  Family studies provide an important tool for understanding etiology of
diseases, with the key aim of discovering evidence of family aggregation and to
determine if such aggregation can be attributed to genetic components.
Heritability and concordance estimates are routinely calculated in twin studies
of diseases, as a way of quantifying such genetic contribution. The endpoint in
these studies are typically defined as occurrence of a disease versus death
without the disease. However, a large fraction of the subjects may still be
alive at the time of follow-up without having experienced the disease thus
still being at risk. Ignoring this right-censoring can lead to severely biased
estimates. We propose to extend the classical liability threshold model with
inverse probability of censoring weighting of complete observations. This leads
to a flexible way of modeling twin concordance and obtaining consistent
estimates of heritability. We apply the method in simulations and to data from
the population based Danish twin cohort where we describe the dependence in
prostate cancer occurrence in twins.


  Crowdfunding has emerged as a widespread strategy for startups seeking
financing, particularly through reward-based methods. However, understanding
its economic impact at both micro and macro levels requires thorough analysis,
often involving advanced studies on past campaigns to extract insights that
aiding companies in optimizing their crowdfunding project types and launch
methodologies. Such analyses are often beyond the scope of basic data analysis
techniques and frequently demand advanced machine learning tools, such as
distributed computing, due to the large volume of data involved. This study
aims to investigate and analyse the targets of reward-based crowdfunding
campaigns through machine learning techniques, employing distributed models and
structures. By harnessing the power of distributed computing, it unravels
intricate patterns and trends within crowdfunding data, thereby empowering
companies to refine their strategies and enhance the efficacy of their funding
endeavors. Through this multifaceted approach, a deeper understanding of the
economic dynamics underlying crowdfunding ecosystems can be attained, fostering
informed decision-making and sustainable growth within the startup landscape.


  We introduce a web of strongly correlated interacting 3+1D topological
superconductors/insulators of 10 particular global symmetry groups of Cartan
classes, realizable in electronic condensed matter systems, and their new SU(N)
generalizations. The symmetries include SU(N), SU(2), U(1), fermion parity,
time reversal and relate to each other through symmetry embeddings. We overview
the lattice Hamiltonian formalism. We complete the list of field theories of
bulk symmetry-protected topological invariants (SPT invariants/partition
functions that exhibit boundary 't Hooft anomalies) via cobordism calculations,
matching their full classification. We also present explicit 4-manifolds that
detect these SPTs. On the other hand, once we dynamically gauge part of their
global symmetries, we arrive in various new phases of SU(N) Yang-Mills (YM)
gauge theories, analogous to quantum spin liquids with emergent gauge fields.
We discuss how coupling YM theories to time reversal-SPTs affects the strongly
coupled theories at low energy. For example, we point out a possibility of
having two deconfined gapless time-reversal symmetric SU(2) YM theories at
$\theta=\pi$ as two distinct conformal field theories, which although are
secretly indistinguishable by correlators of local operators on orientable
spacetimes nor by gapped SPT states, can be distinguished on non-orientable
spacetimes or potentially by correlators of extended operators.


  In this work, we present a learning-based approach to analysis cyberspace
security configuration. Unlike prior methods, our approach has the ability to
learn from past experience and improve over time. In particular, as we train
over a greater number of agents as attackers, our method becomes better at
discovering hidden attack paths for previously methods, especially in
multi-domain cyberspace. To achieve these results, we pose discovering attack
paths as a Reinforcement Learning (RL) problem and train an agent to discover
multi-domain cyberspace attack paths. To enable our RL policy to discover more
hidden attack paths and shorter attack paths, we ground representation
introduction an multi-domain action select module in RL. Our objective is to
discover more hidden attack paths and shorter attack paths by our proposed
method, to analysis the weakness of cyberspace security configuration. At last,
we designed a simulated cyberspace experimental environment to verify our
proposed method, the experimental results show that our method can discover
more hidden multi-domain attack paths and shorter attack paths than existing
baseline methods.


  We present pure-transformer based models for video classification, drawing
upon the recent success of such models in image classification. Our model
extracts spatio-temporal tokens from the input video, which are then encoded by
a series of transformer layers. In order to handle the long sequences of tokens
encountered in video, we propose several, efficient variants of our model which
factorise the spatial- and temporal-dimensions of the input. Although
transformer-based models are known to only be effective when large training
datasets are available, we show how we can effectively regularise the model
during training and leverage pretrained image models to be able to train on
comparatively small datasets. We conduct thorough ablation studies, and achieve
state-of-the-art results on multiple video classification benchmarks including
Kinetics 400 and 600, Epic Kitchens, Something-Something v2 and Moments in
Time, outperforming prior methods based on deep 3D convolutional networks. To
facilitate further research, we release code at
https://github.com/google-research/scenic/tree/main/scenic/projects/vivit


  The extraction of a clean background image by removing foreground occlusion
holds immense practical significance, but it also presents several challenges.
Presently, the majority of de-occlusion research focuses on addressing this
issue through the extraction and synthesis of discrete images from calibrated
camera arrays. Nonetheless, the restoration quality tends to suffer when faced
with dense occlusions or high-speed motions due to limited perspectives and
motion blur. To successfully remove dense foreground occlusion, an effective
multi-view visual information integration approach is required. Introducing the
spike camera as a novel type of neuromorphic sensor offers promising
capabilities with its ultra-high temporal resolution and high dynamic range. In
this paper, we propose an innovative solution for tackling the de-occlusion
problem through continuous multi-view imaging using only one spike camera
without any prior knowledge of camera intrinsic parameters and camera poses. By
rapidly moving the spike camera, we continually capture the dense stream of
spikes from the occluded scene. To process the spikes, we build a novel model
\textbf{SpkOccNet}, in which we integrate information of spikes from continuous
viewpoints within multi-windows, and propose a novel cross-view mutual
attention mechanism for effective fusion and refinement. In addition, we
contribute the first real-world spike-based dataset \textbf{S-OCC} for
occlusion removal. The experimental results demonstrate that our proposed model
efficiently removes dense occlusions in diverse scenes while exhibiting strong
generalization.


  We study the reaction-diffusion process $A + B \to \emptyset$ on uncorrelated
scale-free networks analytically. By a mean-field ansatz we derive analytical
expressions for the particle pair-correlations and the particle density.
Expressing the time evolution of the particle density in terms of the
instantaneous particle pair-correlations, we determine analytically the
`jamming' effect which arises in the case of multicomponent, pair-wise
reactions. Comparing the relevant terms within the differential equation for
the particle density, we find that the `jamming' effect diminishes in the
long-time, low-density limit. This even holds true for the hubs of the network,
despite that the hubs dynamically attract the particles.


  This paper considers a multiple-input multiple-output (MIMO) relay system
with an energy harvesting relay node. All nodes are equipped with multiple
antennas, and the relay node depends on the harvested energy from the received
signal to support information forwarding. In particular, the relay node deploys
power splitting based energy harvesting scheme. The capacity maximization
problem subject to power constraints at both the source and relay nodes is
considered for both fixed source covariance matrix and optimal source
covariance matrix cases. Instead of using existing software solvers, iterative
approaches using dual decomposition technique are developed based on the
structures of the optimal relay precoding and source covariance matrices.
Simulation results demonstrate the performance gain of the joint optimization
against the fixed source covariance matrix case.


  Vacuum fluctuation-induced interactions between macroscopic metallic objects
result in an attractive force between them, a phenomenon known as the Casimir
effect. This force is the result of both plasmonic and photonic modes. For very
thin films, field penetration through the films will modify the allowed modes.
Here, we investigate the Casimir interaction between two ultrathin films from
the perspective of the force distribution over real frequencies for the first
time and find pronounced repulsive contributions to the force due to the highly
confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only
exist in ultrathin films. These contributions are found to persistently occur
around the ENZ frequency of the film and are irrespective of the inter-film
separation. We further associate the ENZ modes with a striking thickness
dependence in the averaged force density for conductive thin films, a metric
signifying a thin-film's acceleration due to Casimir effect. Our results shed
light on the role of the unique vacuum fluctuation modes existing in ultrathin
ENZ materials, which may offer significant potential for engineering the motion
of objects in nanomechanical systems.


  For multispecies ions, we study boundary layer solutions of charge conserving
Poisson-Boltzmann (CCPB) equations [50] (with a small parameter \k{o}) over a
finite one-dimensional (1D) spatial domain, subjected to Robin type boundary
conditions with variable coefficients. Hereafter, 1D boundary layer solutions
mean that as \k{o} approaches zero, the profiles of solutions form boundary
layers near boundary points and become flat in the interior domain. These
solutions are related to electric double layers with many applications in
biology and physics. We rigorously prove the asymptotic behaviors of 1D
boundary layer solutions at interior and boundary points. The asymptotic limits
of the solution values(electric potentials) at interior and boundary points
with a potential gap (related to zeta potential) are uniquely determined by
explicit nonlinear formulas (cannot be found in classical Poisson-Boltzmann
equations) which are solvable by numerical computations.


  This is a review of rare and forbidden decays of the $\tau$ lepton. For the
rare decays, this includes new results on the chiral anomaly decay
$\taupietapio$, new upper limits on the second-class-current decay $\taupieta$,
and the observations of the Cabibbo-suppressed decay $\tauketa$ and the
internal conversion decay $\taueee$. For the forbidden decays, there are new
upper limits on the radiative decays $\tauegamma$ and $\taumugamma$. Some
forbidden decays which have not been previously searched for are also
suggested.


  Concentration and equi-distribution, near the unit circle, in Solomyak's set,
of the union of the Galois conjugates and the beta-conjugates of a Parry number
$\beta$ are characterized by means of the Erd\H{o}s-Tur\'an approach, and its
improvements by Mignotte and Amoroso, applied to the analytical function
$f_{\beta}(z) = -1 + \sum_{i \geq 1} t_i z^i$ associated with the R\'enyi
$\beta$-expansion $d_{\beta}(1)= 0.t_1 t_2 ...$ of unity. Mignotte's
discrepancy function requires the knowledge of the factorization of the Parry
polynomial of $\beta$. This one is investigated using theorems of Cassels,
Dobrowolski, Pinner and Vaaler, Smyth, Schinzel in terms of cyclotomic,
reciprocal non-cyclotomic and non-reciprocal factors. An upper bound of
Mignotte's discrepancy function which arises from the beta-conjugates of
$\beta$ which are roots of cyclotomic factors is linked to the Riemann
hypothesis, following Amoroso. An equidistribution limit theorem, following
Bilu's theorem, is formulated for the concentration phenomenon of conjugates of
Parry numbers near the unit circle. Parry numbers are Perron numbers. Open
problems on non-Parry Perron numbers are mentioned in the context of the
existence of non-unique factorizations of elements of number fields into
irreducible Perron numbers (Lind).


  We study finite field dependent BRST-BFV transformations for dynamical
systems with first- and second-class constraints within the generalized
Hamiltonian formalism. We find explicitly their Jacobians and the form of a
solution to the compensation equation necessary for generating an arbitrary
finite change of gauge-fixing functionals in the path integral.


  Vacuum of Quantum Chromodynamics in very strong (hadron-scale) magnetic
fields exhibits many interesting nonperturbative effects. Some of these effects
can be studied with the help of lattice simulations in quenched QCD. We review
our recent results demonstrating that very strong external magnetic fields lead
to (1) the enhancement of the chiral symmetry breaking [the quark condensate
rises with the increase of the external magnetic field]; (2) the chiral
magnetization of the QCD vacuum [spins of the quarks turn parallel to the
external field]; (3) the chiral magnetic effect [a CP-odd generation of the
electric current of quarks directed along the magnetic field]; (4) a CP-odd
generation of the anomalous quark electric dipole moment along the axis of
magnetic field. The first three effects were already predicted theoretically,
and subsequently observed numerically in our simulations, while the fourth
effect is a new result.


  The application of Deep Learning (DL) for medical diagnosis is often hampered
by two problems. First, the amount of training data may be scarce, as it is
limited by the number of patients who have acquired the condition to be
diagnosed. Second, the training data may be corrupted by various types of
noise. Here, we study the problem of brain tumor detection from magnetic
resonance spectroscopy (MRS) data, where both types of problems are prominent.
To overcome these challenges, we propose a new method for training a deep
neural network that distills particularly representative training examples and
augments the training data by mixing these samples from one class with those
from the same and other classes to create additional training samples. We
demonstrate that this technique substantially improves performance, allowing
our method to reach human-expert-level accuracy with just a few thousand
training examples. Interestingly, the network learns to rely on features of the
data that are usually ignored by human experts, suggesting new directions for
future research.


  We formulate the graviton propagator on de Sitter background in a 2-parameter
family of simple gauges which break de Sitter invariance. Explicit results are
derived for the first order perturbations in each parameter. These results
should be useful in computations to check for gauge dependence of graviton loop
corrections.


  Discussion of "Likelihood Inference for Models with Unobservables: Another
View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]


  We investigate parity-odd non-dissipative transport in an anisotropic Dirac
semi-metal in two spatial dimensions. The analysis is relevant for interacting
electronic systems with merging Dirac points at charge neutrality. For such
systems the dispersion relation is relativistic in one direction and
non-relativistic in the other. We give a proposal how to calculate the Berry
curvature for this system and use it to derive more than one odd viscosities,
in contrast to rotationally invariant systems. We observe that in such a model
the odd part of stress tensor is parameterised by two independent transport
coefficients and one that is identically zero.


  Hydromagnetic dynamo theory provides the prevailing theoretical description
for the origin of magnetic fields in the universe. Here we consider the problem
of kinematic, small-scale dynamo action driven by a random, incompressible,
non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the
statistics of the driving flow are assumed to be instantaneously correlated in
time. Here we compare the results of the model with the dynamo properties of a
simulated flow that has equivalent spatial characteristics as the Kazantsev
flow but different temporal statistics. In particular, the simulated flow is a
solution of the forced Navier-Stokes equations and hence has a finite
correlation time. We find that the Kazantsev model typically predicts a larger
magnetic growth rate and a magnetic spectrum that peaks at smaller scales.
However, we show that by filtering the diffusivity spectrum at small scales it
is possible to bring the growth rates into agreement and simultaneously align
the magnetic spectra.


  In robotic surgery, tool tracking is important for providing safe tool-tissue
interaction and facilitating surgical skills assessment. Despite recent
advances in tool tracking, existing approaches are faced with major
difficulties in real-time tracking of articulated tools. Most algorithms are
tailored for offline processing with pre-recorded videos. In this paper, we
propose a real-time 3D tracking method for articulated tools in robotic
surgery. The proposed method is based on the CAD model of the tools as well as
robot kinematics to generate online part-based templates for efficient 2D
matching and 3D pose estimation. A robust verification approach is incorporated
to reject outliers in 2D detections, which is then followed by fusing inliers
with robot kinematic readings for 3D pose estimation of the tool. The proposed
method has been validated with phantom data, as well as ex vivo and in vivo
experiments. The results derived clearly demonstrate the performance advantage
of the proposed method when compared to the state-of-the-art.


  We continue the study of Specht modules labelled by hook bipartitions for the
Iwahori--Hecke algebra of type $B$ with $e\in\{3,4,\dots\}$ via the cyclotomic
Khovanov--Lauda--Rouquier algebra $\mathscr{H}_n^{\Lambda}$. Over an arbitrary
field, we explicitly determine the graded decomposition submatrices for
$\mathscr{H}_n^{\Lambda}$ comprising rows corresponding to hook bipartitions.


  In this paper, we study how to directly measure the effect of peculiar
velocities in the observed angular power spectra. We do this by constructing a
new anti-symmetric estimator of Large Scale Structure using different dark
matter tracers. We show that the Doppler term is the major component of our
estimator and we show that we can measure it with a signal-to-noise ratio up to
$\sim 50$ using a futuristic SKAO HI galaxy survey. We demonstrate the utility
of this estimator by using it to provide constraints on the Euler equation.


  The primary objective of this thesis is to identify the key dynamical
mechanisms responsible for the superthin stellar discs. We use HI 21cm
radio-synthesis observations and stellar photometry to construct detailed
dynamical models of a sample of superthin galaxies to determine the primary
mechanism responsible for the existence of superthin stellar discs in these
galaxies. Our study is based on a sample of superthin galaxies with $\rm 10<
a/b < 16$ for which H1 21cm radio-synthesis data were already available in the
literature. In addition, we had the two thinnest galaxies in our sample with
$\rm a/b \sim 21$, for which we carried out Giant Meterwave Radio Telescope
(GMRT) 21cm radio-synthesis observations. To identify the physical mechanism
primarily responsible for the superthin vertical structure, we carry out a
Principal Component Analysis of the following dynamical parameters: 1) Dark
matter dominance at inner galactocentric radii given by
$V_{\rm{rot}}/{(R_{c}/R_{d})}$, 2) the ratio of the vertical-to-radial stellar
velocity dispersion $(\sigma_{z,s}/\sigma_{R,s})$, 3) Disc dynamical stability
against local axisymmetric perturbations $Q_{RW}$, 4) Specific angular momentum
of the disc $(j_{*})$, along with $a/b$ for all superthins and the extremely
thin galaxies. We note that the first two principal components explain $\sim$
80$\%$ of the variation in the data, and the major contributions are from
$a/b$, $Q_{RW}$ and $V_{\rm{rot}}/{(R_{c}/R_{d})}$. This possibly indicates
that high values of the disc dynamical stability and dark matter dominance at
inner galactocentric radii are fundamentally responsible for the superthin
stellar discs.


  We present several operator versions of the Dunkl--Williams inequality with
respect to the $p$-angular distance for operators. More precisely, we show that
if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible,
$\frac{1}{r}+\frac{1}{s}=1\,\,(r>1)$ and $p\in\mathbb{R}$, then
\begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \leq
|A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\nonumber
\end{equation*} In the case that $0<p \leq 1$, we remove the invertibility
assumption and show that if $A=U|A|$ and $B=V|B|$ are the polar decompositions
of $A$ and $B$, respectively, $t>0$, then
$$|(U|A|^{p}-V|B|^{p})|A|^{1-p}|^{2}\leq
(1+t)|A-B|^{2}+(1+\frac{1}{t})||B|^{p}|A|^{1-p}-|B||^2 \,.$$ We obtain several
equivalent conditions, when the case of equalities hold.


  We present a novel, language-agnostic approach to "priming" language models
for the task of event extraction, providing particularly effective performance
in low-resource and zero-shot cross-lingual settings. With priming, we augment
the input to the transformer stack's language model differently depending on
the question(s) being asked of the model at runtime. For instance, if the model
is being asked to identify arguments for the trigger "protested", we will
provide that trigger as part of the input to the language model, allowing it to
produce different representations for candidate arguments than when it is asked
about arguments for the trigger "arrest" elsewhere in the same sentence. We
show that by enabling the language model to better compensate for the deficits
of sparse and noisy training data, our approach improves both trigger and
argument detection and classification significantly over the state of the art
in a zero-shot cross-lingual setting.


  We derive the observable gravitational wave (GW) peak frequency ($f$)
distribution of binary black holes (BBHs) that currently reside inside their
globular clusters (GCs), with and without 2.5 Post-Newtonian (2.5PN) effects
included in the dynamical evolution of the BBHs. Recent Newtonian studies have
reported that a notable number of nearby non-merging BBHs, i.e. those BBHs that
are expected to undergo further dynamical interactions before merger, in GCs
are likely to be observable by LISA. However, our 2.5PN calculations show that
the distribution of $\log f$ for the non-merging BBH population above $\sim
10^{-3.5}$ Hz scales as $f^{-34/9}$ instead of the $f^{-2/3}$ scaling found in
the Newtonian case. This leads to an approximately two-orders-of-magnitude
reduction in the expected number of GW sources at $\sim 10^{-3}$ Hz, which lead
us to conclude that observing nearby BBHs with LISA is not as likely as has
been claimed in the recent literature. In fact, our results suggest that it
might be more likely that LISA detects the population of BBHs that will merge
before undergoing further interactions. This interestingly suggests that the
BBH merger rate derived from LIGO can be used to forecast the number of nearby
LISA sources, as well as providing insight into the fraction of BBH mergers
forming in GCs.


  In general, non-minimal models of the dark sector such as Dynamical Dark
Matter posit the existence of an ensemble of individual dark components with
differing masses, cosmological abundances, and couplings to the Standard Model.
Perhaps the most critical among these features is the spectrum of masses, as
this goes a long way towards determining the cosmological abundances and
lifetimes of the corresponding states. Many different underlying theoretical
structures can be imagined for the dark sector, each giving rise to its own
mass spectrum and corresponding density of states. In this paper, by contrast,
we investigate the spectrum of masses that emerges statistically from
underlying processes which are essentially random. We find a density of states
$n(m)$ which decreases as a function of mass and actually has an upper limit
$m_{\rm max}$ beyond which $n(m)=0$. We also demonstrate that this "emergent"
density of states is particularly auspicious from the perspective of the
Dynamical Dark Matter framework, leading to cosmological abundances and decay
widths that are suitably balanced against each other across the dark-matter
ensemble. Thus randomness in the dark sector coexists quite naturally with
Dynamical Dark Matter, and we examine the prospects for observing the signals
of such scenarios in dark-matter indirect-detection experiments.


  In the cold dark matter paradigm, structures form hierarchically, implying
that large structures contain smaller substructures. These subhalos will
enhance signatures of dark matter annihilation such as gamma rays. In the
literature, typical estimates of this boost factor assume a concentration-mass
relation for field halos, to calculate the luminosity of subhalos. However,
since subhalos accreted in the gravitational potential of their host loose mass
through tidal stripping and dynamical friction, they have a quite
characteristic density profile, different from that of the field halos of the
same mass. In this work, we quantify the effect of tidal stripping on the boost
factor, by developing a semi-analytic model that combines mass-accretion
history of both the host and subhalos as well as subhalo accretion rates. We
find that when subhalo luminosities are treated consistently, the boost factor
increases by a factor 2-5, compared to the typical calculation assuming a
field-halo concentration. This holds for host halos ranging from sub-galaxy to
cluster masses and is independent of the subhalo mass function or specific
concentration-mass relation. The results are particularly relevant for indirect
dark matter searches in the extragalactic gamma-ray sky.


  We derive generalised uncertainty relations (GURs) for angular momentum and
spin in the smeared-space model of quantum geometry. The model implements a
minimum length and a minimum linear momentum, and recovers both the generalised
uncertainty principle (GUP) and the extended uncertainty principle (EUP) within
a single formalism. In this paper, we investigate the consequences of these
results for particles with extrinsic and intrinsic angular momentum, and obtain
generalisations of the canonical ${\rm so(3)}$ and ${\rm su(2)}$ algebras. We
find that, although ${\rm SO(3)}$ symmetry is preserved on three-dimensional
slices of an enlarged phase space, individual subcomponents of the generalised
generators obey nontrivial subalgebras. These give rise to GURs for angular
momentum while leaving the canonical commutation relations intact except for a
simple rescaling, $\hbar \rightarrow \hbar + \beta$. The value of the new
parameter, $\beta \simeq \hbar \times 10^{-61}$, is determined by the ratio of
the dark energy density to the Planck density. Here, we assume the former to be
of the order of the Planck length and the latter to be of the order of the de
Sitter momentum $\sim \hbar\sqrt{\Lambda}$, where $\Lambda$ is the cosmological
constant. In the smeared-space model, $\hbar$ and $\beta$ are interpreted as
the quantisation scales for matter and geometry, respectively, and a quantum
state vector is associated with the spatial background. We show that this also
gives rise to a rescaled Lie algebra for generalised spin operators, together
with associated subalgebras that are analogous to those for orbital angular
momentum. Remarkably, consistency of the algebraic structure requires the
quantum state associated with a flat background to be fermionic, with spin
eigenvalues $\pm \beta/2$. Finally, the modified spin algebra leads to GURs for
spin measurements.


  Random graphs (or networks) have gained a significant increase of interest
due to its popularity in modeling and simulating many complex real-world
systems. Degree sequence is one of the most important aspects of these systems.
Random graphs with a given degree sequence can capture many characteristics
like dependent edges and non-binomial degree distribution that are absent in
many classical random graph models such as the Erd\H{o}s-R\'{e}nyi graph model.
In addition, they have important applications in the uniform sampling of random
graphs, counting the number of graphs having the same degree sequence, as well
as in string theory, random matrix theory, and matching theory. In this paper,
we present an OpenMP-based shared-memory parallel algorithm for generating a
random graph with a prescribed degree sequence, which achieves a speedup of
20.5 with 32 cores. One of the steps in our parallel algorithm requires
checking the Erd\H{o}s-Gallai characterization, i.e., whether there exists a
graph obeying the given degree sequence, in parallel. This paper presents the
first non-trivial parallel algorithm for checking the Erd\H{o}s-Gallai
characterization, which achieves a speedup of 23 using 32 cores.


  This paper proposed a Soft Filter Pruning (SFP) method to accelerate the
inference procedure of deep Convolutional Neural Networks (CNNs). Specifically,
the proposed SFP enables the pruned filters to be updated when training the
model after pruning. SFP has two advantages over previous works: (1) Larger
model capacity. Updating previously pruned filters provides our approach with
larger optimization space than fixing the filters to zero. Therefore, the
network trained by our method has a larger model capacity to learn from the
training data. (2) Less dependence on the pre-trained model. Large capacity
enables SFP to train from scratch and prune the model simultaneously. In
contrast, previous filter pruning methods should be conducted on the basis of
the pre-trained model to guarantee their performance. Empirically, SFP from
scratch outperforms the previous filter pruning methods. Moreover, our approach
has been demonstrated effective for many advanced CNN architectures. Notably,
on ILSCRC-2012, SFP reduces more than 42% FLOPs on ResNet-101 with even 0.2%
top-5 accuracy improvement, which has advanced the state-of-the-art. Code is
publicly available on GitHub: https://github.com/he-y/soft-filter-pruning


  There are many selected mapping (SLM) schemes to reduce the peak-to-average
power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM)
signals. Beginning with the conventional SLM scheme, there have been proposed
many low-complexity SLM schemes including Lim's, Wang's, and Baxely's SLM
schemes typically. In this paper, we propose an adaptive generation (AG) method
of OFDM signals in SLM schemes. By generating the alternative OFDM signals
adaptively, unnecessary computational complexity of SLM schemes can be removed
without any degradation of their PAPR reduction performance. In this paper, we
apply the AG method to various SLM schemes which are the conventional SLM
scheme and its low-complexity versions such as Lim's, Wang's, and Baxely's SLM
schemes. Of course, the AG method can be applied to most of existing SLM
schemes easily. The numerical results show that the AG method can reduce their
computational complexity substantially.


  We give an algorithm for computing matrix corepresentations for special
linear and special unitary quantum groups using a combinatorial re-indexing of
basis elements.


  We study a model of selection acting on a diploid population (one in which
each individual carries two copies of each gene) living in one spatial
dimension. We suppose a particular gene appears in two forms (alleles) $A$ and
$a$, and that individuals carrying $AA$ have a higher fitness than $aa$
individuals, while $Aa$ individuals have a lower fitness than both $AA$ and
$aa$ individuals. The proportion of advantageous $A$ alleles expands through
the population approximately according to a travelling wave. We prove that on a
suitable timescale, the genealogy of a sample of $A$ alleles taken from near
the wavefront converges to a Kingman coalescent as the population density goes
to infinity. This contrasts with the case of directional selection in which the
corresponding limit is thought to be the Bolthausen-Sznitman coalescent. The
proof uses 'tracer dynamics'.


  An admixture of 10-20 % of qqqq\bar q components in the Delta(1232) resonance
is shown to reduce the well known underprediction for the decay width for
Delta(1232)->N gamma decay by about half and that of the corresponding helicity
amplitudes from a factor ~ 1.7 to ~ 1.5. The main effect is due to the
quark-antiquark annihilation transitions qqqq\bar q -> qqq gamma, the
consideration of which brings the ratio A_{3/2}/A_{1/2} and consequently the
E2/M1 ratio R_{EM} into agreement with the empirical value. Transitions between
qqqq\bar q components in the resonance and the nucleon qqqq\bar q->qqqq\bar q
gamma are shown to enhance the calculated width by only a few percent, as long
as the probability of the qqqq\bar q component of the Delta(1232) and the
proton is at most ~ 20 %. The transitions qqqq\bar q->qqqq\bar q gamma between
the qqqq\bar q components in the Delta(1232) and the proton do not lead to a
nonzero value for R_{EM}.


  Starbursts are episodes of intense star-formation that occur in the central
regions of galaxies, and dominate the integrated emission from the galaxy. They
are a significant component of the present- day universe, being the site of
$\sim$ 25% of the high-mass star- formation. They offer unique `laboratories'
for testing our ideas about star-formation, the evolution of high-mass stars,
and the physics of the interstellar medium. They serve as local analogs of the
processes that were important in the origin and early evolution of galaxies and
in the heating and chemical enrichment of the inter-galactic medium. In this
contribution I review starbursts from this broad cosmogonical perspective,
stressing several key lessons we have learned from starbursts: 1) Violent,
transient events play a significant role in the origin and evolution of
galaxies. 2) Galaxies do not evolve as `Island Universes': starbursts are
triggered by galaxy interactions and produce outflows of hot
chemically-enriched gas that `pollute' the inter- galactic medium. 3) Dust
dramatically affects of view of high-mass star-formation in starbursts and
(probably) in high-redshift galaxies. Throughout this review I emphasize the
importance of space-based observations in understanding starbursts.


  In this paper, we investigate a novel reconfigurable distributed antennas and
reflecting surface (RDARS) aided multi-user massive MIMO system with imperfect
CSI and propose a practical two-timescale (TTS) transceiver design to reduce
the communication overhead and computational complexity of the system. In the
RDARS-aided system, not only distribution gain but also reflection gain can be
obtained by a flexible combination of the distributed antennas and reflecting
surface, which differentiates the system from the others and also makes the TTS
design challenging. To enable the optimal TTS transceiver design, the
achievable rate of the system is first derived in closed-form. Then the TTS
design aiming at the weighted sum rate maximization is considered. To solve the
challenging non-convex optimization problem with high-order design variables,
i.e., the transmit powers and the phase shifts at the RDARS, a block coordinate
descent based method is proposed to find the optimal solutions in semi-closed
forms iteratively. Specifically, two efficient algorithms are proposed with
provable convergence for the optimal phase shift design, i.e., Riemannian
Gradient Ascent based algorithm by exploiting the unit-modulus constraints, and
Two-Tier Majorization-Minimization based algorithm with closed-form optimal
solutions in each iteration. Simulation results validate the effectiveness of
the proposed algorithm and demonstrate the superiority of deploying RDARS in
massive MIMO systems to provide substantial rate improvement with a
significantly reduced total number of active antennas/RF chains and lower
transmit power when compared to the DAS and RIS-aided systems.


  We review the perturbative evolution of the polarized structure functions g_1
and their associated parton distribution functions, with particular emphasis on
the anomalous coupling of the first moment of the polarized gluon distribution.
We also describe the small x behaviour of polarized parton distributions,
contrasting it with that of the unpolarized distributions. We then explain how
this theoretical analysis affects the extraction of the singlet axial charge
from experimental data on g_1, and show that it may be possible to use such
data to infer the existence of polarized gluons in the nucleon.


  The mass and total width of the eta_c meson have been measured in two-photon
interactions at the SLAC asymmetric B-Factory with the BABAR detector. With a
sample of approximately 2500 reconstructed eta_c -> Ks K pi decays in 88 fb-1
of data, the measured eta_c mass and width are respectively 2982.5 +- 1.1
(stat) +- 0.9 (syst) MeV/c2 and 34.3 +- 2.3 (stat) +- 0.9 (syst) MeV/c2. Using
the same decay mode, a second resonance with 112 +- 24 events is observed with
a mass of 3630.8 +- 3.4 (stat) +- 1.0 (syst) MeV/c2 and width of 17.0 +- 8.3
(stat) +- 2.5 (syst) MeV/c2. This observation is consistent with expectations
for the eta_c(2S) state.


  The collection of open sets of a topological space forms a Heyting algebra,
which leads to the idea of a Heyting algebra as a generalized topological
space. In fact, a sober topological space may be reconstructed from its locale
of open sets. This has given rise to a good theory of presheaves and sheaves
over locales. At the same time, several ring like properties of Heyting
algebras have also been studied. The purpose of this paper is to study a
non-abelian homological theory for modules over Heyting algebras.


  The b-barb and Upsilon production cross section has been measured in
collisions of 920 GeV protons on different nuclear targets using the HERA-B
detector. On the invariant mass spectra of e+e- or mu+mu- events originating
from common vertex, the Upsilon search was performed. The identification of
b-barb events was done using the same sample via inclusive bottom quark decays
into J/psi by exploiting the longitudinal separation of the J/psi -> l+l- decay
vertices from the primary proton nucleus interaction. For both hidden and open
beauty decays, the mu+mu- and the e+e- decay channels have been reconstructed.
The most recent measurement, using data collected in 2002/2003, yields a
preliminary cross section in the combined analysis of sigma(b-barb) =
(12.3(+3.5)(-3.2)) nb/nucleon and for the hidden beauty production the
preliminary measurement of BR(Upsilon -> l+l-) x d sigma(Upsilon ->
l+l-)/dy|_(y=0) = (3.4 +-0.8) pb/nucleon.


  We briefly review the most relevant aspects of complete integrability for
classical systems and identify those aspects which should be present in a
definition of quantum integrability.
  We show that a naive extension of classical concepts to the quantum framework
would not work because all infinite dimensional Hilbert spaces are unitarily
isomorphic and, as a consequence, it would not be easy to define degrees of
freedom. We argue that a geometrical formulation of quantum mechanics might
provide a way out.


  We provide a systematic deterministic numerical scheme to approximate the
volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose
description follows a sparsity pattern. As in previous works (without
sparsity), the underlying strategy is to consider an infinite-dimensional
linear program on measures whose optimal value is the volume of the set. This
is a particular instance of a generalized moment problem which in turn can be
approximated as closely as desired by solving a hierarchy of semidefinite
relaxations of increasing size. The novelty with respect to previous work is
that by exploiting the sparsity pattern we can provide a sparse formulation for
which the associated semidefinite relaxations are of much smaller size. In
addition, we can decompose the sparse relaxations into completely decoupled
subproblems of smaller size, and in some cases computations can be done in
parallel. To the best of our knowledge, it is the first contribution that
exploits sparsity for volume computation of semi-algebraic sets which are
possibly high-dimensional and/or non-convex and/or non-connected.


  We find the metric of small black holes on cylinders, i.e. neutral and static
black holes with a small mass in d-dimensional Minkowski-space times a circle.
The metric is found using an ansatz for black holes on cylinders proposed in
hep-th/0204047. We use the new metric to compute corrections to the
thermodynamics which is seen to deviate from that of the (d+1)-dimensional
Schwarzschild black hole. Moreover, we compute the leading correction to the
relative binding energy which is found to be non-zero. We discuss the
consequences of these results for the general understanding of black holes and
we connect the results to the phase structure of black holes and strings on
cylinders.


  In this brief note, we reconsider the problem of finding Euclidean wormhole
solutions to maximal supergravity in d dimensions. We find that such solutions
exists for all d less than or equal to 9. However, we argue that, in
toroidally-compactified string theories, these saddle points never contribute
to the path integral because of a tension with U-duality.


  We provide closed-form expressions for the first moments (i.e., the volume
and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is,
of a polyhedron intersected with the subset of the three-dimensional real space
located on one side of a paraboloid. These closed-form expressions are derived
following successive applications of the divergence theorem and the judicious
parametrization of the intersection of the polyhedron's faces with the
paraboloid. We provide means for identifying ambiguous discrete intersection
topologies, and propose a corrective procedure for preventing their occurence.
Finally, we put our proposed closed-form expressions and numerical approach to
the test with millions of random and manually engineered polyhedron/paraboloid
intersection configurations. The results of these tests show that we are able
to provide robust machine-accurate estimates of the first moments at a
computational cost that is within one order of magnitude of that of
state-of-the-art half-space clipping algorithms.


  We consider a regular singular Sturm-Liouville operator $L:=-\frac{d^2}{dx^2}
+ \frac{q(x)}{x^2 (1-x)^2}$ on the line segment $[0,1]$. We impose certain
boundary conditions such that we obtain a semi-bounded self-adjoint operator.
It is known that the $\zeta$-function of this operator
$\zeta_L(s)=\sum_{\lambda\in\spec(L)\setminus\{0\}} \lambda^{-s}$ has a
meromorphic continuation to the whole complex plane with 0 being a regular
point. Then, according to Ray and Singer the $\zeta$-regularized determinant of
$L$ is defined by $\detz(L):=\exp(-\zeta_L'(0)).$ In this paper we are going to
express this determinant in terms of the solutions of the homogeneous
differential equation $Ly=0$ generalizing earlier work of S. Levit and U.
Smilansky, T. Dreyfus and H. Dym, and D. Burghelea, L. Friedlander and T.
Kappeler. More precisely we prove the formula $\detz(L)=\frac{\pi W(\psi,\phi)}
{2^{\nu_0+\nu_1} \Gamma(\nu_0+1)\Gamma(\nu_1+1)}.$ Here $\phi, \psi$ is a
certain fundamental system of solutions for the homogeneous equation $Ly=0$,
$W(\phi, \psi)$ denotes their Wronski determinant, and $\nu_0, \nu_1$ are
numbers related to the characteristic roots of the regular singular points $0,
1$.


  Multi-loop integrals can be evaluated numerically using Mellin-Barnes
representations. Here this technique is applied to the calculation of
electroweak two-loop correction with closed fermion loops for two observables:
the effective weak mixing angle for bottom quarks, sin^2{\theta}(eff,bb), and
the branching ratio of the Z boson into bottom quarks, R(b). Good agreement
with a previous result for sin^2{\theta}(eff,bb) is found. The result for R(b)
is new, and a simple parametrization formula is provided which approximates the
full result within integration errors.


  We discuss the discovery potential of a charged Higgs boson in the single top
mode. The models discussed include a CP-conserving and a CP-violating version
of the softly broken $Z_2$ symmetric 2HDM potential. We conclude that the
single top mode could help to constrain the ($m_{H^\pm}$, $\tan \beta$) plane
in several versions of 2HDMs.


  We study a portfolio management problem featuring many-player and mean field
competition, investment and consumption, and relative performance concerns
under the forward performance processes (FPP) framework. We focus on agents
using power (CRRA) type FPPs for their investment-consumption optimization
problem under a common noise Merton market model. We solve both the many-player
and mean field game providing closed-form expressions for the solutions where
the limit of the former yields the latter. In our case, the FPP framework
yields a continuum of solutions for the consumption component as indexed to a
market parameter we coin "market-risk relative consumption preference". The
parameter permits the agent to set a preference for their consumption going
forward in time that, in the competition case, reflects a common market
behaviour. We show the FPP framework, under both competition and
no-competition, allows the agent to disentangle her risk-tolerance and
elasticity of intertemporal substitution (EIS) just like Epstein-Zin
preferences under recursive utility framework and unlike the classical utility
theory one. This, in turn, allows a finer analysis on the agent's consumption
"income" and "substitution" regimes, and, of independent interest, motivates a
new strand of economics research on EIS under the FPP framework. We find that
competition rescales the agent's perception of consumption in a non-trivial
manner. We provide numerical illustrations of our results.


  We present and discuss new spectroscopic observations of the unusual galaxy
J2310-43. The observations cover a wide wavelength range, from 3700 A to 9800 A
allowing the study of both the regions where H alpha and the Ca II ``contrast''
are expected. No evidence for H alpha in emission is found and we thus confirm
the absence of emission lines in the spectrum of J2310-43, ruling out the
possibility that it may host a Seyfert nucleus. The CaII break is clearly
detected and the value of the contrast (38 +/-4 %) is intermediate between that
of a typical elliptical galaxy (about 50 %) and that of a BL Lac object (<25
%). This result imposes limits on the intensity of a possible non-stellar
continuum and, in the light of the radio and X-ray loudness of the source,
draws further attention to the problem of the recognition of a BL Lac object.
Objects like J2310-43 may be more common than previously recognized, and begin
to emerge in surveys of radio-emitting X-ray sources.


  We develop, analyze, and evaluate a novel, supervised, specific-to-general
learner for a simple temporal logic and use the resulting algorithm to learn
visual event definitions from video sequences. First, we introduce a simple,
propositional, temporal, event-description language called AMA that is
sufficiently expressive to represent many events yet sufficiently restrictive
to support learning. We then give algorithms, along with lower and upper
complexity bounds, for the subsumption and generalization problems for AMA
formulas. We present a positive-examples--only specific-to-general learning
method based on these algorithms. We also present a polynomial-time--computable
``syntactic'' subsumption test that implies semantic subsumption without being
equivalent to it. A generalization algorithm based on syntactic subsumption can
be used in place of semantic generalization to improve the asymptotic
complexity of the resulting learning algorithm. Finally, we apply this
algorithm to the task of learning relational event definitions from video and
show that it yields definitions that are competitive with hand-coded ones.


  In equilibrium, at finite temperature below and above the deconfining phase
transition, we have generated lattice SU(2) gauge fields and have exposed them
to smearing in order to investigate the emerging clusters of topological
charge. Analysing in addition the monopole clusters according to the maximally
Abelian gauge, we have been able to characterize part of the topological
clusters to correspond either to non-static calorons or static dyons in the
context of Kraan-van Baal caloron solutions with non-trivial holonomy. We show
that the relative abundance of these calorons and dyons is changing with
temperature and offer an interpretation as dissociation of calorons into dyons
with increasing temperature. The profile of the Polyakov loop inside the
topological clusters and the (model-dependent) accumulated topological cluster
charges support this interpretation. Above the deconfining phase transition
light dyons (according to Kraan-van Baal caloron solutions with almost trivial
holonomy) become the most abundant topological objects. They are presumably
responsible for the magnetic confinement in the deconfined phase.


  We investigate antiferromagnetic spin ladders with nonmagnetic impurities by
variational and numerical (Lanczos and DMRG) methods. The interaction between
the two unpaired spins opposite to the impurities is described by an effective
exchange interaction $J_{eff}$, the magnitude of which depends on the impurity
distance. The magnitude of $J_{eff}$ is different for unpaired spins at the
edges of an open ladder and in the bulk. This difference is related to the
different distribution of the unpaired spin into the bulk of the ladder. The
numerical results are interpreted using matrix product states. Using the DMRG
we calculate the spectrum of low-lying energy levels for up to 6 impurities and
find that these spectra can be reproduced assuming pair interactions with an
accuracy of better than 10\%. We discuss the filling of the ladder gap with
impurity states and argue that in the thermodynamic limit the spin ladder with
a finite concentration of impurities always shows a Curie susceptibility at low
temperatures.


  We investigate the differential geometry of the moduli space of instantons on
S^3 x S^1. Extending previous results, we show that a sigma-model with this
target space can be expected to possess a large N=4 superconformal symmetry,
supporting speculations that this sigma-model may be dual to Type IIB
superstring theory on AdS_3 x S^3 x S^3 x S^1. The sigma-model is parametrized
by three integers -- the rank of the gauge group, the instanton number, and a
"level" (the integer coefficient of a topologically nontrivial B-field,
analogous to a WZW level). These integers are expected to correspond to two
five-brane charges and a one-brane charge. The sigma-model is weakly coupled
when the level, conjecturally corresponding to one of the five-brane changes,
becomes very large, keeping the other parameters fixed. The central charges of
the large N=4 algebra agree, at least semiclassically, with expectations from
the duality.


  We analyze the experimental data for the magnetic susceptibility of the
material ZnCu3(OH)6Cl2 in terms of the Kagome Lattice Heisenberg model (KLHM),
discussing possible role of impurity spins, dilution, exchange anisotropy, and
both out-of-plane and in-plane Dzyaloshinsky-Moriya (DM) anisotropies, with
explicit theoretical calculations using the Numerical Linked Cluster (NLC)
method and exact diagonalization (ED). The high-temperature experimental data
are well described by the pure Heisenberg model with J=170 K. We show that the
sudden upturn in the susceptibility around T=75 K is due to DM interactions. We
also observe that at intermediate temperatures, below T=J, our calculated
susceptibility for KLHM fits well with a power law T^{-0.25}.


  The factorization of hard and soft contributions into the hadronic decays of
B_c meson at large recoils is explored in order to evaluate the decay rates
into the S, P and D-wave charmonia associated with rho and pi. The constraints
of approach applicability and uncertainties of numerical estimates are
discussed. The mode with the J/psi in the final state is evaluated taking into
account the cascade radiative electromagnetic decays of excited P-wave states,
that enlarges the branching ratio by 20-25%.


  We present a parameter estimation technique based on performing joint
measurements of a weak interaction away from the weak-value-amplification
approximation. Two detectors are used to collect full statistics of the
correlations between two weakly entangled degrees of freedom. Without the need
of postselection, the protocol resembles the anomalous amplification of an
imaginary-weak-value-like response. The amplification is induced in the
difference signal of both detectors allowing robustness to different sources of
technical noise, and offering in addition the advantages of balanced signals
for precision metrology. All of the Fisher information about the parameter of
interest is collected, and a phase controls the amplification response. We
experimentally demonstrate the proposed technique by measuring polarization
rotations in a linearly polarized laser pulse. The effective sensitivity and
precision of a split detector is increased when compared to a conventional
continuous-wave balanced detection technique.


  We have carried out and analyzed a set of axisymmetric MHD simulations of the
evolution of a turbulent/diffusive accretion disc around an initially
unmagnetized star. The disc is initially threaded by a weak magnetic field
where the magnetic pressure is significantly less than the kinetic pressure in
the disc. The viscosity and magnetic diffusivity are modelled by two "alpha"
parameters, while the coronal region above the disc is treated using ideal MHD.
The initial magnetic field is taken to consist of three poloidal field loops
threading the disc. The motivation for this study is to understand the
advection of disc matter and magnetic field by the turbulent/diffusive disc. At
early times the innermost field loop twists and its field lines become open.
The twisting of the opened field lines leads to the formation of both an inner
collimated, magnetically-dominated jet, and at larger distances from the axis a
matter dominated uncollimated wind. For later times, the strength of the
magnetic field decreases owing to field reconnection and annihilation in the
disc. For the early times, we have derived from the simulations both the matter
accretion speed in the disc and the accretion speed of the magnetic field. We
show that the derived matter accretion speed agrees approximately with the
predictions of a model where the accretion speed is the sum of two terms, one
due to the disc's viscosity (which gives a radial outflow of angular momentum
in the disc), and a second due to the twisted magnetic field at the disc's
surface (which gives a vertical outflow of angular momentum). For early times
we find that the magnetic contribution is roughly twice the viscous
contribution for the case where the alpha parameters are both equal to 0.1. At
later times the magnetic contribution to the matter speed becomes small
compared to the viscous contribution.


  Quantum mechanics imposes 'monogamy' constraints on the sharing of
entanglement. We show that, despite these limitations, entanglement can be
fully 'promiscuous', i.e. simultaneously present in unlimited two-body and
many-body forms in states living in an infinite-dimensional Hilbert space.
Monogamy just bounds the divergence rate of the various entanglement
contributions. This is demonstrated in simple families of N-mode (N >= 4)
Gaussian states of light fields or atomic ensembles, which therefore enable
infinitely more freedom in the distribution of information, as opposed to
systems of individual qubits. Such a finding is of importance for the
quantification, understanding and potential exploitation of shared quantum
correlations in continuous variable systems. We discuss how promiscuity
gradually arises when considering simple families of discrete variable states,
with increasing Hilbert space dimension towards the continuous variable limit.
Such models are somehow analogous to Gaussian states with asymptotically
diverging, but finite squeezing. In this respect, we find that non-Gaussian
states (which in general are more entangled than Gaussian states), exhibit also
the interesting feature that their entanglement is more shareable: in the
non-Gaussian multipartite arena, unlimited promiscuity can be already achieved
among three entangled parties, while this is impossible for Gaussian, even
infinitely squeezed states.


  We analyse the relation between the activity cycle length and the Rossby
number and collected a sample of 44 main sequence stars with well-known
activity cycle periods and rotation periods. We find a linear behaviour in the
double-logarithmic relation between the Rossby number and cycle period. The
bifurcation into a long and a short period branch is clearly real but it
depends, empirically, on the colour index B-V, indicating a physical dependence
on effective temperature and position on the main sequence. Furthermore, there
is also a correlation between cycle length and convective turnover time with
the relative depth of the convection zone. Based on this, we derive empirical
relations between cycle period and Rossby number, and for the short period
cycle branch relations, we estimate a scatter of the relative deviation between
14% and 28% on the long-period cycle branch. With these relations, we obtain a
good match with the 10.3 yr period for the well known 11-year solar Schwabe
cycle and a long-period branch value of 104 yr for the Gleissberg cycle of the
Sun. Finally, we suggest that the cycles on the short-period branch appear to
be generated in the deeper layers of the convective zone, while long-period
branch cycles seem to be related to fewer deep layers in that zone. We show
that for a broader B-V range, the Rossby number is a more suitable parameter
for universal relation with cycle-rotation than just the rotation period alone.
As proof, we demonstrate that our empirical stellar relations are consistent
with the 11-year solar Schwabe cycle, in contrast to earlier studies using just
the rotation period in their relations. Previous studies have tried to explain
the cycle position of the Sun in the cycle-rotation presentation via other
kinds of dynamo, however, in our study, no evidence is found that would suggest
another type of dynamo for the Sun and other stars.


  With an equilibrium temperature of 1200 K, TrES-1 is one of the coolest hot
Jupiters observed by {\Spitzer}. It was also the first planet discovered by any
transit survey and one of the first exoplanets from which thermal emission was
directly observed. We analyzed all {\Spitzer} eclipse and transit data for
TrES-1 and obtained its eclipse depths and brightness temperatures in the 3.6
{\micron} (0.083 % {\pm} 0.024 %, 1270 {\pm} 110 K), 4.5 {\micron} (0.094 %
{\pm} 0.024 %, 1126 {\pm} 90 K), 5.8 {\micron} (0.162 % {\pm} 0.042 %, 1205
{\pm} 130 K), 8.0 {\micron} (0.213 % {\pm} 0.042 %, 1190 {\pm} 130 K), and 16
{\micron} (0.33 % {\pm} 0.12 %, 1270 {\pm} 310 K) bands. The eclipse depths can
be explained, within 1$\sigma$ errors, by a standard atmospheric model with
solar abundance composition in chemical equilibrium, with or without a thermal
inversion. The combined analysis of the transit, eclipse, and radial-velocity
ephemerides gives an eccentricity $e = 0.033^{+0.015}_{-0.031}$, consistent
with a circular orbit. Since TrES-1's eclipses have low signal-to-noise ratios,
we implemented optimal photometry and differential-evolution Markov-chain Monte
Carlo (MCMC) algorithms in our Photometry for Orbits, Eclipses, and Transits
(POET) pipeline. Benefits include higher photometric precision and \sim10 times
faster MCMC convergence, with better exploration of the phase space and no
manual parameter tuning.


  Vector mean estimation is a central primitive in federated analytics. In
vector mean estimation, each user $i \in [n]$ holds a real-valued vector
$v_i\in [-1, 1]^d$, and a server wants to estimate the mean of all $n$ vectors.
Not only so, we would like to protect each individual user's privacy. In this
paper, we consider the $k$-sparse version of the vector mean estimation
problem, that is, suppose that each user's vector has at most $k$ non-zero
coordinates in its $d$-dimensional vector, and moreover, $k \ll d$. In
practice, since the universe size $d$ can be very large (e.g., the space of all
possible URLs), we would like the per-user communication to be succinct, i.e.,
independent of or (poly-)logarithmic in the universe size.
  In this paper, we are the first to show matching upper- and lower-bounds for
the $k$-sparse vector mean estimation problem under local differential privacy.
Specifically, we construct new mechanisms that achieve asymptotically optimal
error as well as succinct communication, either under user-level-LDP or
event-level-LDP. We implement our algorithms and evaluate them on synthetic as
well as real-world datasets. Our experiments show that we can often achieve one
or two orders of magnitude reduction in error in comparison with prior works
under typical choices of parameters, while incurring insignificant
communication cost.


  In this paper we provide fully covariant proofs of some theorems on
shear-free perfect fluids. In particular, we explicitly show that any
shear-free perfect fluid with the acceleration proportional to the vorticity
vector (including the simpler case of vanishing acceleration) must be either
non-expanding or non-rotating. We also show that these results are not
necessarily true in the Newtonian case, and present an explicit comparison of
shear-free dust in Newtonian and relativistic theories in order to see where
and why the differences appear.


  Observations with the PC2 CCD of the Hubble Space Telescope are described of
two bright QSOs of redshift ~0.3. 1403+434 is IR-bright and radio-quiet, and
2201+315 is radio-loud with extended structure. Exposures were taken with the
F702W and F555W filters. The images are deconvolved on their own and combined
with 0.5 arcsec ground-based images. Both host galaxies have the form and
luminosity of bright ellipticals, with nuclei of 1-2 times higher luminosity.
1403+434 is strongly interacting while 2201+315 may be in later stages of a
merger, both with a smaller companion. Both host galaxies have compact knots
and other small-scale peculiar features. Some general remarks are made based on
the total program sample of 6 QSOs.


  The main hypothesis about Thomas Bayes's intentions to write his famous Essay
on probability is that he wanted to refute the arguments of David Hume against
the reliability of the occurrence of miracles, published in 1748. In this paper
we argue that it was not Bayes's intention to rebut Hume but that his interest
on the "inverse problem" came about as result of his study of the second
edition of Abraham De Moivre's book, The Doctrine of Chances, published in
1738.
  A possible communication of Bayes's breakthrough might have annoyed De
Moivre, leading to a response written for Bayes in the third edition of De
Moivre's book, published in 1756. Among other points, the response claims that
De Moivre was the first to solve the mentioned inverse problem. Under this
perspective Richard Price's letter, written as preface to Bayes's essay, has a
new interpretation, appearing also as a defense of Bayes premiership on a
satisfactory or proper solution.


  We report the first hard X-ray observations with NuSTAR of the BL Lac type
blazar PKS 2155-304, augmented with soft X-ray data from XMM-Newton and
gamma-ray data from the Fermi Large Area Telescope, obtained in April 2013 when
the source was in a very low flux state. A joint NuSTAR and XMM spectrum,
covering the energy range 0.5 - 60 keV, is best described by a model consisting
of a log-parabola component with curvature beta = 0.3(+0.2,-0.1) and a (local)
photon index 3.04 +/- 0.15 at photon energy of 2 keV, and a hard power-law tail
with photon index 2.2 +/- 0.4. The hard X-ray tail can be smoothly joined to
the quasi-simultaneous gamma-ray spectrum by a synchrotron self-Compton
component produced by an electron distribution with index p = 2.2. Assuming
that the power-law electron distribution extends down to the minimum electron
Lorentz factor gamma_min = 1 and that there is one proton per electron, an
unrealistically high total jet power L_p of roughly 10^47 erg/s is inferred.
This can be reduced by two orders of magnitude either by considering a
significant presence of electron-positron pairs with lepton-to-proton ratio of
at least 30, or by introducing an additional, low-energy break in the electron
energy distribution at the electron Lorentz factor gamma_br1 of roughly 100. In
either case, the jet composition is expected to be strongly matter-dominated.


  We study a Bose-Fermi mixture within the framework of the mean-field theory,
including three possible regimes for the fermionic species: fully polarized,
BCS, and unitarity. Starting from the 3D description and using the variational
approximation (VA), we derive 1D and 2D systems of equations, under the
corresponding confining potentials. This method produces a pair of nonlinear
Schr\"{o}dinger (NLS) equations coupled to algebraic equations for the
transverse widths of the confined state. The equations incorporate interactions
between atoms of the same species and between the species, assuming that the
latter can be manipulated by means of the Feshbach resonance (FR). As an
application, we explore spatial density correlations in the ground state (GS)
between the species, concluding that they strongly depend on the sign and
strength of the inter-species interaction. Also studied are the dynamics of the
mixture in a vicinity of the GS and the corresponding spatiotemporal
inter-species correlation. The correlations are strongly affected by the
fermionic component, featuring the greatest variation in the unitary regime.
Results produced by the VA are verified by comparison with full numerical
solutions.


  The recent detection of resolved radio emission from AG Dra by MERLIN
reported by Ogley et al. is discussed in the context of the wind environment
and the physical parameters and geometry of this symbiotic binary system. In
particular, it is shown that the two radio components are closely aligned with
the binary axis, and their separation suggests their origin in jets ejected
from AG Dra during the recent 1995--98 series of oubtbursts.


  We found parity-violating Majorana fermions in a chiral superconductor
Sr2RuO4. The current-voltage curves show an anomalous behavior: The induced
voltage is an even function of the bias current. The magnetic field dependent
results suggest the excitation of the Majorana fermions along the closed chiral
edge current of the single domain under bias current. We also discuss the
relationship between a change of the chirality and spontaneous magnetization of
the single domain Sr2RuO4.


  Independent Component Analysis (ICA) is a popular model for blind signal
separation. The ICA model assumes that a number of independent source signals
are linearly mixed to form the observed signals. We propose a new algorithm,
PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for
ICA with Gaussian noise. The main technical innovation of the algorithm is to
use a fixed point iteration in a pseudo-Euclidean (indefinite "inner product")
space. The use of this indefinite "inner product" resolves technical issues
common to several existing algorithms for noisy ICA. This leads to an algorithm
which is conceptually simple, efficient and accurate in testing.
  Our second contribution is combining PEGI with the analysis of objectives for
optimal recovery in the noisy ICA model. It has been observed that the direct
approach of demixing with the inverse of the mixing matrix is suboptimal for
signal recovery in terms of the natural Signal to Interference plus Noise Ratio
(SINR) criterion. There have been several partial solutions proposed in the ICA
literature. It turns out that any solution to the mixing matrix reconstruction
problem can be used to construct an SINR-optimal ICA demixing, despite the fact
that SINR itself cannot be computed from data. That allows us to obtain a
practical and provably SINR-optimal recovery method for ICA with arbitrary
Gaussian noise.


  We calculate bulk and boundary correlators in JT gravity by summing over
geometries. The answers are reproduced by computing suitable ensemble averages
of correlators of chaotic quantum systems. We then consider bulk correlators at
large spatial separations and find that semiclassical decay eventually makes
way for erratic oscillations around some nonzero answer. There is no cluster
decomposition because of wormholes connecting distant regions. We construct
more microscopic versions of JT gravity which are dual to a single quantum
system by including a set of branes in the gravitational theory the data of
which describes the Hamiltonian of the dual system. We focus on the bulk
description of eigenstates which involves end of the world branes and we
explain how observables factorize due to geometries connecting to these branes.


  Sim\'eon-Denis Poisson was 25 years old when he was appointed Professor of
Mathematics at the \'Ecole Polytechnique in 1806. Elected to the Paris
Acad\'emie des Sciences six years later, he soon became one of its most
influential members. The origin and later developments of the many concepts in
mathematics and physics that bear his name make interesting stories, a few of
which we shall attempt to sketch in this paper.


  When using constellation synergy to image large areas for reconnaissance, it
is required to achieve the coverage capability requirements with minimal
consumption of observation resources to obtain the most optimal constellation
observation scheme. With the minimum number of satellites and meeting the
real-time ground coverage requirements as the optimization objectives, this
paper proposes an optimized design of satellite constellation configuration for
full coverage of large-scale regional imaging by using an improved simulated
annealing algorithm combined with the real-time coverage evaluation method of
hexagonal discretization. The algorithm can adapt to experimental conditions,
has good efficiency, and can meet industrial accuracy requirements. The
effectiveness and adaptability of the algorithm are tested in simulation
applications.


  Gas-grain and gas-phase reactions dominate the formation of molecules in the
interstellar medium (ISM). Gas-grain reactions require a substrate (e.g. a dust
or ice grain) on which the reaction is able to occur. The formation of
molecular hydrogen (H$_2$) in the ISM is the prototypical example of a
gas-grain reaction. In these reactions, an atom of hydrogen will strike a
surface, stick to it, and diffuse across it. When it encounters another
adsorbed hydrogen atom, the two can react to form molecular hydrogen and then
be ejected from the surface by the energy released in the reaction. We perform
in-depth classical molecular dynamics (MD) simulations of hydrogen atoms
interacting with an amorphous water-ice surface. This study focuses on the
first step in the formation process; the sticking of the hydrogen atom to the
substrate. We find that careful attention must be paid in dealing with the
ambiguities in defining a sticking event. The technical definition of a
sticking event will affect the computed sticking probabilities and
coefficients. Here, using our new definition of a sticking event, we report
sticking probabilities and sticking coefficients for nine different incident
kinetic energies of hydrogen atoms [5 K - 400 K] across seven different
temperatures of dust grains [10 K - 70 K]. We find that probabilities and
coefficients vary both as a function of grain temperature and incident kinetic
energy over the range of 0.99 - 0.22.


  Location-sharing services were built upon people's desire to share their
activities and locations with others. By "checking-in" to a place, such as a
restaurant, a park, gym, or train station, people disclose where they are,
thereby providing valuable information about land use and utilization of
services in urban areas. This information may, in turn, be used to design
smarter, happier, more equitable cities. We use data from Foursquare
location-sharing service to identify areas within a major US metropolitan area
with many check-ins, i.e., areas that people like to use. We then use data from
the Twitter microblogging platform to analyze the properties of these areas.
Specifically, we have extracted a large corpus of geo-tagged messages, called
tweets, from a major metropolitan area and linked them US Census data through
their locations. This allows us to measure the sentiment expressed in tweets
that are posted from a specific area, and also use that area's demographic
properties in analysis. Our results reveal that areas with many check-ins are
different from other areas within the metropolitan region. In particular, these
areas have happier tweets, which also encourage people from other areas to
commute longer distances to these places. These findings shed light on human
mobility patterns, as well as how physical environment influences human
emotions.


  Recent analysis of well-tempered metadynamics (WTmetaD) showed that it
converges without mollification artifacts in the bias potential. Here we
explore how metadynamics heals mollification artifacts, how healing impacts
convergence time, and whether alternative temperings may be used to improve
efficiency. We introduce "$\mu$-tempered" metadynamics as a simple tempering
scheme, inspired by a related mollified adaptive biasing potential (mABP), that
results in artifact independent convergence of the free energy estimate. We use
a toy model to examine the role of artifacts in WTmetaD and solvated alanine
dipeptide to compare the well-tempered and $\mu$-tempered frameworks
demonstrating fast convergence for hill widths as large as $60^{\circ}$ for
$\mu$TmetaD.


  This paper presents a machine learning-based method for the detection of the
unique gravitational microlensing signatures of extended dark objects, such as
boson stars, axion miniclusters and subhalos. We adapt MicroLIA, a machine
learning-based package tailored to handle the challenges posed by low-cadence
data in microlensing surveys. Using realistic observational timestamps, our
models are trained on simulated light curves to distinguish between
microlensing by point-like and extended lenses, as well as from other object
classes which give a variable magnitude. We show that boson stars, examples of
objects with a relatively flat mass distribution, can be confidently identified
for $0.8 \lesssim r/r_E\lesssim 3$. Intriguingly, we also find that more
sharply peaked structures, such as NFW-subhalos, can be distinctly recognized
from point-lenses under regular observation cadence. Our findings significantly
advance the potential of microlensing data in uncovering the elusive nature of
extended dark objects. The code and dataset used are also provided.


  Tabular data stands out as one of the most frequently encountered types in
high energy physics. Unlike commonly homogeneous data such as pixelated images,
simulating high-dimensional tabular data and accurately capturing their
correlations are often quite challenging, even with the most advanced
architectures. Based on the findings that tree-based models surpass the
performance of deep learning models for tasks specific to tabular data, we
adopt the very recent generative modeling class named conditional flow matching
and employ different techniques to integrate the usage of Gradient Boosted
Trees. The performances are evaluated for various tasks on different analysis
level with several public datasets. We demonstrate the training and inference
time of most high-level simulation tasks can achieve speedup by orders of
magnitude. The application can be extended to low-level feature simulation and
conditioned generations with competitive performance.


  We quantized the full Einstein equations in a globally hyperbolic spacetime
$N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation
in a fiber bundle $E$ which can be expressed as a product of spatial
eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial
eigenfunctions form a basis in an appropriate Hilbert space while the temporal
eigenfunctions are solutions to a second order ordinary differential equation
in $\mathbb{R}_+$. In case $n\ge 17$ and provided the cosmological constant
$\Lambda$ is negative the temporal eigenfunctions are eigenfunctions of a
self-adjoint operator $\hat H_0$ such that the eigenvalues are countable and
the eigenfunctions form an orthonormal basis of a Hilbert space.


  We study spectral triples over noncommutative principal U(1) bundles. Basing
on the classical situation and the abstract algebraic approach, we propose an
operatorial definition for a connection and compatibility between the
connection and the Dirac operator on the total space and on the base space of
the bundle. We analyze in details the example of the noncommutative three-torus
viewed as a U(1) bundle over the noncommutative two-torus and find all
connections compatible with an admissible Dirac operator. Conversely, we find a
family of new Dirac operators on the noncommutative tori, which arise from the
base-space Dirac operator and a suitable connection.


  This survey presents recent progress on Affective Computing (AC) using mobile
devices. AC has been one of the most active research topics for decades. The
primary limitation of traditional AC research refers to as impermeable
emotions. This criticism is prominent when emotions are investigated outside
social contexts. It is problematic because some emotions are directed at other
people and arise from interactions with them. The development of smart mobile
wearable devices (e.g., Apple Watch, Google Glass, iPhone, Fitbit) enables the
wild and natural study for AC in the aspect of computer science. This survey
emphasizes the AC study and system using smart wearable devices. Various
models, methodologies and systems are discussed in order to examine the state
of the art. Finally, we discuss remaining challenges and future works.


  This paper deals with the relations among structural, topological, and
chemical properties of the E.Coli proteome from the vantage point of the
solubility/aggregation propensity of proteins. Each E.Coli protein is initially
represented according to its known folded 3D shape. This step consists in
representing the available E.Coli proteins in terms of graphs. We first analyze
those graphs by considering pure topological characterizations, i.e., by
analyzing the mass fractal dimension and the distribution underlying both
shortest paths and vertex degrees. Results confirm the general architectural
principles of proteins. Successively, we focus on the statistical properties of
a representation of such graphs in terms of vectors composed of several
numerical features, which we extracted from their structural representation. We
found that protein size is the main discriminator for the solubility, while
however there are other factors that help explaining the solubility degree. We
finally analyze such data through a novel one-class classifier, with the aim of
discriminating among very and poorly soluble proteins. Results are encouraging
and consolidate the potential of pattern recognition techniques when employed
to describe complex biological systems.


  Recent studies by Sol\`a Peracaula, G\'omez-Valent, de Cruz P\'erez and
Moreno-Pulido (2019,2020) have pointed out the intriguing possibility that
Brans-Dicke cosmology with constant vacuum energy density (BD-$\Lambda$CDM) may
be able to alleviate the $H_0$ and $\sigma_8$ tensions that are found in the
framework of the concordance cosmological model (GR-$\Lambda$CDM). The fitting
analyses presented in these works indicate a preference for values of the
effective gravitational coupling appearing in the Friedmann equation, $G$,
about $4-9\%$ larger than Newton's constant (as measured on Earth), and mildy
evolving with the expansion of the universe. The signal reaches the $\sim
3.5\sigma$ c.l. when the prior on $H_0$ from SH0ES and the angular diameter
distances to strong gravitationally lensed quasars measured by H0LICOW are
considered, and the $\sim 3\sigma$ c.l. when only the former is included. Thus,
the improvement in the description of the cosmological datasets relies on the
existence of a mechanism capable of screening the modified gravity effects at
those scales where deviations from standard General Relativity (GR) are highly
constrained, as in the Solar System. In this paper we explore several
extensions of BD-$\Lambda$CDM that can leave the cosmological evolution
basically unaltered at the background and linear perturbations level, while
being able to screen the Brans-Dicke effects inside the regions of interest,
leading to standard GR. We search for weak-field solutions around spherical
static massive objects with no internal pressure and show that, unfortunately,
these mechanisms can only explain very tiny departures of the effective
cosmological gravitational coupling from the one measured locally. This might
hinder the ability of BD-$\Lambda$CDM to alleviate the cosmological tensions.


  We present a characterization of minimal cones of class $C^2$ and $C^1$ in
the first Heisenberg group $\mathbb{H}^1$, with an additional set of examples
of minimal cones that are not of class $C^1$.


  Dual equivalence graphs are a powerful tool in symmetric function theory that
provide a general framework for proving that a given quasisymmetric function is
symmetric and Schur positive. In this paper, we study a larger family of graphs
that includes dual equivalence graphs and define maps that, in certain cases,
transform graphs in this larger family into dual equivalence graphs. This
allows us to broaden the applications of dual equivalence graphs and points the
way toward a broader theory that could solve many important, long-standing
Schur positivity problems.


  For a finite non cyclic group $G$, let $\gamma(G)$ be the smallest integer
$k$ such that $G$ contains $k$ proper subgroups $H_1,\dots,H_k$ with the
property that every element of $G$ is contained in $H_i^g$ for some $i \in
\{1,\dots,k\}$ and $g \in G.$ We prove that if $G$ is a noncyclic permutation
group of degree $n,$ then $\gamma(G)\leq (n+2)/2.$ We then investigate the
structure of the groups $G$ with $\gamma(G)=\sigma(G)$ (where $\sigma(G)$ is
the size of a minimal cover of $G$) and of those with $\gamma(G)=2.$


  We present 21-cm line observations of the spiral galaxy NGC 4559, made with
the Westerbork Synthesis Radio Telescope. We have used them to study the HI
distribution and kinematics, the relative amount and distribution of luminous
and dark matter in this galaxy and, in particular, the presence of extra-planar
gas. Our data do reveal the presence of such a component, in the form of a
thick disk, with a mass of 5.9 x 10^8 Mo (one tenth of the total HI mass) and a
mean rotation velocity 25-50 km/s lower than that of the thin disk. The
extra-planar gas may be the result of galactic fountains but accretion from the
IGM cannot be ruled out. With this study we confirm that lagging, thick HI
layers are likely to be common in spiral galaxies.


  In this note, we give some explicit upper and lower bounds for the summation
$\sum_{0<\gamma\leq T}\frac{1}{\gamma}$, where $\gamma$ is the imaginary part
of nontrivial zeros $\rho=\beta+i\gamma$ of $\zeta(s)$.


  Purpose: Identifying intravenous (IV) contrast use within CT scans is a key
component of data curation for model development and testing. Currently, IV
contrast is poorly documented in imaging metadata and necessitates manual
correction and annotation by clinician experts, presenting a major barrier to
imaging analyses and algorithm deployment. We sought to develop and validate a
convolutional neural network (CNN)-based deep learning (DL) platform to
identify IV contrast within CT scans. Methods: For model development and
evaluation, we used independent datasets of CT scans of head, neck (HN) and
lung cancer patients, totaling 133,480 axial 2D scan slices from 1,979 CT scans
manually annotated for contrast presence by clinical experts. Five different DL
models were adopted and trained in HN training datasets for slice-level
contrast detection. Model performances were evaluated on a hold-out set and on
an independent validation set from another institution. DL models was then
fine-tuned on chest CT data and externally validated on a separate chest CT
dataset. Results: Initial DICOM metadata tags for IV contrast were missing or
erroneous in 1,496 scans (75.6%). The EfficientNetB4-based model showed the
best overall detection performance. For HN scans, AUC was 0.996 in the internal
validation set (n = 216) and 1.0 in the external validation set (n = 595). The
fine-tuned model on chest CTs yielded an AUC: 1.0 for the internal validation
set (n = 53), and AUC: 0.980 for the external validation set (n = 402).
Conclusion: The DL model could accurately detect IV contrast in both HN and
chest CT scans with near-perfect performance.


  In multivariate regression estimation, the rate of convergence depends on the
dimension of the regressor. This fact, known as the curse of the
dimensionality, motivated several works. The additive model, introduced by
Stone (10), offers an efficient response to this problem. In the setting of
continuous time processes, using the marginal integration method, we obtain the
quadratic convergence rate and the asymptotic normality of the components of
the additive model.


  Shear bands are narrow zones of intense shear observed during plastic
deformations of metals at high strain rates. Because they often precede
rupture, their study attracted attention as a mechanism of material failure.
Here, we aim to reveal the onset of localization into shear bands using a
simple model developed from viscoplasticity. We exploit the properties of scale
invariance of the model to construct a family of self-similar focusing
solutions that capture the nonlinear mechanism of shear band formation. The key
step is to de-singularize a reduced system of singular ordinary differential
equations and reduce the problem into the construction of a heteroclinic orbit
for an autonomous system of three first-order equations. The associated
dynamical system has fast and slow time scales, forming a singularly perturbed
problem. The geometric singular perturbation theory is applied to this problem
to achieve an invariant surface. The flow on the invariant surface is analyzed
via the Poincar\'{e}-Bendixson theorem to construct a heteroclinic orbit.


  Regularity of the horizon radius $r_g$ of a collapsing body constrains a
limiting form of a spherically-symmetric energy-momentum tensor near it. Its
non-zero limit belongs to one of four classes that are distinguished only by
two signs. As a result, close to $r_g$ the geometry can always be described by
either an ingoing or outgoing Vaidya metric with increasing or decreasing mass.
If according to a distant outside observer the trapped regions form in finite
time, then the Einstein equations imply violation of the null energy condition.
In this case the horizon radius and its rate of change determine the metric in
its vicinity, and the hypersurface $r = r_g(t)$ is timelike during both the
expansion and contraction of the trapped region. We present the implications of
these results for the firewall paradox and discuss arguments that the required
violation of the null energy condition is incompatible with the standard
analysis of black hole evaporation.


  In this paper, we study the group Fourier transform and the Kohn-Nirenberg
quantization for homogeneous Lie groups as mappings between certain Gelfand
triples. For this, we restrict our considerations to the case, where the
homogeneous Lie group $G$ admits irreducible unitary representations, that are
square integrable modulo the center $Z(G)$ of $G$, and where $\dim Z(G)=1$.
Replacing the Schwartz space by a certain subspace $\mathcal S_*(G)
\hookrightarrow \mathcal S(G)$, we characterise the range of the group Fourier
transform on $\mathcal S_*(G)$ and construct distributions and Gelfand triples
around $L^2(G,\mu)$ and its Fourier image $L^2(\hat G,\hat \mu)$, such that the
Fourier transform becomes a Gelfand triple isomorphism. We give results on the
multiplication of distributions with a large class of vector valued smooth
functions and use this to establish the Kohn-Nirenberg quantization as an
isomorphism for our Gelfand triples and provide an explicit formula for the
Kohn-Nirenberg symbol of an operator.


  Mastering dexterous robotic manipulation of deformable objects is vital for
overcoming the limitations of parallel grippers in real-world applications.
Current trajectory optimisation approaches often struggle to solve such tasks
due to the large search space and the limited task information available from a
cost function. In this work, we propose D-Cubed, a novel trajectory
optimisation method using a latent diffusion model (LDM) trained from a
task-agnostic play dataset to solve dexterous deformable object manipulation
tasks. D-Cubed learns a skill-latent space that encodes short-horizon actions
in the play dataset using a VAE and trains a LDM to compose the skill latents
into a skill trajectory, representing a long-horizon action trajectory in the
dataset. To optimise a trajectory for a target task, we introduce a novel
gradient-free guided sampling method that employs the Cross-Entropy method
within the reverse diffusion process. In particular, D-Cubed samples a small
number of noisy skill trajectories using the LDM for exploration and evaluates
the trajectories in simulation. Then, D-Cubed selects the trajectory with the
lowest cost for the subsequent reverse process. This effectively explores
promising solution areas and optimises the sampled trajectories towards a
target task throughout the reverse diffusion process. Through empirical
evaluation on a public benchmark of dexterous deformable object manipulation
tasks, we demonstrate that D-Cubed outperforms traditional trajectory
optimisation and competitive baseline approaches by a significant margin. We
further demonstrate that trajectories found by D-Cubed readily transfer to a
real-world LEAP hand on a folding task.


  We consider polynomial maps described by so-called "(multivariate) linearized
polynomials". These polynomials are defined using a fixed prime power, say q.
Linearized polynomials have no mixed terms. Considering invertible polynomial
maps without mixed terms over a characteristic zero field, we will only obtain
(up to a linear transformation of the variables) triangular maps, which are the
most basic examples of polynomial automorphisms. However, over the finite field
F_q automorphisms defined by linearized polynomials have (in general) an
entirely different structure. Namely, we will show that the linearized
polynomial maps over F_q are in one-to-one correspondence with matrices having
coefficients in a univariate polynomial ring over F_q. Furthermore, composition
of polynomial maps translates to matrix multiplication, implying that
invertible linearized polynomial maps correspond to invertible matrices.
  This alternate description of the linearized polynomial automorphism subgroup
leads to the solution of many famous conjectures (most notably, the Jacobian
Conjecture) for this kind of polynomials and polynomial maps.


  Nowadays, with the rise of Internet access and mobile devices around the
globe, more people are using social networks for collaboration and receiving
real-time information. Twitter, the microblogging that is becoming a critical
source of communication and news propagation, has grabbed the attention of
spammers to distract users. So far, researchers have introduced various defense
techniques to detect spams and combat spammer activities on Twitter. To
overcome this problem, in recent years, many novel techniques have been offered
by researchers, which have greatly enhanced the spam detection performance.
Therefore, it raises a motivation to conduct a systematic review about
different approaches of spam detection on Twitter. This review focuses on
comparing the existing research techniques on Twitter spam detection
systematically. Literature review analysis reveals that most of the existing
methods rely on Machine Learning-based algorithms. Among these Machine Learning
algorithms, the major differences are related to various feature selection
methods. Hence, we propose a taxonomy based on different feature selection
methods and analyses, namely content analysis, user analysis, tweet analysis,
network analysis, and hybrid analysis. Then, we present numerical analyses and
comparative studies on current approaches, coming up with open challenges that
help researchers develop solutions in this topic.


  Continuous treatments (e.g., doses) arise often in practice, but many
available causal effect estimators are limited by either requiring parametric
models for the effect curve, or by not allowing doubly robust covariate
adjustment. We develop a novel kernel smoothing approach that requires only
mild smoothness assumptions on the effect curve, and still allows for
misspecification of either the treatment density or outcome regression. We
derive asymptotic properties and give a procedure for data-driven bandwidth
selection. The methods are illustrated via simulation and in a study of the
effect of nurse staffing on hospital readmissions penalties.


  We study four-dimensional quantum gravity with negative cosmological constant
in the minisuperspace approximation and compute the partition function for the
$S^3$ boundary geometry. In this approximation scheme the path integrals become
dominated by a class of asymptotically AdS "microstate geometries." Despite the
fact that the theory is pure Einstein gravity without supersymmetry, the result
precisely reproduces, up to higher curvature corrections, the Airy function in
the $S^3$ partition function of the maximally supersymmetric
Chern-Simons-matter (CSM) theory which sums up all perturbative $1/N$
corrections. We also show that this can be interpreted as a concrete
realization of the idea that the CFT partition function is a solution to the
Wheeler-DeWitt equation as advocated in the holographic renormalization group.
Furthermore, the agreement persists upon the inclusion of a string probe and it
reproduces the Airy function in the vev of half-BPS Wilson loops in the CSM
theory. These results may suggest that the supergravity path integrals localize
to the minisuperspace in certain cases and the use of the minisuperspace
approximation in AdS/CFT may be a viable approach to study $1/N$ corrections to
large $N$ CFTs.


  An analytical solution is found for neutron reflection coefficients from
magnetic mirrors with fan-like magnetization. The main feature of the
reflection curves related to this type of magnetization is pointed out. The
results of calculations for some parameters of the system are presented. Time
parity and detailed balance violation in the model are discussed.


  An exponential Luenberger dynamical observer is proposed to estimate the
state of a general class of nonautonomous semilinear parabolic equations. The
result can be applied to the case where the output is given by state
measurements taken at a finite number of spatial points, that is, to the case
where our sensors are a finite number of delta distributions. The output
injection operator is explicit and the derivation of the main result involves
the decomposition of the state space into a direct sum of two oblique
components depending on the set of sensors. Simulations are presented as an
application to the Kuramoto--Sivashinsky models for flame propagation and fluid
flow.


  The search for Beyond the Standard Model (BSM) physics is one of the major
tasks of the LHC, CERN. In these proceedings, I review the status of searches
for Supersymmetry by the ATLAS and CMS collaborations. The efforts in both the
hadronic and leptonic search channels are presented. A special focus is placed
on the treatment of approximately one inverse femtobarn of early LHC data, and
examples of background estimation techniques in such a dataset are given.
Phenomenologically, besides "typical" mSUGRA scenarios, signatures based on
prompt and non-pointing photons, as well as long-lived leptons and hadrons
(R-hadrons) are covered.


  The NAIAD experiment (NaI Advanced Detector) for WIMP dark matter searches at
Boulby mine (UK) is described. The detector consists of an array of
encapsulated and unencapsulated NaI(Tl) crystals with high light yield. Six
crystals are collecting data at present. Data accumulated by four of them (10.6
kg x year exposure) have been used to set upper limits on the WIMP-nucleon
spin-independent and WIMP-proton spin-dependent cross-sections. Pulse shape
analysis has been applied to discriminate between nuclear recoils, as may be
caused by WIMP interactions, and electron recoils due to gamma background.
Various calibrations of crystals are presented.