  We present a complete description of a new physical model with goldstino
supermultiplet for CompHEP software package. The model contains MSSM content
supplemented by three new fields: {\it goldstino} -- two component spinor,
scalar {\it sgoldstino} and pseudoscalar {\it sgoldstino}. To the leading order
in 1/F, where F is the parameter of supersymmetry breaking, and to zero order
in MSSM gauge and Yukawa coupling constants, the interactions between the
component fields of goldstino supermultiplet and MSSM fields are derived. They
correspond to the most attractive for collider studies processes where only one
of these {\it new} particles appears in a final state. In this case light
gravitino behaves exactly as goldstino. For sgoldstinos, as they are R-even, we
include in the package only sgoldstino couplings to goldstino and sgoldstino
couplings to SM fields as the most interesting phenomenologically. All new
coupling constants between the components of goldstino supermultiplet and MSSM
fields are completely determined by the ratios of soft supersymmetry breaking
parameters and F. Thus, in addition to the MSSM coupling constants there are
three new parameters in the package: the scale of supersymmetry breaking,
$\sqrt{F}$, and masses of scalar and pseudoscalar sgoldstinos. The CompHEP
notations for the new fields and parameters are presented. The package was
successfully tested and all relevant results known in literature have been
reproduced with good accuracy. It may be used in order to calculate any
tree-level process with one gravitino or sgoldstino on mass shell. Universality
of the Lagrangian allows to apply the package in study of phenomenology of any
supersymmetric extension of the Standard Model.


  The measurements of the minimum bias events provide valuable information on
the basic properties of the $pp$ interactions. The results at the new highest
energy of $pp$ collisions, $\sqrt{s}$ = 13 TeV, obtained using the ATLAS
detector, are shown. They include distributions of charged particle
pseudorapidity density, transverse momentum and multiplicity. The properties of
the underlying event, determined with respect to a leading high-$p_{T}$
particle, are also presented. In both cases the new results are compared with
those from earlier studies of the $pp$ collisions at $\sqrt{s}$ = 7 TeV.


  We show that the strong coupling physics inherent to the insulating Mott
state in 2D leads to a jump in the chemical potential upon doping and the
emergence of a pseudogap in the single particle spectrum below a characteristic
temperature. The pseudogap arises because any singly-occupied site not
immediately neighbouring a hole experiences a maximum energy barrier for
transport equal to $t^2/U$, where $t$ is the nearest-neighbour hopping integral
and $U$ the on-site repulsion. The resultant pseudogap cannot vanish before
each lattice site, on average, has at least one hole as a near neighbour. The
ubiquituity of this effect in all doped Mott insulators suggests that the
pseudogap in the cuprates has a simple origin.


  Based on Shoenberg assumption of magnetic flux density dependence of
diamagnetic moments which accounts for an instability of strongly correlated
electron gas at the conditions of dHvA effect and diamagnetic phase transition
(DPT) to non-uniform phase, we investigate the morphology of the Condon domains
(CD) in plate-like sample theoretically. At one period of dHvA oscillations the
intrinsic structure of inhomogeneous diamagnetic phase (IDP) is governed by the
first order phase transitions between different non-uniform phases similar to
the high-anisotropy magnetic systems of spin origin, and strongly affected by
temperature, magnetic field and impurity of the sample due to the electron
correlations. The phase diagrams of evolution of IDP with temperature and
small-scale magnetic field in every period of dHvA oscillations are calculated.


  In order to study the gravitational collapse of charged matter we analyze the
simple model of an self-gravitating massless scalar field coupled to the
electromagnetic field in spherical symmetry. The evolution equations for the
Maxwell-Klein-Gordon sector are derived in the 3+1 formalism, and coupled to
gravity by means of the stress-energy tensor of these fields. To solve
consistently the full system we employ a generalized
Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of General Relativity
that is adapted to spherical symmetry. We consider two sets of initial data
that represent a time symmetric spherical thick shell of charged scalar field,
and differ by the fact that one set has zero global electrical charge while the
other has non-zero global charge. For compact enough initial shells we find
that the configuration doesn't disperse and approaches a final state
corresponding to a sub-extremal Reissner-N\"ordstrom black hole with $|Q|<M$.
By increasing the fundamental charge of the scalar field $q$ we find that the
final black hole tends to become more and more neutral. Our results support the
cosmic censorship conjecture for the case of charged matter.


  We show that all M-theory backgrounds which admit more than 29 Killing
spinors are maximally supersymmetric. In particular, we find that the
supercovariant curvature of all backgrounds which preserve 30 supersymmetries,
subject to field equations and Bianchi identities, vanishes, and that there are
no such solutions which arise as discrete quotients of maximally supersymmetric
backgrounds.


  It was recently shown that the string theory duals of certain deformations of
the N=4 gauge theory can be obtained by a combination of T-duality
transformations and coordinate shifts. Here we work out the corresponding
procedure of twisting the dual integrable spin chain and its Bethe ansatz. We
derive the Bethe equations for the complete twisted N=4 gauge theory at one and
higher loops. These have a natural generalization which we identify as twists
involving the Cartan generators of the conformal algebra. The underlying model
appears to be a form of noncommutative deformation of N=4 SYM.


  In this paper, we consider infinite Galois extensions of number fields and
study the relation between their local degrees and the structure of their
Galois groups. It is known that, if $K$ is a number field and $L/K$ is an
infinite Galois extension of group $G$, then the local degrees of $L$ are
uniformly bounded at all rational primes if and only if $G$ has finite
exponent. In this note we show that the non uniform boundedness of the local
degrees is not equivalent to any group theoretical property. More precisely, we
exhibit several groups that admit two different realisations over a given
number field, one with bounded local degrees at a given set of primes and one
with infinite local degrees at the same primes.


  We consider resonant dynamics in a dilute atomic gas falling under gravity
through a periodically pulsed standing-wave laser field. Our numerical
calculations are based on a Monte Carlo method for an incoherent mixture of
noninteracting plane waves, and show that quantum resonances are highly
sensitive to the relative acceleration between the atomic gas and the pulsed
optical standing wave. For particular values of the atomic acceleration, we
observe fractional resonances. We investigate the effect of the initial atomic
momentum width on the fractional resonances, and quantify the sensitivity of
fractional resonances to thermal effects.


  The discovery of new functional and stable materials is a big challenge due
to its complexity. This work aims at the generation of new crystal structures
with desired properties, such as chemical stability and specified chemical
composition, by using machine learning generative models. Compared to the
generation of molecules, crystal structures pose new difficulties arising from
the periodic nature of the crystal and from the specific symmetry constraints
related to the space group. In this work, score-based probabilistic models
based on annealed Langevin dynamics, which have shown excellent performance in
various applications, are adapted to the task of crystal generation. The
novelty of the presented approach resides in the fact that the lattice of the
crystal cell is not fixed. During the training of the model, the lattice is
learned from the available data, whereas during the sampling of a new chemical
structure, two denoising processes are used in parallel to generate the lattice
along the generation of the atomic positions. A multigraph crystal
representation is introduced that respects symmetry constraints, yielding
computational advantages and a better quality of the sampled structures. We
show that our model is capable of generating new candidate structures in any
chosen chemical system and crystal group without any additional training. To
illustrate the functionality of the proposed method, a comparison of our model
to other recent generative models, based on descriptor-based metrics, is
provided.


  This paper is concerned with new results for the circular Eisenstein series
$\varepsilon_r(z)$ as well as with a novel approach to Hilbert-Eisenstein
series $\mathfrak h_r(z)$, introduced by Michael Hauss in 1995. The latter turn
out to be the product of the hyperbolic sinh--function with an explicit closed
form linear combination of digamma functions. The results, which include
differentiability properties and integral representations, are established by
independent and different argumentations. Highlights are new results on the
Butzer--Flocke--Hauss Omega function, one basis for the study of
Hilbert-Eisenstein series, which have been the subject of several recent
papers.


  Many active galactic nuclei (AGN) and particularly narrow-line Seyfert 1
(NLS1) galaxies, usually exhibit blueshifts and blue wings in several emission
lines, which are mainly associated with outflows and strong winds. In order to
study the radial velocity difference between the narrow component of H$\beta$
and the core component of [OIII]$\lambda$5007 and the asymmetric emission of
this forbidden line, we investigate a sample of NLS1 galaxies . One of the aims
of this paper is to analyze the blue wings of the [OIII]$\lambda$5007 profiles
and their relation with the central engine. We have obtained and studied
medium-resolution spectra (190 km s$^{-1}$ FWHM at H$\beta$) of a sample of 28
NLS1 galaxies in the optical range 4300 - 5200\AA. We performed Gaussian
decomposition to the H$\beta$ and [OIII]$\lambda\lambda$4959,5007 emission
profiles in order to study the distinct components of these lines. A new blue
outlier galaxy is found, in which the center of the core component of [OIII] is
blueshifted by 405 km s$^{-1}$ relative to the center of the narrow component
of H$\beta$ line. We confirmed a previously known correlation between the
blueshift and the full width half maximum (FWHM) of the core component of
[OIII]$\lambda$5007 line. We also corroborated the correlation between the
latter and the velocity of the centroid of the blue wing. On the other hand, by
studying the radial velocity difference between the blue end of the asymmetric
emission and the centroid of the core component of [OIII], we found a
correlation between it and the central black hole mass and, therefore, with the
luminosity of the broad component of H$\beta$. Finally, we found a moderate
correlation between the luminosity of the [OIII] blue wing and the black hole
mass.


  The primitive elements of the supersymmetry algebra cohomology as defined in
a companion paper are computed exhaustively for standard supersymmetry algebras
in dimensions D=2 and D=3, for all signatures (t,D-t) and all numbers N of sets
of supersymmetries.


  Diffusion models are promising for joint trajectory prediction and
controllable generation in autonomous driving, but they face challenges of
inefficient inference steps and high computational demands. To tackle these
challenges, we introduce Optimal Gaussian Diffusion (OGD) and Estimated Clean
Manifold (ECM) Guidance. OGD optimizes the prior distribution for a small
diffusion time $T$ and starts the reverse diffusion process from it. ECM
directly injects guidance gradients to the estimated clean manifold,
eliminating extensive gradient backpropagation throughout the network. Our
methodology streamlines the generative process, enabling practical applications
with reduced computational overhead. Experimental validation on the large-scale
Argoverse 2 dataset demonstrates our approach's superior performance, offering
a viable solution for computationally efficient, high-quality joint trajectory
prediction and controllable generation for autonomous driving. Our project
webpage is at https://yixiaowang7.github.io/OptTrajDiff_Page/.


  In this paper the well-known Dubrovin-Novikov problem posed as long ago as
1984 in connection with the Hamiltonian theory of systems of hydrodynamic type,
namely, the classification problem for multidimensional Poisson brackets of
hydrodynamic type, is solved. In contrast to the one-dimensional case, in the
general case, a nondegenerate multidimensional Poisson bracket of hydrodynamic
type cannot be reduced to a constant form by a local change of coordinates.
Generally speaking, such a Poisson bracket is generated by a nontrivial special
infinite-dimensional Lie algebra. In this paper we obtain a classification of
all nonsingular nondegenerate multidimensional Poisson brackets of hydrodynamic
type for any number N of components and for any dimension n by
differential-geometric methods. A key role in the solution of this problem was
played by the theory of compatible metrics that had been earlier constructed by
the present author.


  We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets
using the data on full q-dependences of the equal time structure factor and the
static susceptibility, calculated through high temperature expansions. We also
carry out comparisons with a model of two coupled S=1/2 planes with the
interlayer coupling tuned to the T=0 critical point. We separately determine
the spin-wave velocity c and mass $m=c/\xi$, in addition to the correlation
length, $\xi$, and find that c is temperature dependent; only for $T\alt JS$,
it approaches its known T=0 value $c_0$. Despite this temperature dependent
spin-wave velocity, full q- and $\omega$-dependences of the dynamical
susceptibility $\chi(\bf q,\omega)$ agree with the universal scaling functions
computable for the $\sigma$-model, for temperatures upto $T_0 \sim 0.6c_0/a$.
Detailed comparisons show that below $T_0$ the S=1 model is in the renormalized
classical (RC) regime, the two plane model is in the quantum critical (QC)
regime, and the S=1/2 model exhibits a RC-QC crossover, centered at T=0.55J. In
particular, for the S=1/2 model above this crossover and for the two-plane
model at all T, the spin-wave mass is in excellent agreement with the universal
QC prediction, $m\simeq 1.04\,T$. In contrast, for the S=1/2 model below the
RC-QC crossover, and for the S=1 model at all T, the behavior agrees with the
known RC expression. For all models nonuniversal behavior occurs above $T\sim
0.6c_0/a$. Our results strongly support the conjecture of Chubukov and Sachdev
that the S=1/2 model is close to the T=0 critical point to exhibit QC behavior.


  It has been suggested for quite a long time that galaxy mergers trigger
activities of supermassive black holes (SMBHs) on the grounds of imaging
observations of individual galaxies. To quantitatively examine this hypothesis,
we calculate quasar luminosity functions (LFs) by manipulating the observed
galaxy LFs ($z\lesssim 2$) and theoretical merger rates from semi-analytical
formulations. We find that the model reproduces the observed quasar LFs
provided that the mass ratio ($q$) of the secondary galaxy to the newly formed
one changes with cosmic time. The results show that the fraction of major
mergers decreases from $f_{\rm maj}\sim 0.2$ at $z\sim 2$ to $f_{\rm maj}\to 0$
at $z\sim 0$. As a consequence, the newly formed SMBHs from major mergers at
$z\sim 2$ may acquire a maximal spin due to the orbital angular momentum of the
merging holes. Subsequently, random accretion led by minor mergers rapidly
drives the SMBHs to spin down. Such an evolutionary trend of the SMBH spins is
consistent with that radiative efficiency of accreting SMBHs strongly declines
with cosmic time, reported by Wang et al. (2009). This suggests that minor
mergers are important in triggering activities of SMBHs at low redshift while
major mergers may dominate at high redshift.


  The Audio/Visual Emotion Challenge and Workshop (AVEC 2019) "State-of-Mind,
Detecting Depression with AI, and Cross-cultural Affect Recognition" is the
ninth competition event aimed at the comparison of multimedia processing and
machine learning methods for automatic audiovisual health and emotion analysis,
with all participants competing strictly under the same conditions. The goal of
the Challenge is to provide a common benchmark test set for multimodal
information processing and to bring together the health and emotion recognition
communities, as well as the audiovisual processing communities, to compare the
relative merits of various approaches to health and emotion recognition from
real-life data. This paper presents the major novelties introduced this year,
the challenge guidelines, the data used, and the performance of the baseline
systems on the three proposed tasks: state-of-mind recognition, depression
assessment with AI, and cross-cultural affect sensing, respectively.


  This paper investigates the effect of the structure of the contact network on
the dynamics of the epidemic outbreak. In particular, we focus on the peak
number of critically infected nodes (PCIN), determining the maximum workload of
intensive healthcare units which should be kept low. As a model and simulation
method, we develop a continuous-time Markov chain (CTMC) model and an efficient
simulation-based on Gillespie's Stochastic Simulation Algorithm (SSA). This
methods combine a realistic approximation of the stochastic process not relying
on the assumptions of mean-field models and large asymptotically large
population sizes as in differential equation models, and at the same time an
efficient way to simulate networks of moderate size. The approach is analysed
for different scenarios, based on data from the COVID-19 outbreak and
demographic data from Ukraine. From these results we extract network topology
features that need to be considered to effectively decrease the peak number of
infections. The CTMC simulation is implemented in python and integrated in a
dashboard that can be used for interactive exploration and it is made openly
available.


  This paper develops a new family of estimators, the minimum density power
divergence estimators (MDPDEs), for the parameters of the one-shot device model
as well as a new family of test statistics, Z-type test statistics based on
MDPDEs, for testing the corresponding model parameters. The family of MDPDEs
contains as a particular case the maximum likelihood estimator (MLE) considered
in Balakrishnan and Ling (2012). Through a simulation study, it is shown that
some MDPDEs have a better behavior than the MLE in relation to robustness. At
the same time, it can be seen that some Z-type tests based on MDPDEs have a
better behavior than the classical Z-test statistic also in terms of
robustness.


  Open vocabulary object detection has been greatly advanced by the recent
development of vision-language pretrained model, which helps recognize novel
objects with only semantic categories. The prior works mainly focus on
knowledge transferring to the object proposal classification and employ
class-agnostic box and mask prediction. In this work, we propose CondHead, a
principled dynamic network design to better generalize the box regression and
mask segmentation for open vocabulary setting. The core idea is to
conditionally parameterize the network heads on semantic embedding and thus the
model is guided with class-specific knowledge to better detect novel
categories. Specifically, CondHead is composed of two streams of network heads,
the dynamically aggregated head and the dynamically generated head. The former
is instantiated with a set of static heads that are conditionally aggregated,
these heads are optimized as experts and are expected to learn sophisticated
prediction. The latter is instantiated with dynamically generated parameters
and encodes general class-specific information. With such a conditional design,
the detection model is bridged by the semantic embedding to offer strongly
generalizable class-wise box and mask prediction. Our method brings significant
improvement to the state-of-the-art open vocabulary object detection methods
with very minor overhead, e.g., it surpasses a RegionClip model by 3.0
detection AP on novel categories, with only 1.1% more computation.


  We consider systematic numerical approximation of a viscoelastic phase
separation model that describes the demixing of a polymer solvent mixture. An
unconditionally stable discretisation method is proposed based on a finite
element approximation in space and a variational time discretization strategy.
The proposed method preserves the energy-dissipation structure of the
underlying system exactly and allows to establish a fully discrete nonlinear
stability estimate in natural norms based on the concept of relative energy.
These estimates are used to derive order optimal error estimates for the method
under minimal smoothness assumptions on the problem data, despite the presence
of various strong nonlinearities in the equations. The theoretical results and
main properties of the method are illustrated by numerical simulations which
also demonstrate the capability to reproduce the relevant physical effects
observed in experiments.


  The MAGIC telescopes are a system of two Imaging Atmospheric Cherenkov
Telescopes (IACTs) designed to observe very high energy (VHE) gamma rays above
~50 GeV. However, as IACTs are sensitive to Cherenkov light in the UV/blue and
use photo-detectors with a time response well below the ms scale, MAGIC is also
able to perform simultaneous optical observations. Through an alternative
system installed in the central PMT of MAGIC II camera, the so-called central
pixel, MAGIC is sensitive to short (1ms - 1s) optical pulses. Periodic signals
from the Crab pulsar are regularly monitored. Here we report for the first time
the experimental determination of the sensitivity of the central pixel to
isolated 1-10 ms long optical pulses. The result of this study is relevant for
searches of fast transients such as Fast Radio Bursts (FRBs).


  The decay mode D^0 -> K^0 \bar{K^0} has no factorizable contribution. We
calculate the nonfactorizable chiral loop contributions of order O(p^3)and then
we use a heavy-light type chiral quark model to calculate nonfactorizable tree
level terms, also of order O(p^3), proportional to the gluon condensate.
Calculated chiral loops and the gluon condensate contributions are of the same
order of magnitude as the experimental amplitude.


  The availability of simultaneous X-ray and Very High Energy (VHE)
observations of blazars helps to identify the plausible radiative contributors
to the VHE emission. Under leptonic scenario, the VHE emission from BL Lacs are
attributed to the synchrotron self Compton (SSC) emission. However, many BL
Lacerate (BL Lacs) have shown significant hardening at VHE after correction for
the Extra Galactic Background Light (EBL) attenuation. We study the spectral
hardening of two nearby BL Lac objects, Mkn 421 and Mkn 501 having most number
of simultaneous X-ray and VHE observations available among all the blazars.
These BL Lacs are relatively close and the effect of EBL attenuation is
relatively minimal/negligible. We study the scatter plot between the X-ray
spectral indices and intrinsic VHE indices to identify the plausible origin of
the VHE emission. For Mkn 501, the VHE spectral indices are steeper than X-ray
spectra, suggesting the scattering process happening at extreme Klein-Nishina
regime. On the other hand, for Mkn 421, the VHE spectra is remarkably harder
than the X-ray spectra, which suggests an additional emission mechanism other
than the SSC process. We show this hard VHE spectrum of Mkn 421 can be
explained by considering the inverse Compton (IC) emission from a broken power
law electron distribution with Maxwellian pileup. The possibility of the
hadronic contribution at VHE {\gamma}-rays is also explored by modeling the
hard spectrum under photomeson process.


  We show that the Novikov--Veselov equation (an analog of KdV in dimension 2 +
1) at positive and negative energies does not have solitons with the space
localization stronger than O(|x|^{-3}) as |x| \to \infty.


  We construct a determining form for the surface quasi-geostrophic (SQG)
equation with subcritical dissipation. In particular, we show that the global
attractor for this equation can be embedded in the long-time dynamics of an
ordinary differential equation (ODE) called a determining form. Indeed, there
is a one-to-one correspondence between the trajectories in the global attractor
of the SQG equation and the steady state solutions of the determining form. The
determining form is a true ODE in the sense that its vector field is Lipschitz.
This is shown by combining De Giorgi techniques and elementary harmonic
analysis. Finally, we provide elementary proofs of the existence of
time-periodic solutions, steady state solutions, as well as the existence of
finitely many determining parameters for the SQG equation.


  Linear second order recursive sequences with arbitrary initial conditions
  are studied. For sequences with the same parameters a ring and a group
  is attached, and isomorphisms and homomorphisms are established
  for related parameters. In the group, called the {\it sequence group},
  sequences are identified if they differ by a scalar factor,
  but not if they differ by a shift, which is the case for the Laxton group.
  Prime divisors of sequences are studied with the help of the sequence group
$\mod p$,
  which is always cyclic of order $p\pm 1$.
  Even and odd numbered subsequences are given independent status through
  the introduction of one rational parameter in place of two integer
  parameters. This step brings significant simplifications in the
  algebra.
  All elements of finite order in Laxton groups and sequence
  groups are described effectively.
  A necessary condition is established for a prime $p$
  to be a divisor of a sequence: {\it the norm (determinant) of
  the respective element of the ring must be a quadratic residue $\mod p$}.
  This leads to an uppers estimate of the set of divisors
  by a set of prime density $1/2$. Numerical experiments show that
  the actual density is typically close to $0.35$.
  A conjecture is formulated that the sets of prime divisors of the
  even and odd numbered elements are independent for a large family
  of parameters.


  Some new properties of the chaotic signal have been implemented in
communication system applications recently. However, due to the broadband
property of the chaotic signal, it is very difficult for a practical transducer
or antenna to convert such a broadband signal into a signal that would be
suitable for practical band-limited wireless channel. Thus, the use of chaos
property to improve the performance of conventional communication system
without changing the system configuration becomes a critical issue in
communication with chaos. In this paper, chaotic baseband waveform generated by
a chaotic shaping filter is used to show that this difficulty can be overcome.
The generated continuous-time chaotic waveform is proven to be topologically
conjugate to a symbolic sequence, allowing the encoding of arbitrary
information sequence into the chaotic waveform. A finite impulse response
filter is used to replace the impulse control in order to encode information
into the chaotic signal, simplifying the algorithm for high speed
communication. A wireless communication system is being proposed using the
chaotic signal as the baseband waveform, which is compatible with the general
wireless communication platform. The matched filter and decoding method, using
chaos properties, enhance the communication system performance. The Bit Error
Rate (BER) and computational complexity performances of the proposed wireless
communication system are analyzed and compared with the conventional wireless
systems. The results show that the proposed chaotic baseband waveform of our
wireless communication method has better BER performance in both the static and
time-varying wireless channels. The experimental results, based on the
commonly-used wireless open-access research platform, show that the BER of the
proposed method is superior to the conventional method under a practical
wireless multipath channel.


  We perform electronic structure calculations for the recently synthesized
iron-based superconductor LiFeO$_2$Fe$_2$Se$_2$. In contrast to other
iron-based superconductors, this material comprises two different iron atoms in
3$d^5$ and 3$d^6$ configurations. In band theory, both contribute to the
low-energy electronic structure. Spin-polarized density functional theory
calculations predict an antiferromagnetic metallic ground state with different
moments on the two Fe sites. However, several other almost degenerate magnetic
configurations exist. Due to their different valences, the two iron atoms
behave very differently when local quantum correlations are included through
the dynamical mean-field theory. The contributions from the half-filled 3$d^5$
atoms in the LiFeO$_2$ layer are suppressed and the 3$d^6$ states from the FeSe
layer restore the standard iron-based superconductor fermiology.


  Machine learning-based segmentation in medical imaging is widely used in
clinical applications from diagnostics to radiotherapy treatment planning.
Segmented medical images with ground truth are useful for investigating the
properties of different segmentation performance metrics to inform metric
selection. Regular geometrical shapes are often used to synthesize segmentation
errors and illustrate properties of performance metrics, but they lack the
complexity of anatomical variations in real images. In this study, we present a
tool to emulate segmentations by adjusting the reference (truth) masks of
anatomical objects extracted from real medical images. Our tool is designed to
modify the defined truth contours and emulate different types of segmentation
errors with a set of user-configurable parameters. We defined the ground truth
objects from 230 patient images in the Glioma Image Segmentation for
Radiotherapy (GLIS-RT) database. For each object, we used our segmentation
synthesis tool to synthesize 10 versions of segmentation (i.e., 10 simulated
segmentors or algorithms), where each version has a pre-defined combination of
segmentation errors. We then applied 20 performance metrics to evaluate all
synthetic segmentations. We demonstrated the properties of these metrics,
including their ability to capture specific types of segmentation errors. By
analyzing the intrinsic properties of these metrics and categorizing the
segmentation errors, we are working toward the goal of developing a
decision-tree tool for assisting in the selection of segmentation performance
metrics.


  Network diversity yields context-dependent benefits that are not yet
fully-understood. I elaborate on a recently introduced distinction between tie
strength diversity and information source diversity, and explain when, how, and
why they matter. The issue whether there are benefits to specialization is the
key.


  Let $M_k^!(\Gamma_0^+(3))$ be the space of weakly holomorphic modular forms
of weight $k$ for the Fricke group of level $3$. We introduce a natural basis
for $M_k^!(\Gamma_0^+(3))$ and prove that for almost all basis elements, all of
their zeros in a fundamental domain lie on the circle centered at 0 with radius
$\frac{1}{\sqrt{3}}$.


  The centre of our Milky Way harbours the closest candidate for a supermassive
black hole. The source is thought to be powered by radiatively inefficient
accretion of gas from its environment. This form of accretion is a standard
mode of energy supply for most galactic nuclei. X-ray measurements have already
resolved a tenuous hot gas component from which it can be fed. However, the
magnetization of the gas, a crucial parameter determining the structure of the
accretion flow, remains unknown. Strong magnetic fields can influence the
dynamics of the accretion, remove angular momentum from the infalling gas,
expel matter through relativistic jets and lead to the observed synchrotron
emission. Here we report multi-frequency measurements with several radio
telescopes of a newly discovered pulsar close to the Galactic Centre and show
that its unusually large Faraday rotation indicates a dynamically relevant
magnetic field near the black hole. If this field is accreted down to the event
horizon it provides enough magnetic flux to explain the observed emission from
the black hole, from radio to X-rays.


  The polarization modes of the cosmological microwave background are an
invaluable source of information for cosmology, and a unique window to probe
the energy scale of inflation. Extracting such information from microwave
surveys requires disentangling between foreground emissions and the
cosmological signal, which boils down to solving a component separation
problem. Component separation techniques have been widely studied for the
recovery of CMB temperature anisotropies but quite rarely for the polarization
modes. In this case, most component separation techniques make use of
second-order statistics to discriminate between the various components. More
recent methods, which rather emphasize on the sparsity of the components in the
wavelet domain, have been shown to provide low-foreground, full-sky estimate of
the CMB temperature anisotropies. Building on sparsity, the present paper
introduces a new component separation technique dubbed PolGMCA (Polarized
Generalized Morphological Component Analysis), which refines previous work to
specifically tackle the estimation of the polarized CMB maps: i) it benefits
from a recently introduced sparsity-based mechanism to cope with partially
correlated components, ii) it builds upon estimator aggregation techniques to
further yield a better noise contamination/non-Gaussian foreground residual
trade-off. The PolGMCA algorithm is evaluated on simulations of full-sky
polarized microwave sky simulations using the Planck Sky Model (PSM), which
show that the proposed method achieve a precise recovery of the CMB map in
polarization with low noise/foreground contamination residuals. It provides
improvements with respect to standard methods, especially on the galactic
center where estimating the CMB is challenging.


  In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is
proposed, based on the idea of relaxing MKP to a {\em Bounded Sequential
Multiple Knapsack Problem}, i.e., a multiple knapsack problem in which item
sizes are divisible. Such a relaxation, called sequential relaxation, is
obtained by suitably replacing the items of a MKP instance with items with
divisible sizes. Experimental results on benchmark instances show that the
upper bound is effective when the ratio between the number of items and the
number of knapsacks is small.


  This paper maps the national UK web presence on the basis of an analysis of
the .uk domain from 1996 to 2010. It reviews previous attempts to use web
archives to understand national web domains and describes the dataset. Next, it
presents an analysis of the .uk domain, including the overall number of links
in the archive and changes in the link density of different second-level
domains over time. We then explore changes over time within a particular
second-level domain, the academic subdomain .ac.uk, and compare linking
practices with variables, including institutional affiliation, league table
ranking, and geographic location. We do not detect institutional affiliation
affecting linking practices and find only partial evidence of league table
ranking affecting network centrality, but find a clear inverse relationship
between the density of links and the geographical distance between
universities. This echoes prior findings regarding offline academic activity,
which allows us to argue that real-world factors like geography continue to
shape academic relationships even in the Internet age. We conclude with
directions for future uses of web archive resources in this emerging area of
research.


  We discuss the 3-window modeling of cold, dense QCD matter equations of state
at density relevant to neutron star properties. At low baryon density, n_B < ~
2n_s (n_s: nuclear saturation density), we utilize purely hadronic equations of
state that are constrained by empirical observations at density n_B ~ n_s and
neutron star radii. At high density, n_B > ~ 5n_s, we use the percolated quark
matter equations of state which must be very stiff to pass the two-solar mass
constraints. The intermediate domain at 2 < n_B/n_s < 5 is described as neither
purely hadronic nor percolated quark matter, and the equations of state are
inferred by interpolating hadronic and percolated quark matter equations of
state. Possible forms of the interpolation are severely restricted by the
condition on the (square of) speed of sound, 0 < c_s^2 < 1. The characteristics
of the 3-window equation of state are compared with those of conventional
hybrid and self-bound quark matters. Using a schematic quark model for the
percolated domain, it is argued that the two-solar mass constraint requires the
model parameters to be as large as their vacuum values, indicating that the
gluon dynamics remains strongly non-perturbative to n_B ~ 10n_s. The hyperon
puzzle is also briefly discussed in light of quark descriptions.


  A non-unital algebra in a closed monoidal category is called self-induced if
the multiplication induces an isomorphism between A\otimes_A A and A. For such
an algebra, we define smoothening and roughening functors that retract the
category of modules onto two equivalent subcategories of smooth and rough
modules, respectively. These functors generalise previous constructions for
group representations on bornological vector spaces. We also study the pairs of
adjoint functors between categories of smooth and rough modules that are
induced by bimodules and Morita equivalence.


  We define the Homomorphism Extension (HomExt) problem: given a group $G$, a
subgroup $M \leq G$ and a homomorphism $\varphi: M \to H$, decide whether or
not there exists a homomorphism $\widetilde{\varphi}: G\to H$ extending
$\varphi$, i.e., $\widetilde{\varphi}|_M = \varphi$. This problem arose in the
context of list-decoding homomorphism codes but is also of independent
interest, both as a problem in computational group theory and as a new and
natural problem in NP of unsettled complexity status.
  We consider the case $H=S_m$ (the symmetric group of degree $m$), i.e.,
$\varphi : G \to H$ is a $G$-action on a set of $m$ elements. We assume $G\le
S_n$ is given as a permutation group by a list of generators. We characterize
the equivalence classes of extensions in terms of a multidimensional oracle
subset-sum problem. From this we infer that for bounded $G$ the HomExt problem
can be solved in polynomial time.
  Our main result concerns the case $G=A_n$ (the alternating group of degree
$n$) for variable $n$ under the assumption that the index of $M$ in $G$ is
bounded by poly$(n)$. We solve this case in polynomial time for all $m <
2^{n-1}/\sqrt{n}$. This is the case with direct relevance to homomorphism codes
(Babai, Black, and Wuu, arXiv 2018); it is used as a component of one of the
main algorithms in that paper.


  Single kinesin molecular motors can processively move along a microtubule
(MT) a few micrometers on average before dissociating. However, cellular length
scales over which transport occurs are several hundred microns and more. Why
seemingly unreliable motors are used to transport cellular cargo remains poorly
understood. We propose a new theory for how low processivity, the average
length of a single bout of directed motion, can enhance cellular transport when
motors and cargoes must first diffusively self assemble into complexes. We
employ stochastic modeling to determine the effect of processivity on overall
cargo transport flux. We show that, under a wide range of physiologically
relevant conditions, possessing "infinite" processivity does not maximize flux
along MTs. Rather, we find that low processivity i.e., weak binding of motors
to MTs, is optimal. These results shed light on the relationship between
processivity and transport efficiency and offer a new theory for the
physiological benefits of low motor processivity.


  Hardy's paradox provides an all-versus-nothing fashion to directly certify
that quantum mechanics cannot be completely described by local realistic
theory. However, when considering potential imperfections in experiments, like
imperfect entanglement source and low detection efficiency, the original
Hardy's paradox may induce a rather small Hardy violation and only be realized
by expensive quantum systems. To overcome this problem, we propose a realigned
Hardy's paradox. Compared with the original version of Hardy's paradox, the
realigned Hardy's paradox can dramatically improve the Hardy violation. Then,
we generalize the realigned Hardy's paradox to arbitrary even $n$ dichotomic
measurements. For $n=2$ and $n=4$ cases, the realigned Hardy's paradox can
achieve Hardy values $P(00|A_1B_1)$ approximate $0.4140$ and $0.7734$
respectively compared with $0.09$ of the original Hardy's paradox. Meanwhile,
the structure of the realigned Hardy's paradox is simpler and more robust in
the sense that there is only one Hardy condition rather than three conditions.
One can anticipate that the realigned Hardy's paradox can tolerate more
experimental imperfections and stimulate more fascinating quantum information
applications.


  The overlap formula proposed by Narayanan and Neuberger in chiral gauge
theories is examined. The free chiral and Dirac Green's functions are
constructed in this formalism. Four dimensional anomalies are calculated and
the usual anomaly cancellation for one standard family of quarks and leptons is
verified.


  We address the problem of Gribov copies in lattice QCD. The gluon propagator
is computed, in the Landau gauge, using 302 ($\beta = 5.8$) $12^4$
configurations gauge fixed to different copies. The results of the simulation
shows that: i) the effect of Gribov copies is small (less than 10%); ii) Gribov
copies change essentially the lowest momenta components ($q < 2.6$ GeV); iii)
within the statistical accuracy of our simulation, the effect of Gribov copies
is resolved if statistical errors are multiplied by a factor of two or three.
Moreover, when modelling the gluon propagator, different sets of Gribov copies
produce different sets of parameters not, necessarily, compatible within one
standard deviation. Finally, our data supports a gluon propagator which, for
large momenta, behaves like a massive gluon propagator with a mass of 1.1 GeV.


  We report a Grand Canonical Monte Carlo simulation study of the liquid-vapor
interface of a model fluid exhibiting polydispersity in terms of the particle
size $\sigma$. The bulk density distribution, $\rho^0(\sigma)$, of the system
is controlled by the imposed chemical potential distribution $\mu(\sigma)$. We
choose the latter such that $\rho^0(\sigma)$ assumes a Schulz form with
associated degree of polydispersity $\approx 14%$. By introducing a smooth
attractive wall, a planar liquid-vapor interface is formed for bulk state
points within the region of liquid-vapor coexistence. Owing to fractionation,
the pure liquid phase is enriched in large particles, with respect to the
coexisting vapor. We investigate how the spatial non-uniformity of the density
near the liquid-vapor interface affects the evolution of the local distribution
of particle sizes between the limiting pure phase forms. We find (as previously
predicted by density functional theory, Bellier-Castella {\em et al}, Phys.
Rev. {\bf E65}, 021503 (2002)) a segregation of smaller particles to the
interface. The magnitude of this effect is quantified for various $\sigma$ via
measurements of the relative adsorption. Additionally, we consider the utility
of various estimators for the interfacial width and highlight the difficulties
of isolating the intrinsic contribution of polydispersity to this width.


  For a mixture of interacting Bose gases initially prepared in a regime of
condensation (uncorrelation), it is proved that in the course of the the time
evolution observables of disjoint sets of particles of each species have
correlation functions that remain asymptotically small in the total number of
particles and display a controlled growth in time. This is obtained by means of
ad hoc estimates of Lieb-Robinson type on the propagation of the interaction,
established here for the multi-component Bose mixture.


  Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow
with relative velocity parallel to the interface between them. The interface is
unstable due to a Kelvin-Helmholtz type of instability in which fluid flow
couples with inertial effects to cause an initial small perturbation to grow.
Large amplitude disturbances form stable solitons. We consider the effects of
applied magnetic fields when one of the two fluids is a ferrofluid. The
dispersion relation governing mode growth is modified so that the magnetic
field can destabilize the interface even in the absence of inertial effects.
However, the magnetic field does not affect the speed of wave propagation for a
given wavenumber. We note that the magnetic field creates an effective
interaction between the solitons.


  Motivated by the problem of testing for the existence of a signal of known
parametric structure and unknown ``location'' (as explained below) against a
noisy background, we obtain for the maximum of a centered, smooth random field
an approximation for the tail of the distribution. For the motivating class of
problems this gives approximately the significance level of the maximum score
test. The method is based on an application of a likelihood-ratio-identity
followed by approximations of local fields. Numerical examples illustrate the
accuracy of the approximations.


  Motivated by earlier studies of artificial perceptions of light called
phosphenes, we analyze traveling wave solutions in a chain of periodically
forced coupled nonlinear oscillators modeling this phenomenon. We examine the
discrete model problem in its co-traveling frame and systematically obtain the
corresponding traveling waves in one spatial dimension. Direct numerical
simulations as well as linear stability analysis are employed to reveal the
parameter regions where the traveling waves are stable, and these waves are, in
turn, connected to the standing waves analyzed in earlier work. We also
consider a two-dimensional extension of the model and demonstrate the robust
evolution and stability of planar fronts and annihilation of radial ones.
Finally, we show that solutions that initially feature two symmetric fronts
with bulged centers evolve in qualitative agreement with experimental
observations of phosphenes.


  The ISO-SWS infrared spectroscopic observations of the nucleus of Seyfert
galaxy NGC4151, which are described in a companion paper, are used together
with a compilation of UV to IR narrow emission line data to determine the
spectral shape of the obscured extreme-UV continuum that photoionizes the
narrow line emitting gas in the active galactic nucleus. We present a new
method to determine the best fitting photoionizing continuum and emission line
cloud model from a heterogeneous set of emission line data.
  For NGC4151, we find a best-fit model that reproduces the observed line
fluxes to within a factor of 2 on average, and which is consistent with the
observed geometry of the optical Narrow Line Region (NLR). Our model consists
of a clumpy, optically thick (ionization bounded) gas distribution, with a
hydrogen gas density of ~1000 cm^-3 and a volume filling factor of 6.5*10^-4.
  Our best fitting spectral energy distribution (SED) falls sharply beyond the
Lyman limit and then rises sharply again towards 100 eV. In particular, it does
not display a `Big Blue Bump' signature of a hot accretion disk. We find that
this SED, which best reproduces the NLR line emission on the 100--500 pc scale,
does not have enough UV photons to produce the observed BLR recombination
emission from the inner 1 pc. This suggests that the BLR is photoionized by the
intrinsic continuum source, which does have a strong UV component (perhaps a
Big Blue Bump), but that this UV component is absorbed by material located
between the NLR and BLR. Our analysis suggests that the absorber consists of
\~5*10^19 cm^-2 of neutral hydrogen. Such an absorber was independently
detected by UV absorption lines (Kriss et al. 1992, 1995).


  We show the non existence of manifold structure on certain topological
constructions. The main results of this paper are: (1) The wedge of manifold
with itself is not a manifold. (2) The cone of a manifold is not a manifold.
The main tools for the main result is homological algebra and algebraic
topology.


  A three-level atomic medium can be made transparent to a resonant probe field
in the presence of a strong control field acting on an adjacent atomic
transition to a long-lived state, which can be represented by a highly excited
Rydberg state. The long-range interactions between the Rydberg state atoms then
translate into strong, non-local, dispersive or absorptive interactions between
the probe photons, which can be used to achieve deterministic quantum logic
gates and single photon sources. Here we show that long-range dipole-dipole
exchange interaction with one or more spins -- two-level systems represented by
atoms in suitable Rydberg states -- can play the role of control field for the
optically-dense medium of atoms. This induces transparency of the medium for a
number of probe photons $n_p$ not exceeding the number of spins $n_s$, while
all the excess photons are resonantly absorbed upon propagation. In the most
practical case of a single spin atom prepared in the Rydberg state, the medium
is thus transparent only to a single input probe photon. For larger number of
spins $n_s$, all $n_p \leq n_s$ photon components of the probe field would
experience transparency but with an $n_p$-dependent group velocity.


  We consider an extension of the rollout algorithm that applies to constrained
deterministic dynamic programming, including challenging combinatorial
optimization problems. The algorithm relies on a suboptimal policy, called base
heuristic. Under suitable assumptions, we show that if the base heuristic
produces a feasible solution, the rollout algorithm has a cost improvement
property: it produces a feasible solution, whose cost is no worse than the base
heuristic's cost.
  We then focus on multiagent problems, where the control at each stage
consists of multiple components (one per agent), which are coupled either
through the cost function or the constraints or both. We show that the cost
improvement property is maintained with an alternative implementation that has
greatly reduced computational requirements, and makes possible the use of
rollout in problems with many agents. We demonstrate this alternative algorithm
by applying it to layered graph problems that involve both a spatial and a
temporal structure. We consider in some detail a prominent example of such
problems: multidimensional assignment, where we use the auction algorithm for
2-dimensional assignment as a base heuristic. This auction algorithm is
particularly well-suited for our context, because through the use of prices, it
can advantageously use the solution of an assignment problem as a starting
point for solving other related assignment problems, and this can greatly speed
up the execution of the rollout algorithm.


  Accurately segmenting teeth and identifying the corresponding anatomical
landmarks on dental mesh models are essential in computer-aided orthodontic
treatment. Manually performing these two tasks is time-consuming, tedious, and,
more importantly, highly dependent on orthodontists' experiences due to the
abnormality and large-scale variance of patients' teeth. Some machine
learning-based methods have been designed and applied in the orthodontic field
to automatically segment dental meshes (e.g., intraoral scans). In contrast,
the number of studies on tooth landmark localization is still limited. This
paper proposes a two-stage framework based on mesh deep learning (called
TS-MDL) for joint tooth labeling and landmark identification on raw intraoral
scans. Our TS-MDL first adopts an end-to-end \emph{i}MeshSegNet method (i.e., a
variant of the existing MeshSegNet with both improved accuracy and efficiency)
to label each tooth on the downsampled scan. Guided by the segmentation
outputs, our TS-MDL further selects each tooth's region of interest (ROI) on
the original mesh to construct a light-weight variant of the pioneering
PointNet (i.e., PointNet-Reg) for regressing the corresponding landmark
heatmaps. Our TS-MDL was evaluated on a real-clinical dataset, showing
promising segmentation and localization performance. Specifically,
\emph{i}MeshSegNet in the first stage of TS-MDL reached an averaged Dice
similarity coefficient (DSC) at \textcolor[rgb]{0,0,0}{$0.964\pm0.054$},
significantly outperforming the original MeshSegNet. In the second stage,
PointNet-Reg achieved a mean absolute error (MAE) of $0.597\pm0.761 \, mm$ in
distances between the prediction and ground truth for $66$ landmarks, which is
superior compared with other networks for landmark detection. All these results
suggest the potential usage of our TS-MDL in orthodontics.


  Electric-dipole radiation has the well-known far-field solutions of
transverse electric and magnetic (TEM) fields with peak values propagating
normal to (and going to zero along) the dipole axis. The calculation of these
electromagnetic fields is based on the use of the magnetic vector potential:
Its time derivative and divergence for the electric field E, and its curl for
the magnetic field B. In this paper, we suggest the possibility of additional
radiation fields, namely, those based on the shear of the vector potential. Our
results show that these shear waves have a 1/r dependence on far-field
distance, with four radiative components: (1)-(3) an orthogonal triad
consisting of two transverse waves and a longitudinal wave propagating along
the dipole axis (analogous to an acoustic dipole); and (4) a transverse wave
propagating into the same solid angle as E and B, parallel to the E-field but
with one-half the magnitude of the B-field. If confirmed by experiment,
possible applications include RF communications, novel biomedical sensors, and
a new tool in the search for extra-terrestrial intelligence (SETI).


  We revisit the numerical evolution of Ellis-Bronnikov-Morris-Thorne
wormholes, which are constructed with a massless real ghost scalar field. For
our simulations, we have developed a new code based on the standard 3+1
foliation of spacetime. We confirm that, for the massless symmetric wormhole, a
pulse of regular scalar field causes the wormhole throat to collapse and form
an apparent horizon, while a pulse of ghost scalar field can cause the wormhole
throat to expand. As a new result, we show that it is possible for a pulse of
regular matter to travel through the wormhole and then to send a light signal
back before the wormhole collapses. We also evolve pulses of matter traveling
through massive asymmetric wormholes, which has not previously been simulated.


  A couple of technicalities in the paper M. Bojowald, G. Paily, Phys. Rev. D
87, 044044 (2013) are discussed. The explicit formula given there for the
function entering the modified hypersurface-deformed algebra, which presumably
originates in loop quantum gravity, seems to be oversimplified, and the
embedding of deformed special relativity in deformed general relativity
proposed there for spherically symmetric models raises some questions as well.


  The calculation of electromagnetic field distributions within structured
media is central to the optimization and validation of photonic devices. We
introduce WaveY-Net, a hybrid data- and physics-augmented convolutional neural
network that can predict electromagnetic field distributions with ultra fast
speeds and high accuracy for entire classes of dielectric photonic structures.
This accuracy is achieved by training the neural network to learn only the
magnetic near-field distributions of a system and to use a discrete formalism
of Maxwell's equations in two ways: as physical constraints in the loss
function and as a means to calculate the electric fields from the magnetic
fields. As a model system, we construct a surrogate simulator for periodic
silicon nanostructure arrays and show that the high speed simulator can be
directly and effectively used in the local and global freeform optimization of
metagratings. We anticipate that physics-augmented networks will serve as a
viable Maxwell simulator replacement for many classes of photonic systems,
transforming the way they are designed.


  It is well known that if $G$ admits a f.g. subgroup $H$ with a
weaklyaperiodic SFT (resp. an undecidable domino problem), then $G$itself has a
weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can
replace the property "$H$ is a subgroup of $G$"by "$H$ acts translation-like on
$G$", provided $H$ is finitely presented.In particular:* If $G\_1$ and $G\_2$
are f.g. infinite groups, then $G\_1 \times G\_2$ has a weakly aperiodic SFT
(and actually a undecidable domino problem). In particular the Grigorchuk group
has an undecidable domino problem. * Every infinite f.g. $p$-group admits a
weakly aperiodic SFT.


  Galaxy rotation curves are considered to be convincing evidence for dark
matter or some dynamically equivalent alternative mechanism. Starting only from
the rotation curve data, we present a model independent approach of testing a
general hypothesis that dark matter has the properties of a barotropic fluid.
It is shown how the speed of sound squared can be expressed in terms of
rotation curve data and their radial derivatives and how model independent
constraints can be obtained from the requirements that it is confined between 0
and $c^2$. Using the Milky Way rotation curve data available in the literature,
we obtain the constraints on the barotropic fluid speed of sound and illustrate
the potential of this approach. Technical challenges, limitations and possible
future extensions and improvements of the proposed approach are discussed.


  As a variant of Graph Neural Networks (GNNs), Unfolded GNNs offer enhanced
interpretability and flexibility over traditional designs. Nevertheless, they
still suffer from scalability challenges when it comes to the training cost.
Although many methods have been proposed to address the scalability issues,
they mostly focus on per-iteration efficiency, without worst-case convergence
guarantees. Moreover, those methods typically add components to or modify the
original model, thus possibly breaking the interpretability of Unfolded GNNs.
In this paper, we propose HERTA: a High-Efficiency and Rigorous Training
Algorithm for Unfolded GNNs that accelerates the whole training process,
achieving a nearly-linear time worst-case training guarantee. Crucially, HERTA
converges to the optimum of the original model, thus preserving the
interpretability of Unfolded GNNs. Additionally, as a byproduct of HERTA, we
propose a new spectral sparsification method applicable to normalized and
regularized graph Laplacians that ensures tighter bounds for our algorithm than
existing spectral sparsifiers do. Experiments on real-world datasets verify the
superiority of HERTA as well as its adaptability to various loss functions and
optimizers.


  Effect of the femtosecond and nanosecond UV laser irradiation (below the
ablation threshold) of graphite-like hexagonal boron nitride (hBN) has been
studied. Experiments were carried out with the compacted powder under high
vacuum at room temperature using excimer KrF laser (248 nm). In the nanosecond
operation mode, the laser-induced fluorescence spectra are found strongly
modified depending on the integrated doze, which is attributed to a progressive
enrichment of the surface layer by elemental boron. A slow sample recovery
after the laser irradiation has been observed. On the other hand, in the
femtosecond mode the fluorescence spectra depend on the laser fluence, and the
changes are reversible: low energy fluorescence spectra are restored
immediately when the laser energy decreases. This effect can be explained by a
material bleaching, which favors a bulk centers emission. The ablation
threshold has been determined as 78 mJ/cm2 in the femtosecond laser operational
mode.


  We propose a novel 3D neural network architecture for 3D hand pose estimation
from a single depth image. Different from previous works that mostly run on 2D
depth image domain and require intermediate or post process to bring in the
supervision from 3D space, we convert the depth map to a 3D volumetric
representation, and feed it into a 3D convolutional neural network(CNN) to
directly produce the pose in 3D requiring no further process. Our system does
not require the ground truth reference point for initialization, and our
network architecture naturally integrates both local feature and global context
in 3D space. To increase the coverage of the hand pose space of the training
data, we render synthetic depth image by transferring hand pose from existing
real image datasets. We evaluation our algorithm on two public benchmarks and
achieve the state-of-the-art performance. The synthetic hand pose dataset will
be available.


  In the stochastic matching problem, we are given a general (not necessarily
bipartite) graph $G(V,E)$, where each edge in $E$ is realized with some
constant probability $p > 0$ and the goal is to compute a bounded-degree
(bounded by a function depending only on $p$) subgraph $H$ of $G$ such that the
expected maximum matching size in $H$ is close to the expected maximum matching
size in $G$. The algorithms in this setting are considered non-adaptive as they
have to choose the subgraph $H$ without knowing any information about the set
of realized edges in $G$. Originally motivated by an application to kidney
exchange, the stochastic matching problem and its variants have received
significant attention in recent years.
  The state-of-the-art non-adaptive algorithms for stochastic matching achieve
an approximation ratio of $\frac{1}{2}-\epsilon$ for any $\epsilon > 0$,
naturally raising the question that if $1/2$ is the limit of what can be
achieved with a non-adaptive algorithm. In this work, we resolve this question
by presenting the first algorithm for stochastic matching with an approximation
guarantee that is strictly better than $1/2$: the algorithm computes a subgraph
$H$ of $G$ with the maximum degree $O(\frac{\log{(1/ p)}}{p})$ such that the
ratio of expected size of a maximum matching in realizations of $H$ and $G$ is
at least $1/2+\delta_0$ for some absolute constant $\delta_0 > 0$. The degree
bound on $H$ achieved by our algorithm is essentially the best possible (up to
an $O(\log{(1/p)})$ factor) for any constant factor approximation algorithm,
since an $\Omega(\frac{1}{p})$ degree in $H$ is necessary for a vertex to
acquire at least one incident edge in a realization.


  We consider the problem of online collaborative filtering in the online
setting, where items are recommended to the users over time. At each time step,
the user (selected by the environment) consumes an item (selected by the agent)
and provides a rating of the selected item. In this paper, we propose a novel
algorithm for online matrix factorization recommendation that combines linear
bandits and alternating least squares. In this formulation, the bandit feedback
is equal to the difference between the ratings of the best and selected items.
We evaluate the performance of the proposed algorithm over time using both
cumulative regret and average cumulative NDCG. Simulation results over three
synthetic datasets as well as three real-world datasets for online
collaborative filtering indicate the superior performance of the proposed
algorithm over two state-of-the-art online algorithms.


  This study computes the optimal normal actuation on the surface of a NACA0012
airfoil at an angle of attack of 15{\deg} and a Reynolds number of Re = 1000,
using costs defined for minimal drag and maximal lift. To allow for a general
actuation profile, non-zero actuation is permissible on both the suction and
pressure surfaces. This approach of optimal actuation along the full airfoil
surface augments most other studies that have focused on parametrically varied
open-loop control restricted to the suction surface. The gradient-based
optimization procedure requires the gradient of the cost functional with
respect to the design variables, which is determined using the adjoint of the
governing equations. The optimal actuation profile for the two performance aims
are compared. Where possible, similarities with commonly considered open-loop
actuation in the form of backward traveling waves on the suction surface have
been highlighted. In addition, the key spatial locations on the airfoil surface
for the two optimal control strategies have been compared to earlier works
where actuation has been limited to a sub-domain of the airfoil surface. The
flow features emerging from the optimal actuation variations, and their
consequent influence on the instantaneous aerodynamic coefficients, have been
analyzed. To complement our findings with normal actuation, we also provide in
the appendix: results for a more general form of actuation with independent x
and y components, and for a different optimization window to assess the effect
of this window parameter on the actuation profile and the flow features.


  We consider generic differential equations in $\mathbb{R}$ with a finite
number of hyperbolic equilibria, which are subject to $\omega$--periodic
instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of
the original system (without perturbation), we are able to find all periodic
solutions of the perturbed system and study their stability. In this article,
we establish an algorithm to locate $\omega$--periodic solutions of impulsive
systems of frequency $\omega$, to study their stability and to locate
Saddle-node bifurcations. With our technique, we are able to fully characterise
the asymptotic dynamics of the system under consideration.


  Endovascular intervention training is increasingly being conducted in virtual
simulators. However, transferring the experience from endovascular simulators
to the real world remains an open problem. The key challenge is the virtual
environments are usually not realistically simulated, especially the simulation
images. In this paper, we propose a new method to translate simulation images
from an endovascular simulator to X-ray images. Previous image-to-image
translation methods often focus on visual effects and neglect structure
information, which is critical for medical images. To address this gap, we
propose a new method that utilizes multi-scale semantic matching. We apply
self-domain semantic matching to ensure that the input image and the generated
image have the same positional semantic relationships. We further apply
cross-domain matching to eliminate the effects of different styles. The
intensive experiment shows that our method generates realistic X-ray images and
outperforms other state-of-the-art approaches by a large margin. We also
collect a new large-scale dataset to serve as the new benchmark for this task.
Our source code and dataset will be made publicly available.


  A static spherically symmetric metric in Einstein-scalar-tensor gravity
theory with a scalar field potential $V[\phi]$ is non-singular for all real
values of the coordinates. It does not have a black hole event horizon and
there is no essential singularity at the origin of coordinates. The weak energy
condition $\rho_\phi > 0$ fails to be satisfied for $r\lesssim 1.3r_S$ (where
$r_S$ is the Schwarzschild radius) but the strong energy condition
$\rho_\phi+3p_\phi > 0$ is satisfied. The classical Einstein-scalar-tensor
solution is regular everywhere in spacetime without a black hole event horizon.
However, the violation of the weak energy condition may signal the need for
quantum physics anti-gravity as $r\to 0$. The non-singular static spherically
symmetric solution is stable against the addition of ordinary matter.


  Neural link predictors learn distributed representations of entities and
relations in a knowledge graph. They are remarkably powerful in the link
prediction and knowledge base completion tasks, mainly due to the learned
representations that capture important statistical dependencies in the data.
Recent works in the area have focused on either designing new scoring functions
or incorporating extra information into the learning process to improve the
representations. Yet the representations are mostly learned from the observed
links between entities, ignoring commonsense or schema knowledge associated
with the relations in the graph. A fundamental aspect of the topology of
relational data is the cardinality information, which bounds the number of
predictions given for a relation between a minimum and maximum frequency. In
this paper, we propose a new regularisation approach to incorporate relation
cardinality constraints to any existing neural link predictor without affecting
their efficiency or scalability. Our regularisation term aims to impose
boundaries on the number of predictions with high probability, thus,
structuring the embeddings space to respect commonsense cardinality assumptions
resulting in better representations. Experimental results on Freebase, WordNet
and YAGO show that, given suitable prior knowledge, the proposed method
positively impacts the predictive accuracy of downstream link prediction tasks.


  We proposed a general quantum-computing-based algorithm that harnesses the
exponential power of noisy intermediate-scale quantum (NISQ) devices in solving
partial differential equations (PDE). This variational quantum eigensolver
(VQE)-inspired approach transcends previous idealized model demonstrations
constrained by strict and simplistic boundary conditions. It enables the
imposition of arbitrary boundary conditions, significantly expanding its
potential and adaptability for real-world applications, achieving this "from
ad-hoc to systematic" concept. We have implemented this method using the
fourth-order PDE (the Euler-Bernoulli beam) as example and showcased its
effectiveness with four different boundary conditions. This framework enables
expectation evaluations independent of problem size, harnessing the
exponentially growing state space inherent in quantum computing, resulting in
exceptional scalability. This method paves the way for applying quantum
computing to practical engineering applications.


  The success of Federated Learning (FL) depends on the quantity and quality of
the data owners (DOs) as well as their motivation to join FL model training.
Reputation-based FL participant selection methods have been proposed. However,
they still face the challenges of the cold start problem and potential
selection bias towards highly reputable DOs. Such a bias can result in lower
reputation DOs being prematurely excluded from future FL training rounds,
thereby reducing the diversity of training data and the generalizability of the
resulting models. To address these challenges, we propose the Gradual
Participant Selection scheme for Auction-based Federated Learning (GPS-AFL).
Unlike existing AFL incentive mechanisms which generally assume that all DOs
required for an FL task must be selected in one go, GPS-AFL gradually selects
the required DOs over multiple rounds of training as more information is
revealed through repeated interactions. It is designed to strike a balance
between cost saving and performance enhancement, while mitigating the drawbacks
of selection bias in reputation-based FL. Extensive experiments based on
real-world datasets demonstrate the significant advantages of GPS-AFL, which
reduces costs by 33.65% and improved total utility by 2.91%, on average
compared to the best-performing state-of-the-art approach.


  Plasmonic enhancement of nonlinear optical processes confront severe
limitations arising from the strong dispersion of metal susceptibilities and
small interaction volumes that hamper desirable phase-matching-like conditions.
Maximizing nonlinear interactions in nanoscale systems require simultaneous
excitation of resonant modes that spatially and constructively overlap at all
wavelengths involved in the process. Here, we present a hybrid rectangular
patch antenna design for optimal second harmonic generation (SHG) that is
characterized by a non-centrosymmetric dielectric/ferroelectric material at the
plasmonic hot spot. The optimization of the rectangular patch allows for the
independent tuning of various modes of resonances that can be used to enhance
the SHG process. We explore the angular dependence of SHG in these hybrid
structures and highlight conditions necessary for maximal SHG efficiency.
Furthermore, we propose a novel configuration with a periodically-poled
ferroelectric layer for orders-of-magnitude enhanced SHG at normal incidence.
Such a platform may enable the development of integrated nanoscale light
sources and on-chip frequency converters.


  We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in
the four-dimensional Euclidean space.


  This talk has the goal of introducing two upcoming exciting avenues of
discovery in precision Cosmology: spectral distortions (SDs) and gravitational
waves (GWs). The former signals offer a clear window into the state of the
primordial plasma at times prior to recombination, and thus sheds light on
small-scale primordial perturbations, dark matter decay and black hole
formation to just mention a few scenarios. The latter signals, which are
already offering new insights into the landscape of black hole and neutron star
mergers, will reveal intricate dynamics of the early universe including
primordial black holes, inflationary potentials, and even reheating dynamics.
An elegant link is drawn between these two future observations since primordial
GW backgrounds will source SDs, a coupling which offers unique insight to over
six decades of GW frequencies. More importantly the SD visibility window
bridges the gap between astrophysical high- and cosmological low-frequency
measurements. This means SDs will not only complement other GW observations,
but will be the sole probe of physical processes at certain scales.


  The 21cm emission of neutral hydrogen is a potential probe of the matter
distribution in the Universe after reionisation. Cosmological surveys of this
line intensity will be conducted in the coming years by the SKAO and HIRAX
experiments, complementary to upcoming galaxy surveys. We present the first
forecasts of the cosmological constraints from the combination of the 21cm
power spectrum and bispectrum. Fisher forecasts are computed for the
constraining power of these surveys on cosmological parameters, the BAO
distance functions and the growth function. We also estimate the constraining
power on dynamical dark energy and modified gravity. Finally we investigate the
constraints on the 21cm clustering bias, up to second order. We consider the
effects on the 21cm correlators of the telescope beam, instrumental noise,
foreground avoidance, the Alcock-Paczynski effect and theoretical errors in the
modelling of the correlators. Adding Planck priors, and marginalising over
nuisance parameters, HIRAX achieves sub-percent precision on the $\Lambda$CDM
parameters, with SKAO delivering slightly lower precision. The modified gravity
parameter $\gamma$ is constrained at 1% (HIRAX) and 5% (SKAO). For the dark
energy parameters $w_0,w_a$, HIRAX delivers percent-level precision while SKAO
constraints are weaker. HIRAX achieves sub-percent precision on the BAO
distance functions $D_A,H$, while SKAO reaches 1-2% for $0.6\lesssim z\lesssim
1$. The growth rate $f$ is constrained at a few-percent level for the whole
redshift range of HIRAX and for $0.6\lesssim z\lesssim 1$ by SKAO. The
different performances arise mainly since HIRAX is a packed inteferometer that
is optimised for BAO measurements, while SKAO is not optimised for
interferometer cosmology and operates better in single-dish mode, where the
telescope beam limits access to the smaller scales that are covered by an
interferometer.


  We report on a combined experimental and theoretical study of polarization
self-rotation in an ultracold atomic sample. In the experiments, a probe laser
is tuned in the spectral vicinity of the D1 line to observe polarization
self-rotation in a sample of ultracold Rb prepared in a magneto-optical trap.
Systematic measurements of the rotation angle of the light-polarization ellipse
as a function of laser intensity, initial ellipticity and detuning are made.
The observations, in good agreement with theoretical simulations, are
indicative of the presence of a residual static magnetic field, resulting in
measured asymmetries in the rotation angle for right and left ellipticities. In
this paper we present our detailed experimental results and analysis of the
combined influences of polarization self-rotation and the Faraday effect.


  The disk instability mechanism for giant planet formation is based on the
formation of clumps in a marginally-gravitationally unstable protoplanetary
disk, which must lose thermal energy through a combination of convection and
radiative cooling if they are to survive and contract to become giant
protoplanets. While there is good observational support for forming at least
some giant planets by disk instability, the mechanism has become theoretically
contentious, with different three dimensional radiative hydrodynamics codes
often yielding different results. Rigorous code testing is required to make
further progress. Here we present two new analytical solutions for radiative
transfer in spherical coordinates, suitable for testing the code employed in
all of the Boss disk instability calculations. The testing shows that the Boss
code radiative transfer routines do an excellent job of relaxing to and
maintaining the analytical results for the radial temperature and radiative
flux profiles for a spherical cloud with high or moderate optical depths,
including the transition from optically thick to optically thin regions. These
radial test results are independent of whether the Eddington approximation,
diffusion approximation, or flux-limited diffusion approximation routines are
employed. The Boss code does an equally excellent job of relaxing to and
maintaining the analytical results for the vertical (theta) temperature and
radiative flux profiles for a disk with a height proportional to the radial
distance. These tests strongly support the disk instability mechanism for
forming giant planets.


  We give a 1-sided randomised algorithm to detect when a permutation group of
degree n, given by generators, contains the alternating group of degree n. This
improves on standard methods, and on an algorithm of P. Cameron and J. Cannon.


  Two anomalously weak transitions within the $2 ^3{\rm S}_1~-~3 ^3{\rm P}_J$
manifolds in $^3$He have been identified. Their transition strengths are
measured to be 1,000 times weaker than that of the strongest transition in the
same group. This dramatic suppression of transition strengths is due to the
dominance of the hyperfine interaction over the fine structure interaction. An
alternative selection rule based on \textit{IS}-coupling (where the nuclear
spin is first coupled to the total electron spin) is proposed. This provides
qualitative understanding of the transition strengths. It is shown that the
small deviations from the \textit{IS}-coupling model are fully accounted for by
an exact diagonalization of the strongly interacting states.


  The Fokker-Planck (FP) equation is a linear partial differential equation
which governs the temporal and spatial evolution of the probability density
function (PDF) associated with the response of stochastic dynamical systems. An
exact analytical solution of the FP equation is only available for a limited
subset of dynamical systems. Semi-analytical methods are available for larger,
yet still a small subset of systems, while traditional computational methods;
e.g. Finite Elements and Finite Difference require dividing the computational
domain into a grid of discrete points, which incurs significant computational
costs for high-dimensional systems. Physics-informed learning offers a
potentially powerful alternative to traditional computational schemes. To
evaluate its potential, we present a data-free, physics-informed neural network
(PINN) framework to solve the FP equation for a class of nonlinear stochastic
dynamical systems. In particular, through several examples concerning the
stochastic response of the Duffing, Van der Pol, and the Duffing-Van der Pol
oscillators, we assess the ability and accuracy of the PINN framework in $i)$
predicting the PDF under the combined effect of additive and multiplicative
noise, $ii)$ capturing P-bifurcations of the PDF, and $iii)$ effectively
treating high-dimensional systems. Through comparisons with Monte-Carlo
simulations and the available literature, we show that PINN can effectively
address all of the afore-described points. We also demonstrate that the
computational time associated with the PINN solution can be substantially
reduced by using transfer learning.


  This paper reviews the theory of protostellar debris disks. After a brief
introduction to accretion disk physics, I describe coagulation models of planet
formation in the outer regions of planetesimal disks. Coagulation models for
the Kuiper Belt produce Pluto-sized objects on timescales of 10-40 Myr. These
models yield size distributions which agree with observations of Kuiper Belt
objects with red magnitudes, R = 20-27. Velocity stirring models for other
debris disk systems demonstrate that 500 km or larger objects can stir the
velocities of small objects up to the shattering limit needed to begin a
collisional cascade.


  The random-phase approximation to the ground state correlation energy (RPA)
in combination with exact exchange (EX) has brought Kohn-Sham (KS) density
functional theory one step closer towards a universal, "general purpose first
principles method". In an effort to systematically assess the influence of
several correlation energy contributions beyond RPA, this work presents
dissociation energies of small molecules and solids, activation energies for
hydrogen transfer and non-hydrogen transfer reactions, as well as reaction
energies for a number of common test sets. We benchmark EX+RPA and several
flavors of energy functionals going beyond it: second-order screened exchange
(SOSEX), single excitation (SE) corrections, renormalized single excitation
(rSE) corrections, as well as their combinations. Both the single excitation
correction as well as the SOSEX contribution to the correlation energy
significantly improve upon the notorious tendency of EX+RPA to underbind.
Surprisingly, activation energies obtained using EX+RPA based on a KS reference
alone are remarkably accurate. RPA+SOSEX+rSE provides an equal level of
accuracy for reaction as well as activation energies and overall gives the most
balanced performance, which makes it applicable to a wide range of systems and
chemical reactions.


  Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper,
we introduce the notion of convexity of M. It implies that the momentum image
is convex, the moment map has connected fibers, and the total moment map is
open onto its image. Conversely, the three properties above imply convexity. We
show that most Hamiltonian manifolds occuring "in nature" are convex (e.g., if
M is compact, complex algebraic, or a cotangent bundle). Moreover, every
Hamiltonian manifold is locally convex. This is an expanded version of section
2 of my paper dg-ga/9712010 on Weyl groups of Hamiltonian manifolds.


  Red giant stars are solar-like pulsators presenting mixed-modes. Such modes
consist in a coupling between pressure waves propagating in the external
convective envelope and gravity waves propagating in the radiative interior.
Therefore, the red giant asteroseismology provides us with a direct view on
their core and opens the possibility to monitor the evolution of their core
rotation. Previous measurements of the mean core rotation revealed that angular
momentum is efficiently transferred from the core to the envelope inside red
giants, but the physical mechanisms at work are not yet fully understood. We
thus need stronger observational constraints on the evolution of the red giant
core rotation. In this context, we developed an automated method to determine
the mean core rotation of red giant branch stars observed with Kepler. This
automated method is paving the way for the future PLATO data, representing
hundreds of thousands of potential red giant oscillation spectra. Results
obtained for almost 1200 red giant branch stars indicate that the rate of the
core rotation braking is lower than previously estimated and does not seem to
depend on the stellar mass.


  This paper investigates the maximum throughput for a rechargeable secondary
user (SU) sharing the spectrum with a primary user (PU) plugged to a reliable
power supply. The SU maintains a finite energy queue and harvests energy from
natural resources, e.g., solar, wind and acoustic noise. We propose a
probabilistic access strategy by the SU based on the number of packets at its
energy queue. We investigate the effect of the energy arrival rate, the amount
of energy per energy packet, and the capacity of the energy queue on the SU
throughput under fading channels. Results reveal that the proposed access
strategy can enhance the performance of the SU.


  Capitalizing on large pre-trained models for various downstream tasks of
interest have recently emerged with promising performance. Due to the
ever-growing model size, the standard full fine-tuning based task adaptation
strategy becomes prohibitively costly in terms of model training and storage.
This has led to a new research direction in parameter-efficient transfer
learning. However, existing attempts typically focus on downstream tasks from
the same modality (e.g., image understanding) of the pre-trained model. This
creates a limit because in some specific modalities, (e.g., video
understanding) such a strong pre-trained model with sufficient knowledge is
less or not available. In this work, we investigate such a novel cross-modality
transfer learning setting, namely parameter-efficient image-to-video transfer
learning. To solve this problem, we propose a new Spatio-Temporal Adapter
(ST-Adapter) for parameter-efficient fine-tuning per video task. With a
built-in spatio-temporal reasoning capability in a compact design, ST-Adapter
enables a pre-trained image model without temporal knowledge to reason about
dynamic video content at a small (~8%) per-task parameter cost, requiring
approximately 20 times fewer updated parameters compared to previous work.
Extensive experiments on video action recognition tasks show that our
ST-Adapter can match or even outperform the strong full fine-tuning strategy
and state-of-the-art video models, whilst enjoying the advantage of parameter
efficiency. The code and model are available at
https://github.com/linziyi96/st-adapter


  We consider a tippe top modeled as an eccentric sphere, spinning on a
horizontal table and subject to a sliding friction. Ignoring translational
effects, we show that the system is reducible using a Routhian reduction
technique. The reduced system is a two dimensional system of second order
differential equations, that allows an elegant and compact way to retrieve the
classification of tippe tops in six groups as proposed in [1] according to the
existence and stability type of the steady states.


  Martinus Veltman was the first to point out the inconsistency of the
experimental value for the decay rate of $\pi^0\rightarrow\gamma\gamma$ and its
calculation by J. Steinberger with the very successful concept of the pion as
the (pseudo)Nambu-Goldstone boson of the spontaneously broken global axial
symmetry of strong interactions. That inconsistency has been resolved by J.
Bell and R. Jackiw in their famous paper on the chiral anomalies. We review the
connection between the decay amplitudes of an axion into two gauge bosons in
Abelian vector-like and chiral gauge theories. The axion is the Nambu-Goldstone
boson of a spontaneously broken axial global symmetry of the theory. Similarly
as for the vector-like gauge theory, also in the chiral one the axion decay
amplitude is determined by the anomaly of the current of the axial symmetry in
its non-linear realization. Certain subtlety in the calculation of the anomaly
in chiral gauge theories is emphasised.


  Formation rates of compact-object binaries are often derived from population
synthesis calculations. However, such calculations depend sensitively on a
relatively large number of model input parameters. Given considerable
uncertainty in those model parameters, the predicted inspiral rates for double
compact objects relevant to gravitational-wave interferometric detectors have
been shown to be are uncertain by several orders of magnitude. Typically,
inspiral rates are estimated for only a small set of models with a remarkably
poor coverage of the highly multi-dimensional parameter space (primarily
because of limited computer resources). Here, using as an example seven
population-synthesis model parameters, we show that it is possible to derive
fits of double-compact-object inspiral rates dependent simultaneously on all
seven parameters. We find these fits to be accurate to 50% for binary black
holes and to 40% for binary neutron stars. The availability of such fits
implies that (i) depending on the problem of interest, it is not necessary to
complete large numbers of computationally demanding population synthesis
calculations; and (ii) for the first time, the sufficient exploration of the
relevant phase space and the assessment of the uncertainties involved is not
limited by computational resources and becomes feasible. Finally, we have also
produced a histogram of the (a priori likely) binary black hole inpsiral rate,
assuming our population synthesis models are equally likely. This histogram,
effectively an a priori probability distribution for the BH-BH inspiral rate,
suggests that merger rate is conservatively bounded below by
10^(-8)/yr/Milky-Way-galaxy.


  Photon correlations are investigated for a single laser-excited ion trapped
in front of a mirror. Varying the relative distance between the ion and the
mirror, photon correlation statistics can be tuned smoothly from an
antibunching minimum to a bunching-like maximum. Our analysis concerns the
non-Markovian regime of the ion-mirror interaction and reveals the field
establishment in a half-cavity interferometer.


  Motivated by localization theorems on moduli spaces, we prove a structural
classification of Deligne-Mumford stacks with an action of a torus where the
induced action on the coarse moduli space is trivial. We also establish a
general local structure theorem for morphisms of algebraic stacks.


  Quantizing deep neural networks is an effective method for reducing memory
consumption and improving inference speed, and is thus useful for
implementation in resource-constrained devices. However, it is still hard for
extremely low-bit models to achieve accuracy comparable with that of
full-precision models. To address this issue, we propose learnable companding
quantization (LCQ) as a novel non-uniform quantization method for 2-, 3-, and
4-bit models. LCQ jointly optimizes model weights and learnable companding
functions that can flexibly and non-uniformly control the quantization levels
of weights and activations. We also present a new weight normalization
technique that allows more stable training for quantization. Experimental
results show that LCQ outperforms conventional state-of-the-art methods and
narrows the gap between quantized and full-precision models for image
classification and object detection tasks. Notably, the 2-bit ResNet-50 model
on ImageNet achieves top-1 accuracy of 75.1% and reduces the gap to 1.7%,
allowing LCQ to further exploit the potential of non-uniform quantization.


  In the rapidly evolving field of autonomous systems, the safety and
reliability of the system components are fundamental requirements. These
components are often vulnerable to complex and unforeseen environments, making
natural edge-case generation essential for enhancing system resilience. This
paper presents GENESIS-RL, a novel framework that leverages system-level safety
considerations and reinforcement learning techniques to systematically generate
naturalistic edge cases. By simulating challenging conditions that mimic the
real-world situations, our framework aims to rigorously test entire system's
safety and reliability. Although demonstrated within the autonomous driving
application, our methodology is adaptable across diverse autonomous systems.
Our experimental validation, conducted on high-fidelity simulator underscores
the overall effectiveness of this framework.


  Frustrated magnets are a notorious example where usual perturbative methods
fail. Having recourse to an exact renormalization group approach, one gets a
coherent picture of the physics of Heisenberg frustrated magnets everywhere
between d=2 and d=4: all known perturbative results are recovered in a single
framework, their apparent conflict is explained while the description of the
phase transition in d=3 is found to be in good agreement with the experimental
context.


  Randomised controlled trials in reproductive medicine are often subject to
outcome truncation, where study outcomes are only defined in a subset of
participants. Examples include birthweight (measurable only in the subgroup of
participants who give birth) and miscarriage (which can only occur in
participants who become pregnant). These are typically analysed by making a
comparison between treatment arms within the subgroup (comparing birthweights
in the subgroup who gave birth, or miscarriages in the subgroup who became
pregnant). However, this approach does not represent a randomised comparison
when treatment influences the probability of being observed (i.e. survival).
The practical implications of this for reproductive trials are unclear. We
developed a simulation platform to investigate the implications of outcome
truncation for reproductive medicine trials. We used this to perform a
simulation study, in which we considered the bias, Type 1 error, coverage, and
precision of standard statistical analyses for truncated continuous and binary
outcomes. Increasing treatment effect on the intermediate variable, strength of
confounding between the intermediate and outcome variables, and interactions
between treatment and confounder were found to adversely affect performance.
However, within parameter ranges we would consider to be more realistic, the
adverse effects were generally not drastic. For binary outcomes, the study
highlighted that outcome truncation may lead to none of the participants in a
study arm experiencing the outcome event. This was found to have severe
consequences for inferences, and this may have implications for meta-analysis.


  We study the regularity criteria for weak solutions to the $3D$
incompressible Navier--Stokes equations in terms of the geometry of vortex
structures, taking into account the boundary effects. A boundary regularity
theorem is proved on regular domains with a class of oblique derivative
boundary conditions, providing that the vorticity of the fluid is coherently
aligned. In particular, we establish the boundary regularity on round balls,
half-spaces and right circular cylindrical ducts, subject to the classical
Navier and kinematic boundary conditions.


  The classical Talbot method for the computation of the inverse Laplace
transform is improved for the case where the transform is analytic in the
complex plane except for the negative real axis. First, by using a truncated
Talbot contour rather than the classical contour that goes to infinity in the
left half-plane, faster convergence is achieved. Second, a control mechanism
for improving numerical stability is introduced. These two features are
incorporated into a software code, whose performance is assessed on transforms
from tables as well as from actual applications. It is shown that even when the
transform has singularities off the negative real axis, rapid convergence can
still be achieved in many cases.


  The manufacturing of crystal films lies at the heart of modern
nanotechnology. How to accurately predict the motion of a crystal surface is of
fundamental importance. Many continuum models have been developed for this
purpose, including a number of PDE models, which are often obtained as the
continuum limit of a family of kinetic Monte Carlo models of crystal surface
relaxation that includes both the solid-on-solid and discrete Gaussian models.
In this paper we offer an analytical perspective into some of these models. To
be specific, we study the existence of a weak solution to the boundary value
problem for the equation $ - \Delta e^{-\mbox{div}\left(|\nabla u|^{p-2}\nabla
u\right)}+au=f$, where $p>1, a>0$ are given numbers and $f$ is a given
function. This problem is derived from a crystal surface model proposed by
J.L.~Marzuola and J.~Weare (2013 Physical Review, E 88, 032403). The
mathematical challenge is due to the fact that the principal term in our
equation is an exponential function of a p-Laplacian. Existence of a
suitably-defined weak solution is established under the assumptions that
$p\in(1,2], \ N\leq 4$, and $f\in W^{1,p}$. Our investigations reveal that the
key to our existence assertion is how to control the set where
$-\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right)$ is $\pm\infty$.


  For a universe presently dominated by static or dynamic vacuum energy,
cosmological constant (LCDM) or quintessence (QCDM), we calculate the
asymptotic collapsed mass fraction as function of the present ratio of vacuum
energy to clustered mass, \Omega_{Q0}/\Omega_{m0}. Identifying these collapsed
fractions as anthropic probabilities, we find the value \Omega_{Q0}/\Omega_{m0}
\sim 2 to be reasonably likely in LCDM, and very likely in QCDM.