  The ground state of quantum Rabi model (QRM) exhibits rich nonclassical
states including squeezed state, cat state, and entangled state in different
parameter regimes. In this paper, we firstly use the polaron picture to figure
out the process of superradiant phase transition (SPT) in view of the
nonclassical states. According to the polaron wave functions, the squeezed
state extends to whole parameter regimes, and a small but non-zero weighted
antipolaron is necessary to form novel semi-cat states. Moreover, the behavior
of superradiance in the QRM can be viewed as the same displacement of the cat
states from zero to a finite value, while the ground state becomes entangled
state resulting from the emergence of spin-up state. On the other hand, the
nonclassical states can be intuitively characterized by the Wigner functions
with analytical expressions in the polaron picture, and the Wigner negativity
is also evaluated to measure the nonclassicality. Based on the squeezing and
superradiance, a classification of the coupling strength for the nonclassical
states containing in the ground state is presented, and the process of the SPT
is also revealed by the photon number distribution in Fock space, which is
important to understand the fundamental quantum physics in the QRM. Our work
provides a guidance for preparing the nonclassical states in experiments based
on the QRM.


  Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet
form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$
supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we
study the following properties of harmonic functions, heat kernels and Riesz
transforms for $p\in (2,\infty]$:
  (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat
semigroup;
  (ii) $(RH_p)$: $L^p$-reverse H\"older inequality for the gradients of
harmonic functions;
  (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$);
  (iv) $(GBE)$: a generalised Bakry-\'Emery condition.
  We show that, for $p\in (2,\infty)$, (i), (ii) (iii) are equivalent, while
for $p=\infty$, (i), (ii), (iv) are equivalent.
  Moreover, some of these equivalences still hold under weaker conditions than
the $L^2$-Poincar\'e inequality.
  Our result gives a characterisation of Li-Yau's gradient estimate of heat
kernels for $p=\infty$, while for $p\in (2,\infty)$ it is a substantial
improvement as well as a generalisation of earlier results by
Auscher-Coulhon-Duong-Hofmann [7] and Auscher-Coulhon [6]. Applications to
isoperimetric inequalities and Sobolev inequalities are given. Our results
apply to Riemannian and sub-Riemannian manifolds as well as to non-smooth
spaces, and to degenerate elliptic/parabolic equations in these settings.


  Relation classification is an important NLP task to extract relations between
entities. The state-of-the-art methods for relation classification are
primarily based on Convolutional or Recurrent Neural Networks. Recently, the
pre-trained BERT model achieves very successful results in many NLP
classification / sequence labeling tasks. Relation classification differs from
those tasks in that it relies on information of both the sentence and the two
target entities. In this paper, we propose a model that both leverages the
pre-trained BERT language model and incorporates information from the target
entities to tackle the relation classification task. We locate the target
entities and transfer the information through the pre-trained architecture and
incorporate the corresponding encoding of the two entities. We achieve
significant improvement over the state-of-the-art method on the SemEval-2010
task 8 relational dataset.


  One of the most fundamental characteristic of a complex system is its size
(or volume), which, in many modelling, is represented by the number of its
individual components. Complex systems under investigation nowadays are
typically large and/or time-varying, rendering their identification
challenging. We propose here an accurate and efficient method to determine the
size of (i.e., number of agents in) a complex, diffusively coupled dynamical
system, that leverages the response of the system to an injected probing
signal. For our method to be applicable, we rely on some assumptions on
system's characteristics, namely, on the spectrum of the coupling graph and on
the basin stability of its steady state(s). Even though such assumptions imply
that our method cannot be applied to any instance of diffusively coupled group
of dynamical agents, we argue that it covers relevant and interesting examples.
Furthermore, the simplicity of the approach and its low computational
complexity renders it very interesting for the systems to which it applies.


  Diseases such as diabetic retinopathy and age-related macular degeneration
pose a significant risk to vision, highlighting the importance of precise
segmentation of retinal vessels for the tracking and diagnosis of progression.
However, existing vessel segmentation methods that heavily rely on
encoder-decoder structures struggle to capture contextual information about
retinal vessel configurations, leading to challenges in reconciling semantic
disparities between encoder and decoder features. To address this, we propose a
novel feature enhancement segmentation network (FES-Net) that achieves accurate
pixel-wise segmentation without requiring additional image enhancement steps.
FES-Net directly processes the input image and utilizes four prompt
convolutional blocks (PCBs) during downsampling, complemented by a shallow
upsampling approach to generate a binary mask for each class. We evaluate the
performance of FES-Net on four publicly available state-of-the-art datasets:
DRIVE, STARE, CHASE, and HRF. The evaluation results clearly demonstrate the
superior performance of FES-Net compared to other competitive approaches
documented in the existing literature.


  In this paper we constrain some aspects of the general postinflationary phase
in the context of superconformal $\alpha$-attractor models of inflation. In
particular, we provide constraints on the duration of the reheating process,
$N_{reh}$, and on the reheating temperature, $T_{reh}$, simulating possible and
future results given by the next-generation of cosmological missions. Moreover,
we stress what kinds of equation-of-state parameter, $w_{reh}$, are favored for
different scenarios. The analysis does not depend on the details of the
reheating phase and it is performed assuming different measurements of the
tensor-to-scalar ratio $r$.


  This is a chapter of the planned monograph "Out of Nowhere: The Emergence of
Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and
Christian W\"uthrich and under contract with Oxford University Press. (More
information at www.beyondspacetime.net.) This chapter introduces causal set
theory and identifies and articulates a 'problem of space' in this theory.


  Knowledge distillation (KD) has become a widely used technique in the field
of model compression, which aims to transfer knowledge from a large teacher
model to a lightweight student model for efficient network development. In
addition to the supervision of ground truth, the vanilla KD method regards the
predictions of the teacher as soft labels to supervise the training of the
student model. Based on vanilla KD, various approaches have been developed to
further improve the performance of the student model. However, few of these
previous methods have considered the reliability of the supervision from
teacher models. Supervision from erroneous predictions may mislead the training
of the student model. This paper therefore proposes to tackle this problem from
two aspects: Label Revision to rectify the incorrect supervision and Data
Selection to select appropriate samples for distillation to reduce the impact
of erroneous supervision. In the former, we propose to rectify the teacher's
inaccurate predictions using the ground truth. In the latter, we introduce a
data selection technique to choose suitable training samples to be supervised
by the teacher, thereby reducing the impact of incorrect predictions to some
extent. Experiment results demonstrate the effectiveness of our proposed
method, and show that our method can be combined with other distillation
approaches, improving their performance.


  Recent studies indicate that Vision Transformers (ViTs) are robust against
out-of-distribution scenarios. In particular, the Fully Attentional Network
(FAN) - a family of ViT backbones, has achieved state-of-the-art robustness. In
this paper, we revisit the FAN models and improve their pre-training with a
self-emerging token labeling (STL) framework. Our method contains a two-stage
training framework. Specifically, we first train a FAN token labeler (FAN-TL)
to generate semantically meaningful patch token labels, followed by a FAN
student model training stage that uses both the token labels and the original
class label. With the proposed STL framework, our best model based on
FAN-L-Hybrid (77.3M parameters) achieves 84.8% Top-1 accuracy and 42.1% mCE on
ImageNet-1K and ImageNet-C, and sets a new state-of-the-art for ImageNet-A
(46.1%) and ImageNet-R (56.6%) without using extra data, outperforming the
original FAN counterpart by significant margins. The proposed framework also
demonstrates significantly enhanced performance on downstream tasks such as
semantic segmentation, with up to 1.7% improvement in robustness over the
counterpart model. Code is available at https://github.com/NVlabs/STL.


  Thirty massive clumps associated with bright infrared sources were observed
to detect the infall signatures and characterize infall properties in the
envelope of the massive clumps by APEX telescope in CO(4-3) and C$^{17}$O(3-2)
lines. Eighteen objects have "blue profile" in CO(4-3) line with virial
parameters less than 2, suggesting that global collapse is taking place in
these massive clumps. The CO(4-3) lines were fitted by the two-layer model in
order to obtain infall velocities and mass infall rates. Derived mass infall
rates are from 10$^{-3}$ to 10$^{-1}$ M$_{\odot}$yr$^{-1}$. A positive
relationship between clump mass and infall rate appears to indicate that
gravity plays a dominant role in the collapsing process. Higher luminosity
clump has larger mass infall rate, implying that the clump with higher mass
infall rate has higher star formation rate.


  The recent availability of high-resolution far-infrared (FIR) polarization
observations of galaxies using HAWC+/SOFIA has facilitated studies of
extragalactic magnetic fields in the cold and dense molecular disks.We
investigate if any significant structural differences are detectable in the
kpc-scale magnetic field of the grand design face-on spiral galaxy M51 when
traced within the diffuse (radio) and the dense and cold (FIR) interstellar
medium (ISM). Our analysis reveals a complex scenario where radio and FIR
polarization observations do not necessarily trace the same magnetic field
structure. We find that the magnetic field in the arms is wrapped tighter at
154um than at 3 and 6 cm; statistically significant lower values for the
magnetic pitch angle are measured at FIR in the outskirts (R > 7 kpc) of the
galaxy. This difference is not detected in the interarm region. We find strong
correlations of the polarization fraction and total intensity at FIR and radio
with the gas column density and 12CO(1-0) velocity dispersion. We conclude that
the arms show a relative increase of small-scale turbulent B-fields at regions
with increasing column density and dispersion velocities of the molecular gas.
No correlations are found with HI neutral gas. The star formation rate shows a
clear correlation with the radio polarized intensity, which is not found in
FIR, pointing to a small-scale dynamo-driven B-field amplification scenario.
This work shows that multi-wavelength polarization observations are key to
disentangling the interlocked relation between star formation, magnetic fields,
and gas kinematics in the multi-phase ISM.


  Multimedia documents such as text, images, sounds or videos elicit emotional
responses of different polarity and intensity in exposed human subjects. These
stimuli are stored in affective multimedia databases. The problem of emotion
processing is an important issue in Human-Computer Interaction and different
interdisciplinary studies particularly those related to psychology and
neuroscience. Accurate prediction of users' attention and emotion has many
practical applications such as the development of affective computer
interfaces, multifaceted search engines, video-on-demand, Internet
communication and video games. To this regard we present results of a study
with N=10 participants to investigate the capability of standardized affective
multimedia databases in stimulation of emotion. Each participant was exposed to
picture and video stimuli with previously determined semantics and emotion.
During exposure participants' physiological signals were recorded and estimated
for emotion in an off-line analysis. Participants reported their emotion states
after each exposure session. The a posteriori and a priori emotion values were
compared. The experiment showed, among other reported results, that carefully
designed video sequences induce a stronger and more accurate emotional reaction
than pictures. Individual participants' differences greatly influence the
intensity and polarity of experienced emotion.


  We present models of electrodeposition of ZnO films with organic additives,
with focus on the growth of hybrid films with eosin Y. First we propose a rate
equation model which assumes that the additives form branches with an exposed
part above the ZnO deposit, growing with larger rate than the pure film, and
that the rate of production of ZnO near those branches is proportional to the
height exposed to the solution. This accounts for the production of OH- ions
near the branches and the reactions with Zn++ ions. The steady state solution
shows both species growing with the rate of the branches, and qualitatively
explains their catalytic effect. Subsequently, we propose a more realistic
statistical model for the formation of the hybrid deposits from Zn++ ions, a
hydroxide precursor and eosin in solution. Simple probabilistic rules are used
for reactions of eosin and oxygen, taking into account diffusion from solution
along the same lines of the diffusion-limited aggregation models. The catalytic
effect is represented by the preferencial production of OH- ions near eosin
branches, which form ZnO species. An improvement of the growth rate is possible
only with a rather large diffusion coefficient of eosin in solution compared to
that of hydroxide precursors, in agreement with experimental findings. In the
cases where a series of neighboring eosin clusters competitively grow, the
increase in the growth rate and the high eosin loading observed in the
simulated deposits also agree qualitatively with electrodeposition experiments.


  The Sendov conjecture asserts that if $p(z) = \prod_{j=1}^{N}(z-z_j)$ is a
polynomial with zeros $|z_j| \leq 1$, then each disk $|z-z_j| \leq 1$ contains
a zero of $p'$. Our purpose is the following: Given a zero $z_j$ of order $n
\geq 2$, determine whether there exists $\zeta \not= z_j$ such that $p'(\zeta)
= 0$ and $|z_j - \zeta| \leq 1$. In this paper we present some partial results
on the problem.


  Time-series forecasting models often encounter abrupt changes in a given
period of time which generally occur due to unexpected or unknown events.
Despite their scarce occurrences in the training set, abrupt changes incur loss
that significantly contributes to the total loss. Therefore, they act as noisy
training samples and prevent the model from learning generalizable patterns,
namely the normal states. Based on our findings, we propose a reweighting
framework that down-weights the losses incurred by abrupt changes and
up-weights those by normal states. For the reweighting framework, we first
define a measurement termed Local Discrepancy (LD) which measures the degree of
abruptness of a change in a given period of time. Since a training set is
mostly composed of normal states, we then consider how frequently the temporal
changes appear in the training set based on LD. Our reweighting framework is
applicable to existing time-series forecasting models regardless of the
architectures. Through extensive experiments on 12 time-series forecasting
models over eight datasets with various in-output sequence lengths, we
demonstrate that applying our reweighting framework reduces MSE by 10.1% on
average and by up to 18.6% in the state-of-the-art model.


  We define a formal framework for reasoning about linear-time properties of
quantum systems in which quantum automata are employed in the modeling of
systems and certain closed subspaces of state (Hilbert) spaces are used as the
atomic propositions about the behavior of systems. We provide an algorithm for
verifying invariants of quantum automata. Then automata-based model-checking
technique is generalized for the verification of safety properties recognizable
by reversible automata and omega-properties recognizable by reversible Buechi
automata.


  Higher order finite difference Weighted Essentially Non-Oscillatory (WENO)
schemes for conservation laws are extremely popular because, for
multidimensional problems, they offer high order accuracy at a fraction of the
cost of finite volume WENO or DG schemes. Such schemes come in two
formulations. The very popular classical finite difference WENO (FD-WENO)
method (Shu and Osher, J. Comput. Phys., 83 (1989) 32-78) relies two
reconstruction steps applied to two split fluxes. However, the method cannot
accommodate different types of Riemann solvers and cannot preserve free stream
boundary conditions on curvilinear meshes. This limits its utility. The
alternative finite difference WENO (AFD-WENO) method can overcome these
deficiencies, however, much less work has been done on this method. The reasons
are three-fold. First, it is difficult for the casual reader to understand the
intricate logic that requires higher order derivatives of the fluxes to be
evaluated at zone boundaries. The analytical methods for deriving the update
equation for AFD-WENO schemes are somewhat recondite. To overcome that
difficulty, we provide an easily accessible script that is based on a computer
algebra system in Appendix A of this paper. Second, the method relies on
interpolation rather than reconstruction, and WENO interpolation formulae have
not been documented in the literature as thoroughly as WENO reconstruction
formulae. In this paper, we explicitly provide all necessary WENO interpolation
formulae that are needed for implementing AFD-WENO up to ninth order. The third
reason is that AFD-WENO requires higher order derivatives of the fluxes to be
available at zone boundaries. Since those derivatives are usually obtained by
finite differencing the zone-centered fluxes, they become susceptible to a
Gibbs phenomenon when the solution ...


  We use the Gemini NIFS instrument to map the H$_2 2.1218\mu$m and Br$\gamma$
flux distributions in the inner 0.04-2 kpc of a sample of 36 nearby active
galaxies ($0.001\lesssim z\lesssim0.056$) at spatial resolutions from 4 to 250
pc. We find extended emission in 34 galaxies. In $\sim$55% of them, the
emission in both lines is most extended along the galaxy major axis, while in
the other 45% the extent follows a distinct orientation. The emission of H$_2$
is less concentrated than that of Br$\gamma$, presenting a radius that contains
half of the flux 60% greater, on average. The H$_2$ emission is driven by
thermal processes - X-ray heating and shocks - at most locations for all
galaxies, where $0.4<H_2/Br\gamma<6$. For regions where H$_2$/Br$\gamma>6$
(seen in 40% of the galaxies), shocks are the main H$_2$ excitation mechanism,
while in regions with H$_2$/Br$\gamma<0.4$ (25% of the sample) the H$_2$
emission is produced by fluorescence. The only difference we found between type
1 and type 2 AGN was in the nuclear emission-line equivalent widths, that are
smaller in type 1 than in type 2 due to a larger contribution to the continuum
from the hot dusty torus in the former. The gas masses in the inner 125 pc
radius are in the range $10^1-10^4$ M$_\odot$ for the hot H$_2$ and $10^3-10^6$
M$_\odot$ for the ionised gas and would be enough to power the AGN in our
sample for $10^5-10^8$ yr at their current accretion rates.


  We study the rich structure of periodic stationary solutions of Nagumo
reaction diffusion equation on lattices. By exploring the relationship with
Nagumo equations on cyclic graphs we are able to divide these periodic
solutions into equivalence classes that can be partially ordered and counted.
In order to accomplish this, we use combinatorial concepts such as necklaces,
bracelets and Lyndon words.


  The confinement of most satellite galaxies in the Local Group to thin planes
presents a challenge to the theory of hierarchical galaxy clustering. The
PAndAS collaboration has identified a particularly thin configuration with
kinematic coherence among companions of M31 and there have been long standing
claims that the dwarf companions to the Milky Way lie in a plane roughly
orthogonal to the disk of our galaxy. This discussion investigates the possible
origins of four Local Group planes: the plane similar, but not identical to
that identified by PAndAS, an adjacent slightly tilted plane, and two planes
near the Milky Way: one with nearer galaxies and the other with more distant
ones. Plausible orbits are found by using a combination of Numerical Action
methods and a backward in time integration procedure. For M31, M33, IC10, and
LeoI, solutions are found that are consistent with measurements of their proper
motions. For galaxies in planes, there must be commonalities in their proper
motions, and this constraint greatly limits the number of physically plausible
solutions. Key to the formation of the planar structures has been the
evacuation of the Local Void and consequent build-up of the Local Sheet, a wall
of this void. Most of the M31 companion galaxies were born in early-forming
filamentary or sheet-like substrata that chased M31 out of the void. M31 is a
moving target because of its attraction toward the Milky Way, and the result
has been alignments stretched toward our galaxy. In the case of the
configuration around the Milky Way, it appears that our galaxy was in a
three-way competition for companions with M31 and Centaurus A. Only those
within a modest band fell our way. The Milky Ways' attraction toward the Virgo
Cluster resulted in alignments along the Milky Way-Virgo Cluster line.


  We present deep and precise photometry (F435, F625W, F658N) of Omega Cen
collected with the Advanced Camera for Surveys (ACS) on board the Hubble Space
Telescope (HST). We have identified ~ 6,500 white dwarf (WD) candidates, and
the ratio of WD and Main Sequence (MS) star counts is found to be at least a
factor of two larger than the ratio of CO-core WD cooling and MS lifetimes.
This discrepancy is not explained by the possible occurrence of a He-enhanced
stellar population, since the MS lifetime changes by only 15% when changing
from a canonical (Y=0.25) to a He-enhanced composition (Y=0.42). The presence
of some He-core WDs seems able to explain the observed star counts. The
fraction of He WDs required ranges from 10% to 80% depending on their mean mass
and it is at least five times larger than for field WDs. The comparison in the
Color Magnitude Diagram between theory and observations also supports the
presence of He WDs. Empirical evidence indicates that He WDs have been detected
in stellar systems hosting a large sample of extreme horizontal branch stars,
thus suggesting that a fraction of red giants might avoid the He-core flash.


  In the present paper, we deal mainly with arithmetic properties of Legendre
polynomials by using their orthogonality property. We show that Legendre
polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein
polynomials.


  A schematic two-level model consisting of a "collective" bosonic state and an
"elementary" meson is constructed that provides interpolation from a hadronic
description (a la Rapp/Wambach) to B/R scaling for the description of
properties of vector mesons in dense medium. The development is based on a
close analogy to the degenerate schematic model of Brown for giant resonances
in nuclei.


  Achieving versatile routes to generate crystalline carbon-based
nanostructures has become a fervent pursuit in photocatalysis-related fields.
We demonstrate that the direct electrooxidation of ethanol, performed on Ni
foam, yields ultra-small and highly crystalline graphene-like structures named
carbon quantum dots (CQDs). We perform simulations of various sp2 and sp3
domains in order to understand the optical properties of CQDs by accounting
their contribution as absorbance/luminescent centers in the overall optical
response. Experiments and simulations reveal that absorbance bands for
as-synthesized CQDs are dominated by small sp2 domains comprised of r7
aromatic-rings. After 48 h synthesis, the dispersion transition from yellow to
red, exhibiting new and red shifted absorbance bands. Furthermore, fluorescence
emission is governed by medium-sized sp 2 domains (with aromatic ring counts
r12) and oxygen-containing groups. These oxygen-rich groups within the CQDs,
confirmed by FT-IR and XPS, are responsible for the fast photodegradation of
organic dyes, with B90% of methylene blue (MB) being degraded within the first
5 min of light exposure. Our work provides crucial insights about the
electrochemical synthesis and overall optical properties of carbon
nanostructures, while being effective and reliable toward the degradation of
contaminants in water.


  In fine-grained image recognition (FGIR), the localization and amplification
of region attention is an important factor, which has been explored a lot by
convolutional neural networks (CNNs) based approaches. The recently developed
vision transformer (ViT) has achieved promising results on computer vision
tasks. Compared with CNNs, Image sequentialization is a brand new manner.
However, ViT is limited in its receptive field size and thus lacks local
attention like CNNs due to the fixed size of its patches, and is unable to
generate multi-scale features to learn discriminative region attention. To
facilitate the learning of discriminative region attention without box/part
annotations, we use the strength of the attention weights to measure the
importance of the patch tokens corresponding to the raw images. We propose the
recurrent attention multi-scale transformer (RAMS-Trans), which uses the
transformer's self-attention to recursively learn discriminative region
attention in a multi-scale manner. Specifically, at the core of our approach
lies the dynamic patch proposal module (DPPM) guided region amplification to
complete the integration of multi-scale image patches. The DPPM starts with the
full-size image patches and iteratively scales up the region attention to
generate new patches from global to local by the intensity of the attention
weights generated at each scale as an indicator. Our approach requires only the
attention weights that come with ViT itself and can be easily trained
end-to-end. Extensive experiments demonstrate that RAMS-Trans performs better
than concurrent works, in addition to efficient CNN models, achieving
state-of-the-art results on three benchmark datasets.


  Light-front wavefunctions obtained from holographic light-front QCD are used
to obtain the distributions amplitudes for $K^*$ vector meson. Consequently,
alternate predictions for rare B transitions to $K^*$ form factors are
presented. In this talk, I compare our results for some rare B decay channels
to those obtained from QCD sum rules and available experimental data.


  We present an empirical study on methods for span finding, the selection of
consecutive tokens in text for some downstream tasks. We focus on approaches
that can be employed in training end-to-end information extraction systems, and
find there is no definitive solution without considering task properties, and
provide our observations to help with future design choices: 1) a tagging
approach often yields higher precision while span enumeration and boundary
prediction provide higher recall; 2) span type information can benefit a
boundary prediction approach; 3) additional contextualization does not help
span finding in most cases.


  Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained
analytic solutions for ground-state properties of a whole family of
two-electron spin-compensated harmonically confined model atoms whose different
members are characterized by a specific interparticle potential energy
u($r_{12}$). Here, we make a start on the dynamic generalization of the
harmonic external potential, the motivation being the serious criticism
levelled recently against the foundations of time-dependent density-functional
theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]).
In this context, we derive a simplified expression for the time-dependent
electron density for arbitrary interparticle interaction, which is fully
determined by an one-dimensional non-interacting Hamiltonian. Moreover, a
closed solution for the momentum space density in the Moshinsky model is
obtained.


  Let ${\mathcal {B}}$ be a reducible reduced plane curve. We introduce a new
point of view to study the topology of $(\PP^2, {\mathcal {B}})$ via Galois
covers and Alexander polynomials. We show its effectiveness through examples of
Zariski $N$-plets for conic and conic-quartic configurations.


  This paper discusses the regularity of multiple-valued Dirichlet minimizing
maps into the sphere. It shows that even at branched point, as long as the
normalized energy is small enough, we have the energy decay estimate. Combined
with the previous work by Chun-Chi Lin, we get our first estimate that m-2
dimensional Hausdorff measure of singular set is zero. Furthermore, by looking
at the tangent map and using dimension reduction argument, we show that the
singular set is at least of codimension 3.


  A high-resolution HST/STIS spectrum (R=30,000) is presented of the three
MgII-selected absorption systems (A, B, and C, clustered within 1500km/s) at
z~0.93 toward the quasar PG 1206+459. A WIYN Gunn i-band image of the quasar
field and spectroscopy of two galaxy candidates are also presented. A
multi-phase medium is seen in all three systems, consistent with smaller,
denser clouds producing low-ionization transitions (MgII, FeII, and SiII) and
larger, diffuse clouds giving rise to high-ionization transitions (CIV, NV,
and/or OVI). (1) System A, a multi-cloud, weak MgII absorber at z=0.9254,
requires a super-solar metallicity in both low- and high-ionization phases,
unless an alpha-group enhancement is included. With the unusually complex
velocity structure resolved in the NV profiles, this system is unlikely to
represent a traditional galaxy disk/corona. The most likely candidate host
galaxy is a ~2L^*, apparently warped, spiral at an impact parameter of 43h^-1
kpc. (2) System B, at z=0.9276, has the strongest MgII absorption and has an
approximately solar metallicity in the low-ionization phase. The smooth, broad
high-ionization profiles may indicate a coronal structure similar to that of
the Milky Way. The redshift of an L^* galaxy (z=0.9289), at an impact parameter
of 38h^-1 kpc is consistent with the redshift of this system. (3) System C, at
z=0.9342, has a single component in MgII, separated from the other two systems
by ~1000km/s. It lacks the small, low-ionization cloud characteristic of an
isolated single-cloud, weak MgII absorber. Its absorption properties are
similar to the ``satellite clouds'' of classic strong MgII absorbers, so this
could be a high-velocity cloud in the galaxy group responsible for the systems,
possibly related to a 0.2L^* galaxy at an impact parameter of 43h^-1 kpc.


  This work explores domain generalization (DG) for sound event detection
(SED), advancing adaptability towards real-world scenarios. Our approach
employs a mean-teacher framework with domain generalization to integrate
heterogeneous training data, while preserving the SED model performance across
the datasets. Specifically, we first apply mixstyle to the frequency dimension
to adapt the mel-spectrograms from different domains. Next, we use the adaptive
residual normalization method to generalize features across multiple domains by
applying instance normalization in the frequency dimension. Lastly, we use the
sound event bounding boxes method for post-processing. Our approach integrates
features from bidirectional encoder representations from audio transformers and
a convolutional recurrent neural network. We evaluate the proposed approach on
DCASE 2024 Challenge Task 4 dataset, measuring polyphonic SED score (PSDS) on
the DESED dataset and macro-average pAUC on the MAESTRO dataset. The results
indicate that the proposed DG-based method improves both PSDS and macro-average
pAUC compared to the challenge baseline.


  We analyze the data of the Gamma-Ray Burst/Supernova GRB030329/SN2003dh
system obtained by HETE-2 (GCN [1]), R-XTE (GCN [2]), XMM (Tiengo et al. [3])
and VLT (Hjorth et al. [4]) within our theory (Ruffini et al. [5] and
references therein) for GRB030329. By fitting the only three free parameters of
the EMBH theory, we obtain the luminosity in fixed energy bands for the prompt
emission and the afterglow (see Fig.1). Since the Gamma-Ray Burst (GRB)
analysis is consistent with a spherically symmetric expansion, the energy of
GRB030329 is E = 2.1 * 10^{52} erg, namely ~ 2 * 10^3 times larger than the
Supernova energy. We conclude that either the GRB is triggering an
induced-supernova event or both the GRB and the Supernova are triggered by the
same relativistic process. In no way the GRB can be originated from the
supernova. We also evidence that the XMM observations (Tiengo et al. [3]), much
like in the system GRB980425/SN1998bw (Ruffini et al. [6], Pian et al. [7]),
are not part of the GRB afterglow, as interpreted in the literature (Tiengo et
al. [3]), but are associated to the Supernova phenomenon. A dedicated campaign
of observations is needed to confirm the nature of this XMM source as a newly
born neutron star cooling by generalized URCA processes.


  We consider Sklyanin algebras $S$ with 3 generators, which are quadratic
algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations
$pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. This
class of algebras has enjoyed much attention. In particular, using tools from
algebraic geometry Artin, Tate and Van Den Berg \cite{ATV2} showed that if at
least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of
three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter
regular. More specifically, $S$ is Koszul and has the same Hilbert series as
the algebra of commutative polynomials in 3 indeterminates. It has became
commonly accepted that it is impossible to achieve the same objective by purely
algebraic and combinatorial means like the Gr\"obner basis technique. The
authors have previously dispelled this belief. However our previous proof was
no less complicated than the one based on algebraic geometry. It used a
construcion of a Gr\"obner basis in a suitable one-sided module over $S$ and
had quite a number of cases to consider. In this paper we exhibit a linear
substitution after which it becomes possible to determine the leading monomials
of a reduced Gr\"obner basis for the ideal of relations of $S$ itself (without
passing to a module). We also find out explicitly (in terms of parameters)
which Sklyanin algebras are isomorphic. The only drawback of the new technique
is that it fails if the characteristic of the ground field equals 3.


  The motivation to search for signatures of superconductivity in Weyl
semi-metals and other topological phases lies in their potential for hosting
exotic phenomena such as nonzero-momentum pairing or the Majorana fermion, a
viable candidate for the ultimate realization of a scalable quantum computer.
Until now, however, all known reports of superconductivity in Weyl semimetals
have arisen through surface contact with a sharp tip, focused ion-beam surface
treatment or the application of high pressures. Here, we demonstrate the
observation of superconductivity in single crystals, even an as-grown crystal,
of the Weyl semi-metal tantalum phosphide (TaP), at ambient pressure. A
superconducting transition temperature, $Tc$, varying between 1.7 and 5.3 K, is
observed in different samples, both as-grown and microscopic samples processed
with focused ion beam (FIB) etching. Our data show that the superconductivity
present in the as-grown crystal is inhomogeneous yet exists in the bulk. For
samples fabricated with FIB, we observe, in addition to the bulk
superconductivity, a second superconducting state that resides on the sample
surface. Through measurements of the characteristic fields as a function of
temperature and angle, we are able to confirm the dimensionality of the two
distinct superconducting phases.


  In this paper we consider the gauge theory living on the world-volume of a
stack of N D3-branes of Type 0B/\Omega' I_6(-1)^{F_{L}} and of its orbifolds
C^2/Z_2 and C^3/(Z_2 x Z_2). The gauge theories obtained in the three cases are
a brane realization of ``orientifold field theories'' having the bosonic sector
common with N=4,2,1 super Yang-Mills respectively. In these non-supersymmetric
theories, we investigate the possibility of keeping the gauge/gravity
correspondence that has revealed itself so successful in the case of
supersymmetric theories. In the open string framework we compute the
coefficient of the gauge kinetic term showing that the perturbative behaviour
of the orientifold field theory can be obtained from the closed string channel
in the large N limit, where the theory exhibits Bose-Fermi degeneracy.


  In 1970, on purely theoretical grounds, all total hadronic total cross
sections were predicted to increase without limit for higher and higher
energies. This was contrary to the conventional belief at that time. In 1978,
an accurate phenomenological model was formulated for the case of proton-proton
and antiproton-proton interactions. The parameters for this model were slightly
improved in 1984 using the additional available experimental data. Since then,
for thirty years these parameters have not changed. This development, including
especially the difficult task of formulating this phenomenological model and
the comparison of the predictions of this model with later experimental
results, is summarized.


  The Haze is an excess of microwave intensity emission surrounding the
Galactic centre. It is spatially correlated with the $\gamma$-ray Fermi
bubbles, and with the S-PASS radio polarization plumes, suggesting a possible
common provenance. The models proposed to explain the origin of the Haze,
including energetic events at the Galactic centre and dark matter decay in the
Galactic halo, do not yet provide a clear physical interpretation. In this
paper we present a re-analysis of the Haze including new observations from the
Multi-Frequency Instrument (MFI) of the Q-U-I JOint TEnerife (QUIJOTE)
experiment, at 11 and 13 GHz. We analyze the Haze in intensity and
polarization, characterizing its spectrum. We detect an excess of diffuse
intensity signal ascribed to the Haze. The spectrum at frequencies
11$\,\leq\nu\leq\,$70 GHz is a power-law with spectral index $\beta^{\rm
H}=-2.79\pm0.08$, which is flatter than the Galactic synchrotron in the same
region ($\beta^{\rm S}=-2.98\pm0.04$), but steeper than that obtained from
previous works ($\beta^{\rm H}\sim-2.5$ at 23$\,\leq\,\nu\leq\,$70 GHz). We
also observe an excess of polarized signal in the QUIJOTE-MFI maps in the Haze
area. This is a first hint detection of polarized Haze, or a consequence of
curvature of the synchrotron spectrum in that area. Finally, we show that the
spectrum of polarized structures associated with Galactic centre activity is
steep at low frequencies ($\beta \sim -3.2$ at 2.3 $\leq\nu\leq$ 23 GHz), and
becomes flatter above 11 GHz.


  In this article, a network model incorporating both line-of-sight (LOS) and
non-line-of-sight (NLOS) transmissions is proposed to investigate impacts of
blockages in urban areas on heterogeneous network coverage performance. Results
show that co-existence of NLOS and LOS transmissions has a significant impact
on network performance. We find in urban areas, that deploying more BSs in
different tiers is better than merely deploying all BSs in the same tier in
terms of coverage probability.


  This paper presents a summary of the DFGC 2021 competition. DeepFake
technology is developing fast, and realistic face-swaps are increasingly
deceiving and hard to detect. At the same time, DeepFake detection methods are
also improving. There is a two-party game between DeepFake creators and
detectors. This competition provides a common platform for benchmarking the
adversarial game between current state-of-the-art DeepFake creation and
detection methods. In this paper, we present the organization, results and top
solutions of this competition and also share our insights obtained during this
event. We also release the DFGC-21 testing dataset collected from our
participants to further benefit the research community.


  In this paper we perform a detailed investigation of the Dirichlet
eight-brane of the Type IIA string theory, when the effects of gravity are
included. In particular, consider what happens when one allows the ten-form
field strength $F_{10}$ to vary discontinuously across the worldvolume of the
brane. Since the ten-form is constant on each side of the brane ($d*F_{10} =
0$), a variation in the bulk term $\int F_{10}*F_{10}$ gives rise to a net
pressure acting on the surface of the brane. This means that the infinite
`planar' eight-brane is no longer a static configuration with these boundary
conditions. Instead, a static configuration is found only when the brane
`compactifies' to the topology of an eight-sphere, $S^8$. These spherical
eight-branes are thus bubbles which form boundaries between different phases of
the massive Type IIA supergravity theory. While these bubbles are generically
unstable and will want to expand (or contract), we show that in certain cases
there is a critical radius, $r_c$, at which the (inward) tension of the brane
is exactly counterbalanced by the (outward) force exerted by the pressure
terms. Intuitively, these `compactified' branes are just spherical bubbles
where the effective cosmological constant jumps by a discrete amount as you
cross a brane worldsheet. We argue that these branes will be unstable to
various semi-classical decay processes. We discuss the implications of such
processes for the open strings which have endpoints on the eight-brane.


  Resonant inelastic X-ray scattering (RIXS) has become an important scientific
tool. Nonetheless, conventional high-resolution RIXS measurements (<100 meV),
especially in the soft x-ray range, require large and low-throughput grating
spectrometers that limits measurement accuracy and simplicity. Here, we
computationally investigate the performance of a different method for measuring
RIXS, Photoelectron Spectrometry for Analysis of X-rays (PAX). This method
transforms the X-ray measurement problem of RIXS to an electron measurement
problem, enabling use of compact, high-throughput electron spectrometers. In
PAX, X-rays to be measured are incident on a converter material and the energy
distribution of the resultant photoelectrons, the PAX spectrum, is measured
with an electron spectrometer. The incident X-ray spectrum is then estimated
through a deconvolution algorithm that leverages concepts from machine
learning. We investigate a few example PAX cases. Using the 3d levels of Ag as
a converter material, and with 10$^5$ detected electrons, we accurately
estimate features with 100s of meV width in a model RIXS spectrum. Using a
sharp Fermi edge to encode RIXS spectra, we accurately distinguish 100 meV FWHM
peaks separated by 45 meV with 10$^7$ electrons detected that were photoemitted
from within 0.4 eV of the Fermi level.


  This report introduces a novel optofluidic platform based on piezo-MEMS
technology, capable of identifying subtle variations in the fluid
concentration. The system utilizes piezoelectric micromachined ultrasound
transducers (PMUTs) as receivers to capture sound waves produced by nanosecond
photoacoustic (PA) pulses emanating from a fluid target housed in PDMS
microchannels. Additionally, a dedicated low-noise single-channel amplifier has
been developed to extract the minute analog voltage signals from the PMUTs,
given the inherently weak ultrasound signals generated by fluid targets. The
PMUTs' proficiency in detecting changes in fluid concentration under both
static and time-varying conditions has been documented and verified, confirming
the platform's efficacy in monitoring fluid concentrations.


  We study the stochastic bilinear minimax optimization problem, presenting an
analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant
step size, and presenting variations of the method that yield favorable
convergence. In sharp contrasts with the basic SEG method whose last iterate
only contracts to a fixed neighborhood of the Nash equilibrium, SEG augmented
with iteration averaging provably converges to the Nash equilibrium under the
same standard settings, and such a rate is further improved by incorporating a
scheduled restarting procedure. In the interpolation setting where noise
vanishes at the Nash equilibrium, we achieve an optimal convergence rate up to
tight constants. We present numerical experiments that validate our theoretical
findings and demonstrate the effectiveness of the SEG method when equipped with
iteration averaging and restarting.


  Given a directed graph $G$ and a pair of nodes $s$ and $t$, an $s$-$t$ bridge
of $G$ is an edge whose removal breaks all $s$-$t$ paths of $G$. Similarly, an
$s$-$t$ articulation point of $G$ is a node whose removal breaks all $s$-$t$
paths of $G$. Computing the sequence of all $s$-$t$ bridges of $G$ (as well as
the $s$-$t$ articulation points) is a basic graph problem, solvable in linear
time using the classical min-cut algorithm.
  When dealing with cuts of unit size ($s$-$t$ bridges) this algorithm can be
simplified to a single graph traversal from $s$ to $t$ avoiding an arbitrary
$s$-$t$ path, which is interrupted at the $s$-$t$ bridges. Further, the
corresponding proof is also simplified making it independent of the theory of
network flows.


  In presence of non-adsorbing polymers, colloidal particles experience
ubiquitous attractive interactions induced by depletion forces. Here, we
measure the depletion interaction between a pair of microtubule filaments using
a method that combines single filament imaging with optical trapping. By
quantifying the dependence of filament cohesion on both polymer concentration
and solution ionic strength, we demonstrate that the minimal model of
depletion, based on the Asakura-Oosawa theory, fails to quantitatively describe
the experimental data. By measuring the cohesion strength in two- and three-
filament bundles we verify pairwise additivity of depletion interactions for
the specific experimental conditions. The described experimental technique can
be used to measure pairwise interactions between various biological or
synthetic filaments and complements information extracted from bulk osmotic
stress experiments.


  In the post-pandemic era, wearing face masks has posed great challenge to the
ordinary face recognition. In the previous study, researchers has applied
pretrained VGG16, and ResNet50 to extract features on the elaborate curated
existing masked face recognition (MFR) datasets, RMFRD and SMFRD. To make the
model more adaptable to the real world situation where the sample size is
smaller and the camera environment has greater changes, we created a more
challenging masked face dataset ourselves, by selecting 50 identities with 1702
images from Labelled Faces in the Wild (LFW) Dataset, and simulated face masks
through key point detection. The another part of our study is to solve the
masked face recognition problem, and we chose models by referring to the former
state of the art results, instead of directly using pretrained models, we fine
tuned the model on our new dataset and use the last linear layer to do the
classification directly. Furthermore, we proposed using data augmentation
strategy to further increase the test accuracy, and fine tuned a new networks
beyond the former study, one of the most SOTA networks, Inception ResNet v1.
The best test accuracy on 50 identity MFR has achieved 95%.


  We derive the formulae for the time variation of the gravitational "constant"
G and of the fine structure "constant" \alpha in various models with extra
dimensions and analyze their consistency with the available observational data
for distant supernovae. We find that the reported variation of \alpha
translates into a small variation of G that makes distant supernovae to appear
brighter, in contradiction with recent observations of high z supernovae. The
significance of these results within the framework of some cosmological
scenarios is also discussed. We find, however, that the magnitude of the effect
is not large enough to safely discard the models with extra dimensions studied
here.


  We describe theoretically and observe experimentally the formation of a
surface state in a semi-infnite waveguide array with side-coupled waveguide,
designed to simultaneously achieve Fano and Fabry-Perot resonances. We
demonstrate that the surface mode is compact, with all energy concentrated in
few waveguides at the edge and no field penetration beyond the side-coupled
waveguide position. Furthermore, we show that by broadening the spectral band
in the rest of the waveguide array it is possible to suppress exponentially
localized modes, whereas the Fano state having the eigenvalue embedded in the
continuum is preserved.


  Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a
cofinal family) in many separable metric spaces of interest. To get hold on
uniform homotopy properties of these spaces, a reasonably behaved notion of an
infinite-dimensional metric polyhedron is needed; a specific list of desired
properties was sketched by J. R. Isbell in a series of publications in 1959-64.
In this paper we construct what appears to be the desired theory of uniform
polyhedra; incidentally, considerable information about their metric and
Lipschitz properties is obtained.


  We investigate the expansion of bosons and fermions in a homogeneous lattice
after a sudden removal of the trapping potential using exact numerical methods.
As a main result, we show that in one dimension, both bosonic and fermionic
Mott insulators expand with the same velocity, irrespective of the interaction
strength, provided the expansion starts from the ground state of the trapped
gas. Furthermore, their density profiles become identical during the expansion:
The asymptotic density dynamics is identical to that of initially localized,
non-interacting particles, and the asymptotic velocity distribution is flat.
The expansion velocity for initial correlated Mott insulating states is
therefore independent of the interaction strength and particle statistics.
Interestingly, this non-equilibrium dynamics is sensitive to the interaction
driven quantum phase transition in the Bose-Hubbard model: While being constant
in the Mott phase, the expansion velocity decreases in the superfluid phase and
vanishes for large systems in the non-interacting limit. These results are
compared to the set-up of a recent experiment [PRL 110, 205301 (2013)], where
the trap opening was combined with an interaction quench from infinitely strong
interactions to finite values. We carry out an analogous analysis for a
two-component Fermi gas, with similar observations. In addition, we study the
effect of breaking the integrability of hard-core bosons in different ways:
While the fast ballistic expansion from the ground state of Mott insulators in
one dimension remains unchanged for finite interactions, we observe strong
deviations from this behavior on a two-leg ladder even in the hard-core case.
This change in dynamics bares similarities with the dynamics in the dimensional
crossover from one to two dimensions observed in the aformentioned experimental
study.


  Multi-LiDAR systems have been prevalently applied in modern autonomous
vehicles to render a broad view of the environments. The rapid development of
5G wireless technologies has brought a breakthrough for current cellular
vehicle-to-everything (C-V2X) applications. Therefore, a novel localization and
perception system in which multiple LiDARs are mounted around cities for
autonomous vehicles has been proposed. However, the existing calibration
methods require specific hard-to-move markers, ego-motion, or good initial
values given by users. In this paper, we present a novel approach that enables
automatic multi-LiDAR calibration using two poles stickered with
retro-reflective tape. This method does not depend on prior environmental
information, initial values of the extrinsic parameters, or movable platforms
like a car. We analyze the LiDAR-pole model, verify the feasibility of the
algorithm through simulation data, and present a simple method to measure the
calibration errors w.r.t the ground truth. Experimental results demonstrate
that our approach gains better flexibility and higher accuracy when compared
with the state-of-the-art approach.


  The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest
integer $p$ such that vertices of $G$ can be partitioned into disjoint classes
$X_{1}, ..., X_{p}$ where vertices in $X_{i}$ have pairwise distance greater
than $i$. For $k < t$ we study the packing chromatic number of infinite
distance graphs $D(k, t)$, i.e. graphs with the set $\Z$ of integers as vertex
set and in which two distinct vertices $i, j \in \Z$ are adjacent if and only
if $|i - j| \in \{k, t\}$.
  We generalize results by Ekstein et al. for graphs $D (1, t)$. For
sufficiently large $t$ we prove that $\chi_{\rho}(D(k, t)) \leq 30$ for both
$k$, $t$ odd, and that $\chi_{\rho}(D(k, t)) \leq 56$ for exactly one of $k$,
$t$ odd. We also give some upper and lower bounds for $\chi_{\rho}(D(k, t))$
with small $k$ and $t$.
  Keywords: distance graph; packing coloring; packing chromatic number


  There has been an intense development on the estimation of a sparse
regression coefficient vector in statistics, machine learning and related
fields. In this paper, we focus on the Bayesian approach to this problem, where
sparsity is incorporated by the so-called spike-and-slab prior on the
coefficients. Instead of replying on MCMC for posterior inference, we propose a
fast and scalable algorithm based on variational approximation to the posterior
distribution. The updating scheme employed by our algorithm is different from
the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial
for us to show that our algorithm can achieve asymptotic consistency even when
the feature dimension diverges exponentially fast with the sample size.
Empirical results have demonstrated the effectiveness and efficiency of the
proposed algorithm.


  During epitaxial crystal growth a pattern that has initially been imprinted
on a surface approximately reproduces itself after the deposition of an integer
number of monolayers. Computer simulations of the one-dimensional case show
that the quality of reproduction decays exponentially with a characteristic
time which is linear in the activation energy of surface diffusion. We argue
that this life time of a pattern is optimized, if the characteristic feature
size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface
diffusion constant, $F$ the deposition rate and $d$ the surface dimension.


  We demonstrate in this paper that atomic force microscopy can be successfully
used to gain further insights into the understanding of transformation
toughening in ceria stabilized zirconia. Transformation was induced by stresses
accumulated in the region surrounding propagating cracks in double torsion
samples. The resolution provided by AFM at the surface of the samples made it
possible to observe the formation of self accommodated martensite pairs in the
near crack areas. The potential for transformation is found to decrease with
increasing alloying addition, and is totally suppressed for 16 mol.% CeO2-TZP
samples. A statistical analysis of the martensite pair orientation is
performed, and the relationship with the applied stress and strain fields is
discussed. The contribution to transformation toughening by
transformation-induced plasticity occurring in the formation of martensitic
variant pairs with small net shear is demonstrated. The influence of alloying
addition content on the potential for transformation toughening and fracture
toughness values is finally discussed.


  While sequential recommender systems achieve significant improvements on
capturing user dynamics, we argue that sequential recommenders are vulnerable
against substitution-based profile pollution attacks. To demonstrate our
hypothesis, we propose a substitution-based adversarial attack algorithm, which
modifies the input sequence by selecting certain vulnerable elements and
substituting them with adversarial items. In both untargeted and targeted
attack scenarios, we observe significant performance deterioration using the
proposed profile pollution algorithm. Motivated by such observations, we design
an efficient adversarial defense method called Dirichlet neighborhood sampling.
Specifically, we sample item embeddings from a convex hull constructed by
multi-hop neighbors to replace the original items in input sequences. During
sampling, a Dirichlet distribution is used to approximate the probability
distribution in the neighborhood such that the recommender learns to combat
local perturbations. Additionally, we design an adversarial training method
tailored for sequential recommender systems. In particular, we represent
selected items with one-hot encodings and perform gradient ascent on the
encodings to search for the worst case linear combination of item embeddings in
training. As such, the embedding function learns robust item representations
and the trained recommender is resistant to test-time adversarial examples.
Extensive experiments show the effectiveness of both our attack and defense
methods, which consistently outperform baselines by a significant margin across
model architectures and datasets.


  An important objective of designing lithium-ion rechargeable battery cells is
to maximize their rate performance without compromising the energy density,
which is mainly achieved through computationally expensive numerical
simulations at present. Here we present a simple analytical model for
predicting the rate performance of battery cells limited by electrolyte
transport without any fitting parameters. It exhibits very good agreement with
simulations over a wide range of discharge rate and electrode thickness and
offers a speedup of >10$^5$ times. The optimal electrode properties predicted
by the model are of less than 10% difference from simulation results,
suggesting it as an attractive computational tool for the cell-level battery
architecture design. The model also offers important insights on practical ways
to improve the rate performance of thick electrodes, including avoiding
electrode materials such as LiFePO$_4$ and Li$_4$Ti$_5$O$_{12}$ whose
open-circuit potentials are insensitive to the state of charge and utilizing
lithium metal anode to synergistically accelerate electrolyte transport within
thick cathodes.


  The one-loop polarization operator of neutral gluons in the background
constant Abelian isotopic, $H_{3}$, and hypercharge, $H_{8}$, chromomagnetic
fields combined with $A_0$ electrostatic potential at high temperature is
calculated. The case when $A_0=0$ is investigated separately. The proper time
method is applied. It is found that neutral gluons do not acquire magnetic
masses in the background fields, in contrast to the charged ones. The
application of the results are discussed.


  Faced with the ever-increasing trend of the cellular network scale, how to
quantitatively evaluate the effectiveness of the large-scale deployment of base
stations (BSs) has become a challenging topic. To this end, a deeper
understanding of the cellular network topology is of fundamental significance
to be achieved. In this paper, $ \alpha $-Shape, a powerful algebraic geometric
tool, is integrated into the analysis of real BS location data for six Asian
countries and six European countries, respectively. Firstly, the BS spatial
deployments of both Asian and European countries express fractal features based
on two different testifying metrics, namely the Betti numbers and the Hurst
coefficients. Secondly, it is found out that the log-normal distribution
presents the best match to the cellular network topology when the practical BS
deployment is characterized by the Euler characteristics.


  This paper answers a question raised by Grothendieck in 1970 on the
"Grothendieck closure" of an integral linear group and proves a conjecture of
the first author made in 1980. This is done by a detailed study of the
congruence topology of arithmetic groups, obtaining along the way, an
arithmetic analogue of a classical result of Chevalley for complex algebraic
groups. As an application we also deduce a group theoretic characterization of
thin subgroups of arithmetic groups.


  We show under mild hypotheses that a Quillen adjunction between stable model
categories induces another Quillen adjunction between their left localizations,
and we provide conditions under which the localized adjunction is a Quillen
equivalence. Moreover, we show that in many cases the induced Quillen
equivalence is symmetric monoidal. Using our results we construct a symmetric
monoidal algebraic model for rational cofree $G$-spectra. In the process, we
also show that $L$-complete modules provide an abelian model for derived
complete modules.


  Sweet spot supersymmetry is a phenomenologically and cosmologically perfect
framework to realize a supersymmetric world at short distance. We discuss a
class of dynamical models of supersymmetry breaking and its mediation whose
low-energy effective description falls into this framework. Hadron fields in
the dynamical models play a role of the messengers of the supersymmetry
breaking. As is always true in the models of the sweet spot supersymmetry, the
messenger scale is predicted to be 10^5 GeV < M_mess < 10^{10} GeV. Various
values of the effective number of messenger fields N_mess are possible
depending on the choice of the gauge group.


  We investigate the deformation theory of a class of generalized calibrations
in Riemannian manifolds for which the tangent bundle has reduced structure
group U(n), SU(n), G_2 and Spin(7). For this we use the property of the
associated calibration form to be parallel with respect to a metric connection
which may have non-vanishing torsion. In all these cases, we find that if there
is a moduli space, then it is finite dimensional.
  We present various examples of generalized calibrations that include almost
hermitian manifolds with structure group U(n) or SU(n), nearly parallel G_2
manifolds and group manifolds. We find that some Hopf fibrations are
deformation families of generalized calibrations. In addition, we give
sufficient conditions for a hermitian manifold (M,g,J) to admit Chern and
Bismut connections with holonomy contained in SU(n). In particular we show that
any connected sum of $k \geq 3$ copies of $S^3 \times S^3$ admits a hermitian
structure for which the restricted holonomy of a Bismut connection is contained
in SU(3).


  Within the aim of a dynamical study of on- and off-shell heavy quarks Q in
the quark gluon plasma (QGP) - as produced in relativistic nucleus-nucleus
collisions - we study the heavy quark collisional scattering on partons of the
QGP. The elastic cross sections $\sigma_{q,g-Q}$ are evaluated for perturbative
partons (massless on-shell particles) and for dynamical quasi-particles
(massive off-shell particles as described by the dynamical quasi-particles
model "DQPM") using the leading order Born diagrams. We demonstrate that the
finite width of the quasi-particles in the DQPM has little influence on the
cross sections $\sigma_{q,g-Q}$ except close to thresholds. We, furthermore,
calculate the heavy quark relaxation time as a function of temperature T within
the different approaches using these cross sections.


  The objective of this work is to determine the location of temporal
boundaries between signs in continuous sign language videos. Our approach
employs 3D convolutional neural network representations with iterative temporal
segment refinement to resolve ambiguities between sign boundary cues. We
demonstrate the effectiveness of our approach on the BSLCORPUS, PHOENIX14 and
BSL-1K datasets, showing considerable improvement over the prior state of the
art and the ability to generalise to new signers, languages and domains.


  Increased variability in performance has been associated with the emergence
of several neurological and psychiatric pathologies. However, whether and how
consistency of neuronal activity may also be indicative of an underlying
pathology is still poorly understood. Here we propose a novel method for
evaluating consistency from non-invasive brain recordings. We evaluate the
consistency of the cortical activity recorded with magnetoencephalography in a
group of subjects diagnosed with Mild Cognitive Impairment (MCI), a condition
sometimes prodromal of dementia, during the execution of a memory task. We use
metrics coming from nonlinear dynamics to evaluate the consistency of cortical
regions. A representation known as (parenclitic networks) is constructed, where
atypical features are endowed with a network structure, the topological
properties of which can be studied at various scales. Pathological conditions
correspond to strongly heterogeneous networks, whereas typical or normative
conditions are characterized by sparsely connected networks with homogeneous
nodes. The analysis of this kind of networks allows identifying the extent to
which consistency is affecting the MCI group and the focal points where MCI is
specially severe. To the best of our knowledge, these results represent the
first attempt at evaluating the consistency of brain functional activity using
complex networks theory.


  For a toric variety X_P determined by a rational polyhedral fan P in a
lattice N, Payne shows that the equivariant Chow cohomology of X_P is the
Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use
the Cartan-Eilenberg spectral sequence to analyze the associated reflexive
sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P
and giving criteria for the splitting of the sheaf as a sum of line bundles.
For certain fans associated to the reflection arrangement A_n, we describe a
connection between C^0(P) and logarithmic vector fields tangent to A_n.


  For any generic immersion of a Petersen graph into a plane, the number of
crossing points between two edges of distance one is odd. The sum of the
crossing numbers of all $5$-cycles is odd. The sum of the rotation numbers of
all $5$-cycles is even. We show analogous results for $6$-cycles, $8$-cycles
and $9$-cycles. For any Legendrian spatial embedding of a Petersen graph, there
exists a $5$-cycle that is not an unknot with maximal Thurston-Bennequin
number, and the sum of all Thurston-Bennequin numbers of the cycles is $7$
times the sum of all Thurston-Bennequin numbers of the $5$-cycles. We show
analogous results for a Heawood graph. We also show some other results for some
graphs. We characterize abstract graphs that has a generic immersion into a
plane whose all cycles have rotation number $0$.


  In 1938, Skolem conjectured that $\mathbf{SL}_n(\mathbb{Z})$ is not a
polynomial family for any $n \ge 2$. Carter and Keller disproved Skolem's
conjecture for all $n \ge 3$ by proving that $\mathbf{SL}_n(\mathbb{Z})$ is
boundedly generated by the elementary matrices, and hence a polynomial family
for any $n \ge 3$. Only recently, Vaserstein refuted Skolem's conjecture
completely by showing that $\mathbf{SL}_2(\mathbb{Z})$ is a polynomial family.
An immediate consequence of Vaserstein's theorem also implies that
$\mathbf{SL}_n(\mathbb{Z})$ is a polynomial family for any $n \ge 3$. In this
paper, we prove a function field analogue of Vaserstein's theorem: that is, if
$\mathbf{A}$ is the ring of polynomials over a finite field of odd
characteristic, then $\mathbf{SL}_2(\mathbf{A})$ is a polynomial family in 52
variables. A consequence of our main result also implies that
$\mathbf{SL}_n(\mathbf{A})$ is a polynomial family for any $n \ge 3$.


  Hypothetical long-lived massive colored particles (MCPs or Ys) would be
confined in colorless exotic strongly interacting massive particles (SIMPs) at
color confinement temperature of T_C /sim 200 MeV. Two long-lived MCPs form a
bound state (Y /bar{Y}) at collisions of two SIMPs. We study sensitivities of
MCP annihilation to decay properties of resonances (Y /bar{Y}), and binding
energies or energy levels of exotic SIMPs. The (Y /bar{Y}) formation is assumed
to dominantly proceeds through resonances of (Y/bar{Y}) in this paper. We make
a toy model of the effective cross section for Y /bar{Y} annihilation.
Abundances of SIMPs are then calculated for different sets of parameters
specifying properties of (Y /bar{Y}) resonances, binding energies of SIMPs, the
initial abundance and the mass of MCP. Calculated relic abundances for
respective SIMP species are 2 x 10^{-8}--3 x 10^{-4} times that of baryon. They
can be much higher but cannot be much smaller than the previous estimate. The
abundances can be consistent depending on parameters with the possible scenario
that SIMPs bind to nuclei and subsequent exotic nuclear reactions reduce the
primordial abundance of 7Li or enhance those of 9Be and/or B in the early
universe. A unique information on the quark-hadron phase transition in the
early universe may become available in future by elaborated studies on the
annihilation process with light element abundances as observables.


  In hydrodynamical modeling of ultrarelativistic heavy-ion collisions, the
freeze-out is typically assumed to take place at a surface of constant
temperature or energy density. A more physical approach is to assume that
freeze-out takes place at a surface of constant Knudsen number. We evaluate the
Knudsen number as a ratio of the expansion rate of the system to the pion
scattering rate, and apply the constant Knudsen number freeze-out criterion to
ideal hydrodynamical description of heavy-ion collisions at RHIC
($\sqrt{s_\mathrm{NN}}=200$ GeV) and the LHC ($\sqrt{s_\mathrm{NN}}=2760$ GeV)
energies. We see that once the numerical values of freeze-out temperature and
freeze-out Knudsen number are chosen to produce similar $p_T$ distributions,
the elliptic and triangular anisotropies are similar too, in both
event-by-event and averaged initial state calculations.


  Recently Hall, Murayama and Weiner (Phys. Rev. Lett. 84 (2000) 2572,
[hep-ph/9911341]) claimed that neutrino oscillation data are well accounted for
by a neutrino mass matrix which appears to have random entries. Here this claim
is disputed by constructing a specific counter example. Structure in the
neutrino mass matrix is clearly preferred over random matrices.


  We study Dark Matter production during first order phase transitions from
bubble-plasma collisions. We focus on scenarios where the Dark Matter sector is
secluded and its interaction with the visible sector (including the Standard
Model) originates from dimension-five and dimension-six operators. We find that
such DM is generally heavy and has a large initial velocity, leading to the
possibility of DM being warm today. We differentiate between the cases of
weakly and strongly coupled dark sectors, where, in the latter case, we focus
on glueball DM, which turns out to have very distinct phenomenological
properties. We also systematically compute the Freeze-In production of the dark
sector and compare it with the bubble-plasma DM abundances.


  We extend to the framework of locally $L^0$-convex modules some results from
classical convex analysis. Namely, randomized versions of Mazur lemma and
Krein-Smulian theorem under mild stability properties are provided.


  Coronal loops are building blocks of solar active regions. However, their
formation mechanism is still not well understood. Here we present direct
observational evidence for the formation of coronal loops through magnetic
reconnection as new magnetic fluxes emerge into the solar atmosphere.
Extreme-ultraviolet observations of the Atmospheric Imaging Assembly (AIA)
onboard the Solar Dynamics Observatory (SDO) clearly show the newly formed
loops following magnetic reconnection within a plasma sheet. Formation of the
loops is also seen in the h{\alpha} line-core images taken by the New Vacuum
Solar Telescope. Observations from the Helioseismic and Magnetic Imager onboard
SDO show that a positive-polarity flux concentration moves towards a
negative-polarity one with a speed of ~0.4 km/s, before the formation of
coronal loops. During the loop formation process, we found signatures of flux
cancellation and subsequent enhancement of the transverse field between the two
polarities. The three-dimensional magnetic field structure reconstructed
through a magnetohydrostatic model shows field lines consistent with the loops
in AIA images. Numerous bright blobs with an average width of 1.37 Mm appear
intermittently in the plasma sheet and move upward with a projected velocity of
~114 km/s. The temperature, emission measure and density of these blobs are
about 3 MK, 2.0x10^(28) cm^(-5) and 1.2x10^(10) cm^(-3), respectively. A power
spectral analysis of these blobs indicates that the observed reconnection is
likely not dominated by a turbulent process. We have also identified flows with
a velocity of 20 to 50 km/s towards the footpoints of the newly formed coronal
loops.


  We consider series solutions of the Schr\"odinger equation for the
Bender-Boettcher potentials V(x)=-(ix)^N with integer N. A simple truncation is
introduced which provides accurate results regarding the ground state and first
few excited states for any N. This is illustrated with explicit computations of
energy levels, node structure and expectation values for some integer N.


  Scene understanding using multi-modal data is necessary in many applications,
e.g., autonomous navigation. To achieve this in a variety of situations,
existing models must be able to adapt to shifting data distributions without
arduous data annotation. Current approaches assume that the source data is
available during adaptation and that the source consists of paired multi-modal
data. Both these assumptions may be problematic for many applications. Source
data may not be available due to privacy, security, or economic concerns.
Assuming the existence of paired multi-modal data for training also entails
significant data collection costs and fails to take advantage of widely
available freely distributed pre-trained uni-modal models. In this work, we
relax both of these assumptions by addressing the problem of adapting a set of
models trained independently on uni-modal data to a target domain consisting of
unlabeled multi-modal data, without having access to the original source
dataset. Our proposed approach solves this problem through a switching
framework which automatically chooses between two complementary methods of
cross-modal pseudo-label fusion -- agreement filtering and entropy weighting --
based on the estimated domain gap. We demonstrate our work on the semantic
segmentation problem. Experiments across seven challenging adaptation scenarios
verify the efficacy of our approach, achieving results comparable to, and in
some cases outperforming, methods which assume access to source data. Our
method achieves an improvement in mIoU of up to 12% over competing baselines.
Our code is publicly available at https://github.com/csimo005/SUMMIT.


  We find asymptotic equalities for exact upper bounds of approximations by
Fourier sums in uniform metric on classes of $2\pi$-periodic functions,
representable in the form of convolutions of functions $\varphi$, which belong
to unit balls of spaces $L_{p}$, with generalized Poisson kernels. For obtained
asymptotic equalities we introduce the estimates of remainder, which are
expressed in the explicit form via the parameters of the problem.


  Phase-field simulation (PFS) have revolutionized the understanding of domain
structure and switching behavior in ferroelectric thin films and ceramics.
Generally, PFS is based on solution of a (set) of Ginzburg-Landau equations for
a defined order parameter field(s) under physical boundary conditions (BCs) of
fixed potential or charge. While well-matched to the interfaces in bulk
materials and devices, these BCs are generally not applicable to free
ferroelectric surfaces. Here, we developed a self-consistent phase-field model
with boundary conditions based on electrochemical equilibria. We chose
Pb(Zr0.2Ti0.8)O3 ultrathin film consisting of (001) oriented single tetragonal
domain (Pz) as a model system, and systematically studied the effects of oxygen
partial pressure, temperature and surface ion on the ferroelectric state, and
compared it with the case of complete screening. We have further explored the
polarization switching induced by the oxygen partial pressure and observed
pronounced size effect induced by chemical screening. Our work thus helps to
understand the emergent phenomena in ferroelectric thin films brought about by
the electrochemical ionic surface compensations.


  The relationship between topology and dynamics of complex systems has
motivated continuing interest from the scientific community. In the present
work, we address this interesting topic from the perspective of simple games,
involving two teams playing according to a small set of simple rules, taking
place on four types of complex networks. Starting from a minimalist game,
characterized by full symmetry always leading to ties, four other games are
described in progressive order of complexity, taking into account the presence
of neighbors as well as strategies. Each of these five games, as well as their
specific changes when implemented in four types of networks, are studied in
terms of statistics of the total duration of the game as well as the number of
victories and ties, with several interesting results that substantiate, in some
cases, the importance of the network topology on the respective dynamics. As a
subsidiary result, the visualization of relationships between the data elements
in terms of coincidence similarity networks allowed a more complete and direct
interpretation of the obtained results.


  We show that if $Y_j\subset \mathbb{C}^{n_j}$ is a bounded strongly convex
domain with $C^3$-boundary for $j=1,\dots,q$, and $X_j\subset \mathbb{C}^{m_j}$
is a bounded convex domain for $j=1,\ldots,p$, then the product domain
$\prod_{j=1}^p X_j\subset \mathbb{C}^m$ cannot be isometrically embedded into
$\prod_{j=1}^q Y_j\subset \mathbb{C}^n$ under the Kobayashi distance, if $p>q$.
This result generalises Poincar\'e's theorem which says that there is no
biholomorphic map from the polydisc onto the Euclidean ball in $\mathbb{C}^n$
for $n\geq 2$.
  The method of proof only relies on the metric geometry of the spaces and will
be derived from a result for products of proper geodesic metric spaces with the
sup-metric. In fact, the main goal of the paper is to establish a general
criterion, in terms of certain asymptotic geometric properties of the
individual metric spaces, that yields an obstruction for the existence of an
isometric embedding between product metric spaces.


  Modern machine learning often operates in the regime where the number of
parameters is much higher than the number of data points, with zero training
loss and yet good generalization, thereby contradicting the classical
bias-variance trade-off. This \textit{benign overfitting} phenomenon has
recently been characterized using so called \textit{double descent} curves
where the risk undergoes another descent (in addition to the classical U-shaped
learning curve when the number of parameters is small) as we increase the
number of parameters beyond a certain threshold. In this paper, we examine the
conditions under which \textit{Benign Overfitting} occurs in the random feature
(RF) models, i.e. in a two-layer neural network with fixed first layer weights.
We adopt a new view of random feature and show that \textit{benign overfitting}
arises due to the noise which resides in such features (the noise may already
be present in the data and propagate to the features or it may be added by the
user to the features directly) and plays an important implicit regularization
role in the phenomenon.


  In this theoretical paper, we investigate coherence properties of the
near-resonant light scattered by two atoms exposed to a strong monochromatic
field. To properly incorporate saturation effects, we use a quantum Langevin
approach. In contrast to the standard optical Bloch equations, this method
naturally provides the inelastic spectrum of the radiated light induced by the
quantum electromagnetic vacuum fluctuations. However, to get the right spectral
properties of the scattered light, it is essential to correctly describe the
statistical properties of these vacuum fluctuations. Because of the presence of
the two atoms, these statistical properties are not Gaussian : (i) the spatial
two-points correlation function displays a speckle-like behavior and (ii) the
three-points correlation function does not vanish. We also explain how to
incorporate in a simple way propagation with a frequency-dependent scattering
mean-free path, meaning that the two atoms are embedded in an average
scattering dispersive medium. Finally we show that saturation-induced
nonlinearities strongly modify the atomic scattering properties and, as a
consequence, provide a source of decoherence in multiple scattering. This is
exemplified by considering the coherent backscattering configuration where
interference effects are blurred by this decoherence mechanism. This leads to a
decrease of the so-called coherent backscattering enhancement factor.


  We review recent molecular dynamics simulations of thermally activated
undulations and defects in the lamellar $L_\alpha$ phase of a binary
amphiphile-solvent mixture, using an idealized molecular coarse-grained model:
Solvent particles are represented by beads, and amphiphiles by bead-and-spring
tetramers. We find that our results are in excellent agreement with the
predictions of simple mesoscopic theories: An effective interface model for the
undulations, and a line tension model for the (pore) defects. We calculate the
binding rigidity and the compressibility modulus of the lamellar stack as well
as the line tension of the pore rim. Finally, we discuss implications for
polymer-membrane systems.


  In line with the Coulomb-oscillator model of superconductivity, loop currents
of excited 3s electrons from O^2- ions, passing in the CuO2 plane through
nuclei of nearest-neighbor oxygen quartets, create the antiferromagnetic phase
of undoped copper oxides. Holes, introduced by alkaline-earth doping of
La2CuO4, destroy the loop currents, thereby weakening antiferromagnetism until
it disappears at doping x = 0.02. Further doping of La_2-xAe_xCuO4 gives rise
to incommensurate free-hole density waves whose wavelength is determined by the
spacing of a doping superlattice. Modulating the ordering of the ions' magnetic
moments, the charge-density wave, of incommensurability 2 delta, causes a
magnetic density wave of incommensurability delta. The formula derived for
delta(x) is in excellent agreement with data from X-ray diffraction and neutron
scattering.


  We calculate the s-wave pion-pion scattering length in the isospin I=2
channel in lattice QCD for pion masses ranging from 270 Mev to 485 Mev using
two flavors of maximally twisted mass fermions at a lattice spacing of 0.086
fm. Additionally, we check for lattice artifacts with one calculation at a
finer lattice spacing of 0.067 fm. We use chiral perturbation theory at
next-to-leading order to extrapolate our results. At the physical pion mass, we
find m_pi a_pipi(I=2)=-0.04385(28)(38) for the scattering length, where the
first error is statistical and the second is our estimate of several systematic
effects.


  Recently, we have shown the existence of a finite energy one-half monopole.
In this paper, we would like to introduce electric charge into the one-half
monopole configuration, thus creating a one-half dyon. This one-half dyon
possesses finite energy, magnetic dipole moment and angular momentum. Hence it
is able to rotate in the presence of an external magnetic field. Similar to the
single pole dyons and the MAP dyons, this one-half dyon possesses critical
(maximum) electric charge, total energy, and magnetic dipole moment when the
Higgs self-coupling constant is nonvanishing, and the electric charge parameter
approaches one. This one-half dyon solution does not satisfy the first order
Bogomol'nyi equations and is a non-BPS solution in the limit of vanishing Higgs
self-coupling constant.


  Brute force cross-validation (CV) is a method for predictive assessment and
model selection that is general and applicable to a wide range of Bayesian
models. Naive or `brute force' CV approaches are often too computationally
costly for interactive modeling workflows, especially when inference relies on
Markov chain Monte Carlo (MCMC). We propose overcoming this limitation using
massively parallel MCMC. Using accelerator hardware such as graphics processor
units (GPUs), our approach can be about as fast (in wall clock time) as a
single full-data model fit.
  Parallel CV is flexible because it can easily exploit a wide range data
partitioning schemes, such as those designed for non-exchangeable data. It can
also accommodate a range of scoring rules.
  We propose MCMC diagnostics, including a summary of MCMC mixing based on the
popular potential scale reduction factor ($\widehat{R}$) and MCMC effective
sample size ($\widehat{ESS}$) measures. We also describe a method for
determining whether an $\widehat{R}$ diagnostic indicates approximate
stationarity of the chains, that may be of more general interest for
applications beyond parallel CV. Finally, we show that parallel CV and its
diagnostics can be implemented with online algorithms, allowing parallel CV to
scale up to very large blocking designs on memory-constrained computing
accelerators.


  We prove that a finite coprime linear group G in characteristic p>=(|G|-1)/2
has a regular orbit. This bound on p is best possible. We also give an
application to blocks with abelian defect groups.


  The performance of top taggers, for example in resonance searches, can be
significantly enhanced through an increased set of variables, with a special
focus on final-state radiation. We study the production and the decay of a
heavy gauge boson in the upcoming LHC run. For constant signal efficiency, the
multivariate analysis achieves an increased background rejection by up to a
factor 30 compared to our previous tagger. Based on this study and the
documentation in the Appendix we release a new HEPTopTagger2 for the upcoming
LHC run. It now includes an optimal choice of the size of the fat jet,
N-subjettiness, and different modes of Qjets.


  This article proposes a technique for the geometrically stable modeling of
high-degree B-spline curves based on S-polygon in a float format, which will
allow the accurate positioning of the end points of curves and the direction of
the tangent vectors. The method of shape approximation is described with the
purpose of providing geometrical proximity between the original and
approximating curve. The content of the notion of a harmonious, regular form of
B-spline curve's S-polygon in a float format is revealed as a factor in
achieving a high-quality of fit for the generated curve. The expediency of the
shape modeling method based on S-polygon in a float format at the end portions
of the curve for quality control of curve modeling and editing is
substantiated. The results of a comparative test are presented, demonstrating
the superlative efficacy of using the Mineur-Farin configuration for
constructing constant and monotone curvature curves based on an S-polygon in a
float format. The findings presented in this article confirm that it is
preferable to employ the principle of "constructing a control polygon of a
harmonious form (or the Mineur-Farin configuration) of a parametric polynomial"
to a B-spline curve's S-polygon in a float format, and not to a B-polygon of
the Bezier curve. Recommendations are given for prospective studies in the
field of applying the technique of constructing a high-quality B-spline curves
to the approximation of log-aesthetic curves, Ziatdinov's superspirals, etc.
The authors of the article developed a technique for constructing smooth
connections of B-spline curves with ensuring a high order of smoothness of the
composite curve. The proposed techniques are implemented in the
FairCurveModeler program as a plug-in to engineering CAD systems.


  In this article we will take into account the most complete back-ground with
torsion and curvature, providing the most exhaustive coupling for the Dirac
field: we will discuss the integrability of the interaction of the matter field
and the reduction of the matter field equations.


  We extend Fukushima's result on the finite convergence of an algorithm for
the global convex feasibility problem to the local nonconvex case.


  Electronic Energy Transfer (EET) between chromophores is fundamental in many
natural light-harvesting complexes, serving as a critical step for solar energy
funneling in photosynthetic plants and bacteria. The complicated role of the
environment in mediating this process in natural architectures has been
addressed by recent scanning tunneling microscope (STM) experiments involving
EET between two molecules supported on a solid substrate. These measurements
demonstrated that EET in such conditions has peculiar features, such as a steep
dependence on the donor-acceptor distance, reminiscent of a short-range
mechanism more than of a Forster-like process. By using state of the art hybrid
ab initio electromagnetic modeling, here we provide a comprehensive theoretical
analysis of tip-enhanced EET. In particular, we show that this process can be
understood as a complex interplay of electromagnetic-based molecular plasmonic
processes, whose result may effectively mimic short range effects. Therefore,
the established identification of an exponential decay with Dexter-like effects
does not hold for tip-enhanced EET, and accurate electromagnetic modeling is
needed to identify the EET mechanism.


  The long-time behavior of the solutions for a non-isothermal model in
superfluidity is investigated. The model describes the transition between the
normal and the superfluid phase in liquid 4He by means of a non-linear
differential system, where the concentration of the superfluid phase satisfies
a non-isothermal Ginzburg-Landau equation. This system, which turns out to be
consistent with thermodynamical principles and whose well-posedness has been
recently proved, has been shown to admit a Lyapunov functional. This allows to
prove existence of the global attractor which consists of the unstable manifold
of the stationary solutions. Finally, by exploiting recent techniques of
semigroups theory, we prove the existence of an exponential attractor of finite
fractal dimension which contains the global attractor.


  Relation algebra and its reducts provide us with a strong tool for reasoning
about nondeterministic programs and their partial correctness. Demonic
calculus, introduced to model the behaviour of a machine where the demon is in
control of nondeterminism, has also provided us with an extension of that
reasoning to total correctness.
  We formalise the framework for relational reasoning about total correctness
in nondeterministic programs using semigroups with ordinary composition and
demonic lattice operations. We show that the class of representable demonic
join semigroups is not finitely axiomatisable and that the representation class
of demonic meet semigroups does not have the finite representation property for
its finite members.
  For lattice semigroups (with composition, demonic join and demonic meet) we
show that the representation problem for finite algebras is undecidable,
moreover the finite representation problem is also undecidable. It follows that
the representation class is not finitely axiomatisable, furthermore the finite
representation property fails.


  We present period-luminosity relations for more than 3,200 red variable stars
in the Small Magellanic Cloud observed in the second phase of the Optical
Gravitational Lensing Experiment (OGLE-II). Periods of multiply-periodic light
curve solutions combined with the single-epoch 2MASS JHK_S magnitudes, reveal
very similar distributions to those for the Large Magellanic Cloud in Paper I.
The main features include four pulsating Asymptotic Giant Branch (AGB) ridges,
three distinct short-period sequences below the tip of the Red Giant Branch and
two long-period sequences of ambiguous origin. We derive a relative distance
modulus of the Clouds from the period-luminosity distributions for all stars of
Delta mu_0=0.44 mag, which is in good agreement with recent independent
results. The tip of the Red Giant Branch shows a colour and metallicity
dependence that is in excellent agreement with the empirical results for
globular clusters. We conclude that most variable stars below the TRGB are
indeed RGB stars.


  Let $N \geq 2$ and let $\mathrm{Out}(F_N)$ be the outer automorphism group of
a nonabelian free group of rank $N$. Let
$\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ be the finite index subgroup of
$\mathrm{Out}(F_N)$ which is the kernel of the natural action of
$\mathrm{Out}(F_N)$ on $H_1(F_N,\mathbb{Z}/3\mathbb{Z})$. We show that
$\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ is an $R$-group, that is, for every
$\phi,\psi \in \mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$, if there exists $k \in
\mathbb{N}^*$ such that $\phi^k=\psi^k$, then $\phi=\psi$. This answers a
question of Handel and Mosher. We then use the fact that
$\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ is an $R$-group in order to prove that
the normalizer in $\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ of every abelian
subgroup of $\mathrm{IA}_N(\mathbb{Z}/3\mathbb{Z})$ is equal to its
centralizer. We finally give an alternative proof of a result, due to Feighn
and Handel, that the centralizer of an element of $\mathrm{Out}(F_N)$ which has
only finitely many periodic orbits of conjugacy classes of maximal cyclic
subgroups of $F_N$ is virtually abelian.


  We discuss common properties and reasons for integrability in the class of
multistate Landau-Zener (MLZ) models with all diabatic levels crossing at one
point. Exploring the Stokes phenomenon, we show that each previously solved
model has a dual one, whose scattering matrix can be also obtained
analytically. For applications, we demonstrate how our results can be used to
study conversion of molecular into atomic Bose condensates during passage
through the Feshbach resonance, and provide purely algebraic solutions of the
bowtie and special cases of the driven Tavis-Cummings model (DTCM).


  We present new observations with the Atacama Large Millimeter/submillimeter
Array for a gravitationally-lensed galaxy at $z=9.1$, MACS1149-JD1. [O III]
88-$\mu$m emission is detected at 10$\sigma$ with a spatial resolution of
$\sim0.3$ kpc in the source plane, enabling the most distant morpho-kinematic
study of a galaxy. The [O III] emission is distributed smoothly without any
resolved clumps and shows a clear velocity gradient with $\Delta V_{\rm
obs}/2\sigma_{\rm tot}=0.84\pm0.23$, where $\Delta V_{\rm obs}$ is the observed
maximum velocity difference and $\sigma_{\rm tot}$ is the velocity dispersion
measured in the spatially-integrated line profile, suggesting a rotating
system. Assuming a geometrically thin self-gravitating rotation disk model, we
obtain $V_{\rm rot}/\sigma_V=0.67_{-0.26}^{+0.73}$, where $V_{\rm rot}$ and
$\sigma_V$ are the rotation velocity and velocity dispersion, respectively,
still consistent with rotation. The resulting disk mass of
$0.65_{-0.40}^{+1.37}\times10^{9}$ M$_\odot$ is consistent with being
associated with the stellar mass identified with a 300 Myr-old stellar
population independently indicated by a Balmer break in the spectral energy
distribution. We conclude that the most of the dynamical mass is associated
with the previously-identified mature stellar population that formed at
$z\sim15$.


  TOI-2076 b is a sub-Neptune-sized planet ($R= 2.39 \pm 0.10 {R_\oplus}$) that
transits a young ($204 \pm 50 {MYr}$) bright ($V = 9.2$) K-dwarf hosting a
system of three transiting planets. Using spectroscopic observations with the
NEID spectrograph on the WIYN 3.5 m Telescope, we model the Rossiter-McLaughlin
effect of TOI-2076 b, and derive a sky-projected obliquity of
$\lambda=-3_{-15}^{+16\:\circ}$. Using the size of the star ($R=0.775 \pm0.015
{R_\odot}$), and the stellar rotation period ($P_{\mathrm{rot}}=7.27\pm0.23$
days), we estimate an obliquity of $\psi=18_{-9}^{+10\:\circ}$ ($\psi <
34^\circ$ at 95\% confidence), demonstrating that TOI-2076 b is on a
well-aligned orbit. Simultaneous diffuser-assisted photometry from the 3.5 m
Telescope at Apache Point Observatory rules out flares during the transit.
TOI-2076 b joins a small but growing sample of young planets in compact
multi-planet systems with well-aligned orbits, and is the fourth planet with an
age $\lesssim 300$ Myr in a multi-transiting system with an obliquity
measurement. The low obliquity of TOI-2076 b and the presence of transit timing
variations in the system suggest the TOI-2076 system likely formed via
convergent disk migration in an initially well-aligned disk.