  In this work, some of the NLO QCD corrections for pp -> VVjj + X are
presented. A program in Mathematica based on the structure of FeynCalc which
automatically simplifies a set of amplitudes up to the hexagon level of rank 5
has been created for this purpose. We focus on two different topologies. The
first involves all the virtual contributions needed for quadruple electroweak
vector boson production, i.e. pp -> VVVV + X. In the second, the remaining
"bosonic" corrections to electroweak triple vector boson production with an
additional jet (pp -> VVV j + X) are computed. We show the factorization
formula of the infrared divergences of the bosonic contributions for VVVV and
VVVj production with V=(W,Z,gamma). Stability issues associated with the
evaluation of the hexagons up to rank 5 are studied. The CPU time of the
FORTRAN subroutines rounds the 2 milliseconds and seems to be competitive with
other more sophisticated methods. Additionally, in Appendix A the master
equations to obtain the tensor coefficients up to the hexagon level in the
external momenta convention are presented including the ones needed for small
Gram determinants.


  We close a gap appearing at the same time in the author's thesis "Iterated
rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and
in the author's article "Iterated rings of bounded elements and generalizations
of Schm\"udgen's Positivstellensatz" [2].
  [1] Universit\"at Konstanz (2001), available at
http://www.ub.uni-konstanz.de/kops/volltexte/2002/825/
  [2] Journal f\"ur die reine und angewandte Mathematik 554, 19-45 (2003)


  Influence Maximization (IM) is a famous topic in mobile networks and social
computing, which aims at finding a small subset of users to maximize the
influence spread through online information cascade. Recently, some careful
researchers paid attention to diversity of information dissemination,
especially community-aware diversity, and formulated the diversified IM
problem. The diversity is ubiquitous in a lot of real-world applications, but
they are all based on a given community structure. In social networks, we can
form heterogeneous community structures for the same group of users according
to different metrics. Therefore, how to quantify the diversity based on
multiple community structures is an interesting question. In this paper, we
propose the Composite Community-Aware Diversified IM (CC-DIM) problem, which
aims at selecting a seed set to maximize the influence spread and the composite
diversity over all possible community structures under consideration. To
address the NP-hardness of CC-DIM problem, we adopt the technique of reverse
influence sampling and design a random Generalized Reverse Reachable (G-RR) set
to estimate the objective function. The composition of a random G-RR set is
much more complex than the RR set used for the IM problem, which will lead to
inefficiency of traditional sampling-based approximation algorithms. Because of
this, we further propose a two-stage algorithm, Generalized HIST (G-HIST). It
can not only return a $(1-1/e-\varepsilon)$ approximate solution with at least
$(1-\delta)$ probability, but also improve the efficiency of sampling and ease
the difficulty of searching by significantly reducing the average size of G-RR
sets. Finally, we evaluate our G-HIST on real datasets against existing
algorithms. The experimental results show the effectiveness of our proposed
algorithm and its superiority over other baseline algorithms.


  Legal artificial intelligence (LegalAI) aims to benefit legal systems with
the technology of artificial intelligence, especially natural language
processing (NLP). Recently, inspired by the success of pre-trained language
models (PLMs) in the generic domain, many LegalAI researchers devote their
effort to apply PLMs to legal tasks. However, utilizing PLMs to address legal
tasks is still challenging, as the legal documents usually consist of thousands
of tokens, which is far longer than the length that mainstream PLMs can
process. In this paper, we release the Longformer-based pre-trained language
model, named as Lawformer, for Chinese legal long documents understanding. We
evaluate Lawformer on a variety of LegalAI tasks, including judgment
prediction, similar case retrieval, legal reading comprehension, and legal
question answering. The experimental results demonstrate that our model can
achieve promising improvement on tasks with long documents as inputs.


  Since Sep. 2018, LAMOST started the medium-resolution (R $\sim 7500$)
spectral survey (MRS). We proposed the spectral survey of Galactic nebulae,
including \hii\ regions, HH objects, supernova remnants, planetary nebulae and
the special stars with MRS (LAMOST MRS-N). LAMOST MRS-N covers about 1700
square degrees of the northern Galactic plane within $40^\circ < l < 215^\circ$
and $-5^\circ < b < 5^\circ$. In this 5-year survey, we plan to observe about
500 thousand nebulae spectra. According to the commissioning observations, the
nebulae spectra can provide precise radial velocity with uncertainty less than
1 km s$^{-1}$. These high-precision spectral data are of great significance to
our understanding of star formation and evolution.


  Privacy-preserving computation (PPC) methods, such as secure multiparty
computation (MPC) and homomorphic encryption (HE), are deployed increasingly
often to guarantee data confidentiality in computations over private,
distributed data. Similarly, we observe a steep increase in the adoption of
zero-knowledge proofs (ZKPs) to guarantee (public) verifiability of locally
executed computations. We project that applications that are data intensive and
require strong privacy guarantees, are also likely to require verifiable
correctness guarantees, especially when outsourced. While the combination of
methods for verifiability and privacy protection has clear benefits, certain
challenges stand before their widespread practical adoption. In this work, we
analyze existing solutions that combine verifiability with privacy-preserving
computations over distributed data, in order to preserve confidentiality and
guarantee correctness at the same time. We classify and compare 37 different
schemes, regarding solution approach, security, efficiency, and practicality.
Lastly, we discuss some of the most promising solutions in this regard, and
present various open challenges and directions for future research.


  We study several distinguished function algebras on a Polish group $G$, under
the assumption that $G$ is Roelcke precompact. We do this by means of the
model-theoretic translation initiated by Ben Yaacov and Tsankov: we investigate
the dynamics of $\aleph_0$-categorical metric structures under the action of
their automorphism group. We show that, in this context, every strongly
uniformly continuous function (in particular, every Asplund function) is weakly
almost periodic. We also point out the correspondence between tame functions
and NIP formulas, deducing that the isometry group of the Urysohn sphere is
$\Tame\cap\UC$-trivial.


  We investigate backgrounds of Type IIB string theory with null singularities
and their duals proposed in hep-th/0602107. The dual theory is a deformed N=4
Yang-Mills theory in 3+1 dimensions with couplings dependent on a light-like
direction. We concentrate on backgrounds which become AdS_5 x S^5 at early and
late times and where the string coupling is bounded, vanishing at the
singularity. Our main conclusion is that in these cases the dual gauge theory
is nonsingular. We show this by arguing that there exists a complete set of
gauge invariant observables in the dual gauge theory whose correlation
functions are nonsingular at all times. The two-point correlator for some
operators calculated in the gauge theory does not agree with the result from
the bulk supergravity solution. However, the bulk calculation is invalid near
the singularity where corrections to the supergravity approximation become
important. We also obtain pp-waves which are suitable Penrose limits of this
general class of solutions, and construct the Matrix Membrane theory which
describes these pp-wave backgrounds.


  In the bootstrap percolation model, sites in an $L$ by $L$ square are
initially independently declared active with probability $p$. At each time
step, an inactive site becomes active if at least two of its four neighbours
are active. We study the behaviour as $p \to 0$ and $L \to \infty$
simultaneously of the probability $I(L,p)$ that the entire square is eventually
active. We prove that $I(L,p) \to 1$ if $\liminf p \log L > \lambda$, and
$I(L,p) \to 0$ if $\limsup p \log L < \lambda$, where $\lambda = \pi^2/18$. We
prove the same behaviour, with the same threshold $\lambda$, for the
probability $J(L,p)$ that a site is active by time $L$ in the process on the
infinite lattice. The same results hold for the so-called modified bootstrap
percolation model, but with threshold $\lambda' = \pi^2/6$. The existence of
the thresholds $\lambda,\lambda'$ settles a conjecture of Aizenman and
Lebowitz, while the determination of their values corrects numerical
predictions of Adler, Stauffer and Aharony.


  The emergence and development of a power-law tail (PLT) at the high-density
end of the observed column-density distribution is thought to be indicative for
advanced evolution of star-forming molecular clouds. As shown from many
numerical simulations, it corresponds to a morphologically analogous evolution
of the mass-density distribution (\rhopdf). The latter may display also a
second, shallower PLT at the stage of collapse of the first formed protostellar
cores. It is difficult to estimate the parameters of a possible second PLT due
to resolution constraints. To address the issue, we extend the method for the
extraction of single PLTs from arbitrary density distributions suggested by
Veltchev et al.(2019) to detect a second PLT. The technique is elaborated
through tests on an analytic \rhopdf{} and applied to a set of hydrodynamical
high-resolution simulations of isothermal self-gravitating clouds. In all but
one case two PLTs were detected -- the first slope is always steeper and the
second one is typically $\partial \ln V /\ln \rho \sim -1$. These results are
in a good agreement with numerical and theoretical works and do suggest that
the technique extracts correctly double PLTs from smooth PDFs.


  For several decades a portrait of Johannes Kepler has been widely circulating
among professional astronomers, scientific and academic institutions, and the
general public. Despite its provenance and identification having been
questioned in the early part of the last century, this painting has reached
iconic status. We review its history from its first mention in the literature
in the 1870s to a published but virtually unknown judgment of competent art
experts of the 1920s that the work is in fact an early nineteenth century
forgery. We display the painting in context with other more secure portraits
and suggest that if it is based on anything, the painting may derive from the
well known portrait from life of Michael M\"astlin. This correction takes on
certain urgency since 2021 is the 450th anniversary of Kepler's birth.


  This paper strives for motion expressions guided video segmentation, which
focuses on segmenting objects in video content based on a sentence describing
the motion of the objects. Existing referring video object datasets typically
focus on salient objects and use language expressions that contain excessive
static attributes that could potentially enable the target object to be
identified in a single frame. These datasets downplay the importance of motion
in video content for language-guided video object segmentation. To investigate
the feasibility of using motion expressions to ground and segment objects in
videos, we propose a large-scale dataset called MeViS, which contains numerous
motion expressions to indicate target objects in complex environments. We
benchmarked 5 existing referring video object segmentation (RVOS) methods and
conducted a comprehensive comparison on the MeViS dataset. The results show
that current RVOS methods cannot effectively address motion expression-guided
video segmentation. We further analyze the challenges and propose a baseline
approach for the proposed MeViS dataset. The goal of our benchmark is to
provide a platform that enables the development of effective language-guided
video segmentation algorithms that leverage motion expressions as a primary cue
for object segmentation in complex video scenes. The proposed MeViS dataset has
been released at https://henghuiding.github.io/MeViS.


  Si(111) and Ge(111) surface formation energies were calculated using density
functional theory for various biaxial strain states ranging from -0.04 to 0.04,
and for a wide set of experimentally observed surface reconstructions: 3x3,
5x5, 7x7 dimer-adatom-stacking fault reconstructions and c(2x8), 2x2 and
\sqrt{3}x\sqrt{3} adatoms based surfaces. The calculations are compared with
scanning tunneling microscopy data obtained on stepped Si(111) surfaces and on
Ge islands grown on a Si(111) substrate. It is shown that the surface structure
transformations observed in these strained systems are accounted for by a phase
diagram that relates the equilibrium surface structure to the applied strain.
The calculated formation energy of the unstrained Si(111)-9x9
dimer-adatom-stacking fault surface is reported for the first time and it is
higher than corresponding energies of Si(111)-5x5 and Si(111)-7x7
dimer-adatom-stacking fault surfaces as expected. We predict that the Si(111)
surface should adopt a c(2x8) reconstruction when tensile strain is above 0.03.


  Despite the remarkable success of existing methods for few-shot segmentation,
there remain two crucial challenges. First, the feature learning for novel
classes is suppressed during the training on base classes in that the novel
classes are always treated as background. Thus, the semantics of novel classes
are not well learned. Second, most of existing methods fail to consider the
underlying semantic gap between the support and the query resulting from the
representative bias by the scarce support samples. To circumvent these two
challenges, we propose to activate the discriminability of novel classes
explicitly in both the feature encoding stage and the prediction stage for
segmentation. In the feature encoding stage, we design the Semantic-Preserving
Feature Learning module (SPFL) to first exploit and then retain the latent
semantics contained in the whole input image, especially those in the
background that belong to novel classes. In the prediction stage for
segmentation, we learn an Self-Refined Online Foreground-Background classifier
(SROFB), which is able to refine itself using the high-confidence pixels of
query image to facilitate its adaptation to the query image and bridge the
support-query semantic gap. Extensive experiments on PASCAL-5$^i$ and
COCO-20$^i$ datasets demonstrates the advantages of these two novel designs
both quantitatively and qualitatively.


  The creation of massless scalar particles from the quantum vacuum by
spherical shell with time varying radius is studied. In the general case of
motion the equations are derived for the instantaneous basis expansion
coefficients. The examples are considered when the mean number of particles can
be explicitly evaluated in the adiabatic approximation.


  The response to a local strong non-magnetic impurity in the pseudogap phase
is examined in two distinctly different scenarios: phase-fluctuation (PF) of
pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance
state is generally double-peaked near the Fermi level, and is abruptly
broadened by vortex fluctuations slightly above the transition temperature. In
the DDW scenario, the resonance is single-peaked and remains sharp up to
gradual intrinsic thermal broadening, and the resonance energy is analytically
determined to be at minus of the chemical potential.


  In this paper, we explore the spatial redundancy in video recognition with
the aim to improve the computational efficiency. It is observed that the most
informative region in each frame of a video is usually a small image patch,
which shifts smoothly across frames. Therefore, we model the patch localization
problem as a sequential decision task, and propose a reinforcement learning
based approach for efficient spatially adaptive video recognition (AdaFocus).
In specific, a light-weighted ConvNet is first adopted to quickly process the
full video sequence, whose features are used by a recurrent policy network to
localize the most task-relevant regions. Then the selected patches are inferred
by a high-capacity network for the final prediction. During offline inference,
once the informative patch sequence has been generated, the bulk of computation
can be done in parallel, and is efficient on modern GPU devices. In addition,
we demonstrate that the proposed method can be easily extended by further
considering the temporal redundancy, e.g., dynamically skipping less valuable
frames. Extensive experiments on five benchmark datasets, i.e., ActivityNet,
FCVID, Mini-Kinetics, Something-Something V1&V2, demonstrate that our method is
significantly more efficient than the competitive baselines. Code is available
at https://github.com/blackfeather-wang/AdaFocus.


  The Euler Poisson equations describe important physical phenomena in many
applications such as semiconductor modeling and plasma physics. This paper is
to advance our understanding of critical threshold phenomena in such systems in
the presence of different forces. We identify critical thresholds in two damped
Euler Poisson systems, with and without alignment, both with attractive
potential and spatially varying background state. For both systems, we give
respective bounds for subcritical and supercritical regions in the space of
initial configuration, thereby proving the existence of a critical threshold
for each scenario. Key tools include comparison with auxiliary systems, phase
space analysis of the transformed system.


  Lip-reading aims to infer the speech content from the lip movement sequence
and can be seen as a typical sequence-to-sequence (seq2seq) problem which
translates the input image sequence of lip movements to the text sequence of
the speech content. However, the traditional learning process of seq2seq models
always suffers from two problems: the exposure bias resulted from the strategy
of "teacher-forcing", and the inconsistency between the discriminative
optimization target (usually the cross-entropy loss) and the final evaluation
metric (usually the character/word error rate). In this paper, we propose a
novel pseudo-convolutional policy gradient (PCPG) based method to address these
two problems. On the one hand, we introduce the evaluation metric (refers to
the character error rate in this paper) as a form of reward to optimize the
model together with the original discriminative target. On the other hand,
inspired by the local perception property of convolutional operation, we
perform a pseudo-convolutional operation on the reward and loss dimension, so
as to take more context around each time step into account to generate a robust
reward and loss for the whole optimization. Finally, we perform a thorough
comparison and evaluation on both the word-level and sentence-level benchmarks.
The results show a significant improvement over other related methods, and
report either a new state-of-the-art performance or a competitive accuracy on
all these challenging benchmarks, which clearly proves the advantages of our
approach.


  There is a possibility that the event horizon of a Kerr-like black hole with
perfect fluid dark matter (DM) can be destroyed, providing a potential
opportunity for understanding the weak cosmic censorship conjecture of black
holes. In this study, we analyze the influence of the strength parameter of
perfect fluid DM on the destruction of the event horizon of a Kerr-like black
hole with spinning after injecting a test particle and a scalar field. We find
that, when a test particle is incident on the black hole, the event horizon is
destroyed by perfect fluid dark matter for extremal black holes. For nearly
extremal black holes, when the dark matter parameter satisfies $\alpha \in
\left (-r_{h} , 0\right ) \cup \left ( r_{h} ,k_2\right )$ i.e.$(A<0)$, the
event horizon of the black hole will not be destroyed; when the dark matter
parameter satisfies $\alpha \in\left ( k_1 ,-r_{h} \right ]\cup
\left[0,r_{h}\right ]$ i.e.$(A\ge 0)$, the event horizon of the black hole will
be destroyed. When a classical scalar field is incident into the black hole in
the extremal black hole case, we find that the range of mode patterns of the
scalar field that can disrupt the black hole event horizon is different for
different values of the perfect fluid dark matter strength parameter. In the
nearly extremal black hole case, through our analysis, we have found when
$\alpha\neq0 $ and $\alpha\neq\pm\ r_h$ i.e.$A\neq0$, the event horizon of the
black hole can be disrupted. Our research results indicate that dark matter
might be capable of breaking the black hole horizon, thus potentially violating
the weak cosmic censorship conjecture.


  Purpose: To introduce a novel deep learning based approach for fast and
high-quality dynamic multi-coil MR reconstruction by learning a complementary
time-frequency domain network that exploits spatio-temporal correlations
simultaneously from complementary domains.
  Theory and Methods: Dynamic parallel MR image reconstruction is formulated as
a multi-variable minimisation problem, where the data is regularised in
combined temporal Fourier and spatial (x-f) domain as well as in
spatio-temporal image (x-t) domain. An iterative algorithm based on variable
splitting technique is derived, which alternates among signal de-aliasing steps
in x-f and x-t spaces, a closed-form point-wise data consistency step and a
weighted coupling step. The iterative model is embedded into a deep recurrent
neural network which learns to recover the image via exploiting spatio-temporal
redundancies in complementary domains.
  Results: Experiments were performed on two datasets of highly undersampled
multi-coil short-axis cardiac cine MRI scans. Results demonstrate that our
proposed method outperforms the current state-of-the-art approaches both
quantitatively and qualitatively. The proposed model can also generalise well
to data acquired from a different scanner and data with pathologies that were
not seen in the training set.
  Conclusion: The work shows the benefit of reconstructing dynamic parallel MRI
in complementary time-frequency domains with deep neural networks. The method
can effectively and robustly reconstruct high-quality images from highly
undersampled dynamic multi-coil data ($16 \times$ and $24 \times$ yielding 15s
and 10s scan times respectively) with fast reconstruction speed (2.8s). This
could potentially facilitate achieving fast single-breath-hold clinical 2D
cardiac cine imaging.


  We revisit the full variety of observed temporal and spatial distributions of
energetic solar protons in "gradual" solar energetic-particle (SEP) events
resulting from the spatial variations in the shock waves that accelerate them.
Differences in the shock strength at the solar longitude of a spacecraft and at
the footpoint of its connecting magnetic field line, nominally 55 degrees to
the west, drive much of that variation. The shock wave itself, together with
energetic particles trapped near it by self-amplified Alfven waves, forms an
underlying autonomous structure that can drive across magnetic field lines
intact, spreading proton intensities in a widening SEP longitude distribution.
During the formation of this fundamental structure, historically called an
"energetic storm particle" (ESP) event, many SEPs leak away early, amplifying
waves as they flow along well-connected field lines and broaden the
distribution outward; behind this structure between the shock and the Sun a
"reservoir" of quasi-trapped SEPs forms. Very large SEP events are complicated
by additional extensive wave growth that can spread an extended ESP-like
trapping region. The multiplicity of shock-related processes contributing to
the observed SEP profiles causes correlations of the events to be poorly
represented by the peak intensities commonly used. In fact, the extensive
spatial distributions of SEPs are sometimes interwoven with the structures of
the shocks that have accelerated them and sometimes free. We should consider
new questions: Which extremes of the shock contribute most to the SEPs profile
of an event, (1) the shock at the longitude of a spacecraft, (2) the shock ~55
degrees to the west at the footpoint of the field, or (3) SEPs that have
collected in the reservoir? How does the space-time distribution of SEPs
correspond with the underlying space-time distribution of shock strength?


  Fueled by its recent success in provisioning on-site wireless Internet
access, Wi-Fi is currently perceived as the best positioned technology for
pervasive mobile macro network offloading. However, the broad transitions of
multiple collocated operators towards this new paradigm may result in fierce
competition for the common unlicensed spectrum at hand. In this light, our
paper game-theoretically dissects market convergence scenarios by assessing the
competition between providers in terms of network performance, capacity
constraints, cost reductions, and revenue prospects. We will closely compare
the prospects and strategic positioning of fixed line operators offering Wi-Fi
services with respect to competing mobile network operators utilizing
unlicensed spectrum. Our results highlight important dependencies upon
inter-operator collaboration models, and more importantly, upon the ratio
between backhaul and Wi-Fi access bit-rates. Furthermore, our investigation of
medium- to long-term convergence scenarios indicates that a rethinking of
control measures targeting the large-scale monetization of unlicensed spectrum
may be required, as otherwise the used free bands may become subject to
tragedy-of-commons type of problems.


  Excited states of molecules lie in the heart of photochemistry and chemical
reactions. The recent development in quantum computational chemistry leads to
inventions of a variety of algorithms that calculate the excited states of
molecules on near-term quantum computers, but they require more computational
burdens than the algorithms for calculating the ground states. In this study,
we propose a scheme of supervised quantum machine learning which predicts the
excited-state properties of molecules only from their ground state wavefunction
resulting in reducing the computational cost for calculating the excited
states. Our model is comprised of a quantum reservoir and a classical machine
learning unit which processes the measurement results of single-qubit Pauli
operators with the output state from the reservoir. The quantum reservoir
effectively transforms the single-qubit operators into complicated multi-qubit
ones which contain essential information of the system, so that the classical
machine learning unit may decode them appropriately. The number of runs for
quantum computers is saved by training only the classical machine learning
unit, and the whole model requires modest resources of quantum hardware that
may be implemented in current experiments. We illustrate the predictive ability
of our model by numerical simulations for small molecules with and without
noise inevitable in near-term quantum computers. The results show that our
scheme well reproduces the first and second excitation energies as well as the
transition dipole moment between the ground states and excited states only from
the ground state as an input. We expect our contribution will enhance the
applications of quantum computers in the study of quantum chemistry and quantum
materials.


  Purpose: to compare different methods to calculate Laterality Index (LI), a
metric which allows to evaluate hemispheric brain language dominance in
functional MRI examinations (fMRI).
  Methods: Two methods were considered for calculating LI: LI AVE and LI VOL ,
respectively based on the differences between measurements of average and
volume of fMRI signal in brain hemispheres. Laterality curves were obtained
calculating values of LI VOL with increasing thresholds of fMRI signal and
fitted with sigmoidal functions. A model for dominant and co-dominant
classification based on fit parameters has been developed. The two methods and
the sigmoidal model were applied to two cohorts of 93 epileptic patients and 27
healthy subjects undergoing language fMRI examinations with association,
understanding and fluency tasks.
  Results: Despite the different definitions, LI AVE and LI VOL resulted in
equivalent classification of language lateralization. The agreement of
neuroradiological clinical reports with classification of language
lateralization resulting from the proposed methods ranged from 94.6% to 89.2%
for LI metrics and up to 100% for the sigmoidal model. The fit parameters of
the sigmoidal function defined empirical thresholds useful for classification
between dominant and co-dominant, providing similar values for subjects and
epileptic patients for fluency and association tasks. This result supports the
idea of a unique model for language lateralization classification in epileptic
patients and healthy subjects.
  Conclusions: Language lateralization in fMRI can be effectively assessed by
objective metrics. A novel approach based on sigmoidal fit of laterality curves
resulted in higher agreement with clinical reports providing further
information about the strength of language lateralization.


  We consider two inequivalent truncations of the super D9--brane: the
``Heterotic'' and the ``Type I'' truncation. Both of them lead to an N=1
nonlinear supersymmetrization of the D=10 cosmological constant. The
propagating degrees of freedom in the Heterotic and Type I truncation are given
by the components of a D=10 vector multiplet and a single Majorana-Weyl spinor,
respectively. As a by-product we find that, after the Type I truncation, the
Ramond-Ramond super ten-form provides an interesting reformulation of the
Volkov-Akulov action. These results can be extended to all dimensions in which
spacetime filling D-branes exist, i.e. D=3,4,6 and 10.


  The angular distribution and linear polarization of the fluorescence light
following the resonant photoexcitation is investigated within the framework of
the density matrix and second-order perturbation theory. Emphasis has been
placed on "signatures" for determining the level sequence and splitting of
intermediate (partially) overlapping resonances, if analyzed as a function of
the photon energy of the incident light. Detailed computations within the
multiconfiguration Dirac-Fock method have been performed especially for the
$1s^{2}2s^{2}2p^{6}3s\;\, J_{i}=1/2 \,+\, \gamma_{1} \:\rightarrow\:
(1s^{2}2s2p^{6}3s)_{1}3p_{3/2}\;\, J=1/2, \, 3/2
  \:\rightarrow\: 1s^{2}2s^{2}2p^{6}3s\;\, J_{f}=1/2 \,+\, \gamma_{2}$
photoexcitation and subsequent fluorescence emission of atomic sodium. A
remarkably strong dependence of the angular distribution and linear
polarization of the $\gamma_{2}$ fluorescence emission is found upon the level
sequence and splitting of the intermediate $(1s^{2}2s2p^{6}3s)_{1}3p_{3/2}\;\,
J=1/2, \, 3/2$ overlapping resonances owing to their finite lifetime
(linewidth). We therefore suggest that accurate measurements of the angular
distribution and linear polarization might help identify the sequence and small
splittings of closely-spaced energy levels, even if they can not be
spectroscopically resolved.


  Compact low emittance lattice cell providing large dynamic aperture is
essentual for development of extremely low (pm range) emittance storage rings.
As it is well known, a pair of identical sextupoles connected by a minus-identy
matrix transformer in ideal case of kick-like magnets provides infinite dynamic
aperture. Though the finite sextupole length degrades the aperture, it is still
large enough, and in this report we discuss development of the low emittance
lattice cell providing the -I condition for both horizontal and vertical
chromatic sextupoles. Such cell can be used as a module for lattices of
different emittance and length. As an example we develop a 3 GeV 10 pm
emittance storage ring and study its transverse dynamic aperture.


  We revisit the design space of visualizations aiming at identifying and
relating its components. In this sense, we establish a model to examine the
process through which visualizations become expressive for users. This model
has leaded us to a taxonomy oriented to the human visual perception, a
conceptualization that provides natural criteria in order to delineate a novel
understanding for the visualization design space. The new organization of
concepts that we introduce is our main contribution: a grammar for the
visualization design based on the review of former works and of classical and
state-of-the-art techniques. Like so, the paper is presented as a survey whose
structure introduces a new conceptualization for the space of techniques
concerning visual analysis.


  With the increasing adoption of Deep Neural Network (DNN) models as integral
parts of software systems, efficient operational testing of DNNs is much in
demand to ensure these models' actual performance in field conditions. A
challenge is that the testing often needs to produce precise results with a
very limited budget for labeling data collected in field.
  Viewing software testing as a practice of reliability estimation through
statistical sampling, we re-interpret the idea behind conventional structural
coverages as conditioning for variance reduction. With this insight we propose
an efficient DNN testing method based on the conditioning on the representation
learned by the DNN model under testing. The representation is defined by the
probability distribution of the output of neurons in the last hidden layer of
the model. To sample from this high dimensional distribution in which the
operational data are sparsely distributed, we design an algorithm leveraging
cross entropy minimization.
  Experiments with various DNN models and datasets were conducted to evaluate
the general efficiency of the approach. The results show that, compared with
simple random sampling, this approach requires only about a half of labeled
inputs to achieve the same level of precision.


  The Spherical Proportional Counter is a novel type of radiation detector,
with a low energy threshold (typically below 100 eV) and good energy
resolution. This detector is being developed by the network NEWS, which
includes several applications. We can name between many others Dark Matter
searches, low level radon and neutron counting or low energy neutrino detection
from supernovas or nuclear reactors via neutrino-nucleus elastic scattering. In
this context, this works will present the characterization of a spherical
detector of 1 meter diameter using two argon-based mixtures (with methane and
isobutane) and for gas pressures between 50 and 1250 mbar. In each case, the
energy resolution shows its best value in a wide range of gains, limited by the
ballistic effect at low gains and by ion-backflow at high gains. Moreover, the
best energy resolution shows a degradation with pressure. These effects will be
discussed in terms of gas avalanche properties. Finally, the effect of an
electrical field corrector in the homogenity of the gain and the energy
threshold measured in our setup will be also discussed.


  Combining extensive single particle tracking microscopy data of endogenous
lipid granules in living fission yeast cells with analytical results we show
evidence for anomalous diffusion and weak ergodicity breaking. Namely we
demonstrate that at short times the granules perform subdiffusion according to
the laws of continuous time random walk theory. The associated violation of
ergodicity leads to a characteristic turnover between two scaling regimes of
the time averaged mean squared displacement. At longer times the granule motion
is consistent with fractional Brownian motion.


  Stock market returns are typically analyzed using standard regression, yet
they reside on irregular domains which is a natural scenario for graph signal
processing. To this end, we consider a market graph as an intuitive way to
represent the relationships between financial assets. Traditional methods for
estimating asset-return covariance operate under the assumption of statistical
time-invariance, and are thus unable to appropriately infer the underlying true
structure of the market graph. This work introduces a class of graph spectral
estimators which cater for the nonstationarity inherent to asset price
movements, and serve as a basis to represent the time-varying interactions
between assets through a dynamic spectral market graph. Such an account of the
time-varying nature of the asset-return covariance allows us to introduce the
notion of dynamic spectral portfolio cuts, whereby the graph is partitioned
into time-evolving clusters, allowing for online and robust asset allocation.
The advantages of the proposed framework over traditional methods are
demonstrated through numerical case studies using real-world price data.


  Learning to align multiple datasets is an important problem with many
applications, and it is especially useful when we need to integrate multiple
experiments or correct for confounding. Optimal transport (OT) is a principled
approach to align datasets, but a key challenge in applying OT is that we need
to specify a transport cost function that accurately captures how the two
datasets are related. Reliable cost functions are typically not available and
practitioners often resort to using hand-crafted or Euclidean cost even if it
may not be appropriate. In this work, we investigate how to learn the cost
function using a small amount of side information which is often available. The
side information we consider captures subset correspondence -- i.e. certain
subsets of points in the two data sets are known to be related. For example, we
may have some images labeled as cars in both datasets; or we may have a common
annotated cell type in single-cell data from two batches. We develop an
end-to-end optimizer (OT-SI) that differentiates through the Sinkhorn algorithm
and effectively learns the suitable cost function from side information. On
systematic experiments in images, marriage-matching and single-cell RNA-seq,
our method substantially outperform state-of-the-art benchmarks.


  Combinatorial optimisation problems are ubiquitous in artificial
intelligence. Designing the underlying models, however, requires substantial
expertise, which is a limiting factor in practice. The models typically consist
of hard and soft constraints, or combine hard constraints with an objective
function. We introduce a novel setting for learning combinatorial optimisation
problems from contextual examples. These positive and negative examples show -
in a particular context - whether the solutions are good enough or not. We
develop our framework using the MAX-SAT formalism as it is simple yet powerful
setting having these features. We study the learnability of MAX-SAT models. Our
theoretical results show that high-quality MAX-SAT models can be learned from
contextual examples in the realisable and agnostic settings, as long as the
data satisfies an intuitive "representativeness" condition. We also contribute
two implementations based on our theoretical results: one leverages ideas from
syntax-guided synthesis while the other makes use of stochastic local search
techniques. The two implementations are evaluated by recovering synthetic and
benchmark models from contextual examples. The experimental results support our
theoretical analysis, showing that MAX-SAT models can be learned from
contextual examples. Among the two implementations, the stochastic local search
learner scales much better than the syntax-guided implementation while
providing comparable or better models.


  Graph Neural Network (GNN) research has highlighted a relationship between
high homophily (i.e., the tendency of nodes of the same class to connect) and
strong predictive performance in node classification. However, recent work has
found the relationship to be more nuanced, demonstrating that simple GNNs can
learn in certain heterophilous settings. To resolve these conflicting findings
and align closer to real-world datasets, we go beyond the assumption of a
global graph homophily level and study the performance of GNNs when the local
homophily level of a node deviates from the global homophily level. Through
theoretical and empirical analysis, we systematically demonstrate how shifts in
local homophily can introduce performance degradation, leading to performance
discrepancies across local homophily levels. We ground the practical
implications of this work through granular analysis on five real-world datasets
with varying global homophily levels, demonstrating that (a) GNNs can fail to
generalize to test nodes that deviate from the global homophily of a graph, and
(b) high local homophily does not necessarily confer high performance for a
node. We further show that GNNs designed for globally heterophilous graphs can
alleviate performance discrepancy by improving performance across local
homophily levels, offering a new perspective on how these GNNs achieve stronger
global performance.


  In this paper, we present a new class of operators, which we name to be
$n$-Ritt operators. This produces a discrete analogue of $n$-sectorial
operators and generalizes the notion of Ritt operators. We develop a
$H^\infty$-functional calculus for $n$-Ritt operators and prove an useful
transference result. We also generalize the notions of quadratic functional
calculus and $n$-$R$-Ritt operator and discuss some examples.


  We investigate how spectral properties of a measure preserving system
$(X,\mathcal{B},\mu,T)$ are reflected in the multiple ergodic averages arising
from that system. For certain sequences $a:\mathbb{N}\to\mathbb{N}$ we provide
natural conditions on the spectrum $\sigma(T)$ such that for all
$f_1,\ldots,f_k\in L^\infty$, \begin{equation*} \lim_{N\to\infty} \frac{1}{N}
\sum_{n=1}^N \prod_{j=1}^k T^{ja(n)}f_j = \lim_{N\rightarrow\infty} \frac{1}{N}
\sum_{n=1}^N \prod_{j=1}^k T^{jn}f_j \end{equation*} in $L^2$-norm. In
particular, our results apply to infinite arithmetic progressions $a(n)=qn+r$,
Beatty sequences $a(n)=\lfloor \theta n+\gamma\rfloor$, the sequence of
squarefree numbers $a(n)=q_n$, and the sequence of prime numbers $a(n)=p_n$. We
also obtain a new refinement of Szemer\'edi's theorem via Furstenberg's
correspondence principle.
  ERRATUM: Theorem 7.1 in the paper is incorrect as stated, and the error
originates with Proposition 7.5, part (iii), which was incorrectly quoted from
the literature. In the attached erratum we fix the problem by establishing a
slightly weaker version of Theorem 7.1 and use it to give a new proof of
Theorem 4.2. This ensures that all main results in our main article remain
correct. We thank Zhengxing Lian and Jiahao Qiu for bringing this mistake to
our attention.


  Large-scale quantum computation is likely to require massive quantum error
correction (QEC). QEC codes and circuits are described via the stabilizer
formalism, which represents stabilizer states by keeping track of the operators
that preserve them. Such states are obtained by stabilizer circuits (consisting
of CNOT, Hadamard and Phase only) and can be represented compactly on
conventional computers using Omega(n^2) bits, where n is the number of qubits.
Although techniques for the efficient simulation of stabilizer circuits have
been studied extensively, techniques for efficient manipulation of stabilizer
states are not currently available. To this end, we design new algorithms for:
(i) obtaining canonical generators for stabilizer states, (ii) obtaining
canonical stabilizer circuits, and (iii) computing the inner product between
stabilizer states. Our inner-product algorithm takes O(n^3) time in general,
but observes quadratic behavior for many practical instances relevant to QECC
(e.g., GHZ states). We prove that each n-qubit stabilizer state has exactly
4(2^n - 1) nearest-neighbor stabilizer states, and verify this claim
experimentally using our algorithms. We design techniques for representing
arbitrary quantum states using stabilizer frames and generalize our algorithms
to compute the inner product between two such frames.


  Message-passing concurrency is a popular computation model that underlies
several programming languages like, e.g., Erlang, Akka, and (to some extent) Go
and Rust. In particular, we consider a message-passing concurrent language with
dynamic process spawning and selective receives, i.e., where messages can only
be consumed by the target process when they match a specific constraint (e.g.,
the case of Erlang). In this work, we introduce a notion of trace that can be
seen as an abstraction of a class of causally equivalent executions (i.e.,
which produce the same outcome). We then show that execution traces can be used
to identify message races. We provide constructive definitions to compute
message races as well as to produce so-called race variants, which can then be
used to drive new executions which are not causally equivalent to the previous
ones. This is an essential ingredient of state-space exploration techniques for
program verification.


  Single crystals of CrSbSe$_3$, a structurally pseudo-one-dimensional
ferromagnetic semiconductor, were grown using a high-temperature solution
growth technique and were characterized by x-ray diffraction, anisotropic,
temperature- and field-dependent magnetization, temperature-dependent
resistivity and optical absorption measurements. A band gap of 0.7 eV was
determined from both resistivity and optical measurements. At high
temperatures, CrSbSe$_3$ is paramagnetic and isotropic with a Curie-Weiss
temperature of $\sim$145 K and an effective moment of $\sim$4.1 $\mu_B$/Cr. A
ferromagnetic transition occurs at $T_c$ = 71 K. The $a$-axis, perpendicular to
the chains in the structure, is the magnetic easy axis, while the chain axis
direction, along $b$, is the hard axis. Magnetic isotherms measured around
$T_c$ do not follow the behavior predicted by simple mean field critical
exponents for a second order phase transition. A tentative set of critical
exponents is estimated based on a modified Arrott plot analysis, giving
$\beta\sim$0.25, $\gamma\sim$1.38 and $\delta\sim$6.6.


  The coordinate invariant theory of generalised functions of Colombeau and
Meril is reviewed and extended to enable the construction of multi-index
generalised tensor functions whose transformation laws coincide with their
counterparts in classical distribution theory.


  Mutations sometimes increase contagiousness for evolving pathogens. During an
epidemic, scientists use viral genome data to infer a shared evolutionary
history and connect this history to geographic spread. We propose a model that
directly relates a pathogen's evolution to its spatial contagion dynamics --
effectively combining the two epidemiological paradigms of phylogenetic
inference and self-exciting process modeling -- and apply this
\emph{phylogenetic Hawkes process} to a Bayesian analysis of 23,422 viral cases
from the 2014-2016 Ebola outbreak in West Africa. The proposed model is able to
detect individual viruses with significantly elevated rates of spatiotemporal
propagation for a subset of 1,610 samples that provide genome data. Finally, to
facilitate model application in big data settings, we develop massively
parallel implementations for the gradient and Hessian of the log-likelihood and
apply our high performance computing framework within an adaptively
preconditioned Hamiltonian Monte Carlo routine.


  Building spatiotemporal activity models for people's activities in urban
spaces is important for understanding the ever-increasing complexity of urban
dynamics. With the emergence of Geo-Tagged Social Media (GTSM) records,
previous studies demonstrate the potential of GTSM records for spatiotemporal
activity modeling. State-of-the-art methods for this task embed different
modalities (location, time, and text) of GTSM records into a single embedding
space. However, they ignore Non-GeoTagged Social Media (NGTSM) records, which
generally account for the majority of posts (e.g., more than 95\% in Twitter),
and could represent a great source of information to alleviate the sparsity of
GTSM records. Furthermore, in the current spatiotemporal embedding techniques,
less focus has been given to the users, who exhibit spatially motivated
behaviors. To bridge this research gap, this work proposes USTAR, a novel
online learning method for User-guided SpatioTemporal Activity Representation,
which (1) embeds locations, time, and text along with users into the same
embedding space to capture their correlations; (2) uses a novel collaborative
filtering approach based on two different empirically studied user behaviors to
incorporate both NGTSM and GTSM records in learning; and (3) introduces a novel
sampling technique to learn spatiotemporal representations in an online fashion
to accommodate recent information into the embedding space, while avoiding
overfitting to recent records and frequently appearing units in social media
streams. Our results show that USTAR substantially improves the
state-of-the-art for region retrieval and keyword retrieval and its potential
to be applied to other downstream applications such as local event detection.


  The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac
operator, D(A), for the electron dynamics together with the usual self-energy
of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb
gauge. There are no positrons because the electron wave functions are
constrained to lie in the positive spectral subspace of some Dirac operator, D,
but the model is defined for any number, N, of electrons, and hence describes a
true many-body system. In addition to the electrons there are a number, K, of
fixed nuclei with charges \leq Z. If the fields are not quantized but are
classical, it was shown earlier that such a model is always unstable (the
ground state energy E=-\infty) if one uses the customary D(0) to define the
electron space, but is stable (E > - const.(N+K)) if one uses D(A) itself
(provided the fine structure constant \alpha and Z are not too large). This
result is extended to quantized fields here, and stability is proved for \alpha
=1/137 and Z \leq 42. This formulation of QED is somewhat unusual because it
means that the electron Hilbert space is inextricably linked to the photon Fock
space. But such a linkage appears to better describe the real world of photons
and electrons.


  Visual sensation and perception refers to the process of sensing, organizing,
identifying, and interpreting visual information in environmental awareness and
understanding. Computational models inspired by visual perception have the
characteristics of complexity and diversity, as they come from many subjects
such as cognition science, information science, and artificial intelligence. In
this paper, visual perception computational models oriented deep learning are
investigated from the biological visual mechanism and computational vision
theory systematically. Then, some points of view about the prospects of the
visual perception computational models are presented. Finally, this paper also
summarizes the current challenges of visual perception and predicts its future
development trends. Through this survey, it will provide a comprehensive
reference for research in this direction.


  The subsumption problem with respect to terminologies in the description
logic ALC is EXPTIME-complete. We investigate the computational complexity of
fragments of this problem by means of allowed Boolean operators. Hereto we make
use of the notion of clones in the context of Post's lattice. Furthermore we
consider all four possible quantifier combinations for each fragment
parameterized by a clone. We will see that depending on what quantifiers are
available the classification will be either tripartite or a quartering.


  The paper reports on the observation of a new type of instabilities in the
atomic cloud of a magneto-optical trap (MOT). They appear as large amplitude
self-oscillations, either periodic or erratic, depending on the parameters. An
original model taking into account the shadow effect and an homogeneous
distribution of the atoms in the cloud is developped. It allows us to show that
these instabilities originate on the one hand from an anomalous Hopf
bifurcation, and on the other hand from the extreme sensitivity of the system
to noise.


  We study the effect of point-defect chalcogen vacancies on the optical
properties of monolayer transition metal dichalcogenides using ab initio GW and
Bethe-Salpeter equation calculations. We find that chalcogen vacancies
introduce unoccupied in-gap states and occupied resonant defect states within
the quasiparticle continuum of the valence band. These defect states give rise
to a number of strongly-bound defect excitons and hybridize with excitons of
the pristine system, reducing the valley-selective circular dichroism. Our
results suggest a pathway to tune spin-valley polarization and other optical
properties through defect engineering.


  In the paper we consider a functional-difference operator $H=U+U^{-1}+V$,
where $U$ and $V$ are self-adjoint Weyl operators satisfying $UV=q^{2}VU$ with
$q=e^{\pi i\tau}$ and $\tau>0$. The operator $H$ has applications in the
conformal field theory and in the representation theory of quantum groups.
Using modular quantum dilogarithm - a $q$-deformation of the Euler's
dilogarithm - we define the scattering solution and the Jost solutions, derive
an explicit formula for the resolvent of the self-adjoint operator $H$ in the
Hilbert space $L^{2}(\mathbb{R})$, and prove the eigenfunction expansion
theorem. The latter is a $q$-deformation of the well-known Kontorovich-Lebedev
transform in the theory of special functions. We also present a formulation of
the scattering theory for the operator $H$.


  Denoising diffusion probabilistic models (DDPMs) have achieved unprecedented
success in computer vision. However, they remain underutilized in medical
imaging, a field crucial for disease diagnosis and treatment planning. This is
primarily due to the high computational cost associated with (1) the use of
large number of time steps (e.g., 1,000) in diffusion processes and (2) the
increased dimensionality of medical images, which are often 3D or 4D. Training
a diffusion model on medical images typically takes days to weeks, while
sampling each image volume takes minutes to hours. To address this challenge,
we introduce Fast-DDPM, a simple yet effective approach capable of improving
training speed, sampling speed, and generation quality simultaneously. Unlike
DDPM, which trains the image denoiser across 1,000 time steps, Fast-DDPM trains
and samples using only 10 time steps. The key to our method lies in aligning
the training and sampling procedures to optimize time-step utilization.
Specifically, we introduced two efficient noise schedulers with 10 time steps:
one with uniform time step sampling and another with non-uniform sampling. We
evaluated Fast-DDPM across three medical image-to-image generation tasks:
multi-image super-resolution, image denoising, and image-to-image translation.
Fast-DDPM outperformed DDPM and current state-of-the-art methods based on
convolutional networks and generative adversarial networks in all tasks.
Additionally, Fast-DDPM reduced the training time to 0.2x and the sampling time
to 0.01x compared to DDPM. Our code is publicly available at:
https://github.com/mirthAI/Fast-DDPM.


  Inelastic neutron scattering (INS) experiments have been performed on the
Cu$_3$ triangular molecular nanomagnet using powder samples. In the medium
resolution INS spectrum measured, there are two peaks at $\hbar\omega=0.5$ and
0.6 meV. Comparing the observed $Q$ dependences of these peaks with
calculations, these two INS peaks originate from the Cu$_3$ cluster. From the
observed peak position, width, and intensity, we have determined the optimum
parameters of the spin Hamiltonian consisted of the antiferromagnetic exchange
and the Dzyaloshinsky-Moriya interactions, which can also reproduce the
magnetic susceptibility measurement. In addition, we have directly observed
that the ground state quartet is split into two doublets with the energy
separation of 0.103 meV using high-resolution neutron spectroscopy, which
exactly corresponds to that expected from the optimum parameters obtained from
the medium resolution xperiment. The temperature dependences of the integrated
intensities of the 0.5 and 0.6 meV peaks are well reproduced by the Boltzmann
distribution of the energy levels of the model Hamiltonian below 10 K.
Furthermore, the inelastic peaks were visible even at very high temperatures as
50 K. This indicates extraordinary weak coupling between phonons (or any other
perturbations) and spin states in the Cu$_3$ cluster, compared to the other
known molecular nanomagnets.


  In this paper we investigate multi-agent discrete-event systems with partial
observation. The agents can be divided into several groups in each of which the
agents have similar (isomorphic) state transition structures, and thus can be
relabeled into the same template. Based on the template a scalable supervisor
whose state size and computational cost are independent of the number of agents
is designed for the case of partial observation. The scalable supervisor under
partial observation does not need to be recomputed regardless of how many
agents are added to or removed from the system. We generalize our earlier
results to partial observation by proposing sufficient conditions for safety
and maximal permissiveness of the scalable least restrictive supervisor on the
template level. An example is provided to illustrate the proposed scalable
supervisory synthesis.


  We present a method to derive positions of molecular clouds along the lines
of sight from a quantitative comparison between 2.6 mm CO emission lines and 18
cm OH absorption lines, and apply it to the central kiloparsecs of the Milky
Way. With some simple but justifiable assumptions, we derive a face-on
distribution of the CO brightness and corresponding radial velocity in the
Galactic centre without any help of kinematical models. The derived face-on
distribution of the gas is elongated and inclined so that the Galactic-eastern
(positive longitude) side is closer to us. The gas distribution is dominated by
a barlike central condensation, whose apparent size is 500x200 pc. A ridge
feature is seen to stretch from one end of the central condensation, though its
elongated morphology might be artificial. The velocity field shows clear signs
of noncircular motion in the central condensation. The `expanding molecular
ring' feature corresponds to the peripheral region surrounding the central
condensation with the Galactic-eastern end being closer to us. These
characteristics agree with a picture in which the kinematics of the gas in the
central kiloparsec of the Galaxy is under a strong influence of a barred
potential. The face-on distribution of the in situ pressure of the molecular
gas is derived from the CO multiline analysis. The derived pressure is found to
be highest in the central 100 pc. In this region, the gas is accumulating and
is forming stars.


  Soft condensed matter structures often challenge us with complex many-body
phenomena governed by collective modes spanning wide spatial and temporal
domains. In order to successfully tackle such problems mesoscopic
coarse-grained (CG) statistical models are being developed, providing a
dramatic reduction in computational complexity. CG models provide an
intermediate step in the complex statistical framework of linking the
thermodynamics of condensed phases with the properties of their constituent
atoms and molecules. These allow us to offload part of the problem to the CG
model itself and reformulate the remainder in terms of reduced CG phase space.
However, such exchange of pawns to chess pieces, or ``Hamiltonian
renormalization'', is a radical step and the thermodynamics of the primary
atomic and CG models could be markedly different. Here, we present a
comprehensive study of the phase diagram including binodal and interfacial
properties of a novel soft CG model, which includes finite-range attraction and
supports liquid phases. Although the model is rooted in similar arguments to
the Lennard-Jones (LJ) atomic pair potential, its phase behaviour is
qualitatively different from that of LJ and features several anomalies such as
an unusually broad liquid range, change in concavity of the liquid coexistence
branch with variation of the model parameters, volume contraction on fusion,
temperature of maximum density in the liquid phase and negative thermal
expansion in the solid phase. These results provide new insight into the
connection between simple potential models and complex emergent condensed
matter phenomena.


  It has been predicted theoretically and indirectly confirmed experimentally
that single-layer CrX$_3$ (X=Cl, Br, I) might be the prototypes of topological
magnetic insulators (TMI). In this work, by using first-principles calculations
combined with atomistic spin dynamics we provide a complete picture of the
magnetic interactions and magnetic excitations in CrX$_3$. The focus is here on
the two most important aspects for the actual realization of TMI, namely the
relativistic magnetic interactions and the finite-size (edge) effects. We
compute the full interaction tensor, which includes both Kitaev and
Dzyaloshinskii-Moriya terms, which are considered as the most likely mechanisms
for stabilizing topological magnons. First, we instigate the properties of bulk
CrI$_3$ and compare the simulated magnon spectrum with the experimental data
[Phys. Rev. X 8, 041028 (2018)]. Our results suggest that a large size of
topological gap, seen in experiment ($\approx$ 4 meV), can not be explained by
considering pair-wise spin interactions only. We identify several possible
reasons for this disagreement and suggest that a pronounced magneto-elastic
coupling should be expected in this class of materials. The magnetic
interactions in the monolayers of CrX$_3$ are also investigated. The strength
of the anisotropic interactions is shown to scale with the position of halide
atom in the Periodic Table, the heavier the element the larger is the
anisotropy. Comparing the magnons for the bulk and single-layer CrI$_3$, we
find that the size of the topological gap becomes smaller in the latter case.
Finally, we investigate finite-size effects in monolayers and demonstrate that
the anisotropic couplings between Cr atoms close to the edges are much stronger
than those in ideal periodic structure. This should have impact on the dynamics
of the magnon edge modes in this class of materials.


  Exact diagonalizations with a realistic interaction show that configurations
with four neutrons in a major shell and four protons in another -or the same-
major shell, behave systematically as backbending rotors. The dominance of the
$q\cdot q$ component of the interaction is explained by an approximate form of
SU3 symmetry. It is suggested that these configurations are associated with the
onset of rotational motion in medium and heavy nuclei.


  We study a closed model of a universe filled with viscous fluid and
quintessence matter components. The dynamical equations imply that the universe
might look like an accelerated flat Friedmann-Robertson-Walker (FRW) universe
at low redshift. We consider here dissipative processes which obey a causal
thermodynamics. Here, we account for the entropy production via causal
dissipative inflation.


  Recent experimental work has suggested that electroosmotic flows (EOF)
through conical nanopores exhibit rectification in the opposite sense to the
well-studied effect of ionic current rectification. A positive bias voltage
generates large EOF and small current, while negative voltages generate small
EOF and large current. Here we systematically investigate this effect using
finite-element simulations. We find that inside the pore, the electric field
and salt concentration are inversely correlated, which leads to the inverse
relationship between the magnitudes of EOF and current. Rectification occurs
when the pore is driven into states characterized by different salt
concentrations depending on the sign of the voltage. The mechanism responsible
for this behaviour is concentration polarization, which requires the pore to
exhibit the properties of permselectivity and asymmetry.


  We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple
datasets collected from different tasks, we train a multi-task policy to
perform well in unseen tasks sampled from the same distribution. The task
identities of the unseen tasks are not provided. To perform well, the policy
must infer the task identity from collected transitions by modelling its
dependency on states, actions and rewards. Because the different datasets may
have state-action distributions with large divergence, the task inference
module can learn to ignore the rewards and spuriously correlate $\textit{only}$
state-action pairs to the task identity, leading to poor test time performance.
To robustify task inference, we propose a novel application of the triplet
loss. To mine hard negative examples, we relabel the transitions from the
training tasks by approximating their reward functions. When we allow further
training on the unseen tasks, using the trained policy as an initialization
leads to significantly faster convergence compared to randomly initialized
policies (up to $80\%$ improvement and across 5 different Mujoco task
distributions). We name our method $\textbf{MBML}$
($\textbf{M}\text{ulti-task}$ $\textbf{B}\text{atch}$ RL with
$\textbf{M}\text{etric}$ $\textbf{L}\text{earning}$).


  A sample of 45 symbiotic stars observed in the direction of the galactic
bulge are classified in spectral type using TiO $\lambda \lambda 6180, 7100
\AA$ and VO $\lambda \lambda 7865 \AA$ absorption feature indices and visual
comparison. The effective temperatures obtained are used together with K data
from the literature to estimate the bolometric luminosity of the giant
components if located at d=8.5 kpc. The ($T_{eff}$, $L/L_{\odot}$) pairs are
plotted on the HR diagram together with evolutionary tracks for metal rich
intermediate mass stars. The mass of the giant components seem to be scattered
in the interval ($\sim 1.5 - \sim 4 M_{\odot}$). The giant components of D-type
symbiotics appear as if they were more evolved objects than the corresponding
giants in S-type systems. Nevertheless, it is unlikely that they form an
evolutionary sequence. The results point also to the restriction of the
symbiotic phenomenon to the thermally pulsating phase of the AGB, strengthening
an accelerated mass loss scenario for the latest evolutionary stages of
intermediate mass stars.


  We perform a unified description of the experimental data of the $\pi^+\pi^-$
and $J/\psi\pi^\pm$ invariant mass spectra for $e^+e^- \rightarrow J/\psi
\pi^+\pi^-$ and the $D^0 D^{\ast-}$ mass spectrum for $e^+e^- \rightarrow D^0
D^{\ast-} \pi^+$ at $e^+e^-$ center-of-mass energies 4.23 and 4.26 GeV. The
analysis takes into account open-charm meson loops that contain triangle
singularities, the $J/\psi\pi$-$D\bar D^*$ coupled-channel interaction
respecting unitarity, and the strong $\pi\pi$-$K\bar K$ final state interaction
using dispersion relations. The analysis leads to a precise determination of
the $Z_c(3900)$ pole with the pole mass and width $(3880.7 \pm
1.7_\text{stat}\pm 22.4_\text{syst})$ MeV and $(35.9 \pm 1.4_\text{stat}\pm
15.3_\text{syst})$ MeV, respectively, and hints at that the $D\bar D^*$
molecular and non-molecular components are of similar importance in the
$Z_c(3900)$ formation.


  Recent experiments have demonstrated that small-scale rotary devices
installed in a microfluidic channel can be driven passively by the underlying
flow alone without resorting to conventionally applied magnetic or electric
fields. In this work, we conduct a theoretical and numerical study on such a
flow-driven "watermill" at low Reynolds number, focusing on its hydrodynamic
features. We model the watermill by a collection of equally-spaced rigid rods.
Based on the classical resistive force (RF) theory and direct numerical
simulations, we compute the watermill's instantaneous rotational velocity as a
function of its rod number $N$, position and orientation. When $N \geq 4$, the
RF theory predicts that the watermill's rotational velocity is independent of
$N$ and its orientation, implying the full rotational symmetry (of infinity
order), even though the geometrical configuration exhibits a lower-fold
rotational symmetry; the numerical solutions including hydrodynamic
interactions show a weak dependence on $N$ and the orientation. In addition, we
adopt a dynamical system approach to identify the equilibrium positions of the
watermill and analyse their stability. We further compare the theoretically and
numerically derived rotational velocities, which agree with each other in
general, while considerable discrepancy arises in certain configurations owing
to the hydrodynamic interactions neglected by the RF theory. We confirm this
conclusion by employing the RF-based asymptotic framework incorporating
hydrodynamic interactions for a simpler watermill consisting of two or three
rods and we show that accounting for hydrodynamic interactions can
significantly enhance the accuracy of the theoretical predictions.


  We report the results of our investigation of magnetic, thermodynamic and
dielectric properties of Ca substituted half-doped orthochromite,
Dy0.6Ca0.4Fe0.5Cr0.5O3. Magnetic susceptibility and heat capacity data bring
out that this compound undergoes two antiferromagnetic transitions, one at ~132
and the other at ~22 K. These values are higher than those of DyFe0.5Cr0.5O3.
This finding highlights that non-magnetic hole doping in form of Ca+2 in the
place of magnetic Dy+3 tends to enhance magnetic transition temperatures in
this half-doped orthochromite. We attribute it to possible change in the
valence state of Cr/ Fe-ion ions due to hole doping. Dielectric anomalies are
also seen near the magnetic ordering temperatures indicating magnetodielectric
coupling, which is confirmed by magnetic field dependent dielectric studies.
The most notable observation is that magnetodielectric coupling strength gets
significantly enhanced as compared to DyFe0.5Cr0.5O3. The results reveal that
it is possible to tune magnetodielectric coupling by hole doping in this
system.


  The simplest extension of the Standard Model by only one real singlet scalar
can explain the observed dark matter relic density while giving simultaneously
a strongly first-order electroweak phase transition in the early universe.
However, after imposing the invisible Higgs decay constraint from the LHC, the
parameter space of the single scalar model shrinks to regions with only a few
percent of the DM relic abundance and when adding the direct detection bound,
e.g. from XENON100, it gets excluded completely. In this paper, we extend the
Standard Model with two real guage singlet scalars, here $s$ and $s'$, and show
that the electroweak symmetry breaking may occur via different channels.
Despite very restrictive first-order phase transition conditions for the
two-scalar model in comparison to the single scalar model, there is a viable
space of parameters in different phase transition channels that simultaneously
explains a fraction or the whole dark matter relic density, a strongly
first-order electroweak phase transition and still evading the direct detection
bounds from the latest LUX/XENON experiments while respecting the invisible
Higgs decay width constraint from the LHC.


  This work presents numerical results on the transport of heat and chemical
species by shear-induced turbulence in strongly stratified but thermally
diffusive environments. The shear instabilities driven in this regime are
sometimes called "secular" shear instabilities, and can take place even when
the gradient Richardson number of the flow (the square of the ratio of the
buoyancy frequency to the shearing rate) is large, provided the P\'eclet number
(the ratio of the thermal diffusion timescale to the turnover timescale of the
turbulent eddies) is small. We have identified a set of simple criteria to
determine whether these instabilities can take place or not. Generally
speaking, we find that they may be relevant whenever the thermal diffusivity of
the fluid is very large (typically larger than $10^{14}$cm$^2$/s), which is the
case in the outer layers of high-mass stars ($M\ge 10 M_\odot$) for instance.
Using a simple model setup in which the shear is forced by a spatially
sinusoidal, constant-amplitude body-force, we have identified several regimes
ranging from effectively unstratified to very strongly stratified, each with
its own set of dynamical properties. Unless the system is in one of the two
extreme regimes (effectively unstratified or completely stable), however, we
find that (1) only about 10% of the input power is used towards heat transport,
while the remaining 90% is viscously dissipated; (2) that the effective
compositional mixing coefficient is well-approximated by the model of Zahn
(1992), with $D \simeq 0.02 \kappa_T /J$ where $\kappa_T$ is the thermal
diffusivity and $J$ is the gradient Richardson number. These results need to be
confirmed, however, with simulations in different model setups and at higher
effective Reynolds number.


  Thermoacoustic instabilities in gas turbines and aeroengine combustors falls
within the category of complex systems. They can be described
phenomenologically using nonlinear stochastic differential equations, which
constitute the grounds for output-only model-based system identification. It
has been shown recently that one can extract the governing parameters of the
instabilities, namely the linear growth rate and the nonlinear component of the
thermoacoustic feedback, using dynamic pressure time series only. This is
highly relevant for practical systems, which cannot be actively controlled due
to a lack of cost-effective actuators. The thermoacoustic stability is given by
the linear growth rate, which results from the combination of the acoustic
damping and the coherent feedback from the flame. In this paper, it is shown
that it is possible to quantify the acoustic damping of the system, and thus to
separate its contribution to the linear growth rate from the one of the flame.
This is achieved by post-processing in a simple way simultaneously acquired
chemiluminescence and acoustic pressure data. It provides an additional
approach to further unravel from observed time series the key mechanisms
governing the system dynamics. This straightforward method is illustrated here
using experimental data from a combustion chamber operated at several linearly
stable and unstable operating conditions.


  We explore the phase diagram of strongly interacting matter as a function of
temperature and baryon number density, using a class of models for two-flavor
QCD in which the interaction between quarks is modelled by that induced by
instantons. Our treatment allows us to investigate the possible simultaneous
formation of condensates in the conventional quark--anti-quark channel
(breaking chiral symmetry) and in a quark--quark channel leading to color
superconductivity: the spontaneous breaking of color symmetry via the formation
of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs
via a first order transition between a phase with low (or zero) baryon density
and a high density color superconducting phase. We find color superconductivity
in the high density phase for temperatures less than of order tens to 100 MeV,
and find coexisting $<qq>$ and $<\bar q q>$ condensates in this phase in the
presence of a current quark mass. At high temperatures, the chiral phase
transition is second order in the chiral limit and is a smooth crossover for
nonzero current quark mass. A tricritical point separates the first order
transition at high densities from the second order transition at high
temperatures. In the presence of a current quark mass this tricritical point
becomes a second order phase transition with Ising model exponents, suggesting
that a long correlation length may develop in heavy ion collisions in which the
phase transition is traversed at the appropriate density.


  Graph Neural Network (GNN) architectures are defined by their implementations
of update and aggregation modules. While many works focus on new ways to
parametrise the update modules, the aggregation modules receive comparatively
little attention. Because it is difficult to parametrise aggregation functions,
currently most methods select a ``standard aggregator'' such as
$\mathrm{mean}$, $\mathrm{sum}$, or $\mathrm{max}$. While this selection is
often made without any reasoning, it has been shown that the choice in
aggregator has a significant impact on performance, and the best choice in
aggregator is problem-dependent. Since aggregation is a lossy operation, it is
crucial to select the most appropriate aggregator in order to minimise
information loss. In this paper, we present GenAgg, a generalised aggregation
operator, which parametrises a function space that includes all standard
aggregators. In our experiments, we show that GenAgg is able to represent the
standard aggregators with much higher accuracy than baseline methods. We also
show that using GenAgg as a drop-in replacement for an existing aggregator in a
GNN often leads to a significant boost in performance across various tasks.


  We study a 2-qubit nuclear spin system for realizing an arbitrary geometric
quantum phase gate by means of non-adiabatic operation. A single magnetic pulse
with multi harmonic frequencies is applied to manipulate the quantum states of
2-qubit instantly. Using resonant transition approximation, the time dependent
Hamiltonian of two nuclear spins can be solved analytically. The time evolution
of the wave function is obtained without adiabatic approximation. The
parameters of magnetic pulse, such as the frequency, amplitude, phase of each
harmonic part as well as the time duration of the pulse, are determined for
achieving an arbitrary non-adiabatic geometric phase gate. The derivation of
non-adiabatic geometric controlled phase gates and A-A phase are also
addressed.


  The low frequency part of the gravitational wave spectrum generated by local
physics, such as a phase transition or parametric resonance, is largely fixed
by causality, offering a clean window into the early Universe. In this work,
this low frequency end of the spectrum is analyzed with an emphasis on a
physical understanding, such as the suppressed production of gravitational
waves due to the excitation of an over-damped harmonic oscillator and their
enhancement due to being frozen out while outside the horizon. Due to the
difference between sub-horizon and super-horizon physics, it is inevitable that
there will be a distinct spectral feature that could allow for the direct
measurement of the conformal Hubble rate at which the phase transition
occurred. As an example, free-streaming particles (such as the gravity waves
themselves) present during the phase transition affect the production of
super-horizon modes. This leads to a steeper decrease in the spectrum at low
frequencies as compared to the well-known causal $k^3$ super-horizon scaling of
stochastic gravity waves. If a sizable fraction of the energy density is in
free-streaming particles, they even lead to the appearance of oscillatory
features in the spectrum. If the universe was not radiation dominated when the
waves were generated, a similar feature also occurs at the transition between
sub-horizon to super-horizon causality. These features are used to show
surprising consequences, such as the fact that a period of matter domination
following the production of gravity waves actually increases their power
spectrum at low frequencies.


  We examine the infrared properties of 43 high redshift (0.1<z<1.2),
infrared-luminous galaxies in the Extended Groth Strip (EGS), selected by a
deep 70 micron survey with the Multiband Imaging Photometer on Spitzer (MIPS).
In addition and with reference to starburst-type Spectral Energy Distributions
(SEDs), we derive a set of equations for estimating the total infrared
luminosity (L_IR) in the range 8-1000 microns using photometry from at least
one MIPS band. 42 out of 43 of our sources' optical/infrared SEDs
(lambda_observed < 160 microns) are starburst-type, with only one object
displaying a prominent power-law near-infrared continuum. For a quantitative
analysis, models of radiation transfer in dusty media are fit onto the infrared
photometry, revealing that the majority of galaxies are represented by high
extinction, A_v>35 and for a large fraction (~50 per cent) the SED turns over
into the Rayleigh-Jeans regime at wavelengths longward of 90 microns. For
comparison, we also fit semi-empirical templates based on local galaxy data,
however, these underestimate the far-infrared SED shape by a factor of at least
2 and in extreme cases up to 10 for the majority (~70 per cent) of the sources.
Further investigation of SED characteristics reveals that the mid-infrared
(70/24 microns) continuum slope is decoupled from various galaxy properties
such as the total infrared luminosity and far-infrared peak, quantified by the
L_160/L_70 ratio. In view of these results, we propose that these high-redshift
galaxies have different properties to their local counterparts, in the sense
that large amounts of dust cause heavy obscuration and are responsible for an
additional cold emissive component, appearing as a far-infrared excess in their
SEDs.


  It was conjectured that the augmentation ideal of a dihedral quandle of even
order $n>2$ satisfies $|\Delta^k(\text{R}_n)/\Delta^{k+1}(\text{R}_{n})|=n$ for
all $k\geq 2$. In this article we provide a counterexample against this
conjecture.


  We review recent results in the study of attractor horizon geometries (with
non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in
supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number
n_{V} of Abelian vector multiplets, outlining the fundamentals of the special
Kaehler geometry of the vector multiplets' scalar manifold (of complex
dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS
(non-supersymmetric) ones with non-vanishing central charge.
  For symmetric special Kaehler geometries, we present the complete
classification of the orbits in the symplectic representation of the classical
U-duality group (spanned by the black hole charge configuration supporting the
attractors), as well as of the moduli spaces of non-BPS attractors (spanned by
the scalars which are not stabilized at the black hole event horizon).
  Finally, we report on an analogous classification for N>2-extended, d=4
ungauged supergravities, in which also the 1/N-BPS attractors yield a related
moduli space.


  To promote better performance-bandwidth trade-off for multi-agent perception,
we propose a novel distilled collaboration graph (DiscoGraph) to model
trainable, pose-aware, and adaptive collaboration among agents. Our key
novelties lie in two aspects. First, we propose a teacher-student framework to
train DiscoGraph via knowledge distillation. The teacher model employs an early
collaboration with holistic-view inputs; the student model is based on
intermediate collaboration with single-view inputs. Our framework trains
DiscoGraph by constraining post-collaboration feature maps in the student model
to match the correspondences in the teacher model. Second, we propose a
matrix-valued edge weight in DiscoGraph. In such a matrix, each element
reflects the inter-agent attention at a specific spatial region, allowing an
agent to adaptively highlight the informative regions. During inference, we
only need to use the student model named as the distilled collaboration network
(DiscoNet). Attributed to the teacher-student framework, multiple agents with
the shared DiscoNet could collaboratively approach the performance of a
hypothetical teacher model with a holistic view. Our approach is validated on
V2X-Sim 1.0, a large-scale multi-agent perception dataset that we synthesized
using CARLA and SUMO co-simulation. Our quantitative and qualitative
experiments in multi-agent 3D object detection show that DiscoNet could not
only achieve a better performance-bandwidth trade-off than the state-of-the-art
collaborative perception methods, but also bring more straightforward design
rationale. Our code is available on https://github.com/ai4ce/DiscoNet.


  We construct the entire generalized Kac-Moody Lie algebra as a quotient of
the positive part of another generalized Kac-Moody Lie algebra. The positive
part of a generalized Kac-Moody Lie algebra can be constructed from
representations of quivers using Ringel's Hall algebra construction. Thus we
give a direct realization of the entire generalized Kac-Moody Lie algebra.


  In the age of artificial intelligence (AI), providing learners with suitable
and sufficient explanations of AI-based recommendation algorithm's output
becomes essential to enable them to make an informed decision about it.
However, the rapid development of AI approaches for educational recommendations
and their explainability is not accompanied by an equal level of evidence-based
experimentation to evaluate the learning effect of those explanations. To
address this issue, we propose an experimental web-based tool for evaluating
multimodal and large language model (LLM) based explainability approaches. Our
tool provides a comprehensive set of modular, interactive, and customizable
explainability elements, which researchers and educators can utilize to study
the role of individual and hybrid explainability methods. We design a two-stage
evaluation of the proposed tool, with learners and with educators. Our
preliminary results from the first stage show high acceptance of the tool's
components, user-friendliness, and an induced motivation to use the
explanations for exploring more information about the recommendation.


  This study analyzes crop yield prediction in India from 1997 to 2020,
focusing on various crops and key environmental factors. It aims to predict
agricultural yields by utilizing advanced machine learning techniques like
Linear Regression, Decision Tree, KNN, Na\"ive Bayes, K-Mean Clustering, and
Random Forest. The models, particularly Na\"ive Bayes and Random Forest,
demonstrate high effectiveness, as shown through data visualizations. The
research concludes that integrating these analytical methods significantly
enhances the accuracy and reliability of crop yield predictions, offering vital
contributions to agricultural data science.


  Let $D$ be the irreducible bounded symmetric domain of $2\times2$ complex
matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized
by $\mathrm{U}(2,2)$ with isotropy at the origin given by
$\mathrm{U}(2)\times\mathrm{U}(2)$. Denote by $\mathbb{T}^2$ the subgroup of
diagonal matrices in $\mathrm{U}(2)$. We prove that the set of
$\mathrm{U}(2)\times\mathbb{T}^2$-invariant essentially bounded symbols yield
Toeplitz operators that generate commutative $C^*$-algebras on all weighted
Bergman spaces over $D$. Using tools from representation theory, we also
provide an integral formula for the spectra of these Toeplitz operators.


  Gradient boosting methods based on Structured Categorical Decision Trees
(SCDT) have been demonstrated to outperform numerical and one-hot-encodings on
problems where the categorical variable has a known underlying structure.
However, the enumeration procedure in the SCDT is infeasible except for
categorical variables with low or moderate cardinality. We propose and
implement two methods to overcome the computational obstacles and efficiently
perform Gradient Boosting on complex structured categorical variables. The
resulting package, called StructureBoost, is shown to outperform established
packages such as CatBoost and LightGBM on problems with categorical predictors
that contain sophisticated structure. Moreover, we demonstrate that
StructureBoost can make accurate predictions on unseen categorical values due
to its knowledge of the underlying structure.


  In the Tree Augmentation problem we are given a tree $T=(V,F)$ and a set $E
\subseteq V \times V$ of edges with positive integer costs $\{c_e:e \in E\}$.
The goal is to augment $T$ by a minimum cost edge set $J \subseteq E$ such that
$T \cup J$ is $2$-edge-connected. We obtain the following results.
  Recently, Adjiashvili [SODA 17] introduced a novel LP for the problem and
used it to break the $2$-approximation barrier for instances when the maximum
cost $M$ of an edge in $E$ is bounded by a constant; his algorithm computes a
$1.96418+\epsilon$ approximate solution in time $n^{{(M/\epsilon^2)}^{O(1)}}$.
Using a simpler LP, we achieve ratio $\frac{12}{7}+\epsilon$ in time
$2^{O(M/\epsilon^2)} poly(n)$.This gives ratio better than $2$ for logarithmic
costs, and not only for constant costs.
  One of the oldest open questions for the problem is whether for unit costs
(when $M=1$) the standard LP-relaxation, so called Cut-LP, has integrality gap
less than $2$. We resolve this open question by proving that for unit costs the
integrality gap of the Cut-LP is at most $28/15=2-2/15$. In addition, we will
prove that another natural LP-relaxation, that is much simpler than the ones in
previous work, has integrality gap at most $7/4$.


  We prove an optimal $\Omega(n)$ lower bound on the randomized communication
complexity of the much-studied Gap-Hamming-Distance problem. As a consequence,
we obtain essentially optimal multi-pass space lower bounds in the data stream
model for a number of fundamental problems, including the estimation of
frequency moments.
  The Gap-Hamming-Distance problem is a communication problem, wherein Alice
and Bob receive $n$-bit strings $x$ and $y$, respectively. They are promised
that the Hamming distance between $x$ and $y$ is either at least $n/2+\sqrt{n}$
or at most $n/2-\sqrt{n}$, and their goal is to decide which of these is the
case. Since the formal presentation of the problem by Indyk and Woodruff (FOCS,
2003), it had been conjectured that the naive protocol, which uses $n$ bits of
communication, is asymptotically optimal. The conjecture was shown to be true
in several special cases, e.g., when the communication is deterministic, or
when the number of rounds of communication is limited.
  The proof of our aforementioned result, which settles this conjecture fully,
is based on a new geometric statement regarding correlations in Gaussian space,
related to a result of C. Borell (1985). To prove this geometric statement, we
show that random projections of not-too-small sets in Gaussian space are close
to a mixture of translated normal variables.


  Classical magnets exhibit exotic ground state properties such as spin liquids
and fractionalization, promising a manifestation of superposition and
projective symmetry construction in classical theory. While system-specific
spin-ice or soft-spin models exist, a formal theory for general classical
magnets remains elusive. Here, we introduce a generic symmetry group
construction built from a vector field in a plaquette of classical spins,
demonstrating how classical spins superpose in irreducible representations
(irreps) of the symmetry group. The corresponding probability amplitudes serve
as order parameters and local spins as fragmented excitations. The formalism
offers a many-body vector field representation of diverse ground states,
including spin liquids and fragmented phases described as degenerate ensembles
of irreps. We apply the theory to a frustrated square Kagome lattice, where
spin-ice or soft spin rules are inapt, to describe spin liquids and fragmented
phases, all validated through irreps ensembles and unbiased Monte Carlo
simulation. Our generic theory sheds light on previously unknown aspects of
spin-liquid phases and fragmentation and broadens their applications to other
branches of field theory.


  A search for long-lived neutral particles (N^0's) with masses above 2.2
GeV/c^2 that decay into at least one muon has been performed using an
instrumented decay channel at the NuTeV experiment at Fermilab. Data were
examined for particles decaying into the final states mu mu, mu e, and mu pi.
Three mu mu events were observed over an expected Standard Model background of
0.069 +/- 0.010 events; no events were observed in the other modes.


  We present a study of the dynamic structure factor of the antiferromagnetic
spin-1/2 Heisenberg chain at finite temperatures and finite magnetic fields.
Using Quantum-Monte-Carlo based on the stochastic series expansion and
Maximum-Entropy methods we evaluate the longitudinal and the transverse dynamic
structure factor from vanishing magnetic fields up to and above the threshold
$B_c$ for ferromagnetic saturation, as well as for high and for intermediate
temperatures. We study the field-induced redistribution of spectral weight
contrasting longitudinal versus transverse excitations. At finite fields below
saturation incommensurate low-energy modes are found consistent with zero
temperature Bethe-Ansatz. The crossover between the field induced ferromagnet
above $B_c$ and the Luttinger liquid below $B_c$ is analyzed in terms of the
transverse spin-dynamics. Evaluating sum-rules we assess the quality of the
analytic continuation and demonstrate excellent consistency of the
Maximum-Entropy results.


  Context: Pebble accretion is expected to be the dominant process for the
formation of massive solid planets, such as the cores of giant planets and
super-Earths. So, far, this process has been studied under the assumption that
dust coagulates and drifts throughout the full protoplanetary disk. However,
observations show that many disks are structured in rings that may be due to
pressure maxima, preventing the global radial drift of the dust.
  Aims: We study how the pebble-accretion paradigm changes if the dust is
confined in a ring.
  Results: Planet Type-I migration is stopped in a ring, but not necessarily at
its center. If the entropy-driven corotation torque is desaturated, the planet
is located in a region with a low density of dust, which severely limits its
accretion rate. If instead the planet is near the ring's center, its accretion
rate can be similar to the one it would have in a classic (ring-less) disk of
equivalent dust density. However, the growth rate of the planet is limited by
the diffusion of dust in the ring and the final planet's mass is bounded by the
total ring's mass. The DSHARP rings are too far from the star to allow the
formation of massive planets within the disk's lifetime. However, a similar
ring rescaled to 5 AU could lead to the formation of a planet incorporating the
full ring's mass in less than 1/2 My.
  Conclusions: The existence of rings may not be an obstacle to planet
formation by pebble-accretion. However, for accretion to be effective the
resting position of the planet has to be relatively near the ring's center and
the ring needs to be not too far from the central star. The formation of
planets in rings can explain the existence of giant planets with core masses
smaller than the so-called pebble isolation mass.


  In this paper, a parametric simplex algorithm for solving linear vector
optimization problems (LVOPs) is presented. This algorithm can be seen as a
variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different
from it, the proposed algorithm works in the parameter space and does not aim
to find the set of all efficient solutions. Instead, it finds a solution in the
sense of Loehne [16], that is, it finds a subset of efficient solutions that
allows to generate the whole frontier. In that sense, it can also be seen as a
generalization of the parametric self-dual simplex algorithm, which originally
is designed for solving single objective linear optimization problems, and is
modified to solve two objective bounded LVOPs with the positive orthant as the
ordering cone in Ruszczynski and Vanderbei [21]. The algorithm proposed here
works for any dimension, any solid pointed polyhedral ordering cone C and for
bounded as well as unbounded problems. Numerical results are provided to
compare the proposed algorithm with an objective space based LVOP algorithm
(Benson algorithm in [13]), that also provides a solution in the sense of [16],
and with Evans-Steuer algorithm [12]. The results show that for non-degenerate
problems the proposed algorithm outperforms Benson algorithm and is on par with
Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm [13]
excels the simplex-type algorithms; however, the parametric simplex algorithm
is for these problems computationally much more efficient than Evans-Steuer
algorithm.


  The hot-wall metal-organic chemical vapor deposition (MOCVD), previously
shown to enable superior III-nitride material quality and high performance
devices, has been explored for Mg doping of GaN. We have investigated the Mg
incorporation in a wide doping range ($2.45\times{10}^{18}~cm^{-3}$ up to
$1.10\times{10}^{20}~cm^{-3}$) and demonstrate GaN:Mg with low background
impurity concentrations under optimized growth conditions. Dopant and impurity
levels are discussed in view of Ga supersaturation which provides a unified
concept to explain the complexity of growth conditions impact on Mg acceptor
incorporation and compensation. The results are analysed in relation to the
extended defects, revealed by scanning transmission electron microscopy (STEM),
X-ray diffraction (XRD), and surface morphology, and in correlation with the
electrical properties obtained by Hall effect and capacitance-voltage (C-V)
measurements. This allows to establish a comprehensive picture of GaN:Mg growth
by hot-wall MOCVD providing guidance for growth parameters optimization
depending on the targeted application. We show that substantially lower H
concentration as compared to Mg acceptors can be achieved in GaN:Mg without any
in-situ or post-growth annealing resulting in p-type conductivity in as-grown
material. State-of-the-art $p$-GaN layers with a low-resistivity and a high
free-hole density (0.77 $\Omega$.cm and $8.4\times{10}^{17}~cm^{-3}$,
respectively) are obtained after post-growth annealing demonstrating the
viability of hot-wall MOCVD for growth of power electronic device structures.