  Our motion through the Universe generates a dipole in the temperature
anisotropies of the Cosmic Microwave Background (CMB) and also in the angular
distribution of sources. If the cosmological principle is valid, these two
dipoles are directly linked, such that the amplitude of one determines that of
the other. However, it is a longstanding problem that number counts of radio
sources and of quasars at low and intermediate redshifts exhibit a dipole that
is well aligned with that of the CMB but with about twice the expected
amplitude, leading to a tension reaching up to $4.9 \sigma$. In this paper, we
revisit the theoretical derivation of the dipole in the sources number counts,
explicitly accounting for the redshift evolution of the population of sources.
We argue that if the spectral index and magnification bias of the sources vary
with redshift, the standard theoretical description of the dipole may be
inaccurate. We provide an alternative expression which does not depend on the
spectral index, but instead on the time evolution of the population of sources.
We then determine the values that this evolution rate should have in order to
remove the tension with the CMB dipole.


  Q-enhanced racetrack micro-resonators for the silicon nitride photonics
integration platform have been designed, fabricated and characterized. The
proposed geometries permit to mitigate the impact of radiation loss at curved
waveguides, one of the major limitations of silicon nitride circuits, therefore
providing an increase of the intrinsic Q factor of micro-resonators when
compared with the conventional structures with the same bent radii. The schemes
put forward in this work permit a reduction of the size of the devices that has
a direct impact on the integration scale in this platform. When used in the
curved sections of waveguides routing optical signals within an integrated
photonic circuit, these geometries provide a reduction of the radiation loss
and permit the use of smaller bent radii and to increase the circuit
integration density.


  Nowadays the emerging smart grid technology opens up the possibility of
two-way communication between customers and energy utilities. Demand Response
Management (DRM) offers the promise of saving money for commercial customers
and households while helps utilities operate more efficiently. In this paper,
an Incentive-based Demand Response Optimization (IDRO) model is proposed to
efficiently schedule household appliances for minimum usage during peak hours.
The proposed method is a multi-objective optimization technique based on
Nonlinear Auto-Regressive Neural Network (NAR-NN) which considers energy
provided by the utility and rooftop installed photovoltaic (PV) system. The
proposed method is tested and verified using 300 case studies (household). Data
analysis for a period of one year shows a noticeable improvement in power
factor and customers bill.


  Humans recognize anomalies through two aspects: larger patch-wise
representation discrepancies and weaker patch-to-normal-patch correlations.
However, the previous AD methods didn't sufficiently combine the two
complementary aspects to design AD models. To this end, we find that
Transformer can ideally satisfy the two aspects as its great power in the
unified modeling of patch-wise representations and patch-to-patch correlations.
In this paper, we propose a novel AD framework: FOcus-the-Discrepancy (FOD),
which can simultaneously spot the patch-wise, intra- and inter-discrepancies of
anomalies. The major characteristic of our method is that we renovate the
self-attention maps in transformers to Intra-Inter-Correlation (I2Correlation).
The I2Correlation contains a two-branch structure to first explicitly establish
intra- and inter-image correlations, and then fuses the features of two-branch
to spotlight the abnormal patterns. To learn the intra- and inter-correlations
adaptively, we propose the RBF-kernel-based target-correlations as learning
targets for self-supervised learning. Besides, we introduce an entropy
constraint strategy to solve the mode collapse issue in optimization and
further amplify the normal-abnormal distinguishability. Extensive experiments
on three unsupervised real-world AD benchmarks show the superior performance of
our approach. Code will be available at https://github.com/xcyao00/FOD.


  Angle of arrival (AOA) is widely used to locate a wireless signal emitter in
unmanned aerial vehicle (UAV) localization. Compared with received signal
strength (RSS) and time of arrival (TOA), it has higher accuracy and is not
sensitive to time synchronization of the distributed sensors. However, there
are few works focused on three-dimensional (3-D) scenario. Furthermore,
although maximum likelihood estimator (MLE) has a relatively high performance,
its computational complexity is ultra high. It is hard to employ it in
practical applications. This paper proposed two multiplane geometric center
based methods for 3-D AOA in UAV positioning. The first method could estimate
the source position and angle measurement noise at the same time by seeking a
center of the inscribed sphere, called CIS. Firstly, every sensor could measure
two angles, azimuth angle and elevation angle. Based on that, two planes are
constructed. Then, the estimated values of source position and angle noise are
achieved by seeking the center and radius of the corresponding inscribed
sphere. Deleting the estimation of the radius, the second algorithm, called
MSD-LS, is born. It is not able to estimate angle noise but has lower
computational complexity. Theoretical analysis and simulation results show that
proposed methods could approach the Cramer-Rao lower bound (CRLB) and have
lower complexity than MLE.


  The phase diagram of a biased graphene bilayer is computed and the existence
of a ferromagnetic phase is discussed both in the critical on-site interaction
$U_{c}$ versus doping density and versus temperature. We show that in the
ferromagnetic phase the two planes have unequal magnetization and that the
electronic density is hole like in one plane and electron like in the other. We
give evidence for a \emph{first-order} phase transition between paramagnetic
and ferromagnetic phases induced by doping at zero temperature.


  We explore condensation temperature Tc trends in the unique binary system
Zet1 Ret - Zet2 Ret, to determine whether there is a depletion of refractories,
which could be related to the planet formation process. The star Zet2 Ret hosts
a debris disk which was detected by an IR excess and confirmed by direct
imaging and numerical simulations, while Zet1 Ret does not present IR excess
nor planets. We carried out a high-precision abundance determination in both
components of the binary system via a line-by-line, strictly differential
approach. The stellar parameters Teff , log g, [Fe/H] and vturb were determined
by imposing differential ionization and excitation equilibrium of Fe I and Fe
II lines, with an updated version of the program FUNDPAR. The star Zet1 Ret
resulted slightly more metal rich than Zet2 Ret by 0.02 dex. In the
differential calculation of Zet1 Ret using Zet2 Ret as reference, the
abundances of the refractory elements resulted higher than the volatile
elements, and the trend of the refractory elements with Tc showed a positive
slope. These facts together show a lack of refractory elements in Zet2 Ret (a
debris-disk host) relative to Zet1 Ret. The Tc trend would be in agreement with
the proposed signature of planet formation (Melendez et al. 2009) rather than
possible Galactic Chemical Evolution or age effects, which are largely
diminished here. Then, following the interpretation of Melendez et al. (2009),
we propose an scenario in which the refractory elements depleted in Zet2 Ret
are possibly locked-up in the rocky material that orbits this star and produce
the debris disk observed around this object. We estimated a lower limit of
Mrock = 3 Me for the rocky mass of depleted material, which is compatible with
a rough estimation of 3-50 Me of a debris disk mass around a solar-type star
(Krivov et al. 2008). (abridged)


  This paper describes a programme to study the computing model in CMS after
the next long shutdown near the end of the decade.


  We model, for the first time, the Bondi-Hoyle accretion of a fluid with
velocity gradients onto a Kerr black hole, by numerically solving the fully
relativistic hydrodynamics equations. Specifically, we consider a supersonic
ideal gas, which has velocity gradients perpendicular to the relative motion.
We measure the mass and specific angular accretion rates to illustrate whether
the fluid presents unstable patterns or not. The initial parameters, we
consider in this work, are the velocity gradient $\epsilon_{v}$, the black hole
spin $a$, the asymptotic Mach number ${\cal M}_{\infty}$ and adiabatic index
$\Gamma$. We show that the flow accretion reaches a fairly stationary regime,
unlike in the Newtonian case, where significant fluctuations of the mass and
angular momentum accretion rates are found. On the other hand, we consider a
special case where both density and velocity gradients of the fluid are taken
into account. The spin of the black hole and the asymptotic Newtonian Mach
number, for this case, are $a=0.98$ and ${\cal M}_{\infty}=1$, respectively. A
kind of flip-flop behavior is found at the early times; nevertheless, the
system also reaches a steady state.


  In our quest to win a deeper understanding of how QCD actually works, the
study of the binding of heavy quarkonia and heavy-flavor hadrons to atomic
nuclei offers enormous promise. Modern experimental facilities such as FAIR,
Jefferson Lab at 12 GeV and J-PARC offer exciting new experimental
opportunities to study such systems. These experimental advances are
complemented by new theoretical approaches and predictions, which will both
guide these experimental efforts and be informed and improved by them. This
review will outline the main theoretical approaches, beginning with QCD itself,
summarize recent theoretical predictions and relate them both to past
experiments and those from which we may expect results in the near future.


  The longitudinal resistivity $\rho_{xx}$ of two-dimensional electron gases
formed in wells with two subbands displays ringlike structures when plotted in
a density--magnetic-field diagram, due to the crossings of spin-split Landau
levels (LLs) from distinct subbands. Using spin density functional theory and
linear response, we investigate the shape and spin polarization of these
structures as a function of temperature and magnetic-field tilt angle. We find
that (i) some of the rings "break" at sufficiently low temperatures due to a
quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of
spin polarization ($\sim 50 $%) within, consistent with the NMR data of Zhang
\textit{et al.} [Phys. Rev. Lett. {\bf 98}, 246802 (2007)], and (ii) for
increasing tilting angles the interplay between the anticrossings due to
inter-LL couplings and the exchange-correlation (XC) effects leads to a
collapse of the rings at some critical angle $\theta_c$, in agreement with the
data of Guo \textit{et al.} [Phys. Rev. B {\bf 78}, 233305 (2008)].


  Object detection in point clouds is an important aspect of many robotics
applications such as autonomous driving. In this paper we consider the problem
of encoding a point cloud into a format appropriate for a downstream detection
pipeline. Recent literature suggests two types of encoders; fixed encoders tend
to be fast but sacrifice accuracy, while encoders that are learned from data
are more accurate, but slower. In this work we propose PointPillars, a novel
encoder which utilizes PointNets to learn a representation of point clouds
organized in vertical columns (pillars). While the encoded features can be used
with any standard 2D convolutional detection architecture, we further propose a
lean downstream network. Extensive experimentation shows that PointPillars
outperforms previous encoders with respect to both speed and accuracy by a
large margin. Despite only using lidar, our full detection pipeline
significantly outperforms the state of the art, even among fusion methods, with
respect to both the 3D and bird's eye view KITTI benchmarks. This detection
performance is achieved while running at 62 Hz: a 2 - 4 fold runtime
improvement. A faster version of our method matches the state of the art at 105
Hz. These benchmarks suggest that PointPillars is an appropriate encoding for
object detection in point clouds.


  Using a new metric for generating rotating solutions, we derive in a general
fashion the solution of an imperfect fluid and that of its conformal homolog.
We discuss the conditions that the stress-energy tensors and invariant scalars
be regular. On classical physical grounds, it is stressed that, conformal
fluids used as cores for static or rotating solutions, are exempt from any
malicious behavior in that they are finite and defined everywhere.


  We study the properties of the stochastic gravitational wave background
(SGWB) produced by domain walls (DWs) during inflation without forming a
network. We numerically simulate the DW production caused by a second-order
phase transition and calculate the SGWB spectrum using a
$1000\times1000\times1000$ lattice. We show that the SGWB can be observed
directly by future terrestrial and spatial gravitational wave detectors and
through the B-mode spectrum in CMB. This signal can also explain the common
noise process observed by pulsar timing array experiments. With numerical
simulations, we derive an empirical formula for the strength and qualitative
features of the SGWB spectrum. The details of the SGWB spectrum also contain
information about the later evolution of the universe.


  We demonstrate stable microresonator Kerr soliton frequency combs in a III-V
platform (AlGaAs on SiO$_2$) through quenching of thermorefractive effects by
cryogenic cooling to temperatures between 4~K and 20~K. This cooling reduces
the resonator's thermorefractive coefficient, whose room-temperature value is
an order of magnitude larger than that of other microcomb platforms like
Si$_3$N$_4$, SiO$_2$, and AlN, by more than two orders of magnitude, and makes
soliton states adiabatically accessible. Realizing such phase-stable soliton
operation is critical for applications that fully exploit the ultra-high
effective nonlinearity and high optical quality factors exhibited by this
platform.


  We give a classical analogue to Kerenidis and Prakash's quantum
recommendation system, previously believed to be one of the strongest
candidates for provably exponential speedups in quantum machine learning. Our
main result is an algorithm that, given an $m \times n$ matrix in a data
structure supporting certain $\ell^2$-norm sampling operations, outputs an
$\ell^2$-norm sample from a rank-$k$ approximation of that matrix in time
$O(\text{poly}(k)\log(mn))$, only polynomially slower than the quantum
algorithm. As a consequence, Kerenidis and Prakash's algorithm does not in fact
give an exponential speedup over classical algorithms. Further, under strong
input assumptions, the classical recommendation system resulting from our
algorithm produces recommendations exponentially faster than previous classical
systems, which run in time linear in $m$ and $n$.
  The main insight of this work is the use of simple routines to manipulate
$\ell^2$-norm sampling distributions, which play the role of quantum
superpositions in the classical setting. This correspondence indicates a
potentially fruitful framework for formally comparing quantum machine learning
algorithms to classical machine learning algorithms.


  Modern machine learning pipelines, in particular those based on deep learning
(DL) models, require large amounts of labeled data. For classification
problems, the most common learning paradigm consists of presenting labeled
examples during training, thus providing strong supervision on what constitutes
positive and negative samples. This constitutes a major obstacle for the
development of DL models in radiology--in particular for cross-sectional
imaging (e.g., computed tomography [CT] scans)--where labels must come from
manual annotations by expert radiologists at the image or slice-level. These
differ from examination-level annotations, which are coarser but cheaper, and
could be extracted from radiology reports using natural language processing
techniques. This work studies the question of what kind of labels should be
collected for the problem of intracranial hemorrhage detection in brain CT. We
investigate whether image-level annotations should be preferred to
examination-level ones. By framing this task as a multiple instance learning
problem, and employing modern attention-based DL architectures, we analyze the
degree to which different levels of supervision improve detection performance.
We find that strong supervision (i.e., learning with local image-level
annotations) and weak supervision (i.e., learning with only global
examination-level labels) achieve comparable performance in examination-level
hemorrhage detection (the task of selecting the images in an examination that
show signs of hemorrhage) as well as in image-level hemorrhage detection
(highlighting those signs within the selected images). Furthermore, we study
this behavior as a function of the number of labels available during training.
Our results suggest that local labels may not be necessary at all for these
tasks, drastically reducing the time and cost involved in collecting and
curating datasets.


  MC Dropout is a mainstream "free lunch" method in medical imaging for
approximate Bayesian computations (ABC). Its appeal is to solve out-of-the-box
the daunting task of ABC and uncertainty quantification in Neural Networks
(NNs); to fall within the variational inference (VI) framework; and to propose
a highly multimodal, faithful predictive posterior. We question the properties
of MC Dropout for approximate inference, as in fact MC Dropout changes the
Bayesian model; its predictive posterior assigns $0$ probability to the true
model on closed-form benchmarks; the multimodality of its predictive posterior
is not a property of the true predictive posterior but a design artefact. To
address the need for VI on arbitrary models, we share a generic VI engine
within the pytorch framework. The code includes a carefully designed
implementation of structured (diagonal plus low-rank) multivariate normal
variational families, and mixtures thereof. It is intended as a go-to
no-free-lunch approach, addressing shortcomings of mean-field VI with an
adjustable trade-off between expressivity and computational complexity.


  We obtain an asymptotic formula for the average value of the divisor function
over the integers $n \le x$ in an arithmetic progression $n \equiv a \pmod q$,
where $q=p^k$ for a prime $p\ge 3$ and a sufficiently large integer $k$. In
particular, we break the classical barrier $q \le x^{2/3}$ for such formulas,
and generalise a recent result of R.~Khan (2015), making it uniform in $k$.


  We investigate the space of weights spanned by a large collection of
customized diffusion models. We populate this space by creating a dataset of
over 60,000 models, each of which is a base model fine-tuned to insert a
different person's visual identity. We model the underlying manifold of these
weights as a subspace, which we term weights2weights. We demonstrate three
immediate applications of this space -- sampling, editing, and inversion.
First, as each point in the space corresponds to an identity, sampling a set of
weights from it results in a model encoding a novel identity. Next, we find
linear directions in this space corresponding to semantic edits of the identity
(e.g., adding a beard). These edits persist in appearance across generated
samples. Finally, we show that inverting a single image into this space
reconstructs a realistic identity, even if the input image is out of
distribution (e.g., a painting). Our results indicate that the weight space of
fine-tuned diffusion models behaves as an interpretable latent space of
identities.


  By using kinematical arguments we derive a theorem for the ratio: [production
cross-section of charged-neutral wino pairs plus anything else] over
[production cross-section of charged-neutral lepton pairs plus anything else].
We do that by working out the consequences of substituting the lepton pair with
a wino pair, leaving untouched everything else of the interaction. We apply
this result to the possible production of winos at LHC obtaining a lower bound
for the ratio of the number of charged-winos over charged-leptons tracks and
also find the average charged-wino track length, within a region in the
relevant parameter space (e.g. available energy and mass).


  We review theories of dark matter (DM) beyond the collisionless paradigm,
known as self-interacting dark matter (SIDM), and their observable implications
for astrophysical structure in the Universe. Self-interactions are motivated,
in part, due to the potential to explain long-standing (and more recent) small
scale structure observations that are in tension with collisionless cold DM
(CDM) predictions. Simple particle physics models for SIDM can provide a
universal explanation for these observations across a wide range of mass scales
spanning dwarf galaxies, low and high surface brightness spiral galaxies, and
clusters of galaxies. At the same time, SIDM leaves intact the success of
$\Lambda$CDM cosmology on large scales. This report covers the following
topics: (1) small scale structure issues, including the core-cusp problem, the
diversity problem for rotation curves, the missing satellites problem, and the
too-big-to-fail problem, as well as recent progress in hydrodynamical
simulations of galaxy formation; (2) N-body simulations for SIDM, including
implications for density profiles, halo shapes, substructure, and the interplay
between baryons and self-interactions; (3) semi-analytic Jeans-based methods
that provide a complementary approach for connecting particle models with
observations; (4) merging systems, such as cluster mergers (e.g., the Bullet
Cluster) and minor infalls, along with recent simulation results for mergers;
(5) particle physics models, including light mediator models and composite DM
models; and (6) complementary probes for SIDM, including indirect and direct
detection experiments, particle collider searches, and cosmological
observations. We provide a summary and critical look for all current
constraints on DM self-interactions and an outline for future directions.


  We have focused in the paper on the most prominent and intensively studied
S=1 pseudospin formalism for extended bosonic Hubbard model (EHBM) with
truncation of the on-site Hilbert space to the three lowest occupation states n
= 0, 1, 2. The EHBM Hamiltonian is a paradigmatic model for the highly topical
field of ultracold gases in optical lattices. Generalized non-Heisenberg
effective pseudospin Hamiltonian does provide a deep link with boson system and
physically clear description of "the myriad of phases" from uniform Mott
insulating phases and density waves to two types of superfluids and
supersolids. We argue that the 2D pseudospin system is prone to a topological
phase separation and focus on several types of unconventional skyrmion-like
topological structures in 2D boson systems, which have not been analysed till
now. The structures are characterized by a complicated interplay of insulating
and the two superfluid phases with a single boson and two-boson condensation,
respectively.


  We propose an approach for estimating the relative pose between calibrated
image pairs by jointly exploiting points, lines, and their coincidences in a
hybrid manner. We investigate all possible configurations where these data
modalities can be used together and review the minimal solvers available in the
literature. Our hybrid framework combines the advantages of all configurations,
enabling robust and accurate estimation in challenging environments. In
addition, we design a method for jointly estimating multiple vanishing point
correspondences in two images, and a bundle adjustment that considers all
relevant data modalities. Experiments on various indoor and outdoor datasets
show that our approach outperforms point-based methods, improving
AUC@10$^\circ$ by 1-7 points while running at comparable speeds. The source
code of the solvers and hybrid framework will be made public.


  Dividing sentences in chunks of words is a useful preprocessing step for
parsing, information extraction and information retrieval. (Ramshaw and Marcus,
1995) have introduced a "convenient" data representation for chunking by
converting it to a tagging task. In this paper we will examine seven different
data representations for the problem of recognizing noun phrase chunks. We will
show that the the data representation choice has a minor influence on chunking
performance. However, equipped with the most suitable data representation, our
memory-based learning chunker was able to improve the best published chunking
results for a standard data set.


  Despite the great success achieved by deep learning methods in face
recognition, severe performance drops are observed for large pose variations in
unconstrained environments (e.g., in cases of surveillance and photo-tagging).
To address it, current methods either deploy pose-specific models or frontalize
faces by additional modules. Still, they ignore the fact that identity
information should be consistent across poses and are not realizing the data
imbalance between frontal and profile face images during training. In this
paper, we propose an efficient PoseFace framework which utilizes the facial
landmarks to disentangle the pose-invariant features and exploits a
pose-adaptive loss to handle the imbalance issue adaptively. Extensive
experimental results on the benchmarks of Multi-PIE, CFP, CPLFW and IJB have
demonstrated the superiority of our method over the state-of-the-arts.


  Instead of studying anyon condensation in concrete models, we take an
abstract approach. Assume that a system of anyons, which form a modular tensor
category D, is obtained via an anyon condensation from another system of anyons
(i.e. another modular tensor category C). By a bootstrap analysis, we derive
the relation between C and D from natural physical requirements. It turns out
that the tensor unit of D can be identified with a connected commutative
separable algebra A in C. The modular tensor category D consists of all
deconfined particles and can be identified with the category of local
$A$-modules in C. If this condensation occurs in a 2d region in the C-phase,
then it also produces a 1d gapped domain wall between the C-phase and the
D-phase. The confined and deconfined particles accumulate on the wall and form
a fusion category that is precisely the category of right A-modules in C. We
also consider condensations that are confined to a 1d line. We show how to
determine the algebra A from physical macroscopic data. We provide examples of
anyon condensation in the toric code model, Kitaev quantum double models and
Levin-Wen types of lattice models and in some chiral topological phases. In the
end, we briefly discuss Witt equivalence between 2d topological phases.
  We also attach to this paper an Erratum and Addendum to the original version
of "Anyon condensation and tensor categories" published in [Nucl. Phys. B 886
(2014) 436-482].


  We investigate and quantify various measures of bipartite and tripartite
entanglement in the context of two and three flavor neutrino oscillations. The
bipartite entanglement is analogous to the entanglement swapping resulting from
a beam splitter in quantum optics. For the three neutrino systems various
measures of tripartite entanglement are explored. The significant result is
that a monogamy inequality in terms of negativity leads to a residual
entanglement, implying true tripartite entanglement in the three neutrino
system. This leads us to an analogy of the three neutrino state with a
generalized class of W-state in quantum optics.


  Classical methods such as Principal Component Analysis (PCA) and Canonical
Correlation Analysis (CCA) are ubiquitous in statistics. However, these
techniques are only able to reveal linear relationships in data. Although
nonlinear variants of PCA and CCA have been proposed, these are computationally
prohibitive in the large scale.
  In a separate strand of recent research, randomized methods have been
proposed to construct features that help reveal nonlinear patterns in data. For
basic tasks such as regression or classification, random features exhibit
little or no loss in performance, while achieving drastic savings in
computational requirements.
  In this paper we leverage randomness to design scalable new variants of
nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such
as spectral clustering or LDA. We demonstrate our algorithms through
experiments on real-world data, on which we compare against the
state-of-the-art. A simple R implementation of the presented algorithms is
provided.


  Understanding non-Fermi liquids in dimensions higher than one remains one of
the most formidable challenges in modern condensed matter physics. These
systems, characterized by an abundance of gapless degrees of freedom and the
absence of well-defined quasiparticles, defy conventional analytical
frameworks. Inspired by recent work on the bosonization of Fermi surfaces
[Delacretaz, Du, Mehta, and Son, Physical Review Research, 4, 033131 (2022)],
we present a procedure for bosonizing non-Fermi liquids, which provides a
holistic approach capable of addressing their intricate physics. Our method
involves parameterizing the generalized fermionic distribution function through
a bosonic field that describes frequency-dependent local variations of the
chemical potential in momentum space. We propose an effective action that
produces the collisionless quantum Boltzmann equation as its equation of motion
and can straightforwardly be used for any dimension and Fermi surface of
interest. Even at the quadratic order, this action reproduces highly
non-trivial results obtainable only through involved analysis with alternative
means. By offering a comprehensive description of the physics of non-Fermi
liquids, our work stands as an important building block in advancing the
comprehension of strange metals and associated phenomena.


  We have performed neutron diffraction measurement on a single crystal of
parent compound of iron-based superconductor, BaFe$_2$As$_2$ at 12~K. In order
to investigate in-plane anisotropy of magnetic form factor in the
antiferromagnetic phase, the detwinned single crystal is used in the
measurement. The magnetic structure factor and magnetic form factor are well
explained by the spin densities consisting of $3d_{yz}$ electrons with a
fraction of about 40~\% and the electrons in the other four $3d$ orbitals with
each fraction of about 15~\%. Such anisotropic magnetic form factor is
qualitatively consistent with the anisotropic magnetic behaviors observed in
the antiferromagnetic phase of the parent compound of iron-based
superconductor.


  Core-valence basis sets for the alkali and alkaline earth metals Li, Be, Na,
Mg, K, and Ca are proposed. The basis sets are validated by calculating
spectroscopic constants of a variety of diatomic molecules involving these
elements. Neglect of $(3s,3p)$ correlation in K and Ca compounds will lead to
erratic results at best, and chemically nonsensical ones if chalcogens or
halogens are present. The addition of low-exponent $p$ functions to the K and
Ca basis sets is essential for smooth convergence of molecular properties.
Inclusion of inner-shell correlation is important for accurate spectroscopic
constants and binding energies of all the compounds. In basis set
extrapolation/convergence calculations, the explicit inclusion of alkali and
alkaline earth metal subvalence correlation at all steps is essential for K and
Ca, strongly recommended for Na, and optional for Li and Mg, while in Be
compounds, an additive treatment in a separate `core correlation' step is
probably sufficient. Consideration of $(1s)$ inner-shell correlation energy in
first-row elements requires inclusion of $(2s,2p)$ `deep core' correlation
energy in K and Ca for consistency. The latter requires special CCV$n$Z `deep
core correlation' basis sets. For compounds involving Ca bound to
electronegative elements, additional $d$ functions in the basis set are
strongly recommended. For optimal basis set convergence in such cases, we
suggest the sequence CV(D+3d)Z, CV(T+2d)Z, CV(Q+$d$)Z, and CV5Z on calcium.


  Vortices and their analysis play a critical role in the understanding of
complex phenomena in turbulent flows. Traditional vortex extraction methods,
notably region-based techniques, often overlook the entanglement phenomenon,
resulting in the inclusion of multiple vortices within a single extracted
region. Their separation is necessary for quantifying different types of
vortices and their statistics. In this study, we propose a novel vortex
separation method that extends the conventional contour tree-based segmentation
approach with an additional step termed "layering". Upon extracting a vortical
region using specified vortex criteria (e.g., $\lambda_2$), we initially
establish topological segmentation based on the contour tree, followed by the
layering process to allocate appropriate segmentation IDs to unsegmented cells,
thus separating individual vortices within the region. However, these regions
may still suffer from inaccurate splits, which we address statistically by
leveraging the continuity of vorticity lines across the split boundaries. Our
findings demonstrate a significant improvement in both the separation of
vortices and the mitigation of inaccurate splits compared to prior methods.


  We propose DeepMetaHandles, a 3D conditional generative model based on mesh
deformation. Given a collection of 3D meshes of a category and their
deformation handles (control points), our method learns a set of meta-handles
for each shape, which are represented as combinations of the given handles. The
disentangled meta-handles factorize all the plausible deformations of the
shape, while each of them corresponds to an intuitive deformation. A new
deformation can then be generated by sampling the coefficients of the
meta-handles in a specific range. We employ biharmonic coordinates as the
deformation function, which can smoothly propagate the control points'
translations to the entire mesh. To avoid learning zero deformation as
meta-handles, we incorporate a target-fitting module which deforms the input
mesh to match a random target. To enhance deformations' plausibility, we employ
a soft-rasterizer-based discriminator that projects the meshes to a 2D space.
Our experiments demonstrate the superiority of the generated deformations as
well as the interpretability and consistency of the learned meta-handles.


  Inhomogeneous chemical evolution models of galaxies which try to reproduce
the scatter seen in element-to-iron ratios of metal-poor halo stars are heavily
dependent on theoretical nucleosynthesis yields of core-collapse supernovae.
Hence inhomogeneous models present themselves as a test for stellar nucleosyn-
thesis calculations. Applying an inhomogeneous chemical evolution model to our
Galaxy reveals a number of shortcomings of existing theoretical nucleosynthesis
yields. One problem is the predicted scatter in [O/Fe] and [Mg/Fe] which is too
large compared to the one observed in metal-poor halo stars. This can be either
due to the O or Mg yields or due to the Fe yields (or both). However, O and Mg
are alpha-elements that are produced mainly during hydrostatic burning and thus
are not affected by the theoretical uncertainties afflicting the collapse and
explosion of a massive star. Stellar iron yields, on the other hand, depend
heavily on the choice of the mass-cut between ejecta and proto neutron star and
are therefore very uncertain. We present Fe yield distributions as function of
progenitor mass that are consistent with the abundance distribution of metal-
poor halo stars and are in agreement with observed Ni yields of SNe II with
known progenitor masses. The iron yields of lower-mass SNe II (in the range
10-20 Msol) are well constrained by those observations. Present observations,
however, do not allow to determine a unique solution for higher-mass SNe.
Nevertheless, the main dependence of the stellar iron yield as function of
progenitor mass may be derived and can be used as constraint for future
supernova/hypernova models. The results are of importance for the earliest
stages of galaxy formation when the ISM is dominated by chemical
inhomogeneities and the instantaneous mixing approximation is not valid.


  We provide a direct and elementary proof for the fact that every four point
metric space is positive definite, which was first proved by Meckes based on
some embedding theorems of metric spaces. As an outcome of the direct proof, we
also provide a condition for the magnitude of a finite metric space to obey the
inclusion-exclusion principle with respect to a specific choice of subspaces.


  The CRESST-II experiment is introduced. It uses scintillating crystals as a
target to search for elastic scatterings of dark matter particles. The
detectors are operated in a dilution cryostat at temperatures below 30mK, and
for each particle interaction, the phonon signal as well as the scintillation
light signal are recorded. Recent results from a commissioning run following a
major upgrade are presented. The current limit that can be placed on the
spin-independent WIMP-nucleon scattering cross-section is below 6x10-7 pb for
WIMPs in the mass range from about 40 to 90 GeV/c2.


  In tokamak plasmas, sheared flows perpendicular to the driving temperature
gradients can strongly stabilize linear modes. While the system is linearly
stable, regimes with persistent nonlinear turbulence may develop, i.e. the
system is subcritical. A perturbation with small but finite amplitude may be
sufficient to push the plasma into a regime where nonlinear effects are
dominant and thus allow sustained turbulence. The minimum threshold for
nonlinear instability to be triggered provides a criterion for assessing
whether a tokamak is likely to stay in the quiescent (laminar) regime. At the
critical amplitude, instead of transitioning to the turbulent regime or
decaying to a laminar state, the trajectory will map out the edge of chaos.
Surprisingly, a quasi-traveling-wave solution is found as an attractor on this
edge manifold. This simple advecting solution is qualitatively similar to, but
simpler than, the avalanche-like bursts seen in earlier turbulent simulations
and provides an insight into how turbulence is sustained in subcritical plasma
systems. For large flow shearing rate, the system is only convectively
unstable, and given a localised initial perturbation, will eventually return to
a laminar state at a fixed spatial location.


  Context. Spectroscopic analyses to interpret the spectra of the brightest
supernovae from the UV to the near-IR provide a powerful tool with great
astrophysical potential for the determination of the physical state of the
ejecta, their chemical composition, and the SNe distances even at significant
redshifts.
  Methods. We report on improvements of computing synthetic spectra for SNIa
with respect to i) an improved and sophisticated treatment of thousands of
strong lines that interact intricately with the "pseudo-continuum" formed
entirely by Doppler- shifted spectral lines, ii) an improved and expanded
atomic database, and iii) the inclusion of energy deposition within the ejecta.
  Results. We show that an accelerated lambda iteration procedure we have
developed for the mutual interaction of strong spectral lines appearing in the
atmospheres of SNeIa solves the longstanding problem of transferring the
radiative energy from the UV into the optical regime. In detail we discuss
applications of the diagnostic technique by example of a standard SNIa, where
the comparison of calculated and observed spectra revealed that in the early
phases the consideration of the energy deposition within the spectrum-forming
regions of the ejecta does not qualitatively alter the shape of the spectra.
  Conclusions. The results of our investigation lead to an improved
understanding of how the shape of the spectrum changes radically as function of
depth in the ejecta, and show how different emergent spectra are formed as a
result of the particular physical properties of SNe Ia ejecta and the resulting
peculiarities in the radiative transfer. This provides an important insight
into the process of extracting information from observed SNIa spectra, since
these spectra are a complex product of numerous unobservable SNIa spectral
features which are thus analyzed in parallel to the observable spectral
features.


  Mixture-of-Experts (MoE) models can achieve promising results with outrageous
large amount of parameters but constant computation cost, and thus it has
become a trend in model scaling. Still it is a mystery how MoE layers bring
quality gains by leveraging the parameters with sparse activation. In this
work, we investigate several key factors in sparse expert models. We observe
that load imbalance may not be a significant problem affecting model quality,
contrary to the perspectives of recent studies, while the number of sparsely
activated experts $k$ and expert capacity $C$ in top-$k$ routing can
significantly make a difference in this context. Furthermore, we take a step
forward to propose a simple method called expert prototyping that splits
experts into different prototypes and applies $k$ top-$1$ routing. This
strategy improves the model quality but maintains constant computational costs,
and our further exploration on extremely large-scale models reflects that it is
more effective in training larger models. We push the model scale to over $1$
trillion parameters and implement it on solely $480$ NVIDIA V100-32GB GPUs, in
comparison with the recent SOTAs on $2048$ TPU cores. The proposed giant model
achieves substantial speedup in convergence over the same-size baseline.


  Gamed-based is a new stochastic metaheuristics optimization category that is
inspired by traditional or digital game genres. Unlike SI-based algorithms,
in-dividuals do not work together with the goal of defeating other individuals
and winning the game. Battle royale optimizer (BRO) is a Gamed-based
me-taheuristic optimization algorithm that has been recently proposed for the
task of continuous problems. This paper proposes a modified BRO (M-BRO) in
order to improve balance between exploration and exploitation. For this matter,
an additional movement operator has been used in the movement strategy.
Moreover, no extra parameters are required for the proposed ap-proach.
Furthermore, the complexity of this modified algorithm is the same as the
original one. Experiments are performed on a set of 19 (unimodal and
multimodal) benchmark functions (CEC 2010). The proposed method has been
compared with the original BRO alongside six well-known/recently proposed
optimization algorithms. The results show that BRO with additional movement
operator performs well to solve complex numerical optimization problems
compared to the original BRO and other competitors.


  We establish the equivalence between the notions of weak and viscosity
solutions for non-homogeneous equations whose main operator is the fractional
p-Laplacian and the lower order term depends on $x$, $u$ and $D_s^p u$, being
the last one a type of fractional derivative.


  Capacitively coupled radio-frequency (CCRF) CF_4 plasmas have been found to
exhibit a self-organized striated structure at operating conditions, where the
plasma is strongly electronegative and the ion-ion plasma in the bulk region
(largely composed of CF_3^+ and F^- ions) resonates with the excitation
frequency. In this work we explore the effects of the gas pressure, the RF
voltage, and the electrode gap on this striated structure by Phase Resolved
Optical Emission Spectroscopy and Particle-In-Cell/Monte Carlo Collisions
simulations. The measured electronic excitation patterns at different external
parameters show a good general agreement with the spatio-temporal plots of the
ionization rate obtained from the simulations. For a fixed driving frequency
the minima of the CF_3^+ and F^- ion densities (between the density peaks in
the bulk) are comparable and independent of other external parameters. However,
the ion density maxima generally increase as a function of the pressure or RF
voltage, leading to the enhanced spatial modulation of plasma parameters. The
striation gap (defined as the distance between two ion density peaks) is
approximately inversely proportional to the pressure, while it exhibits a weak
dependence on the RF voltage and the electrode gap. A transition between the
striated and non-striated modes can be observed by changing either the pressure
or the RF voltage; for 13.56 MHz and 18 MHz driving frequencies we present a
phase diagram as a function of the pressure and voltage amplitude parameters.


  Consider a function field $K$ with characteristic $p>0$. We investigate the
$\Lambda$-module structure of the Mordell-Weil group of an abelian variety over
$\mathbb{Z}_p$-extensions of $K$, generalizing results due to Lee. Next, we
study the algebraic structure and prove a control theorem for the S-fine
Mordell-Weil groups, the function field analogue for Wuthrich's fine
Mordell-Weil groups, over a $\mathbb{Z}_p$-extension of $K$. In case of
unramified $\mathbb{Z}_p$-extension, $K_\infty$, we compute the characteristic
ideal of the Pontryagin dual of the S-fine Mordell group. This provides an
answer to an analogue of Greenberg's question for the characteristic ideal of
the dual fine Selmer group in the function field setup. In the $\ell\neq p$
case, we prove the triviality of the $\mu$-invariant for the Selmer group (same
as the fine Selmer group in this case) of an elliptic curve over a
non-commutative $GL_2(\mathbb{Z}_\ell)$-extension of $K$ and thus extending
Conjecture A. In the $\ell=p$ case, we compute the change of $\mu$-invariants
of the dual Selmer groups of elliptic curves under isogeny, giving a lower
bound for the $\mu$-invariant.


  In this paper we examine the interaction of convection, rotation and mean
flows in a thermal annulus. In this system mean flows are driven by
correlations induced by rotation leading to non-trivial Reynolds stresses. The
mean flows act back on the convective turbulence acting as a barrier to
transport. For this system we demonstrate that the Generalised Quasilinear
Approximation (GQL) (Marston et al 2016) may provide a much better
approximation to the complicated full nonlinear dynamics than the widely used
Quasilinear Approximation (QL). This result will enable the construction of
more accurate statistical theories for the description of geophysical and
astrophysical flows.


  In this paper, we study the evolution of the ionization fraction $x_e(z)$
during the epoch of reionization by using the dispersion measurements (DMs) of
fast radio bursts (FRBs). Different from the previous studies, here we turn to
consider the large-scale clustering information of observed DMs of FRB catalog,
which only needs the rough redshift distribution, instead of the exact redshift
information of each FRB. Firstly, we consider the instantaneous
``\texttt{tanh}'' model for $x_e(z)$ and find that including the
auto-correlation information of the mock catalog, about $10^4$ FRBs with the
intrinsic DM scatter of 100 $\rm pc/cm^3$ spanning 20\% of all sky, could
significantly improve the constraint on the width $\Delta_z$ of the model, when
comparing with that from the CMB data alone. The evolution shape of the
ionization fraction will be tightly narrowed, namely the duration of the epoch
of reionization has been shrunk, $z_{\rm dur}<2.24$ (95\% C.L.). Furthermore,
we also use another redshift-asymmetric reionization model and obtain that the
FRB mock catalog could measure the ionization fraction at $z=6$ precisely with
the $1\sigma$ error $\Delta x_e(z=6)=0.012$, which means that the large-scale
clustering information of observed DMs of FRB catalog is very sensitive to the
ionization fraction of the end of reionization epoch. We conclude that the
observation of high-redshift FRBs could be a complementary probe to study the
reionization history in the future.


  In this paper we investigate the critical collapse of an ultrarelativistic
perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of
$\Gamma\to 1$. We calculate the limiting continuously self similar (CSS)
solution and the limiting scaling exponent by exploiting self-similarity of the
solution. We also solve the complete set of equations governing the
gravitational collapse numerically for $(\Gamma-1) = 10^{-2},...,10^{-6}$ and
compare them with the CSS solutions. We also investigate the supercritical
regime and discuss the hypothesis of naked singularity formation in a generic
gravitational collapse. The numerical calculations make use of advanced methods
such as high resolution shock capturing evolution scheme for the matter
evolution, adaptive mesh refinement, and quadruple precision arithmetic. The
treatment of vacuum is also non standard. We were able to tune the critical
parameter up to 30 significant digits and to calculate the scaling exponents
accurately. The numerical results agree very well with those calculated using
the CSS ansatz. The analysis of the collapse in the supercritical regime
supports the hypothesis of the existence of naked singularities formed during a
generic gravitational collapse.


  The use of genetic algorithms for the optimisation of magic angle spinning
NMR pulse sequences is discussed. The discussion uses as an example the
optimisation of the C7 dipolar recoupling pulse sequence, aiming to achieve
improved efficiency for spin systems characterised by large chemical shielding
anisotropies and/or small dipolar coupling interactions. The optimised pulse
sequence is found to be robust over a wide range of parameters, requires only
minimal a priori knowledge of the spin system for experimental implementations
with buildup rates being solely determined by the magnitude of the dipolar
coupling interaction, but is found to be less broadbanded than the original C7
pulse sequence. The optimised pulse sequence breaks the synchronicity between
r.f. pulses and sample spinning.


  This thesis aims to investigate the feasibility of knowledge transfer between
neural networks for medical image segmentation tasks, specifically focusing on
the transfer from a larger multi-task "Teacher" network to a smaller "Student"
network. In the context of medical imaging, where the data volumes are often
limited, leveraging knowledge from a larger pre-trained network could be
useful. The primary objective is to enhance the performance of a smaller
student model by incorporating knowledge representations acquired by a teacher
model that adopts a multi-task pre-trained architecture trained on CT images,
to a more resource-efficient student network, which can essentially be a
smaller version of the same, trained on a mere 50% of the data than that of the
teacher model.
  To facilitate knowledge transfer between the two models, we devised an
architecture incorporating multi-scale feature distillation and supervised
contrastive learning. Our study aims to improve the student model's performance
by integrating knowledge representations from the teacher model. We investigate
whether this approach is particularly effective in scenarios with limited
computational resources and limited training data availability. To assess the
impact of multi-scale feature distillation, we conducted extensive experiments.
We also conducted a detailed ablation study to determine whether it is
essential to distil knowledge at various scales, including low-level features
from encoder layers, for effective knowledge transfer. In addition, we examine
different losses in the knowledge distillation process to gain insights into
their effects on overall performance.


  We consider the fundamental protocol of dense coding of classical information
assuming that noise affects both the forward and backward communication lines
between Alice and Bob. Assuming that this noise is described by the same
quantum channel, we define its dense coding capacity by optimizing over all
adaptive strategies that Alice can implement, while Bob encodes the information
by means of Pauli operators. Exploiting techniques of channel simulation and
protocol stretching, we are able to establish the dense coding capacity of
Pauli channels in arbitrary finite dimension, with simple formulas for
depolarizing and dephasing qubit channels.


  We study the smallest non-trivial matrix model that can be considered to be a
(toy) model of a black hole. The model consists of a pair of $2\times 2$
traceless hermitian matrices with a commutator squared potential and an $SU(2)$
gauge symmetry, plus an $SO(2)$ rotation symmetry. We show that using the
symmetries of the system, all but two of the variables can be separated. The
two variables that remain display chaos and a transition from chaos to
integrability when a parameter related to an $SO(2)$ angular momentum is tuned
to a critical value. We compute the Lyapunov exponents near this transition and
study the critical exponent of the Lyapunov exponents near the critical point.
We compare this transition to extremal rotating black holes.


  Bandwidth smearing is a chromatic aberration due to the finite frequency
bandwidth. In long-baseline optical interferometry terms, it is when the
angular extension of the source is greater than the coherence length of the
interferogram. As a consequence, separated parts of the source will contribute
to fringe packets that are not fully overlapping; it is a transition from the
classical interferometric regime to a double or multiple fringe packet. While
studied in radio interferometry, there has been little work on the matter in
the optical, where observables are measured and derived in a different manner,
and are more strongly impacted by the turbulent atmosphere. We provide here the
formalism and a set of usable equations to model and correct for the impact of
smearing on the fringe contrast and phase, with the case of multiple stellar
systems in mind. The atmosphere is briefly modeled and discussed.


  Factual probing is a method that uses prompts to test if a language model
"knows" certain world knowledge facts. A problem in factual probing is that
small changes to the prompt can lead to large changes in model output. Previous
work aimed to alleviate this problem by optimizing prompts via text mining or
fine-tuning. However, such approaches are relation-specific and do not
generalize to unseen relation types. Here, we propose to use test-time
augmentation (TTA) as a relation-agnostic method for reducing sensitivity to
prompt variations by automatically augmenting and ensembling prompts at test
time. Experiments show improved model calibration, i.e., with TTA, model
confidence better reflects prediction accuracy. Improvements in prediction
accuracy are observed for some models, but for other models, TTA leads to
degradation. Error analysis identifies the difficulty of producing high-quality
prompt variations as the main challenge for TTA.


  In fruit production, critical crop management decisions are guided by bloom
intensity, i.e., the number of flowers present in an orchard. Despite its
importance, bloom intensity is still typically estimated by means of human
visual inspection. Existing automated computer vision systems for flower
identification are based on hand-engineered techniques that work only under
specific conditions and with limited performance. This work proposes an
automated technique for flower identification that is robust to uncontrolled
environments and applicable to different flower species. Our method relies on
an end-to-end residual convolutional neural network (CNN) that represents the
state-of-the-art in semantic segmentation. To enhance its sensitivity to
flowers, we fine-tune this network using a single dataset of apple flower
images. Since CNNs tend to produce coarse segmentations, we employ a refinement
method to better distinguish between individual flower instances. Without any
pre-processing or dataset-specific training, experimental results on images of
apple, peach and pear flowers, acquired under different conditions demonstrate
the robustness and broad applicability of our method.


  Optimal data detection of data transmitted over a linear channel can always
be implemented through the Viterbi algorithm (VA). However, in many cases of
interest the memory of the channel prohibits application of the VA. A popular
and conceptually simple method in this case, studied since the early 70s, is to
first filter the received signal in order to shorten the memory of the channel,
and then to apply a VA that operates with the shorter memory. We shall refer to
this as a channel shortening (CS) receiver. Although studied for almost four
decades, an information theoretic understanding of what such a simple receiver
solution is actually doing is not available.
  In this paper we will show that an optimized CS receiver is implementing the
chain rule of mutual information, but only up to the shortened memory that the
receiver is operating with. Further, we will show that the tools for analyzing
the ensuing achievable rates from an optimized CS receiver are precisely the
same as those used for analyzing the achievable rates of a minimum mean square
error (MMSE) receiver.


  In this work, we give a new method to compute the Hilbert basis of the
semigroup of certain positive divisors supported on the exceptional divisor of
a normal surface singularity. Our approach is purely combinatorial which
permits to avoid the long calculation of the invariants of the ring as it is
presented in the work of Altinok and Tosun.


  We investigate boosted online regression and propose a novel family of
regression algorithms with strong theoretical bounds. In addition, we implement
several variants of the proposed generic algorithm. We specifically provide
theoretical bounds for the performance of our proposed algorithms that hold in
a strong mathematical sense. We achieve guaranteed performance improvement over
the conventional online regression methods without any statistical assumptions
on the desired data or feature vectors. We demonstrate an intrinsic
relationship, in terms of boosting, between the adaptive mixture-of-experts and
data reuse algorithms. Furthermore, we introduce a boosting algorithm based on
random updates that is significantly faster than the conventional boosting
methods and other variants of our proposed algorithms while achieving an
enhanced performance gain. Hence, the random updates method is specifically
applicable to the fast and high dimensional streaming data. Specifically, we
investigate Newton Method-based and Stochastic Gradient Descent-based linear
regression algorithms in a mixture-of-experts setting and provide several
variants of these well-known adaptation methods. However, the proposed
algorithms can be extended to other base learners, e.g., nonlinear, tree-based
piecewise linear. Furthermore, we provide theoretical bounds for the
computational complexity of our proposed algorithms. We demonstrate substantial
performance gains in terms of mean square error over the base learners through
an extensive set of benchmark real data sets and simulated examples.


  The infinite pigeonhole principle for $k$ colors ($\mathsf{RT}_k$) states,
for every $k$-partition $A_0 \sqcup \dots \sqcup A_{k-1} = \mathbb{N}$, the
existence of an infinite subset~$H \subseteq A_i$ for some~$i < k$. This
seemingly trivial combinatorial principle constitutes the basis of Ramsey's
theory, and plays a very important role in computability and proof theory. In
this article, we study the infinite pigeonhole principle at various levels of
the arithmetical hierarchy from both a computability-theoretic and reverse
mathematical viewpoint. We prove that this hierarchy is strict
over~$\mathsf{RCA}_0$ using an elaborate iterated jump control construction,
and study its first-order consequences. This is part of a large
meta-mathematical program studying the computational content of combinatorial
theorems.


  Nash equilibrium (NE) assumes that players always make a best response.
However, this is not always true; sometimes people cooperate even it is not a
best response to do so. For example, in the Prisoner's Dilemma, people often
cooperate. Are there rules underlying cooperative behavior? In an effort to
answer this question, we propose a new equilibrium concept: perfect cooperative
equilibrium (PCE), and two related variants: max-PCE and cooperative
equilibrium. PCE may help explain players' behavior in games where cooperation
is observed in practice. A player's payoff in a PCE is at least as high as in
any NE. However, a PCE does not always exist. We thus consider {\alpha}-PCE,
where {\alpha} takes into account the degree of cooperation; a PCE is a 0-PCE.
Every game has a Pareto-optimal max-PCE (M-PCE); that is, an {\alpha}-PCE for a
maximum {\alpha}. We show that M-PCE does well at predicting behavior in quite
a few games of interest. We also consider cooperative equilibrium (CE), another
generalization of PCE that takes punishment into account. Interestingly, all
Pareto-optimal M-PCE are CE. We prove that, in 2-player games, a PCE (if it
exists), a M-PCE, and a CE can all be found in polynomial time using bilinear
programming. This is a contrast to Nash equilibrium, which is PPAD complete
even in 2-player games [Chen, Deng, and Teng 2009]. We compare M-PCE to the
coco value [Kalai and Kalai 2009], another solution concept that tries to
capture cooperation, both axiomatically and in terms of an algebraic
characterization, and show that the two are closely related, despite their very
different definitions.


  Galaxy cluster masses, rich with cosmological information, can be estimated
from internal dark matter (DM) velocity dispersions, which in turn can be
observationally inferred from satellite galaxy velocities. However, galaxies
are biased tracers of the DM, and the bias can vary over host halo and galaxy
properties as well as time. We precisely calibrate the velocity bias, b_v --
defined as the ratio of galaxy and DM velocity dispersions -- as a function of
redshift, host halo mass, and galaxy stellar mass threshold (Mstarsat), for
massive halos (M200c > 1e13.5 msun) from five cosmological simulations:
IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and
MultiDark Planck-2. We first compare scaling relations for galaxy and DM
velocity dispersion across simulations; the former is estimated using a new
ensemble velocity likelihood method that is unbiased for low galaxy counts per
halo, while the latter uses a local linear regression. The simulations show
consistent trends of b_v increasing with M200c and decreasing with redshift and
Mstarsat. The ensemble-estimated theoretical uncertainty in b_v is 2-3% but
becomes percent-level when considering only the three highest resolution
simulations. We update the mass-richness normalization previously estimated by
Farahi et al. (2016) for an SDSS redMaPPer cluster sample. The improved
accuracy of our b_v estimates reduces the mass normalization uncertainty from
22% to 8%, demonstrating that dynamical estimation techniques can be
competitive with weak lensing in calibrating population mean masses. We discuss
necessary steps for further improving this precision. Our estimates for
b_v(M200c, Mstarsat, z) are made publicly available.


  Subspace clustering is the problem of clustering data points into a union of
low-dimensional linear/affine subspaces. It is the mathematical abstraction of
many important problems in computer vision, image processing and machine
learning. A line of recent work (4, 19, 24, 20) provided strong theoretical
guarantee for sparse subspace clustering (4), the state-of-the-art algorithm
for subspace clustering, on both noiseless and noisy data sets. It was shown
that under mild conditions, with high probability no two points from different
subspaces are clustered together. Such guarantee, however, is not sufficient
for the clustering to be correct, due to the notorious "graph connectivity
problem" (15). In this paper, we investigate the graph connectivity problem for
noisy sparse subspace clustering and show that a simple post-processing
procedure is capable of delivering consistent clustering under certain "general
position" or "restricted eigenvalue" assumptions. We also show that our
condition is almost tight with adversarial noise perturbation by constructing a
counter-example. These results provide the first exact clustering guarantee of
noisy SSC for subspaces of dimension greater then 3.


  We consider an instance of black-box quantum metrology in the Gaussian
framework, where we aim to estimate the amount of squeezing applied on an input
probe, without previous knowledge on the phase of the applied squeezing. By
taking the quantum Fisher information (QFI) as the figure of merit, we evaluate
its average and variance with respect to this phase in order to identify probe
states that yield good precision for many different squeezing directions. We
first consider the case of single-mode Gaussian probes with the same energy,
and find that pure squeezed states maximize the average quantum Fisher
information (AvQFI) at the cost of a performance that oscillates strongly as
the squeezing direction is changed. Although the variance can be brought to
zero by correlating the probing system with a reference mode, the maximum AvQFI
cannot be increased in the same way. A different scenario opens if one takes
into account the effects of photon losses: coherent states represent the
optimal single-mode choice when losses exceed a certain threshold and,
moreover, correlated probes can now yield larger AvQFI values than all
single-mode states, on top of having zero variance.


  We test the effects of varying the cosmological parameter values used in the
strong lens modeling process for the six Hubble Frontier Fields (HFF) galaxy
clusters. The standard procedure for generating high fidelity strong lens
models includes careful consideration of uncertainties in the output models
that result from varying model parameters within the bounds of available data
constraints. It is not, however, common practice to account for the effects of
cosmological parameter value uncertainties. The convention is to instead use a
single fiducial "concordance cosmology" and generate lens models assuming zero
uncertainty in cosmological parameter values. We find that the magnification
maps of the individual HFF clusters vary significantly when lens models are
computed using different cosmological parameter values taken from recent
literature constraints from space- and ground-based experiments. Specifically,
the magnification maps have average variances across the best fit models
computed using different cosmologies that are comparable in magnitude to - and
as much as 2.5 times larger than - the model fitting uncertainties in each best
fit model. We also find that estimates of the mass profiles of the cluster
cores themselves vary only slightly when different input cosmological
parameters are used. We conclude that cosmological parameter uncertainty is a
non-negligible source of uncertainty in lens model products for the HFF
clusters, and that it is important that current and future work which relies on
precision strong lensing models take care to account for this additional source
of uncertainty.


  We examine a quantum Otto engine with a harmonic working medium consisting of
two particles to explore the use of wave function symmetry as an accessible
resource. It is shown that the bosonic system displays enhanced performance
when compared to two independent single particle engines, while the fermionic
system displays reduced performance. To this end, we explore the trade-off
between efficiency and power output and the parameter regimes under which the
system functions as engine, refrigerator, or heater. Remarkably, the bosonic
system operates under a wider parameter space both when operating as an engine
and as a refrigerator.


  HST WFPC2 images in B (F450W) and I (F814W) have been obtained for three
starburst (SB) and two post-starburst (PSB) galaxies in the Coma cluster, and
for three such galaxies in the cluster DC2048-52. V (F555W) and I images for an
additional PSB galaxy in Coma have been extracted from the archive. Seven of
these galaxies were previously classified as E/S0 on the basis of ground-based
images, one as Sa, and the other as an irregular.
  The HST images reveal these SB/PSB galaxies to be heterogeneous in
morphology. Nevertheless a common theme is that many of them, especially the SB
galaxies, tend to have centralized spiral structure that appears simply as a
bright ``bulge''on ground-based images. In addition, while some PSB galaxies
exhibit distinct spiral structure, on the whole they have smoother morphologies
than the SB galaxies. The morphologies and luminosity profiles are generally
consistent with substantial starbursts in the form of centralized spiral
structure (the SB galaxies) which fade into smoother morphologies (the PSB
galaxies), with lingering spectroscopic evidence for past central starbursts.
An important point is that the PSB galaxies retain disks, i.e, they have not
evolved into spheroidal systems.


  The data on the charge-exchange reaction K^+Xe --> K^0 p Xe, obtained with
the bubble chamber DIANA, are reanalyzed using increased statistics and updated
selections. Our previous evidence for formation of a narrow pK^0 resonance with
mass near 1538 MeV is confirmed and reinforced. The statistical significance of
the signal reaches some 8\sigma (6\sigma) when estimated as S/\sqrt{B}
(S/\sqrt{B+S}). The mass and intrinsic width of the \Theta^+ baryon are
measured as m = (1538+-2) MeV and \Gamma = (0.39+-0.10) MeV.


  We consider in this work a model for aggregation, where the coalescing
particles initially have a certain number of potential links (called arms)
which are used to perform coagulations. There are two types of arms, male and
female, and two particles may coagulate only if one has an available male arm,
and the other has an available female arm. After a coagulation, the used arms
are no longer available. We are interested in the concentrations of the
different types of particles, which are governed by a modification of
Smoluchowski's coagulation equation -- that is, an infinite system of nonlinear
differential equations. Using generating functions and solving a nonlinear PDE,
we show that, up to some critical time, there is a unique solution to this
equation. The Lagrange Inversion Formula allows in some cases to obtain
explicit solutions, and to relate our model to two recent models for limited
aggregation. We also show that, whenever the critical time is infinite, the
concentrations converge to a state where all arms have disappeared, and the
distribution of the masses is related to the law of the size of some two-type
Galton-Watson tree. Finally, we consider a microscopic model for coagulation:
we construct a sequence of Marcus-Lushnikov processes, and show that it
converges, before the critical time, to the solution of our modified
Smoluchowski's equation.


  Spin nematics break spin-rotational symmetry while maintaining time-reversal
symmetry, analogous to liquid crystal nematics that break spatial rotational
symmetry while maintaining translational symmetry. Although several candidate
spin nematics have been proposed, the identification and characterization of
such a state remain challenging because the spin-nematic order parameter does
not couple directly to experimental probes. KFe$_{0.8}$Ag$_{1.2}$Te$_2$
(K$_5$Fe$_4$Ag$_6$Te$_{10}$, KFAT) is a local-moment magnet consisting of
well-separated 2$\times$2 Fe clusters, and in its ground state the clusters
order magnetically, breaking both spin-rotational and time-reversal symmetries.
Using uniform magnetic susceptibility and neutron scattering measurements we
find a small strain induces sizable spin anisotropy in the paramagnetic state
of KFAT, manifestly breaking spin-rotational symmetry while retaining
time-reversal symmetry, resulting in a strain-induced spin-nematic state in
which the $2\times2$ clusters act as the spin analogue of molecules in a liquid
crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe
its nematic susceptibility, revealing a divergent-like increase upon cooling,
indicating the ordered ground state is driven by a spin-orbital entangled
nematic order parameter.


  Neural language models (LM) trained on diverse corpora are known to work well
on previously seen entities, however, updating these models with dynamically
changing entities such as place names, song titles and shopping items requires
re-training from scratch and collecting full sentences containing these
entities. We aim to address this issue, by introducing entity-aware language
models (EALM), where we integrate entity models trained on catalogues of
entities into the pre-trained LMs. Our combined language model adaptively adds
information from the entity models into the pre-trained LM depending on the
sentence context. Our entity models can be updated independently of the
pre-trained LM, enabling us to influence the distribution of entities output by
the final LM, without any further training of the pre-trained LM. We show
significant perplexity improvements on task-oriented dialogue datasets,
especially on long-tailed utterances, with an ability to continually adapt to
new entities (to an extent).


  While current state-of-the-art Automatic Speech Recognition (ASR) systems
achieve high accuracy on typical speech, they suffer from significant
performance degradation on disordered speech and other atypical speech
patterns. Personalization of ASR models, a commonly applied solution to this
problem, is usually performed in a server-based training environment posing
problems around data privacy, delayed model-update times, and communication
cost for copying data and models between mobile device and server
infrastructure. In this paper, we present an approach to on-device based ASR
personalization with very small amounts of speaker-specific data. We test our
approach on a diverse set of 100 speakers with disordered speech and find
median relative word error rate improvement of 71% with only 50 short
utterances required per speaker. When tested on a voice-controlled home
automation platform, on-device personalized models show a median task success
rate of 81%, compared to only 40% of the unadapted models.


  Mechanical deformation of amorphous solids can be described as consisting of
an elastic part in which the stress increases linearly with strain, up to a
yield point at which the solid either fractures or starts deforming
plastically. It is well established, however, that the apparent linearity of
stress with strain is actually a proxy for a much more complex behavior, with a
microscopic plasticity that is reflected in diverging nonlinear elastic
coefficients. Very generally, the complex structure of the energy landscape is
expected to induce a singular response to small perturbations. In the athermal
quasistatic regime, this response manifests itself in the form of a scale free
plastic activity. The distribution of the corresponding avalanches should
reflect, according to theoretical mean field calculations (Franz and Spigler,
Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity
of a typical local minimum. In this work, we characterize this distribution for
simple models of glass forming systems, and we find that its scaling is
compatible with the mean field predictions for systems above the jamming
transition. These systems exhibit marginal stability, and scaling relations
that hold in the stationary state are examined and confirmed in the elastic
regime. By studying the respective influence of system size and age, we suggest
that marginal stability is systematic in the thermodynamic limit.


  We discuss a novel alternative method of determining the neutrino mass
ordering in medium baseline experiments with reactor anti-neutrinos. Results on
the potential sensitivity of the new method are also presented.


  We extend a recent computation of the dependence of the free energy, F, on
the noncommutative scale $\theta$ to theories with very different UV
sensitivity. The temperature dependence of $F$ strongly suggests that a reduced
number of degrees of freedom contributes to the free energy in the non-planar
sector, $F_{\rm np}$, at high temperature. This phenomenon seems generic,
independent of the UV sensitivity, and can be traced to modes whose thermal
wavelengths become smaller than the noncommutativity scale. The temperature
dependence of $F_{\rm np}$ can then be calculated at high temperature using
classical statistical mechanics, without encountering a UV catastrophe even in
large number of dimensions. This result is a telltale sign of the low number of
degrees of freedom contributing to $F$ in the non-planar sector at high
temperature. Such behavior is in marked contrast to what would happen in a
field theory with a random set of higher derivative interactions.


  We demonstrate a large light absorptance (80%) in a nanometric layer of
quantum dots in rods (QRs) with a thickness of 23 nm. This behavior is
explained in terms of the coherent absorption by interference of the light
incident at a certain angle onto the very thin QR layer. We exploit this
coherent light absorption to enhance the photoluminescent emission from the
QRs. Up to a seven- and fivefold enhancement of the photoluminescence is
observed for p- and s-polarized incident light, respectively.


  The possible description of the vacuum of quantum gravity through the so
called kappa--Poincare group is analyzed considering some of the consequences
of this symmetry in the path integral formulation of nonrelativistic quantum
theory. This study is carried out with two cases, firstly, a free particle, and
finally, the situation of a particle immersed in a homogeneous gravitational
field. It will be shown that the kappa--Poincare group implies the loss of some
of the basic properties associated to Feynman's path integral. For instance,
loss of the group characteristic related to the time dependence of the
evolution operator, or the breakdown of the composition law for amplitudes of
events occurring successively in time. Additionally some similarities between
the present idea and the so called restricted path integral formalism will be
underlined. These analogies advocate the claim that if the kappa--Poincare
group contains some of the physical information of the quantum gravity vacuum,
then this vacuum could entail decoherence. This last result will also allow us
to consider the possibility of analyzing the continuous measurement problem of
quantum theory from a group--theoretical point of view, but now taking into
account the kappa--Poincare symmetries.


  If one isolated species (corporation) is supposed to evolve following the
logistic mapping, then we are tempted to think that the dynamics of two species
(corporations) can be expressed by a coupled system of two discrete logistic
equations. As three basic relationships between two species are present in
Nature, namely symbiosis, predator-prey and competition, three different models
are obtained. Each model is a cubic two-dimensional discrete logistic-type
equation with its own dynamical properties: stationary regime, periodicity,
quasi-periodicity and chaos. We also propose that these models could be useful
for thinking in the different interactions happening in the economic world, as
for instance for the competition and the collaboration between corporations.
Furthermore, these models could be considered as the basic ingredients to
construct more complex interactions in the ecological and economic networks.


  In this paper a complete description of the linear maps
$\phi:W_{n}\rightarrow W_{n}$ that preserve the Lorentz spectrum is given when
$n=2$ and $W_{n}$ is the space $M_{n}$ of $n\times n$ real matrices or the
subspace $S_{n}$ of $M_{n}$ formed by the symmetric matrices. In both cases, it
has been shown that $\phi(A)=PAP^{-1}$ for all $A\in W_{2}$, where $P$ is a
matrix with a certain structure. It was also shown that such preservers do not
change the nature of the Lorentz eigenvalues (that is, the fact that they are
associated with Lorentz eigenvectors in the interior or on the boundary of the
Lorentz cone). These results extend to $n=2$ those for $n\geq 3$ obtained by
Bueno, Furtado, and Sivakumar (2021). The case $n=2$ has some specificities,
when compared to the case $n\geq3,$ due to the fact that the Lorentz cone in
$\mathbb{R}^{2}$ is polyedral, contrary to what happens when it is contained in
$\mathbb{R}^{n}$ with $n\geq3.$ Thus, the study of the Lorentz spectrum
preservers on $W_n = M_n$ also follows from the known description of the Pareto
spectrum preservers on $M_n$.


  Multiple-Tree Overlay Streaming has attracted a great amount of attention
from researchers in the past years. Multiple-tree streaming is a promising
alternative to single-tree streaming in terms of node dynamics and load
balancing, among others, which in turn addresses the perceived video quality by
the streaming user on node dynamics or when heterogeneous nodes join the
network. This article presents a comprehensive survey of the different
aproaches and techniques used in this research area. In this paper we identify
node-disjointness as the property most approaches aim to achieve. We also
present an alternative technique which does not try to achieve this but does
local optimizations aiming global optimizations. Thus, we identify this
property as not being absolute necessary for creating robust and heterogeneous
multi-tree overlays. We identify two main design goals: robustness and support
for heterogeneity, and classify existing approaches into these categories as
their main focus.


  This paper investigates the decoherence effect resulting from the interaction
of squeezed gravitational waves with a system of massive particles in spatial
superposition. This paper investigates the decoherence effect resulting from
the interaction of squeezed gravitational waves with a system of massive
particles in spatial superposition. We first employ the open quantum system
approach to obtain the established decoherence in a spatial superposition of
massive objects induced by squeezed gravitational waves. Subsequently, we focus
on the spin-1/2 particle system, and our analysis reveals that the decoherence
rate depends on both the squeezing strength and the squeezing angle of the
gravitational waves. Our results demonstrate that squeezed gravitational waves
with squeezing strengths of $r_p\geq1.2$ and a squeezing angle of
$\varphi_p=\pi/2$ can induce a 1 % decoherence within 1 s free falling of a
cloud of spin-1/2 particles. This investigation sheds light on the relationship
between squeezed gravitational waves and the coherence of spatial superposition
states in systems of massive particles and their spin. The dependence of
decoherence on squeezing strength and, in the case of spin-$1/2$ particles, on
the squeezing angle paves the way for further exploration and understanding of
the quantum-gravity connection. We suggest that such an experimental setup
could also be employed to eventually investigate the level of squeezing effect
(and hence quantum-related properties) of gravitational waves produced in the
early universe from inflation.


  We investigate the spatial beam dynamics inside a multimode graded-index
fiber under Raman amplification by adopting a semi-analytical variational
approach. The variational analysis provides us with four coupled ordinary
differential equations that govern the beam's dynamics under Raman gain and are
much faster to solve numerically compared to the full nonlinear wave equation.
Their solution also provides considerable physical insight and allows us to
study the impact of important nonlinear phenomena such as self-focusing and
cross-phase modulation. We first show that the variational results corroborate
well with full numerical simulations and then use them to investigate the
signal's dynamics under different initial conditions such as the initial widths
of the pump and signal beams. This allows us to quantify the conditions under
which the quality of a signal beam can improve, without collapse of the beam
owing to self-focusing. While time-consuming full simulations may be needed
when gain saturation and pump depletion must be included, the variational
method is useful for gaining valuable physical insight and for studying
dependence of the amplified beam's width and amplitude on various physical
parameters in a faster fashion.


  In the classical version of online bipartite matching, there is a given set
of offline vertices (aka agents) and another set of vertices (aka items) that
arrive online. When each item arrives, its incident edges -- the agents who
like the item -- are revealed and the algorithm must irrevocably match the item
to such agents. We initiate the study of class fairness in this setting, where
agents are partitioned into a set of classes and the matching is required to be
fair with respect to the classes. We adopt popular fairness notions from the
fair division literature such as envy-freeness (up to one item),
proportionality, and maximin share fairness to our setting. Our class versions
of these notions demand that all classes, regardless of their sizes, receive a
fair treatment. We study deterministic and randomized algorithms for matching
indivisible items (leading to integral matchings) and for matching divisible
items (leading to fractional matchings). We design and analyze three novel
algorithms. For matching indivisible items, we propose an
adaptive-priority-based algorithm, MATCH-AND-SHIFT, prove that it achieves
1/2-approximation of both class envy-freeness up to one item and class maximin
share fairness, and show that each guarantee is tight. For matching divisible
items, we design a water-filling-based algorithm, EQUAL-FILLING, that achieves
(1-1/e)-approximation of class envy-freeness and class proportionality; we
prove (1-1/e) to be tight for class proportionality and establish a 3/4 upper
bound on class envy-freeness. Finally, we build upon EQUAL-FILLING to design a
randomized algorithm for matching indivisible items, EQAUL-FILLING-OCS, which
achieves 0.593-approximation of class proportionality. The algorithm and its
analysis crucially leverage the recently introduced technique of online
correlated selection (OCS) [Fahrbach et al., 2020].


  We review the development of random-matrix theory (RMT) during the last
decade. We emphasize both the theoretical aspects, and the application of the
theory to a number of fields. These comprise chaotic and disordered systems,
the localization problem, many-body quantum systems, the Calogero-Sutherland
model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions.
The review is preceded by a brief historical survey of the developments of RMT
and of localization theory since their inception. We emphasize the concepts
common to the above-mentioned fields as well as the great diversity of RMT. In
view of the universality of RMT, we suggest that the current development
signals the emergence of a new "statistical mechanics": Stochasticity and
general symmetry requirements lead to universal laws not based on dynamical
principles.


  The inspirals of ``small'' ($1 - 100 M_\odot$) compact bodies through highly
relativistic orbits of massive (several $\times 10^5 M_\odot -$ several $\times
10^6 M_\odot$) black holes are among the most anticipated sources for the LISA
gravitational-wave antenna. The measurement of these waves is expected to map
the spacetime of the larger body with high precision, allowing us to test in
detail the hypothesis that black hole candidates are described by the Kerr
metric of general relativity. In this article, we will briefly describe how
these sources can be used to perform such a test. These proposed measurements
are often described as ``testing relativity''. This description is at best
somewhat glib: Because -- at least to date -- all work related to these
measurements assumes general relativity as the theoretical framework in which
these tests are performed, the measurements cannot be said to ``test
relativity'' in a fundamental way. More accurately, they test the {\it nature
of massive compact bodies within general relativity}. A surprising result for
such a test could point to deviations from general relativity, and would
provide an experimentally motivated direction in which to pursue tests of
gravity theories beyond GR.


  We continue the study of the Tomita-Takesaki modular conjugation for a
massless Dirac field in a generic multicomponent region in $1+1$ spacetime
dimensions. In this paper we focus on the computations for a thermal state on a
circle, namely on the euclidean torus. By analytic continuation from the
modular flow we arrive at an explicit expression for the modular conjugation in
this scenario and derive its relevant limits. In contrast to the case of the
vacuum on the line, this new result has a non-local behaviour even for
connected regions. It also presents a novel contribution coming from the
purification one has to introduce in order to deal with a mixed state: a term
that maps the algebra of operators of the region to a copy of the global one,
the so called 'second world' algebra.


  We convert, within polynomial-time and sequential processing, an NP-Complete
Problem into a real-variable problem of minimizing a sum of Rational Linear
Functions constrained by an Asymptotic-Linear-Program. The coefficients and
constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the
time parameter that tends to positive infinity. The number of variables,
constraints, and rational linear functions in the objective, of the
real-variable problem is bounded by a polynomial function of the size of the
NP-Complete Problem. The NP-Complete Problem has a feasible solution,
if-and-only-if, the real-variable problem has a feasible optimal objective
equal to zero. We thus show the strong NP-hardness of this real-variable
optimization problem.


  We propose a novel network traffic matrix decomposition method named Stable
Principal Component Pursuit with Frequency-Domain Regularization (SPCP-FDR),
which improves the Stable Principal Component Pursuit (SPCP) method by using a
frequency-domain noise regularization function. An experiment demonstrates the
feasibility of this new decomposition method.


  We derive flow equations for cold atomic gases with one macroscopically
populated energy level. The generator is chosen such that the ground state
decouples from all other states in the system as the renormalization group flow
progresses. We propose a self-consistent truncation scheme for the flow
equations at the level of three-body operators and show how they can be used to
calculate the ground state energy of a general $N$-body system. Moreover, we
provide a general method to estimate the truncation error in the calculated
energies. Finally, we test our scheme by benchmarking to the exactly solvable
Lieb-Liniger model and find good agreement for weak and moderate interaction
strengths.


  In this paper, we will study the existence of finite time singularity to
harmonic heat flow and their formation patterns. After works of
Coron-Ghidaglia, Ding and Chen-Ding, one knows blow-up solutions under
smallness of initial energy for m>=3. soon later, 2 dimensional blowup
solutions were found by Chang-Ding-Ye. The first part of this paper is devoted
to construction of new examples of finite time blow-up solutions without
smallness conditions for 3<=m<7. In fact, when considering rotational symmetric
harmonic heat flow from B_1\subset R^m to S^m\subset R^{m+1}, we will prove
that the maximal solution blows up in finite time if b>\vartheta_m, and exists
for all time if 0<b<\pi/2. This result can be regarded as a generalization of
results of Chang-Ding-Ye nad Chang-Ding to higher dimensional case, which
relies on a completely different argument. The second part of the paper study
the rate of blow-up solutions. When M is a bounded domain in R^2 and consider
Dirichlet boundary condition on \partial M, Hamilton has obtained that the
blowup rate must be faster than (T-t)^{-1}. Under a similar setting, it was
later improved a litttle by Topping to (T-t)^{-1}|log(T-t)|. In this paper, we
will extend the results to all Riemmanian surfaces M and improve the rate of
Topping to (T-t)^{-1}a(|log(T-t)|) for any positive nondecreasing function
a(\tau) satisfying $\int^\infty_1\frac{d\tau}{a(\tau)}=+\infty$, which is
comparable to a recent result of Raphael-Schweyer for rotational symmetric
solutions. Turning to the higher dimensional case 3<=m<7, we will demonstrate a
completely different phenomenon by showing that all rotational symmetric
blow-up solutions can not be type II, which is different to the case m>=7 by
Bizon-Wasserman. Finally, we also present result of finite time type I blowup
for heat flow from S^m to S^m\subset R^{m+1}, when 3<=m<7 and degree is no less
than 2.


  Reasoning, a crucial aspect of NLP research, has not been adequately
addressed by prevailing models including Large Language Model. Conversation
reasoning, as a critical component of it, remains largely unexplored due to the
absence of a well-designed cognitive model. In this paper, inspired by
intuition theory on conversation cognition, we develop a conversation cognitive
model (CCM) that explains how each utterance receives and activates channels of
information recursively. Besides, we algebraically transformed CCM into a
structural causal model (SCM) under some mild assumptions, rendering it
compatible with various causal discovery methods. We further propose a
probabilistic implementation of the SCM for utterance-level relation reasoning.
By leveraging variational inference, it explores substitutes for implicit
causes, addresses the issue of their unobservability, and reconstructs the
causal representations of utterances through the evidence lower bounds.
Moreover, we constructed synthetic and simulated datasets incorporating
implicit causes and complete cause labels, alleviating the current situation
where all available datasets are implicit-causes-agnostic. Extensive
experiments demonstrate that our proposed method significantly outperforms
existing methods on synthetic, simulated, and real-world datasets. Finally, we
analyze the performance of CCM under latent confounders and propose theoretical
ideas for addressing this currently unresolved issue.


  The disks that surround young stars are mostly composed of molecular gas,
which is harder to detect and interpret than the accompanying dust. Disk mass
measurements have therefore relied on large and uncertain extrapolations from
the dust to the gas. We have developed a grid of models to study the
dependencies of isotopologue CO line strengths on disk structure and
temperature parameters and find that a combination of 13CO and C18O
observations provides a robust measure of the gas mass. We apply this technique
to Submillimeter Array observations of nine circumstellar disks and published
measurements of six well studied disks. We find evidence for selective
photodissociation of C18O and determine masses to within a factor of about
three. The inferred masses for the nine disks in our survey range from 0.7-6
M_Jup, and all are well below the extrapolation from the interstellar medium
gas-to-dust ratio of 100. This is consistent with the low masses of planets
found around such stars, and may be due to accretion or photoevaporation of a
dust-poor upper atmosphere. However, the masses may be underestimated if there
are more efficient CO depletion pathways than those known in molecular clouds
and cold cores.


  Seyfert narrow line region (NLR) emission line ratios are remarkably uniform,
displaying only ~0.5 dex variation between galaxies, and even less within an
individual object. Previous photoionization and shock models of this region
were unable to explain this observation without the introduction of arbitrary
assumptions or additional parameters. Dusty, radiation pressure dominated
photoionization models provide a simple physical mechanism which can reproduce
this spectral uniformity between different objects. In the first paper of this
series we described this model and its implementation in detail, as well as
presenting grids of model emission lines and examining the model structures.
Here we explore these models further, demonstrating their ability to reproduce
the observed Seyfert line ratios on standard line diagnostic diagrams in both
the optical and UV. We also investigate the effects that the variation of
metallicity, density and ionizing spectrum have upon both the new paradigm and
the standard photoionization models used hitherto. Along with the standard
diagnostic diagrams we provide several new diagnostic diagrams in the UV,
Optical and IR. These new diagrams can provide further tests of the dusty,
radiation pressure photoionization paradigm as well as being used as
diagnostics of the metallicity, density and ionizing spectrum of the emission
line clouds.


  A generalization of the AdS/CFT conjecture postulates a duality between IIA
string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't
Hooft limit. At low temperatures string theory describes black holes, whose
thermodynamics may hence be studied using the dual quantum mechanics. This
quantum mechanics is strongly coupled which motivates the use of lattice
techniques. We argue that, contrary to expectation, the theory when discretized
naively will nevertheless recover continuum supersymmetry as the lattice
spacing is sent to zero. We test these ideas by studying the 4 supercharge
version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both
a naive lattice action and a manifestly supersymmetric action. Using Monte
Carlo methods we simulate the Euclidean theories, and study the lattice
continuum limit, for both thermal and non-thermal periodic boundary conditions,
confirming continuum supersymmetry is recovered for the naive action when
appropriate. We obtain results for the thermal system with N up to 12. These
favor the existence of a single deconfined phase for all non-zero temperatures.
These results are an encouraging indication that the 16 supercharge theory is
within reach using similar methods and resources.