  3D CNN shows its strong ability in learning spatiotemporal representation in
recent video recognition tasks. However, inflating 2D convolution to 3D
inevitably introduces additional computational costs, making it cumbersome in
practical deployment. We consider whether there is a way to equip the
conventional 2D convolution with temporal vision no requiring expanding its
kernel. To this end, we propose the video shuffle, a parameter-free plug-in
component that efficiently reallocates the inputs of 2D convolution so that its
receptive field can be extended to the temporal dimension. In practical, video
shuffle firstly divides each frame feature into multiple groups and then
aggregate the grouped features via temporal shuffle operation. This allows the
following 2D convolution aggregate the global spatiotemporal features. The
proposed video shuffle can be flexibly inserted into popular 2D CNNs, forming
the Video Shuffle Networks (VSN). With a simple yet efficient implementation,
VSN performs surprisingly well on temporal modeling benchmarks. In experiments,
VSN not only gains non-trivial improvements on Kinetics and Moments in Time,
but also achieves state-of-the-art performance on Something-Something-V1,
Something-Something-V2 datasets.


  Recurrent or sustained awkward body postures are among the most frequently
cited risk factors to the development of work-related musculoskeletal disorders
(MSDs). To prevent workers from adopting harmful configurations but also to
guide them toward more ergonomic ones, wearable haptic devices may be the ideal
solution. In this paper, a vibrotactile unit, called ErgoTac, and a
slide-and-squeeze unit, called CUFF, were evaluated in a limbs postural
correction setting. Their capability of providing single-joint (shoulder or
knee) and multi-joint (shoulder and knee at once) guidance was compared in
twelve healthy subjects, using quantitative task-related metrics and subjective
quantitative evaluation. An integrated environment was also built to ease
communication and data sharing between the involved sensor and feedback
systems. Results show good acceptability and intuitiveness for both devices.
ErgoTac appeared as the suitable feedback device for the shoulder, while the
CUFF may be the effective solution for the knee. This comparative study,
although preliminary, was propaedeutic to the potential integration of the two
devices for effective whole-body postural corrections, with the aim to develop
a feedback and assistive apparatus to increase workers' awareness about risky
working conditions and therefore to prevent MSDs.


  In this paper, an expression for the asymptotic growth rate of the number of
small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC)
codes is derived. The expression is compact and generalizes existing results
for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check
and variable nodes with minimum distance 2, it is shown that the growth rate
depends only on these nodes. An important connection between this new result
and the stability condition of D-GLDPC codes over the BEC is highlighted. Such
a connection, previously observed for LDPC and GLDPC codes, is now extended to
the case of D-GLDPC codes.


  Previous X-ray observations toward the Nuclear Star Cluster (NSC) at the
Galactic center have discovered thousands of point sources, most of which were
believed to be cataclysmic variables (CVs), i.e., a white dwarf (WD) accreting
from a low-mass companion. However, the population properties of these CVs
remain unclear, which otherwise contain important information about the
evolutionary history of the NSC. In this work we utilize ultradeep archival
\textit{Chandra} observations to study the spectral properties of the NSC CVs,
in close comparison with those in the Solar vicinity. We find that the NSC CVs
have strong Fe XXV and Fe XXVI lines (both of which show equivalent widths
$\sim200-300$ eV), indicating metal-rich companions. Moreover, their Fe XXVI to
Fe XXV line flux ratio is used to diagnose the characteristic white dwarf mass
($M_{\rm WD}$) of NSC CVs. The results show that the CVs with $L_{\rm 2-10
keV}>6\times10^{31}$ erg s$^{-1}$ have a mean $M_{\rm WD}$ of
$\sim0.6/1.0\,M_{\odot}$ if they are magnetic/non-magnetic CVs; while those
with $L_{\rm 2-10 keV}$ between $1-6\times10^{31}$ erg s$^{-1}$ have a mean
$M_{\rm WD}$ of $\sim0.8/1.2\,M_{\odot}$ if they are magnetic/non-magnetic CVs.
All these \textit{Chandra}-detected CVs collectively contribute $\sim$30-50\%
of the unresolved 20-40 keV X-ray emission from the NSC. The CV population with
massive (i.e., $M_{\rm WD}\sim1.2M_{\odot}$) WDs have not been observed in the
Solar vicinity or the Galactic bulge, and they might have been formed via
dynamical encounters in the NSC.


  We study the ground state and the thermal phase diagram of a two-species
Bose-Hubbard model, with $U(1)\times \mathbb{Z}_2$ symmetry, describing atoms
and molecules on a 2D optical lattice interacting via a Feshbach resonance.
Using quantum Monte Carlo simulations and mean field theory, we show that the
conversion between the two-species, coherently coupling the atomic and
molecular states, has a crucial impact on the Mott-Superfluid transition and
stabilizes an insulating phase with a gap controlled by the conversion term --
\textit{the Feshbach insulator} -- instead of a standard Mott insulating phase.
Depending on the detuning between atoms and molecules, this model exhibits
three phases: the Feshbach insulator, a molecular condensate coexisting with
non condensed atoms and a mixed atomic-molecular condensate. Employing a
finite-size scaling method, we observe 3D XY (3D Ising) transition when $U(1)$
($ \mathbb{Z}_2$) is broken whereas the transition is first-order when both
$U(1)$ and $ \mathbb{Z}_2$ symmetries are spontaneously broken. The finite
temperature phase diagram is also discussed. The thermal disappearance of the
molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with
unusual universal jump in the superfluid density. The loss of the
quasi-long-range coherence of the mixed atomic and molecular superfluid is more
subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless
criticality. We also observe a classical first-order transition between the
mixed superfluid and the normal Bose liquid at low temperature.


  We describe the relation between supersymmetric sigma-models on hyperkahler
manifolds, projective superspace, and twistor space. We review the essential
aspects and present a coherent picture with a number of new results.


  This paper continues the study of cluster algebras initiated in
math.RT/0104151. Its main result is the complete classification of the cluster
algebras of finite type, i.e., those with finitely many clusters. This
classification turns out to be identical to the Cartan-Killing classification
of semisimple Lie algebras and finite root systems, which is intriguing since
in most cases, the symmetry exhibited by the Cartan-Killing type of a cluster
algebra is not at all apparent from its geometric origin.
  The combinatorial structure behind a cluster algebra of finite type is
captured by its cluster complex. We identify this complex as the normal fan of
a generalized associahedron introduced and studied in hep-th/0111053 and
math.CO/0202004. Another essential combinatorial ingredient of our arguments is
a new characterization of the Dynkin diagrams.


  Latent variables often mask cause-effect relationships in observational data
which provokes spurious links that may be misinterpreted as causal. This
problem sparks great interest in the fields such as climate science and
economics. We propose to estimate confounded causal links of time series using
Sequential Causal Effect Variational Autoencoder (SCEVAE) while applying
Knockoff interventions. Knockoff variables have the same distribution as the
originals and preserve the correlation to other variables. This allows for
counterfactuals that are more faithful to the observational distribution. We
show the advantage of Knockoff interventions by applying SCEVAE to synthetic
datasets with both linear and nonlinear causal links. Moreover, we apply SCEVAE
with Knockoffs to real aerosol-cloud-climate observational time series data. We
compare our results on synthetic data to those of a time series deconfounding
method both with and without estimated confounders. We show that our method
outperforms this benchmark by comparing both methods to the ground truth. For
the real data analysis, we rely on expert knowledge of causal links and
demonstrate how using suitable proxy variables improves the causal link
estimation in the presence of hidden confounders.


  Combining ferroelectricity with other properties such as visible light
absorption or long-range magnetic order requires the discovery of new families
of ferroelectric materials. Here, through the analysis of a high-throughput
database of phonon band structures, we identify a new structural family of
anti-Ruddlesden-Popper phases A$_4$X$_2$O (A=Ca, Sr, Ba, Eu, X=Sb, P, As, Bi)
showing ferroelectric and anti-ferroelectric behaviors. The discovered
ferroelectrics belong to the new class of hyperferroelectrics which polarize
even under open-circuit boundary conditions. The polar distortion involves the
movement of O anions against apical A cations and is driven by geometric
effects resulting from internal chemical strains. Within this new structural
family, we show that Eu$_4$Sb$_2$O combines coupled ferromagnetic and
ferroelectric order at the same atomic site, a very rare occurrence in
materials physics.


  Inspired by Katok's examples of Finsler metrics with a small number of closed
geodesics, we present two results on Reeb flows with finitely many periodic
orbits. The first result is concerned with a contact-geometric description of
magnetic flows on the 2-sphere found recently by Benedetti. We give a simple
interpretation of that work in terms of a quaternionic symmetry. In the second
part, we use Hamiltonian circle actions on symplectic manifolds to produce
compact, connected contact manifolds in dimension at least five with
arbitrarily large numbers of periodic Reeb orbits. This contrasts sharply with
recent work by Cristofaro-Gardiner, Hutchings and Pomerleano on Reeb flows in
dimension three. With the help of Hamiltonian plugs and a surgery construction
due to Laudenbach we reprove a result of Cieliebak: one can produce Hamiltonian
flows in dimension at least five with any number of periodic orbits; in
dimension three, with any number greater than one.


  We have simulated the Expanded Owens Valley Solar Array (EOVSA) radio images
generated at multiple frequencies from a model solar active region, embedded in
a realistic solar disk model, and explored the resulting datacube for different
spectral analysis schemes to evaluate the potential for realizing one of
EOVSA's most important scientific goals--coronal magnetography. In this paper,
we focus on modeling the gyroresonance and free-free emission from an on-disk
solar active region model with realistic complexities in electron density,
temperature and magnetic field distribution. We compare the magnetic field
parameters extrapolated from the image datacube along each line of sight after
folding through the EOVSA instrumental profile with the original (unfolded)
parameters used in the model. We find that even the most easily automated,
image-based analysis approach (Level 0) provides reasonable quantitative
results, although they are affected by systematic effects due to finite
sampling in the Fourier (uv) plane. Finally, we note the potential for errors
due to misidentified harmonics of the gyrofrequency, and discuss the prospects
for applying a more sophisticated spectrally-based analysis scheme (Level 1) to
resolve the issue in cases where improved uv coverage and spatial resolution
are available.


  We study the unitary Cayley graph of a matrix semiring. We find bounds for
its diameter, clique number and independence number, and determine its girth.
We also find the relationship between the diameter and the clique number of a
unitary Cayley graph of a semiring $S$ and a matrix semiring over $S$.


  Helical edge states are the hallmark of the quantum spin Hall insulator.
Recently, several experiments have observed transport signatures contributed by
trivial edge states, making it difficult to distinguish between the
topologically trivial and nontrivial phases. Here, we show that helical edge
states can be identified by the random-gate-voltage induced $\Phi_0/2$-period
oscillation of the averaged electron return probability in the interferometer
constructed by the edge states. The random gate voltage can highlight the
$\Phi_0/2$-period Al'tshuler-Aronov-Spivak oscillation proportional to
$\sin^2(2\pi\Phi/\Phi_0)$ by quenching the $\Phi_0$-period Aharonov-Bohm
oscillation. It is found that the helical spin texture induced $\pi$ Berry
phase is key to such weak antilocalization behavior with zero return
probability at $\Phi=0$. In contrast, the oscillation for the trivial edge
states may exhibit either weak localization or antilocalization depending on
the strength of the spin-orbit coupling, which have finite return probability
at $\Phi=0$. Our results provide an effective way for the identification of the
helical edge states. The predicted signature is stabilized by the time-reversal
symmetry so that it is robust against disorder and does not require any fine
adjustment of system.


  Deep neural networks often suffer from overconfidence which can be partly
remedied by improved out-of-distribution detection. For this purpose, we
propose a novel approach that allows for the generation of out-of-distribution
datasets based on a given in-distribution dataset. This new dataset can then be
used to improve out-of-distribution detection for the given dataset and machine
learning task at hand. The samples in this dataset are with respect to the
feature space close to the in-distribution dataset and therefore realistic and
plausible. Hence, this dataset can also be used to safeguard neural networks,
i.e., to validate the generalization performance. Our approach first generates
suitable representations of an in-distribution dataset using an autoencoder and
then transforms them using our novel proposed Soft Brownian Offset method.
After transformation, the decoder part of the autoencoder allows for the
generation of these implicit out-of-distribution samples. This newly generated
dataset then allows for mixing with other datasets and thus improved training
of an out-of-distribution classifier, increasing its performance.
Experimentally, we show that our approach is promising for time series using
synthetic data. Using our new method, we also show in a quantitative case study
that we can improve the out-of-distribution detection for the MNIST dataset.
Finally, we provide another case study on the synthetic generation of
out-of-distribution trajectories, which can be used to validate trajectory
prediction algorithms for automated driving.


  In this paper we review the properties of the black hole entropy in the light
of a general conformal field theory treatment. We find that the properties of
horizons of the BTZ black holes in ADS_{3}, can be described in terms of an
effective unitary CFT_{2} with central charge c=1 realized in terms of the
Fubini-Veneziano vertex operators.
  It is found a relationship between the topological properties of the black
hole solution and the infinite algebra extension of the conformal group in 2D,
SU(2,2), i.e. the Virasoro Algebra, and its subgroup SL(2,Z) which generates
the modular symmetry. Such a symmetry induces a duality for the black hole
solution with angular momentum J\neq 0. On the light of such a global symmetry
we reanalyze the Cardy formula for CFT_{2} and its possible generalization to
D>2 proposed by E. Verlinde.


  A three-dimensional continuum dislocation theory for single crystals
containing curved dislocations is proposed. A set of governing equations and
boundary conditions is derived for the true placement, plastic slips, and loop
functions in equilibrium that minimize the free energy of crystal among all
admissible functions, provided the resistance to the dislocation motion is
negligible. For the non-vanishing resistance to dislocation motion the
governing equations are derived from the variational equation that includes the
dissipation function. A simplified theory for small strains is also provided.
An asymptotic solution is found for the two-dimensional problem of a single
crystal beam deforming in single slip and simple shear.


  We show that a recent assertion [arXiv:1608.01541] that gravitational wave
emission can lead to a repulsive force explaining the accelerated expansion of
the Universe is totally unfounded.


  We show using numerical simulations that vortices in honeycomb pinning arrays
can exhibit a remarkable variety of dynamical phases that are distinct from
those found for triangular and square pinning arrays. In the honeycomb arrays,
it is possible for the interstitial vortices to form dimer or higher n-mer
states which have an additional orientational degree of freedom that can lead
to the formation of vortex molecular crystals. For filling fractions where
dimer states appear, a novel dynamical symmetry breaking can occur when the
dimers flow in one of two possible alignment directions. This leads to
transport in the direction transverse to the applied drive. We show that
dimerization produces distinct types of moving phases which depend on the
direction of the driving force with respect to the pinning lattice symmetry.
When the dimers are driven along certain directions, a reorientation of the
dimers can produce a jamming phenomenon which results in a strong enhancement
in the critical depinning force. The jamming can also cause unusual effects
such as an increase in the critical depinning force when the size of the
pinning sites is reduced.


  We present follow-up spectroscopy to the Calar Alto Deep Imaging Survey
(CADIS), reporting on the quasars in the CADIS 16h-field, and including
preliminary data from two other fields. In this 10' x 10' field we found six
quasars at redshift z>2.2 which are brighter than R=22 mag, while surface
densities determined in previous surveys are reported to be below one on
average. This is the highest reported surface density of high-redshift quasars
within the given limits. We believe this result to be a consequence of the
multicolor database and the search technique used in CADIS.
  Our observations further seem to indicate that the density of high-redshift
quasars is also higher than predicted by the luminosity function of Warren
(1994) by a factor of three, implying that common search methods have
overlooked the majority of high-redshift quasars at this magnitude level. In
particular, an application of the V/V max test to our preliminary list of AGNs
with R<22 mag and z<4 yields <V/V max> = 0.51 +-0.06, characterizing our
preliminary redshift distribution as flat.


  The local dimension spectrum gives a way to quantify fractal properties of a
given measure. It is well understood for self-similar measures without
overlaps. In this article we study the local dimension spectrum for dominated
self-affine measures. Our main results completely characterize the behavior of
the symbolic spectrum, and after detailed analysis on the exact dimensionality
of self-affine measures we exhibit new deterministic results for the local
dimension spectrum on a much wider range than was previously understood.


  We present the first application of the Basis Light-Front Quantization method
to study a simple chiral model of the nucleon-pion system via an ab initio,
non-perturbative, Hamiltonian approach. As a test problem, we consider the
physical proton as the relativistic bound state of the nucleon-pion system.
Based on the chiral model of the nucleon-pion system, we construct the
mass-squared matrix of the system within our light-front basis representation.
We obtain the proton's mass and the corresponding light-front wave function by
solving the eigenvalue problem of the mass-squared matrix. With the resulting
boost-invariant light-front wave function, we also compute the proton's parton
distribution function.


  Fourth order curvature driven interface evolution equations frequently appear
in the natural sciences. Often axisymmetric geometries are of interest, and in
this situation numerical computations are much more efficient. We will
introduce and analyze several new finite element schemes for fourth order
geometric evolution equations in an axisymmetric setting, and for selected
schemes we will show existence, uniqueness and stability results. The presented
schemes have very good mesh and stability properties, as will be demonstrated
by several numerical examples.


  Low-energy cosmic rays (CRs) are confined by self-generated MHD waves in the
mostly neutral ISM. We show that the CR transport equation can be expressed as
a continuity equation for the CR number density involving an effective
convection velocity. Assuming balance between wave growth and ion-neutral
damping, this equation gives a steady-state condition n_cr ~ n_i^1/2 up to a
critical density for free streaming. This relation naturally accounts for the
heretofore unexplained difference in CR ionization rates derived for dense
diffuse clouds (McCall et al. 2003) and dark clouds, and predicts large spatial
variations in the CR heating rate and pressure.


  Measurements and analysis of orbit response matrix have been providing for
decades a formidable tool in the detection of linear lattice imperfections and
their correction. Basically all storage-ring-based synchrotron light sources
across the world make routinely use of this technique in their daily operation,
reaching in some cases a correction of linear optics down to 1% beta beating
and 0.1% coupling. During the design phase of a new storage ring it is also
applied in simulations for the evaluation of magnetic and mechanical
tolerances. However, this technique is known for its intrinsic slowness
compared to other methods based on turn-by-turn beam position data, both in the
measurement and in the data analysis. In this paper analytic formulas are
derived and discussed that shall greatly speed up this second part. The
mathematical formalism based on the Lie algebra and the resonance driving terms
is extended to the off-momentum regime and explicit analytic formulas for the
evaluation of chromatic functions from lattice parameters are also derived. The
robustness of these formulas, which are linear in the magnet strengths, is
tested with different lattice configurations.


  Generally, the performance of a generic detector decreases significantly when
it is tested on a specific scene due to the large variation between the source
training dataset and the samples from the target scene. To solve this problem,
we propose a new formalism of transfer learning based on the theory of a
Sequential Monte Carlo (SMC) filter to automatically specialize a
scene-specific Faster R-CNN detector. The suggested framework uses different
strategies based on the SMC filter steps to approximate iteratively the target
distribution as a set of samples in order to specialize the Faster R-CNN
detector towards a target scene. Moreover, we put forward a likelihood function
that combines spatio-temporal information extracted from the target video
sequence and the confidence-score given by the output layer of the Faster
R-CNN, to favor the selection of target samples associated with the right
label. The effectiveness of the suggested framework is demonstrated through
experiments on several public traffic datasets. Compared with the
state-of-the-art specialization frameworks, the proposed framework presents
encouraging results for both single and multi-traffic object detections.


  Data is expanding at an unimaginable rate, and with this development comes
the responsibility of the quality of data. Data Quality refers to the relevance
of the information present and helps in various operations like decision making
and planning in a particular organization. Mostly data quality is measured on
an ad-hoc basis, and hence none of the developed concepts provide any practical
application. The current empirical study was undertaken to formulate a concrete
automated data quality platform to assess the quality of incoming dataset and
generate a quality label, score and comprehensive report. We utilize various
datasets from healthdata.gov, opendata.nhs and Demographics and Health Surveys
(DHS) Program to observe the variations in the quality score and formulate a
label using Principal Component Analysis(PCA). The results of the current
empirical study revealed a metric that encompasses nine quality ingredients,
namely provenance, dataset characteristics, uniformity, metadata coupling,
percentage of missing cells and duplicate rows, skewness of data, the ratio of
inconsistencies of categorical columns, and correlation between these
attributes. The study also provides an illustrative case study and validation
of the metric following Mutation Testing approaches. This research study
provides an automated platform which takes an incoming dataset and metadata to
provide the DQ score, report and label. The results of this study would be
useful to data scientists as the value of this quality label would instill
confidence before deploying the data for his/her respective practical
application.


  In an earlier paper, we introduced ``bordered knot algebras'', which
  are graded algebras indexed by a pair of integers (m,k). In a
  subsequent paper, we introduced a two-parameter family of
  differential graded algebra, the ``pong algebras'', and identified
  their homology with the bordered knot algebras, and characterized
  the induced A-infinity structure on the homology. The aim of the
  present paper is to give an explicit, combinatorial model for this
  A-infinity structure on the bordered knot algebras, and a further
  weighted deformation of this structure, in the case where k=1.


  We state two structure theorems. First a general structure theorem for the de
Rham-Witt complex, and then the structure of the overconvergent de Rham-Witt
complex, locally on a smooth algebraic variety over a perfect field of positive
characteristic.


  The asymptotic behaviour of two classes of scalar field cosmological models
are studied using the theory of dynamical systems: general relativistic Bianchi
models containing matter and a scalar field with an exponential potential and a
class of spatially homogeneous string cosmological models. The purpose of this
thesis is to examine some of the outstanding problems which currently exist in
cosmology, particularly regarding isotropization and inflation. It is shown
that the matter scaling solutions are unstable to curvature perturbations. It
is then shown that the Bianchi class B exponential potential models can
alleviate the isotropy problem; an open set of models within this class do
isotropize to the future. It is also shown that the presence of an interaction
term in the subclass of isotropic models can lead to inflationary models with
late-time oscillatory behaviour in which the matter is not driven to zero.
Next, within the class of the string cosmologies studied, it is shown that
there is a subclass which do not inflate at late times in the post-big bang
regime. Furthermore, all string models studied typically do not have a
late--time flatness problem. Indeed, it is shown that curvature typically plays
an important r\^{o}le only at intermediate times in most models. It is also
shown that the presence of a positive cosmological constant in the models
studied can lead to interesting physical behaviour, such as multi-bouncing
universes. A mathematical equivalence between general relativistic scalar field
theories and scalar-tensor theories and string theories has been extensively
exploited and thus the results obtained from the string analysis compliment the
results obtained from the Bianchi class B exponential potential analysis.


  Multi-antenna (MIMO) processing is a promising solution to the problem of
jammer mitigation. Existing methods mitigate the jammer based on an estimate of
its subspace (or receive statistics) acquired through a dedicated training
phase. This strategy has two main drawbacks: (i) it reduces the communication
rate since no data can be transmitted during the training phase and (ii) it can
be evaded by smart or multi-antenna jammers that are quiet during the training
phase or that dynamically change their subspace through time-varying
beamforming. To address these drawbacks, we propose joint jammer mitigation and
data detection (JMD), a novel paradigm for MIMO jammer mitigation. The core
idea is to estimate and remove the jammer interference subspace jointly with
detecting the transmit data over multiple time slots. Doing so removes the need
for a dedicated rate-reducing training period while enabling the mitigation of
smart and dynamic multi-antenna jammers. We instantiate our paradigm with
SANDMAN, a simple and practical algorithm for multi-user MIMO uplink JMD.
Extensive simulations demonstrate the efficacy of JMD, and of SANDMAN in
particular, for jammer mitigation.


  We report the detection of WC stars in 5 Wolf-Rayet (WR) galaxies: He 2-10,
NGC 3049, NGC 3125, NGC 5253 and Tol 89. The faint broad CIV5808 line requires
sufficiently high S/N to be detected explaining the non-detection of this WC
feature in previous observations. From the WR emission lines we conclude that
all regions (except NGC 3049) contain a mixed population of WNL, and early WC
stars. A spatial offset between the nebular emission and stellar light is
observed in 2 objects. Due to age differences the nebular structures around the
WR regions are possibly smaller than those mainly energized by SNe. The spatial
distribution of WR stars follows the stellar continuum. We derive the absolute
number of WR stars of different subtypes. The WC/WN ratios have typical values
between 0.2-0.4, and show no clear trend with metallicity (Z). For low-Z
objects, these values are larger than the observed WC/WN ratios in Local Group
objects, but compatible with expectations for short bursts of if stellar
evolution models with high mass loss are used. The ages of the starburst
regions are 3-6 Myr; the burst duration must not exceed 2-4 Myr to account for
the high population of WR stars, even if emission line stars similar to those
in R136 and NGC 3603 are common in starbursts. Within the uncertainties most of
the observed quantities are reproduced by models with a Salpeter IMF. Although
some WR lines are stronger than predicted, no clear case requiring a
significantly flatter IMF is found. IMF slopes much steeper than Salpeter may,
however, not be compatible with our data. (Abridged abstract)


  Human vision is able to capture the part-whole hierarchical information from
the entire scene. This paper presents the Visual Parser (ViP) that explicitly
constructs such a hierarchy with transformers. ViP divides visual
representations into two levels, the part level and the whole level.
Information of each part represents a combination of several independent
vectors within the whole. To model the representations of the two levels, we
first encode the information from the whole into part vectors through an
attention mechanism, then decode the global information within the part vectors
back into the whole representation. By iteratively parsing the two levels with
the proposed encoder-decoder interaction, the model can gradually refine the
features on both levels. Experimental results demonstrate that ViP can achieve
very competitive performance on three major tasks e.g. classification,
detection and instance segmentation. In particular, it can surpass the previous
state-of-the-art CNN backbones by a large margin on object detection. The tiny
model of the ViP family with $7.2\times$ fewer parameters and $10.9\times$
fewer FLOPS can perform comparably with the largest model
ResNeXt-101-64$\times$4d of ResNe(X)t family. Visualization results also
demonstrate that the learnt parts are highly informative of the predicting
class, making ViP more explainable than previous fundamental architectures.
Code is available at https://github.com/kevin-ssy/ViP.


  We propose a novel approach for hyperspectral super-resolution, that is based
on low-rank tensor approximation for a coupled low-rank multilinear (Tucker)
model. We show that the correct recovery holds for a wide range of multilinear
ranks. For coupled tensor approximation, we propose two SVD-based algorithms
that are simple and fast, but with a performance comparable to the
state-of-the-art methods. The approach is applicable to the case of unknown
spatial degradation and to the pansharpening problem.


  We study a discrete nonlinear Schr\"odinger lattice with a parabolic trapping
potential. The model, describing, e.g., an array of repulsive Bose-Einstein
condensate droplets confined in the wells of an optical lattice, is
analytically and numerically investigated. Starting from the linear limit of
the problem, we use global bifurcation theory to rigorously prove that - in the
discrete regime - all linear states lead to nonlinear generalizations thereof,
which assume the form of a chain of discrete dark solitons (as the density
increases). The stability of the ensuing nonlinear states is studied and it is
found that the ground state is stable, while the excited states feature a chain
of stability/instability bands. We illustrate the mechanisms under which
discreteness destabilizes the dark-soliton configurations, which become stable
only inside the continuum regime. Continuation from the anti-continuum limit is
also considered, and a rich bifurcation structure is revealed.


  Given a prime $p$ and a positive integer $k$, let
$\mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$ be the ring of $n \times n$
matrices over $\mathbb{Z}/p^{k}\mathbb{Z}$. We consider the number of solutions
$X \in \mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$ to the polynomial equation
$P(X) = 0$, where $P(t)$ is a monic polynomial in
$(\mathbb{Z}/p^{k}\mathbb{Z})[t]$ whose reduction modulo $p$ is square-free
over the finite field $\mathbb{F}_{p}$ of $p$ elements. Noting that $P(X) = 0$
if and only if $\mathrm{cok}(P(X)) \simeq (\mathbb{Z}/p^{k}\mathbb{Z})^{n}$, we
give a conjectural generalization of counting solutions to $P(X) = 0$ as the
distribution of the cokernel $\mathrm{cok}(P(X))$ of $P(X)$ up to isomorphisms,
where $X$ is a uniform random matrix in
$\mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$. This distribution involves an
explicit formula when we fix the residue class of $X$ modulo $p$. We prove this
conjecture for the special case when the image of $P(t)$ in $\mathbb{F}_{p}[t]$
modulo $p$ is irreducible. We explain how the distribution we obtain is closely
related to the Cohen-Lenstra distribution. Our proof involves algebraic and
combinatorial arguments in linear algebra over $\mathbb{Z}/p^{k}\mathbb{Z}$ and
builds upon a previous work of Cheong and Kaplan.


  In order to solve the minimization of a nonsmooth convex function, we design
an inertial second-order dynamic algorithm, which is obtained by approximating
the nonsmooth function by a class of smooth functions. By studying the
asymptotic behavior of the dynamic algorithm, we prove that each trajectory of
it weakly converges to an optimal solution under some appropriate conditions on
the smoothing parameters, and the convergence rate of the objective function
values is o(t^-2). We also show that the algorithm is stable, that is, this
dynamic algorithm with a perturbation term owns the same convergence properties
when the perturbation term satisfies certain conditions. Finally, we verify the
theoretical results by some numerical experiments.


  In math.CA/0211148 we observed that $\ln(4/ \pi)$ is an "alternating" analog
of Euler's constant $\gamma$. Here we use the binary expansion of an integer to
give a rational series for $\ln(4/ \pi)$ analogous to Vacca's series for
$\gamma$. Also, using a known generalization of Vacca's series to other bases,
we accelerate Addison's series for $\gamma$. Along the way, we give new proofs
of Vacca's and Addison's formulas.


  The absorption spectroscopy of calcium-doped argon clusters is described in
terms of an effective diatomics molecule Ca-(Ar_n), in the framework of
semiclassical vertical transitions. We show how, upon choosing a suitable
reaction coordinate, the effective finite-temperature equilibrium properties
can be obtained for the ground- and excited-surfaces from the potential of mean
force (PMF). An extension of the recent multiple range random-walk method is
used to calculate the PMF over continuous intervals of distances. The
absorption spectra calculated using this single-coordinate description are
found to be in good agreement with the spectra obtained from high-statistics
Monte Carlo data, in various situations. For CaAr$_{13}$, we compare the
performances of two different choices of the reaction coordinate. For CaAr_37,
the method is seen to be accurate enough to distinguish between different
low-energy structures. Finally, the idea of casting the initial many-body
problem into a single degree of freedom problem is tested on the spectroscopy
of calcium in bulk solid argon.


  With their rapid, violent variability and broad featureless continuum
emission, blazars have puzzled astronomers for over two decades. Today blazars
represent the only extragalactic objects detected in high-energy gamma-rays.
Their spectral energy distributions (SEDs) are characteristically
double-humped, with lower-energy emission originating as synchrotron radiation
in a relativistically beamed jet, and higher-energy emission due to
inverse-Compton processes. This has accentuated the biases inherent in any
survey to favor objects which are bright in the survey band, and should serve
as a cautionary note both to those designing new surveys as well as theorists
attempting to model blazar properties. The location of the synchrotron peak
determines which blazar population is dominant at GeV and TeV energies. At GeV
energies, low-energy peaked, high luminosity objects, which have high $L_C/L_S$
ratios, dominate, while at TeV energies, high-energy peaked objects are all
that is seen. I review the differences between low-energy peaked and
high-energy peaked blazars, and models to explain those differences. I also
look at efforts to bridge the gap between these classes with new surveys. Two
new surveys have detected a large population of high-energy peaked emission
line blazars (FSRQ), with properties somewhat different from previously known
objects. This discovery has the potential to revolutionize blazar physics in a
way comparable to the discovery of X-ray selected BL Lacs ten years ago by {\it
Einstein}. I cull from the new and existing surveys a list of $z<0.1$
high-energy peaked blazars which should be targets for new TeV telescopes.
Among these are several high-energy peaked FSRQ.


  Reparametrization invariance relations are determined for the inclusive decay
spectra of heavy hadrons. They connect the leading order result to the lambda_1
term, and the lambda_2 and rho_2 terms, and imply that the lambda_1 and rho_2
terms in the total rate occur in the combinations 1+lambda_1/(2m_Q^2) and
lambda_2-rho_2/m_Q. The relations are satisfied by the known results for the
hadronic decay tensors for B -> X e nu, B -> X gamma and B -> X e+ e- decays.
An interesting field-theory result, the connection between currents in full and
effective theories and the change in currents under field redefinitions, is
discussed. The hadron masses are given to order (Lambda_QCD)^3/m_Q^2 including
radiative corrections, and provide an example illustrating the relation between
renormalization and reparametrization invariance and mu-independence of 1/m_Q^3
corrections to physical quantities.


  A hereditary property of combinatorial structures is a collection of
structures (e.g. graphs, posets) which is closed under isomorphism, closed
under taking induced substructures (e.g. induced subgraphs), and contains
arbitrarily large structures. Given a property P, we write P_n for the
collection of distinct (i.e., non-isomorphic) structures in a property P with n
vertices, and call the function n -> |P_n| the speed (or unlabelled speed) of
P. Also, we write P^n for the collection of distinct labelled structures in P
with vertices labelled 1,...,n, and call the function n -> |P^n| the labelled
speed of P.
  The possible labelled speeds of a hereditary property of graphs have been
extensively studied, and the aim of this paper is to investigate the possible
speeds of other combinatorial structures, namely posets and oriented graphs.
More precisely, we show that (for sufficiently large n), the labelled speed of
a hereditary property of posets is either 1, or exactly a polynomial, or at
least 2^n - 1. We also show that there is an initial jump in the possible
unlabelled speeds of hereditary properties of posets, tournaments and directed
graphs, from bounded to linear speed, and give a sharp lower bound on the
possible linear speeds in each case.


  We propose a simple model of dark matter and CP violation and consider the
associated triple and quadruple productions of 125 GeV Higgs bosons at the
Large Hadron Collider (LHC). In the model, the dark matter is a vector-like
dark fermion $(\bar{\chi}, \chi)$ interacting with the Standard Model only
through a complex messenger scalar $S$ which is an electroweak singlet. New
sources of CP violation reside in the most general scalar potential involving
the doublet $H$ and the singlet $S$, as well as in the dark Yukawa coupling
between $S$ and $(\bar{\chi}, \chi)$. We study current experimental constraints
from Higgs measurements, searches for new scalars at the LHC, precision
electroweak measurements, EDM measurements, dark matter relic density, as well
as direct and indirect detections of dark matter. A smoking-gun signature of CP
violation could come from the Higgs-to-Higgs decays, $h_3\to h_2h_1$, where
$h_3/h_2/h_1$ are the heaviest scalar, second heaviest scalar and the SM-like
125-GeV Higgs, respectively. Taking into account other Higgs-to-Higgs decays,
such as $h_3\to 2h_2$ and $h_3/h_2\to 2h_1$, then gives rise to novel $3h_1$
and $4h_1$ final states, which have yet to be searched for experimentally. We
present four benchmarks and show the event rates for $3h_1$ and $4h_1$ final
states could be as large as ${\cal O}(10)\ {\rm fb}$ and ${\cal O}(1)\ {\rm
fb}$, respectively, at the 14-TeV LHC. This work opens up a new frontier of
searching for triple and quadruple Higgs bosons at a high energy collider.


  In 2014, Ibrahim M Alabdulmohsin wrote a paper called "Summability Calculus"
where he developed a method to generalize sigma notation to non-integer upper
bounds. His paper included a theorem, known as Theorem 6.1.1 (denoted here as
Lemma 2.1 because of its simplicity and location in this paper), but doesn't
study it much. Another paper by Mueller and Schleicher also analyzed this
formula, but doesn't integrate or differentiate the formula and states some
specific applications. This paper will analyze the simple formula that
generalizes sigma notation to non-integer upper and lower bounds. We state and
prove this formula in Section 2. Section 3 states a few algebraic properties
for the sum and product formulae and shows how differentiation of sums and
products works. Because integrating a product is challenging, we only analyze
the integration of sums in the fourth part of Section 3. In Section 4 we apply
the formula in the second section to create analytic continuations for
functions defined as partial sums, formulate an infinite series representation
to any limit, create a great approximation for functions that approach a
certain limit, make an analytic continuation for products, and calculate the
sum of anti-derivatives. We then conclude with a discussion of the material of
this paper.


  Various classes of exotic singularity models have been studied as possible
mimic models for the observed recent acceleration of the universe. Here we
further study one of these classes and, under the assumption that they are
phenomenological toy models for the behavior of an underlying scalar field
which also couples to the electromagnetic sector of the theory, obtain the
corresponding behavior of the fine-structure constant $\alpha$ for particular
choices of model parameters that have been previously shown to be in reasonable
agreement with cosmological observations. We then compare this predicted
behavior with available measurements of $\alpha$, thus constraining this
putative coupling to electromagnetism. We find that values of the coupling
which would provide a good fit to spectroscopic measurements of $\alpha$ are in
more than three-sigma tension with local atomic clock bounds. Future
measurements by ESPRESSO and ELT-HIRES will provide a definitive test of these
models.


  The fearures of the correlation method used in time-of-flight spectrometry of
ultracold neutrons are analyzed. The time-of-flight spectrometer for the energy
range of ultracold neutrons is described, and results of its testing by
measuring spectra of neutrons passing through interference filters are
presented.


  We introduce the idea of bosonic see-saw mechanism in analogy with the
see-saw mechanism. Bosonic see-saw is a new symmetry breaking mechanism and we
apply it to explain electroweak symmetry breaking as an inevitable consequence
of supersymmetry breaking. The breaking of electroweak symmetry occurs at tree
level once supersymmetry is broken. Absence of color/charge breaking in this
model is related to doublet-triplet splitting in grand unified theory. An
extension of MSSM with a weak triplet shows very interesting results especially
when mu =0. It provides the most natural understanding of why we have only
electroweak symmetry breaking rather than having color/charge breaking. In the
limit mu=0, the model predicts very light chargino mass, 104 GeV while Higgs is
heavy, 130 GeV.


  Superrotations of asymptotically flat spacetimes in four dimensions can be
interpreted in terms of including cosmic strings within the phase space of
allowed solutions. In this paper we explore the implications of the inclusion
of cosmic branes on the asymptotic structure of vacuum spacetimes in dimension
d > 4. We first show that only cosmic (d-3)-branes are Riemann flat in the
neighbourhood of the brane, and therefore only branes of such dimension passing
through the celestial sphere can respect asymptotic local flatness. We derive
the asymptotically locally flat boundary conditions associated with including
cosmic branes in the phase space of solutions. We find the asymptotic expansion
of vacuum spacetimes in d=5 with such boundary conditions; the expansion is
polyhomogenous, with logarithmic terms arising at subleading orders in the
expansion. The asymptotically locally flat boundary conditions identified here
are associated with an extended asymptotic symmetry group, which may be
relevant to soft scattering theorems and memory effects.


  We propose and develop an efficient implementation of the robust tabu search
heuristic for sparse quadratic assignment problems. The traditional
implementation of the heuristic applicable to all quadratic assignment problems
is of O(N^2) complexity per iteration for problems of size N. Using multiple
priority queues to determine the next best move instead of scanning all
possible moves, and using adjacency lists to minimize the operations needed to
determine the cost of moves, we reduce the asymptotic complexity per iteration
to O(N log N ). For practical sized problems, the complexity is O(N).


  Deploying reconfigurable intelligent surface (RIS) to enhance wireless
transmission is a promising approach. In this paper, we investigate large-scale
multi-RIS-assisted multi-cell systems, where multiple RISs are deployed in each
cell. Different from the full-buffer scenario, the mutual interference in our
system is not known a priori, and for this reason we apply the load coupling
model to analyze this system. The objective is to minimize the total resource
consumption subject to user demand requirement by optimizing the reflection
coefficients in the cells. The cells are highly coupled and the overall problem
is non-convex. To tackle this, we first investigate the single-cell case with
given interference, and propose a low-complexity algorithm based on the
Majorization-Minimization method to obtain a locally optimal solution. Then, we
embed this algorithm into an algorithmic framework for the overall multi-cell
problem, and prove its feasibility and convergence to a solution that is at
least locally optimal. Simulation results demonstrate the benefit of RIS in
time-frequency resource utilization in the multi-cell system.


  Electron correlation effects are essential for an accurate ab initio
description of molecules. A quantitative a priori knowledge of the single- or
multi-reference nature of electronic structures as well as of the dominant
contributions to the correlation energy can facilitate the decision regarding
the optimum quantum chemical method of choice. We propose concepts from quantum
information theory as orbital entanglement measures that allow us to evaluate
the single- and multi-reference character of any molecular structure in a given
orbital basis set. By studying these measures we can detect possible artifacts
of small active spaces.


  For two probability measures $\rho$ and $\pi$ on $[-1,1]^{\mathbb{N}}$ we
investigate the approximation of the triangular Knothe-Rosenblatt transport
$T:[-1,1]^{\mathbb{N}}\to [-1,1]^{\mathbb{N}}$ that pushes forward $\rho$ to
$\pi$. Under suitable assumptions, we show that $T$ can be approximated by
rational functions without suffering from the curse of dimension. Our results
are applicable to posterior measures arising in certain inference problems
where the unknown belongs to an (infinite dimensional) Banach space. In
particular, we show that it is possible to efficiently approximately sample
from certain high-dimensional measures by transforming a lower-dimensional
latent variable.


  A neutron number dependence of the E1 0+ --> 1- reduced transition
probability in spherical even--even nuclei is analysed within the Q--phonon
approach in the fermionic space to describe the structure of collective states.
Microscopic calculations of the E1 0+ --> 1- transition matrix elements are
carried out for the Xe isotopes based on the RPA for the ground state wave
function. A satisfactory description of the experimental data is obtained.


  We present a polarisation map of the warm dust emission from the minispiral
in the central parsec of the Galactic centre. The observations were made at a
wavelength of 12.5 microns with CanariCam mounted on the 10.4-m Gran Telescopio
Canarias. The magnetic field traced by the polarised emission from aligned dust
grains is consistent with previous observations, but the increased resolution
of the present data reveals considerably more information on the detailed
structure of the B field and its correspondence with the filamentary emission
seen in both mid-infrared continuum emission and free-free emission at cm
wavelengths. The magnetic field appears to be compressed and pushed by the
outflows from luminous stars in the Northern Arm, but it is not disordered by
them. We identify some magnetically coherent filaments that cross the Northern
Arm at a Position Angle of ~45 degrees, and which may trace orbits inclined to
the primary orientation of the Northern Arm and circumnuclear disk. In the
East-West bar, the magnetic fields implied by the polarization in the lower
intensity regions lie predominantly along the bar at a Position Angle of 130 -
140 degrees. In contrast to the Northern Arm, the brighter regions of the bar
tend to have lower degrees of polarization with a greater divergence in
position angle compared to the local diffuse emission. It appears that the
diffuse emission in the East-West bar traces the underlying field and that the
bright compact sources are unrelated objects presumably projected onto the bar
and with different field orientations


  We describe results of modeling the effects on Earth-like planets of
long-duration gamma-ray bursts (GRBs) within a few kiloparsecs. A primary
effect is generation of nitrogen oxide compounds which deplete ozone. Ozone
depletion leads to an increase in solar UVB radiation at the surface, enhancing
DNA damage, particularly in marine microorganisms such as phytoplankton. In
addition, we expect increased atmospheric opacity due to buildup of nitrogen
dioxide produced by the burst and enhanced precipitation of nitric acid. We
review here previous work on this subject and discuss recent developments,
including further discussion of our estimates of the rates of impacting GRBs
and the possible role of short-duration bursts.


  Constructing personalized and anthropomorphic agents holds significant
importance in the simulation of social networks. However, there are still two
key problems in existing works: the agent possesses world knowledge that does
not belong to its personas, and it cannot eliminate the interference of diverse
persona information on current actions, which reduces the personalization and
anthropomorphism of the agent. To solve the above problems, we construct the
social media agent based on personalized knowledge and dynamic persona
information. For personalized knowledge, we add external knowledge sources and
match them with the persona information of agents, thereby giving the agent
personalized world knowledge. For dynamic persona information, we use current
action information to internally retrieve the persona information of the agent,
thereby reducing the interference of diverse persona information on the current
action. To make the agent suitable for social media, we design five basic
modules for it: persona, planning, action, memory and reflection. To provide an
interaction and verification environment for the agent, we build a social media
simulation sandbox. In the experimental verification, automatic and human
evaluations demonstrated the effectiveness of the agent we constructed.


  The numerical method of Kahan applied to quadratic differential equations is
known to often generate integrable maps in low dimensions and can in more
general situations exhibit preserved measures and integrals. Computerized
methods based on discrete Darboux polynomials have recently been used for
finding these measures and integrals. However, if the differential system
contains many parameters, this approach can lead to highly complex results that
can be difficult to interpret and analyze. But this complexity can in some
cases be substantially reduced by using aromatic series. These are a
mathematical tool introduced independently by Chartier and Murua and by
Iserles, Quispel and Tse. We develop an algorithm for this purpose and derive
some necessary conditions for the Kahan map to have preserved measures and
integrals expressible in terms of aromatic functions. An important reason for
the success of this method lies in the equivariance of the map from vector
fields to their aromatic funtions. We demonstrate the algorithm on a number of
examples showing a great reduction in complexity compared to what had been
obtained by a fixed basis such as monomials.


  We study the spin relaxation torque in nonmagnetic or ferromagnetic metals
with nonuniform spin-orbit coupling within the Keldysh Green's function
formalism. In non-magnet, the relaxation torque is shown to arise when the
spin-orbit coupling is not uniform. In the absence of an external field, the
spin current induced by the relaxation torque is proportional to the vector
chirality of Rashba-type spin-orbit field (RSOF). In the presence of an
external field, on the other hand, spin relaxation torque arises from the
coupling of the external field and vector chirality of RSOF. Our result
indicates that spin-sink or source effects are controlled by designing RSOF in
junctions.


  We present a spectral analysis of four LMC WC-type Wolf-Rayet (WR) stars
(BAT99-8, BAT99-9, BAT99-11, and BAT99-52) to shed light on two evolutionary
questions surrounding massive stars. The first is: are WO-type WR stars more
oxygen enriched than the WC-type stars, indicating further chemical evolution,
or are the strong high-excitation oxygen lines in the WO-type stars an
indication of higher temperatures. This study will act as a baseline for
answering the question of where WO-type stars fall in WR evolution. Each star's
spectrum, extending from 1100~\AA\ to 25000~\AA, was modeled using \cmfgen\ to
determine the star's physical properties such as luminosity, mass-loss rate,
and chemical abundances. The oxygen abundance is a key evolutionary diagnostic,
and with higher resolution data and an improved stellar atmosphere code, we
found the oxygen abundance to be up to a factor of 5 lower than previous
studies. The second evolutionary question revolves around the formation of WR
stars: Do they evolve by themselves or is a close companion star necessary for
their formation? Using our derived physical parameters, we compared our results
to the Geneva single-star evolutionary models and the BPASS binary evolutionary
models. We found that both the Geneva solar metallicity models and BPASS LMC
metallicity models are in agreement with the four WC-type stars, while the
Geneva LMC metallicity models are not. Therefore, these four WC4 stars could
have been formed either via binary or single-star evolution.


  In this paper we introduce our system for the task of Irony detection in
English tweets, a part of SemEval 2018. We propose representation learning
approach that relies on a multi-layered bidirectional LSTM, without using
external features that provide additional semantic information. Although our
model is able to outperform the baseline in the validation set, our results
show limited generalization power over the test set. Given the limited size of
the dataset, we think the usage of more pre-training schemes would greatly
improve the obtained results.


  The one-loop contribution of the excited Kaluza-Klein (KK) modes of the
$SU_L(2)$ gauge group on the off-shell $WW\gamma$ and $WWZ$ vertices is
calculated in the context of a pure Yang-Mills theory in five dimensions and
its phenomenological implications discussed. The use of a gauge-fixing
procedure for the excited KK modes that is covariant under the standard gauge
transformations of the $SU_L(2)$ group is stressed. A gauge-fixing term and the
Faddeev-Popov ghost sector for the KK gauge modes that are separately invariant
under the standard gauge transformations of $SU_L(2)$ are presented. It is
shown that the one-loop contributions of the KK modes to the off-shell
$WW\gamma$ and $WWZ$ vertices are free of ultraviolet divergences and
well-behaved at high energies. It is found that for a size of the fifth
dimension of $R^{-1}\sim 1TeV$, the one-loop contribution of the KK modes to
these vertices is about one order of magnitude lower than the corresponding
standard model radiative correction. This contribution is similar to the one
estimated for new gauge bosons contributions in other contexts. Tree-level
effects on these vertices induced by operators of higher canonical dimension
are also investigated. It is found that these effects are lower than those
generated at the one-loop order by the KK gauge modes.


  The enriched finite element basis -- wherein the finite element basis is
enriched with atom-centered numerical functions -- has recently been shown to
be a computationally efficient basis for systematically convergent all-electron
DFT ground-state calculations. In this work, we present the expressions to
compute variationally consistent ionic forces and stress tensor for
all-electron DFT calculations in the enriched finite element basis. In
particular, we extend the formulation of configurational forces in Motamarri &
Gavini (Phys. Rev. B 2018) to the enriched finite element basis and elucidate
the additional contributions arising from the enrichment functions. We
demonstrate the accuracy of the formulation by comparing the computed forces
and stresses for various benchmark systems with those obtained from
finite-differencing the ground-state energy. Further, we also benchmark our
calculations against Gaussian basis for molecular systems and against the
LAPW+lo basis for periodic systems.


  We investigate the multipartite entanglement of a uniformly curved quantum 3D
space region with boundary, realised in terms of spin networks defined on a
graph with non trivial SU(2) holonomies, in the framework of loop quantum
gravity. The presence of intrinsic curvature in the region is encoded in
closure (topological) defects associated with tag-spins attached to the
vertices of the graph. For such states, we generalise the bulk-to-boundary
mapping as to include the space of tags in an extended boundary space: bulk
information is shared among generically entangled boundary surfaces and
intrinsic curvature degrees of freedom. We model the quantum region on a
tripartite system composed by two (complementary) boundary subregions and the
set of bulk tags. Via replica techniques, we can compute the typical value of
the logarithmic negativity of the reduced boundary, described as an open
quantum system, in a large spin regime. We find three entanglement regimes,
depending on the ratio between the number of tags (curvature) and the area of
the dual surface at the boundary. These are well described by the generalised
Page curve of a tripartite random state. In particular, we find area scaling
behaviour for negativity in case of small curvature, while for large curvature
the negativity vanishes, suggesting an effective thermalization of the
boundary. Remarkably, the PPT character of the mixed boundary state corresponds
to a change in the effective topology of the network, with the two boundary
subregions becoming disconnected.


  We study deterministic matrix completion problem, i.e., recovering a low-rank
matrix from a few observed entries where the sampling set is chosen as the edge
set of a Ramanujan graph. We first investigate projected gradient descent (PGD)
applied to a Burer-Monteiro least-squares problem and show that it converges
linearly to the incoherent ground-truth with respect to the condition number
\k{appa} of ground-truth under a benign initialization and large samples. We
next apply the scaled variant of PGD to deal with the ill-conditioned case when
\k{appa} is large, and we show the algorithm converges at a linear rate
independent of the condition number \k{appa} under similar conditions. Finally,
we provide numerical experiments to corroborate our results.


  Superconducting (Li1-xFex)OHFe1-ySe films are attractive for both the basic
research and practical application. However, the conventional vapor deposition
techniques are not applicable in synthesizing the films of such a complex
system. So no intrinsic charge transport measurements on the films are
available so far to reveal the nature of charge carriers, which is fundamental
to understanding the iron-based superconductivity mechanism. Herein we report a
soft chemical film technique (matrix-assisted hydrothermal epitaxial growth),
by which we have succeeded in growing a series of (Li1-xFex)OHFe1-ySe films
covering the whole superconducting regime, with the superconducting transition
temperature (Tc) from 4 K up to 42 K. This film technique opens up a new way
for fabricating other complex functional materials as well. Furthermore, our
systematic transport investigation on the film samples indicates that both the
electron and hole carriers contribute to the charge transport, with the
scattering rates deviating from the Fermi liquid. We find that the
superconductivity occurs upon the electron and hole mobility becoming
divergent. And in the high Tc samples, the electron carriers are found much
more mobile than the holes, a feature distinct from the low Tc samples. Hence,
our transport results provide key insights into the underlying physics for
iron-based high-Tc superconductivity.


  The field of Recommender Systems (RecSys) has been extensively studied to
enhance accuracy by leveraging users' historical interactions. Nonetheless,
this persistent pursuit of accuracy frequently engenders diminished diversity,
culminating in the well-recognized "echo chamber" phenomenon. Diversified
RecSys has emerged as a countermeasure, placing diversity on par with accuracy
and garnering noteworthy attention from academic circles and industry
practitioners. This research explores the realm of diversified RecSys within
the intricate context of knowledge graphs (KG). These KGs act as repositories
of interconnected information concerning entities and items, offering a
propitious avenue to amplify recommendation diversity through the incorporation
of insightful contextual information. Our contributions include introducing an
innovative metric, Entity Coverage, and Relation Coverage, which effectively
quantifies diversity within the KG domain. Additionally, we introduce the
Diversified Embedding Learning (DEL) module, meticulously designed to formulate
user representations that possess an innate awareness of diversity. In tandem
with this, we introduce a novel technique named Conditional Alignment and
Uniformity (CAU). It adeptly encodes KG item embeddings while preserving
contextual integrity. Collectively, our contributions signify a substantial
stride towards augmenting the panorama of recommendation diversity within the
realm of KG-informed RecSys paradigms.


  We extend the Helac-Dipoles package with the implementation of a new
subtraction formalism, first introduced by Nagy and Soper in the formulation of
an improved parton shower. We discuss a systematic, semi-numerical approach for
the evaluation of the integrated subtraction terms for both massless and
massive partons, which provides the missing ingredient for a complete
implementation. In consequence, the new scheme can now be used as part of a
complete NLO QCD calculation for processes with arbitrary parton masses and
multiplicities. We assess its overall performance through a detailed comparison
with results based on Catani-Seymour subtraction. The importance of random
polarization and color sampling of the external partons is also examined.


  An umbral type formalism is used to derive integrals involving products of
Laguerre polynomials and other special functions.


  The Dobrushin comparison theorem is a powerful tool to bound the difference
between the marginals of high-dimensional probability distributions in terms of
their local specifications. Originally introduced to prove uniqueness and decay
of correlations of Gibbs measures, it has been widely used in statistical
mechanics as well as in the analysis of algorithms on random fields and
interacting Markov chains. However, the classical comparison theorem requires
validity of the Dobrushin uniqueness criterion, essentially restricting its
applicability in most models to a small subset of the natural parameter space.
In this paper we develop generalized Dobrushin comparison theorems in terms of
influences between blocks of sites, in the spirit of Dobrushin-Shlosman and
Weitz, that substantially extend the range of applicability of the classical
comparison theorem. Our proofs are based on the analysis of an associated
family of Markov chains. We develop in detail an application of our main
results to the analysis of sequential Monte Carlo algorithms for filtering in
high dimension.


  We provide the first computational treatment of fused-heads constructions
(FH), focusing on the numeric fused-heads (NFH). FHs constructions are noun
phrases (NPs) in which the head noun is missing and is said to be `fused' with
its dependent modifier. This missing information is implicit and is important
for sentence understanding. The missing references are easily filled in by
humans but pose a challenge for computational models. We formulate the handling
of FH as a two stages process: identification of the FH construction and
resolution of the missing head. We explore the NFH phenomena in large corpora
of English text and create (1) a dataset and a highly accurate method for NFH
identification; (2) a 10k examples (1M tokens) crowd-sourced dataset of NFH
resolution; and (3) a neural baseline for the NFH resolution task. We release
our code and dataset, in hope to foster further research into this challenging
problem.


  We consider an open quantum system described by a Lindblad-type master
equation with two times-scales. The fast time-scale is strongly dissipative and
drives the system towards a low-dimensional decoherence-free space. To perform
the adiabatic elimination of this fast relaxation, we propose a geometric
asymptotic expansion based on the small positive parameter describing the
time-scale separation. This expansion exploits geometric singular perturbation
theory and center-manifold techniques. We conjecture that, at any order, it
provides an effective slow Lindblad master equation and a completely positive
parameterization of the slow invariant sub-manifold associated to the
low-dimensional decoherence-free space. By preserving complete positivity and
trace, two important structural properties attached to open quantum dynamics,
we obtain a reduced-order model that directly conveys a physical interpretation
since it relies on effective Lindbladian descriptions of the slow evolution. At
the first order, we derive simple formulae for the effective Lindblad master
equation. For a specific type of fast dissipation, we show how any Hamiltonian
perturbation yields Lindbladian second-order corrections to the first-order
slow evolution governed by the Zeno-Hamiltonian. These results are illustrated
on a composite system made of a strongly dissipative harmonic oscillator, the
ancilla, weakly coupled to another quantum system.


  In this paper, we study Bertrand surface offsets by considering the dual
geodesic trihedron(dual Darboux frame) of the ruled surfaces. We obtain the
relationships between the invariants of Bertrand trajectory ruled surfaces.
Furthermore, we obtain the conditions for these surface offset to be
developable.


  Time series data may exhibit clustering over time and, in a multiple time
series context, the clustering behavior may differ across the series. This
paper is motivated by the Bayesian non--parametric modeling of the dependence
between the clustering structures and the distributions of different time
series. We follow a Dirichlet process mixture approach and introduce a new
class of multivariate dependent Dirichlet processes (DDP). The proposed DDP are
represented in terms of vector of stick-breaking processes with dependent
weights. The weights are beta random vectors that determine different and
dependent clustering effects along the dimension of the DDP vector. We discuss
some theoretical properties and provide an efficient Monte Carlo Markov Chain
algorithm for posterior computation. The effectiveness of the method is
illustrated with a simulation study and an application to the United States and
the European Union industrial production indexes.


  Donaldson defined a parabolic flow on Kahler manifolds which arises from
considering the action of a group of symplectomorphisms on the space of smooth
maps between manifolds. One can define a moment map for this action, and then
consider the gradient flow of the square of its norm. Chen discovered the same
flow from a different viewpoint and called it the J-flow, since it corresponds
to the gradient flow of his J-functional, which is related to Mabuchi's
K-energy. In this paper, we show that in the case of Kahler surfaces with two
Kahler forms satisfying a certain inequality, the J-flow converges to a zero of
the moment map.


  Using the multi-fluid approach, we investigate streaming and thermal
instabilities of the electron-ion plasma with homogeneous cold cosmic rays
drifting perpendicular to the background magnetic field. Perturbations across
the magnetic field are considered. The back-reaction of cosmic rays resulting
in the streaming instability is taken into account. The thermal instability is
shown not to be subject to the action of cosmic rays in the model under
consideration. The dispersion relation for the thermal instability has been
derived which includes sound velocities of plasma and cosmic rays, Alfv\'{e}n
and cosmic ray drift velocities. The relation between these parameters
determines the kind of thermal instability from Parker's to Field's type
instability. The results obtained can be useful for a more detailed the
investigation of electron-ion astrophysical objects such as galaxy clusters
including the dynamics of streaming cosmic rays.


  We derive an exact solution to the problem of spin snake states induced in a
nonhomogeneous magnetic field by a combined action of the Rashba spin-orbit and
Zeeman fields. In an antisymmetric magnetic field the spin snake states are
nonlocal composite particles, originating from spatially separated entangled
spins. Adding an external homogeneous magnetic field breaks the spin-parity
symmetry gapping out the spectral branches, which results in a regular beating
pattern of the spin current. These new phenomena in a helical liquid of snake
states are proposed for an experimental realization.


  The characterization of exoplanets relies on that of their host star.
However, stellar evolution models cannot always be used to derive the mass and
radius of individual stars, because many stellar internal parameters are poorly
constrained. Here, we use the probability density functions (PDFs) of directly
measured parameters to derive the joint PDF of the stellar and planetary mass
and radius. Because combining the density and radius of the star is our most
reliable way of determining its mass, we find that the stellar (respectively
planetary) mass and radius are strongly (respectively moderately) correlated.
We then use a generalized Bayesian inference analysis to characterize the
possible interiors of 55 Cnc e. We quantify how our ability to constrain the
interior improves by accounting for correlation. The information content of the
mass-radius correlation is also compared with refractory element abundance
constraints. We provide posterior distributions for all interior parameters of
interest. Given all available data, we find that the radius of the gaseous
envelope is $0.08 \pm 0.05 R_p$. A stronger correlation between the planetary
mass and radius (potentially provided by a better estimate of the transit
depth) would significantly improve interior characterization and reduce
drastically the uncertainty on the gas envelope properties.


  Chromospheric evaporation is observed as Doppler blueshift during solar
flares. It plays one of key roles in dynamics and energetics of solar flares,
however, its mechanism is still unknown. In this paper we present a detailed
analysis of spatially-resolved multi-wavelength observations of chromospheric
evaporation during an M 1.0 class solar flare (SOL2014-06-12T21:12) using data
from the NASA's IRIS (Interface Region Imaging Spectrograph) and HMI/SDO
(Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory)
telescopes, and VIS/NST (Visible Imaging Spectrometer at New Solar Telescope)
high-resolution observations, covering the temperature range from 10^4 K to
10^7 K. The results show that the averaged over the region Fe XXI blueshift of
the hot evaporating plasma is delayed relative to the C II redshift of the
relatively cold chromospheric plasma by about 1 min. The spatial distribution
of the delays is not uniform across the region and can be as long as 2 min in
several zones. Using vector magnetograms from HMI we reconstruct the magnetic
field topology and the quasi-separatrix layer (QSL) and find that the blueshift
delay regions as well as the H-alpha flare ribbons are connected to the region
of magnetic polarity inversion line (PIL) and an expanding flux rope via a
system of low-lying loop arcades with height < ~4.5 Mm. This allows us to
propose an interpretation of the chromospheric evaporation based on the
geometry of local magnetic fields, and the primary energy source associated
with the PIL.


  For non-equilibrium systems of interacting particles and for interacting
diffusions in d dimensions, a novel fluctuation relation is derived. The
theorem establishes a quantitative relation between the probabilities of
observing two current values in different spatial directions. The result is a
consequence of spatial symmetries of the microscopic dynamics, generalizing in
this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal
symmetry. This new perspective opens up the possibility of direct experimental
measurements of fluctuation relations of vectorial observables.


  The implementation of polarization-based quantum communication is limited by
signal loss and decoherence caused by the birefringence of a single-mode fiber.
We investigate the Knill dynamical decoupling scheme, implemented using
half-wave plates, to minimize decoherence and show that a fidelity greater than
$99\%$ can be achieved in absence of rotation error and fidelity greater than
$96\%$ can be achieved in presence of rotation error. Such a scheme can be used
to preserve any quantum state with high fidelity and has potential application
for constructing all optical quantum delay line, quantum memory, and quantum
repeater.


  Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a
binomial prime ideal. We investigate when the ideal $I$ can be "split" into the
sum of two smaller toric ideals. For a general toric ideal $I$, we give a
sufficient condition for this splitting in terms of the integer matrix that
defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we
give additional splittings of $I_G$ related to subgraphs of $G$. When there
exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases
we can describe the (multi-)graded Betti numbers of $I$ in terms of the
(multi-)graded Betti numbers of $I_1$ and $I_2$.


  Recently, the reconfigurable intelligent surface (RIS), benefited from the
breakthrough on the fabrication of programmable meta-material, has been
speculated as one of the key enabling technologies for the future six
generation (6G) wireless communication systems scaled up beyond massive
multiple input multiple output (Massive-MIMO) technology to achieve smart radio
environments. Employed as reflecting arrays, RIS is able to assist MIMO
transmissions without the need of radio frequency chains resulting in
considerable reduction in power consumption. In this paper, we investigate the
joint design of transmit beamforming matrix at the base station and the phase
shift matrix at the RIS, by leveraging recent advances in deep reinforcement
learning (DRL). We first develop a DRL based algorithm, in which the joint
design is obtained through trial-and-error interactions with the environment by
observing predefined rewards, in the context of continuous state and action.
Unlike the most reported works utilizing the alternating optimization
techniques to alternatively obtain the transmit beamforming and phase shifts,
the proposed DRL based algorithm obtains the joint design simultaneously as the
output of the DRL neural network. Simulation results show that the proposed
algorithm is not only able to learn from the environment and gradually improve
its behavior, but also obtains the comparable performance compared with two
state-of-the-art benchmarks. It is also observed that, appropriate neural
network parameter settings will improve significantly the performance and
convergence rate of the proposed algorithm.


  We study, by means of computer simulations, the crystal-melt interface of
three different systems: hard-spheres, Lennard Jones and the TIP4P/2005 water
model. In particular, we focus on the dynamics of surface waves. We observe
that the processes involved in the relaxation of surface waves are
characterized by distinct time scales: a slow one related to the continuous
recrystallization and melting, that is governed by capillary forces; and a fast
one which we suggest to be due to a combination of processes that quickly cause
small perturbations to the shape of the interface (like e. g. Rayleigh waves,
subdiffusion, or attachment/detachment of particles to/from the crystal). The
relaxation of surface waves becomes dominated by the slow process as the
wavelength increases. Moreover, we see that the slow relaxation is not
influenced by the details of the microscopic dynamics. In a time scale
characteristic for the diffusion of the liquid phase, the relaxation dynamics
of the crystal-melt interface of water is around one order of magnitude slower
than that of Lennard Jones or hard spheres, which we ascribe to the presence of
orientational degrees of freedom in the water molecule. Finally, we estimate
the rate of crystal growth from our analysis of the capillary wave dynamics and
compare it with previous simulation studies and with experiments for the case
of water.


  Grid diagrams encode useful geometric information about knots in S^3. In
particular, they can be used to combinatorially define the knot Floer homology
of a knot K in S^3, and they have a straightforward connection to Legendrian
representatives of K in (S^3, \xi_\st), where \xi_\st is the standard, tight
contact structure. The definition of a grid diagram was extended to include a
description for links in all lens spaces, resulting in a combinatorial
description of the knot Floer homology of a knot K in L(p, q) for all p > 0. In
the present article, we explore the connection between lens space grid diagrams
and the contact topology of a lens space. Our hope is that an understanding of
grid diagrams from this point of view will lead to new approaches to the Berge
conjecture, which claims to classify all knots in S^3 upon which surgery yields
a lens space.


  The capacitated tree cover problem with edge loads is a variant of the tree
cover problem, where we are given facility opening costs, edge costs and loads,
as well as vertex loads. We try to find a tree cover of minimum cost such that
the total edge and vertex load of each tree does not exceed a given bound. We
present an $\mathcal{O}(m\log n)$ time 3-approximation algorithm for this
problem.
  This is achieved by starting with a certain LP formulation. We give a
combinatorial algorithm that solves the LP optimally in time $\mathcal{O}(m\log
n)$. Then, we show that a linear time rounding and splitting technique leads to
an integral solution that costs at most 3 times as much as the LP solution.
Finally, we prove that the integrality gap of the LP is $3$, which shows that
we can not improve the rounding step in general.


  We show that the transverse field Ising model undergoes a zero temperature
phase transition for a $G_\delta$ set of ergodic transverse fields. We apply
our results to the special case of quasiperiodic transverse fields, in one
dimension we find a sharp condition for the existence of a phase transition.


  Let $p$ be a prime and $n$ a positive integer such that $\sqrt{\frac p2} + 1
\leq n \leq \sqrt{p}$. For any arithmetic progression $A$ of length $n$ in
$\mathbb{F}_p$, we establish an asymptotic formula for the number of directions
determined by $A \times A \subset \mathbb{F}_p^2$. The key idea is to reduce
the problem to counting the number of solutions to the bilinear Diophantine
equation $ad+bc=p$ in variables $1\le a,b,c,d\le n$; our asymptotic formula for
the number of solutions is of independent interest.


  We theoretically demonstrate a one-to-one mapping between the direction of
electron ionization and the phase delay between a linearly polarized VUV and a
circular IR laser pulse. To achieve this, we use an ultrashort VUV pulse that
defines the moment in time and space when an above threshold electron is
released in the IR pulse. The electron can then be accelerated to high
velocities escaping in a direction completely determined by the phase delay
between the two pulses. The dipole matrix element to transition from an initial
bound state of the N$_2$ molecule, considered in this work, to the continuum is
obtained using quantum mechanical techniques that involve computing accurate
continuum molecular states. Following release of the electron in the IR pulse,
we evolve classical trajectories, neglecting the Coulomb potential and
accounting for quantum interference, to compute the distribution of the
direction and magnitude of the final electron momentum. The concept we
theoretically develop can be implemented to produce nanoscale ring currents
that generate large magnetic fields.


  We study the phase structure of N = 1 supersymmetric Sp(2N_c) gauge theories
with 2N_f fundamentals, an adjoint, and vanishing superpotential. Using
a-maximization, we derive analytic expressions for the values of N_f below
which the first several gauge-invariant operators in the chiral ring violate
the unitarity bound and become free fields. In doing so we are able to
explicitly check previous conjectures about the behavior of this theory made by
Luty, Schmaltz, and Terning. We then compare this to an analysis of the first
two 'deconfined' dual descriptions based on the gauge groups Sp(2N_f+2) x
SO(2N_c+5) and Sp(2N_f+2) x SO(4N_f+4) x Sp(2N_c+2), finding precise agreement.
In particular, we find no evidence for non-obvious accidental symmetries or the
appearance of a mixed phase in which one of the dual gauge groups becomes free.


  Assuming the Majorana masses of $\nu_e$ and the linear combination $c
\nu_\tau - s \nu_\mu$ to be equal from their couplings to a heavy scalar
triplet $\xi$, I show that their radiative splitting is given by $\Delta
m^2/m_\nu^2 = (3 c^2/4 \pi^2) (G_F/\sqrt 2) m_\tau^2 \ln (m_\xi^2/m_W^2)$. This
is applicable to the small-angle matter-enhanced oscillation solution of the
solar neutrino deficit and restricts $m_\nu$ to be between 0.20 and 0.36 eV if
$c^2 = 0.7$ and $m_\xi = 10^{14}$ GeV.


  We present BeppoSAX results on the nearby starburst galaxy NGC 253. Although
extended, a large fraction of the X-ray emission comes from the nuclear region.
Preliminary analysis of the LECS/MECS/PDS ~0.2-60 keV data from the central 4'
region indicates that the continuum is well fitted by two thermal models: a
``soft'' component with kT ~ 0.9 keV, and a ``hard'' component with kT ~ 6 keV
absorbed by a column density of ~ 1.2 x10**22 cm-2. For the first time in this
object, the Fe K line at 6.7 keV is detected, with an equivalent width of ~ 300
eV. This detection, together with the shape of the 2--60 keV continuum, implies
that most of the hard X-ray emission is thermal in origin, and constrains the
iron abundances of this component to be ~0.25 of solar. Other lines clearly
detected are Si, S and Fe L/Ne, in agreement with previous ASCA results. We
discuss our results in the context of the starburst-driven galactic superwind
model.


  Momentum dependent charge excitations of a two-leg ladder are investigated by
resonant inelastic x-ray scattering of (La,Sr,Ca)14Cu24O41. In contrast to the
case of a square lattice, momentum dependence of the Mott gap excitation of the
ladder exhibits little change upon hole-doping, indicating the formation of
hole pairs. Theoretical calculation based on a Hubbard model qualitatively
explains this feature. In addition, experimental data shows intraband
excitation as continuum intensity below the Mott gap and it appears at all the
momentum transfers simultaneously. The intensity of the intraband excitation is
proportional to the hole concentration of the ladder, which is consistent with
optical conductivity measurements.


  For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a
decomposition of the unit element $1_\A$ into orthogonal idempotents (not
necessary primitive) satisfying some conditions. By using this decomposition,
the cellular basis $\ZC$ can be partitioned into some pieces with good
properties. Then by using a certain map $\a$, we give a coarse partition of
$\ZC$ whose refinement is the original partition. We construct a Levi type
subalgebra $\aA$ of $\A$ and its quotient algebra $\oA$, and also construct a
parabolic type subalgebra $\tA$ of $\A$, which contains $\aA$ with respect to
the map $\a$. Then, we study the relation of standard modules, simple modules
and decomposition numbers among these algebras. Finally, we study the
relationship of blocks among these algebras.


  The problem of astrometry is revisited from the perspective of analyzing the
attainability of well-known performance limits (the Cramer-Rao bound) for the
estimation of the relative position of light-emitting (usually point-like)
sources on a CCD-like detector using commonly adopted estimators such as the
weighted least squares and the maximum likelihood. Novel technical results are
presented to determine the performance of an estimator that corresponds to the
solution of an optimization problem in the context of astrometry. Using these
results we are able to place stringent bounds on the bias and the variance of
the estimators in close form as a function of the data. We confirm these
results through comparisons to numerical simulations under a broad range of
realistic observing conditions. The maximum likelihood and the weighted least
square estimators are analyzed. We confirm the sub-optimality of the weighted
least squares scheme from medium to high signal-to-noise found in an earlier
study for the (unweighted) least squares method. We find that the maximum
likelihood estimator achieves optimal performance limits across a wide range of
relevant observational conditions. Furthermore, from our results, we provide
concrete insights for adopting an adaptive weighted least square estimator that
can be regarded as a computationally efficient alternative to the optimal
maximum likelihood solution. We provide, for the first time, close-form
analytical expressions that bound the bias and the variance of the weighted
least square and maximum likelihood implicit estimators for astrometry using a
Poisson-driven detector. These expressions can be used to formally assess the
precision attainable by these estimators in comparison with the minimum
variance bound.


  A definition is given of seriate sets as being sets constituted out of
structured collections of objects which are recursively internally self-
similar. Fundamental (geometrical) objects of Dimension N are conceived to be
constituted out of seriate sets of fundamental objects of Dimension N-1,
starting with points assigned to Dimension 0. Syntactical rules to enable such
objects to be systematically named and combined, are set out. A series of
formal proofs of theorems relative to objects of Dimensions 1 and 2 are worked
through. A proof that four colours are sufficient to colour any five area map
is given in illustration.
  I know most/all will think all the above impossible, and necessarily the work
of some crazy. If it is wrong I believe it is wrong in interesting ways. The
underlying idea is easily grasped without working through the theorems given,
so I would be grateful to hear from anyone as to why it is wrong - and not
simply because it must be so.


  One of the virtues of peer review is that it provides a self-regulating
selection mechanism for scientific work, papers and projects. Peer review as a
selection mechanism is hard to evaluate in terms of its efficiency. Serious
efforts to understand its strengths and weaknesses have not yet lead to clear
answers. In theory peer review works if the involved parties (editors and
referees) conform to a set of requirements, such as love for high quality
science, objectiveness, and absence of biases, nepotism, friend and clique
networks, selfishness, etc. If these requirements are violated, what is the
effect on the selection of high quality work? We study this question with a
simple agent based model. In particular we are interested in the effects of
rational referees, who might not have any incentive to see high quality work
other than their own published or promoted. We find that a small fraction of
incorrect (selfish or rational) referees can drastically reduce the quality of
the published (accepted) scientific standard. We quantify the fraction for
which peer review will no longer select better than pure chance. Decline of
quality of accepted scientific work is shown as a function of the fraction of
rational and unqualified referees. We show how a simple quality-increasing
policy of e.g. a journal can lead to a loss in overall scientific quality, and
how mutual support-networks of authors and referees deteriorate the system.


  The modified Gauss-Bonnet gravity can be motivated by a number of physical
reasons, including: the uniqueness of a gravitational Lagrangian in four and
higher dimensions and the leading order $\alpha^\prime$ corrections in
superstring theory. Such an effective theory of scalar-tensor gravity has been
modeled in the recent past to explain both the initial cosmological singularity
problem and the observationally supported cosmological perturbations. Here I
present an overview of the recent developments in the use of modified
Gauss-Bonnet gravity to explain current observations, touching on key
cosmological and astrophysical constraints applicable to theories of
scalar-tensor gravity. The Gauss-Bonnet type modification of Einstein's theory
admits nonsingular solutions for a wide range of scalar-curvature couplings. It
also provides plausible explanation to some outstanding cosmological
conundrums, including: the transition from matter dominance to dark energy and
the late time cosmic acceleration. The focus is placed here to constrain such
an effective theory of gravity against the recent cosmological and
astrophysical observations.


  Topological Data Analysis (TDA) provides a toolkit for the study of the shape
of high dimensional and complex data. While operating on a space of persistence
diagrams is cumbersome, persistence norms provide a simple real value measure
of multivariate data which is seeing greater adoption within finance. A growing
literature seeks links between persistence norms and the summary statistics of
the data being analysed. This short note targets the demonstration of
differences in the persistence norms of the Datasaurus datasets of Matejka and
Fitzmaurice. We show that persistence norms can be used as additional measures
that often discriminate datasets with the same collection of summary
statistics. Treating each of the data sets as a point cloud we construct the
$L_1$ and $L_2$ persistence norms in dimensions 0 and 1. We show multivariate
distributions with identical covariance and correlation matrices can have
considerably different persistence norms. Through the example, we remind users
of persistence norms of the importance of checking the distribution of the
point clouds from which the norms are constructed.


  By pulsed-laser deposition epitaxial thin films of Sr_2FeMoO_6 have been pre-
pared on (100) SrTiO_3 substrates. Already for a deposition temperature of 320
C epitaxial growth is achieved. Depending on deposition parameters the films
show metallic or semiconducting behavior. At high (low) deposition temperature
the Fe,Mo sublattice has a rock-salt (random) structure. The metallic samples
have a large negative magnetoresistance which peaks at the Curie temperature.
The magnetic moment was determined to 4 mu_B per formula unit (f.u.), in
agreement with the expected value for an ideal ferrimagnetic arrangement. We
found an ordinary Hall coefficient of -6.01x10^{-10} m^3/As at 300 K,
corresponding to an electronlike charge-carrier density of 1.3 per Fe,Mo-pair.
In the semiconducting films the magnetic moment is reduced to 1 mu_B/f.u. due
to disorder in the Fe,Mo sublattice. In low fields an anomalous holelike
contribution dominates the Hall voltage, which vanishes at low temperatures for
the metallic films only.


  For any $\epsilon >0$ we show the existence of continuous periodic weak
solutions $v$ of the Euler equations which do not conserve the kinetic energy
and belong to the space $L^1_t (C_x^{\frac{1}{3}-\epsilon})$, namely $x\mapsto
v (x,t)$ is $(\frac{1}{3}-\epsilon)$-H\"older continuous in space at a.e. time
$t$ and the integral $\int [v(\cdot, t)]_{\frac{1}{3}-\epsilon} dt$ is finite.
A well-known open conjecture of L. Onsager claims that such solutions exist
even in the class $L^\infty_t (C_x^{\frac{1}{3}-\epsilon})$.


  In this short note, for countably infinite amenable group actions, we provide
topological proofs for the following results: Bowen topological entropy
(dimensional entropy) of the whole space equals the usual topological entropy
along tempered F{\o}lner sequences; the Hausdorff dimension of an amenable
subshift (for certain metric associated to some F{\o}lner sequence) equals its
topological entropy. This answers questions by Zheng and Chen (Israel Journal
of Mathematics 212 (2016), 895-911) and Simpson (Theory Comput. Syst. 56
(2015), 527-543).


  We formulate a phenomenological description of thin ferromagnetic layers with
inversion asymmetry where the single-domain magnetic dynamics experiences
magnon current-induced torques and leads to magnon-motive forces. We first
construct a phenomenological theory based on irreversible thermodynamics,
taking into account the symmetries of the system. Furthermore, we confirm that
these effects originate from Dzyaloshinskii-Moriya interactions from the
analysis based on the stochastic Landau-Lifshitz-Gilbert equation. Our
phenomenological results generalize to a general form of Dzyaloshinskii-Moriya
interactions and to other systems, such as pyrochlore crystals and chiral
magnets. Possible applications include spin current generation, magnetization
reversal and magnonic cooling.


  I give a brief presentation of recent results on the equivalence of BFKL and
CCFM small-x final states, and discuss their implications for phenomenology.


  We use a microscopic three-cluster model with the $\alpha+\alpha+n$
configuration to analyze with astrophysical interests the photodisintegration
cross section of $^9$Be. The valence neutron in $^9$Be is treated in the
molecular orbit model (MO), including continuum states by the box
discretization method. It is shown that good agreement is achieved with the
recently measured B(E1) transition probability from the ground state to the
first 1/2$^+$ state when the box size is enlarged, resulting in reasonable
reproduction of the experimental data for the photodisintegration cross
section. The Coulomb dissociation of $^9$Be is also discussed.