  We consider generative adversarial networks (GAN) for estimating parameters
in a deep generative model. The data-generating distribution is assumed to
concentrate around some low-dimensional structure, making the target
distribution singular to the Lebesgue measure. Under this assumption, we obtain
convergence rates of a GAN type estimator with respect to the Wasserstein
metric. The convergence rate depends only on the noise level, intrinsic
dimension and smoothness of the underlying structure. Furthermore, the rate is
faster than that obtained by likelihood approaches, which provides insights
into why GAN approaches perform better in many real problems. A lower bound of
the minimax optimal rate is also investigated.


  Let $\sigma =\{\sigma_{i} | i\in I\}$ be some partition of the set of all
primes $\Bbb{P}$, $G$ a finite group and $\sigma (G) =\{\sigma_{i}
|\sigma_{i}\cap \pi (G)\ne \emptyset \}$. A set ${\cal H}$ of subgroups of $G$
is said to be a complete Hall $\sigma $-set of $G$ if every member $\ne 1$ of
${\cal H}$ is a Hall $\sigma_{i}$-subgroup of $G$ for some $\sigma_{i}\in
\sigma $ and ${\cal H}$ contains exactly one Hall $\sigma_{i}$-subgroup of $G$
for every $\sigma_{i}\in \sigma (G)$. A subgroup $A$ of $G$ is said to be
${\sigma}$-permutable in $G$ if $G$ possesses a complete Hall $\sigma $-set and
$A$ permutes with each Hall $\sigma_{i}$-subgroup $H$ of $G$, that is, $AH=HA$
for all $i \in I$. We characterize finite groups with distributive lattice of
the ${\sigma}$-permutable subgroups.


  Large real-world networks are typically scale-free. Recent research has shown
that such graphs are described best in a geometric space. More precisely, the
internet can be mapped to a hyperbolic space such that geometric greedy routing
performs close to optimal (Bogun\'a, Papadopoulos, and Krioukov. Nature
Communications, 1:62, 2010). This observation pushed the interest in hyperbolic
networks as a natural model for scale-free networks. Hyperbolic random graphs
follow a power-law degree distribution with controllable exponent $\beta$ and
show high clustering (Gugelmann, Panagiotou, and Peter. ICALP, pp. 573-585,
2012).
  For understanding the structure of the resulting graphs and for analyzing the
behavior of network algorithms, the next question is bounding the size of the
diameter. The only known explicit bound is $\mathcal O((\log
n)^{32/((3-\beta)(5-\beta)) + 1})$ (Kiwi and Mitsche. ANALCO, pp. 26-39, 2015).
We present two much simpler proofs for an improved upper bound of $\mathcal
O((\log n)^{2/(3-\beta)})$ and a lower bound of $\Omega(\log n)$.


  This paper questions the effectiveness of a modern predictive uncertainty
quantification approach, called \emph{evidential deep learning} (EDL), in which
a single neural network model is trained to learn a meta distribution over the
predictive distribution by minimizing a specific objective function. Despite
their perceived strong empirical performance on downstream tasks, a line of
recent studies by Bengs et al. identify limitations of the existing methods to
conclude their learned epistemic uncertainties are unreliable, e.g., in that
they are non-vanishing even with infinite data. Building on and sharpening such
analysis, we 1) provide a sharper understanding of the asymptotic behavior of a
wide class of EDL methods by unifying various objective functions; 2) reveal
that the EDL methods can be better interpreted as an out-of-distribution
detection algorithm based on energy-based-models; and 3) conduct extensive
ablation studies to better assess their empirical effectiveness with real-world
datasets. Through all these analyses, we conclude that even when EDL methods
are empirically effective on downstream tasks, this occurs despite their poor
uncertainty quantification capabilities. Our investigation suggests that
incorporating model uncertainty can help EDL methods faithfully quantify
uncertainties and further improve performance on representative downstream
tasks, albeit at the cost of additional computational complexity.


  Over the past several years, in order to solve the problem of malicious abuse
of facial manipulation technology, face manipulation detection technology has
obtained considerable attention and achieved remarkable progress. However, most
existing methods have very impoverished generalization ability and robustness.
In this paper, we propose a novel method for face manipulation detection, which
can improve the generalization ability and robustness by bag-of-local-feature.
Specifically, we extend Transformers using bag-of-feature approach to encode
inter-patch relationships, allowing it to learn local forgery features without
any explicit supervision. Extensive experiments demonstrate that our method can
outperform competing state-of-the-art methods on FaceForensics++, Celeb-DF and
DeeperForensics-1.0 datasets.


  Pulsar timing observations are usually analysed with least-square-fitting
procedures under the assumption that the timing residuals are uncorrelated
(statistically "white"). Pulsar observers are well aware that this assumption
often breaks down and causes severe errors in estimating the parameters of the
timing model and their uncertainties. Ad hoc methods for minimizing these
errors have been developed, but we show that they are far from optimal.
Compensation for temporal correlation can be done optimally if the covariance
matrix of the residuals is known using a linear transformation that whitens
both the residuals and the timing model. We adopt a transformation based on the
Cholesky decomposition of the covariance matrix, but the transformation is not
unique. We show how to estimate the covariance matrix with sufficient accuracy
to optimize the pulsar timing analysis. We also show how to apply this
procedure to estimate the spectrum of any time series with a steep red
power-law spectrum, including those with irregular sampling and variable error
bars, which are otherwise very difficult to analyse.


  We compute the flux of relic neutrino background (R$\nu$B) up-scattered by
ultra-high-energy (UHE) cosmic rays (CRs) in clusters that act as
CR-reservoirs. The long trapping times of UHECRs make this flux larger than
that of R$\nu$B up-scattered by UHECRs on their way to Earth, which we also
compute. We find that IceCube excludes R$\nu$B weighted overdensities larger
than $10^{10}$ in clusters, and that PUEO, RNO-G, GRAND and IceCube-Gen2 will
test values down to $10^{8}$. Our treatment incorporates the momentum transfer
dependence of the neutrino-nucleus cross section, deep inelastic scattering, a
mixed UHECR composition, and flavour information on the up-scattered R$\nu$B
fluxes for both cases of neutrino mass spectrum with normal and inverted
ordering, providing new handles to possibly disentangle the up-scattered
R$\nu$B from cosmogenic neutrinos.


  Several recent deep learning (DL) based techniques perform considerably well
on image-based multilingual text detection. However, their performance relies
heavily on the availability and quality of training data. There are numerous
types of page-level document images consisting of information in several
modalities, languages, fonts, and layouts. This makes text detection a
challenging problem in the field of computer vision (CV), especially for
low-resource or handwritten languages. Furthermore, there is a scarcity of
word-level labeled data for text detection, especially for multilingual
settings and Indian scripts that incorporate both printed and handwritten text.
Conventionally, Indian script text detection requires training a DL model on
plenty of labeled data, but to the best of our knowledge, no relevant datasets
are available. Manual annotation of such data requires a lot of time, effort,
and expertise. In order to solve this problem, we propose TEXTRON, a Data
Programming-based approach, where users can plug various text detection methods
into a weak supervision-based learning framework. One can view this approach to
multilingual text detection as an ensemble of different CV-based techniques and
DL approaches. TEXTRON can leverage the predictions of DL models pre-trained on
a significant amount of language data in conjunction with CV-based methods to
improve text detection in other languages. We demonstrate that TEXTRON can
improve the detection performance for documents written in Indian languages,
despite the absence of corresponding labeled data. Further, through extensive
experimentation, we show improvement brought about by our approach over the
current State-of-the-art (SOTA) models, especially for handwritten Devanagari
text. Code and dataset has been made available at
https://github.com/IITB-LEAP-OCR/TEXTRON


  An effective mass of charge carriers that is significantly larger that the
mass of a free electron develops at low temperatures in certain lanthanide- and
actinide-based metals, including those formed with plutonium, due to strong
electron-electron interactions. This heavy-fermion mass is reflected in a
substantially enhanced electronic coefficient of specific heat $\gamma$, which
for elemental Pu itself is much larger than that of normal metals. By our
definition, there are twelve Pu-based heavy-fermion compounds, most discovered
recently, whose basic properties are known and discussed. Relative to other
examples, these Pu-based heavy-fermion systems are particularly complex due in
part to the possible simultaneous presence of multiple, nearly degenerate
5f$^n$ configurations. This complexity poses significant opportunities as well
as challenges, including understanding the origin of unconventional
superconductivity in some of these materials.


  For a subexponential density, so far, there has been no positive conclusion
or counter example to show whether it is almost decreasing. In this paper, a
subexponential density supported on $\mathbb{R}^+\cup\{0\}$ without the almost
decrease is constructed by a little skillful method. The density is a positive
piecewise linear function with a more normal shape. Correspondingly, there
exists a local subexponential distribution which is not locally almost
decreasing. Based on an example of Cline \cite{C1986}, some similar results are
also obtained for the long-tailed density excluding the subexponential density
and the local long-tailed distribution excluding the local subexponential
distribution. Finally, the paper shows that, for the local subexponentiality of
a distribution supported on $\mathbb{R}$, the local almost decreasing condition
is necessary in some sense.


  In Bayesian statistics, the choice of prior distribution is often debatable,
especially if prior knowledge is limited or data are scarce. In imprecise
probability, sets of priors are used to accurately model and reflect prior
knowledge. This has the advantage that prior-data conflict sensitivity can be
modelled: Ranges of posterior inferences should be larger when prior and data
are in conflict. We propose a new method for generating prior sets which, in
addition to prior-data conflict sensitivity, allows to reflect strong
prior-data agreement by decreased posterior imprecision.


  Purpose: To develop a 3D distortion-free reduced-FOV diffusion-prepared GRE
sequence and demonstrate its in-vivo application for diffusion imaging of the
spinal cord in healthy volunteers. Methods: A 3D multi-shot reduced-FOV
diffusion-prepared GRE (RFOV-DP-GRE) acquisition is achieved using a
slice-selective tip-down pulse in the phase encoding direction in the diffusion
preparation, combined with magnitude stabilisers. The efficacy of the developed
reduced FOV approach and accuracy of ADC estimates were evaluated in a phantom.
In addition, 5 healthy volunteers were enrolled and scanned at 3T using the
proposed sequence and a standard spin echo diffusion-weighted single-shot EPI
sequence (DW-SS-EPI) for spinal cord imaging. Image quality, perceived SNR and
image distortion were assessed by two expert readers and quantitative
measurements of apparent SNR were performed. Results: The phantom scan
demonstrates the efficacy of the proposed reduced FOV approach. Consistent ADC
estimates were measured with RFOV-DP-GRE when compared with DW-SS-EPI. In-vivo,
RFOV-DP-GRE demonstrated improved image quality and reduced perceived
distortion, while maintaining perceived SNR compared to DW-SS-EPI. Conclusion:
3D Distortion-free diffusion-prepared imaging can be achieved using the
proposed sequence


  The elements of Markoff triples are given by coefficients in certain matrix
products defined by Christoffel words, and the Markoff injectivity conjecture,
a long-standing open problem (also known as the uniqueness conjecture), is then
equivalent to injectivity on Christoffel words. A $q$-analog of these matrix
products has been proposed recently, and we prove that injectivity on
Christoffel words holds for this $q$-analog. The proof is based on the
evaluation at $q = \exp(i\pi/3)$. Other roots of unity provide some information
on the original problem, which corresponds to the case $q=1$. We also extend
the problem to arbitrary words and provide a large family of pairs of words
where injectivity does not hold.


  In STOC'95 [ADMSS'95] Arya et al. showed that any set of $n$ points in
$\mathbb R^d$ admits a $(1+\epsilon)$-spanner with hop-diameter at most 2
(respectively, 3) and $O(n \log n)$ edges (resp., $O(n \log \log n)$ edges).
They also gave a general upper bound tradeoff of hop-diameter at most $k$ and
$O(n \alpha_k(n))$ edges, for any $k \ge 2$. The function $\alpha_k$ is the
inverse of a certain Ackermann-style function at the $\lfloor k/2 \rfloor$th
level of the primitive recursive hierarchy, where $\alpha_0(n) = \lceil n/2
\rceil$, $\alpha_1(n) = \left\lceil \sqrt{n} \right\rceil$, $\alpha_2(n) =
\lceil \log{n} \rceil$, $\alpha_3(n) = \lceil \log\log{n} \rceil$, $\alpha_4(n)
= \log^* n$, $\alpha_5(n) = \lfloor \frac{1}{2} \log^*n \rfloor$, \ldots.
Roughly speaking, for $k \ge 2$ the function $\alpha_{k}$ is close to $\lfloor
\frac{k-2}{2} \rfloor$-iterated log-star function, i.e., $\log$ with $\lfloor
\frac{k-2}{2} \rfloor$ stars. Also, $\alpha_{2\alpha(n)+4}(n) \le 4$, where
$\alpha(n)$ is the one-parameter inverse Ackermann function, which is an
extremely slowly growing function.
  Whether or not this tradeoff is tight has remained open, even for the cases
$k = 2$ and $k = 3$. Two lower bounds are known: The first applies only to
spanners with stretch 1 and the second is sub-optimal and applies only to
sufficiently large (constant) values of $k$. In this paper we prove a tight
lower bound for any constant $k$: For any fixed $\epsilon > 0$, any
$(1+\epsilon)$-spanner for the uniform line metric with hop-diameter at most
$k$ must have at least $\Omega(n \alpha_k(n))$ edges.


  We consider relay selection technique in a cooperative cellular network where
user terminals act as mobile relays to help the communications between base
station (BS) and mobile station (MS). A novel relay selection scheme, called
Joint Uplink and Downlink Relay Selection (JUDRS), is proposed in this paper.
Specifically, we generalize JUDRS in two key aspects: (i) relay is selected
jointly for uplink and downlink, so that the relay selection overhead can be
reduced, and (ii) we consider to minimize the weighted total energy consumption
of MS, relay and BS by taking into account channel quality and traffic load
condition of uplink and downlink. Information theoretic analysis of the
diversity-multiplexing tradeoff demonstrates that the proposed scheme achieves
full spatial diversity in the quantity of cooperating terminals in this
network. And numerical results are provided to further confirm a significant
energy efficiency gain of the proposed algorithm comparing to the previous best
worse channel selection and best harmonic mean selection algorithms.


  Consider the following statement:
  $B(t, \Delta t)$: a $t$ years old person NN will survive another $\Delta t$
years, where $t, \Delta t\in \mathbb{R}$ are nonnegative real numbers. We know
only that NN is $t$ years old and nothing about the health conditions, gender,
race, nationality, etc. We bet that $B(t, \Delta t)$ holds. It seems that our
odds are very good, for any $t$ provided $\Delta t$ is small enough, say, $1 /
365$ (that is, one day). However, this is not that obvious and depends on the
life-time probabilistic distribution. Let $F(t)$ denote the probability to live
at most $t$ years and set $\Phi(t) = 1 - F(t)$.
  Clearly, $\Phi(t) \rightarrow 0$ as $t \rightarrow \infty$. It is not
difficult to verify that $Pr(B(t, \Delta t)) \rightarrow 0$ as $t \rightarrow
\infty$, for any fixed $\Delta t$, whenever the convergence of $\Phi$ is fast
enough (say, super-exponential). Statistics provide arguments (based on an
extrapolation yet) that this is the case. Hence, for an arbitrarily small
positive $\Delta t $ and $\epsilon$ there exists a sufficiently large $t$ such
that $Pr(B(t, \Delta t)) < \epsilon$, which means that we should not bet... in
theory. However, in practice we can bet safely, because for the inequality
$Pr(B(t, \Delta t)) < 1/2$ a very large $t$ is required. For example, $\Delta t
= 1/365$ may require $t > 125$ years for some typical distributions $F$
considered in the literature. Yet, on Earth there is no person of such age.
Thus, our odds are good, either because the chosen testee NN is not old enough,
or for technical (or, more precisely, statistical) reasons -- absence of a
testee. This situation is similar to the famous St.Petersburg Paradox.


  Most programming languages, besides C, provide a native abstraction for
character strings, but string APIs vary widely in size, expressiveness, and
subjective convenience across languages. In Pharo, while at first glance the
API of the String class seems rich, it often feels cumbersome in practice; to
improve its usability, we faced the challenge of assessing its design. However,
we found hardly any guideline about design forces and how they structure the
design space, and no comprehensive analysis of the expected string operations
and their different variations. In this article, we first analyse the Pharo 4
String library, then contrast it with its Haskell, Java, Python, Ruby, and Rust
counterparts. We harvest criteria to describe a string API, and reflect on
features and design tensions. This analysis should help language designers in
understanding the design space of strings, and will serve as a basis for a
future redesign of the string library in Pharo.


  Motivated by the trade-off between noise-robustness and data-consistency for
joint 3D map reconstruction and rotation estimation in single particle
cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting
(ESL), a measure-based lifting scheme for regularising and approximating the
global minimiser of a smooth function over a Riemannian manifold. Under a
uniqueness assumption on the minimiser we show several theoretical results, in
particular well-posedness of the method and an error bound due to the induced
bias with respect to the global minimiser. Additionally, we use the developed
theory to integrate the measure-based lifting scheme into an alternating update
method for joint homogeneous 3D map reconstruction and rotation estimation,
where typically tens of thousands of manifold-valued minimisation problems have
to be solved and where regularisation is necessary because of the high noise
levels in the data. The joint recovery method is used to test both the
theoretical predictions and algorithmic performance through numerical
experiments with Cryo-EM data. In particular, the induced bias due to the
regularising effect of ESL empirically estimates better rotations, i.e.,
rotations closer to the ground truth, than global optimisation would.


  Differential cross sections for elastic Compton scattering from $^4$He have
been measured with high statistical precision at the High Intensity
$\gamma$-ray Source at laboratory scattering angles of $55^\circ$, $90^\circ$,
and $125^\circ$ using a quasi-monoenergetic photon beam with a weighted mean
energy value of $81.3$ MeV. The results are compared to previous measurements
and similar fore-aft asymmetry in the angular distribution of the differential
cross sections is observed. This experimental work is expected to strongly
motivate the development of effective-field-theory calculations of Compton
scattering from $^4$He to fully interpret the data.


  We construct global-in-time, unique solutions of the two-dimensional Euler
equations in a Yudovich type space and a $\rm bmo$-type space. First, we show
the regularity of solutions for the two-dimensional Euler equations in the
Spanne space involving an unbounded and non-decaying vorticity. Next, we
establish an estimate with a logarithmic loss of regularity for the transport
equation in a bmo-type space by developing classical analysis tool such as the
John-Nirenberg inequality. We also optimize estimates of solutions to the
vorticity-stream formulation of the two-dimensional Euler equations with a
bi-Lipschitz vector field in bmo-type space by combining an observation
introduced by Yodovich with the so-called "quasi-conformal property" of the
incompressible.


  We present 43 GHz VLA spectra for 51 AGB sources with the goal of verifying
an infrared (IR) color cut intended to separate Carbon-rich (C) and Oxygen-rich
(O) AGB sources throughout the Galaxy. The color cut is a simple line in the
$[K_s]-[A]$ versus $[A]-[E]$ color-color diagram based on 2MASS and MSX
photometry, and was originally derived from SiO detection rates in the Bulge
Asymmetries and Dynamical Evolution (BAaDE) sample. The division is fully
supported by the spectra presented here, which show that SiO maser detections
lie on the O-rich side, and SiO nondetections and a single HC$_3$N detection
are found on the C-rich side of the division. We further compare the color cut
with classifications of the sources based on Low-Resolution Spectra (LRS) from
the Infrared Astronomical Satellite (IRAS), and find good agreement, verifying
that the division is a reliable and efficient method for differentiating O- and
C-rich AGB sources. These observations also demonstrate that single lines
detected in the BAaDE survey around 42.9 GHz are almost certainly the
$^{29}$SiO v=0 line. SiO maser sources where this rare isotopologue transition
is brighter than the dominant $^{28}$SiO lines have not been reported before,
and our observations show that these sources can reverse their behavior such
that the typical ratios of $^{28}$SiO and $^{29}$SiO are restored within a few
years.


  In this work, we review previously developed coarse-grained (CG) particle
models for biological membrane and red blood cells (RBCs) and discuss the
advantages of the CG particle method over the continuum and atomic simulations
on modeling biological phenomena. CG particle models can largely increase the
length scale and time scale of atomic simulations by eliminating fast degrees
of freedom while preserving the mesoscopic structures and properties of the
simulated system. One the other hand, CG particle models can be used to capture
microstructural alternations in diseased RBCs and simulate topological changes
of biological membrane and RBCs, which are major challenges to typical
continuum representations of membrane and RBCs. The power and versatility of
the CG particle methods are demonstrated through simulating the dynamical
processes involving significant topological changes, such as lipid
self-assembly, vesicle fusion and membrane budding.


  We present an analysis of 991 heartbeat stars (HBSs) from the OGLE Collection
of Variable Stars (OCVS). The sample consists of 512 objects located toward the
Galactic bulge (GB), 439 in the Large Magellanic Cloud (LMC) and 40 in the
Small Magellanic Cloud (SMC). We model the $I$-band OGLE light curves using an
analytical model of flux variations, reflecting tidal deformations between
stars. We present distributions of the model parameters that include the
eccentricity, orbital inclination, and argument of the periastron, but also the
period-amplitude diagrams. On the Hertzsprung-Russell (HR) diagram, our HBS
sample forms two separate groups of different evolutionary status. The first
group of about 90 systems, with short orbital periods ($P\lesssim50$~days),
consists of an early-type primary star lying on (or close to) the main sequence
(MS). The second group of about 900 systems, with long orbital periods
($P\gtrsim100$~days), contains a red giant (RG). The position of RG HBSs on the
period-luminosity diagram strongly indicates their binary nature. They appear
to be a natural extension of confirmed binary systems that include the OGLE
ellipsoidal and Long Secondary Period (LSP) variables. We also present a
time-series analysis leading to detection of tidally-excited oscillations
(TEOs). We identify such pulsations in about 5\% of stars in the sample with a
total number of 78 different modes. This first relatively large homogeneous
sample of TEOs allowed us to construct a diagram revealing the correlation
between the TEO's orbital harmonic number and the eccentricity of the host
binary system.


  This article is about how the "SP theory of intelligence" and its realisation
in the "SP machine" may, with advantage, be applied to the management and
analysis of big data. The SP system -- introduced in the article and fully
described elsewhere -- may help to overcome the problem of variety in big data:
it has potential as "a universal framework for the representation and
processing of diverse kinds of knowledge" (UFK), helping to reduce the
diversity of formalisms and formats for knowledge and the different ways in
which they are processed. It has strengths in the unsupervised learning or
discovery of structure in data, in pattern recognition, in the parsing and
production of natural language, in several kinds of reasoning, and more. It
lends itself to the analysis of streaming data, helping to overcome the problem
of velocity in big data. Central in the workings of the system is lossless
compression of information: making big data smaller and reducing problems of
storage and management. There is potential for substantial economies in the
transmission of data, for big cuts in the use of energy in computing, for
faster processing, and for smaller and lighter computers. The system provides a
handle on the problem of veracity in big data, with potential to assist in the
management of errors and uncertainties in data. It lends itself to the
visualisation of knowledge structures and inferential processes. A
high-parallel, open-source version of the SP machine would provide a means for
researchers everywhere to explore what can be done with the system and to
create new versions of it.


  In this paper we address the following two closely related questions. First,
we complete the classification of finite symmetry groups of type IIA string
theory on $K3\times \mathbb R^6$, where Niemeier lattices play an important
role. This extends earlier results by including points in the moduli space with
enhanced gauge symmetries in spacetime, or, equivalently, where the world-sheet
CFT becomes singular. After classifying the symmetries as abstract groups, we
study how they act on the BPS states of the theory. In particular, we classify
the conjugacy classes in the T-duality group $O^+(\Gamma^{4,20})$ which
represent physically distinct symmetries. Subsequently, we make two conjectures
regarding the connection between the corresponding twining genera of $K3$ CFTs
and Conway and umbral moonshine, building upon earlier work on the relation
between moonshine and the $K3$ elliptic genus.


  We propose a Higgs-related but spin $1/2$ dark matter candidate with a mass
that is comparable to that of the Higgs. This particle is a WIMP with an
R-parity of $-1$, but it can be distinguished from a neutralino by its
unconventional couplings to W and Z bosons. Charged spin 1/2 particles of a new
kind are also predicted at higher energy.


  This paper is based on the paper "Locally free sheaves on complex
supermanifolds" of A.L.Onishchik, E.G. Vishnyakova, where two classification
theorems for locally free sheaves on supermanifolds were proved and a spectral
sequence for a locally free sheaf of modules E was obtained. We consider
another filtration of the locally free sheaf E, the corresponding
classification theorem and the spectral sequence, which is more convenient in
some cases. The methods, which we are using here, are similar to the methods of
the paper mentioned above.
  The first spectral sequence of this kind was constructed by A.L. Onishchik
for the tangent sheaf of a supermanifold. However, the spectral sequence
considered in this paper is not a generalization of Onishchik's spectral
sequence.


  Use of telecommunication technologies for remote, continuous monitoring of
patients can enhance effectiveness of emergency ambulance care during transport
from rural areas to a regional center hospital. However, the communication
along the various routes in rural areas may have wide bandwidth ranges from 2G
to 4G; some regions may have only lower satellite bandwidth available.
Bandwidth fluctuation together with real-time communication of various clinical
multimedia pose a major challenge during rural patient ambulance transport.;
AB@The availability of a pre-transport route-dependent communication bandwidth
database is an important resource in remote monitoring and clinical multimedia
transmission in rural ambulance transport. Here, we present a geo-communication
dataset from extensive profiling of 4 major US mobile carriers in Illinois,
from the rural location of Hoopeston to the central referral hospital center at
Urbana. In collaboration with Carle Foundation Hospital, we developed a
profiler, and collected various geographical and communication traces for
realistic emergency rural ambulance transport scenarios. Our dataset is to
support our ongoing work of proposing "physiology-aware DASH", which is
particularly useful for adaptive remote monitoring of critically ill patients
in emergency rural ambulance transport. It provides insights on ensuring higher
Quality of Service (QoS) for most critical clinical multimedia in response to
changes in patients' physiological states and bandwidth conditions. Our dataset
is available online for research community.


  We address black-box convex optimization problems, where the objective and
constraint functions are not explicitly known but can be sampled within the
feasible set. The challenge is thus to generate a sequence of feasible points
converging towards an optimal solution. By leveraging the knowledge of the
smoothness properties of the objective and constraint functions, we propose a
novel zeroth-order method, SZO-QQ, that iteratively computes quadratic
approximations of the constraint functions, constructs local feasible sets and
optimizes over them. We prove convergence of the sequence of the objective
values generated at each iteration to the minimum. Through experiments, we show
that our method can achieve faster convergence compared with state-of-the-art
zeroth-order approaches to convex optimization.


  To address the computational challenges of ab initio molecular dynamics and
the accuracy limitations of empirical force fields, the introduction of machine
learning force fields has proven effective in various systems including metals
and inorganic materials. However, in large-scale organic systems, the
application of machine learning force fields is often hindered by impediments
such as the complexity of long-range intermolecular interactions and molecular
conformations, as well as the instability in long-time molecular simulations.
Therefore, we propose a universal multiscale higher-order equivariant model
combined with active learning techniques, efficiently capturing the complex
long-range intermolecular interactions and molecular conformations. Compared to
existing equivariant models, our model achieves the highest predictive
accuracy, and magnitude-level improvements in computational speed and memory
efficiency. In addition, a bond length stretching method is designed to improve
the stability of long-time molecular simulations. Utilizing only 901 samples
from a dataset with 120 atoms, our model successfully extends high precision to
systems with hundreds of thousands of atoms. These achievements guarantee high
predictive accuracy, fast simulation speed, minimal memory consumption, and
robust simulation stability, satisfying the requirements for high-precision and
long-time molecular simulations in large-scale organic systems.


  Using tropical geometry one can translate problems in enumerative geometry to
combinatorial problems. Thus tropical geometry is a powerful tool in
enumerative geometry over the complex and real numbers. Results from
$\mathbb{A}^1$-homotopy theory allow to enrich classical enumerative geometry
questions and get answers over an arbitrary field. In the resulting area,
$\mathbb{A}^1$-enumerative geometry, the answer to these questions lives in the
Grothendieck-Witt ring of the base field $k$. In this paper, we use tropical
methods in this enriched set up by showing B\'ezout's theorem and a
generalization, namely the Bernstein-Kushnirenko theorem, for tropical
hypersurfaces enriched in $\operatorname{GW}(k)$.


  With a sample of (225.2\pm2.8)*10^{6} J/psi events registered in the BESIII
detector, J/psi->gamma pi^+ pi^- eta' is studied using two eta' decay modes:
eta'->pi^+ pi^- eta and eta' -> gamma rho^0. The X(1835), which was previously
observed by BESII, is confirmed with a statistical significance that is larger
than 20\sigma. In addition, in the pi^+pi^-eta' invariant mass spectrum, the
X(2120) and the X(2370), are observed with statistical significances larger
than 7.2\sigma and 6.4\sigma, respectively. For the X(1835), the angular
distribution of the radiative photon is consistent with expectations for a
pseudoscalar.


  Self-similarity has been the paradigmatic picture for the pinch-off of a
drop. Here we will show through high-speed imaging and boundary integral
simulations that the inverse problem, the pinch-off of an air bubble in water,
is not self-similar in a strict sense: A disk is quickly pulled through a water
surface, leading to a giant, cylindrical void which after collapse creates an
upward and a downward jet. Only in the limiting case of large Froude number the
neck radius $h$ scales as $h(-\log h)^{1/4} \propto \tau^{1/2}$, the purely
inertial scaling. For any finite Froude number the collapse is slower, and a
second length-scale, the curvature of the void, comes into play. Both
length-scales are found to exhibit power-law scaling in time, but with
different exponents depending on the Froude number, signaling the
non-universality of the bubble pinch-off.


  It is shown here that the extraction of quasinormal modes (QNMs) within the
first Born approximation of the scattering amplitude is mathematically not well
founded. Indeed, the constraints on the existence of the scattering amplitude
integral lead to inequalities for the imaginary parts of the QNM frequencies.
For instance, in the Schwarzschild case, $0 \leq \omega_I < \kappa$ (where
$\kappa$ is the surface gravity at the horizon) invalidates the poles deduced
from the first Born approximation method, namely, $\omega_n = i n \kappa$.


  This is a continuation of the study, begun by Ceccherini-Silberstein and
Woess, of context-free pairs of groups and the related context-free graphs in
the sense of Muller and Schupp. Instead of the cones (connected components with
respect to deletion of finite balls with respect to the graph metric), a more
general approach to context-free graphs is proposed via tree sets consisting of
cuts of the graph, and associated structure trees. The existence of tree sets
with certain "good" properties is studied. With a tree set, a natural
context-free grammar is associated. These investigations of the structure of
context free pairs, resp. graphs are then applied to study random walk
asymptotics via complex analysis.


  Electric field-controlled, two-dimensional (2D) exciton dynamics in
transition metal dichalcogenide monolayers is a current research focus in
condensed matter physics. We have experimentally investigated the spectral and
temporal properties of the A-exciton in a molybdenum diselenide (MoSe2)
monolayer under controlled variation of a vertical, electric dc field at room
temperature. By using steady-state and time-resolved photoluminescence
spectroscopies, we have observed dc field-induced spectral shifts and linewidth
broadenings that are consistent with the shortening of the exciton's
non-radiative lifetime due to field-induced dissociation. We discuss the
implications of the results for future developments in nanoscale metrology and
exploratory, optoelectronics technologies based on layered, 2D semiconductors.


  We present experimental evidence of the successful closed-loop optimization
of the dynamics of cold atoms in an optical lattice. We optimize the loading of
an ultracold atomic gas minimizing the excitations in an array of
one-dimensional tubes (3D-1D crossover) and we perform an optimal crossing of
the quantum phase-transition from a Superfluid to a Mott-Insulator in a
three-dimensional lattice. In both cases we enhance the experiment performances
with respect to those obtained via adiabatic dynamics, effectively speeding up
the process by more than a factor three while improving the quality of the
desired transformation.


  The hadronic structure of the photon F2gamma is measured as a function of
Bjorken x and of the photon virtuality Q2 using deep-inelastic scattering data
taken by the OPAL detector at LEP at e+e- centre-of-mass energies from 183 to
209 GeV. Previous OPAL measurements of the x dependence of F2gamma are extended
to an average Q2 of <Q2>=780GeV2 using data in the kinematic range 0.15 < x <
0.98. The Q2 evolution of F2gamma is studied for 12.1 < <Q2> < 780GeV2 using
three ranges of x. As predicted by QCD, the data show positive scaling
violations in F2gamma for the central x region 0.10-0.60. Several
parameterisations of F2gamma are in qualitative agreement with the measurements
whereas the quark-parton model prediction fails to describe the data.


  We apply our recent work on empirical estimates of quantum speedups to the
practical task of community detection in complex networks. We design several
quantum variants of a popular classical algorithm -- the Louvain algorithm for
community detection -- and first study their complexities in the usual way,
before analysing their complexities empirically across a variety of artificial
and real inputs. We find that this analysis yields insights not available to us
via the asymptotic analysis, further emphasising the utility in such an
empirical approach. In particular, we observe that a complicated quantum
algorithm with a large asymptotic speedup might not be the fastest algorithm in
practice, and that a simple quantum algorithm with a modest speedup might in
fact be the one that performs best. Moreover, we repeatedly find that overheads
such as those arising from the need to amplify the success probabilities of
quantum sub-routines such as Grover search can nullify any speedup that might
have been suggested by a theoretical worst- or expected-case analysis.


  We study the three-dimensional (3D) spatially-resolved distribution of the
energy density of light in a 3D scattering medium upon the excitation of open
transmission channels. The open transmission channels are excited by spatially
shaping the incident optical wavefronts. To probe the local energy density, we
excite isolated fluorescent nanospheres distributed inside the medium. From the
spatial fluorescent intensity pattern we obtain the position of each
nanosphere, while the total fluorescent intensity gauges the energy density.
Our 3D spatially-resolved measurements reveal that the local energy density
versus depth (z) is enhanced up to 26X at the back surface of the medium, while
it strongly depends on the transverse (x; y) position. We successfully
interpret our results with a newly developed 3D model that considers the
time-reversed diffusion starting from a point source at the back surface. Our
results are relevant for white LEDs, random lasers, solar cells, and biomedical
optics.


  The braid group appears in many scientific fields and its representations are
instrumental in understanding topological quantum algorithms, topological
entropy, classification of manifolds and so on. In this work, we study planer
diagrams which are Kauffman's reduction of the braid group algebra to the
Temperley-Lieb algebra. We introduce an algorithm for computing all planer
diagrams in a given dimension. The algorithm can also be used to multiply
planer diagrams and find their matrix representation.


  Functioning and interaction of distributed devices and concurrent algorithms
are analyzed in the context of the theory of algorithms. Our main concern here
is how and under what conditions algorithmic interactive devices can be more
powerful than the recursive models of computation, such as Turing machines.
Realization of such a higher computing power makes these systems
superrecursive. We find here five sources for superrecursiveness in
interaction. In addition, we prove that when all of these sources are excluded,
the algorithmic interactive system in question is able to perform only
recursive computations. These results provide computer scientists with
necessary and sufficient conditions for achieving superrecursiveness by
algorithmic interactive devices.


  Deep learning techniques have dominated the literature on aspect-based
sentiment analysis (ABSA), achieving state-of-the-art performance. However,
deep models generally suffer from spurious correlations between input features
and output labels, which hurts the robustness and generalization capability by
a large margin. In this paper, we propose to reduce spurious correlations for
ABSA, via a novel Contrastive Variational Information Bottleneck framework
(called CVIB). The proposed CVIB framework is composed of an original network
and a self-pruned network, and these two networks are optimized simultaneously
via contrastive learning. Concretely, we employ the Variational Information
Bottleneck (VIB) principle to learn an informative and compressed network
(self-pruned network) from the original network, which discards the superfluous
patterns or spurious correlations between input features and prediction labels.
Then, self-pruning contrastive learning is devised to pull together
semantically similar positive pairs and push away dissimilar pairs, where the
representations of the anchor learned by the original and self-pruned networks
respectively are regarded as a positive pair while the representations of two
different sentences within a mini-batch are treated as a negative pair. To
verify the effectiveness of our CVIB method, we conduct extensive experiments
on five benchmark ABSA datasets and the experimental results show that our
approach achieves better performance than the strong competitors in terms of
overall prediction performance, robustness, and generalization. Code and data
to reproduce the results in this paper is available at:
https://github.com/shesshan/CVIB.


  The success of grain boundary (GB) plane orientation fundamental zone (FZ)
has connected GB structures across multiple crystallographic characters with
their properties in a unique insight, but quantitative understandings of the
structure-property relationship therein are still lacking. Based on the
well-known Read-Shockley relationship, a theoretical derivation is proposed to
predict low angle GB energies as a function of FZ parameters, which forms a
standard energy function that accurately captures the simulated energy trends
in a simple and clear manner. The theorization presented here is therefore
expected to be a starting point for modern GB energy functions.


  The intrinsic near-infrared photoluminescence observed in long single walled
carbon nanotubes is systematically quenched in ultrashort single-walled carbon
nanotubes (usCNTs, below 100 nm length) due to their short dimension as
compared to the exciton diffusion length. It would however be key for number of
applications to have such tiny nanostructure displaying photoluminescence
emission to complement their unique physical, chemical and biological
properties. Here we demonstrate that intense photoluminescence can be created
in usCNTs (~40 nm length) upon incorporation of emissive sp3-defect sites in
order to trap excitons. Using super-resolution imaging at <25 nm resolution, we
directly reveal the localization of excitons at the defect sites on individual
usCNTs. They are found preferentially localized at nanotube ends which can be
separated by less than 40 nm and behave as independent emitters. The
demonstration and control of bright near-infrared photoluminescence in usCNTs
through exciton trapping opens the possibility to engineering tiny carbon
nanotubes for applications in various domains of research including quantum
optics and bioimaging.


  We prove that $D^0$-$\bar D^0$ mixing in the standard model occurs only at
second order in U-spin breaking. The U-spin subgroup of SU(3) is found to be a
powerful tool for analyzing the cancellation of intermediate-state
contributions to the $D^0$--$\od^0$ mixing parameter $y = \Delta \Gamma/(2
\Gamma)$. Cancellations due to states {\it within a single U-spin triplet} are
shown to be valid to first order in U-spin breaking. Illustrations are given
for triplets consisting of (a) pairs of charged pions and kaons; (b) pairs of
neutral pseudoscalar members of the meson octet; (c) charged
vector-pseudoscalar pairs, and (d) states of four charged kaons and pions.


  Active nematics are influenced by alignment angle singularities called
topological defects. The localization of these defects is of major interest for
biological applications. The total distortion of alignment angles due to
defects is evaluated using Frank free energy, which is one of the criteria used
to determine the location and stability of these defects. Previous work used
the line integrals of a complex potential associated with the alignments for
the energy calculation (Miyazako and Nara, R. Soc. Open Sci., 2022), which has
a high computational cost. We propose analytical formulas for the free energy
in the presence of multiple topological defects in confined geometries. The
formulas derived here are an analogue of Kirchhoff-Routh functions in vortex
dynamics. The proposed formulas are explicit with respect to the defect
locations and conformal maps, which enables the explicit calculation of the
energy extrema. The formulas are applied to calculate the locations of defects
in so-called doublets and triplets by solving simple polynomial formulas. A
stability analysis is also conducted to detect whether defect pairs with
charges $\pm 1/2$ are stable or unstable in triplet regions. Our numerical
results are shown to match the experimental results (Ienaga {\em et al.,} Soft
Matter, 2023).


  We present an analysis of the properties of the electron velocity
distribution during island coalescence in asymmetric reconnection with and
without guide field. In a previous study, three main domains were identified,
in the case without guide field, as X-, D- and M-regions featuring different
reconnection evolutions {Cazzola et al. 2015). These regions are also
identified here in the case with guide field. We study the departure from
isotropic and gyrotropic behavior by means of different robust detection
algorithms proposed in the literature. While in the case without guide field
these metrics show an overall agreement, when the guide field is present a
discrepancy in the agyrotropy within some relevant regions is observed, such as
at the separatrices and inside magnetic islands. Moreover, in light of the new
observations from the Multiscale MagnetoSpheric mission, an analysis of the
electron velocity phase-space in these domains is presented.


  Let $N$ and $M$ be positive integers satisfying $1\le M\le N$, and let
$0<p_0<p_1<1$. Define a process $\{X_n\}_{n=0}^\infty$ on $\mathbb{Z}$ as
follows. At each step, the process jumps either one step to the right or one
step to the left, according to the following mechanism. For the first $N$
steps, the process behaves like a random walk that jumps to the right with
probability $p_0$ and to the left with probability $1-p_0$. At subsequent steps
the jump mechanism is defined as follows: if at least $M$ out of the $N$ most
recent jumps were to the right, then the probability of jumping to the right is
$p_1$; however, if fewer than $M$ out of the $N$ most recent jumps were to the
right, then the probability of jumping to the right is $p_0$. We calculate the
speed of the process. Then we let $N\to\infty$ and $\frac MN\to r\in[0,1]$, and
calculate the limiting speed. More generally, we consider the above questions
for a random walk with a finite number $l$ of threshold levels,
$(M_i,p_i)_{i=1}^l$, above the pre-threshold level $p_0$, as well as for one
model with $l=N$ such thresholds.


  Firstly we consider a finite dimensional Markov semigroup generated by Dunkl
laplacian with drift terms. Using gradient bounds we show that for small
coefficients this semigroup has an invariant measure. We then extend this
analysis to an infinite dimensional semigroup on
$(\mathbb{R}^N)^{\mathbb{Z}^d}$ which we construct using gradient bounds, and
finally we study the existence of invariant measures and ergodicity properties.


  We study the decomposition of the Riemannian curvature R tensor of an almost
quaternion-Hermitian manifold under the action of its structure group
Sp(n)Sp(1). Using the minimal connection, we show that most components are
determined by the intrinsic torsion \xi and its covariant derivative
\widetilde\nabla\xi and determine relations between the decompositions of
\xi\otimes\xi, \widetilde\nabla\xi and R. We pay particular attention to the
behaviour of the Ricci curvature and the q-Ricci curvature.


  In the effective field theory formalism nuclear forces are organized as a low
energy expansion. Usually the lowest order in this expansion corresponds to the
non-perturbative iteration of the one-pion exchange potential and a few
contact-range operators as to ensure renormalization group invariance. Here we
consider an alternative expansion in which two-pion exchange becomes the lowest
order finite range interaction and as such is expected to be iterated. A
comparison of this new expansion with the standard one shows a better
convergence pattern for a few selected partial waves ($^1S_0$, $^3P_0$ and
$^3S_1$-$^3D_1$) in two-nucleon scattering, in particular for the $^1S_0$
channel (though both expansions converge well). We briefly comment on the
possible theoretical grounds for the expansion around two-pion exchange from
the point of view of effective field theory.


  In this short note I present a tauberian conjecture that I consider to be the
simplest and the best tauberian reformulation of RH using good variation
theory. The method applies also to the Grand Riemann Hypothesis.


  Taking into account that the real quantum materials are engineered
generically at a finite chemical potential, we investigate the Einstein ring
structure for the lensed response of the complex scalar field as a probe wave
on the charged AdS black hole in the context of AdS/CFT. On the one hand, we
find that the resulting Einstein ring radius has no variation with the chemical
potential, which is similar to the behavior for the weakly interacting quantum
system. On the other hand, not only can such a ring exist well within the
screen, but also the temperature dependence of its radius exhibits a distinct
feature in the sense that it displays an appreciable increase at low
temperatures while the ring keeps unchanged right at the edge of the screen for
the weakly interacting system. Note that such a Einstein ring emerges in the
large frequencies and can be well captured by the photon sphere away from the
black hole horizon in the geometric optics approximation, thus such a distinct
feature may be regarded as a universal behavior associated with the high energy
modes of the strongly coupled system which has a gravity dual.


  We study an alternative geometrical approach on the problem of classical
cosmological singularity. It is based on a generalized function $f (x, y) =
x^{2} + y^{2} = (1 - z)z^{n}$ which consists of a cusped coupled isosurface.
Such a geometry is computed and discussed into the context of Friedmann
singularity-free cosmology where a pre-big bang scenario is considered.
Assuming that the mechanism of cusp formation is described by non-linear
oscillations of a pre-big bang extended very high energy density field ($> 3
\times 10^{94} kg/m^{3} $), we show that the action under the gravitational
field follows a tautochrone of revolution, understood here as the primary
projected geometry that alternatively replaces the Friedmann singularity in the
standard big bang theory. As shown here this new approach allows us to
interpret the nature of both matter and dark energy from first geometric
principles.


  This is a Thesis submitted for the degree of Doctor Philosophiae at
S.I.S.S.A./I.S.A.S.


  Extensive literature has shown that finite impulse response (FIR)
interferometers can be engineered to be insensitive under variations of
different physical parameters, e.g., to ensure flat-top response and/or
tolerance to fabrication errors. In this context, I will show how the Bloch
sphere representation can be a very powerful design tool providing superior
physical insight into the working principle of autocorrective devices like
broadband 50:50 splitters or flat-top interleavers, that can be therefore
designed through simple analytical formulas. I will eventually review the
recent progress in practical implementation of the autocorrective designs in
the micron-scale silicon photonics platform of VTT.


  It has been recently shown that the electroweak baryogenesis mechanism is
feasible in Standard Model extensions containing extra fermions with large
Yukawa couplings. We show here that the lightest of these fermionic fields can
naturally be a good candidate for cold dark matter. We find regions in the
parameter space where the thermal relic abundance of this particle is
compatible with the dark matter density of the Universe as determined by the
WMAP experiment. We study direct and indirect dark matter detection for this
model and compare with current experimental limits and prospects for upcoming
experiments. We find, contrary to the standard lore, that indirect detection
searches are more promising than direct detection ones, and they already
exclude a portion of the parameter space.


  This paper addresses the problem of recovering projective camera matrices
from collections of fundamental matrices in multiview settings. We make two
main contributions. First, given ${n \choose 2}$ fundamental matrices computed
for $n$ images, we provide a complete algebraic characterization in the form of
conditions that are both necessary and sufficient to enabling the recovery of
camera matrices. These conditions are based on arranging the fundamental
matrices as blocks in a single matrix, called the $n$-view fundamental matrix,
and characterizing this matrix in terms of the signs of its eigenvalues and
rank structures. Secondly, we propose a concrete algorithm for projective
structure-from-motion that utilizes this characterization. Given a complete or
partial collection of measured fundamental matrices, our method seeks camera
matrices that minimize a global algebraic error for the measured fundamental
matrices. In contrast to existing methods, our optimization, without any
initialization, produces a consistent set of fundamental matrices that
corresponds to a unique set of cameras (up to a choice of projective frame).
Our experiments indicate that our method achieves state of the art performance
in both accuracy and running time.


  This paper has been withdrawn by the authors. Please see arXiv:1302.6058. We
consider the sequential joint detection and estimation problem. Minimizing the
average stopping time subject to a combination of detection and estimation
constraints we obtain the optimal triplet of stopping time, detector and
estimator. In the joint detection and estimation problem the primary goal is to
detect and estimate together, as opposed to the conventional testing of
composite hypotheses where the primary goal is to detect only. For the first
time in the literature we develop optimal solution to the sequential joint
detection and estimation problem. In the sequential version of the problem,
different from the fixed sample size version, optimal stopping time is also
sought, complicating the solution considerably.


  Cosmological structures grow differently in theories of gravity which are
modified as compared to Einstein's General relativity (GR). Cosmic microwave
background (CMB) fluctuation patterns at the last scattering surface are lensed
by these structures along the photon path to the observer. The observed CMB
pattern therefore keeps trace of the growth history of structures. We show that
observations of the CMB lensing bi-spectrum offer an interesting way to
constrain deviations from GR in a broad class of scalar-tensor theories of
gravity called "beyond Horndeski". We quantify how the constraints on generic
parameters describing the deviations from GR depend on the effective multipole
range of the analysis. Our results further indicate that an accurate nonlinear
correction of the matter bi-spectrum in the modified gravity considered is
necessary when the bi-spectrum is used to probe scales beyond a multipole
$\ell_{\rm max} \gtrsim 1500$. We also found that the results are insensitive
to details of the implementation of the screening mechanism, at very small
scales. We finally demonstrate the potential of the lensing bi-spectrum to
provide a blind reconstruction of the redshift evolution of our modified
gravity parameters by combining the analysis of CMB and low-z source lensing
data.


  The ages, metallicities, alpha-elements and integrals of motion of globular
clusters (GCs) accreted by the Milky Way from disrupted satellites remain
largely unchanged over time. Here we have used these conserved properties in
combination to assign 76 GCs to 5 progenitor satellite galaxies -- one of which
we dub the Koala dwarf galaxy. We fit a leaky-box chemical enrichment model to
the age-metallicity distribution of GCs, deriving the effective yield and the
formation epoch of each satellite. Based on scaling relations of GC counts we
estimate the original halo mass, stellar mass and mean metallicity of each
satellite. The total stellar mass of the 5 accreted satellites contributed
around 10$^{9}$ M$_{\odot}$ in stars to the growth of the Milky Way but over
50\% of the Milky Way's GC system. The 5 satellites formed at very early times
and were likely accreted 8--11 Gyr ago, indicating rapid growth for the Milky
Way in its early evolution. We suggest that at least 3 satellites were
originally nucleated, with the remnant nucleus now a GC of the Milky Way.
Eleven GCs are also identified as having formed ex-situ but could not be
assigned to a single progenitor satellite.


  Experimental results for mesonic $b \to s \mu^+ \mu^-$ decays show a pattern
of deviations from Standard-Model predictions, which could be due to new
fundamental physics or due to an insufficient understanding of hadronic
effects. Additional information on the $b \to s \mu^+ \mu^-$ transition can be
obtained from $\Lambda_b$ decays. This was recently done using the process
$\Lambda_b \to \Lambda \mu^+ \mu^-$, where the $\Lambda$ is the lightest
strange baryon. A further interesting channel is $\Lambda_b \to p^+ K^- \mu^+
\mu^-$, where the $p^+ K^-$ final state receives contributions from multiple
higher-mass $\Lambda$ resonances. The narrowest and most prominent of these is
the $\Lambda(1520)$, which has $J^P=\frac32^-$. Here we present an ongoing
lattice QCD calculation of the relevant $\Lambda_b \to \Lambda(1520)$ form
factors. We discuss the choice of interpolating field for the $\Lambda(1520)$,
and explain our method for extracting the fourteen $\Lambda_b \to
\Lambda(1520)$ helicity form factors from correlation functions that are
computed in the $\Lambda(1520)$ rest frame. We present preliminary numerical
results at a pion mass of 340 MeV and a lattice spacing of 0.11 fm. This
calculation uses a domain-wall action for the $u$, $d$, and $s$ quarks and a
relativistic heavy-quark action for the $b$ quark, and is based on gauge-field
configurations generated by the RBC and UKQCD Collaborations.


  "How much information about a system $\mathcal{S}$ can one extract from a
fragment $\mathcal{F}$ of the environment $\mathcal{E}$ that decohered it?" is
the central question of Quantum Darwinism. To date, most answers relied on the
quantum mutual information of $\mathcal{SF}$, or on the Holevo bound on the
channel capacity of $\mathcal{F}$ to communicate the classical information
encoded in $\mathcal{S}$. These are reasonable upper bounds on what is really
needed but much harder to calculate -- the accessible information in the
fragment $\mathcal{F}$ about $\mathcal{S}$. We consider a model based on
imperfect c-not gates where all the above can be computed, and discuss its
implications for the emergence of objective classical reality. We find that all
relevant quantities, such as the quantum mutual information as well as various
bounds on the accessible information exhibit similar behavior. In the regime
relevant for the emergence of objective classical reality this includes scaling
independent of the quality of the imperfect c-not gates or the size of
$\mathcal{E}$, and even nearly independent of the initial state of
$\mathcal{S}$.


  Super-resolution (SR) networks have been investigated for a while, with their
mobile and lightweight versions gaining noticeable popularity recently.
Quantization, the procedure of decreasing the precision of network parameters
(mostly FP32 to INT8), is also utilized in SR networks for establishing mobile
compatibility. This study focuses on a very important but mostly overlooked
post-training quantization (PTQ) step: representative dataset (RD), which
adjusts the quantization range for PTQ. We propose a novel pipeline (clip-free
quantization pipeline, CFQP) backed up with extensive experimental
justifications to cleverly augment RD images by only using outputs of the FP32
model. Using the proposed pipeline for RD, we can successfully eliminate
unwanted clipped activation layers, which nearly all mobile SR methods utilize
to make the model more robust to PTQ in return for a large overhead in runtime.
Removing clipped activations with our method significantly benefits overall
increased stability, decreased inference runtime up to 54% on some SR models,
better visual quality results compared to INT8 clipped models - and outperforms
even some FP32 non-quantized models, both in runtime and visual quality,
without the need for retraining with clipped activation.


  The first measurements of $\mathrm{K^{*}(892)^{0}}$ resonance production as a
function of charged-particle multiplicity in Xe$-$Xe collisions at
$\sqrt{s_{\mathrm{NN}}}=$ 5.44 TeV and pp collisions at $\sqrt{s}=$ 5.02 TeV
using the ALICE detector are presented. The resonance is reconstructed at
midrapidity ($|y|< 0.5$) using the hadronic decay channel $\mathrm{K^{*0}}
\rightarrow \mathrm{K^{\pm} \pi^{\mp}}$. Measurements of transverse-momentum
integrated yield, mean transverse-momentum, nuclear modification factor of
$\mathrm{K^{*0}}$, and yield ratios of resonance to stable hadron
($\mathrm{K^{*0}}$/K) are compared across different collision systems (pp,
p$-$Pb, Xe$-$Xe, and Pb$-$Pb) at similar collision energies to investigate how
the production of $\mathrm{K^{*0}}$ resonances depends on the size of the
system formed in these collisions. The hadronic rescattering effect is found to
be independent of the size of colliding systems and mainly driven by the
produced charged-particle multiplicity, which is a proxy of the volume of
produced matter at the chemical freeze-out. In addition, the production yields
of $\mathrm{K^{*0}}$ in Xe$-$Xe collisions are utilized to constrain the
dependence of the kinetic freeze-out temperature on the system size using the
hadron resonance gas in partial chemical equilibrium (HRG-PCE) model.


  Simplicial complexes are a versatile and convenient paradigm on which to
build all the tools and techniques of the logic of knowledge, on the assumption
that initial epistemic models can be described in a distributed fashion. Thus,
we can define: knowledge, belief, bisimulation, the group notions of mutual,
distributed and common knowledge, and also dynamics in the shape of simplicial
action models. We give a survey on how to interpret all such notions on
simplicial complexes, building upon the foundations laid in prior work by
Goubault and others.


  By means of powder neutron diffraction we investigate changes in the magnetic
structure of the coplanar non-collinear antiferromagnet Mn$_3$Ge caused by an
application of hydrostatic pressure up to 5\phantom{ }GPa. At ambient
conditions the kagom\'e layers of Mn atoms in Mn$_3$Ge order in a triangular
120$^{\circ}$ spin structure. Under high pressure the spins acquire a uniform
out-of-plane canting, gradually transforming the magnetic texture to a
non-coplanar configuration. With increasing pressure the canted structure fully
transforms into the collinear ferromagnetic one. We observed that magnetic
order is accompanied by a noticeable magnetoelastic effect, namely, spontaneous
magnetostriction. The latter induces an in-plane magnetostrain of the hexagonal
unit cell at ambient pressure and flips to an out-of-plane strain at high
pressures in accordance with the change of the magnetic structure.


  We determine the proportion of $[3\times 3;3]$-MRD codes over ${\mathbb F}_q$
within the space of all $3$-dimensional $3\times3$-rank-metric codes over the
same field. This shows that for these parameters MRD codes are sparse in the
sense that the proportion tends to $0$ as $q\rightarrow\infty$. This is so far
the only parameter case for which MRD codes are known to be sparse. The
computation is accomplished by reducing the space of all such rank-metric codes
to a space of specific bases and subsequently making use of a result by
Menichetti (1973) on 3-dimensional semifields.


  In this chapter we share our experience in running ten editions of the Green
Lab course at the Vrije Universiteit Amsterdam, the Netherlands. The course is
given in the Software Engineering and Green IT track of the Computer Science
Master program of the VU. The course takes place every year over a 2-month
period and teaches Computer Science students the fundamentals of Empirical
Software Engineering in the context of energy-efficient software. The
peculiarity of the course is its research orientation: at the beginning of the
course the instructor presents a catalog of scientifically relevant goals, and
each team of students signs up for one of them and works together for 2 months
on their own experiment for achieving the goal. Each team goes over the classic
steps of an empirical study, starting from a precise formulation of the goal
and research questions to context definition, selection of experimental
subjects and objects, definition of experimental variables, experiment
execution, data analysis, and reporting. Over the years, the course became
well-known within the Software Engineering community since it led to several
scientific studies that have been published at various scientific conferences
and journals. Also, students execute their experiments using
\textit{open-source tools}, which are developed and maintained by researchers
and other students within the program, thus creating a virtuous community of
learners where students exchange ideas, help each other, and learn how to
collaboratively contribute to open-source projects in a safe environment.


  Due to the outstanding capability of capturing underlying data distributions,
deep learning techniques have been recently utilized for a series of
traditional database problems. In this paper, we investigate the possibilities
of utilizing deep learning for cardinality estimation of similarity selection.
Answering this problem accurately and efficiently is essential to many data
management applications, especially for query optimization. Moreover, in some
applications the estimated cardinality is supposed to be consistent and
interpretable. Hence a monotonic estimation w.r.t. the query threshold is
preferred. We propose a novel and generic method that can be applied to any
data type and distance function. Our method consists of a feature extraction
model and a regression model. The feature extraction model transforms original
data and threshold to a Hamming space, in which a deep learning-based
regression model is utilized to exploit the incremental property of cardinality
w.r.t. the threshold for both accuracy and monotonicity. We develop a training
strategy tailored to our model as well as techniques for fast estimation. We
also discuss how to handle updates. We demonstrate the accuracy and the
efficiency of our method through experiments, and show how it improves the
performance of a query optimizer.


  Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3),
for which a complete characterization of the rate region is provided. This
characterization answers in the affirmative the open question whether there
exists a non-vanishing gap between the optimal bandwidth-storage tradeoff of
the functional-repair regenerating codes (i.e., the cut-set bound) and that of
the exact-repair regenerating codes. The converse proof relies on the existence
of symmetric optimal solutions. For the achievability, only one non-trivial
corner point of the rate region needs to be addressed, for which an explicit
binary code construction is given.


  According to theorems of Shnirelman and followers, in the semiclassical limit
the quantum wavefunctions of classically ergodic systems tend to the
microcanonical density on the energy shell. We here develop a semiclassical
theory that relates the rate of approach to the decay of certain classical
fluctuations. For uniformly hyperbolic systems we find that the variance of the
quantum matrix elements is proportional to the variance of the integral of the
associated classical operator over trajectory segments of length $T_H$, and
inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg
time, $\bar\rho$ being the mean density of states. Since for these systems the
classical variance increases linearly with $T_H$, the variance of the matrix
elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians
with a mixed phase space and the stadium billiard, our results predict a slower
decay due to sticking in marginally unstable regions. Numerical computations
supporting these conclusions are presented for the bakers map and the hydrogen
atom in a magnetic field.


  Light black holes could have formed in the very early universe through the
collapse of large primordial density fluctuations. These primordial black holes
(PBHs), if light enough, would have evaporated by now because of the emission
of Hawking radiation; thus they could not represent a sizable fraction of dark
matter today. However, they could have left imprints in the early cosmological
epochs. We will discuss the impact of massless graviton emission by (rotating)
PBHs before the onset of big bang nucleosynthesis (BBN) and conclude that this
contribution to dark radiation is constrained by the cosmic microwave
background (CMB) (with the future CMB Stage 4) and BBN in the lighter portion
of the PBH mass range, under the hypothesis that they dominated the energy
density of the universe.


  In-plane wave propagation in a periodic rectangular grid beam structure,
which includes rotational inertia (so-called 'Rayleigh beams'), is analyzed
both with a Floquet-Bloch exact formulation for free oscillations and with a
numerical treatment (developed with PML absorbing boundary conditions) for
forced vibrations (including Fourier representation and energy flux
evaluations), induced by a concentrated force or moment. A complex interplay is
observed between axial and flexural vibrations (not found in the common
idealization of out-of-plane motion), giving rise to several forms of vibration
localization: 'X-', 'cross-' and 'star-' shaped, and channel propagation. These
localizations are triggered by several factors, including rotational inertia
and slenderness of the beams and the type of forcing source (concentrated force
or moment). Although the considered grid of beams introduces an orthotropy in
the mechanical response, a surprising 'isotropization' of the vibration is
observed at special frequencies. Moreover, rotational inertia is shown to
'sharpen' degeneracies related to Dirac cones (which become more pronounced
when the aspect ratio of the grid is increased), while the slenderness can be
tuned to achieve a perfectly flat band in the dispersion diagram. The obtained
results can be exploited in the realization of metamaterials designed to
control wave propagation.


  Discourse parsing is largely dominated by greedy parsers with
manually-designed features, while global parsing is rare due to its
computational expense. In this paper, we propose a simple chart-based neural
discourse parser that does not require any manually-crafted features and is
based on learned span representations only. To overcome the computational
challenge, we propose an independence assumption between the label assigned to
a node in the tree and the splitting point that separates its children, which
results in tractable decoding. We empirically demonstrate that our model
achieves the best performance among global parsers, and comparable performance
to state-of-art greedy parsers, using only learned span representations.


  Deception boosts security for systems and components by denial, deceit,
misinformation, camouflage and obfuscation. In this work an extensive overview
of the deception technology environment is presented. Taxonomies, theoretical
backgrounds, psychological aspects as well as concepts, implementations, legal
aspects and ethics are discussed and compared.


  If the fifth dimension is one-dimensional connected manifold, up to
diffeomorphic, the only possible space-time will be $M^4 \times R^1$, $M^4
\times R^1/Z_2$, $M^4 \times S^1$ and $M^4 \times S^1/Z_2$. And there exist two
possibilities on cosmology constant along the fifth dimension: the cosmology
constant is constant, and the cosmology constant is sectional constant. We
construct the general models with parallel 3-branes and with constant/sectional
constant cosmology constant along the fifth dimension on those kinds of the
space-time, and point out that for compact fifth dimension, the sum of the
brane tensions is zero, for non-compact fifth dimension, the sum of the brane
tensions is positive. We assume the observable brane which includes our world
should have positive tension, and obtain that the gauge hierarchy problem can
be solved in those scenarios. We also discuss some simple models.


  A method is proposed of obtaining (2+1)-dimensional non- linear equations
with non-analytic dispersion relations. Bilocal formalism is shown to make it
possible to represent these equations in a form close to that for their
counterparts in 1+1 dimensions.


  We study a class of 2-variable polynomials called exact polynomials which
contains $A$-polynomials of knot complements. The Mahler measure of these
polynomials can be computed in terms of a volume function defined on the
vanishing set of the polynomial. We prove that the local extrema of the volume
function are on the 2-dimensional torus and give a closed formula for the
Mahler measure in terms of these extremal values. This formula shows that the
Mahler measure of an irreducible and exact polynomial divided by $\pi$ is
greater than the amplitude of the volume function. We also prove a
$K$-theoretical criterium for a polynomial to be a factor of an $A$-polynomial
and give a topological interpretation of its Mahler measure.


  The single-layered ruthenate Sr$_2$RuO$_4$ is one of the most enigmatic
unconventional superconductors. While for many years it was thought to be the
best candidate for a chiral $p$-wave superconducting ground state, desirable
for topological quantum computations, recent experiments suggest a singlet
state, ruling out the original $p$-wave scenario. The superconductivity as well
as the properties of the multi-layered compounds of the ruthenate perovskites
are strongly influenced by a van Hove singularity in proximity of the Fermi
energy. Tiny structural distortions move the van Hove singularity across the
Fermi energy with dramatic consequences for the physical properties. Here, we
determine the electronic structure of the van Hove singularity in the surface
layer of Sr$_2$RuO$_4$ by quasiparticle interference imaging. We trace its
dispersion and demonstrate from a model calculation accounting for the full
vacuum overlap of the wave functions that its detection is facilitated through
the octahedral rotations in the surface layer.


  In this study, the role of solvent viscosity ratio ($\beta$) on the creeping
flow characteristics of Oldroyd-B fluid over a channel-confined circular
cylinder has been explored numerically. The hydrodynamic model equations have
been solved by RheoTool, an open-source toolbox based on OpenFOAM, employing
the finite volume method for extensive ranges of Deborah number ($De =
0.025-1.5$) and solvent viscosity ratio ($\beta = 0.1-0.9$) for the fixed wall
blockage ($B = 0.5$). The present investigation has undergone extensive
validation, with available literature under specific limited conditions, before
obtaining detailed results for the relevant flow phenomena such as streamline,
pressure and stress contour profiles, pressure coefficient ($C_p$), wall shear
stress ($\tau_w$), normal stress ($\tau_{xx}$), first normal stress difference
($N_{1}$), and drag coefficient ($C_{\text{D}}$).The flow profiles have
exhibited a distinctive behavior characterized by a loss of symmetry in the
presence of pronounced viscoelastic and polymeric effects. The results for low
$De$ notably align closely with those for Newtonian fluids, and the drag
coefficient ($C_D$) remains relatively constant regardless of $\beta$, as the
viscoelastic influence is somewhat subdued. As $De$ increases, the influence of
viscoelasticity becomes more pronounced, while a decrease in $\beta$ leads to
an escalation in polymeric effects; an increase in the $C_D$ value is observed
as $\beta$ increases. Within this parameter range, the prevailing force
governing the flow is the pressure drag force.


  Liquid Staking Tokens (LSTs) function as tokenized representations of staked
native assets while also accruing staking rewards. They emerged as a preferred
method of staking within Proof of Stake (PoS) blockchains, owing to their ease
of use and tradability. In this Systematization of Knowledge (SoK), we
establish a general framework describing the design choices and protocols
underlying liquid staking. We then employ the framework to systematically
compare the top LST implementations, examining their node operator selection,
validator operations, and staking rewards distribution models. We further
discuss security concerns associated with liquid staking, its implications for
PoS blockchain security, and Distributed Validator technology (DVT) as a
potential solution. Finally, we empirically analyze LSTs' performance and find
that the design choices and market events affect peg stability; particularly,
LSTs with centralized governance and operations are more efficient in tracking
staking rewards.


  We present the first interferometric polarization maps of the NGC2024 FIR5
molecular core obtained with the BIMA array at approximately 2 arcsec
resolution. We measure an average position angle of -60+-6 degrees in the main
core of FIR5 and 54+-9 degrees in the eastern wing of FIR5. The morphology of
the polarization angles in the main core of FIR5 suggests that the field lines
are parabolic with a symmetry axis approximately parallel to the major axis of
the putative disk in FIR5, which is consistent with the theoretical scenario
that the gravitational collapse pulled the field lines into an hour-glass
shape. The polarization percentage decreases toward regions with high intensity
and close to the center of the core, suggesting that the dust alignment
efficiency may decrease at high density. The plane-of-sky field strength can be
estimated with the modified Chandrasekhar-Fermi formula, and the small
dispersion of the polarization angles in FIR5 suggests that the magnetic field
is strong ($\gtrsim$ 2mG) and perhaps dominates the turbulent motions in the
core.


  Quantum memory is a central component for quantum information processing
devices, and will be required to provide high-fidelity storage of arbitrary
states, long storage times and small access latencies. Despite growing interest
in applying physical-layer error-suppression strategies to boost fidelities, it
has not previously been possible to meet such competing demands with a single
approach. Here we use an experimentally validated theoretical framework to
identify periodic repetition of a high-order dynamical decoupling sequence as a
systematic strategy to meet these challenges. We provide analytic
bounds-validated by numerical calculations-on the characteristics of the
relevant control sequences and show that a "stroboscopic saturation" of
coherence, or coherence plateau, can be engineered, even in the presence of
experimental imperfection. This permits high-fidelity storage for times that
can be exceptionally long, meaning that our device-independent results should
prove instrumental in producing practically useful quantum technologies.


  Convolutional neural networks (CNN) are known to be an effective means to
detect and analyze images. Their power is essentially based on the ability to
extract out images common features. There exist, however, images involving
unique, irregular features or details. Such is a collection of unusual children
drawings reflecting the kids imagination and individuality. These drawings were
analyzed by means of a CNN constructed by means of Keras-TensorFlow. The same
problem - on a significantly higher level - was solved with newly developed
family of networks called IgNet that is described in this paper. It proved able
to learn by 100 % all the categorical characteristics of the drawings. In the
case of a regression task (learning the young artists ages) IgNet performed
with an error of no more than 0.4 %. The principles are discussed of IgNet
design that made it possible to reach such substantial results with rather
simple network topology.


  We consider the statistical properties of photon detection with imperfect
detectors that exhibit dark counts and less than unit efficiency, in the
context of tomographic reconstruction. In this context, the detectors are used
to implement certain POVMs that would allow to reconstruct the quantum state or
quantum process under consideration. Here we look at the intermediate step of
inferring outcome probabilities from measured outcome frequencies, and show how
this inference can be performed in a statistically sound way in the presence of
detector imperfections. Merging outcome probabilities for different sets of
POVMs into a consistent quantum state picture has been treated elsewhere
[K.M.R. Audenaert and S. Scheel, New J. Phys. 11, 023028 (2009)]. Single-photon
pulsed measurements as well as continuous wave measurements are covered.


  Quasinormal modes of massless test scalar field in the background of
gravitational field for a non-extremal dilatonic dyonic black hole are
explored. The dyon-like black hole solution is considered in the gravitational
$4d$ model involving two scalar fields and two 2-forms. It is governed by two
2-dimensional dilatonic coupling vectors $\vec{\lambda}_i$ obeying
$\vec{\lambda}_i (\vec{\lambda}_1 + \vec{\lambda}_2) > 0$, $i =1,2$. The first
law of black hole thermodynamics is given and the Smarr relation is verified.
Quasinormal modes for a massless scalar (test) field in the eikonal
approximation are obtained and analysed. These modes depend upon a
dimensionless parameter $a$ ($0 < a \leq 2$) which is a function of
$\vec{\lambda}_i$. For limiting strong ($a = +0$) and weak ($a = 2$) coupling
cases, they coincide with the well-known results for the Schwarzschild and
Reissner-Nordstr\"om solutions. It is shown that the Hod conjecture, connecting
the damping rate and the Hawking temperature, is satisfied for $0 < a \leq 1$
and all allowed values of parameters.


  The r-th order nonlinearity of a Boolean function is the minimum number of
elements that have to be changed in its truth table to arrive at a Boolean
function of degree at most r. It is shown that the (suitably normalised) r-th
order nonlinearity of a random Boolean function converges strongly for all r\ge
1. This extends results by Rodier for r=1 and by Dib for r=2. The methods in
the present paper are mostly of elementary combinatorial nature and also lead
to simpler proofs in the cases that r=1 or 2.


  Word embedding models have become a fundamental component in a wide range of
Natural Language Processing (NLP) applications. However, embeddings trained on
human-generated corpora have been demonstrated to inherit strong gender
stereotypes that reflect social constructs. To address this concern, in this
paper, we propose a novel training procedure for learning gender-neutral word
embeddings. Our approach aims to preserve gender information in certain
dimensions of word vectors while compelling other dimensions to be free of
gender influence. Based on the proposed method, we generate a Gender-Neutral
variant of GloVe (GN-GloVe). Quantitative and qualitative experiments
demonstrate that GN-GloVe successfully isolates gender information without
sacrificing the functionality of the embedding model.


  We present that a statistical method known as the Complexity-Entropy analysis
is useful to characterize a state of plasma turbulence and flux in the resonant
magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The
RMP ELM suppression phase with the stochastic pedestal top temperature
fluctuation can be distinguished from the natural ELM free phase with the
chaotic fluctuation. It is discussed that the stochastic temperature
fluctuation localized near the pedestal top can be originated from the narrow
layer of the field penetration near the pedestal top. The forced magnetic
island can emit the resonant drift wave of comparable sizes (relatively low-k)
in the RMP ELM suppression phase, and it can results in the generation of
stochastic higher wavenumber fluctuations coupled to tangled fields around the
island. The analysis of the ion saturation current measurement around the main
outer striking point on the divertor shows that it also becomes more stochastic
as the stronger plasma response to the RMP field is expected.


  This article tells the story of the founding of the Compass Project at UC
Berkeley and describes its impacts. The Compass Project is a self-formed group
of graduate and undergraduate students in the physical sciences. Its goals are
to improve undergraduate physics education, provide our members with
opportunities for professional development, and increase retention of students,
especially those from populations typically underrepresented in the physical
sciences. Compass fosters a diverse, collaborative student community by
providing a wide range of services, including a summer program, fall and spring
semester courses, mentoring, a research lecture series, and other academic and
social support.


  Deep learning is playing an instrumental role in the design of the next
generation of communication systems. In this letter, we address the massive
MIMO interconnect's bandwidth constraint relaxation using autoencoders. The
autoencoder is trained to learn the received signal structure so that a low
dimension latent variable is transferred as opposed to the original high
dimension signal. For an efficient implementation, the approach suggests to
separately deploy the autoencoder components, namely the encoder and the
decoder, in massive MIMO radio head and central processing units respectively.
The simulation results show that one can relax the interconnect's bandwidth by
a factor of up to 16 with non-substantial performance degradation of the
centralized and the decentralized processing. Fortunately, such a loss can be
compensated by running few extra iterations in the detection process which
renders the autoencoder-iterative detection an interconnect's bandwidth and
computational complexity design trade-off.


  We explore an unusual nature of chemical bonding of the thorium atom with a
ring of six carbon atoms (hexagon) in novel carbon materials. Our ab initio
calculations of Th-based metallofullerenes (Th@C60, Th@C20) and Th bound to
benzene or coronene at the Hartree-Fock level with the second order
perturbation (MP2) correction accounting for the van der Waals interactions,
demonstrate that the optimal position of the thorium atom is where it faces the
center of a hexagon and is located at a distance of 2.01-2.07 A from the
center. For Th encapsulated in C60 it is found at 2.01 A, whereas the other
local energy minima are shifted to larger energies (0.22 eV and higher). Inside
C60 the highest local minimum at 1.17 eV is observed when Th faces the center
of the five member carbon ring (pentagon). Based on our calculations for Th
with benzene and coronene where the global minimum for Th corresponds to its
position at 2.05 A (benzene) or 2.02 A (coronene) from the hexagon center, we
conclude that a well pronounced minimum is likely to present in graphene and in
a single wall carbon nanotube. The ground state of Th is singlet, other high
spin states (triplet and quintet) lie higher in energy (> 1.62 eV). We discuss
a potential use of the carbon nanomaterials with the 229Th isotope having the
nuclear transition of the optical range, for metrological purposes.


  In this paper, we give the general form of spherically symmetric Finsler
metrics in $R^n$ and surprisedly find that many well-known Finsler metrics
belong to this class. Then we explicitly express projective metrics of this
type. The necessary and sufficient conditions that projective Finsler metrics
with spherical symmetry have constant flag curvature are also obtained.


  The era of ubiquitous, affordable wireless connectivity has opened doors to
countless practical applications. In this context, ambient backscatter
communication (AmBC) stands out, utilizing passive tags to establish
connections with readers by harnessing reflected ambient radio frequency (RF)
signals. However, conventional data detectors face limitations due to their
inadequate knowledge of channel and RF-source parameters. To address this
challenge, we propose an innovative approach using a deep neural network (DNN)
for channel state estimation (CSI) and signal detection within AmBC systems.
Unlike traditional methods that separate CSI estimation and data detection, our
approach leverages a DNN to implicitly estimate CSI and simultaneously detect
data. The DNN model, trained offline using simulated data derived from channel
statistics, excels in online data recovery, ensuring robust performance in
practical scenarios. Comprehensive evaluations validate the superiority of our
proposed DNN method over traditional detectors, particularly in terms of bit
error rate (BER). In high signal-to-noise ratio (SNR) conditions, our method
exhibits an impressive approximately 20% improvement in BER performance
compared to the maximum likelihood (ML) approach. These results underscore the
effectiveness of our developed approach for AmBC channel estimation and signal
detection. In summary, our method outperforms traditional detectors, bolstering
the reliability and efficiency of AmBC systems, even in challenging channel
conditions.


  The nuclear quadruple moment is a fundamental character associated to the
nuclei, this moment is related to the not purely spherical distribution in the
nuclei, indeed its measure allows us to survey the geometric deformation of the
nuclei of its spherical shape. The measurement methods of the quadruple moment
is to study the electrical energy hyperfine interaction between the quadruple
moment and the electric field gradient due to atomics electrons, one of the
methods is the nuclear quadruple resonance NQR which is observed at the
transitions between energy levels splits by the effect of the quadruple
interaction and induced by a radio frequency field.


  We extend some classical results - such as Quillen's Theorem A, the
Grothendieck construction, Thomason's Theorem and the characterisation of
homotopically cofinal functors - from the homotopy theory of small categories
to polynomial monads and their algebras.
  As an application we give a categorical proof of the Dwyer-Hess and Turchin
results concerning the explicit double delooping of spaces of long knots.


  When a top quark decays there is a large amount of angular correlation, in
its rest frame, between its spin orientation and the direction of flight of the
charged lepton from its decay. In this letter we investigate the prospects of
measuring this angular correlation using the MC@NLO framework. The strength of
the correlation is investigated for different spin bases. The robustness
against variations of PDF sets and uncertainties, factorization scale
dependence, center-of-mass energy, and the jet R-parameter, is also examined.


  The simultaneous optimization of the centroid estimation and the separation
estimation of two incoherent optical point sources is restricted by a tradeoff
relation through an incompatibility coefficient. At the Rayleigh distance the
incompatibility coefficient vanishes and thus the tradeoff relation no longer
restricts the simultaneous optimization of measurement for a joint estimation.
We construct such a joint optimal measurement by an elaborated analysis on the
operator algebra of the symmetric logarithmic derivative. Our work not only
confirms the existence of a joint optimal measurement for this specific imaging
model, but also gives a promising method to characterize the condition on
measurement compatibility for general multiparameter estimation problems.


  In this work the supersymmetric gauge invariant action for the massive
Abelian $N$$=$$1$ super-{\QED} in the Atiyah-Ward space-time ({\DDdd}) is
formulated. The questions concerning the scheme of the gauge invariance in
{\DDdd} by means of gauging the massive $N$$=$$1$ super-{\QED} are
investigated. We study how to ensure the gauge invariance at the expenses of
the introduction of a complex vector superfield. We discuss the Wess-Zumino
gauge and thereupon we conclude that in this gauge, only the imaginary part of
the complex vector field, $B_{\m}$, gauges a $U(1)$-symmetry, whereas its real
part gauges a Weyl symmetry. We build up the gauge invariant massive term by
introducing a pair of chiral and anti-chiral superfields with opposite
$U(1)$-charges. We carry out a dimensional reduction {\it{\`a la}} Scherk of
the massive $N$$=$$1$ super-{\QED} action from {\DDdd} to {\Ddd}. Truncations
are needed in order to suppress non-physical modes and one ends up with a
parity-preserving $N$$=$$1$ super-QED$_{1+2}$ (rather than $N$$=$$2$) in
$D$$=$$1$$+$$2$. Finally, we show that the $N$$=$$1$ super-QED$_{1+2}$ we have
got is the supersymmetric version ofthe ${\tau}_{3}$QED .


  A search for a dark matter (DM) annihilation signal into $\gamma$-rays toward
the direction of the Canis Major (CMa) overdensity is presented. The nature of
CMa is still controversial and one scenario represents it as a dwarf galaxy,
making it an interesting candidate for DM annihilation searches. A total of 9.6
hours of high quality data were collected with the H.E.S.S. array of Imaging
Atmospheric Cherenkov Telescopes (IACTs) and no evidence for a very high energy
$\gamma$-ray signal is found. Upper limits on the CMa dwarf galaxy mass of the
order of 10$^{9}$ M$_{\odot}$ are derived at the 95% C.L. assuming neutralino
masses in the range 500 GeV - 10 TeV and relatively large annihilation
cross-sections. Constraints on the velocity-weighted annihilation cross section
$<\sigma v>$, are calculated for specific WIMP scenarios, using a NFW model for
the DM halo profile and taking advantage of numerical simulations of
hierarchical structure formation. 95% C.L. exclusion limits of the order of 5
$\times$ 10$^{-24}$ cm$^{3}$ s$^{-1}$ are reached in the 500 GeV - 10 TeV DM
particle mass interval, assuming a total halo mass of 3 $\times$ 10$^{8}$
M$_{\odot}$.


  A representation of polymer self-consistent field theory equivalent to
quantum density functional theory is given in terms of non-orthogonal basis
sets. Molecular integrals and self-consistent equations for spherically
symmetric systems using Gaussian basis functions are given, and the binding
energies and radial electron densities of neutral atoms hydrogen through
krypton are calculated. An exact electron self-interaction correction is
adopted and the Pauli-exclusion principle is enforced through ideas of polymer
excluded-volume. The atoms hydrogen through neon are additionally examined
without some approximations which permit cancellation of errors. Correlations
are neglected for both cases in the interest of simplicity and comparisons are
made with Hartree-Fock theory. The implications of the Pauli-exclusion
potential and its approximate form are discussed, and the Pauli model is
analyzed using scaling theory for the uniform electron density case where the
correct form of the Thomas-Fermi quantum kinetic energy and the Dirac exchange
correction are recovered.


  The proof of the Tits alternative for $Out(F_n)$ is completed. The main tool
is a Kolchin type theorem, proved in this paper. It states that a finitely
generated subgroup of $Out(F_n)$ consisting of unipotent automorphisms can be
conjugated into an upper-triangular subgroup (this is interpreted via
train-tracks).


  Recently, Yan and Gao proposed a quantum secret sharing protocol between
multiparty ($m$ members in group 1) and multiparty ($n$ members in group 2)
using a sequence of single photons (Phys. Rev. A \textbf{72}, 012304 (2005)).
We find that it is secure if the quantum signal transmitted is only a single
photon but insecure with a multi-photon signal as some agents can get the
information about the others' message if they attack the communication with a
Trojan horse. However, security against this attack can be attained with a
simple modification.