  Vista Variables in the Via Lactea (VVV) is an ESO Public Survey that is
performing a variability survey of the Galactic bulge and part of the inner
disk using ESO's Visible and Infrared Survey Telescope for Astronomy (VISTA).
The survey covers 520 deg^2 of sky area in the ZYJHK_S filters, for a total
observing time of 1929 hours, including ~ 10^9 point sources and an estimated ~
10^6 variable stars. Here we describe the current status of the VVV Survey, in
addition to a variety of new results based on VVV data, including light curves
for variable stars, newly discovered globular clusters, open clusters, and
associations. A set of reddening-free indices based on the ZYJHK_S system is
also introduced. Finally, we provide an overview of the VVV Templates Project,
whose main goal is to derive well-defined light curve templates in the near-IR,
for the automated classification of VVV light curves.


  Recent experiments have detected 4He supersolidity, but the observed
transition is rather unusual. In this paper, we describe a supersolid as a
normal lattice suffused by a Bose gas. With this approach, we can explain the
central aspects of the recent observations as well as previous experimental
results. We conclude that detailed balance is violated in part of the 4He phase
diagram, so that even in steady state contact with a thermal reservoir, the
material is not in equilibrium.


  We report on a theoretical study of the electronic, optical and
magneto-optical properties of digital ferromagnetic hetero-structures based on
$Mn$ $\delta$--doped $GaAs$. We consider different structures corresponding to
$Mn$ contents within the range 12-50\% and we study how the system changes as a
function of the doping concentration. Our first--principles approach includes
the spin-orbit interaction in a fully relativistic pseudopotential scheme and
the local fields effect in the description of the optical absorption. We show
that $Mn$ $\delta$-doped $GaAs$ shares many properties with the uniformly doped
$Ga_{1-x}Mn_xAs$ system, i.e. half-metallicity, similar absorption spectra, and
moderate Kerr rotation angles in the visible spectral region.


  The Surface Brightness Fluctuation (SBF) method is a powerful tool for
determining distances to early-type galaxies. The method measures the intrinsic
variance in a galaxy's surface brightness distribution to determine its
distance with an accuracy of about 5%. Here, we discuss the mathematical
formalism behind the SBF technique, its calibration, and the practicalities of
how measurements are performed. We review the various sources of uncertainties
that affect the method and discuss how they can be minimized or controlled
through careful observations and data analysis. The SBF technique has already
been successfully applied to a large number of galaxies and used for deriving
accurate constraints on the Hubble-Lema\^itre constant $H_0$. An approved JWST
program will greatly reduce the systematic uncertainties by establishing a firm
zero-point calibration using tip of the red giant branch (TRGB) distances. We
summarize the existing results and discuss the excellent potential of the SBF
method for improving the current constraints on $H_0$.


  To provide focus to my review of charm theory at the B-Physics and
CP-Violation conference, I consider theoretical issues related to possible
charm studies at B-factories. A few topics of interest to the author are
stressed -- rare decays, CP-violating asymmetries and ${\bar D}^0 - D^0$
mixing.


  Inductive logic programming, or relational learning, is a powerful paradigm
for machine learning or data mining. However, in order for ILP to become
practically useful, the efficiency of ILP systems must improve substantially.
To this end, the notion of a query pack is introduced: it structures sets of
similar queries. Furthermore, a mechanism is described for executing such query
packs. A complexity analysis shows that considerable efficiency improvements
can be achieved through the use of this query pack execution mechanism. This
claim is supported by empirical results obtained by incorporating support for
query pack execution in two existing learning systems.


  For the TREC-8 routing, one specific filter is built for each topic. Each
filter is a classifier trained to recognize the documents that are relevant to
the topic. When presented with a document, each classifier estimates the
probability for the document to be relevant to the topic for which it has been
trained. Since the procedure for building a filter is topic-independent, the
system is fully automatic.
  By making use of a sample of documents that have previously been evaluated as
relevant or not relevant to a particular topic, a term selection is performed,
and a neural network is trained. Each document is represented by a vector of
frequencies of a list of selected terms. This list depends on the topic to be
filtered; it is constructed in two steps. The first step defines the
characteristic words used in the relevant documents of the corpus; the second
one chooses, among the previous list, the most discriminant ones. The length of
the vector is optimized automatically for each topic. At the end of the term
selection, a vector of typically 25 words is defined for the topic, so that
each document which has to be processed is represented by a vector of term
frequencies.
  This vector is subsequently input to a classifier that is trained from the
same sample. After training, the classifier estimates for each document of a
test set its probability of being relevant; for submission to TREC, the top
1000 documents are ranked in order of decreasing relevance.


  This paper aims to design robust Edge Intelligence using semantic
communication for time-critical IoT applications. We systematically analyze the
effect of image DCT coefficients on inference accuracy and propose the
channel-agnostic effectiveness encoding for offloading by transmitting the most
meaningful task data first. This scheme can well utilize all available
communication resource and strike a balance between transmission latency and
inference accuracy. Then, we design an effectiveness decoding by implementing a
novel image augmentation process for convolutional neural network (CNN)
training, through which an original CNN model is transformed into a Robust CNN
model. We use the proposed training method to generate Robust MobileNet-v2 and
Robust ResNet-50. The proposed Edge Intelligence framework consists of the
proposed effectiveness encoding and effectiveness decoding. The experimental
results show that the effectiveness decoding using the Robust CNN models
perform consistently better under various image distortions caused by channel
errors or limited communication resource. The proposed Edge Intelligence
framework using semantic communication significantly outperforms the
conventional approach under latency and data rate constraints, in particular,
under ultra stringent deadlines and low data rate.


  Influence Maximization (IM), which aims to select a set of users from a
social network to maximize the expected number of influenced users, has
recently received significant attention for mass communication and commercial
marketing. Existing research efforts dedicated to the IM problem depend on a
strong assumption: the selected seed users are willing to spread the
information after receiving benefits from a company or organization. In
reality, however, some seed users may be reluctant to spread the information,
or need to be paid higher to be motivated. Furthermore, the existing IM works
pay little attention to capture user's influence propagation in the future
period as well. In this paper, we target a new research problem, named
Reconnecting Top-l Relationships (RTlR) query, which aims to find l number of
previous existing relationships but being stranged later, such that
reconnecting these relationships will maximize the expected benefit of
influenced users by the given group in a future period. We prove that the RTlR
problem is NP-hard. An efficient greedy algorithm is proposed to answer the
RTlR queries with the influence estimation technique and the well-chosen link
prediction method to predict the near future network structure. We also design
a pruning method to reduce unnecessary probing from candidate edges. Further, a
carefully designed order-based algorithm is proposed to accelerate the RTlR
queries. Finally, we conduct extensive experiments on real-world datasets to
demonstrate the effectiveness and efficiency of our proposed methods.


  The appearance of the same object may vary in different scene images due to
perspectives and occlusions between objects. Humans can easily identify the
same object, even if occlusions exist, by completing the occluded parts based
on its canonical image in the memory. Achieving this ability is still a
challenge for machine learning, especially under the unsupervised learning
setting. Inspired by such an ability of humans, this paper proposes a
compositional scene modeling method to infer global representations of
canonical images of objects without any supervision. The representation of each
object is divided into an intrinsic part, which characterizes globally
invariant information (i.e. canonical representation of an object), and an
extrinsic part, which characterizes scene-dependent information (e.g., position
and size). To infer the intrinsic representation of each object, we employ a
patch-matching strategy to align the representation of a potentially occluded
object with the canonical representations of objects, and sample the most
probable canonical representation based on the category of object determined by
amortized variational inference. Extensive experiments are conducted on four
object-centric learning benchmarks, and experimental results demonstrate that
the proposed method not only outperforms state-of-the-arts in terms of
segmentation and reconstruction, but also achieves good global object
identification performance.


  A spinor theory on a space with linear Lie type noncommutativity among
spatial coordinates is presented. The model is based on the Fourier space
corresponding to spatial coordinates, as this Fourier space is commutative.
When the group is compact, the real space exhibits lattice characteristics (as
the eigenvalues of space operators are discrete), and the similarity of such a
\emph{lattice} with ordinary lattices is manifested, among other things, in a
phenomenon resembling the famous \emph{fermion doubling} problem. A projection
is introduced to make the dynamical number of spinors equal to that
corresponding to the ordinary space. The actions for free and interacting
spinors (with Fermi-like interactions) are presented. The Feynman rules are
extracted and 1-loop corrections are investigated.


  The existing large scale weak lensing surveys typically reserve the best
seeing conditions for a certain optical band to minimize shape measurement
errors and maximize the number of usable background galaxies. This is because
most popular shear measurement methods contain explicit or implicit thresholds
on the galaxy-to-PSF (point spread function) size ratio, below which their
shape measurement errors increase abruptly. Using the DECaLS data, we have
previously demonstrated that the Fourier\_Quad method performs very well on
poorly resolved galaxy images in general. It is therefore a ready tool for
shear measurement with multi-band images regardless of their seeing conditions.
In this paper, we apply the Fourier\_Quad pipeline on the multi-band images
from the third public data release of the Hyper Suprime-Cam Subaru Strategic
Program. We show that the shear catalogs from the five optical bands
(g/r/i/z/y) all pass the field-distortion test with very high accuracy. Using
the LOWZ and CMASS galaxies as foreground lenses, we show that the errorbar in
the galaxy-galaxy lensing measurement can be decreased by factors around 15\%
by combining shear catalogs from different bands. This indicates that it is
worthful to do multi-bands shear measurements for a better shear statistics.


  With a rigorous renormalization group approach, we study the pressure of the
two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless
transition line, i.e. the boundary of the dipole region in the
activity-temperature phase-space.


  The interaction between edge dislocations and carbon nanotubes (CNTs)
embedded into an Al matrix is investigated. Both pristine and Ni-coated CNTs
are considered. It is demonstrated that the embedded CNTs lead to a flow stress
contribution equivalent to that of an array of non-shearable inclusions that
are by-passed via the Orowan mechanism. The strain hardening mechanism
associated with multiple dislocation passes shows, however, characteristic
differences from the Orowan picture that indicate that the embedded CNTs behave
analogous to embedded voids.


  We present for the first time a detailed spectroscopic study of chemical
element abundances of metal-poor RR Lyrae stars in the Large and Small
Magellanic Cloud (LMC and SMC). Using the MagE echelle spectrograph at the 6.5m
Magellan telescopes, we obtain medium resolution (R ~ 2000 - 6000) spectra of
six RR Lyrae stars in the LMC and three RR Lyrae stars in the SMC. These stars
were chosen because their previously determined photometric metallicities were
among the lowest metallicities found for stars belonging to the old populations
in the Magellanic Clouds. We find the spectroscopic metallicities of these
stars to be as low as [Fe/H]_{spec} = -2.7dex, the lowest metallicity yet
measured for any star in the Magellanic Clouds. We confirm that for metal-poor
stars, the photometric metallicities from the Fourier decomposition of the
lightcurves are systematically too high compared to their spectroscopic
counterparts. However, for even more metal-poor stars below [Fe/H]_{phot} <
-2.8dex this trend is reversed and the spectroscopic metallicities are
systematically higher than the photometric estimates. We are able to determine
abundance ratios for ten chemical elements, which extend the abundance
measurements of chemical elements for RR Lyrae stars in the Clouds beyond
[Fe/H] for the first time. For the overall [alpha/Fe] ratio, we obtain an
overabundance of 0.36dex, which is in very good agreement with results from
metal-poor stars in the Milky Way halo as well as from the metal-poor tail in
dwarf spheroidal galaxies. Comparing the abundances with those of the stars in
the Milky Way halo we find that the abundance ratios of stars of both
populations are consistent with another. Therefore we conclude that from a
chemical point of view early contributions from Magellanic-type galaxies to the
formation of the Galactic halo as claimed in cosmological models are plausible.


  Robotic assistance for experimental manipulation in the life sciences is
expected to enable favorable outcomes, regardless of the skill of the
scientist. Experimental specimens in the life sciences are subject to
individual variability hence require intricate algorithms for successful
autonomous robotic control. As a use case, we are studying the creation of
cranial windows in mice. This operation requires the removal of an
8-mm-circular patch of the skull, which is approximately 300 um thick, but the
shape and thickness of the mouse skull significantly varies depending on the
strain of mouse, sex, and age. In this work, we propose an autonomous robotic
drilling method with no offline planning, consisting of a trajectory planning
block with execution-time feedback with completion level recognition based on
image and force information. The force information allows for completion-level
resolution to increase 10 fold. We evaluate the proposed method in two ways.
First, in an eggshell drilling task and achieved a success rate of 95% and
average drilling time of 7.1 min out of 20 trials. Second, in postmortem mice
and with a success rate of 70% and average drilling time of 9.3 min out of 20
trials.


  Linear layouts are a graph visualization method that can be used to capture
an entry pattern in an adjacency matrix of a given graph. By reordering the
node indices of the original adjacency matrix, linear layouts provide knowledge
of latent graph structures. Conventional linear layout methods commonly aim to
find an optimal reordering solution based on predefined features of a given
matrix and loss function. However, prior knowledge of the appropriate features
to use or structural patterns in a given adjacency matrix is not always
available. In such a case, performing the reordering based on data-driven
feature extraction without assuming a specific structure in an adjacency matrix
is preferable. Recently, a neural-network-based matrix reordering method called
DeepTMR has been proposed to perform this function. However, it is limited to a
two-mode reordering (i.e., the rows and columns are reordered separately) and
it cannot be applied in the one-mode setting (i.e., the same node order is used
for reordering both rows and columns), owing to the characteristics of its
model architecture. In this study, we extend DeepTMR and propose a new one-mode
linear layout method referred to as AutoLL. We developed two types of neural
network models, AutoLL-D and AutoLL-U, for reordering directed and undirected
networks, respectively. To perform one-mode reordering, these AutoLL models
have specific encoder architectures, which extract node features from an
observed adjacency matrix. We conducted both qualitative and quantitative
evaluations of the proposed approach, and the experimental results demonstrate
its effectiveness.


  We employ the ADHM method to derive the moduli space of two instantons in
U(1) gauge theory on a noncommutative space. We show by an explicit
hyperK\"ahler quotient construction that the relative metric of the moduli
space of two instantons on $R^4$ is the Eguchi-Hanson metric and find a unique
threshold bound state. For two instantons on $R^3\times S^1$, otherwise known
as calorons, we give the asymptotic metric and conjecture a completion. We
further discuss the relationship of caloron moduli spaces of A, D and E groups
to the Coulomb branches of three dimensional gauge theory. In particular, we
show that the Coulomb branch of SU(2) gauge group with a single massive adjoint
hypermultiplet coincides with the above two caloron moduli space.


  We present the BFKL equation as a reggeon Bethe-Salpeter equation and discuss
the use of reggeon diagrams to obtain 2-2 and 2-4 reggeon interactions at
$O(g^4)$. We then outline the dispersion theory basis of multiparticle
$j$-plane analysis and describe how a gauge theory can be studied by combining
Ward identity constraints with the group structure of reggeon interactions. The
derivation of gluon reggeization, the $O(g^2)$ BFKL kernel, and $O(g^4)$
corrections, is described within this formalism. We give an explicit expression
for the $O(g^4)$ forward ``parton'' kernel in terms of logarithms and evaluate
the eigenvalues. A separately infra-red finite component with a holomorphically
factorizable spectrum is shown to be present and conjectured to be a new
leading-order partial-wave amplitude. A comparison is made with Kirschner's
discussion of $O(g^4)$ contributions from the multi-Regge effective action.


  We present the results of a Spitzer search for obscured AGN in the Chandra
Deep Field-North, using both radio-excess and mid-infrared power-law selection.
AGN selected via the former technique tend to lie at z ~ 1, have SEDs dominated
by the 1.6 micron stellar bump, and have Seyfert-like X-ray luminosities (when
detected in the X-ray). In contrast, the IRAC (3.6-8.0 micron) power-law
selected AGN lie at higher redshifts of z ~ 2, and comprise a significant
fraction of the most X-ray luminous AGN in the CDF-N. While there is almost no
overlap in the AGN samples selected via these two methods, their X-ray
detection fractions are very similar. Only 40% and 55% of the radio-excess and
power-law samples are detected in the 2 Ms X-ray catalog, respectively. The
majority of the AGN selected via both methods are consistent with being
obscured (N_H > 10^(22) cm^-2), but not Compton-thick (N_H > 10^(24) cm^-2),
although Compton-thick candidates exist in both samples. We place an upper
limit of <82% (or < 4:1) on the obscured fraction of the power-law sample,
consistent with predictions from the cosmic X-ray background. The sources
selected via the power-law criteria comprise a subset of AGN selected via other
IRAC color-color cuts. While smaller in number than the color-selected samples
in the deep fields, the power-law sample suffers from less contamination by
star-forming galaxies.


  An empirical investigation of active/continuous authentication for
smartphones is presented in this paper by exploiting users' unique application
usage data, i.e., distinct patterns of use, modeled by a Markovian process.
Variations of Hidden Markov Models (HMMs) are evaluated for continuous user
verification, and challenges due to the sparsity of session-wise data, an
explosion of states, and handling unforeseen events in the test data are
tackled. Unlike traditional approaches, the proposed formulation does not
depend on the top N-apps, rather uses the complete app-usage information to
achieve low latency. Through experimentation, empirical assessment of the
impact of unforeseen events, i.e., unknown applications and unforeseen
observations, on user verification is done via a modified edit-distance
algorithm for simple sequence matching. It is found that for enhanced
verification performance, unforeseen events should be incorporated in the
models by adopting smoothing techniques with HMMs. For validation, extensive
experiments on two distinct datasets are performed. The marginal smoothing
technique is the most effective for user verification in terms of equal error
rate (EER) and with a sampling rate of 1/30s^{-1} and 30 minutes of historical
data, and the method is capable of detecting an intrusion within ~2.5 minutes
of application use.


  In this sequel to arXiv:0905.3327, we continue to study the congruence
properties of the alternating version of multiple harmonic sums. As contrast to
the study of multiple harmonic sums where Bernoulli numbers and Bernoulli
polynomials play the key roles, in the alternating setting the Euler numbers
and the Euler polynomials are also essential.


  The issues raised in the preceding comment of Bourges et al.
[arXiv:1710.08173, Phys. Rev. B 98, 016501 (2018)] are shown to be unfounded.
We highlight the complications caused by inhomogeneous beam polarization that
can occur when using polarized neutron diffraction to detect small magnetic
moments.


  Solids are distinguished from fluids by their ability to resist shear. In
traditional solids, the resistance to shear is associated with the emergence of
broken translational symmetry as exhibited by a non-uniform density pattern. In
this work, we focus on the emergence of shear-rigidity in a class of solids
where this paradigm is challenged. Dry granular materials have no energetically
or entropically preferred density modulations. We show that, in contrast to
traditional solids, the emergence of shear rigidity in these granular solids is
a collective process, which is controlled solely by boundary forces, the
constraints of force and torque balance, and the positivity of the contact
forces. We develop a theoretical framework based on these constraints, which
connects rigidity to broken translational symmetry in the space of forces, not
positions of grains. We apply our theory to experimentally generated
shear-jammed (SJ) states and show that these states are indeed characterized by
a persistent, non-uniform density modulation in force space, which emerges at
the shear-jamming transition.


  The dynamics of a hadronizing quark matter drop is investigated with a
hybrid-like model, which takes into account equilibrium as well as
non-equilibrium features of the process. We study the the particle rates from
the hadronizing plasma, which have to be put in relation to the whole time
evolution of the system. The impact of finite-size effects on the distillation
process is considered. $H^0$-Dibaryon yields are estimated. Microscopic
calculations of hypercluster formation at AGS and SPS are presented.


  We show that information on the probability density of local fluctuations can
be obtained from a numerical renormalisation group calculation of a reduced
density matrix. We apply this approach to the Anderson-Holstein impurity model
to calculate the ground state probability density $\rho(x)$ for the
displacement $x$ of the local oscillator. From this density we can deduce an
effective local potential for the oscillator and compare its form with that
obtained from a semiclassical approximation as a function of the coupling
strength. The method is extended to infinite dimensional Holstein-Hubbard model
using dynamical mean field theory. We use this approach to compare the
probability densities for the displacement of the local oscillator in the
normal, antiferromagnetic and charge ordered phases.


  Single-walled carbon nanotube encapsulated in boron nitrite nanotube
(SWCNT@BNNT) is a novel nanomaterial with a one-dimensional van der Waals
(1D-vdW) heterostructure. In this paper, we demonstrated that the SWCNT@BNNT
has an enhanced optical power tolerance compared to that of the pristine SWCNT
while exhibiting an optical saturable absorption properties. Under optical
power intensity of 13kW/cm2, the lifetime of the SWCNT@BNNT is found to be
2,270 times longer than SWCNT for 1% degradation in absorbance. A short-cavity
mode-locked laser with a high repetition rate of 1 GHz has been realized using
the SWCNT@BNNT as the saturable absorber. We have shown that the technique of
fabricating nanomaterial with a 1D-vdW heterostructure can modify and enhance
the optical properties of the encapsulated nanomaterials.


  Single-pixel imaging (SPI) is a potential computational imaging technique
which produces image by solving an illposed reconstruction problem from few
measurements captured by a single-pixel detector. Deep learning has achieved
impressive success on SPI reconstruction. However, previous poor reconstruction
performance and impractical imaging model limit its real-world applications. In
this paper, we propose a deep unfolding network with hybrid-attention
Transformer on Kronecker SPI model, dubbed HATNet, to improve the imaging
quality of real SPI cameras. Specifically, we unfold the computation graph of
the iterative shrinkagethresholding algorithm (ISTA) into two alternative
modules: efficient tensor gradient descent and hybrid-attention multiscale
denoising. By virtue of Kronecker SPI, the gradient descent module can avoid
high computational overheads rooted in previous gradient descent modules based
on vectorized SPI. The denoising module is an encoder-decoder architecture
powered by dual-scale spatial attention for high- and low-frequency aggregation
and channel attention for global information recalibration. Moreover, we build
a SPI prototype to verify the effectiveness of the proposed method. Extensive
experiments on synthetic and real data demonstrate that our method achieves the
state-of-the-art performance. The source code and pre-trained models are
available at https://github.com/Gang-Qu/HATNet-SPI.


  Bicycle infrastructure networks must meet the needs of cyclists to position
cycling as a viable transportation choice in cities. In particular, protected
infrastructure should be planned cohesively for the whole city and spacious
enough to accommodate all cyclists safely and prevent cyclist congestion -- a
common problem in cycling cities like Copenhagen. Here, we devise an adaptive
method for optimal bicycle network design and for evaluating congestion
criticalities on bicycle paths. The method goes beyond static network measures,
using computationally efficient adaptation rules inspired by Optimal Transport
on the dynamically updating multilayer network of roads and protected bicycle
lanes. Street capacities and cyclist flows reciprocally control each other to
optimally accommodate cyclists on streets with one control parameter that
dictates the preference of bicycle infrastructure over roads. Applying our
method to Copenhagen confirms that the city's bicycle network is generally
well-developed. However, we are able to identify the network's bottlenecks, and
we find, at a finer scale, disparities in network accessibility and
criticalities between different neighborhoods. Our model and results are
generalizable beyond this particular case study to serve as a scalable and
versatile tool for aiding urban planners in designing cycling-friendly cities.


  Multi-role dialogue understanding comprises a wide range of diverse tasks
such as question answering, act classification, dialogue summarization etc.
While dialogue corpora are abundantly available, labeled data, for specific
learning tasks, can be highly scarce and expensive. In this work, we
investigate dialogue context representation learning with various types
unsupervised pretraining tasks where the training objectives are given
naturally according to the nature of the utterance and the structure of the
multi-role conversation. Meanwhile, in order to locate essential information
for dialogue summarization/extraction, the pretraining process enables external
knowledge integration. The proposed fine-tuned pretraining mechanism is
comprehensively evaluated via three different dialogue datasets along with a
number of downstream dialogue-mining tasks. Result shows that the proposed
pretraining mechanism significantly contributes to all the downstream tasks
without discrimination to different encoders.


  D. Prasad showed that the sign of a self-dual representation of a finite or
$p$-adic reductive group is often detected by a central element. We study the
extension of his results to some more general situations and make some
observations about the consequences of his results.


  In this paper, we propose an advanced methodology for the detection of 3D
objects and precise estimation of their spatial positions from a single image.
Unlike conventional frameworks that rely solely on center-point and dimension
predictions, our research leverages a deep convolutional neural network-based
3D object weighted orientation regression paradigm. These estimates are then
seamlessly integrated with geometric constraints obtained from a 2D bounding
box, resulting in derivation of a comprehensive 3D bounding box. Our novel
network design encompasses two key outputs. The first output involves the
estimation of 3D object orientation through the utilization of a
discrete-continuous loss function. Simultaneously, the second output predicts
objectivity-based confidence scores with minimal variance. Additionally, we
also introduce enhancements to our methodology through the incorporation of
lightweight residual feature extractors. By combining the derived estimates
with the geometric constraints inherent in the 2D bounding box, our approach
significantly improves the accuracy of 3D object pose determination, surpassing
baseline methodologies. Our method is rigorously evaluated on the KITTI 3D
object detection benchmark, demonstrating superior performance.


  In 1997, Liberati and Pollifrone in Phys. Rev. D56 (1997) 6458
(hep-th/9708014) achieved a new formulation of the Bekenstein-Hawking formula,
where the entropy and the Euler characteristic are related by $S=\chi A/8$. In
this work we present a relation between the low-energy absorption cross section
for minimally coupled fermions and the Euler characteristic of
(3+1)-dimensional spherically symmetric black holes, i.e. $\sigma =\chi
g_h^{-1}A$. Based on the relation, using the Gauss--Bonnet--Chern theorem and
the $\phi$-mapping method, an absorption cross section density is introduced to
describe the topology of the absorption cross section. It is shown that the
absorption cross section and its density are determined by the singularities of
the timelike Killing vector field of the spacetime and these singularities
carry the topological numbers, Hopf indices and Brouwer degrees, naturally.


  We devise a systematic method to determine the Fisher information required
for resolving two incoherent point sources with a diffraction-limited linear
imaging device. The resulting Cram\'er-Rao bound gives the lowest variance
achievable for an unbiased estimator. When only intensity in the image plane is
recorded, this bound diverges as the separation between the sources tends to
zero, an effect which has been dubbed as Rayleigh's curse. However, this curse
can be lifted using suitable coherent measurements. In particular, we determine
a class of measurements that can be easily implemented as projections on the
orthogonalised derivatives of the point spread function of the system.


  INTRODUCTION: Previous studies have applied normative modeling on a single
neuroimaging modality to investigate Alzheimer Disease (AD) heterogeneity. We
employed a deep learning-based multimodal normative framework to analyze
individual-level variation across ATN (amyloid-tau-neurodegeneration) imaging
biomarkers.
  METHODS: We selected cross-sectional discovery (n = 665) and replication
cohorts (n = 430) with available T1-weighted MRI, amyloid and tau PET.
Normative modeling estimated individual-level abnormal deviations in
amyloid-positive individuals compared to amyloid-negative controls. Regional
abnormality patterns were mapped at different clinical group levels to assess
intra-group heterogeneity. An individual-level disease severity index (DSI) was
calculated using both the spatial extent and magnitude of abnormal deviations
across ATN.
  RESULTS: Greater intra-group heterogeneity in ATN abnormality patterns was
observed in more severe clinical stages of AD. Higher DSI was associated with
worse cognitive function and increased risk of disease progression.
  DISCUSSION: Subject-specific abnormality maps across ATN reveal the
heterogeneous impact of AD on the brain.


  Let M be a compact Riemannian manifold with smooth boundary. We obtain the
exact long time asymptotic behaviour of the heat kernel on abelian coverings of
M with mixed Dirichlet and Neumann boundary conditions. As an application, we
study the long time behaviour of the abelianized winding of reflected Brownian
motions in M. In particular, we prove a Gaussian type central limit theorem
showing that when rescaled appropriately, the fluctuations of the abelianized
winding are normally distributed with an explicit covariance matrix.


  The FASTSUM Collaboration has developed a comprehensive research programme in
thermal QCD using 2+1 flavour, anisotropic ensembles. In this talk, we
summarise some of our recent results including thermal hadron spectrum
calculations using our ``Generation 2L'' ensembles which have pion masses of
239(1) MeV. These include open charm mesons and charm baryons. We also
summarise our work using the Backus Gilbert approach to determining the
spectral function of the NRQCD bottomonium system. Finally, we review our
determination of the interquark potential in the same system, but using our
``Generation 2'' ensembles which have heavier pion masses of 384(4) MeV.


  The techniques used in this paper are based on the exterior calculus of
Maurer-Cartan forms, and Weingarten surfaces are used to illustrate the methods
that apply to quadratic exterior equations with constant coefficients.
Isothermic {\it surfaces of constant astigmatism} (non-linear Weingarten
surfaces whose difference of principal curvatures is a constant) are shown to
represent dual surfaces of isothermic surfaces which satisfy the relation $H +
\alpha K = 0$.


  The purpose of this paper is to study the relation between the $C^0$-topology
and the topology induced by the spectral norm on the group of Hamiltonian
diffeomorphisms of a closed symplectic manifold. Following the approach of
Buhovsky-Humili\`ere-Seyfaddini, we prove the $C^0$-continuity of the spectral
norm for complex projective spaces and negative monotone symplectic manifolds.
The case of complex projective spaces provides an alternative approach to the
$C^0$-continuity of the spectral norm proven by Shelukhin. We also prove a
partial $C^0$-continuity of the spectral norm for rational symplectic
manifolds. Some applications such as the Arnold conjecture in the context of
$C^0$-symplectic topology are also discussed.


  Frugal computing is becoming an important topic for environmental reasons. In
this context, several techniques have been proposed to reduce the storage of
scientific data by dedicated compression methods specially tailored for arrays
of floating-point numbers. While these techniques are quite efficient to save
memory, they introduce additional computations to compress and decompress the
data before processing them. In this article, we introduce a new lossy,
fixed-rate compression technique for 2D-arrays of floating-point numbers which
allows one to compute directly on the compressed data, without decompressing
them. We obtain important speedups since less operations are needed to compute
among the compressed data and since no decompression and re-compression is
needed. More precisely, our technique makes it possible to perform basic linear
algebra operations such as addition, multiplication by a constant among
compressed matrices and dot product and matrix multiplication among partly
uncompressed matrices. This work has been implemented into a tool named blaz
and a comparison with the well-known compressor zfp in terms of execution-time
and accuracy is presented.


  We study the prospects for extracting detailed statistical properties of the
Sunyaev-Zel'dovich (SZ) effect associated with large scale structure using
upcoming multifrequency CMB experiments. The greatest obstacle to detecting the
large-angle signal is the confusion noise provided by the primary anisotropies
themselves, and to a lesser degree galactic and extragalactic foregrounds. We
employ multifrequency subtraction techniques and the latest foregrounds models
to determine the detection threshold for the Boomerang, MAP (several microK)
and Planck CMB (sub microK) experiments. Calibrating a simplified biased-tracer
model of the gas pressure off recent hydrodynamic simulations, we estimate the
SZ power spectrum, skewness and bispectrum through analytic scalings and N-body
simulations of the dark matter. We show that the Planck satellite should be
able to measure the SZ effect with sufficient precision to determine its power
spectrum and higher order correlations, e.g. the skewness and bispectrum.
Planck should also be able to detect the cross correlation between the SZ and
gravitational lensing effect in the CMB. Detection of these effects will help
determine the properties of the as yet undetected gas, including the manner in
which the gas pressure traces the dark matter.


  Extraction of relevant pathological terms from radiology reports is important
for correct image label generation and disease population studies. In this
letter, we compare the performance of some known application program interface
(APIs) for the task of thoracic abnormality extraction from radiology reports.
We explored several medical domain specific annotation tools like Medical Text
Indexer(MTI) with Non-MEDLINE and Mesh On Demand(MOD) options and generic
Natural Language Understanding (NLU) API provided by the IBM cloud. Our results
show that although MTI and MOD are intended for extracting medical terms, their
performance is worst compared to generic extraction API like IBM NLU. Finally,
we trained a DNN-based Named Entity Recognition (NER) model to extract the key
concept words from radiology reports. Our model outperforms the medical
specific and generic API performance by a large margin. Our results demonstrate
the inadequacy of generic APIs for pathology extraction task and establish the
importance of domain specific model training for improved results. We hope that
these results motivate the research community to release larger de-identified
radiology reports corpus for building high accuracy machine learning models for
the important task of pathology extraction.


  We consider $N\times N$ Hermitian or symmetric random matrices with
independent entries. The distribution of the $(i,j)$-th matrix element is given
by a probability measure $\nu_{ij}$ whose first two moments coincide with those
of the corresponding Gaussian ensemble. We prove that the joint probability
distribution of the components of eigenvectors associated with eigenvalues
close to the spectral edge agrees with that of the corresponding Gaussian
ensemble. For eigenvectors associated with bulk eigenvalues, the same
conclusion holds provided the first four moments of the distribution $\nu_{ij}$
coincide with those of the corresponding Gaussian ensemble. More generally, we
prove that the joint eigenvector-eigenvalue distributions near the spectral
edge of two generalized Wigner ensembles agree, provided that the first two
moments of the entries match and that one of the ensembles satisfies a level
repulsion estimate. If in addition the first four moments match then this
result holds also in the bulk.


  Building on work by Alishahi-Dowlin, we extract a new knot invariant $\lambda
\ge 0$ from universal Khovanov homology. While $\lambda$ is a lower bound for
the unknotting number, in fact more is true: $\lambda$ is a lower bound for the
proper rational unknotting number (the minimal number of rational tangle
replacements preserving connectivity necessary to relate a knot to the unknot).
Moreover, we show that for all $n \ge 0$, there exists a knot K with
$\lambda(K) = n$. Along the way, following Thompson, we compute the Bar-Natan
complexes of rational tangles.


  We investigate the usage of convolutional neural networks (CNNs) for the slot
filling task in spoken language understanding. We propose a novel CNN
architecture for sequence labeling which takes into account the previous
context words with preserved order information and pays special attention to
the current word with its surrounding context. Moreover, it combines the
information from the past and the future words for classification. Our proposed
CNN architecture outperforms even the previously best ensembling recurrent
neural network model and achieves state-of-the-art results with an F1-score of
95.61% on the ATIS benchmark dataset without using any additional linguistic
knowledge and resources.


  The Strong Cosmic Censorship conjecture states that for generic initial data
to Einstein's field equations, the maximal globally hyperbolic development is
inextendible. We prove this conjecture in the class of orthogonal Bianchi class
B perfect fluids and vacuum spacetimes, by showing that unboundedness of
certain curvature invariants such as the Kretschmann scalar is a generic
property. The only spacetimes where this scalar remains bounded exhibit local
rotational symmetry or are of plane wave equilibrium type.
  We further investigate the qualitative behaviour of solutions towards the
initial singularity. To this end, we work in the expansion-normalised variables
introduced by Hewitt-Wainwright and show that a set of full measure, which is
also a countable intersection of open and dense sets in the state space, yields
convergence to a specific subarc of the Kasner parabola. We further give an
explicit construction enabling the translation between these variables and
geometric initial data to Einstein's equations.


  Comparing the parameterized post-Newtonian parameter $\gamma$ values for
different types of particles, or the same type of particles with different
energies is an important method to test the Einstein Equivalence Principle
(EEP). Assuming that the observed time delays are dominated by the
gravitational potential of the Laniakea supercluster of galaxies, better
results of EEP constraints can be obtained. In this paper, we apply photons
from three kinds of cosmic transients, including TeV blazars, gamma-ray bursts
as well as fast radio bursts to constrain EEP. With a gravitational field far
more stronger than a single galaxy, we obtain 4--5 orders of magnitude more
stringent than the pervious results.


  Let us have in S^2, R^2 or H^2 a pair of convex bodies, for S^2 different
from S^2, such that the intersections of any congruent copies of them are
centrally symmetric. Then our bodies are congruent circles. If the
intersections of any congruent copies of them are axially symmetric, then our
bodies are circles.
  Let us have in S^2, R^2 or H^2 proper closed convex subsets K,L with interior
points, such that the numbers of the connected components of the boundaries of
K and L are finite. If the intersections of any congruent copies of K and L are
centrally symmetric, then K and L are congruent circles, or, for R^2, parallel
strips. We describe all pairs of such subsets K,L, whose any congruent copies
have an intersection with axial symmetry. For S^2, R^2 and H^2 there are 1, 5
and 9 cases, resp.
  Let us have in S^d, R^d or H^d proper closed convex C^2_+ subsets K,L with
interior points, such that all sufficiently small intersections of their
congruent copies are symmetric w.r.t. a particular hyperplane. Then the
boundary components of both K and L are congruent, and each of them is a
sphere, a parasphere or a hypersphere.
  Let us have a pair of convex bodies in S^d, R^d or H^d, which have at any
boundary points supporting spheres, for S^d of radius less than \pi/2. If the
convex hull of the union of any congruent copies of these bodies is centrally
symmetric, then our bodies are congruent balls, for S^d of radius less than
\pi/2. An analogous statement holds for symmetry w.r.t. a particular
hyperplane. For d=2 suppose the existence of the above supporting circles, for
S^2 of radius less than \pi/2, and for S^2 smoothness of K and L. If we suppose
axial symmetry of all the above convex hulls, then our bodies are circles, for
S^2 of radii less than \pi/2.


  We consider delayed sums of the type S_{n+an}-Sn where a_n is possibly a
positive integer valued random variable satisfying certain conditions and S_n
is the sum of independent random variables X_n with distribution functions F_n
in {G_1, G_2} . We study the limiting behavior of delayed sums and prove laws
of the iterated logarithm of Chover- type. These results extend the results in
Vasudeva and Divanji (1992) and Chen (2008).


  The generation of photon pairs in single quantum dots is based on a process
that is, in its nature, deterministic. However, an efficient extraction of
these photon pairs from a high-index semiconductor host material requires
engineering of the photonic environment. We report on a micropillar-based
device featuring an extraction efficiency of 69.4(10)$\%$ that is achieved by
harnessing a broadband operation suitable for extraction of photon pairs
emitted from a single quantum dot. Opposing the approaches that rely solely on
Purcell enhancement to realize the enhancement of the extraction efficiency,
our solution exploits a suppression of the emission into the modes other than
the cavity mode. Our technological implementation requires modest fabrication
effort enabling higher device yields that can be scaled up to meet the growing
needs of quantum technologies. Furthermore, the design of the device can be
further optimized to allow for an extraction efficiency of 85$\%$.


  In this paper, Auslander-Reiten triangles are introduced into algebraic
topology, and it is proved that their existence characterizes Poincare duality
spaces.
  Invariants in the form of quivers are also introduced, and Auslander-Reiten
triangles and quivers over spheres are computed.
  The quiver over the d-dimensional sphere turns out to consist of d-1
components, each isomorphic to ZA_{\infty}. So quivers are sufficiently
sensitive invariants to tell spheres of different dimension apart.


  Pool-based active learning (AL) is a promising technology for increasing
data-efficiency of machine learning models. However, surveys show that
performance of recent AL methods is very sensitive to the choice of dataset and
training setting, making them unsuitable for general application. In order to
tackle this problem, the field Learning Active Learning (LAL) suggests to learn
the active learning strategy itself, allowing it to adapt to the given setting.
In this work, we propose a novel LAL method for classification that exploits
symmetry and independence properties of the active learning problem with an
Attentive Conditional Neural Process model. Our approach is based on learning
from a myopic oracle, which gives our model the ability to adapt to
non-standard objectives, such as those that do not equally weight the error on
all data points. We experimentally verify that our Neural Process model
outperforms a variety of baselines in these settings. Finally, our experiments
show that our model exhibits a tendency towards improved stability to changing
datasets. However, performance is sensitive to choice of classifier and more
work is necessary to reduce the performance the gap with the myopic oracle and
to improve scalability. We present our work as a proof-of-concept for LAL on
nonstandard objectives and hope our analysis and modelling considerations
inspire future LAL work.


  Motivated by applications of multi-agent learning in noisy environments, this
paper studies the robustness of gradient-based learning dynamics with respect
to disturbances. While disturbances injected along a coordinate corresponding
to any individual player's actions can always affect the overall learning
dynamics, a subset of players can be disturbance decoupled---i.e., such
players' actions are completely unaffected by the injected disturbance. We
provide necessary and sufficient conditions to guarantee this property for
games with quadratic cost functions, which encompass quadratic one-shot
continuous games, finite-horizon linear quadratic (LQ) dynamic games, and
bilinear games. Specifically, disturbance decoupling is characterized by both
algebraic and graph-theoretic conditions on the learning dynamics, the latter
is obtained by constructing a game graph based on gradients of players' costs.
For LQ games, we show that disturbance decoupling imposes constraints on the
controllable and unobservable subspaces of players. For two player bilinear
games, we show that disturbance decoupling within a player's action coordinates
imposes constraints on the payoff matrices. Illustrative numerical examples are
provided.


  Generative AI tools such as chatGPT are poised to change the way people
engage with online information. Recently, Microsoft announced their "new Bing"
search system which incorporates chat and generative AI technology from OpenAI.
Google has announced plans to deploy search interfaces that incorporate similar
types of technology. These new technologies will transform how people can
search for information. The research presented here is an early investigation
into how people make use of a generative AI chat system (referred to simply as
chat from here on) as part of a search process, and how the incorporation of
chat systems with existing search tools may effect users search behaviors and
strategies.
  We report on an exploratory user study with 10 participants who used a
combined Chat+Search system that utilized the OpenAI GPT-3.5 API and the Bing
Web Search v5 API. Participants completed three search tasks. In this pre-print
paper of preliminary results, we report on ways that users integrated AI chat
into their search process, things they liked and disliked about the chat
system, their trust in the chat responses, and their mental models of how the
chat system generated responses.


  The success of Transformer models has pushed the deep learning model scale to
billions of parameters. Due to the limited memory resource of a single GPU,
However, the best practice for choosing the optimal parallel strategy is still
lacking, since it requires domain expertise in both deep learning and parallel
computing.
  The Colossal-AI system addressed the above challenge by introducing a unified
interface to scale your sequential code of model training to distributed
environments. It supports parallel training methods such as data, pipeline,
tensor, and sequence parallelism, as well as heterogeneous training methods
integrated with zero redundancy optimizer. Compared to the baseline system,
Colossal-AI can achieve up to 2.76 times training speedup on large-scale
models.


  Generative Adversarial Networks (GANs) have become predominant in image
generation tasks. Their success is attributed to the training regime which
employs two models: a generator G and discriminator D that compete in a minimax
zero sum game. Nonetheless, GANs are difficult to train due to their
sensitivity to hyperparameter and parameter initialisation, which often leads
to vanishing gradients, non-convergence, or mode collapse, where the generator
is unable to create samples with different variations. In this work, we propose
a novel Generative Adversarial Stacked Convolutional Autoencoder(GASCA) model
and a generative adversarial gradual greedy layer-wise learning algorithm
de-signed to train Adversarial Autoencoders in an efficient and incremental
manner. Our training approach produces images with significantly lower
reconstruction error than vanilla joint training.


  We report experimental measurements for ultrathin (< 15 nm) van der Waals
heterostructures exhibiting external quantum efficiencies exceeding 50%, and
show that these structures can achieve experimental absorbance > 90%. By
coupling electromagnetic simulations and experimental measurements, we show
that pn WSe2/MoS2 heterojunctions with vertical carrier collection can have
internal photocarrier collection efficiencies exceeding 70%.


  In this paper we prove a conjecture stated by the first two authors
establishing the closure of the numerical range of a certain class of
$n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges
of two tridiagonal $(n+1) \times (n+1)$ matrices. Furthermore, when $n+1$ is
odd, we show that the size of such matrices simplifies to $\frac{n}{2}+1$.


  For superconducting nanowire with the pairing of extended s-type symmetry,
Rashba spin-orbit interaction in a magnetic field, the influence of strong
intersite charge correlations on single-particle Majorana excitations is
analyzed. This problem is investigated on the basis of the density matrix
renormalization group numerical method. It is shown that with an increase in
the repulsion intensity of electrons located at the neighboring sites, two
subbands emerge in the lower Hubbard band of the open system. Based on
calculations of the Majorana polarization and degeneracy of the entanglement
spectrum, it was found that a topologically nontrivial phase with one edge
state survives at the edge of each of the subbands where the concentration of
electrons or holes is minimal.


  I conjecture that a flat 10D compact universe emerged out of nothing (By
``nothing'' I mean no notion of space and time) with all it's symmetries
intact: Poincare invariance, conformal invariance and supersymmetry, it's
massless moduli fields, and a zero energy density. Its subsequent evolution and
spontaneous breaking of these symmetries or by quantum fluctuations leads to
topological defects on this superspace which are the fields we observe (or
haven't yet observed) propagating in this spacetime. By the law of naturalness
it will restore all these broken symmetries. In recent years, the cosmological
constant problem has metamorphosed to a new problem of finding a selection
mechanism that selects our vacuum out of a string theory landscape or resign to
anthropic reasoning. I provide a new perspective for solving this problem using
a multistep approach based on the wavefunction, inflation and conformal
symmetry.


  Based on different projection geometry, a fisheye image can be presented as a
parameterized non-rectilinear image. Deep neural networks(DNN) is one of the
solutions to extract parameters for fisheye image feature description. However,
a large number of images are required for training a reasonable prediction
model for DNN. In this paper, we propose to extend the scale of the training
dataset using parameterized synthetic images. It effectively boosts the
diversity of images and avoids the data scale limitation. To simulate different
viewing angles and distances, we adopt controllable parameterized projection
processes on transformation. The reliability of the proposed method is proved
by testing images captured by our fisheye camera. The synthetic dataset is the
first dataset that is able to extend to a big scale labeled fisheye image
dataset. It is accessible via: http://www2.leuphana.de/misl/fisheye-data-set/.


  In this paper, we study the design and analysis of experiments conducted on a
set of units over multiple time periods where the starting time of the
treatment may vary by unit. The design problem involves selecting an initial
treatment time for each unit in order to most precisely estimate both the
instantaneous and cumulative effects of the treatment. We first consider
non-adaptive experiments, where all treatment assignment decisions are made
prior to the start of the experiment. For this case, we show that the
optimization problem is generally NP-hard, and we propose a near-optimal
solution. Under this solution, the fraction entering treatment each period is
initially low, then high, and finally low again. Next, we study an adaptive
experimental design problem, where both the decision to continue the experiment
and treatment assignment decisions are updated after each period's data is
collected. For the adaptive case, we propose a new algorithm, the
Precision-Guided Adaptive Experiment (PGAE) algorithm, that addresses the
challenges at both the design stage and at the stage of estimating treatment
effects, ensuring valid post-experiment inference accounting for the adaptive
nature of the design. Using realistic settings, we demonstrate that our
proposed solutions can reduce the opportunity cost of the experiments by over
50%, compared to static design benchmarks.


  In this paper, we generalize the Heintze-Kobayashi-Wolf theory to homogeneous
Finsler geometry, by proving two main theorems. First, any connected negatively
curved homogeneous Finsler manifold is isometric to a Lie group endowed with a
left invariant metric, and that Lie group must be simply connected and
solvable. Second, the requirement in Heintze's criterion is necessary and
sufficient for a real solvable Lie algebra to generate a Lie group which admits
negatively curved left invariant Finsler metrics.


  Next generation radio telescopes, such as the Square Kilometre Array (SKA)
and Next Generation Very Large Array (ngVLA), require precise microwave
frequency reference signals to be transmitted over fiber links to each dish to
coherently sample astronomical signals. Such telescopes employ phase
stabilization systems to suppress the phase noise imparted on the reference
signals by environmental perturbations on the links; however, the stabilization
systems are bandwidth limited by the round-trip time of light travelling on the
fiber links. A phase-locked Receiver Module (RM) is employed on each dish to
suppress residual phase noise outside of the round-trip bandwidth. The SKA RM
must deliver a 3.96 GHz output signal with 4 MHz of tuning range and less than
100 fs of timing jitter. We present an RM architecture to meet both
requirements. Analytical modelling of the RM predicts 30 fs of output jitter
when the reference signal is integrated between 1 Hz and 2.8 GHz. The proposed
RM was conceived with best practice electromagnetic compatibility in mind, and
to meet size, weight and power requirements for the SKA dish indexer. As the
ngVLA reference design also incorporates a round-trip phase stabilization
system, this RM may be applicable to future ngVLA design.


  A systematic procedure is proposed for better understanding the evolution
laws of black holes in terms of pure quantum states. We start with the two
opposed regions I and II in the Penrose diagram, and study the evolution of
matter in these regions, using the algebra derived earlier from the Shapiro
effect in quantum particles. Since this spacetime has two distinct asymptotic
regions, one must assume that there is a mechanism that reduces the number of
states. In earlier work we proposed that region II describes the angular
antipodes of region I, the `antipodal identification', but this eventually
leads to contradictions. Our much simpler proposal is now that all states
defined in region II are exact quantum clones of those in region I. This
indicates more precisely how to restore unitarity by making all quantum states
observable, and in addition suggests that generalisations towards other black
hole structures will be possible. An apparent complication is that the wave
function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian,
but this complication can be well-understood in a realistic interpretation of
quantum mechanics.


  We develop a generalisation of Mercer's theorem to operator-valued kernels in
infinite dimensional Hilbert spaces. We then apply our result to deduce a
Karhunen-Lo\`eve theorem, valid for mean-square continuous Hilbertian
functional data, i.e. flows in Hilbert spaces. That is, we prove a series
expansion with uncorrelated coefficients for square-integrable random flows in
a Hilbert space, that holds uniformly over time.


  In this paper, we use the flag curvature formula for homogeneous Finsler
spaces in our previous work to classify odd dimensional smooth coset spaces
admitting positively curved reversible homogeneous Finsler metrics. We will
show that the most features of L. B\'{e}rard-Bergery's classification results
for odd dimensional positively curved Riemannian homogeneous spaces can be
generalized to reversible Finsler spaces.


  Charmonium production cross-section in proton-proton collisions is measured
at the centre-of-mass energy $\sqrt{s}=13\,TeV$ using decays to $p\bar{p}$
final state. The study is performed using a data sample corresponding to an
integrated luminosity of $2.2\,{fb}^{-1}$ collected in 2018 with the $LHCb$
detector. The production cross-section of the $\eta_c$ meson is measured in a
rapidity range of $2.0 < y < 4.0$ and in a transverse momentum range of $5.0 <
p_{T} < 20.0\,{GeV/\it{c}}$, which is extended compared with previous $LHCb$
analyses. The differential cross-section is measured in bins of $p_{T}$ and,
for the first time, of $y$. Upper limits, at 90% and 95% confidence levels, on
the $\eta_c(2S)$ and $h_c(1P)$ prompt production cross-sections are determined
for the first time.


  We revisit a classical problem in computational geometry: finding the
largest-volume axis-aligned empty box (inside a given bounding box) amidst $n$
given points in $d$ dimensions. Previously, the best algorithms known have
running time $O(n\log^2n)$ for $d=2$ (by Aggarwal and Suri [SoCG'87]) and near
$n^d$ for $d\ge 3$. We describe faster algorithms with running time (i)
$O(n2^{O(\log^*n)}\log n)$ for $d=2$, (ii) $O(n^{2.5+o(1)})$ time for $d=3$,
and (iii) $\widetilde{O}(n^{(5d+2)/6})$ time for any constant $d\ge 4$.
  To obtain the higher-dimensional result, we adapt and extend previous
techniques for Klee's measure problem to optimize certain objective functions
over the complement of a union of orthants.


  The luminosity of the Tip of the Red Giant Branch (TRGB) provides an
excellent measure of galaxy distances and is easily determined in the resolved
images of nearby galaxies observed with Hubble Space Telescope. There is now a
large amount of archival data relevant to the TRGB methodology and which offers
comparisons with other distance estimators. Zero-point issues related to the
TRGB distance scale are reviewed in this paper. Consideration is given to the
metallicity dependence of the TRGB, the transformations between HST flight
systems and Johnson-Cousins photometry, the absolute magnitude scale based on
Horizontal Branch measurements, and the effects of reddening. The zero-point of
the TRGB is established with a statistical accuracy of 1%, modulo the
uncertainty in the magnitude of the Horizontal Branch, with a typical rms
uncertainty of 3% in individual galaxy distances at high Galactic latitude. The
zero-point is consistent with the Cepheids period-luminosity relation scale but
invites reconsideration of the claimed metallicity dependence with that method.
The maser distance to NGC 4258 is consistent with TRGB but presently has lower
accuracy.


  We conduct a comprehensive analysis of the accreting X-ray pulsar, Hercules
X-1, utilizing data from IXPE and NuSTAR. IXPE performed five observations of
Her X-1, consisting of three in the Main-on state and two in the Short-on
state. Our time-resolved analysis uncovers the linear correlations between the
flux and polarization degree as well as the pulse fraction and polarization
degree. Geometry parameters are rigorously constrained by fitting the
phase-resolved modulations of Cyclotron Resonance Scattering Feature and
polarization angle with a simple dipole model and Rotating Vector Model
respectively, yielding roughly consistent results. The changes of $\chi_{\rm
p}$ (the position angle of the pulsar's spin axis on the plane of the sky)
between different Main-on observations suggest the possible forced precession
of the neutron star crust. Furthermore, a linear association between the energy
of Cyclotron Resonance Scattering Feature and polarization angle implies the
prevalence of a dominant dipole magnetic field, and their phase-resolved
modulations likely arise from viewing angle effects.


  In this paper a Monte Carlo generator, GaGaRes, is presented which can be
used to describe two-photon resonance production in e^+e^- collisions. The
program can generate the five lowest-lying C=+1 meson states of any q\bar{q}
combination together with the outgoing electron and positron. The dependence on
the photon virtualities Q_1^2 and Q_2^2 is fully taken into account. The
program also generates the density matrices of the resonance, which form an
essential tool in the description of the decay of the resonances. Furthermore,
the program is applicable for all tagging conditions.


  In this thesis, first, we investigate the metrological usefulness of a family
of states known as unpolarized Dicke states, which turn to be very sensitive to
the magnetic field. Quantum mechanics plays a central role in achieving such a
high precision. Second, we investigate possible lower bounds on the quantum
Fisher information, a quantity that characterizes the usefulness of a state for
quantum metrology, using the theory of Legendre transforms such that we obtain
tight lower bounds based on few measurements of the initial quantum state that
will be used for metrology. And last but not least, we investigate gradient
magnetometry, i.e., we develop a theory to study the sensitivity of some states
on the change in space of the magnetic field.


  Creation of images using generative adversarial networks has been widely
adapted into multi-modal regime with the advent of multi-modal representation
models pre-trained on large corpus. Various modalities sharing a common
representation space could be utilized to guide the generative models to create
images from text or even from audio source. Departing from the previous methods
that solely rely on either text or audio, we exploit the expressiveness of both
modality. Based on the fusion of text and audio, we create video whose content
is consistent with the distinct modalities that are provided. A simple approach
to automatically segment the video into variable length intervals and maintain
time consistency in generated video is part of our method. Our proposed
framework for generating music video shows promising results in application
level where users can interactively feed in music source and text source to
create artistic music videos. Our code is available at
https://github.com/joeljang/music2video.


  The spin asymmetries in SIDIS associated with $T$-odd TMDs are presented in a
light-front quark-diquark model of a proton. To incorporate the effects of the
final state interaction, the light front wave functions are modified to have a
phase factor which is essential to have Sivers or Boer-Mulders functions. The
Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.


  Maps of the Galactic electron-positron annihilation radiation show evidence
for three distinct and significant features: (1) a central bulge source, (2)
emission in the Galactic plane, and (3) an enhancement of emission at positive
latitudes above the Galactic Center. In this paper, we explore the possibility
that Sgr A East, a very prominent radio structure surrounding the Galactic
nucleus, may be a significant contributer to the central bulge feature. The
motivation for doing so stems from a recently proposed link between this radio
object and the EGRET gamma-ray source 2EG J1746-2852. If this association is
correct, then Sgr A East is also expected to be a source of copious positron
production. The results presented here show that indeed Sgr A East must have
produced a numerically significant population of positrons, but also that most
of them have not yet had sufficient time to thermalize and annihilate. As such,
Sgr A East by itself does not appear to be the dominant current source of
annihilation radiation, but it will be when the positrons have cooled
sufficiently and they have become thermalized. This raises the interesting
possibility that the bulge component may be due to the relics of earlier
explosive events like the one that produced Sgr A East.


  We present a systematic measurement of the X-ray emission asymmetries in the
K-shell dielectronic, trielectronic, and quadruelectronic recombination of free
electrons into highly charged ions. Iron ions in He-like through O-like charge
states were produced in an electron beam ion trap, and the electron-ion
collision energy was scanned over the recombination resonances. Two identical
X-ray detectors mounted head-on and side-on with respect to the electron beam
propagation recorded X-rays emitted in the decay of resonantly populated
states. The degrees of linear polarization of X-rays inferred from observed
emission asymmetries benchmark distorted-wave predictions of the Flexible
Atomic Code (FAC) for several dielectronic recombination satellite lines. The
present method also demonstrates its applicability for diagnostics of energy
and direction of electron beams inside hot anisotropic plasmas. Both
experimental and theoretical data can be used for modeling of hot astrophysical
and fusion plasmas.


  We propose extended 3HDM and 4HDM models where the SM gauge symmetry is
enlarged by the spontaneously broken $S_4$ group, the preserved $Z_2$ and
broken $Z_4$ cyclic symmetries. Each model has three active $SU(2)$ scalar
doublets, in addition, the first one has an extra inert scalar singlet, whereas
the second model has an inert scalar doublet. Furthermore, each model has
several extra gauge singlet scalars, which are triplets under $S_4$. Both
models yield the same structure of the mass matrices for the fermion sector,
where a radiative seesaw generates the tiny light active neutrinos masses at
one-loop level, through the $S_4$ triplets. The presence of flavor changing
neutral currents mediated by heavy scalars allowed us to study the
$(K^0-\overline{K}^0)$ and $(B_{d,s}^0-\overline{B}_{d,s}^0)$ meson mixings, in
the parameter space that currently satisfies the experimental constraints. On
the other hand, due to the preserved $Z_2$ symmetry, our proposed models have
stable scalar and fermionic dark matter candidates. Furthermore, these models
are consistent with the current pattern of SM fermion masses and mixings, with
the measured dark matter relic abundance and successfully accommodate the
constraints arising from meson oscillations and oblique parameters. The extra
scalars in our models provide radiative corrections to the oblique parameters,
where due to the presence of the scalar inert doublet, renders the 4HDM less
restrictive than the 3HDM one.


  We implemented a gradient-based algorithm for transition state search which
uses Gaussian process regression. Besides a description of the algorithm, we
provide a method to find the starting point for the optimization if only the
reactant and product minima are known. We perform benchmarks on 27 test systems
against the dimer method and partitioned rational function optimization as
implemented in the DL-FIND library. We found the new optimizer to significantly
decrease the number of required energy and gradient evaluations.


  Digital data transfer can be protected by means of suitable error correcting
codes. Among the families of state-of-the-art codes, LDPC (Low Density
Parity-Check) codes have received a great deal of attention recently, because
of their performance and flexibility of operation, in wireless and mobile radio
channels, as well as in cable transmission systems. In this paper, we present a
class of rate-adaptive LDPC codes, obtained as properly punctured simplex
codes. These codes allow for the use of an efficient soft-decision decoding
algorithm, provided that a condition called row-column constraint is satisfied.
This condition is tested on small-length codes, and then extended to
medium-length codes. The puncturing operations we apply do not influence the
satisfaction of the row-column constraint, assuring that a wide range of code
rates can be obtained. We can reach code rates remarkably higher than those
obtainable by the original simplex code, and the price in terms of minimum
distance turns out to be relatively small, leading to interesting trade-offs in
the resulting asymptotic coding gain.


  We present a generalization to the N-dimensional case for the nucleation
coefficient of a spherical p-brane, separating two (anti-)de Sitter spacetimes.
We use a semiclassical approximation based on the analytical continuation to
the Euclidean sector of a suitable effective action describing a p-brane in
General Relativity.


  The rotations of the polarization angle (PA) with time (energy) can lead to
the depolarization of the time-integrated (energy-integrated) polarization.
However, we don't know how and when it will rotate. Here, we consider the
magnetic reconnection model to investigate the polarizations, especially the PA
rotations of GRB prompt emission. For the large-scale ordered aligned magnetic
field configuration, we find that PAs will evolve with time (energy) for
off-axis observations. Our studies show that the rotations of the PAs are due
to the changes of the ``observed shape'' of the emitting region (before
averaged). We apply our models to the single pulse burst of GRB 170101A and GRB
170114A with time-resolved PA observations. We find it can interpret the
violent PA variation of GRB 170101A. The model could not predict the twice
$90^{\circ}$ PA changes in GRB 170114A. Detailed model should be considered.


  This report presents a down-conversion method involving digital sideband
separation for the Yuan Tseh Lee Array to double the processing bandwidth. The
receiver consists of a MMIC HEMT LNA frontend operating at a wavelength of 3
mm, and sub-harmonic mixers that output signals at intermediate frequencies of
2 - 18 GHz. The sideband separation scheme involves an analog 90 degree hybrid
followed by two mixers that provide down conversion of the IF signal to a pair
of in phase (I) and quadrature (Q) signals in baseband. The I and Q baseband
signals are digitized using 5 Giga sample per second analog to digital
converters. A second hybrid is digitally implemented using field programmable
gate arrays to produce two sidebands, each with a bandwidth of 1.6 GHz. The 2 x
1.6 GHz band can be tuned to cover any 3.2 GHz window within the aforementioned
IF range of the array. Sideband rejection ratios (SRRs) above 20 dB can be
obtained across the 3.2 GHz bandwidth by equalizing the power and delay between
the I and Q baseband signals. Furthermore, SRRs above 30 dB can be achieved
when calibration is applied.


  Transmission spectra of H$_2$O+CO$_2$ mixtures have been recorded, at 296,
325 and 366 K, for various pressures and mixture compositions using two
experimental setups. Their analysis enables to retrieve values of the
'continuum' absorption by the CO$_2$-broadened H$_2$O line wings between 100
and 1500 cm$^{-1}$. The results are in good agreement with those, around 1300
cm$^{-1}$, of the single previous experimental study available. Comparisons are
also made with direct predictions based on line-shape correction factors $\chi$
calculated, almost thirty years ago, using a quasistatic approach and an input
H$_2$O-CO$_2$ intermolecular potential. They show that this model quite nicely
predicts, with slightly overestimated values, the continuum over a spectral
range where it varies by more than three orders of magnitude. An empirical
correction is proposed, based on the experimental data, which should be useful
for radiative transfer and climate studies in CO$_2$ rich planetary
atmospheres.


  We report on the results of a four-year long X-ray monitoring campaign of the
central 1.2 square degrees of our Galaxy, performed with Chandra and XMM-Newton
between 2005 and 2008. Our study focuses on the properties of transient X-ray
sources that reach 2-10 keV luminosities of >1E34 erg/s for an assumed distance
of 8 kpc. There are 17 known X-ray transients within the field of view of our
campaign, eight of which were detected in outburst during our observations: the
transient neutron star low-mass X-ray binaries GRS 1741-2853, AX J1745.6-2901,
SAX J1747.0-2853, KS 1741-293 and GRO J1744-28, and the unclassified X-ray
transients XMM J174457-2850.3, CXOGC J174535.5-290124 and CXOGC
J174541.0-290014. We present their X-ray spectra and flux evolution during our
campaign, and discuss these results in light of their historic activity. Our
main results include the detection of two thermonuclear X-ray bursts from SAX
J1747.0-2853 that were separated by an unusually short time interval of 3.8
min. We detected a thermonuclear X-ray burst and a ~1600-s X-ray eclipse from
AX J1745.6-2901. Both XMM J174457-2850.3 and GRO J1744-28 displayed weak X-ray
activity above their quiescent levels that is indicative of low-level
accretion. In addition to the eight known X-ray transients, we discovered a
previously unknown X-ray source that we designate XMMU J174654.1-291542. Based
on its X-ray properties and the possible association with an infrared source,
we tentatively classify this object as a cataclysmic variable. No new
transients were found during our campaign, reinforcing the conclusion of
previous authors that most X-ray transients recurring on a time scale of less
than a decade have now been identified near the Galactic centre.


  We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be
taken to Hermitian Hamiltonians via a non-unitary transformation and vice
versa. We also show that for some specific Hamiltonians such non-unitary
transformations may be associated, via a fractional-Wick rotation, to complex
time.


  Topological spin structures, such as magnetic skyrmions, hold great promises
for data storage applications, thanks to their inherent stability. In most
cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric
systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while
spontaneous skyrmion lattices have been reported in centrosymmetric itinerant
magnets with long-range interactions. Here, a spontaneous anti-biskyrmion
lattice with unique topology and chirality is predicted in the monolayer of a
semiconducting and centrosymmetric metal halide, NiI$_2$. Our first-principles
and Monte Carlo simulations reveal that the anisotropies of the short-range
symmetric exchange, when combined with magnetic frustration, can lead to an
emergent chiral interaction that is responsible for the predicted topological
spin structures. The proposed mechanism finds a prototypical manifestation in
two-dimensional magnets, thus broadening the class of materials that can host
spontaneous skyrmionic states.


  Particle acceleration during the magnetorotational instability (MRI) in a
collisionless accretion disk was investigated by using a particle-in-cell (PIC)
simulation. We discuss the important role that magnetic reconnection plays not
only on the saturation of MRI but also on the relativistic particle generation.
The plasma pressure anisotropy of $p_{\perp} > p_{\para}$ induced by the action
of MRI dynamo leads to rapid growth in magnetic reconnection, resulting in the
fast generation of nonthermal particles with a hard power-law spectrum. This
efficient particle acceleration mechanism involved in a collisionless accretion
disk may be a possible model to explain the origin of high energy particles
observed around massive black holes.


  After 15 years, in late 2018, the magnetar XTE J1810-197 underwent a second
recorded X-ray outburst event and reactivated as a radio pulsar. We initiated
an X-ray monitoring campaign to follow the timing and spectral evolution of the
magnetar as its flux decays using Swift, XMM-Newton, NuSTAR, and NICER
observations. During the year-long campaign, the magnetar reproduced similar
behaviour to that found for the first outburst, with a factor of two change in
its spin-down rate from $\sim7.2\times10^{-12}$ s s$^{-1}$ to
$\sim1.5\times10^{-11}$ s s$^{-1}$ after two months. Unique to this outburst,
we confirm the peculiar energy-dependent phase shift of the pulse profile.
Following the initial outburst, the spectrum of XTE J1810-197 is well-modelled
by multiple blackbody components corresponding to a pair of non-concentric, hot
thermal caps surrounded by a cooler one, superposed to the colder star surface.
We model the energy-dependent pulse profile to constrain the viewing and
surface emission geometry and find that the overall geometry of XTE J1810-197
has likely evolved relative to that found for the 2003 event.


  Distillation, or purification, is central to the practical use of quantum
resources in noisy settings often encountered in quantum communication and
computation. Conventionally, distillation requires using some restricted 'free'
operations to convert a noisy state into one that approximates a desired pure
state. Here, we propose to relax this setting by only requiring the
approximation of the measurement statistics of a target pure state, which
allows for additional classical postprocessing of the measurement outcomes. We
show that this extended scenario, which we call virtual resource distillation,
provides considerable advantages over standard notions of distillation,
allowing for the purification of noisy states from which no resources can be
distilled conventionally. We show that general states can be virtually
distilled with a cost (measurement overhead) that is inversely proportional to
the amount of existing resource, and we develop methods to efficiently estimate
such cost via convex and semidefinite programming, giving several computable
bounds. We consider applications to coherence, entanglement, and magic
distillation, and an explicit example in quantum teleportation (distributed
quantum computing). This work opens a new avenue for investigating generalized
ways to manipulate quantum resources.


  Radio astronomy has benefited greatly from advances in technology and will
continue to do so in the future. In fact, we are experiencing a revolution in
the way radio astronomy is conducted as our instruments allow us now to
directly "digitize" our photons. This has enormous consequences, since we can
greatly benefit from the continuing advances in digital electronics,
telecommunication and computing. The results are dramatic increase in
observable bandwidths, FoVs, frequency coverage and collecting area. The global
efforts will culminate in the construction of the SKA as the world's largest
and most powerful telescope. On the way projects like LOFAR, LEAP and others
will revolutionize many areas of astrophysics and fundamental physics.
Observations of pulsars will play a central role in these scientific
endeavours. We briefly summarize here some recent scientific developments that
help us in defining our expectations for the the new generation of radio
telescopes for pulsar astrophysics.


  We investigate the innermost stable circular orbit (ISCO) of a test particle
moving on the equatorial plane around rotating relativistic stars such as
neutron stars. First, we derive approximate analytic formulas for the angular
velocity and circumferential radius at the ISCO making use of an approximate
relativistic solution which is characterized by arbitrary mass, spin, mass
quadrupole, current octapole and mass $2^4$-pole moments. Then, we show that
the analytic formulas are accurate enough by comparing them with numerical
results, which are obtained by analyzing the vacuum exterior around numerically
computed geometries for rotating stars of polytropic equation of state. We
demonstrate that contribution of mass quadrupole moment for determining the
angular velocity and, in particular, the circumferential radius at the ISCO
around a rapidly rotating star is as important as that of spin.


  In this article, continuing the work done in the previous paper (M. Fathi
2012), we apply a Lagrangian formalism to demonstrate the shape of the geodesic
motion for a massive charged particle which is falling freely in a de Sitter
spacetime. We will show that a spiral shape of the trajectory is available, due
to the logarithmic behavior of time, with respect to the proper time.


  Motivated by the recent interests in spin$-2$ massive gravitons, we study the
structure of neutron star in the context of massive gravity. The modifications
of TOV equation in the presence of massive gravity are explored in $4$ and
higher dimensions. Next, by considering the modern equation of state for the
neutron star matter (which is extracted by the lowest order constrained
variational (LOCV) method with the AV$18$ potential), different physical
properties of the neutron star (such as Le Chatelier's principle, stability and
energy conditions) are investigated. It is shown that consideration of the
massive gravity has specific contributions into the structure of neutron star
and introduces new prescriptions for the massive astrophysical objects. The
mass-radius relation is examined and the effects of massive gravity on the
Schwarzschild radius, average density, compactness, gravitational redshift and
dynamical stability are studied. Finally, a relation between mass and radius of
neutron star versus the Planck mass is extracted.


  The Directed Grid Theorem, stating that there is a function $f$ such that a
directed graphs of directed treewidth at least $f(k)$ contains a directed grid
of size at least $k$ as a butterfly minor, after being a conjecture for nearly
20 years, has been proven in 2015 by Kawarabayashi and Kreutzer. However, the
function $f$ obtained in the proof is very fast growing.
  In this work, we show that if one relaxes directed grid to bramble of
constant congestion, one can obtain a polynomial bound. More precisely, we show
that for every $k \geq 1$ there exists $t = \mathcal{O}(k^{48} \log^{13} k)$
such that every directed graph of directed treewidth at least $t$ contains a
bramble of congestion at most $8$ and size at least $k$.


  Multi-terminal Aharonov-Bohm (AB) rings are ideal building blocks for quantum
networks (QNs) thanks to their ability to map input states into controlled
coherent superpositions of output states. We report on experiments performed on
three-terminal GaAs/Al_(x)Ga_(1-x)As AB devices and compare our results with a
scattering-matrix model including Lorentz forces and decoherence. Our devices
were studied as a function of external magnetic field (B) and gate voltage at
temperatures down to 350 mK. The total output current from two terminals while
applying a small bias to the third lead was found to be symmetric with respect
to B with AB oscillations showing abrupt phase jumps between 0 and pi at
different values of gate voltage and at low magnetic fields, reminiscent of the
phase-rigidity constraint due to Onsager-Casimir relations. Individual outputs
show quasi-linear dependence of the oscillation phase on the external electric
field. We emphasize that a simple scattering-matrix approach can not model the
observed behavior and propose an improved description that can fully describe
the observed phenomena. Furthermore, we shall show that our model can be
successfully exploited to determine the range of experimental parameters that
guarantee a minimum oscillation visibility, given the geometry and coherence
length of a QN.


  We give a direct global proof for the existence of symplectic realizations of
arbitrary Poisson manifolds.


  The purpose of this article is to prove that Gersten's conjecture for a
commutative discrete valuation ring is true. Combining with the result of
\cite{GL87}, we learn that Gersten's conjecture is true if the ring is a
commutative regular local, smooth over a commutative discrete valuation ring.


  The total yields of the all well-established light mesonic resonances (up to
the $\phi$(1020) meson) are estimated in neutrinonuclear interactions at < E_nu
> = 10 GeV, using the data obtained with SKAT bubble chamber. For some
resonances, the yields in the forward and backward hemispheres in the hadronic
c.m.s. are also extracted. From the comparison of the obtained and available
higher-energy data, an indication is obtained that the resonance yields rise
almost linearly as a function of the mean mass < W > of the neutrinoproduced
hadronic system. The fractions of pions originating from the light resonance
decays are inferred.


  Comment on the paper "Absence of the Mott Glass Phase in 1D Disordered
Fermionic Systems" by T. Nattermann, A. Petkovic, Z. Ristivojevic, and F.
Schutze, Phys. Rev. Lett. 99, 186402 (2007).


  The spectral theory for operator pencils and operator differential-algebraic
equations is studied. Special focus is laid on singular operator pencils and
three different concepts of singular operator pencils are introduced. The
concepts are analyzed in detail and examples are presented that illustrate the
subtle differences. It is investigated how these concepts are related to
uniqueness of the underlying algebraic-differential operator equation, showing
that, in general, classical results known from the finite dimensional case of
matrix pencils and differential-algebraic equations do not prevail. The results
are then studied in the setting of structured operator pencils arising in
dissipative differential-algebraic equations. Here, unlike in the general
infinite-dimensional case, the uniqueness of solutions is closely related to
the singularity of the pencil.


  An introduction to nuclear theory is given starting from the quantum
chromodynamics foundations for quark and gluon fields, then discussing
properties of pions and nucleons, interactions between nucleons, structure of
the deuteron and light nuclei, and finishing at the description of heavy
nuclei. It is shown how concepts of different energy and size scales and ideas
related to effective fields and symmetry breaking, enter our description of
nuclear systems.


  We develop a novel framework to study smooth and strongly convex optimization
algorithms, both deterministic and stochastic. Focusing on quadratic functions
we are able to examine optimization algorithms as a recursive application of
linear operators. This, in turn, reveals a powerful connection between a class
of optimization algorithms and the analytic theory of polynomials whereby new
lower and upper bounds are derived. Whereas existing lower bounds for this
setting are only valid when the dimensionality scales with the number of
iterations, our lower bound holds in the natural regime where the
dimensionality is fixed. Lastly, expressing it as an optimal solution for the
corresponding optimization problem over polynomials, as formulated by our
framework, we present a novel systematic derivation of Nesterov's well-known
Accelerated Gradient Descent method. This rather natural interpretation of AGD
contrasts with earlier ones which lacked a simple, yet solid, motivation.


  Understanding the physical mechanisms behind thermal effects in phosphors is
crucial for white light-emitting diodes (WLEDs) applications, as thermal
quenching of their photoluminescence might render them useless. The two
chemically close Eu-doped \Hosta and \Hostb crystals are typical phosphors
studied for WLEDs. The first one sustains efficient light emission at
100$^{\circ}$C while the second one emits very little light at that
temperature. Herein, we analyze from first principles their electronic
structure and atomic geometry, before and after absorption/emission of light.
Our results, in which the Eu-5d levels are obtained inside the band gap thanks
to the removal of an electron from the 4f$^7$ shell, attributes the
above-mentioned experimental difference to an auto-ionization model of the
thermal quenching, based on the energy difference between Eu$_{\text{5d}}$ and
the conduction band minimum. For both Eu-doped phosphors, we identify the
luminescent center, and we show that the atomic relaxation in their excited
state is of crucial importance for a realistic description of the emission
characteristics.


  We present results of a joint {\sl Chandra} and {\sl XMM-Newton} analysis of
the Fornax Cluster, the nearest galaxy cluster in the southern sky. Signatures
of merger-induced gas sloshing can be seen in the X-ray image. We identify four
sloshing cold fronts in the intracluster medium, residing at radii of 3\,kpc
(west), 10\,kpc (northeast), 30\,kpc (southwest) and 200\,kpc (east). Despite
spanning over two orders of magnitude in radius, all four cold fronts fall onto
the same spiral pattern that wraps around the BCG NGC~1399, likely all
initiated by the infall of NGC~1404. The most evident front is to the
northeast, 10\,kpc from the cluster center, which separates low-entropy
high-metallicity gas and high-entropy low-metallicity gas. The metallicity map
suggests that gas sloshing, rather than an AGN outburst, is the driving force
behind the redistribution of the enriched gas in this cluster. The innermost
cold front resides within the radius of the strong cool core. The sloshing time
scale within the cooling radius, calculated from the Brunt-V$\ddot{\rm
a}$s$\ddot{\rm a}$l$\ddot{\rm a}$ frequency, is an order of magnitude shorter
than the cooling time. It is plausible that gas sloshing can contribute to the
heating of the cool core, provided that gas of different entropies can be mixed
effectively via Kelvin-Helmholtz instability. The estimated age of the
outermost front suggests that this is not the first infall of NGC~1404.


  In comparison to classical shallow representation learning techniques, deep
neural networks have achieved superior performance in nearly every application
benchmark. But despite their clear empirical advantages, it is still not well
understood what makes them so effective. To approach this question, we
introduce deep frame approximation: a unifying framework for constrained
representation learning with structured overcomplete frames. While exact
inference requires iterative optimization, it may be approximated by the
operations of a feed-forward deep neural network. We indirectly analyze how
model capacity relates to frame structures induced by architectural
hyperparameters such as depth, width, and skip connections. We quantify these
structural differences with the deep frame potential, a data-independent
measure of coherence linked to representation uniqueness and stability. As a
criterion for model selection, we show correlation with generalization error on
a variety of common deep network architectures and datasets. We also
demonstrate how recurrent networks implementing iterative optimization
algorithms can achieve performance comparable to their feed-forward
approximations while improving adversarial robustness. This connection to the
established theory of overcomplete representations suggests promising new
directions for principled deep network architecture design with less reliance
on ad-hoc engineering.


  Diabetic retinopathy (DR) is a complication of diabetes and usually takes
decades to reach sight-threatening levels. Accurate and robust detection of DR
severity is critical for the timely management and treatment of diabetes.
However, most current DR grading methods suffer from insufficient robustness to
data variability (\textit{e.g.} colour fundus images), posing a significant
difficulty for accurate and robust grading. In this work, we propose a novel DR
grading framework CLIP-DR based on three observations: 1) Recent pre-trained
visual language models, such as CLIP, showcase a notable capacity for
generalisation across various downstream tasks, serving as effective baseline
models. 2) The grading of image-text pairs for DR often adheres to a
discernible natural sequence, yet most existing DR grading methods have
primarily overlooked this aspect. 3) A long-tailed distribution among DR
severity levels complicates the grading process. This work proposes a novel
ranking-aware prompting strategy to help the CLIP model exploit the ordinal
information. Specifically, we sequentially design learnable prompts between
neighbouring text-image pairs in two different ranking directions.
Additionally, we introduce a Similarity Matrix Smooth module into the structure
of CLIP to balance the class distribution. Finally, we perform extensive
comparisons with several state-of-the-art methods on the GDRBench benchmark,
demonstrating our CLIP-DR's robustness and superior performance. The
implementation code is available
\footnote{\url{https://github.com/Qinkaiyu/CLIP-DR}


  We introduce a new version of deep state-space models (DSSMs) that combines a
recurrent neural network with a state-space framework to forecast time series
data. The model estimates the observed series as functions of latent variables
that evolve non-linearly through time. Due to the complexity and non-linearity
inherent in DSSMs, previous works on DSSMs typically produced latent variables
that are very difficult to interpret. Our paper focus on producing
interpretable latent parameters with two key modifications. First, we simplify
the predictive decoder by restricting the response variables to be a linear
transformation of the latent variables plus some noise. Second, we utilize
shrinkage priors on the latent variables to reduce redundancy and improve
robustness. These changes make the latent variables much easier to understand
and allow us to interpret the resulting latent variables as random effects in a
linear mixed model. We show through two public benchmark datasets the resulting
model improves forecasting performances.