  A good representation for arbitrarily complicated data should have the
capability of semantic generation, clustering and reconstruction. Previous
research has already achieved impressive performance on either one. This paper
aims at learning a disentangled representation effective for all of them in an
unsupervised way. To achieve all the three tasks together, we learn the forward
and inverse mapping between data and representation on the basis of a symmetric
adversarial process. In theory, we minimize the upper bound of the two
conditional entropy loss between the latent variables and the observations
together to achieve the cycle consistency. The newly proposed RepGAN is tested
on MNIST, fashionMNIST, CelebA, and SVHN datasets to perform unsupervised
classification, generation and reconstruction tasks. The result demonstrates
that RepGAN is able to learn a useful and competitive representation. To the
author's knowledge, our work is the first one to achieve both a high
unsupervised classification accuracy and low reconstruction error on MNIST.
Codes are available at https://github.com/yzhouas/RepGAN-tensorflow.


  In this article, the state estimation problems with unknown process noise and
measurement noise covariances for both linear and nonlinear systems are
considered. By formulating the joint estimation of system state and noise
parameters into an optimization problem, a novel adaptive Kalman filter method
based on conjugate-computation variational inference, referred to as CVIAKF, is
proposed to approximate the joint posterior probability density function of the
latent variables. Unlike the existing adaptive Kalman filter methods utilizing
variational inference in natural-parameter space, CVIAKF performs optimization
in expectation-parameter space, resulting in a faster and simpler solution.
Meanwhile, CVIAKF divides optimization objectives into conjugate and
non-conjugate parts of nonlinear dynamical models, whereas conjugate
computations and stochastic mirror-descent are applied, respectively.
Remarkably, the reparameterization trick is used to reduce the variance of
stochastic gradients of the non-conjugate parts. The effectiveness of CVIAKF is
validated through synthetic and real-world datasets of maneuvering target
tracking.


  Physics-related and model-based vessel trajectory prediction is highly
accurate but requires specific knowledge of the vessel under consideration
which is not always practical. Machine learning-based trajectory prediction
models do not require expert knowledge, but rely on the implicit knowledge
extracted from massive amounts of data. Several deep learning (DL) methods for
vessel trajectory prediction have recently been suggested. The DL models
developed typically only process information about the (dis)location of vessels
defined with respect to a global reference system. In the context of inland
navigation, this can be problematic, since without knowledge of the limited
navigable space, irrealistic trajectories are likely to be determined. If
spatial constraintes are introduced, e.g., by implementing an additional
submodule to process map data, however, overall complexity increases. Instead
of processing the vessel displacement information on the one hand and the
spatial information on the other hand, the paper proposes the merging of both
information. Here, fairway-related and navigation-related displacement
information are used directly. In this way, the previously proposed
context-sensitive Classification Transformer (CSCT) shows an improved spatial
awareness. Additionally, the CSCT is adapted to assess the model uncertainty by
enabling dropout during inference. This approach is trained on different inland
waterways to analyze its generalizability. As the improved CSCT obtains lower
prediction errors and enables to estimate the trustworthiness of each
prediction, it is more suitable for safety-critical applications in inland
navigation than previously developed models.


  This paper proposes three novel resource and user scheduling algorithms with
contiguous frequency-domain resource allocation (FDRA) for wireless
communications systems. The first proposed algorithm jointly schedules users
and resources selected adaptively from both ends of the bandwidth part (BWP),
while the second and third ones apply disjoint user and resource selection with
either single-end or dual-end BWP strategies. Distinct from existing contiguous
FDRA approaches, the proposed ones comply with standards specifications for
fifth-generation (5G) and beyond 5G communications, and have lower
computational complexity hence are more practical. Simulation results show that
all of the proposed algorithms can achieve near-optimal performance in terms of
throughput and packet loss rate for low to moderate traffic load, and the first
one can still perform relatively well even with a large number of users.


  Star trackers are primarily optical devices that are used to estimate the
attitude of a spacecraft by recognising and tracking star patterns. Currently,
most star trackers use conventional optical sensors. In this application paper,
we propose the usage of event sensors for star tracking. There are potentially
two benefits of using event sensors for star tracking: lower power consumption
and higher operating speeds. Our main contribution is to formulate an
algorithmic pipeline for star tracking from event data that includes novel
formulations of rotation averaging and bundle adjustment. In addition, we also
release with this paper a dataset for star tracking using event cameras. With
this work, we introduce the problem of star tracking using event cameras to the
computer vision community, whose expertise in SLAM and geometric optimisation
can be brought to bear on this commercially important application.


  This paper proposes an early detection method for cluster structural changes.
Cluster structure refers to discrete structural characteristics, such as the
number of clusters, when data are represented using finite mixture models, such
as Gaussian mixture models. We focused on scenarios in which the cluster
structure gradually changed over time. For finite mixture models, the concept
of mixture complexity (MC) measures the continuous cluster size by considering
the cluster proportion bias and overlap between clusters. In this paper, we
propose MC fusion as an extension of MC to handle situations in which multiple
mixture numbers are possible in a finite mixture model. By incorporating the
fusion of multiple models, our approach accurately captured the cluster
structure during transitional periods of gradual change. Moreover, we introduce
a method for detecting changes in the cluster structure by examining the
transition of MC fusion. We demonstrate the effectiveness of our method through
empirical analysis using both artificial and real-world datasets.


  We construct Holographic Space-time models that reproduce the dynamics of $1
+ 1$ dimensional string theory. The necessity for a dilaton field in the $1 +
1$ effective Lagrangian for classical geometry, the appearance of fermions, and
even the form of the universal potential in the canonical $1$ matrix model,
follow from general HST considerations. We note that 't Hooft's ansatz for the
leading contribution to the black hole S-matrix, accounts for the entire
S-matrix in these models in the limit that the string scale coincides with the
Planck scale, up to transformations between near horizon and asymptotic
coordinates. These $1 + 1$ dimensional models are describable as decoupling
limits of the near horizon geometry of higher dimensional extremal black holes
or black branes, and this suggests that deformations of the simplest model are
equally physical. After proposing a notion of "relevant deformations", we
describe deformations, which contain excitations corresponding to linear
dilaton black holes, some of which can be considered as UV completions of the
CGHS model. We study the question of whether the AMPS paradox can be formulated
in those models. It cannot, because the classical in-fall time to the
singularity of linear dilaton black holes, is independent of the black hole
mass. This result is reproduced by our HST models. We argue that it is related
to the absence of quasi-normal modes of these black hole solutions, which is
itself related to the fact that the horizon has zero area. This is compatible
with the resolution of the AMPS paradox proposed in previous work with
Fischler, according to which the compatibility conditions of HST identify the
long non-singular sojourn of observers behind the horizon, with the dynamics of
equilibration on the horizon as seen by a detector which has not yet fallen
through the horizon.


  We present a model in which the supersonic motions observed in molecular
clouds are driven by gravitational energy released as large structures fragment
into smaller ones. The fragmentation process begins in large molecular clouds,
and continues down to fragments of a critical mass, at which gravitational
confinement may be replaced by pressure confinement. The power laws that
describe the scaling of density and mass, and number spectra and mass spectra
of the fragments are given in terms of that of the observed velocity dispersion
of the fragments. The results agree reasonably well with observations over the
range from several to about a third of a million solar masses.


  Two beam broadening methods for active electronically scanned array (AESA)
antennas with uniform amplitude excitation are proposed and compared: phase
tapering optimization (PTO) and a novel time-varying phase tapering (TPT). The
PTO is a simple and efficient approach assuming continuous polynomial phase
distribution and requiring optimization of only few parameters. The TPT is
valid mainly for radar applications, taking advantage of the fact that radars
typically transmit pulse trains for coherent integration. By varying the array
elements' phases from pulse to pulse, the TPT achieves effective amplitude
tapering, thus providing a method of beam shaping, occasionally with a simple
analytic form. The TPT also makes it possible to produce beam shaping with very
low side lobe levels in comparison to the PTO. As a preliminary step, the
dimensionality of the radiation pattern characterization for all scan
directions is reduced from five to only two variables. This is crucial for
efficient optimization of the radiation pattern which needs to be evaluated
over a judiciously specified two-dimensional domain.


  The alliance polynomial of a graph $G$ with order $n$ and maximum degree
$\Delta$ is the polynomial $A(G; x) = \sum_{k=-\Delta}^{\Delta} A_{k}(G) \,
x^{n+k}$, where $A_{k}(G)$ is the number of exact defensive $k$-alliances in
$G$. We obtain some properties of $A(G; x)$ and its coefficients for regular
graphs. In particular, we characterize the degree of regular graphs by the
number of non-zero coefficients of their alliance polynomial. Besides, we prove
that the family of alliance polynomials of $\Delta$-regular graphs with small
degree is a very special one, since it does not contain alliance polynomials of
graphs which are not $\Delta$-regular. By using this last result and direct
computation we find that the alliance polynomial determines uniquely each cubic
graph of order less than or equal to $10$.


  The active tuning of the structural colour in photonic crystals by an
electric field represents an effective external stimulus with impact on light
transmission manipulation. In this work we present this effect in a photonic
crystal device with alternating layers of Silver and Titanium dioxide
nanoparticles showing shifts of around 10 nm for an applied voltage of 10 V
only. The accumulation of charges at the metal/dielectric interface with
applied electric field leads to an effective increase of the charges
contributing to the plasma frequency in Silver. This initiates a blue shift of
the Silver plasmon band with a simultaneous blue shift of the photonic band gap
as a result of the change in Silver dielectric function, i.e. decrease of the
effective refractive index. These results are the first demonstration of active
colour tuning in Silver/TiO2 nanoparticle based photonic crystals and open the
route to metal/dielectric based photonic crystals as electro-optic switches.


  Audio-visual zero-shot learning aims to classify samples consisting of a pair
of corresponding audio and video sequences from classes that are not present
during training. An analysis of the audio-visual data reveals a large degree of
hyperbolicity, indicating the potential benefit of using a hyperbolic
transformation to achieve curvature-aware geometric learning, with the aim of
exploring more complex hierarchical data structures for this task. The proposed
approach employs a novel loss function that incorporates cross-modality
alignment between video and audio features in the hyperbolic space.
Additionally, we explore the use of multiple adaptive curvatures for hyperbolic
projections. The experimental results on this very challenging task demonstrate
that our proposed hyperbolic approach for zero-shot learning outperforms the
SOTA method on three datasets: VGGSound-GZSL, UCF-GZSL, and ActivityNet-GZSL
achieving a harmonic mean (HM) improvement of around 3.0%, 7.0%, and 5.3%,
respectively.


  We study BPS spectra of D-branes on local Calabi-Yau threefolds
$\mathcal{O}(-p)\oplus\mathcal{O}(p-2)\to \mathbb{P}^1$ with $p=0,1$,
corresponding to $\mathbb{C}^3/\mathbb{Z}_{2}$ and the resolved conifold.
Nonabelianization for exponential networks is applied to compute directly
unframed BPS indices counting states with D2 and D0 brane charges. Known
results on these BPS spectra are correctly reproduced by computing new types of
BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their
wall-crossing. We also develop the notion of exponential BPS graphs for the
simplest toric examples, and show that they encode both the quiver and the
potential associated to the Calabi-Yau via geometric engineering.


  We introduce a new notion of rank for unitary representations of semisimple
groups over a local field of characteristic zero. The theory is based on
Kirillov's method of orbits for nilpotent groups over local fields. When the
semisimple group is classical, we prove that the new theory is essentially
equivalent to Howe's theory of N-rank.


  The need for raw large raw corpora has dramatically increased in recent years
with the introduction of transfer learning and semi-supervised learning methods
to Natural Language Processing. And while there have been some recent attempts
to manually curate the amount of data necessary to train large language models,
the main way to obtain this data is still through automatic web crawling. In
this paper we take the existing multilingual web corpus OSCAR and its pipeline
Ungoliant that extracts and classifies data from Common Crawl at the line
level, and propose a set of improvements and automatic annotations in order to
produce a new document-oriented version of OSCAR that could prove more suitable
to pre-train large generative language models as well as hopefully other
applications in Natural Language Processing and Digital Humanities.


  First order shape optimization methods, in general, require a large number of
iterations until they reach a locally optimal design. While higher order
methods can significantly reduce the number of iterations, they exhibit only
local convergence properties, necessitating a sufficiently close initial guess.
In this work, we present an unregularized shape-Newton method and combine shape
optimization with homotopy (or continuation) methods in order to allow for the
use of higher order methods even if the initial design is far from a solution.
The idea of homotopy methods is to continuously connect the problem of interest
with a simpler problem and to follow the corresponding solution path by a
predictor-corrector scheme. We use a shape-Newton method as a corrector and
arbitrary order shape derivatives for the predictor. Moreover, we apply
homotopy methods also to the case of multi-objective shape optimization to
efficiently obtain well-distributed points on a Pareto front. Finally, our
results are substantiated with a set of numerical experiments.


  In complex networks, nodes that share similar structural characteristics
often exhibit similar roles (e.g type of users in a social network or the
hierarchical position of employees in a company). In order to leverage this
relationship, a growing literature proposed latent representations that
identify structurally equivalent nodes. However, most of the existing methods
require high time and space complexity. In this paper, we propose VNEstruct, a
simple approach for generating low-dimensional structural node embeddings, that
is both time efficient and robust to perturbations of the graph structure. The
proposed approach focuses on the local neighborhood of each node and employs
the Von Neumann entropy, an information-theoretic tool, to extract features
that capture the neighborhood's topology. Moreover, on graph classification
tasks, we suggest the utilization of the generated structural embeddings for
the transformation of an attributed graph structure into a set of augmented
node attributes. Empirically, we observe that the proposed approach exhibits
robustness on structural role identification tasks and state-of-the-art
performance on graph classification tasks, while maintaining very high
computational speed.


  We present a detailed benchmarking of different treatments of the QCD
evolution of unpolarized PDFs at approximate $N^3LO$ ($aN^3LO$) order in the
QCD coupling. Namely, the implementations in the public $aN^3LO$ releases of
the MSHT and NNPDF global PDF fitters, as well as that of the theoretical
FHMRUVV collaboration are compared. This follows the same procedure as in
previous benchmarking exercises at lower order, that is by considering the
impact of this evolution on a set of simple toy PDFs.


  Submodularity is one of the most well-studied properties of problem classes
in combinatorial optimization and many applications of machine learning and
data mining, with strong implications for guaranteed optimization. In this
thesis, we investigate the role of submodularity in provable non-convex
optimization and validation of algorithms. A profound understanding which
classes of functions can be tractably optimized remains a central challenge for
non-convex optimization. By advancing the notion of submodularity to continuous
domains (termed "continuous submodularity"), we characterize a class of
generally non-convex and non-concave functions -- continuous submodular
functions, and derive algorithms for approximately maximizing them with strong
approximation guarantees. Meanwhile, continuous submodularity captures a wide
spectrum of applications, ranging from revenue maximization with general
marketing strategies, MAP inference for DPPs to mean field inference for
probabilistic log-submodular models, which renders it as a valuable domain
knowledge in optimizing this class of objectives. Validation of algorithms is
an information-theoretic framework to investigate the robustness of algorithms
to fluctuations in the input/observations and their generalization ability. We
investigate various algorithms for one of the paradigmatic unconstrained
submodular maximization problem: MaxCut. Due to submodularity of the MaxCut
objective, we are able to present efficient approaches to calculate the
algorithmic information content of MaxCut algorithms. The results provide
insights into the robustness of different algorithmic techniques for MaxCut.


  We introduce a novel approach based on elastic and inelastic scattering rates
to extract the hyper-surface of the chemical freeze-out from a hadronic
transport model in the energy range from E$_\mathrm{lab}=1.23$ AGeV to
$\sqrt{s_\mathrm{NN}}=62.4$ GeV. For this study, the Ultra-relativistic Quantum
Molecular Dynamics (UrQMD) model combined with a coarse-graining method is
employed. The chemical freeze-out distribution is reconstructed from the pions
through several decay and re-formation chains involving resonances and taking
into account inelastic, pseudo-elastic and string excitation reactions. The
extracted average temperature and baryon chemical potential are then compared
to statistical model analysis. Finally we investigate various freeze-out
criteria suggested in the literature. We confirm within this microscopic
dynamical simulation, that the chemical freeze-out at all energies coincides
with $\langle E\rangle/\langle N\rangle\approx1$ GeV, while other criteria,
like $s/T^3=7$ and $n_\mathrm{B}+n_\mathrm{\bar{B}}\approx0.12$ fm$^{-3}$ are
limited to higher collision energies.


  We have observed the energy structure in the density of occupied states of
graphene grown on n-type 6H-SiC (0001). The structure revealed with
photoelectron spectroscopy is described by creation of the quantum well states
whose number and the energy position (E1 = 0.3 eV, E2 = 1.2 eV, E3 = 2.6 eV )
coincide with the calculated ones for deep (V = 2.9 eV) and narrow (d = 2.15 A)
quantum well formed by potential relief of the valence bands in the structure
graphene/n-SiC. We believe that the quantum well states should be formed also
in graphene on dielectric and in suspended graphene.


  Using high-resolution hydrodynamics simulations, we show that equal-mass
binaries accreting from a circumbinary disk evolve toward an orbital
eccentricity of $e \simeq 0.45$, unless they are initialized on a nearly
circular orbit with $e \lesssim 0.08$, in which case they further circularize.
The implied bi-modal eccentricity distribution resembles that seen in post-AGB
stellar binaries. Large accretion spikes around periapse impart a tell-tale,
quasi-periodic, bursty signature on the light curves of eccentric binaries. We
predict that intermediate-mass and massive black hole binaries at $z \lesssim
10$ entering the \emph{LISA} band will have measurable eccentricities in the
range $e \simeq 10^{-3} - 10^{-2}$, if they have experienced a gas-driven
phase. On the other hand, GW190521 would have entered the LIGO/Virgo band with
undetectable eccentricity $\sim 10^{-6}$ if it had been driven into the
gravitational wave regime by a gas disk.


  A graph $G$ is said to be \textit{determined by its generalized spectrum}
(DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with
cospectral complements implies that $H$ is isomorphic to $G$. In \cite{WX,WX1},
Wang and Xu gave some methods for determining whether a family of graphs are
DGS. In this paper, we shall review some of the old results and present some
new ones along this line of research.


  In conventional scattering theory, by large-distance asymptotics, at the cost
of losing the information of the distance between target and observer, one
imposes a large-distance asymptotics to achieve a scattering wave function
which can be represented explicitly by a scattering phase shift. In this paper,
without large-distance asymptotics, we establish an arbitrary-dimensional
scattering theory. Arbitrary-dimensional scattering wave functions, scattering
boundary conditions, cross sections, and phase shifts are given without
large-distance asymptotics. The importance of an arbitrary-dimensional
scattering theory is that the dimensional renormalization procedure in quantum
field theory needs an arbitrary-dimensional result. Moreover, we give a
discussion of one- and two-dimensional scatterings.


  The order of the Milnor fiber monodromy operator of a central hyperplane
arrangement is shown to be combinatorially determined. In particular, a
necessary and sufficient condition for the triviality of this monodromy
operator is given.
  It is known that the complement of a complex hyperplane arrangement is
cohomologically Tate and, if the arrangement is defined over $\Q$, has
polynomial count. We show that these properties hold for the corresponding
Milnor fibers if the monodromy is trivial.
  We construct a hyperplane arrangement defined over $\Q$, whose Milnor fiber
has a nontrivial monodromy operator, is cohomologically Tate, and has not
polynomial count. Such examples are shown not to exist in low dimensions.


  We present Hall effect, $R_{xy}(H)$, and magnetoresistance, $R_{xx}(H)$,
measurements of ultrathin films of Ni, Co and Fe with thicknesses varying
between 0.2-8 nm and resistances between 1 M$\Omega$ - 100 $\Omega.$ Both
measurements show that films having resistance above a critical value, $R_{C}$,
(thickness below a critical value, $d_{C}$) show no signs for ferromagnetism.
Ferromagnetism appears only for films with $R<R_{C}$, where $R_{C}$ is material
dependent. We raise the possibility that the reason for the absence of
spontaneous magnetization is suppression of itinerant ferromagnetism by
electronic disorder in the strong localization regime.


  We study the feedback of star formation and nuclear activity on the chemistry
of molecular gas in NGC1068, a nearby (D=14Mpc) Seyfert 2 barred galaxy, by
analyzing if the abundances of key molecular species like ethynyl (C2H), a
classical tracer of PDR, change in the different environments of the disk of
the galaxy. We have used ALMA to map the emission of the hyperfine multiplet of
C2H(N=1-0) and its underlying continuum emission in the central
r~35"(2.5kpc)-region of the disk of NGC1068 with a spatial resolution
1.0"x0.7"(50-70pc). We have developed a set of time-dependent chemical models
to determine the origin of the C2H gas. A sizeable fraction of the total C2H
line emission is detected from the r~1.3kpc starburst (SB) ring. However, the
brightest C2H emission originates from a r~200pc off-centered circumnuclear
disk (CND), where evidence of a molecular outflow has been previously found in
other molecular tracers imaged by ALMA. We also detect significant emission
that connects the CND with the outer disk. We derived the fractional abundances
of C2H (X(C2H)) assuming LTE conditions. Our estimates range from X(C2H)~a few
10^-8 in the SB ring up to X(C2H)~ a few 10^-7 in the outflow region. PDR
models that incorporate gas-grain chemistry are able to account for X(C2H) in
the SB ring for moderately dense (n(H2)>10^4 cm^-3) and moderately
UV-irradiated gas (UV-field<10xDraine field) in a steady-state regime. However,
the high fractional abundances estimated for C2H in the outflow region can only
be reached at very early times (T< 10^2-10^3 yr) in models of UV/X-ray
irradiated dense gas (n(H2)>10^4-10^5) cm^-3). We interpret that the transient
conditions required to fit the high values of X(C2H) in the outflow are likely
due to UV/X-ray irradiated non-dissociative shocks associated with the highly
turbulent interface between the outflow and the molecular gas in NGC1068.


  A measurement of the lateral distribution of Cherenkov light in Extensive Air
Showers (EAS) at E0 = 10-100 TeV and a study of the compatibility of the photon
number spectra with the expectations from the direct measurements of p and He
spectra and the Corsika-QGSJET propagation code in the atmosphere have been
performed at the National Gran Sasso Laboratories by the EAS-TOP and MACRO
arrays. The telescope array of EAS-TOP has been used as the Cherenkov light
detector. The muon tracking system of MACRO in the deep underground Gran Sasso
Laboratories (Emuon> 1.3 TeV) served as the EAS detector, including core
localization and arrival direction.


  Evolved Wolf-Rayet stars form a key aspect of massive star evolution, and
their strong outflows determine their final fates. In this study, we calculate
grids of stellar models for a wide range of initial masses at five
metallicities (ranging from solar down to just 2% solar). We compare a recent
hydrodynamically-consistent wind prescription with two earlier frequently-used
wind recipes in stellar evolution and population synthesis modelling, and we
present the ranges of maximum final masses at core He-exhaustion for each wind
prescription and metallicity Z. Our model grids reveal qualitative differences
in mass-loss behaviour of the wind prescriptions in terms of "convergence".
Using the prescription from Nugis & Lamers the maximum stellar black hole is
found to converge to a value of 20-30Msun, independent of host metallicity,
however when utilising the new physically-motivated prescription from Sander &
Vink there is no convergence to a maximum black hole mass value. The final mass
is simply larger for larger initial He-star mass, which implies that the upper
black hole limit for He-stars below the pair-instability gap is set by prior
evolution with mass loss, or the pair instability itself. Quantitatively, we
find the critical Z for pair-instability (Z_PI) to be as high as 50% Zsolar,
corresponding to the host metallicity of the LMC. Moreover, while the Nugis &
Lamers prescription would not predict any black holes above the approx 130Msun
pair-instability limit, with Sander & Vink winds included, we demonstrate a
potential channel for very massive helium stars to form such massive black
holes at ~2% Zsolar or below.


  An increasing number of early-type (O and Wolf-Rayet) colliding wind binaries
(CWBs) is known to accelerate particles up to relativistic energies. In this
context, non-thermal emission processes such as inverse Compton (IC) scattering
are expected to produce a high energy spectrum, in addition to the strong
thermal emission from the shock-heated plasma. SIMBOL-X will be the ideal
observatory to investigate the hard X-ray spectrum (above 10 keV) of these
systems, i.e. where it is no longer dominated by the thermal emission. Such
observations are strongly needed to constrain the models aimed at understanding
the physics of particle acceleration in CWB. Such systems are important
laboratories for investigating the underlying physics of particle acceleration
at high Mach number shocks, and probe a different region of parameter space
than studies of supernova remnants.


  Multi-view representation learning aims to capture comprehensive information
from multiple views of a shared context. Recent works intuitively apply
contrastive learning to different views in a pairwise manner, which is still
scalable: view-specific noise is not filtered in learning view-shared
representations; the fake negative pairs, where the negative terms are actually
within the same class as the positive, and the real negative pairs are
coequally treated; evenly measuring the similarities between terms might
interfere with optimization. Importantly, few works study the theoretical
framework of generalized self-supervised multi-view learning, especially for
more than two views. To this end, we rethink the existing multi-view learning
paradigm from the perspective of information theory and then propose a novel
information theoretical framework for generalized multi-view learning. Guided
by it, we build a multi-view coding method with a three-tier progressive
architecture, namely Information theory-guided hierarchical Progressive
Multi-view Coding (IPMC). In the distribution-tier, IPMC aligns the
distribution between views to reduce view-specific noise. In the set-tier, IPMC
constructs self-adjusted contrasting pools, which are adaptively modified by a
view filter. Lastly, in the instance-tier, we adopt a designed unified loss to
learn representations and reduce the gradient interference. Theoretically and
empirically, we demonstrate the superiority of IPMC over state-of-the-art
methods.


  A distinguishable physical property between a naked singularity and a
black-hole, formed during a gravitational collapse has important implications
for both experimental and theoretical relativity. We examine the energy
radiated during the spherically symmetric Gravitational collapse in this
context within the framework of general relativity. It is shown that total
energy radiated(Mass Loss) during the collapse ending in a naked singularity
scenario cannot be more than the case when a collapse scenario ends in a
black-hole. In cases of interest(for example stars having same mass, size, and
internal composition) considered here the total energy released in the collapse
ending in a black hole can be considerably more than the case otherwise.


  The static and dynamic structure factors of an interacting Fermi gas along
the BCS-BEC crossover are calculated at momentum transfer $\hbar{\bf k}$ higher
than the Fermi momentum. The spin structure factor is found to be very
sensitive to the correlations associated with the formation of molecules. On
the BEC side of the crossover, even close to unitarity, clear evidence is found
for a molecular excitation at $\hbar^2 k^2 /4m$, where $m$ is the atomic mass.
Both quantum Monte Carlo and dynamic mean-field results are presented.


  The convergence properties of numerical Regge calculus as an approximation to
continuum vacuum General Relativity is studied, both analytically and
numerically. The Regge equations are evaluated on continuum spacetimes by
assigning squared geodesic distances in the continuum manifold to the squared
edge lengths in the simplicial manifold. It is found analytically that,
individually, the Regge equations converge to zero as the second power of the
lattice spacing, but that an average over local Regge equations converges to
zero as (at the very least) the third power of the lattice spacing. Numerical
studies using analytic solutions to the Einstein equations show that these
averages actually converge to zero as the fourth power of the lattice spacing.


  The question of whether the anomalously large $B \to K\eta' $ and $B \to
K\eta' X $ (inclusive) branching ratios are consistent with the standard model
or a sign of new physics is still open and in the experimental court. The
nature of the extra hadron $X$ in $B \to K\eta' X $ is completely unknown.
Directions for investigation and analysis of inclusive data are suggested as
well as for comparable inclusive data on $B \to K\eta X $.
  New data confirming the prediction $BR(K^\pm \rho^o) = BR(K^\pm \omega)$
support flavor-topology $B \to VP$ sum rules based on the OZI rule and
emphasize the sharp contrast with the failure of the analogous $B \to PP $ sum
rule due to the anomalously large $BR(B \to K\eta')$. Confirmation of OZI
validity in B-decay analyses for VP final states suggests improving data on the
analogous neutral decay difference $BR(B^o \to K^o \rho^o) - BR(B^o \to K^o
\omega)$ which measures tree-penguin interference and possible direct CP
violation.
  A successful approximate isospin sum rule is rearranged and reinterpreted to
pinpoint tree-penguin interference in $B \to K \pi$ and $B \to K \rho$
transitions. The magnitude of the interference is shown to still be at the
statistical noise level with present data.


  For the first time, we have measured the optical noise equivalent power (NEP)
in titanium (Ti) superconducting hot-electron nanobolometers (nano-HEBs). The
bolometers were 2{\mu}mx1{\mu}mx20nm and 1{\mu}mx1{\mu}mx20nm planar
antenna-coupled devices. The measurements were done at {\lambda} = 460 {\mu}m
using a cryogenic black body radiation source delivering optical power from a
fraction of a femtowatt to a few 100s of femtowatts. A record low NEP =
3x10^{-19} W/Hz^{1/2} at 50 mK has been achieved. This sensitivity meets the
requirements for SAFARI instrument on the SPICA telescope. The ways for further
improvement of the nano-HEB detector sensitivity are discussed.


  A realization of Majorana fermions is proposed in the frustrated magnets via
the topological proximity effect. Specifically, we consider a theoretical
model, where a topological insulator is coupled to a frustrated magnetic
material through the spin exchange interaction. Using the renormalization
group-based self-consistent mean-field approach, and calculating the
self-energy correction due to the topological insulator, we find that the spin
texture and the spin-momentum locking of the Dirac cone will be inherited by
the spinons in the nearby frustrated magnets. This leads to a particular
topological state of matter that supports the Majorana excitations. Unlike the
conventional realization in SC systems, these Majorana fermions are the
combination of spinons and anti-spinons, rather than electrons and holes. They
can participate in the transport of spinons, leading to nontrivial properties
of the spin transport.


  In this paper, we derive the Cramer-Rao bound (CRB) for blind channel
estimation in redundant block transmission systems, a lower bound for the mean
squared error of any blind channel estimators. The derived CRB is valid for any
full-rank linear redundant precoder, including both zero-padded (ZP) and
cyclic-prefixed (CP) precoders. A simple form of CRBs for multiple complex
parameters is also derived and presented which facilitates the CRB derivation
of the problem of interest. A comparison is made between the derived CRBs and
performances of existing subspace-based blind channel estimators for both CP
and ZP systems. Numerical results show that there is still some room for
performance improvement of blind channel estimators.


  The Min proteins from Escherichia coli can self-organize into traveling waves
on supported lipid bilayers. In Proc. Natl. Acad. Sci. USA 109, 15283 (2012) we
showed that these waves are guided along the boundaries of membrane patches. We
introduced an effective two-dimensional model reproducing the observed
patterns. In arXiv:1403.5934v1, Jacob Halatek and Erwin Frey contest the
ability of our effective two-dimensional model to describe the dynamics of Min
proteins on patterned supported lipid bilayers. We thank Halatek and Frey for
their interest in our work and for again highlighting the importance of
dimensionality and geometry for pattern formation by the Min proteins. Here we
reply in detail to the objections by Halatek and Frey and show that (1) our
effective two-dimensional model reproduces the observed patterns on isolated
patches and that (2) a three-dimensional version of our model produces similar
patterns on square patches.


  We study strong-field double ionization in a three-electron atom by applying
a simplified, reduced-dimensionality model with three active electrons. The
influence of the spin-induced symmetry of the spatial part of the wavefunction
on the final two-photoectron momentum distribution is discussed. We identify
partial momentum distributions originating from different sets of spins of
outgoing electrons providing in this way a quantum support connection between
V-structure and direct ionization typically explained classically. Changes in
the momentum distribution with increasing field amplitude obtained in our
simplified model are shown to be well-correlated with experimental data known
from the literature. The possible relation between the observed dependencies
and different ionization mechanisms is discussed.


  We analyse the Anderson-Higgs mechanism of photon mass acquisition in a
plasma and study the contribution to the mass from the orbital angular momentum
acquired by a beam of photons when it crosses a spatially structured charge
distribution. To this end we apply Proca-Maxwell equations in a static plasma
with a particular spatial distribution of free charges, notably a plasma
vortex, that is able to impose orbital angular momentum (OAM) onto light. In
addition to the mass acquisition of the conventional Anderson-Higgs mechanism,
we find that the photon acquires an additional mass from the OAM and that this
mass reduces the Proca photon mass.


  Generalized planning studies the computation of general solutions for a set
of planning problems. Computing general solutions with correctness guarantee
has long been a key issue in generalized planning. Abstractions are widely used
to solve generalized planning problems. Solutions of sound abstractions are
those with correctness guarantees for generalized planning problems. Recently,
Cui et al. proposed a uniform abstraction framework for generalized planning.
They gave the model-theoretic definitions of sound and complete abstractions
for generalized planning problems. In this paper, based on Cui et al.'s work,
we explore automatic verification of sound abstractions for generalized
planning. We firstly present the proof-theoretic characterization for sound
abstraction. Then, based on the characterization, we give a sufficient
condition for sound abstractions which is first-order verifiable. To implement
it, we exploit regression extensions, and develop methods to handle counting
and transitive closure. Finally, we implement a sound abstraction verification
system and report experimental results on several domains.


  We present optical photometry and spectroscopy of five type Ia supernovae
discovered by the Nearby Supernova Factory selected to be spectroscopic
analogues of the candidate super-Chandrasekhar-mass events SN 2003fg and SN
2007if. Their spectra are characterized by hot, highly ionized photospheres
near maximum light, for which SN 1991T supplies the best phase coverage among
available close spectral templates. Like SN 2007if, these supernovae are
overluminous (-19.5 < M_V < -20) and the velocity of the Si II 6355 absorption
minimum is consistent with being constant in time from phases as early as a
week before, and up to two weeks after, $B$-band maximum light. We interpret
the velocity plateaus as evidence for a reverse-shock shell in the ejecta
formed by interaction at early times with a compact envelope of surrounding
material, as might be expected for SNe resulting from the mergers of two white
dwarfs. We use the bolometric light curves and line velocity evolution of these
SNe to estimate important parameters of the progenitor systems, including
nickel-56 mass, total progenitor mass, and masses of shells and surrounding
carbon/oxygen envelopes. We find that the reconstructed total progenitor mass
distribution of the events (including SN 2007if) is bounded from below by the
Chandrasekhar mass, with SN 2007if being the most massive. We discuss the
relationship of these events to the emerging class of super-Chandrasekhar-mass
SNe Ia, estimate the relative rates, compare the mass distribution to that
expected for double-degenerate SN Ia progenitors from population synthesis, and
consider implications for future cosmological Hubble diagrams.


  Greedy-NMS inherently raises a dilemma, where a lower NMS threshold will
potentially lead to a lower recall rate and a higher threshold introduces more
false positives. This problem is more severe in pedestrian detection because
the instance density varies more intensively. However, previous works on NMS
don't consider or vaguely consider the factor of the existent of nearby
pedestrians. Thus, we propose Nearby Objects Hallucinator (NOH), which
pinpoints the objects nearby each proposal with a Gaussian distribution,
together with NOH-NMS, which dynamically eases the suppression for the space
that might contain other objects with a high likelihood. Compared to
Greedy-NMS, our method, as the state-of-the-art, improves by $3.9\%$ AP,
$5.1\%$ Recall, and $0.8\%$ $\text{MR}^{-2}$ on CrowdHuman to $89.0\%$ AP and
$92.9\%$ Recall, and $43.9\%$ $\text{MR}^{-2}$ respectively.


  The solution of linear systems of equations is the basis of many other
quantum algorithms, and recent results provided an algorithm with optimal
scaling in both the condition number $\kappa$ and the allowable error
$\epsilon$ [PRX Quantum \textbf{3}, 0403003 (2022)]. That work was based on the
discrete adiabatic theorem, and worked out an explicit constant factor for an
upper bound on the complexity. Here we show via numerical testing on random
matrices that the constant factor is in practice about 1,500 times smaller than
the upper bound found numerically in the previous results. That means that this
approach is far more efficient than might naively be expected from the upper
bound. In particular, it is over an order of magnitude more efficient than
using a randomised approach from [arXiv:2305.11352] that claimed to be more
efficient.


  This report describes a minimalistic set of methods engineered to anchor
clinical events onto a temporal space. Specifically, we describe methods to
extract clinical events (e.g., Problems, Treatments and Tests), temporal
expressions (i.e., time, date, duration, and frequency), and temporal links
(e.g., Before, After, Overlap) between events and temporal entities. These
methods are developed and validated using high quality datasets.


  Faltings in 1983 proved that a necessary and sufficient condition for two
abelian varieties $A$ and $B$ to be isogenous over a number field $K$ is that
the local factors of the L-series of $A$ and $B$ are equal for almost all
primes of $K$ ; for each such prime this implies that $A$ and $B$ have the same
number of points over the residue field. We show in this article that for
abelian varieties faithfully of type GSp (a class containing the abelian
varieties with endomorphism ring $\mathbb{Z}$ and of odd dimension) `having the
same number of points' may be replaced by `the number of points have the same
prime divisors' and still gives a sufficient condition for $A$ and $B$ to be
$K$-isogenous. The proof is based on ideas of Serre \cite{serreim72} and
Frey-Jarden \cite{FJ} and follows closely Hall-Perucca \cite{hallp} who proved
the result for elliptic curves.


  We derive the Hamiltonian mass for general relativistic initial data sets
with asymptotically Schwarzschild-de Sitter ends.


  While deep learning models have greatly improved the performance of most
artificial intelligence tasks, they are often criticized to be untrustworthy
due to the black-box problem. Consequently, many works have been proposed to
study the trustworthiness of deep learning. However, as most open datasets are
designed for evaluating the accuracy of model outputs, there is still a lack of
appropriate datasets for evaluating the inner workings of neural networks. The
lack of datasets obviously hinders the development of trustworthiness research.
Therefore, in order to systematically evaluate the factors for building
trustworthy systems, we propose a novel and well-annotated sentiment analysis
dataset to evaluate robustness and interpretability. To evaluate these factors,
our dataset contains diverse annotations about the challenging distribution of
instances, manual adversarial instances and sentiment explanations. Several
evaluation metrics are further proposed for interpretability and robustness.
Based on the dataset and metrics, we conduct comprehensive comparisons for the
trustworthiness of three typical models, and also study the relations between
accuracy, robustness and interpretability. We release this trustworthiness
evaluation dataset at \url{https://github/xyz} and hope our work can facilitate
the progress on building more trustworthy systems for real-world applications.


  With the aim to assess the role of dense environments in galaxy interactions,
properties we present an analysis of close galaxy pairs in groups and clusters,
obtained from the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7). We
identified pairs that reside in groups by cross-correlating the total galaxy
pair catalogue with the SDSS-DR7 group catalogue from Zapata et al. (2009). We
classify pair galaxies according to the intensity of interaction. We analysed
the effect of high density environments on different classes of galaxy-galaxy
interactions and we have also studied the impact of the group global
environment on pair galaxies. We find that galaxy pairs are more concentrated
towards the group centres with respect to the other group galaxy members, and
disturbed pairs show a preference to contain the brightest galaxy in the
groups. The color-magnitude relation exhibits significant differences between
pair galaxies and the control sample, consisting in color tails with a clear
excess of extremely blue and red galaxies for merging systems. In addition,
pair galaxies show a significant excess of young stellar populations with
respect to galaxies in the control sample; this finding suggests that, in dense
environments, strong interactions produce an important effect in modifying
galaxy properties. We find that the fraction of star forming galaxies decreases
toward the group centre; however, galaxy pairs show a more efficient star
formation activity than galaxies without a close companion. We have also found
that pair galaxies prefer groups with low density global environments with
respect to galaxies of the corresponding control sample. Blue, young stellar
population galaxies prefer groups within low density global environments.


  Every properly colored graph with $\chi(G)=k$ colors has edge-disjoint Kempe
"backbones", Kempe chains anchored by color-critical vertices for each pair of
colors. Certain color permutations arrange these backbones into a clique-like
structure, a strengthening of strong immersions of complete graphs. This
strengthened immersion is suggested as a template for identifying the disjoint
subgraphs comprising Hadwiger's conjectured $K_k$ minor present in
$k$-chromatic graphs.


  Let $A$ be an $AH$ algebra, that is, $A$ is the inductive limit
$C^{*}$-algebra of
$$A_{1}\xrightarrow{\phi_{1,2}}A_{2}\xrightarrow{\phi_{2,3}}A_{3}\longrightarrow\cdots\longrightarrow
A_{n}\longrightarrow\cdots$$ with
$A_{n}=\bigoplus_{i=1}^{t_{n}}P_{n,i}M_{[n,i]}(C(X_{n,i}))P_{n,i}$, where
$X_{n,i}$ are compact metric spaces, $t_{n}$ and $[n,i]$ are positive integers,
and $P_{n,i}\in M_{[n,i]}(C(X_{n,i}))$ are projections. Suppose that $A$ has
the ideal property: each closed two-sided ideal of $A$ is generated by the
projections inside the ideal, as a closed two-sided ideal. Suppose that
$\sup_{n,i}dim(X_{n,i})<+\infty$. In this article, we prove that $A$ can be
written as the inductive limit of $$B_{1}\longrightarrow
B_{2}\longrightarrow\cdots\longrightarrow B_{n}\longrightarrow\cdots,$$ where
$B_{n}=\bigoplus_{i=1}^{s_{n}}Q_{n,i}M_{\{n,i\}}(C(Y_{n,i}))Q_{n,i}$, where
$Y_{n,i}$ are $\{pt\}$, $[0,1]$,$ S^{1}$,$ T_{II, k},$ $T_{III, k}$ and $S^{2}$
(all of them are connected simplicial complexes of dimension at most three),
$s_{n}$ and $\{n,i\}$ are positive integers and $Q_{n,i}\in
M_{\{n,i\}}(C(Y_{n,i}))$ are projections. This theorem unifies and generalizes
the reduction theorem for real rank zero $AH$ algebras due to Dadarlat and Gong
([D], [G3] and [DG]) and the reduction theorem for simple $AH$ algebras due to
Gong (see [G4]).


  In this paper we study non-central almost subnormal subgroups of the
multiplicative group of a division ring satisfying a non-zero generalized
rational identity. The main result generalizes Chiba's theorem on subnormal
subgroups. As an application, we get a theorem on almost subnormal subgroups
satisfying a generalized algebraic rational identity. The last theorem has
several corollaries which generalize completely or partially some previous
results.


  We consider monotonicity problems for graph searching games. Variants of
these games - defined by the type of moves allowed for the players - have been
found to be closely connected to graph decompositions and associated width
measures such as path- or tree-width. Of particular interest is the question
whether these games are monotone, i.e. whether the cops can catch a robber
without ever allowing the robber to reach positions that have been cleared
before. The monotonicity problem for graph searching games has intensely been
studied in the literature, but for two types of games the problem was left
unresolved. These are the games on digraphs where the robber is invisible and
lazy or visible and fast. In this paper, we solve the problems by giving
examples showing that both types of games are non-monotone. Graph searching
games on digraphs are closely related to recent proposals for digraph
decompositions generalising tree-width to directed graphs. These proposals have
partly been motivated by attempts to develop a structure theory for digraphs
similar to the graph minor theory developed by Robertson and Seymour for
undirected graphs, and partly by the immense number of algorithmic results
using tree-width of undirected graphs and the hope that part of this success
might be reproducible on digraphs using a directed tree-width. Unfortunately
the number of applications for the digraphs measures introduced so far is still
small. We therefore explore the limits of the algorithmic applicability of
digraph decompositions. In particular, we show that various natural candidates
for problems that might benefit from digraphs having small directed tree-width
remain NP-complete even on almost acyclic graphs.


  Despite the importance of AGN in galaxy evolution, accurate AGN
identification is often challenging, as common AGN diagnostics can be confused
by contributions from star formation and other effects (e.g.,
Baldwin-Phillips-Terlevich diagrams). However, one promising avenue for
identifying AGNs are ``coronal emission lines" (``CLs"), which are highly
ionized species of gas with ionization potentials $\ge$ 100 eV. These CLs may
serve as excellent signatures for the strong ionizing continuum of AGN. To
determine if CLs are in fact strong AGN tracers, we assemble and analyze the
largest catalog of optical CL galaxies using the Sloan Digital Sky Survey's
Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) catalog. We detect
CL emission in 71 MaNGA galaxies, out of the 10,010 unique galaxies from the
final MaNGA catalog, with $\ge$ 5$\sigma$ confidence. In our sample, we measure
[NeV]$\lambda$3347, $\lambda$3427, [FeVII]$\lambda$3586, $\lambda$3760,
$\lambda$6086, and [FeX]$\lambda$6374 emission and crossmatch the CL galaxies
with a catalog of AGNs that were confirmed with broad line, X-ray, IR, and
radio observations. We find that [NeV] emission, compared to [FeVII] and [FeX]
emission, is best at identifying high luminosity AGN. Moreover, we find that
the CL galaxies with the least dust extinction yield the most iron CL
detections. We posit that the bulk of the iron CLs are destroyed by dust grains
in the galaxies with the highest [OIII] luminosities in our sample, and that
AGN in the galaxies with low [OIII] luminosities are possibly too weak to be
detected using traditional techniques.


  In this paper we include dependency structures for electricity price
forecasting and forecasting evaluation. We work with off-peak and peak time
series from the German-Austrian day-ahead price, hence we analyze bivariate
data. We first estimate the mean of the two time series, and then in a second
step we estimate the residuals. The mean equation is estimated by OLS and
elastic net and the residuals are estimated by maximum likelihood. Our
contribution is to include a bivariate jump component on a mean reverting jump
diffusion model in the residuals. The models' forecasts are evaluated using
four different criteria, including the energy score to measure whether the
correlation structure between the time series is properly included or not. In
the results it is observed that the models with bivariate jumps provide better
results with the energy score, which means that it is important to consider
this structure in order to properly forecast correlated time series.


  Data-driven discoveries require identifying relevant data relationships from
a sea of complex, unstructured, and heterogeneous scientific data. We propose a
hybrid methodology that extracts metadata and leverages scientific domain
knowledge to synthesize a new dataset from the original to construct knowledge
graphs. We demonstrate our approach's effectiveness through a case study on the
natural hazard engineering dataset on ``LEAP Liquefaction'' hosted on
DesignSafe. Traditional lexical search on DesignSafe is limited in uncovering
hidden relationships within the data. Our knowledge graph enables complex
queries and fosters new scientific insights by accurately identifying relevant
entities and establishing their relationships within the dataset. This
innovative implementation can transform the landscape of data-driven
discoveries across various scientific domains.


  First, let $K \subset B(0,1) \subset \mathbb{R}^{2}$ be a set with
$\mathcal{H}_{\infty}^{1}(K) \sim 1$, and write $\pi_{e}(K)$ for the orthogonal
projection of $K$ into the line spanned by $e \in S^{1}$. For $1/2 \leq s < 1$,
write $$E_{s} := \{e : N(\pi_{e}(K),\delta) \leq \delta^{-s}\}, $$ where
$N(A,r)$ is the $r$-covering number of the set $A$. It is well-known -- and
essentially due to R. Kaufman -- that $N(E_{s},\delta) \lessapprox
\delta^{-s}$. Using the polynomial method, I prove that $$ N(E_{s},r)
\lessapprox
\min\left\{\delta^{-s}\left(\frac{\delta}{r}\right)^{1/2},r^{-1}\right\}, \quad
\delta \leq r \leq 1.$$ I construct examples showing that the exponents in the
bound are sharp for $\delta \leq r \leq \delta^{s}$.
  The second theorem concerns projections of $1$-Ahlfors-David regular sets.
Let $A \geq 1$ and $1/2 \leq s < 1$ be given. I prove that, for $p = p(A,s) \in
\mathbb{N}$ large enough, the finite set of unit vectors $S_{p} := \{e^{2\pi i
k/p} : 0 \leq k < p\}$ has the following property. If $K \subset B(0,1)$ is
non-empty and $1$-Ahlfors-David regular with regularity constant at most $A$,
then $$\frac{1}{p} \sum_{e \in S_{p}} N(\pi_{e}(K),\delta) \geq \delta^{-s}$$
for all small enough $\delta > 0$. In particular, $\overline{\dim}_{\text{B}}
\pi_{e}(K) \geq s$ for some $e \in S_{p}$.


  Let $v$ be a product of at most three not necessarily distinct primes. We
prove that there exists no strong external difference family with more than two
subsets in abelian group $G$ of order $v$, except possibly when $G=C_p^3$ and
$p$ is a prime greater than $3 \times 10^{12}$.


  In these notes we reformulate the classical Hilbert-Mumford criterion for GIT
stability in terms of algebraic stacks, this was independently done by
Halpern-Leinster. We also give a geometric condition that guarantees the
existence of separated coarse moduli spaces for the substack of stable objects.
This is then applied to construct coarse moduli spaces for torsors under
parahoric group schemes over curves.


  Single photons are of paramount importance to future quantum technologies,
including quantum communication and computation. Nonlinear photonic devices
using parametric processes offer a straightforward route to generating photons,
however additional nonlinear processes may come into play and interfere with
these sources. Here we analyse these sources in the presence of multi-photon
processes for the first time. We conduct experiments in silicon and gallium
indium phosphide photonic crystal waveguides which display inherently different
nonlinear absorption processes, namely two-photon (TPA) and three-photon
absorption (ThPA), respectively. We develop a novel model capturing these
diverse effects which is in excellent quantitative agreement with measurements
of brightness, coincidence-to-accidental ratio (CAR) and second-order
correlation function g(2)(0), showing that TPA imposes an intrinsic limit on
heralded single photon sources. We devise a new figure of merit, the quantum
utility (QMU), enabling direct comparison and optimisation of single photon
sources.


  We study the correspondence between the non-trivial topological properties
associated with the individual valleys of gapped bilayer graphene (BLG), as a
prototypical multi-valley system, and the gapless modes at its edges and other
interfaces. We find that the exact connection between the valley-specific Hall
conductivity and the number of gapless edge modes does not hold in general, but
is dependent on the boundary conditions, even in the absence of intervalley
coupling. This non-universality is attributed to the absence of a well-defined
topological invariant within a given valley of BLG; yet, a more general
topological invariant may be defined in certain cases, which explains the
distinction between the BLG-vacuum and BLG-BLG interfaces.


  We report the first detection of doubly-deuterated methanol (CHD2OH), as well
as firm detections of the two singly-deuterated isotopomers of methanol (CH2DOH
and CH3OD), towards the solar-type protostar IRAS16293-2422. From the present
multifrequency observations, we derive the following abundance ratios:
[CHD2OH]/[CH3OH] = 0.2 +/- 0.1, [CH2DOH]/[CH3OH] = 0.9 +/- 0.3, [CH3OD]/[CH3OH]
= 0.04 +/- 0.02. The total abundance of the deuterated forms of methanol is
greater than that of its normal hydrogenated counterpart in the circumstellar
material of IRAS16293-2422, a circumstance not previously encountered.
Formaldehyde, which is thought to be the chemical precursor of methanol,
possesses a much lower fraction of deuterated isotopomers (~ 20%) with respect
to the main isotopic form in IRAS16293-2422. The observed fractionation of
methanol and formaldehyde provides a severe challenge to both gas-phase and
grain-surface models of deuteration. Two examples of the latter model are
roughly in agreement with our observations of CHD2OH and CH2DOH if the
accreting gas has a large (0.2-0.3) atomic D/H ratio. However, no gas-phase
model predicts such a high atomic D/H ratio, and hence some key ingredient
seems to be missing.


  In the search for a novel MRI contrast agent which relies on T1 shortening
due to quadrupolar interaction between Bi nuclei and protons, a fast scanning
wideband system for zero-field nuclear quadrupole resonance (NQR) spectroscopy
is required. Established NQR probeheads with motor-driven tune-match stages are
usually bulky and slow, which can be prohibitive if it comes to Bi compounds
with low SNR (excessive averaging) and long quadrupolar T1 times. Moreover many
experiments yield better results at low temperatures such as 77K (liquid
nitrogen, LN) thus requiring easy to use cryo-probeheads. In this paper we
present electronically tuned wideband probeheads for bands in the frequency
range 20 - 120 MHz which can be immersed in LN and which enable very fast
explorative scans over the whole range. To this end we apply an interleaved
subspectrum sampling strategy (ISS) which relies on the electronic tuning
capability. The superiority of the new concept is demonstrated with an
experimental scan of triphenylbismuth from 24-116 MHz both at room temperature
and in LN. Especially for the first transition which exhibits extremely long T1
times (64ms) and low signal the new approach allows an acceleration factor by
more than 100 when compared to classical methods.


  With the Single-Instance Multi-Tenancy (SIMT) model for composite
Software-as-a-Service (SaaS) applications, a single composite application
instance can host multiple tenants, yielding the benefits of better service and
resource utilization, and reduced operational cost for the SaaS provider. An
SIMT application needs to share services and their aggregation (the
application) among its tenants while supporting variations in the functional
and performance requirements of the tenants. The SaaS provider requires a
middleware environment that can deploy, enact and manage a designed SIMT
application, to achieve the varied requirements of the different tenants in a
controlled manner. This paper presents the SDSN@RT (Software-Defined Service
Networks @ RunTime) middleware environment that can meet the aforementioned
requirements. SDSN@RT represents an SIMT composite cloud application as a
multi-tenant service network, where the same service network simultaneously
hosts a set of virtual service networks (VSNs), one for each tenant. A service
network connects a set of services, and coordinates the interactions between
them. A VSN realizes the requirements for a specific tenant and can be
deployed, configured, and logically isolated in the service network at runtime.
SDSN@RT also supports the monitoring and runtime changes of the deployed
multi-tenant service networks. We show the feasibility of SDSN@RT with a
prototype implementation, and demonstrate its capabilities to host SIMT
applications and support their changes with a case study. The performance study
of the prototype implementation shows that the runtime capabilities of our
middleware incur little overhead.


  In this paper we argue that data science is a coherent and novel approach to
empirical problems that, in its most general form, does not build understanding
about phenomena. Within the new type of mathematization at work in data
science, mathematical methods are not selected because of any relevance for a
problem at hand; mathematical methods are applied to a specific problem only by
'forcing', i.e. on the basis of their ability to reorganize the data for
further analysis and the intrinsic richness of their mathematical structure. In
particular, we argue that deep learning neural networks are best understood
within the context of forcing optimization methods. We finally explore the
broader question of the appropriateness of data science methods in solving
problems. We argue that this question should not be interpreted as a search for
a correspondence between phenomena and specific solutions found by data science
methods; rather, it is the internal structure of data science methods that is
open to precise forms of understanding.


  The main goal of this work is to study the sub-Laplacian of the unit sphere
which is obtained by lifting with respect to the Hopf fibration the Laplacian
of the quaternionic projective space. We obtain in particular explicit formulas
for its heat kernel and deduce an expression for the Green function of the
conformal sub-Laplacian and small-time asymptotics. As a byproduct of our study
we also obtain several results related to the sub-Laplacian of a projected Hopf
fibration.


  Our understanding of the Universe critically depends on the fundamental
knowledge of particles and fields, which represents a central endeavor of
modern high-energy physics. Energy frontier particle colliders - arguably,
among the largest, most complex and advanced scientific instruments of modern
times - for many decades have been at the forefront of scientific discoveries
in high-energy physics. Due to technology advances and beam physics
breakthroughs, the colliding beam facilities have progressed immensely and now
operate at energies and luminosities many orders of magnitude greater than the
pioneering instruments of the early 1960s. While the Large Hadron Collider and
the Super-KEKB factory represent the frontier hadron and lepton colliders of
today, respectively, future colliders are an essential component of a strategic
vision for particle physics. Conceptual studies and technical developments for
several exciting near- and medium-term future collider options are underway
internationally. Analysis of numerous proposals and studies for far-future
colliders indicate the limits of the collider beam technology due to machine
size, cost, and power consumption, and call for a paradigm shift of the
particle physics research at ultra-high energy but low luminosity colliders
approaching or exceeding 1 PeV center-of-mass energy scale.


  Ensemble defenses, are widely employed in various security-related
applications to enhance model performance and robustness. The widespread
adoption of these techniques also raises many questions: Are general ensembles
defenses guaranteed to be more robust than individuals? Will stronger adaptive
attacks defeat existing ensemble defense strategies as the cybersecurity arms
race progresses? Can ensemble defenses achieve adversarial robustness to
different types of attacks simultaneously and resist the continually adjusted
adaptive attacks? Unfortunately, these critical questions remain unresolved as
there are no platforms for comprehensive evaluation of ensemble adversarial
attacks and defenses in the cybersecurity domain. In this paper, we propose a
general Cybersecurity Adversarial Robustness Evaluation (CARE) platform aiming
to bridge this gap.


  We discuss some formal aspects of quantum anomalies with an emphasis on the
regularization of field theory. We briefly review how ambiguities in
perturbation theory have been resolved by various regularization schemes. To
single out the true quantum anomaly among ambiguities, the combined ideas of
PCAC, soft pion limit and renormalizability were essential. As for the formal
treatment of quantum anomalies, we mainly discuss the path integral formulation
both in continuum and lattice theories. In particular, we discuss in some
detail the recent development in the treatment of chiral anomalies in lattice
gauge theory.


  We report here our comparative analysis of active galactic nucleus (AGN) and
star formation (SF) characteristics of a sample of narrow-line Seyfert 1 (NLS1)
and broad-line Seyfert 1 (BLS1) galaxies. Our sample consisted of 373 BLS1 and
240 NLS1 galaxies spanning the redshift 0.02 to 0.8. The broad-band spectral
energy distribution, constructed using data from the ultra-violet to the
far-infrared, was modelled using CIGALE to derive the basic properties of our
sample. We searched for differences in stellar mass, star formation rate (SFR),
and AGN luminosity in the two populations. We also estimated new
radiation-pressure corrected black hole masses for our sample of BLS1 and NLS1
galaxies. While the virial black hole mass (MBH) of BLS1 galaxies is similar to
their radiation-pressure corrected MBH values, the virial MBH values of NLS1
galaxies are underestimated. We found that NLS1 galaxies have a lower MBH of
log (MBH) = 7.45 +/- 0.27 and a higher log (Eddington ratio) of -0.72 +/- 0.22
than BLS1 galaxies, which have log (MBH) and log (Eddington ratio) of 8.04 +/-
0.26 and -1.08 +/- 0.24, respectively. The distributions of stellar mass, SFR,
and specific star formation (sSFR = SFR/stellar mass) for the two populations
are indistinguishable. This analysis is based on an independent approach and
contradicts reports in the literature that NLS1 galaxies have a higher SF than
BLS1 galaxies. While we found that AGN luminosity increases with stellar mass,
luminosity of SF flattens at high stellar mass for both BLS1 and NLS1 galaxies.
The reason may be that SF is suppressed by AGN feedback at stellar mass higher
than 10^11 solar mass or that the AGN fuelling mechanism is decoupled from SF.
Separating the sample into radio-detected and radio-undetected subsamples, we
found no difference in their SF properties suggesting that the effect of AGN
jets on SF is negligible.


  We give a characterization of the strong degrees of categoricity of
computable structures greater or equal to $\mathbf 0''$. They are precisely the
\emph{treeable} degrees -- the least degrees of paths through computable trees
-- that compute $\mathbf 0''$. As a corollary, we obtain several new examples
of degrees of categoricity. Among them we show that every degree $\mathbf d$
with $\mathbf 0^{(\alpha)}\leq \mathbf d\leq \mathbf 0^{(\alpha+1)}$ for
$\alpha$ a computable ordinal greater than $2$ is the strong degree of
categoricity of a rigid structure. Using quite different techniques we show
that every degree $\mathbf d$ with $\mathbf 0'\leq \mathbf d\leq \mathbf 0''$
is the strong degree of categoricity of a structure. Together with the above
example this answers a question of Csima and Ng. To complete the picture we
show that there is a degree $\mathbf d$ with $\mathbf 0'< \mathbf d< \mathbf
0''$ that is not the degree of categoricity of a rigid structure.


  Attention computation takes both the time complexity of $O(n^2)$ and the
space complexity of $O(n^2)$ simultaneously, which makes deploying Large
Language Models (LLMs) in streaming applications that involve long contexts
requiring substantial computational resources. In recent OpenAI DevDay (Nov 6,
2023), OpenAI released a new model that is able to support a 128K-long
document, in our paper, we focus on the memory-efficient issue when context
length $n$ is much greater than 128K ($n \gg 2^d$). Considering a single-layer
self-attention with Query, Key, and Value matrices $Q, K, V \in \mathbb{R}^{n
\times d}$, the polynomial method approximates the attention output $T \in
\mathbb{R}^{n \times d}$. It accomplishes this by constructing $U_1, U_2 \in
\mathbb{R}^{n \times t}$ to expedite attention ${\sf Attn}(Q, K, V)$
computation within $n^{1+o(1)}$ time executions. Despite this, computing the
approximated attention matrix $U_1U_2^\top \in \mathbb{R}^{n \times n}$ still
necessitates $O(n^2)$ space, leading to significant memory usage. In response
to these challenges, we introduce a new algorithm that only reads one pass of
the data in a streaming fashion. This method employs sublinear space $o(n)$ to
store three sketch matrices, alleviating the need for exact $K, V$ storage.
Notably, our algorithm exhibits exceptional memory-efficient performance with
super-long tokens. As the token length $n$ increases, our error guarantee
diminishes while the memory usage remains nearly constant. This unique
attribute underscores the potential of our technique in efficiently handling
LLMs in streaming applications.


  We obtain a result concerning the stability under the interpolation with
functional parameter method for the approximation spaces of
Lorentz-Marcinkiewicz type and also for the approximation spaces generated by
symmetric norming functions of a certain type.


  We describe all Lyapunov spectra that can be obtained by perturbing the
derivatives along periodic orbits of a diffeomorphism. The description is
expressed in terms of the finest dominated splitting and Lyapunov exponents
that appear in the limit of a sequence of periodic orbits, and involves the
majorization partial order. Among the applications, we give a simple criterion
for the occurrence of universal dynamics.


  Half-metals are a class of materials that are metallic only for one spin
direction, and are essential for spintronics applications where one needs to
read, write, store and transfer spin-data. This spin sensitivity appears to
restrict them to be magnetic, and the known examples indeed are. The
fabrication of real spintronic devices from such materials is often hampered,
however, by stray magnetic fields, domain walls, short spin coherence times,
scattering on magnetic atoms or magnetically active interfaces, and other
characteristics that come along with the magnetism. The surfaces of topological
insulators, or Dirac or Weyl semimetals, could be an alternative, but
production of high-quality thin films without the presence of the bulk states
at the Fermi level remains very challenging. Here we introduce non-magnetic
half-metals and demonstrate that this state is realized in IrBiSe. Using
angle-resolved photoemission spectroscopy and band structure calculations we
find a record-high Dresselhaus spin-orbit splitting, fully spin-polarized
remnant Fermi surfaces and a chiral 3D spin-texture, all with no magnetism
present. Promising applications include using IrBiSe as a source of
spin-polarized electrons, and lightly doped IrBiSe is expected to generate
electric-field-controlled spin-polarized currents, free from back scattering,
and could host triplet superconductivity.


  It is very important to adhere strictly to ethical and social influences when
delivering most of our life to artificial intelligence systems. With industry
4.0, the internet of things, data analysis and automation have begun to be of
great importance in our lives. With the Yapanese version of Industry 5.0, it
has come to our attention that machine-human interaction and human intelligence
are working in harmony with the cognitive computer. In this context, robots
working on artificial intelligence algorithms co-ordinated with the development
of technology have begun to enter our lives. But the consequences of the recent
complaints of the Robots have been that important issues have arisen about how
to be followed in terms of intellectual property and ethics. Although there are
no laws regulating robots in our country at present, laws on robot ethics and
rights abroad have entered into force. This means that it is important that we
organize the necessary arrangements in the way that robots and artificial
intelligence are so important in the new world order. In this study, it was
aimed to examine the existing rules of machine and robot ethics and to set an
example for the arrangements to be made in our country, and various discussions
were given in this context.


  Adopting Dirac's brane variation prescription, the energy-momentum tensor of
a brane gets supplemented by a geometrical (embedding originated) dark
component. While the masslessness of the graviton is preserved, and the Newton
force law is recovered, the corresponding Newton constant is necessarily lower
than the one which governs FRW cosmology. This has the potential to puzzle out
cosmological dark matter, a subsequent conjecture concerning galactic dark
matter follows.


  Zernike polynomials are one of the most widely used mathematical descriptors
of optical aberrations in the fields of imaging and adaptive optics. Their
mathematical orthogonality as well as isomorphisms with experimentally
observable aberrations make them a very powerful tool in solving numerous
problems in beam optics. However, Zernike aberrations show cross-coupling
between individual modes when used in combination with Gaussian beams, an
effect that has not been extensively studied. Here we propose a novel framework
that is capable of explaining the fundamental cross-compensation of Zernike
type aberrations, both in low-aberration and high-aberration regimes. Our
approach is based on analysing the coupling between Zernike modes and different
classes of Laguerre-Gauss modes which allows investigating aberrated beams not
only on a single plane but also during their 3D propagation.


  In this paper, we propose a No-Reference Image Quality Assessment (NRIQA)
guided cut-off point selection (CPS) strategy to enhance the performance of a
fine-grained classification system. Scores given by existing NRIQA methods on
the same image may vary and not be as independent of natural image
augmentations as expected, which weakens their connection and explainability to
fine-grained image classification. Taking the three most commonly adopted image
augmentation configurations -- cropping, rotating, and blurring -- as the entry
point, we formulate a two-step mechanism for selecting the most discriminative
subset from a given image dataset by considering both the confidence of model
predictions and the density distribution of image qualities over several NRIQA
methods. Concretely, the cut-off points yielded by those methods are aggregated
via majority voting to inform the process of image subset selection. The
efficacy and efficiency of such a mechanism have been confirmed by comparing
the models being trained on high-quality images against a combination of high-
and low-quality ones, with a range of 0.7% to 4.2% improvement on a commercial
product dataset in terms of mean accuracy through four deep neural classifiers.
The robustness of the mechanism has been proven by the observations that all
the selected high-quality images can work jointly with 70% low-quality images
with 1.3% of classification precision sacrificed when using ResNet34 in an
ablation study.


  Various biological sensory systems exhibit a response to a relative change of
the stimulus, often referred to as fold-change detection. In the last few years
fold-change detecting mechanisms, based on transcriptional networks, have been
proposed. Here we present fold-change detecting mechanism, based on
protein-protein interactions, consisting of two interacting proteins. This
mechanism, in contrast to previously proposed mechanisms, does not consume
chemical energy and is not subject to transcriptional and translational noise.
We show by analytical and numerical calculations, that the mechanism can have a
fast, precise and efficient response for parameters that are relevant to
eukaryotic cells.


  Following the suggestion of Schwope et al that the magnetic cataclysmic
variable RX J2115-5840 maybe a near-synchronous polar, we obtained optical
polarimetry of this system over a 2 week period. From a power spectrum of the
circular polarimetry data we determine that the spin period of the white dwarf
and the binary orbital period which differ by 1.2%. RX J2115-5840 is thus the
fourth near synchronous polar and has the shortest spin-orbit beat period: 6.3
days. By folding the data on spin, beat and orbital periods we find evidence
that the accretion stream is directed towards opposite magnetic poles as the
stream precesses around the white dwarf on the spin-orbit beat period. The
phasing requires that the accretion flow must be directed onto the same
magnetic field line at all spin-orbit beat phases implying that at some phases
the flow must follow a path around the white dwarf before accreting. This is
difficult to reconcile with simple views of how the accretion stream attaches
onto the magnetic field of the white dwarf.


  We study the evolution of circumstellar massive disks around the primary star
of a binary system focusing on the computation of disk eccentricity. In
particular, we concentrate on its dependence on the binary eccentricity.
Self-gravity is included in our numerical simulations. Our standard model
assumes a semimajor axis for the binary of 30 AU, the most probable value
according to the present binary statistics.


  We investigate the transition from suppression to enhancement of J/psi mesons
produced in ultra-relativistic nuclear collisions in the framework of the
statistical hadronization model. The calculations are confronted with the most
recent data from the RHIC accelerator. This comparison yields first direct
evidence for generation of J/psi mesons at the phase boundary. Based on the
success of this approach we make specific predictions for LHC energy.


  We study phase shifts of the propagating slow waves in coronal loops invoking
the effects of thermal conductivity, compressive viscosity, radiative losses
and heating-cooling imbalance. We derive a general dispersion relation and
solve it to determine phase shifts of density and temperature perturbations
relative to the velocity and their dependence on equilibrium parameters
($\rho_0$, $T_0$). We estimate phase difference ($\Delta \phi$) between density
and temperature perturbations and its dependence on $\rho_0$ and $T_0$. The
effect of viscosity on the phase shifts was found negligible. The role of
radiative losses along with h/c imbalance for chosen specific heating function
($H(\rho, T) \propto \rho^{-0.5} T^{-3}$) in determining phase shifts, is found
to be significant for the high density and low temperature loops. The h/c
imbalance can increase the phase difference ($\Delta \phi \approx 140^\circ$)
for low temperature loops compared to the constant heating case ($\Delta \phi
\approx 30^\circ$). We derive a general expression for the polytropic index. We
find that in the presence of thermal conduction alone, the polytropic index
remains close to its classical value for all the considered $\rho_0$ and $T_0$.
However, it reduces to a value $1.2$ when loop density is decreased by an order
of magnitude compared to its normal coronal value. We find that the inclusion
of radiative losses, with or without h/c imbalance, cannot explain the observed
polytropic index. The thermal ratio ($d$) needs to be enhanced by an order of
magnitude, in order to explain its observed value $1.1 \pm 0.02$ in the solar
loops. We also explore the role of different heating functions for typical
coronal parameters and found that although the polytropic index remains close
to its classical value, the phase difference is highly dependent on the form of
heating function (The abstract is restructured for arxiv).


  Using the attractor mechanism and the relation between the quantization of
$H^{3}(M)$ and topological strings on a Calabi Yau threefold $M$ we define a
map from BPS black holes into coherent states. This map allows us to represent
the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the
phase space $H^{3}(M)$. This distribution function is a mixed
Husimi/anti-Husimi distribution corresponding to the different normal ordering
prescriptions for the string coupling and deviations of the complex structure
moduli. From the integral representation of this distribution function in terms
of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV)
conjecture in the region "at infinity" of the complex structure moduli space.
The physical meaning of the OSV corrections are briefly discussed in this
limit.


  We study polynomials p(x) satisfying a differential equation of the form
p"(x)-h'(x)p'(x)+H(x)p(x)=0, where h(x)=x^3/3+ax. We prove a conjecture of A.
Eremenko and A. Gabrielov.


  We investigate the relationship between the existence of directional
derivatives for cone-convex functions with values in a Banach space Y and
isomorphisms between Y and c0.


  A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any
matrix of the form $U = \alpha A + \beta I + \gamma J + \delta D$ with $\alpha
\neq 0$, where $I$ is the identity matrix, $J$ is the all-ones matrix and $D$
is the diagonal matrix with the vertex degrees. In the case that $G$ is the
disjoint union of regular graphs, we present an expression for the
characteristic polynomials of the various universal adjacency matrices in terms
of the characteristic polynomials of the adjacency matrices of the components.
As a consequence we obtain a formula for the characteristic polynomial of the
Seidel matrix of $G$, and the signless Laplacian of the complement of $G$ (i.e.
the join of regular graphs).


  The star HE 1305-0007 is a metal-poor double-enhanced star with metallicity
[Fe/H] $=-2.0$, which is just at the upper limit of the metallicity for the
observed double-enhanced stars. Using a parametric model, we find that almost
all s-elements were made in a single neutron exposure. This star should be a
member of a post-common-envelope binary. After the s-process material has
experienced only one neutron exposure in the nucleosynthesis region and is
dredged-up to its envelope, the AGB evolution is terminated by the onset of
common-envelope evolution. Based on the high radial-velocity of HE 1305-0007,
we speculate that the star could be a runaway star from a binary system, in
which the AIC event has occurred and produced the r-process elements.


  We investigate binary mixtures of large colloids interacting through soft
potentials with small, ideal depletants. We show that softness has a dramatic
effect on the resulting colloid-colloid effective potential when the
depletant-to-colloid size ratio $q$ is small, with significant consequences on
the colloidal phase behaviour. We also provide an exact relation that allows us
to obtain the effective pair potential for {\it any} type of colloid-depletant
interactions in the case of ideal depletants, without having to rely on
complicated and expensive full-mixture simulations. We also show that soft
repulsion among depletants further enhances the tendency of colloids to
aggregate. Our theoretical and numerical results demonstrate that --- in the
limit of small $q$ --- soft mixtures cannot be mapped onto hard systems and
hence soft depletion is not a mere extension of the widely used Asakura-Oosawa
potential.


  Nanoflares, short and intense heat pulses within spatially unresolved
magnetic strands, are now considered a leading candidate to solve the coronal
heating problem. However, the frequent occurrence of nanoflares requires that
flare-hot plasma be present in the corona at all times. Its detection has
proved elusive until now, in part because the intensities are predicted to be
very faint. Here we report on the analysis of an active region observed with
five filters by Hinode/XRT in November 2006. We have used the filter ratio
method to derive maps of temperature and emission measure both in soft and hard
ratios. These maps are approximate in that the plasma is assumed to be
isothermal along each line-of-sight. Nonetheless, the hardest available ratio
reveals the clear presence of plasma around 10 MK. To obtain more detailed
information about the plasma properties, we have performed Monte Carlo
simulations assuming a variety of non-isothermal emission measure distributions
along the lines-of-sight. We find that the observed filter ratios imply
bi-modal distributions consisting of a strong cool (log T ~ 6.3-6.5) component
and a weaker (few percent) and hotter (6.6 < log T < 7.2) component. The data
are consistent with bi-modal distributions along all lines of sight, i.e.,
throughout the active region. We also find that the isothermal temperature
inferred from a filter ratio depends sensitively on the precise temperature of
the cool component. A slight shift of this component can cause the hot
component to be obscured in a hard ratio measurement. Consequently, temperature
maps made in hard and soft ratios tend to be anti-correlated. We conclude that
this observation supports the presence of widespread nanoflaring activity in
the active region.


  We present a random number generation scheme based on measuring the phase
fluctuations of a laser with a simple and compact experimental setup. A simple
model is established to analyze the randomness and the simulation result based
on this model fits well with the experiment data. After the analog to digital
sampling and suitable randomness extraction integrated in the field
programmable gate array, the final random bits are delivered to a PC, realizing
a 5.4 Gbps real time quantum random number generation. The final random bit
sequences have passed all the NIST and DIEHARD tests.


  A field excited by an emitter can be enhanced due to presence of closely
located inclusions. In this paper we consider such field enhancement when
inclusions are disks of the same radii, and the emitter is of dipole type and
located in the narrow region between two inclusions. We derive quantitatively
precise estimates of the field enhancement in the narrow region. The estimates
reveal that the field is enhanced by a factor of $\epsilon^{-1/2}$ in most
area, where $\epsilon$ is the distance between two inclusions. This factor is
the same as that of gradient blow-up when there is a smooth back-ground field,
not a field excited by an emitter. The method of deriving estimates shows
clearly that enhancement is due to potential gap between two inclusions.


  Tidal effects on clumps of material during random non-stationary accretion
onto a black hole produce phenomena with distinct temporal characteristics in
observed light-curves. During such non-stationary accretion events, the shape
of the accreting object evolves in time, and observable quasi-periodic
phenomena with variable quasi-periods are produced. A number of characteristic
light-curves, obtained with numerical simulations, will be shown. Their
relevance to observed phenomena will be briefly discussed.


  We give a brief overview of a simple and unified way, called the prepotential
approach, to treat both exact and quasi-exact solvabilities of the
one-dimensional Schr\"odinger equation. It is based on the prepotential
together with Bethe ansatz equations. Unlike the the supersymmetric method for
the exactly-solvable systems and the Lie-algebraic approach for the
quasi-exactly solvable problems, this approach does not require any knowledge
of the underlying symmetry of the system. It treats both quasi-exact and exact
solvabilities on the same footing. In this approach the system is completely
defined by the choice of two polynomials and a set of Bethe ansatz equations.
The potential, the change of variables as well as the eigenfunctions and
eigenvalues are determined in the same process. We illustrate the approach by
several paradigmatic examples of Hermitian and non-Hermitian Hamiltonians with
real energies. Hermitian systems with complex energies, called the quasinormal
modes, are also presented. Extension of the approach to the newly discovered
rationally extended models is briefly discussed.


  We present an approach for multi-robot consistent distributed localization
and semantic mapping in an unknown environment, considering scenarios with
classification ambiguity, where objects' visual appearance generally varies
with viewpoint. Our approach addresses such a setting by maintaining a
distributed posterior hybrid belief over continuous localization and discrete
classification variables. In particular, we utilize a viewpoint-dependent
classifier model to leverage the coupling between semantics and geometry.
Moreover, our approach yields a consistent estimation of both continuous and
discrete variables, with the latter being addressed for the first time, to the
best of our knowledge. We evaluate the performance of our approach in a
multi-robot semantic SLAM simulation and in a real-world experiment,
demonstrating an increase in both classification and localization accuracy
compared to maintaining a hybrid belief using local information only.


  Short abstract: We present fully 3-D simulations of supersonic, radiatively
cooling intermittent jets with intermediate and long variability periods (that
is, periods of the order of or longer than, the dynamical time scale of the
jet). Variations of intermediate period elucidate the formation and evolution
of chains of internal regularly spaced radiative shocks, which in this work are
identified with the observed emission knots of protostellar jets. Variations of
long period elucidate the formation of multiple bow shock structures separated
by long trails of diffuse gas, which resemble those observed in systems like
HH111 and HH46/47. The time variability of the outflow is probably associated
with observed irruptive events in the accretion process around the protostars.
In our simulations, the outflow variations are produced by periodically turning
on the outflow with a highly supersonic velocity and periodically turning off
it to a low velocity regime. In the case of velocity variations of intermediate
period, we find, as in previous work, that the shock structures form a train of
regularly spaced emitting features which move away from the source with a
velocity close to that of the outflow, have high radial motions, and produce
low intensity spectra, as required by the observations. As they propagate
downstream, the shocks widen and dissipate due to the expulsion of material
sideways to the cocoon by the high pressure gradients of the postshock gas.
This fading explains the most frequent occurence of knots closer to the driving
source. In the case of the long period velocity variability, our simulations
have produced a pair of bow-shock-like structures separated by a trail almost


  Let G be a finite group and \rho: G--> End(E) be a group representation of G
on a coherent sheaf over an integral scheme. The purpose of this paper shall
give a decomposition theorem of such representations in non-splitting
components and apply this results to the studie of Galois covers


  In this paper, we prove that the bound \[ \max \{ |8A-7A|,|5f(A)-4f(A)| \}
\gg |A|^{\frac{3}{2} + \frac{1}{54}-o(1)} \] holds for all $A \subset \mathbb
R$, and for all convex functions $f$ which satisfy an additional technical
condition. This technical condition is satisfied by the logarithmic function,
and this fact can be used to deduce a sum-product estimate \[ \max \{ |16A| ,
|A^{(16)}| \} \gg |A|^{\frac{3}{2} + c}, \] for some $c>0$. Previously, no
sum-product estimate over $\mathbb R$ with exponent strictly greater than $3/2$
was known for any number of variables. Moreover, the technical condition on $f$
seems to be satisfied for most interesting cases, and we give some further
applications. In particular, we show that \[ |AA| \leq K|A| \implies \,\forall
d \in \mathbb R \setminus \{0 \}, \,\, |\{(a,b) \in A \times A : a-b=d \}| \ll
K^C |A|^{\frac{2}{3}-c'}, \] where $c,C>0$ are absolute constants.


  We explore the relationship between four-dimensional N=2 quantum field
theories and their associated BPS quivers. For a wide class of theories
including super-Yang-Mills theories, Argyres-Douglas models, and theories
defined by M5-branes on punctured Riemann surfaces, there exists a quiver which
implicitly characterizes the field theory. We study various aspects of this
correspondence including the quiver interpretation of flavor symmetries,
gauging, decoupling limits, and field theory dualities. In general a given
quiver describes only a patch of the moduli space of the field theory, and a
key role is played by quantum mechanical dualities, encoded by quiver
mutations, which relate distinct quivers valid in different patches. Analyzing
the consistency conditions imposed on the spectrum by these dualities results
in a powerful and novel mutation method for determining the BPS states. We
apply our method to determine the BPS spectrum in a wide class of examples,
including the strong coupling spectrum of super-Yang-Mills with an ADE gauge
group and fundamental matter, and trinion theories defined by M5-branes on
spheres with three punctures.


  We use the IllustrisTNG cosmological hydrodynamical simulation to study the
evolution of star formation rate (SFR)-density relation over cosmic time. We
construct several samples of galaxies at different redshifts from $z=2.0$ to
$z=0.0$, which have the same comoving number density. The SFR of galaxies
decreases with local density at $z=0.0$, but its dependence on local density
becomes weaker with redshift. At $z\gtrsim1.0$, the SFR of galaxies increases
with local density (reversal of the SFR-density relation), and its dependence
becomes stronger with redshift. This change of SFR-density relation with
redshift still remains even when fixing the stellar masses of galaxies. The
dependence of SFR on the distance to a galaxy cluster also shows a change with
redshift in a way similar to the case based on local density, but the reversal
happens at a higher redshift, $z\sim1.5$, in clusters. On the other hand, the
molecular gas fraction always decreases with local density regardless of
redshift at $z=0.0-2.0$ even though the dependence becomes weaker when we fix
the stellar mass. Our study demonstrates that the observed reversal of the
SFR-density relation at $z\gtrsim1.0$ can be successfully reproduced in
cosmological simulations. Our results are consistent with the idea that
massive, star-forming galaxies are strongly clustered at high redshifts,
forming larger structures. These galaxies then consume their gas faster than
those in low-density regions through frequent interactions with other galaxies,
ending up being quiescent in the local universe.


  We study the use of amortized optimization to predict optimal transport (OT)
maps from the input measures, which we call Meta OT. This helps repeatedly
solve similar OT problems between different measures by leveraging the
knowledge and information present from past problems to rapidly predict and
solve new problems. Otherwise, standard methods ignore the knowledge of the
past solutions and suboptimally re-solve each problem from scratch. We
instantiate Meta OT models in discrete and continuous settings between
grayscale images, spherical data, classification labels, and color palettes and
use them to improve the computational time of standard OT solvers. Our source
code is available at http://github.com/facebookresearch/meta-ot