  Based on the newly developed real-space spin-parallel pairing and
superconducting theory, we explore a simple explanation for the observed
checkerboard patterns in hole-doped Ca{2-x}Na{x}CuO{2}Cl{2} cuprate
superconductor. At a hole concentration x=1/8=0.125, the analytical results
show that there exists a phase competition between non-superconducting 4a*4b
(a=b) checkerboard phase and 8a*2c superconducting vortex phase, where a, b and
c are the lattice constants of the superconductor. At a lower hole
concentration x=1/16=0.0625, it is revealed that the metastable
4\sqrt{2}a*4\sqrt{2}a checkerboard phase can reorganize itself into a more
stable octahedron phase with the 4a*4a checkerboard symmetry.


  The human brain is a complex inter-wired system that emerges spontaneous
functional fluctuations. In spite of tremendous success in the experimental
neuroscience field, a system-level understanding of how brain anatomy supports
various neural activities remains elusive. Capitalizing on the unprecedented
amount of neuroimaging data, we present a physics-informed deep model to
uncover the coupling mechanism between brain structure and function through the
lens of data geometry that is rooted in the widespread wiring topology of
connections between distant brain regions. Since deciphering the puzzle of
self-organized patterns in functional fluctuations is the gateway to
understanding the emergence of cognition and behavior, we devise a geometric
deep model to uncover manifold mapping functions that characterize the
intrinsic feature representations of evolving functional fluctuations on the
Riemannian manifold. In lieu of learning unconstrained mapping functions, we
introduce a set of graph-harmonic scattering transforms to impose the
brain-wide geometry on top of manifold mapping functions, which allows us to
cast the manifold-based deep learning into a reminiscent of MLP-Mixer
architecture (in computer vision) for Riemannian manifold. As a
proof-of-concept approach, we explore a neural-manifold perspective to
understand the relationship between (static) brain structure and (dynamic)
function, challenging the prevailing notion in cognitive neuroscience by
proposing that neural activities are essentially excited by brain-wide
oscillation waves living on the geometry of human connectomes, instead of being
confined to focal areas.


  A weak law of large numbers is established for a sequence of systems of N
classical point particles with logarithmic pair potential in $\bbR^n$, or
$\bbS^n$, $n\in \bbN$, which are distributed according to the configurational
microcanonical measure $\delta(E-H)$, or rather some regularization thereof,
where H is the configurational Hamiltonian and E the configurational energy.
When $N\to\infty$ with non-extensive energy scaling $E=N^2 \vareps$, the
particle positions become i.i.d. according to a self-consistent Boltzmann
distribution, respectively a superposition of such distributions. The
self-consistency condition in n dimensions is some nonlinear elliptic PDE of
order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2,
this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with
applications to point vortices, 2D Coulomb and magnetized plasmas and
gravitational systems. It is then also known in conformal differential
geometry, where it is the central equation in Nirenberg's problem of prescribed
Gaussian curvature. For constant Gauss curvature it becomes Liouville's
equation, which also appears in two-dimensional so-called quantum Liouville
gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in
statistical mechanics, it originated from a study of the conformal invariance
of Maxwell's electromagnetism and has made its appearance in some recent model
of four-dimensional quantum gravity. In differential geometry, the Paneitz
equation and its higher order n generalizations have applications in the
conformal geometry of n-manifolds, but no physical applications yet for general
n. Interestingly, though, all the Paneitz equations have an interpretation in
terms of statistical mechanics.


  Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable
surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and
sufficient conditions under which two torsion elements in $\mathrm{Mod}(S_g)$
will have conjugates that generate a finite split non-abelian metacyclic
subgroup of $\mathrm{Mod}(S_g)$. As applications of the main result, we give a
complete characterization of the finite dihedral and the generalized
quaternionic subgroups of $\mathrm{Mod}(S_g)$ up to a certain equivalence that
we will call weak conjugacy. Furthermore, we show that any finite-order mapping
class whose corresponding orbifold is a sphere, has a conjugate that lifts
under certain finite-sheeted regular cyclic covers of $S_g$. Moreover, for $g
\geq 5$, we show the existence of an infinite dihedral subgroup of
$\mathrm{Mod}(S_g)$ that is generated by an involution and a root of a bounding
pair map of degree $3$. Finally, we provide a complete classification of the
weak conjugacy classes of the non-abelian finite split metacyclic subgroups of
$\mathrm{Mod}(S_3)$ and $\mathrm{Mod}(S_5)$. We also describe nontrivial
geometric realizations of some of these actions.


  Since the early work of Hagen in 1852 and Beverloo et al. in 1961, the flow
rate of granular material discharging through a circular orifice from a silo
has been described by means of dimensional analysis and experimental fits, and
explained through the "free fall arch" model. Here, in contrast with the
traditional approach, we derive a differential equation based on the energy
balance of the system. This equation is consistent with the well known Beverloo
rule thanks to a compensation of energy terms. Moreover, this new equation can
be used to explore new conditions for silo discharges. In particular, we show
how the effect of friction on the flow rate can be predicted. The theory is
validated using discrete element method simulations.


  Hermitian linear complementary dual codes are linear codes whose intersection
with their Hermitian dual code is trivial. The largest minimum weight among
quaternary Hermitian linear complementary dual codes of dimension $2$ is known
for each length. We give the complete classification of optimal quaternary
Hermitian linear complementary dual codes of dimension $2$.


  We demonstrate that two-dimensional crystals made of active particles can
experience extremely large spontaneous deformations without melting. Using
particles mostly interacting via pairwise repulsive forces, we show that such
active crystals maintain long-range bond order and algebraically-decaying
positional order, but with an exponent $\eta$ not limited by the $\tfrac{1}{3}$
bound given by the (equilibrium) KTHNY theory. We rationalize our findings
using linear elastic theory and show the existence of two well-defined
effective temperatures quantifying respectively large-scale deformations and
bond-order fluctuations. The root of these phenomena lies in the sole
time-persistence of the intrinsic axes of particles, and they should thus be
observed in many different situations.


  We study the dynamics of a thick polar epithelium subjected to the action of
both an electric and a flow field in a planar geometry. We develop a
generalized continuum hydrodynamic description and describe the tissue as a two
component fluid system. The cells and the interstitial fluid are the two
components and we keep all terms allowed by symmetry. In particular we keep
track of the cell pumping activity for both solvent flow and electric current
and discuss the corresponding orders of magnitude. We study the growth dynamics
of tissue slabs, their steady states and obtain the dependence of the cell
velocity, net cell division rate, and cell stress on the flow strength and the
applied electric field. We find that finite thickness tissue slabs exist only
in a restricted region of phase space and that relatively modest electric
fields or imposed external flows can induce either proliferation or death.


  Covarion models of character evolution describe inhomogeneities in
substitution processes through time. In phylogenetics, such models are used to
describe changing functional constraints or selection regimes during the
evolution of biological sequences. In this work the identifiability of such
models for generic parameters on a known phylogenetic tree is established,
provided the number of covarion classes does not exceed the size of the
observable state space. `Generic parameters' as used here means all parameters
except possibly those in a set of measure zero within the parameter space.
Combined with earlier results, this implies both the tree and generic numerical
parameters are identifiable if the number of classes is strictly smaller than
the number of observable states.


  We express any Courant algebroid bracket by means of a metric connection, and
construct a Courant algebroid structure on any orthogonal Whitney sum $E\oplus
C$ where E is a given Courant algebroid and C is a flat, pseudo- Euclidean
vector bundle. Then, we establish the general expression of the bracket of a
transitive Courant algebroid, i.e., a Courant algebroid with a surjective
anchor, and describe a class of transitive Courant algebroids which are Whitney
sums of a Courant subalgebroid with neutral metric and Courant-like bracket and
a pseudo-Euclidean vector bundle with a flat, metric connection. In particular,
this class contains all the transitive Courant algebroids of minimal rank; for
these, the flat term mentioned above is zero. The results extend to regular
Courant algebroids, i.e., Courant algebroids with a constant rank anchor. The
paper ends with miscellaneous remarks and an appendix on Dirac linear spaces.


  There has recently been great interest in neural rendering methods. Some
approaches use 3D geometry reconstructed with Multi-View Stereo (MVS) but
cannot recover from the errors of this process, while others directly learn a
volumetric neural representation, but suffer from expensive training and
inference. We introduce a general approach that is initialized with MVS, but
allows further optimization of scene properties in the space of input views,
including depth and reprojected features, resulting in improved novel-view
synthesis. A key element of our approach is our new differentiable point-based
pipeline, based on bi-directional Elliptical Weighted Average splatting, a
probabilistic depth test and effective camera selection. We use these elements
together in our neural renderer, that outperforms all previous methods both in
quality and speed in almost all scenes we tested. Our pipeline can be applied
to multi-view harmonization and stylization in addition to novel-view
synthesis.


  We try to use scale-invariance and the large-N limit to find a non-trivial 4d
O(N) scalar field model with controlled UV behavior and naturally light scalar
excitations. The principle is to fix interactions by requiring the effective
action for space-time dependent background fields to be finite and
scale-invariant when regulators are removed. We find a line of non-trivial UV
fixed-points in the large-N limit, parameterized by a dimensionless coupling.
They reduce to classical la phi^4 theory when hbar -> 0. For hbar non-zero,
neither action nor measure is scale-invariant, but the effective action is.
Scale invariance makes it natural to set a mass deformation to zero. The model
has phases where O(N) invariance is unbroken or spontaneously broken. Masses of
the lightest excitations above the unbroken vacuum are found. We derive a
non-linear equation for oscillations about the broken vacuum. The interaction
potential is shown to have a locality property at large-N. In 3d, our
construction reduces to the line of large-N fixed-points in |phi|^6 theory.


  The paper is dedicated to the close analogy between these two theories - some
problems lying at the very root of Spectral Geometry are viewed in the context
of Semiclassics, and vise versa. The treatment starts from a very basic level
and gradually goes into the deep, ending up with some rather up to date
results. There are many examples concerning effective actions in QCD and String
Theory, functional determinants, first integrals from asymptotic expansions,
path quantization etc. The major theorems are only given brief explanations and
simple constructive proofs, but some rather practical formulae are obtained in
return. There is a small exercise at the end - obtaining explicit expressions
for the spectral variations of the Robin problem for a planar domain. The final
result is purely in the spirit of the familiar Sationary Perturbation Theory.
The idea for investigating this particular problem (in the context of an old
exact inverse result obtained by Guillemin and Melrose), very much motivating
most of the work, belongs to my scientific advisor Dr. Petko Nikolov.


  In metal nanoparticles (NPs) supracrystals, the metallic core provides some
key properties, e.g. magnetization, plasmonic response or conductivity, with
the ligand molecules giving rise to others like solubility, assembly or
interaction with biomolecules. The formation of these supracrystals depends on
a complex interplay between many forces, some stemming from the core, some from
the ligands. At present, there is no known approach to characterize the local
order of ligand molecules or their dynamics with atomic spatial resolution.
Here, we develop a methodology based on small-angle ultrafast electron
diffraction combined with angular cross-correlation analysis to characterize a
two-dimensional supracrystal of dodecanethiol-coated gold NPs. We retrieve the
static arrangement of the ligands, showing that at equilibrium they order in a
preferential orientation on the NPs surface and throughout the two-dimensional
supracrystal. Upon light excitation, positional disorder is induced in the
supracrystal, while its overall homogeneity is surprisingly found to
transiently increase. This suggests that transient annealing of the
supracrystal takes place within few picoseconds (ps). This methodology will
enable the systematic investigation of the dynamical structural properties of
nano-assembled materials containing light elements, relevant for biological
applications.


  We employ surface differential calculus to derive models for Kirchhoff plates
including in-plane membrane deformations. We also extend our formulation to
structures of plates. For solving the resulting set of partial differential
equations, we employ a finite element method based on elements that are
continuous for the displacements and discontinuous for the rotations, using
$C^0$-elements for the discretisation of the plate as well as for the membrane
deformations. Key to the formulation of the method is a convenient definition
of jumps and averages of forms that are $d$-linear in terms of the element edge
normals.


  It is shown that maximally efficient protocols for secure direct quantum
communications can be constructed using any arbitrary orthogonal basis. This
establishes that no set of quantum states (e.g. GHZ states, W states, Brown
states or Cluster states) has an advantage over the others, barring the
relative difficulty in physical implementation. The work provides a wide choice
of states for experimental realization of direct secure quantum communication
protocols. We have also shown that this protocol can be generalized to a
completely orthogonal state based protocol of Goldenberg-Vaidman (GV) type. The
security of these protocols essentially arises from duality and monogamy of
entanglement. This stands in contrast to protocols that employ non-orthogonal
states, like Bennett-Brassard 1984 (BB84), where the security essentially comes
from non-commutativity in the observable algebra.


  Let N be a (n+1)-dimensional globally hyperbolic Lorentzian manifold with a
compact Cauchy hypersurface. We consider curvature flows in N with different
curvature functions F (including the mean curvature, the gauss curvature and
the second elementary symmetric polynomial) and a volume preserving term. Under
suitable assumptions we prove the long time existence of the flow and the
exponential convergence of the corresponding graphs in the $C^\infty$-topology
to a hypersurface of constant F-curvature. Furthermore we examine stability
properties and foliations of constant F-curvature hypersurfaces.


  It has been argued that if light Higgs bosons do not exist then the
self--interactions of $W$'s become strong in the TeV region and can be observed
in longitudinal $WW$ scattering. We present a model with many inelastic
channels in the $WW$ scattering process, corresponding to the creation of heavy
fermion pairs. The presence of these heavy fermions affects the elastic
scattering of $W$'s by propagating in loops, greatly reducing the amplitudes in
some charge channels. Consequently, the symmetry--breaking sector cannot be
fully explored by using, for example, the $W^+W^+$ mode alone; all $WW
\rightarrow WW$ scattering modes must be measured.}


  Affective polarization and increasing social divisions affect social mixing
and the spread of information across online and physical spaces, reinforcing
social and electoral cleavages and influencing political outcomes. Here, using
aggregated and de-identified co-location and online network data, we
investigate the relationship between partisan exposure and voting patterns in
the USA by comparing three dimensions of partisan exposure: physical proximity
and exposure to the same social contexts, online social ties, and residential
sorting. By leveraging various statistical modeling approaches, we consistently
find that partisan exposure in the physical space, as captured by co-location
patterns, more accurately predicts electoral outcomes in US counties,
outperforming online and residential exposures across metropolitan and
non-metro areas. Moreover, our results show that physical partisan proximity is
the best predictor of voting patterns in swing counties, where the election
results are most uncertain. We also estimate county-level experienced partisan
segregation and examine its relationship with individuals' demographic and
socioeconomic characteristics. Focusing on metropolitan areas, our results
confirm the presence of extensive partisan segregation in the US and show that
offline partisan isolation, both considering physical encounters or residential
sorting, is higher than online segregation and is primarily associated with
educational attainment. Our findings emphasize the importance of physical space
in understanding the relationship between social networks and political
behavior, in contrast to the intense scrutiny focused on online social networks
and elections.


  Classical work of Lee, Schultz, and Stolz relates the smooth transformation
groups of exotic spheres to the stable homotopy groups of spheres. In this
note, we apply recent progress on the latter to produce smooth circle and
cyclic group actions on certain exotic spheres.


  Bayesian parameter inference is an essential tool in modern cosmology, and
typically requires the calculation of $10^5$--$10^6$ theoretical models for
each inference of model parameters for a given dataset combination. Computing
these models by solving the linearised Einstein-Boltzmann system usually takes
tens of CPU core-seconds per model, making the entire process very
computationally expensive.
  In this paper we present \textsc{connect}, a neural network framework
emulating \textsc{class} computations as an easy-to-use plug-in for the popular
sampler \textsc{MontePython}. \textsc{connect} uses an iteratively trained
neural network which emulates the observables usually computed by
\textsc{class}. The training data is generated using \textsc{class}, but using
a novel algorithm for generating favourable points in parameter space for
training data, the required number of \textsc{class}-evaluations can be reduced
by two orders of magnitude compared to a traditional inference run. Once
\textsc{connect} has been trained for a given model, no additional training is
required for different dataset combinations, making \textsc{connect} many
orders of magnitude faster than \textsc{class} (and making the inference
process entirely dominated by the speed of the likelihood calculation).
  For the models investigated in this paper we find that cosmological parameter
inference run with \textsc{connect} produces posteriors which differ from the
posteriors derived using \textsc{class} by typically less than $0.01$--$0.1$
standard deviations for all parameters. We also stress that the training data
can be produced in parallel, making efficient use of all available compute
resources. The \textsc{connect} code is publicly available for download at
\url{https://github.com/AarhusCosmology}.


  Information-Centric Fog Computing enables a multitude of nodes near the
end-users to provide storage, communication, and computing, rather than in the
cloud. In a fog network, nodes connect with each other directly to get content
locally whenever possible. As the topology of the network directly influences
the nodes' connectivity, there has been some work to compute the graph
centrality of each node within that network topology. The centrality is then
used to distinguish nodes in the fog network, or to prioritize some nodes over
others to participate in the caching fog. We argue that, for an
Information-Centric Fog Computing approach, graph centrality is not an
appropriate metric. Indeed, a node with low connectivity that caches a lot of
content may provide a very valuable role in the network.
  To capture this, we introduce acontent-based centrality (CBC) metric which
takes into account how well a node is connected to the content the network is
delivering, rather than to the other nodes in the network. To illustrate the
validity of considering content-based centrality, we use this new metric for a
collaborative caching algorithm. We compare the performance of the proposed
collaborative caching with typical centrality based, non-centrality based, and
non-collaborative caching mechanisms. Our simulation implements CBC on three
instances of large scale realistic network topology comprising 2,896 nodes with
three content replication levels. Results shows that CBC outperforms benchmark
caching schemes and yields a roughly 3x improvement for the average cache hit
rate.


  We study the short-periodic component of stellar activity with a cycle
periods Pcyc up to 1000 days using the Kepler mission photometry of
fast-rotating (rotational periods from 1 to 4 days) stars with spectra of M4V
to F3V. Applying the originally developed two non-spectral methods, we measured
the effective period of stellar cycles in 462 objects. The obtained results are
in accordance with previous measurements by Vida et al. (2014), do not seem to
result from a beating effect. The performed measurements of Pcyc cluster in a
specific branch which covers the previously unstudied region in the
Saar-Brandenburg (1999) diagram, and connects the branch of inactive stars with
the area populated by super-active objects. It is shown that the formation of
the discovered branch is due to the alpha-quenching effect, which saturates the
magnetic dynamo and decreases the cycle periods with the increase of inverted
Rossby number. This finding is important in the context of the discussion on
catastrophic quenching and other heuristic approximations of the non-linear
alpha-effect.


  In an earlier paper, Oruba, Soward & Dormy (J.Fluid Mech., vol.818, 2017,
pp.205-240) considered the primary quasi-steady geostrophic (QG) motion of a
constant density fluid of viscosity $\nu$ that occurs during linear spin-down
in a cylindrical container of radius $L$ and height $H$, rotating rapidly
(angular velocity $\Omega$) about its axis of symmetry subject to mixed rigid
and stress-free boundary conditions for the case $L=H$. Direct Numerical
Simulation (DNS) at large $L= 10 H$ and Ekman number $E=\nu/H^2\Omega=10^{-3}$
by Oruba, Soward & Dormy (J.Fluid Mech., sub judice and referred to as Part I)
reveals significant inertial wave activity on the spin-down time-scale. The
analytic study in Part I, based on $E\ll 1$, builds on the results of Greenspan
& Howard (J.Fluid Mech., vol.17, 1963, pp.385-404) for an infinite plane layer
$L\to\infty$. At large but finite distance $r^\dag$ from the symmetry axis, the
meridional (QG-)flow, that causes the QG-spin down, is blocked by the lateral
boundary $r^\dag=L$, which provides the primary QG-trigger for the inertial
waves studied in Part I. For the laterally unbounded layer, Greenspan & Howard
also identified inertial waves of maximum frequency (MF), which are a
manifestation of the transient Ekman layer. The blocking of the MF-waves by the
lateral boundary provides a secondary MF-trigger for yet more inertial waves.
Here we obtain analytic results for the wave activity caused by the
combined-trigger (QG+MF) that faithfully captures the character of the
laterally unbounded base flow including its transients. The results are
compared with the inertial wave part of the DNS (the so called "filtered DNS"
or simply "FNS"), for which the agreement is excellent and accounts for minor
discrepancies evident in the Part I results for the QG-trigger.


  Mobile sensing has been recently proposed for sampling spatial fields, where
mobile sensors record the field along various paths for reconstruction.
Classical and contemporary sampling typically assumes that the sampling
locations are approximately known. This work explores multiple sampling
strategies along random paths to sample and reconstruct a two dimensional
bandlimited field. Extensive simulations are carried out, with insights from
sensing matrices and their properties, to evaluate the sampling strategies.
Their performance is measured by evaluating the stability of field
reconstruction from field samples. The effect of location unawareness on some
sampling strategies is also evaluated by simulations.


  We report on research carried out to improve teaching and student engagement
in the introductory astronomy course at the University of Cape Town. This
course is taken by a diverse range of students, including many from
educationally disadvantaged backgrounds. We describe the development of an
instrument, the Introductory Astronomy Questionnaire (IAQ), which we
administered as pre- and post-tests to students enrolled in the course. The
instrument comprised a small number of questions which probed three areas of
interest: student motivation and expectations, astronomy content, and
worldview. Amongst our findings were that learning gains were made in several
conceptual areas, and that students appeared to develop a more nuanced view of
the nature of astronomy. There was some evidence that the course had a positive
impact on students' worldviews, particularly their attitudes towards science.
We also identified a promising predictor of course success that could in future
be used to identify students requiring special teaching intervention.


  Scaling up contrastive language-image pretraining (CLIP) is critical for
empowering both vision and multimodal models. We present EVA-CLIP-18B, the
largest and most powerful open-source CLIP model to date, with 18-billion
parameters. With only 6-billion training samples seen, EVA-CLIP-18B achieves an
exceptional 80.7% zero-shot top-1 accuracy averaged across 27 widely recognized
image classification benchmarks, outperforming its forerunner EVA-CLIP
(5-billion parameters) and other open-source CLIP models by a large margin.
Remarkably, we observe a consistent performance improvement with the model size
scaling of EVA-CLIP, despite maintaining a constant training dataset of
2-billion image-text pairs from LAION-2B and COYO-700M. This dataset is openly
available and much smaller than the in-house datasets (e.g., DFN-5B, WebLI-10B)
employed in other state-of-the-art CLIP models. EVA-CLIP-18B demonstrates the
potential of EVA-style weak-to-strong visual model scaling. With our model
weights made publicly available, we hope to facilitate future research in
vision and multimodal foundation models.


  The challenging physics program at the International Linear Collider (ILC)
poses stringent requirements on the performance of its tracking system. A large
volume time projection chamber (TPC) is considered a good candidate for such a
tracker. Whereas conventional TPCs used a wired based gas amplification system,
a future TPC is likely to make use of micro pattern gas detectors as e. g. gas
electron multipliers (GEMs) for gas amplification. This talk gives an overview
over recent achievements from the R&D activities to build a TPC with a GEM
based gas amplification system. This includes charge transfer studies through
multiple GEM structures, field cage design and spatial resolution measurements
in high magnetic fields.


  The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian
approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level
using as input the non-perturbative ghost and gluon propagators previously
determined within the variational approach. The obtained ghost-gluon vertex is
IR finite but IR enhanced compared to the bare one by 15% to 25%, depending on
the kinematical momentum regime.


  A new coding scheme for image transmission over noisy channel is proposed.
Similar to standard image compression, the scheme includes a linear transform
followed by successive refinement scalar quantization. Unlike conventional
schemes, in the proposed system the quantized transform coefficients are
linearly mapped into channel symbols using systematic linear encoders. This
fixed-to-fixed length "linear index coding" approach avoids the use of an
explicit entropy coding stage (e.g., arithmetic or Huffman coding), which is
typically fragile to channel post-decoding residual errors. We use linear codes
over GF(4), which are particularly suited for this application, since they are
matched to the dead-zone quantizer symbol alphabet and to the QPSK modulation
used on the deep-space communication channel. We optimize the proposed system
where the linear codes are systematic Raptor codes over GF(4). The rateless
property of Raptor encoders allows to achieve a "continuum" of coding rates, in
order to accurately match the channel coding rate to the transmission channel
capacity and to the quantized source entropy rate for each transform subband
and refinement level. Comparisons are provided with respect to the
concatenation of state-of-the-art image coding and channel coding schemes used
by Jet Propulsion Laboratories (JPL) for the Mars Exploration Rover (MER)
Mission.


  In this short note, we show that the problem of computing the recursive
teaching dimension (RTD) for a concept class (given explicitly as input)
requires $n^{\Omega(\log n)}$-time, assuming the exponential time hypothesis
(ETH). This matches the running time $n^{O(\log n)}$ of the brute-force
algorithm for the problem.


  A variational formula for the Cram\'er transform of series of weighted,
independent symmetric Bernoulli random variables (Rademacher series) is given.


  Millisecond pulsars are rather weakly-magnetized neutron stars which are
thought to have been spun up by disc accretion, with magnetic linkage between
the star and the disc playing a key role. Their spin history depends
sensitively on details of the magnetic field structure, but idealized models
from the 1980s and 1990s are still commonly used for calculating the magnetic
field components. This paper is the third in a series presenting results from a
step-by-step analysis which we are making of the problem, starting with very
simple models and then progressively including additional features one at a
time, with the aim of gaining new insights into the mechanisms involved. In our
first two papers, the magnetic field structure in the disc was calculated for a
standard Shakura and Sunyaev model, by solving the magnetic induction equation
numerically in the stationary limit within the kinematic approximation; here we
consider a more general velocity field in the disc, including backflow. We find
that the profiles of the poloidal and toroidal components of the magnetic field
are fairly similar in the two cases but that they can be very different from
those in the models mentioned above, giving important consequences for the
torque exerted on the central object. In particular we find that, contrary to
what is usually thought, some regions of the disc outward of the co-rotation
point (rotating more slowly than the neutron star) may nevertheless contribute
to spinning up the neutron star on account of the detailed structure of the
magnetic field in those parts of disc.


  arXiv is a popular pre-print server focusing on natural science disciplines
(e.g. physics, computer science, quantitative biology). As a platform with
focus on easy publishing services it does not provide enhanced search
functionality -- but offers programming interfaces which allow external parties
to add these services. This paper presents extensions of the open source
framework arXiv Sanity Preserver (SP). With respect to the original framework,
it derestricts the topical focus and allows for text-based search and
visualisation of all papers in arXiv. To this end, all papers are stored in a
unified back-end; the extension provides enhanced search and ranking facilities
and allows the exploration of arXiv papers by a novel user interface.


  The COVID-19 crisis has emphasized the need for scientific methods such as
machine learning to speed up the discovery of solutions to the pandemic.
Harnessing machine learning techniques requires quality data, skilled personnel
and advanced compute infrastructure. In Africa, however, machine learning
competencies and compute infrastructures are limited. This paper demonstrates a
cross-border collaborative capacity building approach to the application of
machine learning techniques in discovering answers to COVID-19 questions.


  We consider the inverse problem of determining the Lam\'e moduli for a
piecewise constant elasticity tensor ${\mathbb C}= \sum_{j} {\mathbb C}_j
\chi_{D_j}$, where $\{D_j\}$ is a known finite partition of the body $\Omega$,
from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates
can be derived under $C^{1,\alpha}$ regularity assumptions on the interfaces.


  We reconsider the classic problem of estimating accurately a 2D
transformation from point matches between images containing outliers. RANSAC
discriminates outliers by randomly generating minimalistic sampled hypotheses
and verifying their consensus over the input data. Its response is based on the
single hypothesis that obtained the largest inlier support. In this article we
show that the resulting accuracy can be improved by aggregating all generated
hypotheses. This yields RANSAAC, a framework that improves systematically over
RANSAC and its state-of-the-art variants by statistically aggregating
hypotheses. To this end, we introduce a simple strategy that allows to rapidly
average 2D transformations, leading to an almost negligible extra computational
cost. We give practical applications on projective transforms and
homography+distortion models and demonstrate a significant performance gain in
both cases.


  Several recent studies have demonstrated that attention-based networks, such
as Vision Transformer (ViT), can outperform Convolutional Neural Networks
(CNNs) on several computer vision tasks without using convolutional layers.
This naturally leads to the following questions: Can a self-attention layer of
ViT express any convolution operation? In this work, we prove that a single ViT
layer with image patches as the input can perform any convolution operation
constructively, where the multi-head attention mechanism and the relative
positional encoding play essential roles. We further provide a lower bound on
the number of heads for Vision Transformers to express CNNs. Corresponding with
our analysis, experimental results show that the construction in our proof can
help inject convolutional bias into Transformers and significantly improve the
performance of ViT in low data regimes.


  Within the framework proposed by Caron-Huot and Wilhelm, we give a recipe for
computing infrared anomalous dimensions purely on-shell, efficiently up to two
loops in any massless theory. After introducing the general formalism and
reviewing the one-loop recipe, we extract a practical formula that relates
two-loop infrared anomalous dimensions to certain two- and three-particle phase
space integrals with tree-level form factors of conserved operators. We then
provide several examples of the use of the two-loop formula and comment on some
of its formal aspects, especially the cancellation of 'one-loop squared'
spurious terms. The present version of the paper is augmented with a detailed
treatment of the structure of infrared divergences in massless theories of
scalars and fermions up to two loops. In the calculation we encounter divergent
phase space integrals and show in detail how these cancel among each other as
required by the finiteness of the anomalous dimension. As a non-trivial check
of the method, we also perform the computation with a standard diagrammatic
approach, finding perfect agreement.


  Dynamical origin of duality between gauge theory and gravity is studied using
the dual transformation and the formation of graviton as a collective
excitation of dual gauge bosons. In this manner, electric-magnetic duality in
gauge theory is reduced to the duality between gauge theory and gravity.


  In this note we show that the weight enumerators of a real quantum error
correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain
identities. One consequence of these identities is that if the code is error
detecting then it is automatically error correcting for free; implying a
relationship between transversality and code distance.


  Chip-integrated optical frequency combs are attractive optical sources in
comb applications requiring high-repetition-rate, low power consumption, or
compact size. Spontaneous soliton formation via Kerr parametric oscillation is
a promising generation principle in these frequency combs, and has been
demonstrated in several material platforms over the past decade. Of these
materials, AlGaAs has one of the largest Kerr nonlinearity coefficients
allowing low pump threshold comb generation. However, bright soliton generation
using this material has only been possible at cryogenic temperature because of
the large thermo-optic effect at room temperature, which hinders stable access
to the soliton regime. Here, we report self-stabilized single soliton
generation in AlGaAs microresonators at room temperature by utilizing a rising
soliton step in large free-spectral-range resonators. With sub-milliWatt
optical pump power, 1 THz repetition-rate soliton generation is demonstrated.
Perfect soliton crystal formation and soliton breather states are also
observed. Besides the advantages of large optical nonlinearity, the devices are
natural candidates for integration with III-V pump lasers.


  We study a ${{\IZ}}_2$ orbifold of Type 0B string theory by reflection of six
of the coordinates (this theory may also be thought of as a ${{\IZ}}_4$
orbifold of Type IIB string theory by a rotation by $\pi$ in three independent
planes). We show that the only massless mode localized on the fixed fourplane
$\IR^{3,1}$ is a U(1) gauge field. After introducing D3-branes parallel to the
fixed fourplane we find non-supersymmetric non-abelian gauge theories on their
worldvolume. One of our results is that the theory on equal numbers of electric
and magnetic D3-branes placed at the fourplane is the ${{\IZ}}_4$ orbifold of
${\cal N}=4$ supersymmetric Yang-Mills theory by the center of its R-symmetry
group.


  We investigate the dynamics of a one-dimensional $p$-wave superconductor with
next-nearest-neighbor hopping and superconducting interaction derived from a
three-spin interacting Ising model in transverse field by mapping to Majorana
fermions. The next-nearest-neighbor hopping term leads a new topological phase
containing two zero-energy Majorana modes at each end of an open chain,
compared to a nearest-neighbor $p$-wave superconducting chain. We study the
Majorana survival probability (MSP) of a particular Majorana edge state when
the initial Hamiltonian ($H_i$) is changed to the quantum critical as well as
off-critical final Hamiltonian ($H_f$) which additionally contains an impurity
term ($H_{imp}$) that breaks the time-reversal invariance. For the off-critical
quenching inside the new topological phase with $H_f= H_i +H_{imp}$, and small
impurity strength ($\lambda_d$), we observe a perfect oscillation of the MSP as
a function of time with a single frequency (determined by the impurity strength
$\lambda_d$) that can be analyzed from an equivalent two-level problem. On the
other hand, the MSP shows a beating like structure with time for quenching to
the phase boundary separating the topological phase (with two edge Majoranas at
each edge) and the non-topological phase where the additional frequency is
given by inverse of the system size. We attribute this behavior of the MSP to
the modification of the energy levels of the final Hamiltonian due to the
application of the impurity term.


  Generally, it is common that cited papers are earlier than citing papers. But
we found three different cases, with more undiscovered. In this letter, we
attempted to explain the reasons. However, negative time lag between citing and
cited papers may mislead us when we study the characteristics of science.


  With the advent of high-performance computing techniques, the data for
analysis has grown significantly. Here, graphic processing unit (GPU) based
program kernels are discussed to exploit parallelism in the analysis codes
specific to molecular simulations trajectories and data, hence reducing the
time consumption. Commonly computed properties of systems which utilize static
and dynamic correlations are considered. In static properties, order metrics
based on two-particle correlations are shown to exhibit 10-50x speedups
relative to conventional serial CPU codes. Efficiency in finding three-particle
correlations, which are relatively more time consuming calculations, are also
shown to be 10-45x faster depending on system size. In the case of dynamic
properties, the viscosity is computed using Green-Kubo formalism at a 10-25x
faster rate depending on the correlation time and total trajectory length.
Similarly, for mean square displacement calculations, the speedup of
approximately 40-80x is achieved for all system sizes and simulation times.
Particularly for these embarrassingly parallel computationally intensive
problems, the compute unified device architecture application programming
interface affords maximum scale up with minimum implementation time. It is
shown that all the GPU codes render 1-2 order of magnitude reduction in the
analyses times. Hence these codes, in conjunction with GPU accelerated
molecular simulations, can lead to an overall improved and efficient
performance.


  We study a stochastic epidemic model consisting of elements (organisms in a
community or cells in tissue) with fixed positions, in which damage or disease
is transmitted by diffusing agents ("signals") emitted by infected individuals.
The signals decay as well as diffuse; since they are assumed to be produced in
large numbers, the signal concentration is treated deterministically. The
model, which includes four cellular states (susceptible, transformed, depleted,
and removed), admits various interpretations: spread of an infection or
infectious disease, or of damage in a tissue in which injured cells may
themselves provoke further damage, and as a description of the so-called
radiation-induced bystander effect, in which the signals are molecules capable
of inducing cell damage and/or death in unirradiated cells. The model exhibits
a continuous phase transition between spreading and nonspreading phases. We
formulate two mean-field theory (MFT) descriptions of the model, one of which
ignores correlations between the cellular state and the signal concentration,
and another that treats such correlations in an approximate manner. Monte Carlo
simulations of the spread of infection on the square lattice yield values for
the critical exponents and the fractal dimension consistent with the dynamic
percolation universality class.


  Lizards and insects can strongly attach to walls and then detach applying
negligible additional forces. We propose a simple mechanical model of this
phenomenon which implies active muscle control. We show that the detachment
force may depend not only on the properties of the adhesive units, but also on
the elastic interaction among these units. By regulating the scale of such
cooperative interaction, the organism can actively switch between two modes of
adhesion: delocalized (pull off) and localized (peeling).


  Let G be an infinite discrete group and bG its Cech-Stone compactification.
Using the well known fact that a free ultrafilter on an infinite set is
nonmeasurable, we show that for each element p of the remainder bG G, left
multiplication L_p:bG \to bG is not Borel measurable. Next assume that G is
abelian. Let D \subset \ell^\infty(G)$ denote the subalgebra of distal
functions on G and let G^D denote the corresponding universal distal (right
topological group) compactification of G. Our second result is that the
topological center of G^D (i.e. the set of p in G^D for which L_p:G^D \to G^D
is a continuous map) is the same as the algebraic center and that for G=Z (the
group of integers) this center coincides with the canonical image of G in G^D.


  The partonic structure of hadrons plays an important role in a vast array of
high-energy and nuclear physics experiments. It also underpins the theoretical
understanding of hadron structure. Recent developments in lattice QCD offer new
opportunities for reliably studying partonic structure from first principles.
Here we report on the use of the Feynman-Hellmann theorem to study the forward
Compton amplitude in the unphysical region. We demonstrate how this amplitude
provides direct constraint on hadronic inelastic structure functions. The use
of external momentum transfer allows us to study the $Q^2$ evolution to explore
the onset of asymptotic scaling and reveal higher-twist effects in partonic
structure.


  We prove the existence and uniqueness of weak solutions of the three
dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain
the existence of weak solutions with small $L^2$-norm which may display
codimension-one discontinuities in density, pressure, magnetic field and
velocity gradient. The weak solutions we consider here exhibit just enough
regularity and structure which allow us to develop uniqueness and continuous
dependence theory for the compressible MHD equations. Our results generalise
and extend those for the intermediate weak solutions of compressible
Navier-Stokes equations.


This paper has been withdrawn by the author.


  Chatterjee (2021) introduced a novel independence test that is rank-based,
asymptotically normal and consistent against all alternatives. One limitation
of Chatterjee's test is its low statistical power for detecting monotonic
relationships. To address this limitation, in our previous work (Zhang, 2024,
Commun. Stat. - Theory Methods), we proposed to combine Chatterjee's and
Spearman's correlations into a max-type test and established the asymptotic
joint normality. This work examines three key extensions of the combined test.
First, motivated by its original asymmetric form, we extend the
Chatterjee-Spearman test to a symmetric version, and derive the asymptotic null
distribution of the symmetrized statistic. Second, we investigate the
relationships between Chatterjee's correlation and other popular rank
correlations, including Kendall's tau and quadrant correlation. We demonstrate
that, under independence, Chatterjee's correlation and any of these rank
correlations are asymptotically joint normal and independent. Simulation
studies demonstrate that the Chatterjee-Kendall test has better power than the
Chatterjee-Spearman test. Finally, we explore two possible extensions to the
multivariate case. These extensions expand the applicability of the rank-based
combined tests to a broader range of scenarios.


  I present a selection of results on locally conformally K\"ahler geometry
published after 1997. The proofs are mainly sketched, some of them are even
omitted. Several open problems are indicated in the end.


  We report NICMOS wide-band and polarimetric observations of four
proto-planetary nebulae. Molecular hydrogen emission is detected near the ends
of the bipolar lobes of IRAS 17150-3224, which is evidence for the interaction
of a fast, collimated outflow with the remnant of the asymptotic giant branch
wind.


  Two new optimization techniques based on projections onto convex space (POCS)
framework for solving convex optimization problems are presented. The dimension
of the minimization problem is lifted by one and sets corresponding to the cost
function are defined. If the cost function is a convex function in R^N the
corresponding set is also a convex set in R^{N+1}. The iterative optimization
approach starts with an arbitrary initial estimate in R^{N+1} and an orthogonal
projection is performed onto one of the sets in a sequential manner at each
step of the optimization problem. The method provides globally optimal
solutions in total-variation (TV), filtered variation (FV), L_1, and entropic
cost functions. A new denoising algorithm using the TV framework is developed.
The new algorithm does not require any of the regularization parameter
adjustment. Simulation examples are presented.


  Tunka-Rex is the radio extension of Tunka-133, a 1 km^2 air-Cherenkov
Detector for air showers in Siberia. Tunka-Rex began operation on October 8th
2012 with 20 radio antennas. Its main goals are to explore the possible
precision of the radio detection technique in determination of primary energy
and mass. Each radio antenna station consists of two perpendicular aligned
active SALLA antennas, which receive the radio signal from air showers. The
preamplified radio signal is transmitted to local cluster centers of the
Tunka-133 DAQ, where it is filtered, amplified and digitized. To reconstruct
the radio signal it is crucial to understand how it is affected in each of
these steps. Thus, we have studied the combined response of the antenna, with
its directional pattern and the analog electronics chain, consisting of a
Low-Noise Amplifier and a filter amplifier. We discuss the hardware setup of
Tunka-Rex and how a description of its response is obtained. Furthermore, we
estimate systematic uncertainties on the reconstructed radio signal due to
hardware effects (e.g., slight variations of the electronics properties).
Finally, we present background measurements with the actual Tunka-Rex antennas.


  Computer-aided diagnosis for medical imaging is a well-studied field that
aims to provide real-time decision support systems for physicians. These
systems attempt to detect and diagnose a plethora of medical conditions across
a variety of image diagnostic technologies including ultrasound, x-ray, MRI,
and CT. When designing AI models for these systems, we are often limited by
little training data, and for rare medical conditions, positive examples are
difficult to obtain. These issues often cause models to perform poorly, so we
needed a way to design an AI model in light of these limitations. Thus, our
approach was to incorporate expert domain knowledge into the design of an AI
model. We conducted two qualitative think-aloud studies with doctors trained in
the interpretation of lung ultrasound diagnosis to extract relevant domain
knowledge for the condition Pneumothorax. We extracted knowledge of key
features and procedures used to make a diagnosis. With this knowledge, we
employed knowledge engineering concepts to make recommendations for an AI model
design to automatically diagnose Pneumothorax.


  The transition from Tayor vortex flow to wavy-vortex flow is revisited. The
Self-Sustaining Process (SSP) of Waleffe [Phys. Fluids 9, 883-900 (1997)]
proposes that a key ingredient in transition to turbulence in wall-bounded
shear flows is a three-step process involving rolls advecting streamwise
velocity, leading to streaks which become unstable to a wavy perturbation whose
nonlinear interaction with itself feeds the rolls. We investigate this process
in Taylor-Couette flow. The instability of Taylor-vortex flow to wavy-vortex
flow, a process which is the inspiration for the second phase of the SSP, is
shown to be caused by the streaks, with the rolls playing a negligible role, as
predicted by Jones [J. Fluid Mech. 157, 135-162 (1985)] and demonstrated by
Martinand et al. [Phys. Fluids 26, 094102 (2014)]. In the third phase of the
SSP, the nonlinear interaction of the waves with themselves reinforces the
rolls. We show this both quantitatively and qualitatively, identifying physical
regions in which this reinforcement is strongest, and also demonstrate that
this nonlinear interaction depletes the streaks.


  Change-point analysis is thriving in this big data era to address problems
arising in many fields where massive data sequences are collected to study
complicated phenomena over time. It plays an important role in processing these
data by segmenting a long sequence into homogeneous parts for follow-up
studies. The task requires the method to be able to process large datasets
quickly and deal with various types of changes for high-dimensional data. We
propose a new approach making use of approximate $k$-nearest neighbor
information from the observations, and derive an analytic formula to control
the type I error. The time complexity of our proposed method is $O\left(dn(\log
n+k \log d)+nk^2\right)$ for an $n$-length sequence of $d$-dimensional data.
The test statistic we consider incorporates a useful pattern for moderate- to
high- dimensional data so that the proposed method could detect various types
of changes in the sequence. The new approach is also asymptotic distribution
free, facilitating its usage for a broader community. We apply our method to
fMRI datasets and Neuropixels datasets to illustrate its effectiveness.


  Motivated by the recent evidence for direct CP-violation in D0 -> h+h-
decays, we provide an exhaustive study of both Cabibbo-favored and
Cabibbo-suppressed (singly and doubly) D0 -> h1+h2-l+l- decays. In particular,
we study the Dalitz plot for the long-distance contributions in the
(m_{ll}^2,m_{hh}^2) parameter space. We find that near-resonant effects, i.e.,
D0 -> V(h1+h2-)l+l- with V=\rho,K*,\phi, are sizeable and even dominant (over
Bremsstrahlung) for the \mu+\mu- decay modes, bringing the branching ratios
close to the LHCb reach. We also provide a detailed study of the angular
asymmetries for such decays and identify signatures for new physics detection.
In particular, new physics signals can be neatly isolated in asymmetries
involving the semileptonic operator Q_{10}, where for typical new physics
scenarios the effects can be as sizeable as O(1%) for the doubly
Cabibbo-suppressed modes.


  A formally exact discrete multi-resolution representation of quantum field
theory on a light front is presented. The formulation uses an orthonormal basis
of compactly supported wavelets to expand the fields restricted to a light
front. The representation has a number of useful properties. First, light front
preserving Poincar\'e transformations can be computed by transforming the
arguments of the basis functions. The discrete field operators, which are
defined by integrating the product of the field and the basis functions over
the light front, represent localized degrees of freedom on the light-front
hyperplane. These discrete fields are irreducible and the vacuum is formally
trivial. The light-front Hamiltonian and all of the Poincar\'e generators are
linear combinations of normal ordered products of the discrete field operators
with analytically computable constant coefficients. The representation is
discrete and has natural resolution and volume truncations like lattice
formulations. Because it is formally exact it is possible to systematically
compute corrections for eliminated degrees of freedom.


  This is the Ph.D. dissertation of the author. The project has been motivated
by the conjecture that the Hopkins-Miller tmf spectrum can be described in
terms of `spaces' of conformal field theories. In this dissertation, spaces of
field theories are constructed as classifying spaces of categories whose
objects are certain types of field theories. If such a category has a symmetric
monoidal structure and its components form a group, by work of Segal, its
classifying space is an infinite loop space and defines a cohomology theory.
This has been carried out for two classes of field theories: (i) For each
integer n, there is a category SEFT_n whose objects are the Stolz-Teichner
(1|1)-dimensional super Euclidean field theories of degree n. It is proved that
the classifying space |SEFT_n| represents degree-n K or KO cohomology,
depending on the coefficients of the field theories. (ii) For each integer n,
there is a category AFT_n whose objects are a kind of (2|1)-dimensional field
theories called `annular field theories,' defined using supergeometric versions
of circles and annuli only. It is proved that the classifying space |AFT_n|
represents the degree-n elliptic cohomology associated with the Tate curve. To
the author's knowledge, this is the first time the definitions of
low-dimensional supersymmetric field theories are given in full detail.


  For a reductive group $G$ over a non-archimedean local field, with some
assumptions on (residue) characteristic we give an method to compute certain
orbital integrals using a method close to that of Goresky-Kottiwitz-MacPherson
but in a different language. These orbital integrals allow us to compute the
Shalika germs at some ``very elliptic'' elements in terms of number of rational
points on some quasi-finite covers of the Hessenberg varieties of GKM, which
are subvarieties of (partial) flag varieties. Such values of Shalika germs
determine the Harish-Chandra local character expansions of the so-called very
supercuspidal representations.


  About 3 sigma deviation from the standard model prediction of muon anomalous
magnetic moment (muon g-2) has been reported. We consider new physics beyond
the standard model which has new Yukawa interactions with muon. We compute new
contributions to muon g-2 and corrections to electroweak observables, and show
the consistent region of parameter space. We find that in a simple model where
the chirality flip of muon occurs only in the external muon line in one-loop
muon g-2 diagrams, it is necessary to introduce the relatively large new Yukawa
coupling and the electroweak scale new particles. On the other hand, in a model
where the chirality flip can occur in the internal fermion line of one loop
muon g-2 diagrams, we can obtain favorable g-2 contributions without large
Yukawa coupling, and they are consistent with the precision electroweak
observables. Finally, we discuss effects of new particles for muon g-2 on the
Higgs boson decay h to 2 photons and direct productions of these particles at
the LHC experiment.


  In this study, we propose an over-the-air computation (OAC) scheme to
calculate the majority vote (MV) for federated edge learning (FEEL). With the
proposed approach, edge devices (EDs) transmit the signs of local stochastic
gradients, i.e., votes, by activating one of two orthogonal resources. The MVs
at the edge server (ES) are obtained with non-coherent detectors by exploiting
the accumulations on the resources. Hence, the proposed scheme eliminates the
need for channel state information (CSI) at the EDs and ES. In this study, we
analyze various gradient-encoding strategies through the weight functions and
waveform configurations over orthogonal frequency division multiplexing (OFDM).
We show that specific weight functions that enable absentee EDs (i.e.,
hard-coded participation with absentees (HPA)) or weighted votes (i.e.,
soft-coded participation (SP)) can substantially reduce the probability of
detecting the incorrect MV. By taking path loss, power control, cell size, and
fading channel into account, we prove the convergence of the distributed
learning for a non-convex function for HPA. Through simulations, we show that
the proposed scheme with HPA and SP can provide high test accuracy even when
the time-synchronization and the power control are not ideal under
heterogeneous data distribution scenarios.


  This paper introduces the notion of pseudo-independence on the sublinear
expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical
conditional expectation, and the relations between pseudo-independence and
Peng's independence are detailed discussed. Law of large numbers and central
limit theorem for pseudo-independent random variables are obtained, and a
purely probabilistic proof of Peng's law of large numbers is also given. In the
end, some relevant counterexamples are indicated that Peng's law of large
numbers and central limit theorem are invalid only with the first and second
moment conditions respectively.


  It is pointed out that in the warped string compactification, motion of
anti-D-branes near the bottom of a throat behaves like dark matter. Several
scenarios for production of the dark matter are suggested, including one based
on the D/anti-D interaction at the late stage of D/anti-D inflation.


  When the Moon is at quarter, its terminator generally does not appear to be
orthogonal to a straight line connecting the Moon with the Sun. A purely
geometric, intuitive interpretation of this at first sight puzzling observation
is suggested here.


  The broad-line region (BLR) disappears in many low-luminosity AGNs, the
reason of which is still controversial. The BLRs in AGNs are believed to be
associated with the outflows from the accretion disks. Most of the
low-luminosity AGNs (LLAGNs) contain advection dominated accretion flows
(ADAFs), which are very hot and have a positive Bernoulli parameter. ADAFs are
therefore associated with strong outflows. We estimate the cooling of the
outflows from the ADAFs, and find that the gases in such hot outflows always
cannot be cooled efficiently by bremsstrahlung radiation. The ADAF may co-exist
with the standard disk, i.e., the inner ADAF connects to the outer thin
accretion disk at radius R_tr, in the sources accreting at slightly lower than
the critical rate. For the ADAFs with >0.001 L_edd, a secondary small inner
cold disk is suggested to co-exist with the ADAF due to the condensation
process. We estimate the Compton cooling of the outflow, of which the soft seed
photons either come from the outer cold disk or the secondary inner cold disk.
It is found that the gas in the outflow far from the ADAF may be efficiently
cooled to form BLR clouds due to the soft seed photons emitted from the cold
disks, provided the transition radius of the ADAF to the outer cold disk is
small or/and the secondary small cold disk has a luminosity >0.003L_edd. The
BLR clouds can still be formed in the outflows from the outer cold thin disks,
if the transition radius is not very large. For the sources with <0.001L_edd,
the inner small cold disk is evaporated completely in the ADAF and outer thin
accretion disk may be suppressed by the ADAF, which leads to the disappearance
of the BLR. The physical implications of this scenario on the double-peaked
broad-line emitters are also discussed.


  Orthogonal frequency division multiplexing (OFDM) has been widely applied in
current communication systems. The artificial intelligence (AI)-aided OFDM
receivers are currently brought to the forefront to replace and improve the
traditional OFDM receivers. In this study, we first compare two AI-aided OFDM
receivers, namely, data-driven fully connected deep neural network and
model-driven ComNet, through extensive simulation and real-time video
transmission using a 5G rapid prototyping system for an over-the-air (OTA)
test. We find a performance gap between the simulation and the OTA test caused
by the discrepancy between the channel model for offline training and the real
environment. We develop a novel online training system, which is called
SwitchNet receiver, to address this issue. This receiver has a flexible and
extendable architecture and can adapt to real channels by training only several
parameters online. From the OTA test, the AI-aided OFDM receivers, especially
the SwitchNet receiver, are robust to real environments and promising for
future communication systems. We discuss potential challenges and future
research inspired by our initial study in this paper.


  We calculate the predictions for lepton flavour violating (LFV) tau and muon
decays, $l_j \to l_i \gamma$, $l_j \to 3 l_i$, $\mu-e$ conversion in nuclei and
LFV semileptonic tau decays $\tau \to \mu PP$ with $PP= \pi^+\pi^-, \pi^0\pi^0,
K^+K^-, K^0 {\bar K}^0$ $\tau \to \mu P$ with $P=\pi^0, \eta, \eta'$ and $\tau
\to \mu V$ with $V = \rho^0, \phi$, performing the hadronisation of quark
bilinears within the chiral framework. We work within a SUSY-seesaw context
where the particle content of the Minimal Supersymmetric Standard Model is
extended by three right-handed neutrinos plus their corresponding SUSY
partners, and where a seesaw mechanism for neutrino mass generation is
implemented. Two different scenarios with either universal or non-universal
soft supersymmetry breaking Higgs masses at the gauge coupling unification
scale are considered. After comparing the predictions with present experimental
bounds and future sensitivities, the most promising processes are particularly
emphasised.


  We give the first example of systolic freedom over torsion coefficients. The
phenomenon is a bit unexpected (contrary to a conjecture of Gromov's) and more
delicate than systolic freedom over the integers.


  In topological insulators, massive surface bands resulting from local
symmetry breaking are believed to exhibit a half-quantized Hall conductance.
However, such scenarios are obviously inconsistent with the
Thouless-Kohmoto-Nightingale-Nijs theorem, which states that a single band in a
lattice with a finite Brillouin zone can only have an integer-quantized Hall
conductance. To explore this, we investigate the band structures of a lattice
model describing the magnetic topological insulator film that supports the
axion insulator, Chern insulator, and semi-magnetic topological insulator
phases. We reveal that the gapped and gapless surface bands in the three phases
are characterized by an integer-quantized Hall conductance and a half-quantized
Hall conductance, respectively. This result is distinct from the previous
consensus that the gapped surface band is responsible for the half-quantized
Hall conductance and the gapless band should exhibit zero Hall response. We
propose an effective model to describe the three phases and show that the
low-energy dispersion of the surface bands inherits from the surface Dirac
fermions. The gapped surface band manifests a nearly half-quantized Hall
conductance at low energy near the center of Brillouin zone, but is compensated
by another nearly half-quantized Hall conductance at high energy near the
boundary of Brillouin zone because a single band can only have an
integer-quantized Hall conductance. The gapless state hosts a zero Hall
conductance at low energy but is compensated by another half-quantized Hall
conductance at high energy, and thus the half-quantized Hall conductance can
only originate from the gapless band. Moreover, we calculate the layer-resolved
Hall conductance of the system. The conclusion suggests that the individual
gapped surface band alone does not support the half-quantized surface Hall
effect in a lattice model.


  Recent approaches in causal inference have proposed estimating average causal
effects that are local to some subpopulation, often for reasons of efficiency.
These inferential targets are sometimes data-adaptive, in that they are
dependent on the empirical distribution of the data. In this short note, we
show that if researchers are willing to adapt the inferential target on the
basis of efficiency, then extraordinary gains in precision can be obtained.
Specifically, when causal effects are heterogeneous, any asymptotically normal
and root-$n$ consistent estimator of the population average causal effect is
superefficient for a data-adaptive local average causal effect. Our result
illustrates the fundamental gain in statistical certainty afforded by
indifference about the inferential target.


  This paper describes a solution for the MedAI competition, in which
participants were required to segment both polyps and surgical instruments from
endoscopic images. Our approach relies on a double encoder-decoder neural
network which we have previously applied for polyp segmentation, but with a
series of enhancements: a more powerful encoder architecture, an improved
optimization procedure, and the post-processing of segmentations based on
tempered model ensembling. Experimental results show that our method produces
segmentations that show a good agreement with manual delineations provided by
medical experts.


  In the Heliosphere, power-law particle distributions are observed e.g.
upstream of interplanetary shocks, which can result from superdiffusive
transport. This non-Gaussian transport regime may result from intermittent
magnetic field structures. Recently, we showed that a L\'evy flight model
reproduces the observed features at shocks: power-law distributions upstream
and enhanced intensities at the shock. We extend the L\'evy flight model to
study the impact of superdiffusive transport on particle acceleration at
shocks. The acceleration time scale and spectral slope are compared to Gaussian
diffusion and a L\'evy walk model. The fractional transport equation is solved
by sampling the number density with the corresponding stochastic differential
equation that is driven by an alpha-stable L\'evy distribution. For both
Gaussian and superdiffusive transport we use a modified version of CRPropa 3.2.
We obtain the number density and energy spectra for constant and
energy-dependent anomalous diffusion and find, compared to the case of Gaussian
diffusion, harder energy spectra at the shock as well as faster acceleration.
The spectral slope is even harder than predicted for L\'evy walks. L\'evy
flight models of superdiffusive transport lead to observed features in the
Heliosphere. We further show that superdiffusive transport impacts the
acceleration process by changing the probability to escape the shock. The
flexibility of the L\'evy flight model allows for further studies in the
future, taking the shock geometry and magnetic field structure into account.


  We discuss the calculation of the field theory stress tensor from the dual
geometry for two recent proposals for gravity duals of non-relativistic
conformal field theories. The first of these has a Schrodinger symmetry
including Galilean boosts, while the second has just an anisotropic scale
invariance (the Lifshitz case). For the Lifshitz case, we construct an
appropriate action principle. We propose a definition of the non-relativistic
stress tensor complex for the field theory as an appropriate variation of the
action in both cases. In the Schrodinger case, we show that this gives
physically reasonable results for a simple black hole solution and agrees with
an earlier proposal to determine the stress tensor from the familiar AdS
prescription. In the Lifshitz case, we solve the linearised equations of motion
for a general perturbation around the background, showing that our stress
tensor is finite on-shell.


  We study the deflection of light in the background of a "wiggly" cosmic
string, and investigate whether it is possible to detect cosmic strings by
means of weak gravitational lensing. For straight strings without small-scale
structure there are no signals. In the case of strings with small-scale
structure leading to a local gravitational attractive force towards the string,
there is a small signal, namely a preferential elliptical distortion of the
shape of background galaxies in the direction corresponding to the projection
of the string onto the sky. The signal can be statistically distinguished from
the signal produced by a linear distribution of black holes by employing an
ellipticity axis distribution statistic.


  Temporal context is key to the recognition of expressions of emotion.
Existing methods, that rely on recurrent or self-attention models to enforce
temporal consistency, work on the feature level, ignoring the task-specific
temporal dependencies, and fail to model context uncertainty. To alleviate
these issues, we build upon the framework of Neural Processes to propose a
method for apparent emotion recognition with three key novel components: (a)
probabilistic contextual representation with a global latent variable model;
(b) temporal context modelling using task-specific predictions in addition to
features; and (c) smart temporal context selection. We validate our approach on
four databases, two for Valence and Arousal estimation (SEWA and AffWild2), and
two for Action Unit intensity estimation (DISFA and BP4D). Results show a
consistent improvement over a series of strong baselines as well as over
state-of-the-art methods.


  In recent years, cloud storage technology has been widely used in many fields
such as education, business, medical and more because of its convenience and
low cost. With the widespread applications of cloud storage technology, data
access control methods become more and more important in cloud-based network.
The ciphertext policy attribute-based encryption (CP-ABE) scheme is very
suitable for access control of data in cloud storage. However, in many
practical scenarios, all attributes of a user cannot be managed by one
authority, so many multi-authority CP-ABE schemes have emerged. Moreover, cloud
servers are usually semi-trusted, which may leak user information. Aiming at
the above problems, we propose a fine-grained access control scheme with
versatility for cloud storage based on multi-authority CP-ABE, named vFAC. The
proposed vFAC has the features of large universe, no key escrow problem,
online/offline mechanism, hidden policy, verifiability and user revocation.
Finally, we demonstrate vFAC is static security under the random oracle model.
Through the comparison of several existing schemes in terms of features,
computational overhead and storage cost, we can draw a conclusion that vFAC is
more comprehensive and scalable.


  We analyse the stability and dynamics of an ion chain confined inside a
high-finesse optical resonator. When the dipolar transition of the ions
strongly couples to one cavity mode, the mechanical effects of light modify the
chain properties close to a structural transition. We focus on the linear chain
close to the zigzag instability and show that linear and zigzag arrays are
bistable for certain strengths of the laser pumping the cavity. For these
regimes the chain is cooled into one of the configurations by cavity-enhanced
photon scattering. The excitations of these structures mix photonic and
vibrational fluctuations, which can be entangled at steady state. These
features are signalled by Fano-like resonances in the spectrum of light at the
cavity output.


  Transport through a single molecular conductor is considered, showing
negative differential conductance behavior associated with phonon-mediated
electron tunneling processes. This theoretical work is motivated by a recent
experiment by Leroy et al. using a carbon nanotube contacted by an STM tip
[Nature {\bf 432}, 371 (2004)], where negative differential conductance of the
breathing mode phonon side peaks could be observed. A peculiarity of this
system is that the tunneling couplings which inject electrons and those which
collect them on the substrate are highly asymmetrical. A quantum dot model is
used, coupling a single electronic level to a local phonon, forming polaron
levels. A "half-shuttle" mechanism is also introduced. A quantum kinetic
formulation allows to derive rate equations. Assuming asymmetric tunneling
rates, and in the absence of the half-shuttle coupling, negative differential
conductance is obtained for a wide range of parameters. A detailed explanation
of this phenomenon is provided, showing that NDC is maximal for intermediate
electron-phonon coupling. In addition, in absence of a gate, the "floating"
level results in two distinct lengths for the current plateaus, related to the
capacitive couplings at the two junctions. It is shown that the "half-shuttle"
mechanism tends to reinforce the negative differential regions, but it cannot
trigger this behavior on its own.


  We show that the bound from the electroweak data on the size of extra
dimensions accessible to all the standard model fields is rather loose. These
"universal" extra dimensions could have a compactification scale as low as 300
GeV for one extra dimension. This is because the Kaluza-Klein number is
conserved and thus the contributions to the electroweak observables arise only
from loops. The main constraint comes from weak-isospin violation effects. We
also compute the contributions to the S parameter and the $Zb\bar{b}$ vertex.
The direct bound on the compactification scale is set by CDF and D0 in the few
hundred GeV range, and the Run II of the Tevatron will either discover extra
dimensions or else it could significantly raise the bound on the
compactification scale. In the case of two universal extra dimensions, the
current lower bound on the compactification scale depends logarithmically on
the ultra-violet cutoff of the higher dimensional theory, but can be estimated
to lie between 400 and 800 GeV. With three or more extra dimensions, the cutoff
dependence may be too strong to allow an estimate.


  The basic mechanism how gerbes arise in quantum field theory is explained; in
particular the case of chiral fermions in background fields is treated. The
role of of various gauge group extensions (central extensions of loop groups
and their generalizations) is also explained, in relation to index theory
computation of the Dixmier-Douady class of a gerbe.


This paper has been withdrawn by the author due to the result being known


  Most generative models for clustering implicitly assume that the number of
data points in each cluster grows linearly with the total number of data
points. Finite mixture models, Dirichlet process mixture models, and
Pitman--Yor process mixture models make this assumption, as do all other
infinitely exchangeable clustering models. However, for some tasks, this
assumption is undesirable. For example, when performing entity resolution, the
size of each cluster is often unrelated to the size of the data set.
Consequently, each cluster contains a negligible fraction of the total number
of data points. Such tasks therefore require models that yield clusters whose
sizes grow sublinearly with the size of the data set. We address this
requirement by defining the \emph{microclustering property} and introducing a
new model that exhibits this property. We compare this model to several
commonly used clustering models by checking model fit using real and simulated
data sets.


  In this contribution we review a series of simple one dimensional lattice
models that with an appropriate choice of parameters can account for various
anomalous features of the behaviour of complex systems such as water. In
particular, we will focus on the presence of $p-T$ fluid-solid coexistence
lines with negative slope (i.e. solids that melt upon compression), solid
phases less dense than the liquid phase, and the existence of temperatures of
maximum density. We will see how a simple two-parameter model can reproduce the
phase behaviour of a range of systems well known for their anomalous behaviour
regarding the temperature and pressure dependence of properties such as
density, diffusivity or viscosity.


  Semantic segmentation using convolutional neural networks (CNNs) is the
state-of-the-art for many medical image segmentation tasks including myocardial
segmentation in cardiac MR images. However, the predicted segmentation maps
obtained from such standard CNN do not allow direct quantification of regional
shape properties such as regional wall thickness. Furthermore, the CNNs lack
explicit shape constraints, occasionally resulting in unrealistic
segmentations. In this paper, we use a CNN to predict shape parameters of an
underlying statistical shape model of the myocardium learned from a training
set of images. Additionally, the cardiac pose is predicted, which allows to
reconstruct the myocardial contours. The integrated shape model regularizes the
predicted contours and guarantees realistic shapes. We enforce robustness of
shape and pose prediction by simultaneously performing pixel-wise semantic
segmentation during training and define two loss functions to impose
consistency between the two predicted representations: one distance-based loss
and one overlap-based loss. We evaluated the proposed method in a 5-fold cross
validation on an in-house clinical dataset with 75 subjects and on the ACDC and
LVQuan19 public datasets. We show the benefits of simultaneous semantic
segmentation and the two newly defined loss functions for the prediction of
shape parameters. Our method achieved a correlation of 99% for left ventricular
(LV) area on the three datasets, between 91% and 97% for myocardial area,
98-99% for LV dimensions and between 80% and 92% for regional wall thickness.


  Many water-based optimization metaheuristics have been introduced during the
last decade, both for combinatorial and for continuous optimization. Despite
the strong similarities of these methods in terms of their underlying natural
metaphors (most of them emulate, in some way or another, how drops
collaboratively form paths down to the sea), in general the resulting
algorithms are quite different in terms of their searching approach or their
solution construction approach. For instance, each entity may represent a
solution by itself or, alternatively, entities may construct solutions by
modifying the landscape while moving. A researcher or practitioner could assume
that the degree of similarity between two water-based metaheuristics heavily
depends on the similarity of the natural water mechanics they emulate, but this
is not the case. In order to bring some clarity to this mosaic of apparently
related metaheuristics, in this paper we introduce them, explain their
mechanics, and highlight their differences.


  We prove that all non-degenerate relative equilibria of the planar Newtonian
$n$--body problem can be continued to spaces of constant curvature $\kappa$,
positive or negative, for small enough values of this parameter. We also
compute the extension of some classical relative equilibria to curved spaces
using numerical continuation. In particular, we extend Lagrange's triangle
configuration with different masses to both positive and negative curvature
spaces.


  The ultimate fate of the universe, infinite expansion or a big crunch, can be
determined by measuring the redshifts, apparent brightnesses, and intrinsic
luminosities of very distant supernovae. Recent developments have provided
tools that make such a program practicable: (1) Studies of relatively nearby
Type Ia supernovae (SNe Ia) have shown that their intrinsic luminosities can be
accurately determined; (2) New research techniques have made it possible to
schedule the discovery and follow-up observations of distant supernovae,
producing well over 50 very distant (z = 0.3 -- 0.7) SNe Ia to date. These
distant supernovae provide a record of changes in the expansion rate over the
past several billion years. By making precise measurements of supernovae at
still greater distances, and thus extending this expansion history back far
enough in time, we can distinguish the slowing caused by the gravitational
attraction of the universe's mass density Omega_M from the effect of a possibly
inflationary pressure caused by a cosmological constant Lambda. We report here
the first such measurements, with our discovery of a Type Ia supernova (SN
1997ap) at z = 0.83. Measurements at the Keck II 10-m telescope make this the
most distant spectroscopically confirmed supernova. Over two months of
photometry of SN 1997ap with the Hubble Space Telescope and ground-based
telescopes, when combined with previous measurements of nearer SNe Ia, suggests
that we may live in a low mass-density universe. Further supernovae at
comparable distances are currently scheduled for ground and space-based
observations.


  Chiral symmetry, first entering in nuclear physics in the 1970's for which
Gerry Brown played a seminal role, has led to a stunningly successful framework
for describing strongly-correlated nuclear dynamics both in finite and infinite
systems. We review how the early germinal idea, conceived with the soft-pion
theorems in the pre-QCD era, has evolved into a highly predictive theoretical
framework for nuclear physics, aptly assessed by Steven Weinberg: "it (chiral
effective field theory) allows one to show in a fairly convincing way that what
they (nuclear physicists) have been doing all along... is the correct first
step in a consistent approximation scheme." Our review recounts both how the
theory presently fares in confronting Nature and how one can understand its
extremely intricate workings in terms of the multifaceted aspects of chiral
symmetry, namely, chiral perturbation theory, skyrmions, Landau Fermi-liquid
theory, the Cheshire cat phenomenon, and hidden local and mended symmetries.


  For a description of large-amplitude collective motion associated with
nuclear pairing, requantization of time-dependent mean-field dynamics is
performed using the stationary-phase approximation (SPA) to the path integral.
We overcome the difficulty of the SPA, which is known to be applicable to
integrable systems only, by developing a requantization approach combining the
SPA with the adiabatic self-consistent collective coordinate method (ASCC+SPA).
We apply the ASCC+SPA to multi-level pairing models, which are non-integrable
systems, to study the nuclear pairing dynamics. The ASCC+SPA gives a reasonable
description of low-lying excited $0^+$ states in non-integrable pairing
systems.


  A crucial test any proposed evolutionary scenario must pass is can the birth
rate of the sources we see be sustained by the proposed progenitor population?
In this review, I investigate the methods used to determine the birth rates of
normal and millisecond radio pulsars and summarise recent results for these two
distinct neutron star populations.


  We study neutrino mass matrices with one texture equality and the neutrino
mixing matrix having either its first (TM$_1$) or second (TM$_2$) column
identical to that of the tribimaximal mixing matrix. We found that out of total
fifteen possible neutrino mass matrices with one texture equality, only seven
textures are compatible with $TM_1$ mixing and six textures are compatible with
$TM_2$ mixing in the light of the current neutrino oscillation data. These
textures have interesting implications for the presently unknown parameters
such as the neutrino mass scale, effective Majorana neutrino mass, the
atmospheric mixing and the Dirac- and Majorana-type CP violating phases. We,
also, present the $S_{3}$ group motivation for some of these textures.


  We propose a repeat-until-success protocol to improve the performance of
probabilistic quantum repeaters. Quantum repeaters rely on passive static
linear optics elements and photodetectors to perform Bell-state measurements
(BSMs). Conventionally, the success rate of these BSMs cannot exceed 50%, which
is an impediment for entanglement swapping between distant quantum memories.
Every time that a BSM fails, entanglement needs to be re-distributed between
the corresponding memories in the repeater link. The key ingredient in our
scheme is a repeatable BSM. Although it too relies only on linear optics and
photo-detection, it ideally allows us to repeat every BSM until it succeeds.
This, in principle, can turn a probabilistic quantum repeater into a
deterministic one. Under realistic conditions, where our measurement devices
are lossy, our repeatable BSMs may also fail. However, we show that by using
additional threshold detectors, we can improve the entanglement generation rate
between one and two orders of magnitude as compared to the probabilistic
repeater systems that rely on conventional BSMs. This improvement is sufficient
to make the performance of probabilistic quantum repeaters comparable with some
of existing proposals for deterministic quantum repeaters.


  Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick
model that incorporates the pairing interaction. It is a schematic model that
describes the interplay between particle-hole and pair correlations. It was
proposed in the 1960's by D. Agassi as a model to simulate the properties of
the quadrupole plus pairing model.
  Purpose: The aim of this work is to extend a previous study by Davis and
Heiss generalizing the Agassi model and analyze in detail the phase diagram of
the model as well as the different regions with coexistence of several phases.
  Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov
(HFB) approximation, introducing two variational parameters that play the role
of order parameters. We also compare the HFB calculations with the exact ones.
  Results: We obtain the phase diagram of the model and classify the order of
the different quantum phase transitions appearing in the diagram. The phase
diagram presents broad regions where several phases, up to three, coexist.
Moreover, there is also a line and a point where four and five phases are
degenerated, respectively.
  Conclusions: The phase diagram of the extended Agassi model presents a rich
variety of phases. Phase coexistence is present in extended areas of the
parameter space. The model could be an important tool for benchmarking novel
many-body approximations.


  The pseudoscalar and vector four-quark states $bb\overline{c}\overline{c}$
are studied in the context of the QCD sum rule method. We model $T_{\mathrm{
PS}} $ and $T_{\mathrm{V}}$ as structures built of diquarks $
b^{T}C\gamma_{5}b$, $\overline{c}C\overline{c}^{T}$ and $b^{T}C\gamma _{5}b$ ,
$\overline{c}C\gamma_{\mu}\gamma_{5}\overline{c}^{T}$, respectively, with $ C$
being the charge conjugation matrix. The spectroscopic parameters of the
tetraquarks $T_{\mathrm{PS}}$ and $T_{\mathrm{V}}$, i.e., their masses and
current couplings are calculated using QCD two-point sum rule method. We
evaluate the full widths of $T_{\mathrm{PS}}$ and $T_{\mathrm{V}}$ by taking
into account their kinematically allowed decay channels. In the case of the
pseudoscalar particle they are processes $T_{\mathrm{PS}} \to
B_{c}^{-}B_{c}^{\ast -}$, $B_{c}^{-}B_{c}^{-}(1^{3}P_{0})$ and $B_{c}^{\ast
-}B_{c}^{-}(1^{1}P_{1})$. The vector state $T_{\mathrm{V}}$ can dissociate to
meson pairs $2 B_{c}^{-}$, $2 B_{c}^{\ast -}$ and $
B_{c}^{-}B_{c}^{-}(1^{1}P_{1})$. Partial widths of these decays are determined
by the strong couplings at relevant tetraquark-meson-meson vertices, which
evaluated in the context of the three-point sum rule approach. Predictions
obtained for the mass and full width of the pseudoscalar $m =(13.092\pm
0.095)~\mathrm{GeV}$, $\Gamma _{\mathrm{PS} }=(63.7\pm 9.4)~\mathrm{MeV}$ and
vector $\widetilde{m} =(13.15\pm 0.10)~ \mathrm{GeV}$,
$\Gamma_{\mathrm{V}}=(57.5.3\pm 8.6)~\mathrm{MeV}$ tetraquarks can be useful
for analyses of different four-quark resonances.


  We present a theoretical study on the nonlinear dynamics and stationary
states of an inhomogeneously broadened spin ensemble coupled to a single-mode
cavity driven by an external drive with constant amplitude. Assuming a sizeable
number of constituents within the ensemble allows us to use a semiclassical
approach and to formally reduce the theoretical description to the
Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the
critical slowing-down effect, quench dynamics, and asymptotic behavior of the
system near a steady-state dissipative phase transition accompanied by a
bistability effect. Some of our theoretical findings have recently been
successfully verified in a specific experimental realization based on a spin
ensemble of negatively charged nitrogen-vacancy centers in diamond strongly
coupled to a single-mode microwave cavity (see Science Adv. 3, e1701626
(2017)).


  We discuss various aspects of noncommutative geometry of smooth subalgebras
of Bunce-Deddens-Toeplitz Algebras.


  The AcerMC Monte Carlo generator is dedicated to the generation of Standard
Model background processes which were recognised as critical for the searches
at LHC, and generation of which was either unavailable or not straightforward
so far. The program itself provides a library of the massive matrix elements
(coded by MADGRAPH) and native phase space modules for generation of a set of
selected processes. The hard process event can be completed by the initial and
final state radiation, hadronisation and decays through the existing interface
with either PYTHIA, HERWIG or ARIADNE event generators and (optionally) TAUOLA
and PHOTOS. Interfaces to all these packages are provided in the distribution
version. The matrix element codes have been derived with the help of the
MADGRAPH package. The phase-space generation is based on the multi-channel
self-optimising approach using the modified Kajantie-Byckling formalism for
phase space construction and further smoothing of the phase space was obtained
by using a modified ac-VEGAS algorithm.


  High-dimensional logistic regression is widely used in analyzing data with
binary outcomes. In this paper, global testing and large-scale multiple testing
for the regression coefficients are considered in both single- and
two-regression settings. A test statistic for testing the global null
hypothesis is constructed using a generalized low-dimensional projection for
bias correction and its asymptotic null distribution is derived. A lower bound
for the global testing is established, which shows that the proposed test is
asymptotically minimax optimal over some sparsity range. For testing the
individual coefficients simultaneously, multiple testing procedures are
proposed and shown to control the false discovery rate (FDR) and falsely
discovered variables (FDV) asymptotically. Simulation studies are carried out
to examine the numerical performance of the proposed tests and their
superiority over existing methods. The testing procedures are also illustrated
by analyzing a data set of a metabolomics study that investigates the
association between fecal metabolites and pediatric Crohn's disease and the
effects of treatment on such associations.


  The scattering of massless fermions off magnetically charged dilatonic black
holes is reconsidered and a violation of unitarity is found. Even for a single
species of fermion it is possible for a particle to disappear into the black
hole with its information content.


  We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody
group $G$ (affine or not) over a nonarchimedean local field $K$. It has a
canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a
sub-semigroup $W^+$ of the affine Weyl group $W$. The multiplication is given
by structure constants $a^ {\mathbf u}_{\mathbf w,\mathbf v}\in N=Z_{\geq0}$ :
$T_{\mathbf w}*T_{\mathbf v}=\sum_{\mathbf u\in P_{\mathbf w,\mathbf v}} a^
{\mathbf u}_{\mathbf w,\mathbf v} T_{\mathbf u}$. A conjecture, by Bravermann,
Kazhdan, Patnaik, Gaussent and the authors, tells that $a^ {\mathbf u}_{\mathbf
w,\mathbf v}$ is a polynomial, with coefficients in $N$, in the parameters
$q_{i}-1,q'_{i}-1$ of $G$ over $K$. We prove this conjecture when $\mathbf w$
and $\mathbf v$ are spherical or, more generally, when they are said generic:
this includes all cases of $\mathbf w,\mathbf v\in W^+$ if $G$ is of affine or
strictly hyperbolic type. In the split affine case (where $q_i=q'_i=q$,
$\forall i$) we get a universal Iwahori-Hecke algebra with the same basis
$(T_{\mathbf w})_{\mathbf w\in W^+}$ over a polynomial ring $Z[Q]$; it
specializes to our Iwahori-Hecke algebra when one sets $Q=q$.


  With a parametric form of the equation of state parameter of dark energy, a
quintessence potential has been reconstructed. The potential is found to be a
generalization of a double exponential potential. The constraints on the
parameters are obtained by maximum likelihood analysis using observational
Hubble data, type Ia supernova data, baryon acoustic oscillation data and the
CMB shift parameter data. Th emodel shows preference towards the phantom
behaviour of dark energy.


  We use \Pab\ (1282~nm) observations from the Hubble Space Telescope ($\HST$)
G141 grism to study the star-formation and dust attenuation properties of a
sample of 29 low-redshift ($z < 0.287$) galaxies in the CANDELS Ly$\alpha$
Emission at Reionization (CLEAR) survey. We first compare the nebular
attenuation from $\Pab/\Ha$ with the stellar attenuation inferred from the
spectral energy distribution, finding that the galaxies in our sample are
consistent with an average ratio of the continuum attenuation to the nebular
gas of 0.44, but with a large amount of excess scatter beyond the observational
uncertainties. Much of this scatter is linked to a large variation between the
nebular dust attenuation as measured by (space-based) $\Pab$ to (ground-based)
$\Ha$ to that from (ground-based) $\Ha/\Hb$. This implies there are important
differences between attenuation measured from grism-based / wide-aperture
$\Pab$ fluxes and the ground-based / slit-measured Balmer decrement. We next
compare star-formation rates (SFRs) from $\Pab$ to those from dust-corrected
UV. We perform a survival analysis to infer a census of \Pab\ emission implied
by both detections and non-detections. We find evidence that galaxies with
lower stellar mass have more scatter in their ratio of \Pab\ to
attenuation-corrected UV SFRs. When considering our \Pab\ detection limits,
this observation supports the idea that lower mass galaxies experience
"burstier" star-formation histories. Together, these results show that \Pab\ is
a valuable tracer of a galaxy's SFR, probing different timescales of
star-formation and potentially revealing star-formation that is otherwise
missed by UV and optical tracers.