  Relativistic shocks accelerate particles by the first order Fermi mechanism.
These particles then emit synchrotron emission in the post shock gas. We have
developed a numerical code which integrates the relativistic Euler equations
for fluid dynamics with a general equation of state, together with the
Liouville equation for the accelerated particles. We present tests of this code
and, in addition, we use it to study the gamma ray burst afterglow predicted by
the fireball model, along with the hydrodynamics of a relativistic blastwave.
  We find that, while, broadly speaking, the behaviour of the emission is
similar to that already predicted with semi-analytic approaches, the detailed
behaviour is somewhat different. The ``breaks'' in the synchrotron spectrum
behave differently with time, and the spectrum above the final break is harder
than previously expected. These effects are due to the incorporation of the
geometry of the (spherical) blastwave, along with relativistic beaming and
adiabatic cooling of the energetic particles leading to a mix, in the observed
spectrum, between recently injected "uncooled" particles and the older "cooled"
population in different parts of the evolving, inhomogeneous flow.


  It is shown that by realizing the project of intensive $\gamma $ beams with
large energy (project PLC) an essential flux of light Goldstone particles
(axions, arions, familons, majorons) will be generated. The light higgs can be
observed via interaction with matter. The probability of light higgs - electron
production by absorption of several laser photons simultaneously is calculated.


  In this note, we prove that the $\pd$- and $\barpd$-operators introduced by
Gualtieri for a generalized complex structure coincide with the $\bdees$- and
$\bdel$-operators introduced by Alekseev-Xu for Evens-Lu-Weinstein modules of a
Lie bialgebroid.


  Simulating sample correlation matrices is important in many areas of
statistics. Approaches such as generating Gaussian data and finding their
sample correlation matrix or generating random uniform $[-1,1]$ deviates as
pairwise correlations both have drawbacks. We develop an algorithm for adding
noise, in a highly controlled manner, to general correlation matrices. In many
instances, our method yields results which are superior to those obtained by
simply simulating Gaussian data. Moreover, we demonstrate how our general
algorithm can be tailored to a number of different correlation models. Using
our results with a few different applications, we show that simulating
correlation matrices can help assess statistical methodology.


  Simple algebraic groups of type $F_4$ defined over a field $k$ are the full
automorphism groups of Albert algebras over $k$. Let $A$ be an Albert algebra
over a field $k$ of arbitrary characteristic. We prove that there is an isotope
$A^{(v)}$ of $A$ such that the group $\text{\bf Aut}(A^{(v)})$ is $R$-trivial,
in the sense of Manin.


  Like (co)homology group theory of formal Hamiltonian vector fields on
symplectic vector spaces, we try studying homology group theory on symplecit
tori introducing the notion of weight.


  We search for the strange pentaquark $\Theta^+$ using kaon interactions in
the material of the Belle detector. No signal is observed in the $p K_S$ final
state, while in the $p K^-$ final state we observe $\sim 1.6 \cdot 10^4$
$\Lambda(1520) \to p K^-$ decays. We set an upper limit on the ratio of
$\Theta^+$ to $\Lambda(1520)$ yields $\sigma(\Theta^+) / \sigma(\Lambda(1520))
< 2%$ at 90% CL assuming that the $\Theta^+$ is narrow. We also report on
searches for strange and charmed pentaquarks in B meson decays. These results
are obtained from a 155$fb^{-1}$ data sample collected with the Belle detector
near the $\Upsilon(4S)$ resonance, at the KEKB asymmetric energy $e^+ e^-$
collider.


  The "no-hair" theorem states that astrophysical black holes are fully
characterised by just two numbers: their mass and spin. The gravitational-wave
emission from a perturbed black-hole consists of a superposition of damped
sinusoids, known as \textit{quasi-normal modes}. Quasi-normal modes are
specified by three integers $(\ell,m,n)$: the $(\ell, m)$ integers describe the
angular properties and $(n)$ specifies the (over)tone. If the no-hair theorem
holds, the frequencies and damping times of quasi-normal modes are determined
uniquely by the mass and spin of the black hole, while phases and amplitudes
depend on the particular perturbation. Current tests of the no-hair theorem,
attempt to identify these modes in a semi-agnostic way, without imposing priors
on the source of the perturbation. This is usually known as \textit{black-hole
spectroscopy}. Applying this framework to GW150914, the measurement of the
first overtone led to the confirmation of the theorem to $20\%$ level. We show,
however, that such semi-agnostic tests cannot provide strong evidence in favour
of the no-hair theorem, even for extremely loud signals, given the increasing
number of overtones (and free parameters) needed to fit the data. This can be
solved by imposing prior assumptions on the origin of the perturbed black hole
that can further constrain the explored parameters: in particular, our
knowledge that the ringdown is sourced by a binary black hole merger. Applying
this strategy to GW150914 we find a natural log Bayes factor of $\sim 6.5$ in
favour of the Kerr nature of its remnant, indicating that the hairy object
hypothesis is disfavoured with $<1:600$ with respect to the Kerr black-hole
one.


  With years of Kepler data currently available, it can now be attempted to
measure variations in planetary transit depths over time. To do so, it is of
primary importance to understand which systematic effects may affect the
measurement of transits. We aim to measure the stability of Kepler measurements
over years of observations. We present a study of the depth of about 500
transit events of the Hot Jupiter HAT-P-7b, using 14 quarters (Q0-Q13) of data
from the Kepler Satellite. We find a systematic variation in the depth of the
primary transit, related to quarters of data and recurring yearly. These
seasonal variations are about 1%. Within seasons, we find no evidence for
trends. We speculate that the cause of the seasonal variations could be unknown
field crowding or instrumental artifacts. Our results show that care must be
taken when combining transits throughout different quarters of Kepler data.
Measuring the relative planetary radius of HAT-P-7b without taking these
systematic effects into account leads to unrealistically low error estimates.
This effect could be present in all Kepler targets. If so, relative radius
measurements of all Hot Jupiters to a precision much better than 1% are
unrealistic.


  We present the results of an X-ray spectral analysis of 153 galaxy clusters
observed with the Chandra, XMM-Newton, and Suzaku space telescopes. These
clusters, which span 0 < z < 1.5, were drawn from a larger, mass-selected
sample of galaxy clusters discovered in the 2500 square degree South Pole
Telescope Sunyaev Zel'dovich (SPT-SZ) survey. With a total combined exposure
time of 9.1 Ms, these data yield the strongest constraints to date on the
evolution of the metal content of the intracluster medium (ICM). We find no
evidence for strong evolution in the global (r<R500) ICM metallicity (dZ/dz =
-0.06 +/- 0.04 Zsun), with a mean value at z=0.6 of <Z> = 0.23 +/- 0.01 Zsun
and a scatter of 0.08 +/- 0.01 Zsun. These results imply that >60% of the
metals in the ICM were already in place at z=1 (at 95% confidence), consistent
with the picture of an early (z>1) enrichment. We find, in agreement with
previous works, a significantly higher mean value for the metallicity in the
centers of cool core clusters versus non-cool core clusters. We find weak
evidence for evolution in the central metallicity of cool core clusters (dZ/dz
= -0.21 +/- 0.11 Zsun), which is sufficient to account for this enhanced
central metallicity over the past ~10 Gyr. We find no evidence for metallicity
evolution outside of the core (dZ/dz = -0.03 +/- 0.06 Zsun), and no significant
difference in the core-excised metallicity between cool core and non-cool core
clusters. This suggests that strong radio-mode AGN feedback does not
significantly alter the distribution of metals at r>0.15R500. Given the
limitations of current-generation X-ray telescopes in constraining the ICM
metallicity at z>1, significant improvements on this work will likely require
next-generation X-ray missions.


  $^{13}$CO(J=2--1) and C$^{18}$O(J=2--1) observations of the molecular cloud
G285.90+4.53 (Cloud~16) in the Carina Flare supershell (GSH287+04-17) with the
APEX telescope are presented. With an algorithm DENDROFIND we identify 51
fragments and compute their sizes and masses. We discuss their mass spectrum
and interpret it as being the result of the shell fragmentation process
described by the pressure assisted gravitational instability - PAGI. We
conclude that the explanation of the clump mass function needs a combination of
gravity with pressure external to the shell.


  The propagation of gamma-rays over cosmological distances is the subject of
extensive theoretical and observational research at GeV and TeV energies. The
mean free path of gamma-rays in the cosmic web is limited above 100 GeV due to
the production of electrons and positrons on the cosmic optical and infrared
backgrounds. Electrons and positrons cool in the intergalactic medium while
gyrating in its magnetic fields, which could cause either its global heating or
the production of lower-energy secondary gamma-rays. The energy distribution of
gamma-rays surviving the cosmological journey carries observed absorption
features that gauge the emissivity of baryonic matter over cosmic time,
constrain the distance scale of $\Lambda$CDM cosmology, and limit the
alterations of the interaction cross section. Competitive constraints are in
particular placed on the cosmic star-formation history as well as on phenomena
expected from quantum gravity and string theory, such as the coupling to
hypothetical axion-like particles or the violation of Lorentz invariance.
Recent theoretical and observational advances offer a glimpse of the
multi-wavelength and multi-messenger path that the new generation of gamma-ray
observatories is about to open.


  Uncertainty quantification approaches have been more critical in large
language models (LLMs), particularly high-risk applications requiring reliable
outputs. However, traditional methods for uncertainty quantification, such as
probabilistic models and ensemble techniques, face challenges when applied to
the complex and high-dimensional nature of LLM-generated outputs. This study
proposes a novel geometric approach to uncertainty quantification using convex
hull analysis. The proposed method leverages the spatial properties of response
embeddings to measure the dispersion and variability of model outputs. The
prompts are categorized into three types, i.e., `easy', `moderate', and
`confusing', to generate multiple responses using different LLMs at varying
temperature settings. The responses are transformed into high-dimensional
embeddings via a BERT model and subsequently projected into a two-dimensional
space using Principal Component Analysis (PCA). The Density-Based Spatial
Clustering of Applications with Noise (DBSCAN) algorithm is utilized to cluster
the embeddings and compute the convex hull for each selected cluster. The
experimental results indicate that the uncertainty of the model for LLMs
depends on the prompt complexity, the model, and the temperature setting.


  Strong WW scattering at the LHC is discussed as a manifestation of
electroweak symmetry breaking in the absence of a light Higgs boson. The
general framework of the Higgs mechanism -- with or without a Higgs boson -- is
reviewed, and unitarity is shown to fix the scale of strong WW scattering.
Strong WW scattering is also shown to be a possible outcome of five-dimensional
models, which do not employ the usual Higgs mechanism at the TeV scale.
Precision electroweak constraints are briefly discussed. Illustrative LHC
signals are reviewed for models with QCD-like dynamics, stressing the
complementarity of the W^{\pm}Z and like-charge W^+W^+ + W^-W^- channels.


  We review the mechanisms of supersymmetry breaking mediation that occur in
sequestered models, where the visible and the hidden sectors are separated by
an extra dimension and communicate only via gravitational interactions. By
locality, soft breaking terms are forbidden at the classical level and reliably
computable within an effective field theory approach at the quantum level. We
present a self-contained discussion of these radiative gravitational effects
and the resulting pattern of soft masses, and give an overview of realistic
model building based on this set-up. We consider both flat and warped extra
dimensions, as well as the possibility that there be localized kinetic terms
for the gravitational fields.


  We analyse the proof of Bell's inequality and demonstrate that this
inequality is related to one particular model of probability theory, namely
Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical)
statistical correction to Bell's inequality. Such an additional term in the
right hand side of Bell's inequality can be considered as a probability
invariant of a quantum state. This is a measure of nonreproducibility of hidden
variables in different runs of experiments. Experiments to verify Bell's
inequality can be considered as just experiments to estimate this constant. It
seems that Bell's inequality could not be used as a crucial reason to deny
local realism. We consider deterministic as well as stochastic hidden variables
models.


  Space Division Multiplexing (SMD) is a very attractive technique for
addressing the ever-growing demands in transmission capacity by enabling the
use of a new parameter \textemdash\ space \textemdash\ to increase the number
of channels in multi-mode fibers. One key component to build a spatially
multiplexed-based optical network is a spatial multiplexer and demultiplexer
combining signals from multiple single-mode fibers into as many channels in a
multi-mode fiber. In this article, we report the fabrication and
characterization of a pair of 45-mode spatial multiplexer and demultiplexer
saturating all the modes of a standard 50~$\mu$m core graded-index (OM2)
multi-mode fiber. The multiplexers are based on Multi-Plane Light Conversion
(MPLC), a technique that enables the control of the transverse shape of the
light by multiple reflections on specifically designed phase plates. We show
that by using a separable variable basis of modes, such as Hermite-Gaussian
(HG) modes, we are able to drastically reduce the number of reflections hence
reducing the insertion losses and modal crosstalks. The multiplexers typically
show an average 4~dB insertion loss and -28~dB cross-talk across the C band.
Finally, we emphasize the use of this higher-order modes multiplexer to explore
the propagation properties inside multi-mode fibers and more specifically the
mode group crosstalks as well as the impact of fiber bending.


  Calibrating robots into their workspaces is crucial for manipulation tasks.
Existing calibration techniques often rely on sensors external to the robot
(cameras, laser scanners, etc.) or specialized tools. This reliance complicates
the calibration process and increases the costs and time requirements.
Furthermore, the associated setup and measurement procedures require
significant human intervention, which makes them more challenging to operate.
Using the built-in force-torque sensors, which are nowadays a default component
in collaborative robots, this work proposes a self-calibration framework where
robot-environmental spatial relations are automatically estimated through
compliant exploratory actions by the robot itself. The self-calibration
approach converges, verifies its own accuracy, and terminates upon completion,
autonomously purely through interactive exploration of the environment's
geometries. Extensive experiments validate the effectiveness of our
self-calibration approach in accurately establishing the robot-environment
spatial relationships without the need for additional sensing equipment or any
human intervention.


  It is common for video-on-demand and music streaming services to adopt a user
interface composed of several recommendation lists, i.e. widgets or swipeable
carousels, each generated according to a specific criterion or algorithm (e.g.
most recent, top popular, recommended for you, editors' choice, etc.).
Selecting the appropriate combination of carousel has significant impact on
user satisfaction. A crucial aspect of this user interface is that to measure
the relevance a new carousel for the user it is not sufficient to account
solely for its individual quality. Instead, it should be considered that other
carousels will already be present in the interface. This is not considered by
traditional evaluation protocols for recommenders systems, in which each
carousel is evaluated in isolation, regardless of (i) which other carousels are
displayed to the user and (ii) the relative position of the carousel with
respect to other carousels. Hence, we propose a two-dimensional evaluation
protocol for a carousel setting that will measure the quality of a
recommendation carousel based on how much it improves upon the quality of an
already available set of carousels. Our evaluation protocol takes into account
also the position bias, i.e. users do not explore the carousels sequentially,
but rather concentrate on the top-left corner of the screen.
  We report experiments on the movie domain and notice that under a carousel
setting the definition of which criteria has to be preferred to generate a list
of recommended items changes with respect to what is commonly understood.


  Nuclei are unique analyzers for the early stage of the space-time development
of hadronization. DIS at medium energies is especially suitable for this task
being sensitive to hadronization dynamics, since the production length is
comparable with the nuclear size. This was the driving motivation to propose
measurements at HERMES using nuclear targets, and to provide predictions based
on a pQCD model of hadronization [1]. Now when the first results of the
experiment are released [2,3], one can compare the predictions with the data.
The model successfully describes with no adjustment the nuclear effects for
various energies, zh, pT, and Q2, for different flavors and different nuclei.
It turns out that the main source of nuclear suppression of the hadron
production rate is attenuation of colorless pre-hadrons in the medium. An
alternative model [4] is based upon an ad hoc assumption that the colorless
pre-hadron is produced outside the nucleus. This model has apparent problems
attempting to explain certain features of the results from HERMES. A good
understanding of the hadronization dynamics is important for proper
interpretation of the strong suppression of high-pT hadrons observed in heavy
ion collisions at RHIC. We demonstrate that the production length is even
shorter in this case and keeps contracting with rising pT.


  Photon propagator for power-law inflation is considered in the general
covariant gauges within the canonical quantization formalism. Photon mode
functions in covariant gauges are considerably more complicated than their
scalar counterparts, except for the special choice of the gauge-fixing
parameter we call the simple covariant gauge. We explicitly construct the
position space photon propagator in the simple covariant gauge, and find the
result considerably more complicated than its scalar counterpart. This is
because of the need for explicitly inverting the Laplace operator acting on the
scalar propagator, which results in Appell's fourth function. Our propagator
correctly reproduces the de Sitter and flat space limits. We use this
propagator to compute two simple observables: the off-coincident field
strength-field strength correlator and the energy-momentum tensor, both of
which yield consistent results. As a spinoff of our computation we also give
the exact expression for the Coulomb gauge propagator in power-law inflation in
arbitrary dimensions.


  We study the Faraday patterns generated by spin-orbit-coupling induced
parametric resonance in a spinor Bose-Einstein condensate with repulsive
interaction. The collective elementary excitations of the Bose-Einstein
condensate, including density waves and spin waves, are coupled as the result
of the Raman-induced spin-orbit coupling and a quench of the relative phase of
two Raman lasers without the modulation of any of the system's parameters. We
observed several higher parametric resonance tongues at integer multiples of
the driving frequency and investigated the interplay between Faraday
instabilities and modulation instabilities when we quench the
spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to
plane-wave phase. If the detuning is equal to zero, the wave number of
combination resonance barely changes as the strength of spin-orbit coupling
increases. If the detuning is not equal to zero after a quench, a single
combination resonance tongue will split into two parts.


  While there has been remarkable progress in the performance of visual
recognition algorithms, the state-of-the-art models tend to be exceptionally
data-hungry. Large labeled training datasets, expensive and tedious to produce,
are required to optimize millions of parameters in deep network models. Lagging
behind the growth in model capacity, the available datasets are quickly
becoming outdated in terms of size and density. To circumvent this bottleneck,
we propose to amplify human effort through a partially automated labeling
scheme, leveraging deep learning with humans in the loop. Starting from a large
set of candidate images for each category, we iteratively sample a subset, ask
people to label them, classify the others with a trained model, split the set
into positives, negatives, and unlabeled based on the classification
confidence, and then iterate with the unlabeled set. To assess the
effectiveness of this cascading procedure and enable further progress in visual
recognition research, we construct a new image dataset, LSUN. It contains
around one million labeled images for each of 10 scene categories and 20 object
categories. We experiment with training popular convolutional networks and find
that they achieve substantial performance gains when trained on this dataset.


  An associated Nijenhuis tensor of endomorphisms in the tangent bundle is
introduced. Special attention is paid to such tensors for an almost
hypercomplex structure and the metric of Hermitian-Norden type. There are
studied relations between the six associated Nijenhuis tensors as well as their
vanishing. It is given a geometric interpretation of the vanishing of these
tensors as a necessary and sufficient condition for the existence of a unique
connection with totally skew-symmetric torsion tensor. Similar idea is used in
the paper of T. Friedrich and S. Ivanov in Asian J. Math. (2002) for some other
structures. Finally, an example of a 4-dimensional manifold of the considered
type with vanishing associated Nijenhuis tensors is given.


  The block-based coding structure in the hybrid video coding framework
inevitably introduces compression artifacts such as blocking, ringing, etc. To
compensate for those artifacts, extensive filtering techniques were proposed in
the loop of video codecs, which are capable of boosting the subjective and
objective qualities of reconstructed videos. Recently, neural network based
filters were presented with the power of deep learning from a large magnitude
of data. Though the coding efficiency has been improved from traditional
methods in High-Efficiency Video Coding (HEVC), the rich features and
information generated by the compression pipeline has not been fully utilized
in the design of neural networks. Therefore, in this paper, we propose the
Residual-Reconstruction-based Convolutional Neural Network (RRNet) to further
improve the coding efficiency to its full extent, where the compression
features induced from bitstream in form of prediction residual is fed into the
network as an additional input to the reconstructed frame. In essence, the
residual signal can provide valuable information about block partitions and can
aid reconstruction of edge and texture regions in a picture. Thus, more
adaptive parameters can be trained to handle different texture characteristics.
The experimental results show that our proposed RRNet approach presents
significant BD-rate savings compared to HEVC and the state-of-the-art CNN-based
schemes, indicating that residual signal plays a significant role in enhancing
video frame reconstruction.


  Deep Convolutional Neural Network (CNN) is a special type of Neural Networks,
which has shown exemplary performance on several competitions related to
Computer Vision and Image Processing. Some of the exciting application areas of
CNN include Image Classification and Segmentation, Object Detection, Video
Processing, Natural Language Processing, and Speech Recognition. The powerful
learning ability of deep CNN is primarily due to the use of multiple feature
extraction stages that can automatically learn representations from the data.
The availability of a large amount of data and improvement in the hardware
technology has accelerated the research in CNNs, and recently interesting deep
CNN architectures have been reported. Several inspiring ideas to bring
advancements in CNNs have been explored, such as the use of different
activation and loss functions, parameter optimization, regularization, and
architectural innovations. However, the significant improvement in the
representational capacity of the deep CNN is achieved through architectural
innovations. Notably, the ideas of exploiting spatial and channel information,
depth and width of architecture, and multi-path information processing have
gained substantial attention. Similarly, the idea of using a block of layers as
a structural unit is also gaining popularity. This survey thus focuses on the
intrinsic taxonomy present in the recently reported deep CNN architectures and,
consequently, classifies the recent innovations in CNN architectures into seven
different categories. These seven categories are based on spatial exploitation,
depth, multi-path, width, feature-map exploitation, channel boosting, and
attention. Additionally, the elementary understanding of CNN components,
current challenges, and applications of CNN are also provided.


  Machine learning models can greatly improve the search for strong
gravitational lenses in imaging surveys by reducing the amount of human
inspection required. In this work, we test the performance of supervised,
semi-supervised, and unsupervised learning algorithms trained with the ResNetV2
neural network architecture on their ability to efficiently find strong
gravitational lenses in the Deep Lens Survey (DLS). We use galaxy images from
the survey, combined with simulated lensed sources, as labeled data in our
training datasets. We find that models using semi-supervised learning along
with data augmentations (transformations applied to an image during training,
e.g., rotation) and Generative Adversarial Network (GAN) generated images yield
the best performance. They offer 5--10 times better precision across all recall
values compared to supervised algorithms. Applying the best performing models
to the full 20 deg$^2$ DLS survey, we find 3 Grade-A lens candidates within the
top 17 image predictions from the model. This increases to 9 Grade-A and 13
Grade-B candidates when $1$% ($\sim2500$ images) of the model predictions are
visually inspected. This is $\gtrsim10\times$ the sky density of lens
candidates compared to current shallower wide-area surveys (such as the Dark
Energy Survey), indicating a trove of lenses awaiting discovery in upcoming
deeper all-sky surveys. These results suggest that pipelines tasked with
finding strong lens systems can be highly efficient, minimizing human effort.
We additionally report spectroscopic confirmation of the lensing nature of two
Grade-A candidates identified by our model, further validating our methods.


  We derive an explicit simple formula for expectations of all Schur functions
in the real Ginibre ensemble. It is a positive integer for all entries of the
partition even and zero otherwise. The result can be used to determine the
average of any analytic series of elementary symmetric functions by Schur
function expansion.


  Transport based distances, such as the Wasserstein distance and earth mover's
distance, have been shown to be an effective tool in signal and image analysis.
The success of transport based distances is in part due to their Lagrangian
nature which allows it to capture the important variations in many signal
classes. However these distances require the signal to be nonnegative and
normalized. Furthermore, the signals are considered as measures and compared by
redistributing (transporting) them, which does not directly take into account
the signal intensity. Here we study a transport-based distance, called the
$TL^p$ distance, that combines Lagrangian and intensity modelling and is
directly applicable to general, non-positive and multi-channelled signals. The
framework allows the application of existing numerical methods. We give an
overview of the basic properties of this distance and applications to
classification, with multi-channelled, non-positive one and two-dimensional
signals, and color transfer.


  We present a new neural architecture for wide-coverage Natural Language
Understanding in Spoken Dialogue Systems. We develop a hierarchical multi-task
architecture, which delivers a multi-layer representation of sentence meaning
(i.e., Dialogue Acts and Frame-like structures). The architecture is a
hierarchy of self-attention mechanisms and BiLSTM encoders followed by CRF
tagging layers. We describe a variety of experiments, showing that our approach
obtains promising results on a dataset annotated with Dialogue Acts and Frame
Semantics. Moreover, we demonstrate its applicability to a different, publicly
available NLU dataset annotated with domain-specific intents and corresponding
semantic roles, providing overall performance higher than state-of-the-art
tools such as RASA, Dialogflow, LUIS, and Watson. For example, we show an
average 4.45% improvement in entity tagging F-score over Rasa, Dialogflow and
LUIS.


  We show that the basic dynamical rules of quantum physics can be derived from
its static properties and the condition that superluminal communication is
forbidden. More precisely, the fact that the dynamics has to be described by
linear completely positive maps on density matrices is derived from the
following assumptions: (1) physical states are described by rays in a Hilbert
space, (2) probabilities for measurement outcomes at any given time are
calculated according to the usual trace rule, (3) superluminal communication is
excluded. This result also constrains possible non-linear modifications of
quantum physics.


  Particle transport through a duct by Lambertian reflection from duct walls is
again considered. This popular transport example has been solved by most
numerical transport methods except notably one- the method of doubling. We
shall show that the method of doubling provides every bit as, or more, accurate
reflectances and transmittances as the numerical discrete ordinates (NDO) and
analytical discrete ordinates (ADO) methods with less mathematical and
numerical effort.


  For certain classes of negative definite symbols $q(x,\xi)$ and state space
dependent Bernstein function $f(x,s)$ we prove that $-p(x,D)$, the
pseudo-differential operator with symbol $-p(x,\xi)=-f(x,q(x,\xi))$, extends to
the generator of a Feller semigroup. Our result extends previously known
results related to operators of variable (fractional) order of differentiation,
or variable order fractional powers. New concrete examples are given.


  We introduce the notion of fibrewise sectional category via a Whitehead-Ganea
construction. Fibrewise sectional category is the analogue of the ordinary
sectional category in the fibrewise setting and also the natural generalization
of the fibrewise unpointed LS category in the sense of Iwase-Sakai. On the
other hand the fibrewise pointed version is the generalization of the fibrewise
pointed LS category in the sense of James-Morris. After giving their main
properties we also establish some comparisons between such two versions.


  We derive a formula for the index of a Dirac operator on a compact,
even-dimensional incomplete edge space satisfying a "geometric Witt condition".
We accomplish this by cutting off to a smooth manifold with boundary, applying
the Atiyah-Patodi-Singer index theorem, and taking a limit. We deduce
corollaries related to the existence of positive scalar curvature metrics on
incomplete edge spaces.


  The problems of optimizing the value of an arbitrary observable of the
two-level system at both a fixed time and the shortest possible time is
theoretically explored. Complete identification and classification along with
comprehensive analysis of globally optimal control policies and traps (i.e.
policies which are locally but not globally optimal) is presented. The central
question addressed is whether the control landscape remains trap-free if
control constraints of the inequality type are imposed. The answer is
astonishingly controversial, namely, although formally it is always negative,
in practice it is positive provided that the control time is fixed and chosen
long enough.


  We consider a communication scenario where a source communicates with a
destination over a directed layered relay network. Each relay performs analog
network coding where it scales and forwards the signals received at its input.
In this scenario, we address the question: What portion of the maximum
end-to-end achievable rate can be maintained if only a fraction of relay nodes
available at each layer are used?
  We consider, in particular, the Gaussian diamond network (layered network
with a single layer of relay nodes) and a class of symmetric layered networks.
For these networks we show that each relay layer increases the additive gap
between the optimal analog network coding performance with and without network
simplification (using k instead of N relays in each layer, k < N) by no more
than log(N/k)^2 bits and the corresponding multiplicative gap by no more than a
factor of (N/k)^2, asymptotically (in source power). To the best of our
knowledge, this work offers the first characterization of the performance of
network simplification in general layered amplify-and-forward relay networks.
Further, unlike most of the current approximation results that attempt to bound
optimal rates either within an additive gap or a multiplicative gap, our
results suggest a new rate approximation scheme that allows for the
simultaneous computation of additive and multiplicative gaps.


  Given a quadratic CR manifold $\mathcal{M}$ embedded in a complex space, we
study Paley-Wiener-Schwartz theorems for spaces of Schwartz functions and
tempered distributions on $\mathcal{M}$.


  The effects of bond randomness on the ground-state structure, phase diagram
and critical behavior of the square lattice ferromagnetic Blume-Capel (BC)
model are discussed. The calculation of ground states at strong disorder and
large values of the crystal field is carried out by mapping the system onto a
network and we search for a minimum cut by a maximum flow method. In finite
temperatures the system is studied by an efficient two-stage Wang-Landau (WL)
method for several values of the crystal field, including both the first- and
second-order phase transition regimes of the pure model. We attempt to explain
the enhancement of ferromagnetic order and we discuss the critical behavior of
the random-bond model. Our results provide evidence for a strong violation of
universality along the second-order phase transition line of the random-bond
version.


  We investigate the question of the nature of compact stars, considering they
may be neutron stars or hybrid stars containing a quark core, within the
present constraints given by gravitational waves, radio-astronomy, X-ray
emissions from millisecond pulsars and nuclear physics. A Bayesian framework is
used to combine together all these constraints and to predict tidal
deformabilities and radii for a 1.4~M$_\odot$ compact star. We find that
present gravitation wave and radio-astronomy data favors stiff nucleonic EoS
compatible with nuclear physics and that GW170817 waveform is best described
for binary hybrid stars. Binary neutron stars with soft EoS could however not
be totally excluded. In all cases, these %In addition, this data favor stiff
quark matter, independently of the nuclear EoS, with a low value for the
transition density ($n_\mathrm{tr}\in[0.18,0.35]~\mathrm{fm}^{-3}$). Combining
these results with constraints from X-ray observation supports the existence
$1.4$~M$_\odot$ mass hybrid star, with a radius predicted to be about
$R_{1.4}=12.22(45)$~km.


  Large language models (LLMs) have demonstrated remarkable prowess in language
understanding and generation. Advancing from foundation LLMs to
instructionfollowing LLMs, instruction tuning plays a vital role in aligning
LLMs to human preferences. However, the existing LLMs are usually focused on
English, leading to inferior performance in non-English languages. In order to
improve the performance for non-English languages, it is necessary to collect
language-specific training data for foundation LLMs and construct
language-specific instructions for instruction tuning, both of which are heavy
loads. To minimize human workload, we propose to transfer the capabilities of
language generation and instruction following from English to other languages
through an interactive translation task. We have developed BayLing, an
instruction-following LLM by utilizing LLaMA as the foundation LLM and
automatically constructing interactive translation instructions for instructing
tuning. Extensive assessments demonstrate that BayLing achieves comparable
performance to GPT-3.5-turbo, despite utilizing a considerably smaller
parameter size of only 13 billion. Experimental results on translation tasks
show that BayLing achieves 95% of single-turn translation capability compared
to GPT-4 with automatic evaluation and 96% of interactive translation
capability compared to GPT-3.5-turbo with human evaluation. To estimate the
performance on general tasks, we created a multi-turn instruction test set
called BayLing-80. The experimental results on BayLing-80 indicate that BayLing
achieves 89% of performance compared to GPT-3.5-turbo. BayLing also
demonstrates outstanding performance on knowledge assessment of Chinese GaoKao
and English SAT, second only to GPT-3.5-turbo among a multitude of
instruction-following LLMs. Demo, homepage, code and models of BayLing are
available.


  Recent discoveries of gravitational wave (GW) signals from astrophysical
compact binary systems of neutron stars and black holes have firmly established
them as prime sources for advanced GW detectors. Theoretical templates of
expected signals from such systems have been used to filter the detector data
using the \emph{matched filtering} technique. An efficient grid over the
parameter space at a fixed minimal match has a direct impact on improving the
computational efficiency of these searches. We present the construction of
three-dimensional template banks (in component masses and an effective spin
parameter) by incorporating several new optimizations to the hybrid
geometric-random template placement algorithm that we proposed recently. These
optimizations allow us to create more efficient template banks in future
compact binary searches by shrinking the hybrid banks by $\sim 34\%$ in
comparison to the basic algorithm. Such optimized banks are also found to be
$\sim 22\%$ smaller than the optimized stochastic bank constructed over a
nominal range of parameters. We also construct an explicit hybrid template bank
with parameters identical to the `uber-bank' used in the recently-concluded CBC
searches in the second observation run of the Advanced LIGO and Virgo
detectors. We demonstrate a reduction of more than 53,000 templates over the
stochastic template bank at a near-identical coverage as determined by fitting
factor studies. A computationally efficient technique for semi-numerical
calculation of the parameter space metric, applicable for aligned-spin waveform
family, is also outlined. The resulting hybrid template banks can be generated
much faster in comparison to the stochastic banks, and are ready to be used in
the upcoming observation runs of Advanced LIGO and Virgo.


  Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed
point equations with data variables, used for, e.g., verification of modal
mu-calculus formulae for process algebraic specifications with data.
  Solving a PBES is usually done by instantiation to a Parity Game and then
solving the game. Practical game solvers exist, but the instantiation step is
the bottleneck.
  We enhance the instantiation in two steps. First, we transform the PBES to a
Parameterised Parity Game (PPG), a PBES with each equation either conjunctive
or disjunctive. Then we use LTSmin, that offers transition caching, efficient
storage of states and both distributed and symbolic state space generation, for
generating the game graph. To that end we define a language module for LTSmin,
consisting of an encoding of variables with parameters into state vectors, a
grouped transition relation and a dependency matrix to indicate the
dependencies between parts of the state vector and transition groups.
  Benchmarks on some large case studies, show that the method speeds up the
instantiation significantly and decreases memory usage drastically.


  In this paper, we will evaluate the performance of graph neural networks in
two distinct domains: computer vision and reinforcement learning. In the
computer vision section, we seek to learn whether a novel non-redundant
representation for images as graphs can improve performance over trivial pixel
to node mapping on a graph-level prediction graph, specifically image
classification. For the reinforcement learning section, we seek to learn if
explicitly modeling solving a Rubik's cube as a graph problem can improve
performance over a standard model-free technique with no inductive bias.


  While LDPC codes have been demonstrated with desirable error correcting
properties, this has come at a cost of diverging from the geometrical
constraints of many hardware platforms. Viewing codes as the groundspace of a
Hamiltonian, we consider engineering a simulation Hamiltonian reproducing some
relevant features of the code. Techniques from Hamiltonian simulation theory
are used to build a simulation of LDPC codes using only 2D nearest-neighbour
interactions at the cost of an energy penalty polynomial in the system size. We
derive guarantees for the simulation that allows us to approximately reproduce
the ground state of the code Hamiltonian, approximating a $[[N,
\Omega(\sqrt{N}), \Omega(\sqrt{N})]]$ code in 2D. The key ingredient is a new
constructive tool to simulate an $l$-long interaction between two qubits by a
1D chain of $l$ nearest-neighbour interacting qubits using $\mathrm{poly}( l)$
interaction strengths. This is an exponential advantage over the existing
gadgets for this routine which facilitates the first $\epsilon$-simulation of
\emph{arbitrary sparse} Hamiltonian on $n$ qubits with a Hamiltonian on a 2D
lattice of $O(n^2)$ qubits with interaction strengths scaling as
$O\left(\mathrm{poly}(n,1/\epsilon)\right)$.


  We examine charge correlations and instabilities in the pseudogap phase of
high-$T_c$ cuprates modeled by $d$-density wave ordering. The latter has a gap
symmetry similar to the one observed in the $d$-wave superconductor. We use
$t$-$J$ model to describe the charge correlations in the presence of
electron-phonon interaction. Our finding suggest that the charge instability in
the normal state is dominating at an incommensurate wavevector along (1, 1)
instead of (1, 0) for a realistic interaction parameter. The dominance at the
diagonal wavevector is further enhanced if the coupling between electron and
bond-buckling $B_{1g}$ phonon is incorporated. On the other hand, a dominating
charge-density correlation develops along (1, 0) at an incommensurate
wavevector in the $d$-density wave ordered state, which shows a qualitative
agreement with the experiments. The correlation becomes robust only in the
presence of $B_{1g}$ phonon.


  Evaluation benchmarks are the cornerstone of measuring capabilities of large
language models (LLMs), as well as driving progress in said capabilities.
Originally designed to make claims about capabilities (or lack thereof) in
fully pretrained models, evaluation benchmarks are now also extensively used to
decide between various training choices. Despite this widespread usage, we
rarely quantify the variance in our evaluation benchmarks, which dictates
whether differences in performance are meaningful. Here, we define and measure
a range of metrics geared towards measuring variance in evaluation benchmarks,
including seed variance across initialisations, and monotonicity during
training. By studying a large number of models -- both openly available and
pretrained from scratch -- we provide empirical estimates for a variety of
variance metrics, with considerations and recommendations for practitioners. We
also evaluate the utility and tradeoffs of continuous versus discrete
performance measures and explore options for better understanding and reducing
this variance. We find that simple changes, such as framing choice tasks (like
MMLU) as completion tasks, can often reduce variance for smaller scale
($\sim$7B) models, while more involved methods inspired from human testing
literature (such as item analysis and item response theory) struggle to
meaningfully reduce variance. Overall, our work provides insights into variance
in evaluation benchmarks, suggests LM-specific techniques to reduce variance,
and more generally encourages practitioners to carefully factor in variance
when comparing models.


  Compared to the well-studied topic of human mobility in real geographic
space, very few studies focus on human mobility in virtual space, such as
interests, knowledge, ideas, and so forth. However, it relates to the issues of
management of public opinions, knowledge diffusion, and innovation. In this
paper, we assume that the interests of a group of online users can span a
Euclidean space which is called interest space, and the transfers of user
interests can be modeled as the Levy Flight on the interest space. To consider
the interaction between users, we assume that the random walkers are not
independent but interact each other indirectly via the digital resources in the
interest space. The model can successfully reproduce a set of scaling laws for
describing the growth of the attention flow networks of real online
communities, and the ranges of the exponents of the scaling are similar with
the empirical data. Further, we can infer parameters for describing the
individual behaviors of the users according to the scaling laws of the
empirical attention flow network. Our model can not only provide theoretical
understanding on human online behaviors, but also has wide potential
applications, such as dissemination and management of public opinions, online
recommendation, etc.


  Conceptual knowledge is fundamental to human cognition and knowledge bases.
However, existing knowledge probing works only focus on evaluating factual
knowledge of pre-trained language models (PLMs) and ignore conceptual
knowledge. Since conceptual knowledge often appears as implicit commonsense
behind texts, designing probes for conceptual knowledge is hard. Inspired by
knowledge representation schemata, we comprehensively evaluate conceptual
knowledge of PLMs by designing three tasks to probe whether PLMs organize
entities by conceptual similarities, learn conceptual properties, and
conceptualize entities in contexts, respectively. For the tasks, we collect and
annotate 24k data instances covering 393 concepts, which is COPEN, a COnceptual
knowledge Probing bENchmark. Extensive experiments on different sizes and types
of PLMs show that existing PLMs systematically lack conceptual knowledge and
suffer from various spurious correlations. We believe this is a critical
bottleneck for realizing human-like cognition in PLMs. COPEN and our codes are
publicly released at https://github.com/THU-KEG/COPEN.


  This paper addresses the problem of creating simplifiers for logic formulas
based on conditional term rewriting. In particular, the paper focuses on a
program synthesis application where formula simplifications have been shown to
have a significant impact. We show that by combining machine learning
techniques with constraint-based synthesis, it is possible to synthesize a
formula simplifier fully automatically from a corpus of representative
problems, making it possible to create formula simplifiers tailored to specific
problem domains. We demonstrate the benefits of our approach for synthesis
benchmarks from the SyGuS competition and automated grading.


  We calculate all gauge invariant Barr-Zee type contributions to fermionic
electric dipole moments (EDMs) in the two-Higgs doublet models (2HDM) with
softly broken Z2 symmetry. We start by studying the tensor structure of h to
VV' part in the Barr-Zee diagrams, and we calculate the effective couplings in
a gauge invariant way by using the pinch technique. Then we calculate all
Barr-Zee diagrams relevant for electron and neutron EDMs. We make bounds on the
parameter space in type-I, type-II, type-X, and type-Y 2HDMs. The electron and
neutron EDMs are complementary to each other in discrimination of the 2HDMs.
Type-II and type-X 2HDMs are strongly constrained by recent ACME experiment's
result, and future experiments of electron and neutron EDMs may search O(10)
TeV physics.


  A standard tool for classifying the complexity of equivalence relations on
$\omega$ is provided by computable reducibility. This reducibility gives rise
to a rich degree structure. The paper studies equivalence relations, which
induce minimal degrees with respect to computable reducibility. Let $\Gamma$ be
one of the following classes: $\Sigma^0_{\alpha}$, $\Pi^0_{\alpha}$,
$\Sigma^1_n$, or $\Pi^1_n$, where $\alpha \geq 2$ is a computable ordinal and
$n$ is a non-zero natural number. We prove that there are infinitely many
pairwise incomparable minimal equivalence relations that are properly in
$\Gamma$.


  As the rapid development of Intelligent Tutoring Systems (ITS) in the past
decade, tracing the students' knowledge state has become more and more
important in order to provide individualized learning guidance. This is the
main idea of Knowledge Tracing (KT), which models students' mastery of
knowledge concepts (KCs, skills needed to solve a question) based on their past
interactions on platforms. Plenty of KT models have been proposed and have
shown remarkable performance recently. However, the majority of these models
use concepts to index questions, which means the predefined skill tags for each
question are required in advance to indicate the KCs needed to answer that
question correctly. This makes it pretty hard to apply on large-scale online
education platforms where questions are often not well-organized by skill tags.
In this paper, we propose Q-matrix-based Attentive Knowledge Tracing (QAKT), an
end-to-end style model that is able to apply the attentive method to scenes
where no predefined skill tags are available without sacrificing its
performance. With a novel hybrid embedding method based on the q-matrix and
Rasch model, QAKT is capable of modeling problems hierarchically and learning
the q-matrix efficiently based on students' sequences. Meanwhile, the
architecture of QAKT ensures that it is friendly to questions associated with
multiple skills and has outstanding interpretability. After conducting
experiments on a variety of open datasets, we empirically validated that our
model shows similar or even better performance than state-of-the-art KT
methods. Results of further experiments suggest that the q-matrix learned by
QAKT is highly model-agnostic and more information-sufficient than the one
labeled by human experts, which could help with the data mining tasks in
existing ITSs.


  There is a considerable interest in developing algorithms that can predict
audio quality of perceptually coded signals to avoid the cost of extensive
listening tests during development time. While many established algorithms for
predicting the perceived quality of signals with monaural (timbral) distortions
are available (PEAQ, POLQA), predicting the quality degradation of stereo and
multi-channel spatial signals is still considered a challenge. Audio quality
degradation arising from spatial distortions is usually measured in terms of
well known inter-aural cue distortion measures such as Inter-aural Level
Difference Distortions (ILDD), Inter-aural Time Difference Distortions (ITDD)
and Inter-aural Cross Correlation Distortions (IACCD). However, the extent to
which their interaction influences the overall audio quality degradation in
complex signals as expressed - for example - in a multiple stimuli test is not
yet thoroughly studied. We propose a systematic approach that introduces
controlled combinations of spatial distortions on a representative set of
signals and evaluates their influence on overall perceived quality degradation
by analyzing listening test scores over said signals. From this study we derive
guidelines for designing meaningful distortion measures that consider
inter-aural cue distortion interactions.


  An uncertainty relation is introduced for a symmetric arrangement of three
mutually unbiased bases in continuous variable phase space, and then used to
derive a bipartite entanglement criterion based on the variance of global
operators composed of these three phase space variables. We test this criterion
using spatial variables of photon pairs, and show that the entangled photons
are correlated in three pairs of bases.


  The measurement of the missing transverse energy Etmiss is fundamental for
many analyses at LHC. Good Etmiss resolution and calibration are essential for
searches of new physics as well as precise measurements. We describe a refined
reconstruction and calibration of Etmiss developed by ATLAS and its
performances on events containing Z and W bosons. The data sample was collected
in proton-proton collisions at a center-of-mass energy of 7 TeV, and
corresponds to an integrated luminosity of about 36 pb-1. The determination of
the absolute scale of the Etmiss, fundamental for determining systematic
uncertainties in all analysis involving Etmiss measurements, is also presented.


  The paper is devoted to a design of a common bounded feedback control
steering a system of an arbitrary number of linear oscillators to the
equilibrium. At high energies, the control is based on the asymptotic theory of
reachable sets of linear systems. With decreasing of the energy, a similar
control with a reduced upper bound is used. On the final stage, the control is
constructed by using the method of common Lyapunov functions. Special attention
is paid to the cases of one and two oscillators.


  In this paper, we introduce a simple but quite effective recognition
framework dubbed D-PCN, aiming at enhancing feature extracting ability of CNN.
The framework consists of two parallel CNNs, a discriminator and an extra
classifier which takes integrated features from parallel networks and gives
final prediction. The discriminator is core which drives parallel networks to
focus on different regions and learn complementary representations. The
corresponding joint training strategy is introduced which ensures the
utilization of discriminator. We validate D-PCN with several CNN models on two
benchmark datasets: CIFAR-100 and ImageNet32x32, D-PCN enhances all models. In
particular it yields state of the art performance on CIFAR-100 compared with
related works. We also conduct visualization experiment on fine-grained
Stanford Dogs dataset and verify our motivation. Additionally, we apply D-PCN
for segmentation on PASCAL VOC 2012 and also find promotion.


  We present an analytic frequency-domain gravitational waveform model for an
inspiraling binary whose center-of-mass undergoes a small acceleration, assumed
to be constant during the detection, such as when it orbits a distant tertiary
mass. The center-of-mass acceleration along the line of sight is incorporated
as a new parameter that perturbs the standard TaylorF2 model. We calculate the
wave phase to 3rd post-Newtonian order and first order in the acceleration. It
is shown that acceleration most significantly modifies the wave phase in the
low frequency portion of the signal, so ground-based detectors with a good
sensitivity at low frequencies are the most effective at detecting this effect.
We present a Fisher information calculation to quantify the detectability of
this effect at advanced LIGO A Plus, Cosmic Explorer, and Einstein Telescope
over the mass range of neutron stars and stellar-mass black holes, and discuss
degeneracy between acceleration and other parameters. We also determine the
parameter space where the acceleration is large enough that the wave phase
model would have to be extended to nonlinear orders in the acceleration.


  Given a presilting object in a triangulated category, we find necessary and
sufficient conditions for the existence of a complement. This is done both for
classic (pre)silting objects and for large (pre)silting objects. The key
technique is the study of associated co-t-structures. As a consequence of our
techniques we recover some known cases of the existence of complements,
including for derived categories of some hereditary abelian categories and for
silting-discrete algebras. Moreover, we also show that a finite-dimensional
algebra is silting discrete if and only if every bounded large silting complex
is equivalent to a compact one.


  After a short review of recent progresses in 2D Euler equations with random
initial conditions and noise, some of the recent results are improved by
exploiting a priori estimates on the associated infinite dimensional
Fokker-Planck equation. The regularity class of solutions investigated here
does not allow energy- or enstrophy-type estimates, but only bounds in
probability with respect to suitable distributions of the initial conditions.
This is a remarkable application of Fokker-Planck equations in infinite
dimensions. Among the example of random initial conditions we consider Gibbsian
measures based on renormalized kinetic energy.


  We revisit the Thompson sampling algorithm to control an unknown linear
quadratic (LQ) system recently proposed by Ouyang et al (arXiv:1709.04047). The
regret bound of the algorithm was derived under a technical assumption on the
induced norm of the closed loop system. In this technical note, we show that by
making a minor modification in the algorithm (in particular, ensuring that an
episode does not end too soon), this technical assumption on the induced norm
can be replaced by a milder assumption in terms of the spectral radius of the
closed loop system. The modified algorithm has the same Bayesian regret of
$\tilde{\mathcal{O}}(\sqrt{T})$, where $T$ is the time-horizon and the
$\tilde{\mathcal{O}}(\cdot)$ notation hides logarithmic terms in~$T$.


  The XMM-Newton pointing towards the magnetic cataclysmic variable UZ For
finds the source to be a factor > 10^3 fainter than previous EXOSAT and ROSAT
observations. The source was not detected for the majority of a 22 ksec
exposure with the EPIC cameras, suggesting that the accretion rate either
decreased, or stopped altogether. However a 1.1 ksec burst was detected from UZ
For during the observation. Spectral fits favour optically thin, kT = 4.4 keV
thermal emission. Detection of the burst by the on-board Optical Monitor
indicates that this was most probably an accretion event. The 0.1-10 keV
luminosity of 2.1 x 10^30 erg/s is typical for accretion shock emission from
high state polars and would result from the potential energy release of ~ 10^16
g of gas. There is no significant soft excess due to reprocessing in the white
dwarf atmosphere.


  The core concept of quantum simulation is the mapping of an inaccessible
quantum system onto a controllable one by identifying analogous dynamics. We
map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto
a multi-level superconducting Josephson circuit. Resonant drives determine the
particle mass and momentum and the quantum state represents the internal spinor
dynamics, which are cast in the language of multi-level quantum optics. The
degeneracy of the Dirac spectrum corresponds to a degeneracy of bright/dark
states within the system and particle spin and helicity are employed to
interpret the multi-level dynamics. We simulate the Schwinger mechanism of
electron-positron pair production by introducing an analogous electric field as
a doubly degenerate Landau-Zener problem. All proposed measurements can be
performed well within typical decoherence times. This work opens a new avenue
for experimental study of the Dirac equation and provides a tool for control of
complex dynamics in multi-level systems.


  Modern statistical applications involving large data sets have focused
attention on statistical methodologies which are both efficient computationally
and able to deal with the screening of large numbers of different candidate
models. Here we consider computationally efficient variational Bayes approaches
to inference in high-dimensional heteroscedastic linear regression, where both
the mean and variance are described in terms of linear functions of the
predictors and where the number of predictors can be larger than the sample
size. We derive a closed form variational lower bound on the log marginal
likelihood useful for model selection, and propose a novel fast greedy search
algorithm on the model space which makes use of one step optimization updates
to the variational lower bound in the current model for screening large numbers
of candidate predictor variables for inclusion/exclusion in a computationally
thrifty way. We show that the model search strategy we suggest is related to
widely used orthogonal matching pursuit algorithms for model search but yields
a framework for potentially extending these algorithms to more complex models.
The methodology is applied in simulations and in two real examples involving
prediction for food constituents using NIR technology and prediction of disease
progression in diabetes.


  We study the optimal pricing strategies of a monopolist selling a divisible
good (service) to consumers that are embedded in a social network. A key
feature of our model is that consumers experience a (positive) local network
effect. In particular, each consumer's usage level depends directly on the
usage of her neighbors in the social network structure. Thus, the monopolist's
optimal pricing strategy may involve offering discounts to certain agents, who
have a central position in the underlying network.
  First, we consider a setting where the monopolist can offer individualized
prices and derive an explicit characterization of the optimal price for each
consumer as a function of her network position. In particular, we show that it
is optimal for the monopolist to charge each agent a price that is proportional
to her Bonacich centrality in the social network. In the second part of the
paper, we discuss the optimal strategy of a monopolist that can only choose a
single uniform price for the good and derive an algorithm polynomial in the
number of agents to compute such a price. Thirdly, we assume that the
monopolist can offer the good in two prices, full and discounted, and study the
problem of determining which set of consumers should be given the discount. We
show that the problem is NP-hard, however we provide an explicit
characterization of the set of agents that should be offered the discounted
price. Next, we describe an approximation algorithm for finding the optimal set
of agents. We show that if the profit is nonnegative under any feasible price
allocation, the algorithm guarantees at least 88% of the optimal profit.
Finally, we highlight the value of network information by comparing the profits
of a monopolist that does not take into account the network effects when
choosing her pricing policy to those of a monopolist that uses this information
optimally.


  We aim to study the excitation conditions of the molecular gas in the
rotating disk of the Red Rectangle, the only post-Asymptotic-Giant-Branch
object in which the existence of an equatorial rotating disk has been
demonstrated. For this purpose, we developed a complex numerical code that
accurately treats radiative transfer in 2-D, adapted to the study of molecular
lines from rotating disks.
  We present far-infrared Herschel/HIFI observations of the 12CO and 13CO
J=6-5, J=10-9, and J=16-15 transitions in the Red Rectangle. We also present
our code in detail and discuss the accuracy of its predictions, from comparison
with well-tested codes. Theoretical line profiles are compared with the
empirical data to deduce the physical conditions in the disk by means of model
fitting.
  We conclude that our code is very efficient and produces reliable results.
The comparison of the theoretical predictions with our observations reveals
that the temperature of the Red Rectangle disk is typically ~ 100-150 K, about
twice as high as previously deduced from mm-wave observations of lower-J lines.
We discuss the relevance of these new temperature estimates for understanding
the thermodynamics and dynamics of this prototype object, as well as for
interpreting observations of other rarely studied post-AGB disks. Despite our
sophisticated treatment of the line formation, our model cannot explain the
relatively strong line-wing emission for intermediate-J transitions. We argue
that a model including a rotating disk only cannot reproduce these data and
suggest that there is an additional extended (probably bipolar) structure
expanding at about 7--15 km/s.


  We demonstrate the generation of vortex solitons in a model of dissipative
optical media with the singular anti-cubic (AC) nonlinearity, by launching a
vorticity-carrying Gaussian input into the medium modeled by the cubic-quintic
complex Ginzburg-Landau equation with the additional AC term. The effect of the
latter term on the beam propagation is investigated in detail. An analytical
result is produced for the asymptotic form of fundamental and vortical solitons
at r --> 0, which is determined by the AC term. Numerical simulations identify
parameter domains which maintain stable dissipative solitons in the form of
vortex clusters. The number of vortices in the clusters is equal to the
vorticity embedded in the Gaussian input.


  The methods used to prove the main result must be incorrect, as they can be
used to arrive at a contradiction with previously known results. Thus the paper
was withdrawn.


  We present a general analysis of the thermodynamics of spinning black
p-branes of string and M-theory. This is carried out both for the
asymptotically-flat and near-horizon case, with emphasis on the latter. In
particular, we use the conjectured correspondence between the near-horizon
brane solutions and field theories with 16 supercharges in various dimensions
to describe the thermodynamic behavior of these field theories in the presence
of voltages under the R-symmetry. Boundaries of stability are computed for all
spinning branes both in the grand canonical and canonical ensemble, and the
effect of multiple angular momenta is considered. A recently proposed
regularization of the field theory is used to compute the corresponding
boundaries of stability at weak coupling. For the D2, D3, D4, M2 and M5-branes
the critical values of Omega/T in the weak and strong coupling limit are
remarkably close. Finally, we also show that for the spinning D3-brane the tree
level R^4 correction supports the conjecture of a smooth interpolating function
between the free energy at weak and strong coupling.


  We show that Jacobi's bound for the order of a system of ordinary
differential equations stands in the case of a diffiety defined by a
quasi-regular system. We extend the result when there are less equations than
variables and characterize the case when the bound is reached.


  Triply-periodic networks are among the most complex and functionally valuable
self-assembled morphologies, yet they form in nearly every class of biological
and synthetic soft matter building blocks. In contrast to simpler assembly
motifs -- spheres, cylinders, layers -- TPN assemblies require molecules to
occupy variable local domain shapes, confounding attempts to understand their
formation. Here, we examine the double-gyroid (DG) network phase of block
copolymer (BCP) melts, a prototypical soft self-assembly system, by using a
geometric formulation of the strong stretching theory (SST) of BCP melts. The
theory establishes the direct link between molecular BCP packing,
thermodynamics of melt assembly and the {\it medial map}, a generic geometric
measure of the center of complex shapes. We show that "medial packing" is
essential for thermodynamic stability of DG in strongly-segregated melts,
reconciling a long-standing contradiction between infinite- and
finite-segregation theories, corroborating our SST predictions at
finite-segregation via self-consistent field calculations. Additionally, we
find a previously unrecognized non-monotonic dependence of DG stability on the
elastic asymmetry, the comparative entropic stiffness of matrix-forming to
tubular-network forming blocks. The composition window of stable DG --
intermediate to competitor lamellar and columnar phases -- widens both for
large and small elastic asymmetry, seemingly overturning the heuristic view
that packing frustration is localized to the tubular domains. This study
demonstrates utility of geometric optimization of {\it medial tesselations} for
understanding in soft-molecular assembly. As such, the particular medial-based
approach deployed here is readily generalizable to study packing frustration
far beyond the case of DG morphologies in neat BCP assemblies.


  The binary Goldbach conjecture asserts that every even integer greater than
$4$ is the sum of two primes. In a preceding paper we have proved that there
exists a positive integer $K_\alpha$ such that every even integer $x > p_k^2$
can be expressed as the sum of two primes, where $p_k$ is the $k$th prime
number and $k > K_\alpha$. In this paper we provide an estimation for
$K_\alpha$, and from this result it follows that the binary Goldbach conjecture
is true.


  Many problems at the intersection of combinatorics and computer science
require solving for a permutation that optimally matches, ranks, or sorts some
data. These problems usually have a task-specific, often non-differentiable
objective function that data-driven algorithms can use as a learning signal. In
this paper, we propose the Sinkhorn Policy Gradient (SPG) algorithm for
learning policies on permutation matrices. The actor-critic neural network
architecture we introduce for SPG uniquely decouples representation learning of
the state space from the highly-structured action space of permutations with a
temperature-controlled Sinkhorn layer. The Sinkhorn layer produces continuous
relaxations of permutation matrices so that the actor-critic architecture can
be trained end-to-end. Our empirical results show that agents trained with SPG
can perform competitively on sorting, the Euclidean TSP, and matching tasks. We
also observe that SPG is significantly more data efficient at the matching task
than the baseline methods, which indicates that SPG is conducive to learning
representations that are useful for reasoning about permutations.


  We introduce the game INFLUENCE, a scoring combinatorial game, played on a
directed graph where each vertex is either colored black or white. The two
players, Black and White play alternately by taking a vertex of their color and
all its successors (for Black) or all its predecessors (for White). The score
of each player is the number of vertices he has taken.
  We prove that INFLUENCE is a nonzugzwang game, meaning that no player has
interest to pass at any step of the game, and thus belongs to Milnor's
universe. We study this game in the particular class of paths where black and
white are alternated. We give an almost tight strategy for both players when
there is one path. More precisely, we prove that the first player always gets a
strictly better score than the second one, but that the difference between the
score is bounded by 5. Finally, we exhibit some graphs for which the initial
proportion of vertices of the color of a player is as small as possible but
where this player can get almost all the vertices.


  By exploiting the permutation symmetry of Dick states, we derive closed
analytical expressions of Schmidt decompositions for {\it all} possible
bipartitions of a system described by this kind of state. This allows us to
exhaustively compute the entropy of entanglement of the bipartitions and, thus,
compare the their entanglement extent. We also address the multipartite
character of Dicke states by calculating the purity of balanced bipartitions to
determine the potential of multipartite entanglement (the average purity). In
particular, we found that the entanglement of $W$ states remains constant as
the number of qubits is increased. As a final application we define a family of
multipartite entanglement witnesses and compute their resistance against random
and systematic imperfections. It is shown that in some circumstances, for a
fixed white noise fraction, the entanglement becomes detectable only if one
{\it increases} the amount of systematic imperfection in the state.


  We show that one can define a spectral curve for the Cauchy-Riemann operator
on a punctured elliptic curve if one imposes appropriate boundary conditions.
Algebraic curves of the type thus obtained appear as irreducible components of
spectral curves of minimal tori with planar ends in R^3. It appears that these
curves coincide with the spectral curves of certain elliptic KP solitons as
studied by Krichever.


  Proposed space-based gravitational-wave detectors such as BBO and DECIGO can
detect ~10^6 neutron-star binaries and determine luminosity distance to the
binaries with a high precision. Combining the luminosity distance and
electromagnetically-derived redshift, one would be able to probe cosmological
expansion out to high redshift. In this paper, we show that the Hubble
parameter as a function of redshift can be directly measured with monopole and
dipole components of the luminosity distance on the sky. As a result, the
measurement accuracies of the Hubble parameter in each redshift bin up to z=1
are 3-14 %, 1.5-8 %, and 0.8-4% for the observation time 1 yr, 3 yr, and 10 yr,
respectively.


  Continuous high-precision photometry of stars, provided by space missions
such as CoRoT, Kepler, and K2, represents a unique way to study stellar
rotation and magnetism. The coupling of these studies of the surface dynamics
with asteroseismology is changing our view to surface and internal dynamics. In
this proceedings I will provide the latest developments in the understanding of
surface and internal rotation and magnetic fields. I will also discuss the
possible discovery of strong internal magnetic fields of dynamo origin in the
convective cores of stars above 1.2-1.4 solar masses. I will finish by
providing constraints on gyrochronology laws for low-mass stars and put the Sun
into context of its magnetism when compared to other solar-analog stars.


  I briefly describe a simple routine for emission-line profiles fitting by
Gaussian curves or Gauss-Hermite series. The PROFIT (line-PROfile FITting)
routine represent a new alternative for use in fits data cubes, as those from
Integral Field Spectroscopy or Fabry-Perot Interferometry, and may be useful to
better study the emission-line flux distributions and gas kinematics in
distinct astrophysical objects, such as the central regions of galaxies and
star forming regions. The PROFIT routine is written in IDL language and is
available at http://www.ufsm.br/rogemar/software.html.
  The PROFIT routine was used to fit the [Fe II]1.257um emission-line profiles
for about 1800 spectra of the inner 350 pc of the Seyfert galaxy Mrk1066
obtained with Gemini NIFS and shows that the line profiles are better
reproduced by Gauss-Hermite series than by the commonly used Gaussian curves.
The two-dimensional map of the h_3 Gauss-Hermite moment shows its highest
absolute values in regions close to the edge of the radio structure. These high
values may be originated in an biconical outflowing gas associated with the
radio jet - previously observed in the optical [O III] emission. The analysis
of this kinematic component indicates that the radio jet leaves the center of
the galaxy with the north-west side slightly oriented towards us and the
south-east side away from us, being partially hidden by the disc of the galaxy.


  The field-induced ordering transition in the quantum spin system
NiCl$_2$$\cdot$4SC(NH$_2$)$_2$ is studied by means of neutron diffraction, AC
magnetometry and relaxation calorimetry. The interpretation of the data is
strongly influenced by a finite distribution of transition fields in the
samples, which was present but disregarded in previous studies. Taking this
effect into account, we find that the order-parameter critical exponent is
inconsistent with the BEC universality class even at temperatures below 100 mK.
All results are discussed in comparison with previous measurements and with
recent similar studies of disordered
Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$.


  The formation of interstellar water has been commonly accepted to occur on
the surfaces of icy dust grains in dark molecular clouds at low temperatures
(10-20 K), involving hydrogenation reactions of oxygen allotropes. As a result
of the large abundances of molecular hydrogen and atomic oxygen in these
regions, the reaction H2 + O has been proposed to contribute significantly to
the formation of water as well. However, gas phase experiments and
calculations, as well as solid-phase experimental work contradict this
hypothesis. Here, we use precisely executed temperature programmed desorption
(TPD) experiments in an ultra-high vacuum setup combined with kinetic Monte
Carlo simulations to establish an upper limit of the water production starting
from H2 and O. These reactants are brought together in a matrix of CO2 in a
series of (control) experiments at different temperatures and with different
isotopological compositions. The amount of water detected with the quadrupole
mass spectrometer upon TPD is found to originate mainly from contamination in
the chamber itself. However, if water is produced in small quantities on the
surface through H2 + O, this can only be explained by a combined classical and
tunneled reaction mechanism. An absolutely conservative upper limit for the
reaction rate is derived with a microscopic kinetic Monte Carlo model that
converts the upper limit into a maximal possible reaction rate. Incorporating
this rate into simulations run for astrochemically relevant parameters, shows
that the upper limit to the contribution of the reaction H2 + O in OH, and
hence water formation, is 11% in dense interstellar clouds. Our combined
experimental and theoretical results indicate however, that this contribution
is likely to be much lower.


  We construct global generalized solutions to the chemotaxis system
  \begin{align*}
  \begin{cases}
  u_t = \Delta u - \nabla \cdot (u \nabla v) + \lambda(x) u - \mu(x)
u^\kappa,\\
  v_t = \Delta v - v + u
  \end{cases}
  \end{align*} in smooth, bounded domains $\Omega \subset \mathbb R^n$, $n \geq
2$, for certain choices of $\lambda, \mu$ and $\kappa$.
  Here, inter alia, the selections $\mu(x) = |x|^\alpha$ with $\alpha < 2$ and
$\kappa = 2$as well as $\mu \equiv \mu_1 > 0$ and $\kappa >
\min\{\frac{2n-2}{n}, \frac{2n+4}{n+4}\}$ are admissible (in both cases for any
sufficiently smooth $\lambda$).
  While the former case appears to be novel in general, in the two- and
three-dimensional setting, the latter improves on a recent result by Winkler
(Adv. Nonlinear Anal. 9 (2019), no. 1, 526-566), where the condition $\kappa >
\frac{2n+4}{n+4}$ has been imposed. In particular, for $n = 2$, our result
shows that taking any $\kappa > 1$ suffices to exclude the possibility of
collapse into a persistent Dirac distribution.


  Motivated by the LMC's impact on the integral of motion space of the stellar
halo, we run an $N$-body merger simulation to produce a population of halo-like
stars. We subsequently move to a test particle simulation, in which the LMC
perturbs this debris. When an axisymmetric potential is assumed for the final
snapshot of the $N$-body merger remnant, a series of vertical striations in
$(L_z, E)$ space form as the LMC approaches its pericentre. These result from
the formation of overdensities in angular momentum owing to a relationship
between the precession rate of near radial orbits and the torquing of these
orbits by the LMC. This effect is heavily dependent on the shape of the inner
potential. If a quadrupole component of the potential is included these
striations become significantly less apparent due to the difference in
precession rate between the two potentials. The absence of these features in
data, and the dramatic change in orbital plane precession rate, discourages the
use of an axisymmetric potential for highly eccentric orbits accreted from a
massive GSE-like merger. Given the link between appearance of these striations
and the shape of the potential, this effect may provide a new method of
constraining the axisymmetry of the halo.


  Physics-informed Neural Networks (PINNs) is a method for numerical simulation
that incorporates a loss function corresponding to the governing equations into
a neural network. While PINNs have been explored for their utility in inverse
analysis, their application in acoustic analysis remains limited. This study
presents a method to identify loss parameters in acoustic tubes using PINNs. We
categorized the loss parameters into two groups: one dependent on the tube's
diameter and another constant, independent of it. The latter were set as the
trainable parameters of the neural network. The problem of identifying the loss
parameter was formulated as an optimization problem, with the physical
properties being determined through this process. The neural network
architecture employed was based on our previously proposed ResoNet, which is
designed for analyzing acoustic resonance. The efficacy of the proposed method
is assessed through both forward and inverse analysis, specifically through the
identification of loss parameters. The findings demonstrate that it is feasible
to accurately identify parameters that significantly impact the sound field
under analysis. By merely altering the governing equations in the loss
function, this method could be adapted to various sound fields, suggesting its
potential for broad application.


  We show that for a sufficiently big \textit{brick} $B$ of the
$(2n+1)$-dimensional Heisenberg group $H_n$ over the finite field
$\mathbb{F}_p$, the product set $B\cdot B$ contains at least $|B|/p$ many
cosets of some non trivial subgroup of $H_n$.


  Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar
curvature with outermost minimal boundary, converging in the pointed $C^0$
Cheeger--Gromov sense to an asymptotically flat limit space, we show that the
total mass of the limit is bounded above by the liminf of the total masses of
the sequence. In other words, total mass is lower semicontinuous under such
convergence. In order to prove this, we use Huisken's isoperimetric mass
concept, together with a modified weak mean curvature flow argument. We include
a brief discussion of Huisken's work before explaining our extension of that
work. The results are all specific to three dimensions.


  For X = R, C, or H it is well known that cusp cross-sections of finite volume
X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds
modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the
(4n+3)-dimensional quaternionic Heisenberg group N_{4n+3}(H). We give a
necessary and sufficient condition for such manifolds to be diffeomorphic to a
cusp cross-section of an arithmetic X-hyperbolic (n+1)-orbifold. A principal
tool in the proof of this classification theorem is a subgroup separability
result which may be of independent interest.


  Building a new generation of fission reactors in the United States presents
many technical and regulatory challenges. One important challenge is the need
to share and present results from new high-fidelity, high-performance
simulations in an easily usable way. Since modern multiscale, multi-physics
simulations can generate petabytes of data, they will require the development
of new techniques and methods to reduce the data to familiar quantities of
interest (e.g., pin powers, temperatures) with a more reasonable resolution and
size. Furthermore, some of the results from these simulations may be new
quantities for which visualization and analysis techniques are not immediately
available in the community and need to be developed.
  This paper describes a new system for managing high-performance simulation
results in a domain-specific way that naturally exposes quantities of interest
for light water and sodium-cooled fast reactors. It describes requirements to
build such a system and the technical challenges faced in its development at
all levels (simulation, user interface, etc.). An example comparing results
from two different simulation suites for a single assembly in a light-water
reactor is presented, along with a detailed discussion of the system's
requirements and design.


  In this article, we introduce a notion of non-degeneracy, with respect to
certain Newton polyhedra, for rational functions over non-Archimedean locals
fields of arbitrary characteristic. We study the local zeta functions attached
to non-degenerate rational functions, we show the existence of a meromorphic
continuation for these zeta functions, as rational functions of $q^{-s}$, and
give explicit formulas. In contrast with the classical local zeta functions,
the meromorphic continuation of zeta functions for rational functions have
poles with positive and negative real parts.


  We present the results of an extended narrow-band H{\alpha} study of the
massive galaxy cluster XMMU J2235.3-2557 at z = 1.39. This paper represents a
follow up study to our previous investigation of star-formation in the cluster
centre, extending our analysis out to a projected cluster radius of 1.5 Mpc.
Using the Near InfraRed Imager and Spectrograph (NIRI) on Gemini North we
obtained deep H narrow-band imaging corresponding to the rest-frame wavelength
of H{\alpha} at the cluster's redshift. We identify a total of 163 potential
cluster members in both pointings, excluding stars based on their near-IR
colours derived from VLT/HAWK-I imaging. Of these 163 objects 14 are
spectroscopically confirmed cluster members, and 20% are excess line-emitters.
We find no evidence of star formation activity within a radius of 200 kpc of
the brightest cluster galaxy in the cluster core. Dust-corrected star formation
rates (SFR) of excess emitters outside this cluster quenching radius, RQ \sim
200 kpc, are on average <SFR> = 2.7 \pm 1.0 M\odot yr-1, but do not show
evidence of increasing star-formation rates toward the extreme 1.5 Mpc radius
of the cluster. No individual cluster galaxy exceeds an SFR of 6 M\odot yr-1 .
Massive galaxies (log M\ast /M\odot > 10.75) all have low specific SFRs (SSFRs,
i.e. SFR per unit stellar mass). At fixed stellar mass, galaxies in the cluster
centre have lower SSFRs than the rest of the cluster galaxies, which in turn
have lower SSFRs than field galaxies at the same redshift by a factor of a few
to 10. For the first time we can demonstrate through measurements of individual
SFRs that already at very early epochs (at an age of the Universe of \sim4.5
Gyr) the suppression of star-formation is an effect of the cluster environment
which persists at fixed galaxy stellar mass. [Erratum added after the original
paper]


  Gauge theory and thermalization are both foundations of physics and nowadays
are both topics of essential importance for modern quantum science and
technology. Simulating lattice gauge theories (LGTs) realized recently with
ultracold atoms provides a unique opportunity for carrying out a correlated
study of gauge theory and thermalization in the same setting. Theoretical
studies have shown that an Ising quantum phase transition exists in this
implemented LGT, and quantum thermalization can also signal this phase
transition. Nevertheless, it remains an experimental challenge to accurately
determine the critical point and controllably explore the thermalization
dynamics in the quantum critical regime due to the lack of techniques for
locally manipulating and detecting matter and gauge fields. Here, we report an
experimental investigation of the quantum criticality in the LGT from both
equilibrium and non-equilibrium thermalization perspectives by equipping the
single-site addressing and atom-number-resolved detection into our LGT
simulator. We accurately determine the quantum critical point agreed with the
predicted value. We prepare a $|Z_{2}\rangle$ state deterministically and study
its thermalization dynamics across the critical point, leading to the
observation that this $|Z_{2}\rangle$ state thermalizes only in the critical
regime. This result manifests the interplay between quantum many-body scars,
quantum criticality, and symmetry breaking.


  The hippocampus is a crucial brain structure associated with various
psychiatric disorders, and its automatic and precise segmentation is essential
for studying these diseases. In recent years, deep learning-based methods have
made significant progress in hippocampus segmentation. However, training deep
neural network models requires substantial computational resources and time, as
well as a large amount of labeled training data, which is often difficult to
obtain in medical image segmentation. To address this issue, we propose a new
parameter-efficient fine-tuning method called LoRA-PT. This method transfers
the pre-trained UNETR model on the BraTS2021 dataset to the hippocampus
segmentation task. Specifically, the LoRA-PT method categorizes the parameter
matrix of the transformer structure into three sizes, forming three 3D tensors.
Through tensor singular value decomposition, these tensors are decomposed to
generate low-rank tensors with the principal singular values and singular
vectors, while the remaining singular values and vectors form the residual
tensor. During the fine-tuning, we only update the low-rank tensors, i.e. the
principal tensor singular values and vectors, while keeping the residual tensor
unchanged. We validated the proposed method on three public hippocampus
datasets. Experimental results show that LoRA-PT outperforms existing
parameter-efficient fine-tuning methods in segmentation accuracy while
significantly reducing the number of parameter updates. Our code is available
at https://github.com/WangangCheng/LoRA-PT/tree/LoRA-PT.


  We show that the use of momentum-space optical interferometry, which avoids
any spatial overlap between two parts of a macroscopic quantum state, presents
a unique way to study coherence phenomena in polariton condensates. In this
way, we address the longstanding question in quantum mechanics: "\emph{Do two
components of a condensate, which have never seen each other, possess a
definitive phase?}" [P. W. Anderson, \emph{Basic Notions of Condensed Matter
Physics} (Benjamin, 1984)]. A positive answer to this question is
experimentally obtained here for light-matter condensates, created under
precise symmetry conditions, in semiconductor microcavities taking advantage of
the direct relation between the angle of emission and the in-plane momentum of
polaritons.


  For a complex simple Lie algebra of type A_l,B_l,C_l or D_l, given a family
of elements f_\lambda\ in commutative ring Z[\Lambda], we show that f_\lambda\
is just the formal character of the Weyl module V(\lambda) if f_\lambda\
satisfy several natural conditions. Hence we give a necessary and sufficient
condition for constructing a family of g_l-modules from a family of
g_{l-1}-modules.


  We present a new experimental design procedure that divides a set of
experimental units into two groups so that the two groups are balanced on a
prespecified set of covariates and being almost as random as complete
randomization. Under complete randomization, the difference in covariate
balance as measured by the standardized average between treatment and control
will be $O_p(n^{-1/2})$. If the sample size is not too large this may be
material. In this article, we present an algorithm which greedily switches
assignment pairs. Resultant designs produce balance of the much lower order
$O_p(n^{-3})$ for one covariate. However, our algorithm creates assignments
which are, strictly speaking, non-random. We introduce two metrics which
capture departures from randomization: one in the style of entropy and one in
the style of standard error and demonstrate our assignments are nearly as
random as complete randomization in terms of both measures. The results are
extended to more than one covariate, simulations are provided to illustrate the
results and statistical inference under our design is discussed. We provide an
open source R package available on CRAN called GreedyExperimentalDesign which
generates designs according to our algorithm.


  Transition metal dichalcogenides such as MoS$_2$ represent promising
candidates for building blocks of ultra-thin nanophotonic devices. For such
applications, vertically-oriented MoS$_2$ (v-MoS$_2$) nanosheets could be
advantageous as compared to conventional horizontal MoS$_2$ (h-MoS$_2$) given
that their inherent broken symmetry would favor an enhanced nonlinear response.
However, the current lack of a controllable and reproducible fabrication
strategy for v-MoS$_2$ limits the exploration of this potential. Here we
present a systematic study of the growth of v-MoS$_2$ nanosheets based on the
sulfurization of a pre-deposited Mo-metal seed layer. We demonstrate that the
sulfurization process at high temperatures is driven by the diffusion of Sulfur
from the vapor-solid interface to the Mo seed layer. Furthermore, we verify an
enhanced nonlinear response in the resulting v-MoS$_2$ nanostructures as
compared to their horizontal counterparts. Our results represent a stepping
stone towards the fabrication of low-dimensional TMD-based nanostructures for
versatile nonlinear nanophotonic devices.


  Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where
Q is a finite alphabet and Z is a set of entities; they generalise Cellular
Automata and Boolean networks. An update schedule dictates when each entity
updates its state according to its local function fi : Q Z $\rightarrow$ Q. One
major question is to study the behaviour of a given automata networks under
different update schedules. In this paper, we study automata networks that are
invariant under many different update schedules. This gives rise to two
definitions, locally commutative and globally commu-tative networks. We
investigate the relation between commutativity and different forms of locality
of update functions; one main conclusion is that globally commutative networks
have strong dynamical properties, while locally commutative networks are much
less constrained. We also give a complete classification of all globally
commutative Boolean networks.


  Accurate calculation of the phase lags of quasi-periodic oscillations (QPOs)
will provide insight into their origin. In this paper we investigate the phase
lag correction method which has been applied to calculate the intrinsic phase
lags of the QPOs in MAXI J1820+070. We find that the traditional additive model
between BBN and QPOs in the time domain is rejected, but the convolution model
is accepted. By introducing a convolution mechanism in the time domain, the
Fourier cross-spectrum analysis shows that the phase lags between QPOs
components in different energy bands will have a simple linear relationship
with the phase lags between the total signals, so that the intrinsic phase lags
of the QPOs can be obtained by linear correction. The power density spectrum
(PDS) thus requires a multiplicative model to interpret the data. We briefly
discuss a physical scenario for interpreting the convolution. In this scenario,
the corona acts as a low-pass filter, the Green's function containing the noise
is convolved with the QPOs to form the low-frequency part of the PDS, while the
high-frequency part requires an additive component. We use a multiplicative PDS
model to fit the data observed by Insight-HXMT. The overall fitting results are
similar compared to the traditional additive PDS model. Neither the width nor
the centroid frequency of the QPOs obtained from each of the two PDS models
were significantly different, except for the r.m.s. of the QPOs. Our work thus
provides a new perspective on the coupling of noise and QPOs.


  The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in
an $n$-book with the vertices of $G$ on the spine and each edge to the pages
without crossing each other. If the degree of vertices of $G$ at most one in
each page, the $n$-book embedding is $matching$. The $matching~ book~
thickness$ of graph $G$ is the smallest $n$ so that $G$ can be matching
embedded in an $n$-book. In this paper, the matching book thickness of the
biconnected outerplanar graphs is determined.