting from the $3D$ problem as $h$
goes to zero, using simultaneous homogenization and dimension reduction
techniques. The obtained model generalizes the poroelastic plate model derived
by A. Mikeli\'c et. al. in 2015 using dimension reduction techniques from $3D$
Biot's equations in the sense that it also covers the case of contacts of
poroelastic and (poro)elastic plate as well as the evolution equation with
inertial term.


  Large deviations of conservative interacting particle systems, such as the
zero range process, about their hydrodynamic limit and their respective rate
functions lead to the analysis of the skeleton equation; a degenerate
parabolic-hyperbolic PDE with irregular drift. We develop a robust
well-posedness theory for such PDEs in energy-critical spaces based on concepts
of renormalized solutions and the equation's kinetic form. We establish these
properties by proving that renormalized solutions are equivalent to classical
weak solutions, extending concepts of [DiPerna, Lions; Ann. Math., 1989],
[Ambrosio; Invent. Math., 2004] to the nonlinear setting.
  The relevance of the results toward large deviations in interacting particle
systems is demonstrated by applications to the identification of l.s.c.
envelopes of restricted rate functions, to zero noise large deviations for
conservative (singular) SPDE, and to the $\Gamma$-convergence of rate
functions. The first of these solves a long-standing open problem in the large
deviations for zero range processes. The second makes rigorous an informal link
between the non-equilibrium statistical mechanics approaches of macroscopic
fluctuation theory and fluctuating hydrodynamics.


  We discuss the phase structure of QCD for $N_f=2$ and $N_f=2+1$ dynamical
quark flavours at finite temperature and baryon chemical potential. It emerges
dynamically from the underlying fundamental interactions between quarks and
gluons in our work. To this end, starting from the perturbative high-energy
regime, we systematically integrate-out quantum fluctuations towards low
energies by using the functional renormalisation group. By dynamically
hadronising the dominant interaction channels responsible for the formation of
light mesons and quark condensates, we are able to extract the phase diagram
for $\mu_B/T \lesssim 6$. We find a critical endpoint at
$(T_\text{CEP},{\mu_B}_{\text{CEP}})=(107, 635)\,\text{MeV}$. The curvature of
the phase boundary at small chemical potential is $\kappa=0.0142(2)$, computed
from the renormalised light chiral condensate $\Delta_{l,R}$. Furthermore, we
find indications for an inhomogeneous regime in the vicinity and above the
chiral transition for $\mu_B\gtrsim 417$ MeV. Where applicable, our results are
in very good agreement with the most recent lattice results. We also compare to
results from other functional methods and phenomenological freeze-out data.
This indicates that a consistent picture of the phase structure at finite
baryon chemical potential is beginning to emerge. The systematic uncertainty of
our results grows large in the density regime around the critical endpoint and
we discuss necessary improvements of our current approximation towards a
quantitatively precise determination of QCD phase diagram.


  Electromagnetic interactions of protons and alpha particles are modeled in a
form that is suitable for Monte Carlo simulation of the transport of charged
particles. The differential cross section (DCS) for elastic collisions with
neutral atoms is expressed as the product of the DCS for collisions with the
bare nucleus and a correction factor that accounts for the screening of the
nuclear charge by the atomic electrons. The screening factor is obtained as the
ratio of the DCS for scattering of the projectile by an atom with a point
nucleus and the parameterized Dirac-Hartree-Fock-Slater (DHFS) electron
density, calculated from the eikonal approximation, and the Rutherford DCS for
collisions with the bare point nucleus. Inelastic collisions, which cause
electronic excitations of the material, are described by means of the
plane-wave Born approximation, with an empirical simple model of the
generalized oscillator strength (GOS) that combines several extended
oscillators with resonance energies and strengths determined from the atomic
configurations and from the empirical mean excitation energy of the material.
The contributions from inner subshells are renormalized to agree with realistic
ionization cross sections calculated numerically from the DHFS self-consistent
model of atoms by means of the plane-wave Born approximation. The resulting DCS
allows analytical random sampling of individual hard inelastic interactions.


  We construct the moduli space of Spin(7)-instantons on a hermitian complex
vector bundle over a closed 8-dimensional manifold endowed with a (possibly
non-integrable) Spin(7)-structure. We find suitable perturbations that achieve
regularity of the moduli space, so that it is smooth and of the expected
dimension over the irreducible locus.


  Two main results are presented: 1) a new class of applied problems that lead
to equations with $(p,q)$-Laplace is presented; 2) a method for solving
nonlinear boundary value problems involving $(p,q)$-Laplace with measurable
unbounded coefficients is introduced. In the main result, the existence,
uniqueness, and stability of the nonnegative weak solution to the equations of
the form
  $$
  -{\rm div}(\rho|\nabla u|^{q-2} \nabla u)-{\rm div}(|\nabla u|^{p-2}\nabla
u)=\lambda b |u|^{q-2}u,~~p>q
  $$
  are proven. Additionally, an explicit formula that expresses the solution of
the equation through the inverse optimal solution of the spectral problem
  $$-{\rm div}(\rho|\nabla \phi|^{q-2}\nabla \phi)=\lambda b|\phi|^{q-2}\phi$$
  is presented. The advantage of the method is that the inverse optimal problem
has a visible geometry and a simple variational structure, which makes it easy
to solve it and, as a consequence, find a solution to the associated nonlinear
boundary value problem.


  In this article, we study the Higgs vector bundles $(E,\theta)$ over a
compact Calabi-Yau manifolds $X$. We use Yang-Mills-Higgs flow to prove that if
a semistable Higgs bundle with vanishing Chern classes over a compact connected
Calabi-Yau manifold, then the Higgs field $\theta$ is trivial. In particular,
the vector bundle $E$ must be semistable.


  In this paper, we present the performance analysis of asymmetric dual-hop
RF/FSO system with multiple relays. The RF channels follow the correlated
Rayleigh fading while the optical links are subject to the Gamma-Gamma fading.
To select the candidate relay to forward the communication, we assume Partial
Relay Selection (PRS) with outdated Channel State Information (CSI). Unlike the
vast majority of work in this area, we introduce the impairments to the relays
and the destination. We will propose three impairment models called Soft
Envelope Limiter (SEL), Traveling Wave Tube Amplifier (TWTA) and IQ Imbalance
in order to compare the resilience of our system with the RF one against the
hardware impairments. Closed-from of the outage probability (OP) is derived in
terms of Meijer's G function as well as the upper bound of the ergodic capacity
(EC). The Bit Error Rate (BER) and the exact EC are evaluated numerically.
Finally, analytical and numerical results are presented and validated by Monte
Carlo simulation.


  In this work, Rydberg energy levels of the triatomic hydrogen molecule
($\rm{H_3}$) are studied with multichannel quantum-defect theory. We extract
the body-frame p-wave quantum defects from highly accurate \emph{ab initio}
electronic potential surfaces and calculate the quantum defects of higher
momentum states by using the long-range multipole potential model. To obtain
laboratory-frame quantum defects, we perform a rovibrational-frame
transformation with accurate rovibrational states of $\rm{H_3^+}$. Finally, we
use the laboratory-frame quantum defects to calculate Rydberg energy levels for
the fundamental neutral triatomic molecule $\rm{H_3}$.


  Let R and S be two irreducible root systems spanning the same vector space
and having the same Weyl group W, such that S (but not necessarily R) is
reduced. For each such pair (R,S) we construct a family of W-invariant
orthogonal polynomials in several variables, whose coefficients are rational
functions of parameters $q,t_1,t_2,...,t_r$, where r (=1,2 or 3) is the number
of W-orbits in R. For particular values of these parameters, these polynomials
give the values of zonal spherical functions on real and p-adic symmetric
spaces. Also when R=S is of type $A_n$, they conincide with the symmetric
polynomials described in I. G. Macdonald, Symmetric Functions and Hall
Polynomials, 2nd edition, Oxford University Press (1995), Chapter VI.


  The Hard X-ray Modulation Telescope (HXMT) is a Chinese space telescope
mission. It is scheduled for launch in 2015. The telescope will perform an
all-sky survey in hard X-ray band (1 - 250 keV), a series of deep imaging
observations of small sky regions as well as pointed observations. In this work
we present a conceptual method to reconstruct light curves from HXMT imaging
observation directly, in order to monitor time-varying objects such as GRB, AXP
and SGR in hard X-ray band with HXMT imaging observations.


  We present criteria for the Cohen-Macaulayness of a monomial ideal in terms
of its primary decomposition. These criteria allow us to use tools of graph
theory and of linear programming to study the Cohen-Macaulayness of monomial
ideals which are intersections of prime ideal powers. We can characterize the
Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a
Stanley-Reisner ideal in terms of the simplicial complex. These
characterizations show that the simplicial complex must be very compact if some
symbolic power is Cohen-Macaulay. In particular, all symbolic powers are
Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We
also prove that the Cohen-Macaulayness can pass from a symbolic power to
another symbolic powers in different ways.


  In this paper we investigate a natural extension of the Standard Model that
involves varying coupling constants. This is a general expectation in any
fundamental theory such as string theory, and there are good reasons for why
new physics could appear at reachable energy scales. We investigate the
collider phenomenology of models with varying gauge couplings where the
variations are associated with real singlet scalar fields. We introduce three
different heavy scalar fields that are responsible for the variations of the
three gauge couplings of the Standard Model. This gives rise to many
interesting collider signatures that we explore, resulting in exclusion limits
based on the most recent LHC data, and predictions of the future discovery
potential at the high-luminosity LHC.


  Recent advancements in language and vision assistants have showcased
impressive capabilities but suffer from a lack of transparency, limiting
broader research and reproducibility. While open-source models handle general
image tasks effectively, they face challenges with the high computational
demands of complex visually-situated text understanding. Such tasks often
require increased token inputs and large vision modules to harness
high-resolution information. Striking a balance between model size and data
importance remains an open question. This study aims to redefine the design of
vision-language models by identifying key components and creating efficient
models with constrained inference costs. By strategically formulating datasets,
optimizing vision modules, and enhancing supervision techniques, we achieve
significant improvements in inference throughput while maintaining high
performance. Extensive experiments across models ranging from 160M to 13B
parameters offer insights into model optimization. We will fully open-source
our codebase, models, and datasets at https://github.com/naver-ai/elva .


  Projection Over Convex Sets (POCS) is one of the most widely used algorithms
in geophysical data processing to interpolate seismic data. Whilst usually
described as a modification of the Gerchberg-Saxton algorithm, a formal
understanding of the underlying objective function and its implication for the
associated optimization process is lacking to date in the literature. We show
that the POCS algorithm can be interpreted as the application of the
Half-Quadratic Splitting (HQS) method to the $L_0$ norm of the projected sought
after data (where the projection can be any orthonormal transformation),
constrained on the available traces. Similarly, the popular, apparently
heuristic strategy of using a decaying threshold in POCS is revealed to be the
result of the continuation strategy that HQS must employ to converge to a
solution of the minimizer. Finally, we prove that for off-the-grid receivers,
the POCS algorithms must operate in an inner-outer fashion (i.e., an inverse
problem is solved at each outer iteration). In light of our new theoretical
understanding, we suggest the use of a modern solver such as the Chambolle-Pock
Primal-Dual algorithm and show that this can lead to a new POCS-like method
with superior interpolation capabilities at nearly the same computational cost
of the industry-standard POCS method.


  The NA60 experiment at the CERN SPS has studied low-mass dimuon production in
158A GeV In-In collisions. A significant excess of pairs is observed above the
yield expected from neutral meson decays, consistent with a dominant
contribution from $\pi\pi\to\rho\to\mu\mu$. This paper presents precision
results on the mass and transverse momentum spectra of the excess pairs. The
space-time averaged rho spectral function associated to the measured mass
distribution shows a significant broadening, but essentially no mass shift. The
slope parameter $T_{eff}$ extracted from the spectra rises with dimuon mass up
to the $\rho$, followed by a sudden decline above. While the initial rise is
consistent with the expectations for radial flow of a hadronic decay source,
the decline indicates a transition to an emission source with much smaller
flow, possibly of partonic origin.


  We develop a new method for analyzing moduli problems related to the stack of
pure coherent sheaves on a polarized family of projective schemes. It is an
infinite-dimensional analogue of geometric invariant theory. We apply this to
two familiar moduli problems: the stack of $\Lambda$-modules and the stack of
pairs. In both examples, we construct a $\Theta$-stratification of the stack,
defined in terms of a polynomial numerical invariant, and we construct good
moduli spaces for the open substacks of semistable points. One of the essential
ingredients is the construction of higher dimensional analogues of the affine
Grassmannian for the moduli problems considered.


  The Era of the First Stars is one of the last unknown frontiers for
exploration: a poorly understood billion years missing from our cosmological
timeline. We have now developed several methods for finally filling in the lost
billion years of the history of our Universe: stellar archaeology, detecting
primordial hydrogen using 21 cm cosmological emission, and observing the
earliest galaxies, most recently using the James Webb Space Telescope. This
review will summarise why the first stars and galaxies are unique and worthy of
observation, and the methods employed by the groundbreaking telescopes aiming
to detect them.


  With the burgeoning development in the realm of large language models (LLMs),
the demand for efficient incremental training tailored to specific industries
and domains continues to increase. Currently, the predominantly employed
frameworks lack modular design, it often takes a lot of coding work to
kickstart the training of LLM. To address this, we present "LMTuner", a highly
usable, integrable, and scalable system for training LLMs expeditiously and
with minimal user-input. LMTuner comprises three main modules - the
Interaction, Training, and Inference Modules. We advocate that LMTuner's
usability and integrality alleviate the complexities in training large language
models. Remarkably, even a novice user could commence training large language
models within five minutes. Furthermore, it integrates DeepSpeed frameworks and
supports Efficient Fine-Tuning methodologies like Low Rank Adaptation (LoRA),
Quantized LoRA (QLoRA), etc., enabling the training of language models scaling
from 300M to a whopping 130B parameters using a single server. The LMTuner's
homepage (https://wengsyx.github.io/LMTuner/)and screencast video
(https://youtu.be/nsXmWOmN3rE) are now publicly available.


  The multi-particle states and rotational properties of two-particle bands in
$^{254}$No are investigated by the cranked shell model (CSM) with pairing
correlations treated by a particle-number conserving (PNC) method. For the
first time, the rotational bands on top of two-particle $K^{\pi}=3^+,8^-$ and
$10^+$ states and the pairing reduction are studied theoretically in
$^{254}$No. The experimental excitation energies and moments of inertia for the
multi-particle state are reproduced well by the calculation. Better agreement
with the data are achieved by including the high-order deformation
$\varepsilon_{6}$ which leads to enlarged $Z=100$ and $N=152$ deformed shell
gaps. The rise of the $J^{(1)}$ in these two-particle bands compared with the
ground-state band is attributed to the pairing reduction due to the Pauli
blocking effects.


  Gaussian processes are valuable tools for non-parametric modelling, where
typically an assumption of stationarity is employed. While removing this
assumption can improve prediction, fitting such models is challenging. In this
work, hierarchical models are constructed based on Gaussian Markov random
fields with stochastic spatially varying parameters. Importantly, this allows
for non-stationarity while also addressing the computational burden through a
sparse banded representation of the precision matrix. In this setting,
efficient Markov chain Monte Carlo (MCMC) sampling is challenging due to the
strong coupling a posteriori of the parameters and hyperparameters. We develop
and compare three adaptive MCMC schemes and make use of banded matrix
operations for faster inference. Furthermore, a novel extension to
multi-dimensional settings is proposed through an additive structure that
retains the flexibility and scalability of the model, while also inheriting
interpretability from the additive approach. A thorough assessment of the
efficiency and accuracy of the methods in nonstationary settings is presented
for both simulated experiments and a computer emulation problem.


  In the light of the COVID-19 pandemic, deep learning methods have been widely
investigated in detecting COVID-19 from chest X-rays. However, a more pragmatic
approach to applying AI methods to a medical diagnosis is designing a framework
that facilitates human-machine interaction and expert decision making. Studies
have shown that categorization can play an essential rule in accelerating
real-world decision making. Inspired by descriptive document clustering, we
propose a domain-independent explanatory clustering framework to group
contextually related instances and support radiologists' decision making. While
most descriptive clustering approaches employ domain-specific characteristics
to form meaningful clusters, we focus on model-level explanation as a more
general-purpose element of every learning process to achieve cluster
homogeneity. We employ DeepSHAP to generate homogeneous clusters in terms of
disease severity and describe the clusters using favorable and unfavorable
saliency maps, which visualize the class discriminating regions of an image.
These human-interpretable maps complement radiologist knowledge to investigate
the whole cluster at once. Besides, as part of this study, we evaluate a model
based on VGG-19, which can identify COVID and pneumonia cases with a positive
predictive value of 95% and 97%, respectively, comparable to the recent
explainable approaches for COVID diagnosis.


  We consider a population evolving under mutation and selection. The genotype
of an individual is a word of length $\ell$ over a finite alphabet. Mutations
occur during reproduction, independently on each locus; the fitness depends on
the Hamming class (the distance to a reference sequence $w^*$). Evolution is
driven according to the classical Wright--Fisher process. We focus on the
proportion of the different classes under the invariant measure of the process.
We consider the regime where the length of the genotypes $\ell$ goes to
infinity, and both the population size and the inverse of the mutation rate are
of order $\ell$. We prove the existence of a critical curve, which depends both
on the population size and the mutation rate. Below the critical curve, the
proportion of any fixed class converges to $0$, whereas above the curve, it
converges to a positive quantity, for which we give an explicit formula.


  We study the problem of finding the Artin L-functions with the smallest
conductor for a given Galois type. We adapt standard analytic techniques to our
novel situation of fixed Galois type and get much improved lower bounds on the
smallest conductor. For small Galois types we use complete tables of number
fields to determine the actual smallest conductor.


  We consider theoretically the electron--electron interaction induced
exchange-correlation effects in the lowest subband of a quasi-one-dimensional
GaAs quantum wire structures. We calculate, within the leading order dynamical
screening approximation ({\em i.e.} the so-called $GW$ approximation of the
electron gas theory), the electron self-energy, spectral function, momentum
distribution function, inelastic scattering rate, band gap renormalization,
and, the many-body renormalization factor both at zero and finite temperatures,
and, both with and without impurity scattering effects. We also calculate the
effects of finite temperatures and finite impurity scattering on the many-body
properties. We propose the possibility of a hot-electron transistor device with
a large negative differential resistance which is based on the sudden onset of
plasmon emission by energetic ballistic electrons in one dimension. The issue
of the existence or non-existence of the Fermi surface among the interacting
one-dimensional quantum wire electrons is critically discussed based on our
numerical results.