  We propose two spectral algorithms for partitioning nodes in directed graphs
respectively with a cyclic and an acyclic pattern of connection between groups
of nodes. Our methods are based on the computation of extremal eigenvalues of
the transition matrix associated to the directed graph. The two algorithms
outperform state-of-the art methods for directed graph clustering on synthetic
datasets, including methods based on blockmodels, bibliometric symmetrization
and random walks. Our algorithms have the same space complexity as classical
spectral clustering algorithms for undirected graphs and their time complexity
is also linear in the number of edges in the graph. One of our methods is
applied to a trophic network based on predator-prey relationships. It
successfully extracts common categories of preys and predators encountered in
food chains. The same method is also applied to highlight the hierarchical
structure of a worldwide network of Autonomous Systems depicting business
agreements between Internet Service Providers.


  This is the first paper in a series devoted to review the main properties of
galaxies designated S0 in the Hubble classification system. Our aim is to
gather abundant and, above all, robust information on the most relevant
physical parameters of this poorly-understood morphological type and their
possible dependence on the environment that could later be used to assess their
possible formation channel(s). The adopted approach combines the
characterisation of the fundamental features of the optical spectra of
$68{,}043$ S0 with heliocentric $z\lesssim 0.1$ with the exploration of a
comprehensive set of their global attributes. A principal component analysis is
used to reduce the huge number of dimensions of the spectral data to a
low-dimensional space facilitating a bias-free machine-learning-based
classification of the galaxies. This procedure has revealed that objects
bearing the S0 designation consist, despite their similar morphology, of two
separate sub-populations with statistically inconsistent physical properties.
Compared to the absorption-dominated S0, those with significant nebular
emission are, on average, somewhat less massive, more luminous with less
concentrated light profiles, have a younger, bluer and metal-poorer stellar
component, and avoid high-galaxy-density regions. Noteworthy is the fact that
the majority of members of this latter class, which accounts for at least a
quarter of the local S0 population, show star formation rates and spectral
characteristics entirely similar to those seen in late spirals. Our findings
suggest that star-forming S0 might be less rare than hitherto believed and
raise the interesting possibility of identifying them with plausible
progenitors of their quiescent counterparts.


  Recent advancements in large language models (LLMs) aim to tackle
heterogeneous human expectations and values via multi-objective preference
alignment. However, existing methods are parameter-adherent to the policy
model, leading to two key limitations: (1) the high-cost repetition of their
alignment algorithms for each new target model; (2) they cannot expand to
unseen objectives due to their static alignment objectives. In this work, we
propose Meta-Objective Aligner (MetaAligner), a model that performs conditional
weak-to-strong correction for weak responses to approach strong responses.
MetaAligner is the first policy-agnostic and generalizable method for
multi-objective preference alignment, which enables plug-and-play alignment by
decoupling parameter updates from the policy models and facilitates zero-shot
preference alignment for unseen objectives via in-context learning.
Experimental results show that MetaAligner achieves significant and balanced
improvements in multi-objective alignments on 10 state-of-the-art policy
models, and outperforms previous alignment methods with down to 15.71x less GPU
training hours. The model also effectively aligns unseen objectives, marking
the first step towards generalizable multi-objective preference alignment.


  In this paper, we present a novel linear algorithm to estimate the 6 DoF
relative pose from consecutive frames of stereo rolling shutter (RS) cameras.
Our method is derived based on the assumption that stereo cameras undergo
motion with constant velocity around the center of the baseline, which needs 9
pairs of correspondences on both left and right consecutive frames. The stereo
RS images enable the recovery of depth maps from the semi-global matching (SGM)
algorithm. With the estimated camera motion and depth map, we can correct the
RS images to get the undistorted images without any scene structure assumption.
Experiments on both simulated points and synthetic RS images demonstrate the
effectiveness of our algorithm in relative pose estimation.


  We study a general $2 \times 2$ symmetric, entangled, quantum game. When one
player has access only to classical strategies while the other can use the full
range of quantum strategies, there are ``miracle'' moves available to the
quantum player that can direct the result of the game towards the quantum
player's preferred result regardless of the classical player's strategy. The
advantage pertaining to the quantum player is dependent on the degree of
entanglement. Below a critical level, dependent on the payoffs in the game, the
miracle move is of no advantage.


  The issue of the transformations of units is treated, mainly, in a
geometrical context. It is shown that Weyl-integrable geometry is a consistent
framework for the formulation of the gravitational laws since the basic law on
which this geometry rests is invariant under point-dependent transformations of
units. Riemann geometry does not fulfill this requirement. Spacetime
singularities are then shown to be a consequence of a wrong choice of the
geometrical formulation of the laws of gravitation. This result is discussed,
in particular, for the Schwrazschild black hole and for
Friedmann-Robertson-Walker cosmology. Arguments are given that point at
Weyl-integrable geometry as a geometry implicitly containing the quantum
effects of matter. The notion of geometrical relativity is presented. This
notion may represent a natural extension of general relativity to include
invariance under the group of units transformations.


  An accurate numerical consideration of 1D spinless fermion model with
next-nearest neighbour (NNN) interactions is carried out for the electron
concentrations 4/7. It is shown that depending on the parameters of the model
it can be either Luttinger liquid or bipolaron liquid. In the former case
competing interactions can result in a smooth behavior of one-electron
distribution function at the Fermi surface with a divergence in the second
derivative with respect to the quasimomentum (and not in the first one, as
usual). In this connection, uncommon photoemission spectra for some 1D
conductors can be explained qualitatively.


  The choice of sentence encoder architecture reflects assumptions about how a
sentence's meaning is composed from its constituent words. We examine the
contribution of these architectures by holding them randomly initialised and
fixed, effectively treating them as as hand-crafted language priors, and
evaluating the resulting sentence encoders on downstream language tasks. We
find that even when encoders are presented with additional information that can
be used to solve tasks, the corresponding priors do not leverage this
information, except in an isolated case. We also find that apparently
uninformative priors are just as good as seemingly informative priors on almost
all tasks, indicating that learning is a necessary component to leverage
information provided by architecture choice.


  Independent component analysis (ICA) has been used in many applications,
including self-interference cancellation for in-band full-duplex wireless
systems and anomaly detection in industrial internet of things. This paper
presents a high-throughput and highly efficient configurable preprocessing
accelerator for the ICA algorithm. The proposed ICA accelerator has three major
blocks that perform data centering, covariance matrix for computation, and
eigenvalue decomposition (EVD). Specifically, the proposed accelerator is based
on a high-performance matrix multiplication array (MMA). The proposed MMA
architecture uses time-multiplexed processing so that the efficiency of
hardware utilization is greatly enhanced. Furthermore, the processing flow
utilizes parallel processing such that the centering, the calculation of the
covariance matrix, and EVD are conducted simultaneously and are individually
pipelined to maximize throughput. This paper presents the architecture, circuit
design, and performance estimates based on post-layout extraction of the
proposed preprocessing ICA accelerator. The proposed design achieves a
throughput of 40.7 kMatrices per second at complexity of 73.3 kGE.


  Based on the needs of convergence proofs of preconditioned proximal point
methods, we introduce notions of partial strong submonotonicity and partial
(metric) subregularity of set-valued maps. We study relationships between these
two concepts, neither of which is generally weaker or stronger than the other
one. For our algorithmic purposes, the novel submonotonicity turns out to be
easier to employ than more conventional error bounds obtained from
subregularity. Using strong submonotonicity, we demonstrate the linear
convergence of the Primal-Dual Proximal splitting method to some strictly
complementary solutions of example problems from image processing and data
science. This is without the conventional assumption that all the objective
functions of the involved saddle point problem are strongly convex.


  Let $p$ be a prime number and let $n$ be a non-zero natural number. We
compute the descending Loewy series of the algebra $R\_n/pR\_n$, where $R\_n$
denotes the ring of virtual ordinary characters of the symmetric group $S\_n$.


  Visual saliency patterns are the result of a variety of factors aside from
the image being parsed, however existing approaches have ignored these. To
address this limitation, we propose a novel saliency estimation model which
leverages the semantic modelling power of conditional generative adversarial
networks together with memory architectures which capture the subject's
behavioural patterns and task dependent factors. We make contributions aiming
to bridge the gap between bottom-up feature learning capabilities in modern
deep learning architectures and traditional top-down hand-crafted features
based methods for task specific saliency modelling. The conditional nature of
the proposed framework enables us to learn contextual semantics and
relationships among different tasks together, instead of learning them
separately for each task. Our studies not only shed light on a novel
application area for generative adversarial networks, but also emphasise the
importance of task specific saliency modelling and demonstrate the plausibility
of fully capturing this context via an augmented memory architecture.


  The promising performances of CNNs often overshadow the need to examine
whether they are doing in the way we are actually interested. We show through
experiments that even over-parameterized models would still solve a dataset by
recklessly leveraging spurious correlations, or so-called 'shortcuts'. To
combat with this unintended propensity, we borrow the idea of printer test page
and propose a novel approach called White Paper Assistance. Our proposed method
involves the white paper to detect the extent to which the model has preference
for certain characterized patterns and alleviates it by forcing the model to
make a random guess on the white paper. We show the consistent accuracy
improvements that are manifest in various architectures, datasets and
combinations with other techniques. Experiments have also demonstrated the
versatility of our approach on fine-grained recognition, imbalanced
classification and robustness to corruptions.


  Let $M_n= \fsu X1n$ be a sum of independent random variables such that $
X_k\leq 1$, $\E X_k =0$ and $\E X_k^2=\s_k^2$ for all $k$. Hoeffding 1963,
Theorem 3, proved that $$\P{M_n \geq nt}\leq H^n(t,p),\quad H(t,p)=
\bgl(1+qt/p\bgr)^{p +qt} \bgl({1-t}\bgr)^{q -qt}$$ with $$q=\ffrac
1{1+\s^2},\quad p=1-q, \quad \s^2 =\ffrac {\s_1^2+...+\s_n^2}n,\quad 0<t<1.$$
Bentkus 2004 improved Hoeffding's inequalities using binomial tails as upper
bounds. Let $\ga_k =\E X_k^3/\s_k^3$ and $ \vk_k= \E X_k^4/\s_k^4$ stand for
the skewness and kurtosis of $X_k$. In this paper we prove (improved)
counterparts of the Hoeffding inequality replacing $\s^2$ by certain functions
of $\fs \ga 1n$ respectively $\fs \vk 1n$. Our bounds extend to a general
setting where $X_k$ are martingale differences, and they can combine the
knowledge of skewness and/or kurtosis and/or variances of ~$X_k$. Up to factors
bounded by $e^2/2$ the bounds are final. All our results are new since no
inequalities incorporating skewness or kurtosis control so far are known.


  We introduce a new color index consisting of two spectral band width to
measure TiO absorption band strength centered at 567 nm. Based on the most
up-to-date line list for TiO we regenerate a grid of synthesized spectra and
investigate the temperature sensitivity of the index. The new index behave
similar to older Wing TiO-index where itdecreas emonotonically from coolest
atmosphere with Teff =2800 up to Teff =4000 where the TiO molecules
disassociate. To further examine the feasibility of the new index we reproduce
the calibration using a list of observed high resolution spectra and found
similar results. This index extend TiO absorption band capability to measure
effective temperature of late K to M stars to visual spectrum where it is more
accessible to small telescopes for long term dedicated observation.


  We introduce a fabrication method for gate-all-around nanowire field-effect
transistors. Single nanowires were aligned perpendicular to underlying bottom
gates using a resist-trench alignment technique. Top gates were then defined
aligned to the bottom gates to form gate-all-around structures. This approach
overcomes significant limitations in minimal obtainable gate length and
gate-length control in previous horizontal wrap-gated nanowire transistors that
arise because the gate is defined by wet etching. In the method presented here
gate-length control is limited by the resolution of the
electron-beam-lithography process. We demonstrate the versatility of our
approach by fabricating a device with an independent bottom gate, top gate, and
gate-all-around structure as well as a device with three independent
gate-all-around structures with 300 nm, 200 nm, and 150 nm gate length. Our
method enables us to achieve sub-threshold swings as low as 38 mV/dec at 77 K
for a 150 nm gate length.


  To begin with, it is pointed out that the form of the quantum probabil- ity
formula originates in the very initial state of the object system as seen when
the state is expanded with the eigen-projectors of the measured ob- servable.
Making use of the probability reproducibility condition, which is a key concept
in unitary measurement theory, one obtains the relevant coher- ent distribution
of the complete-measurement results in the final unitary- measurement state in
agreement with the mentioned probability formula. Treating the transition from
the final unitary, or premeasurement, state, where all possible results are
present, to one complete-measurement result sketchily in the usual way, the
well-known probability formula is derived. In conclusion it is pointed out that
the entire argument is only formal unless one makes it physical assuming that
the quantum probability law is valid in the extreme case of probability-one
(certain) events (projectors).


  Chronic kidney disease (CKD) has a poor prognosis due to excessive risk
factors and comorbidities associated with it. The early detection of CKD faces
challenges of insufficient medical histories of positive patients and
complicated risk factors. In this paper, we propose the TRACE (Transformer-RNN
Autoencoder-enhanced CKD Detector) framework, an end-to-end prediction model
using patients' medical history data, to deal with these challenges. TRACE
presents a comprehensive medical history representation with a novel key
component: a Transformer-RNN autoencoder. The autoencoder jointly learns a
medical concept embedding via Transformer for each hospital visit, and a latent
representation which summarizes a patient's medical history across all the
visits. We compared TRACE with multiple state-of-the-art methods on a dataset
derived from real-world medical records. Our model has achieved 0.5708 AUPRC
with a 2.31% relative improvement over the best-performing method. We also
validated the clinical meaning of the learned embeddings through visualizations
and a case study, showing the potential of TRACE to serve as a general disease
prediction model.


  The current research regarding the Riemann zeros suggests the existence of a
non-trivial algebraic/analytic structure on the set of Riemann zeros. The
duality between primes and Riemann zeta function zeros suggests some new goals
and aspects to be studied: {\em adelic duality} and the {\em POSet of prime
numbers}.
  The article presents computational evidence of the structure of the imaginary
parts $t$ of the non-trivial zeros of the Riemann zeta function $\rho=1/2+it$,
called in this article the {\em Riemann Spectrum}, using the study of their
distribution.
  The novelty represents in considering the associated characters $p^{it}$,
towards an algebraic point of view, than rather in the sense of Analytic Number
Theory. This structure is tentatively interpreted in terms of adelic
characters, and the duality of the rationals.
  Second, the POSet structure of prime numbers studied, is tentatively mirrored
via duality in the Riemann spectrum. A direct study of the convergence of their
Fourier series, along Pratt trees, is proposed.
  Further considerations, relating the Riemann Spectrum, adelic characters and
distributions, in terms of Hecke idelic characters, local zeta integrals
(Mellin transform) and $\omega$-eigen-distributions, are explored following.


  The true nature of the Hyades and Sirius superclusters is still an open
question. In this contribution, we confront Eggen's hypothesis that they are
cluster remnants with the results of a kinematic analysis of more than 6000 K
and M giants in the solar neighbourhood. This analysis includes new radial
velocity data from a large survey performed with the Coravel spectrometer,
complemented by Hipparcos parallaxes and Tycho-2 proper motions (Famaey et al.
2004). A maximum-likelihood method, based on a bayesian approach, has been
applied to the data, in order to make full use of all the available data
(including less precise parallaxes) and to derive the properties of the
different kinematic subgroups. Two such subgroups can be identified with the
Hyades and Sirius superclusters. Stars belonging to them span a very wide range
of age, which is difficult to account for in Eggen's scenario. These groups are
thus most probably "dynamical streams" related to the dynamical perturbation by
spiral waves rather than to cluster remnants.
  In this scenario, the Hyades and Ursa Major clusters just happen to be in the
Hyades and Sirius streams, which are purely dynamical features that have
nothing to do with the remnants of more massive primordial clusters. This
mechanism could be the key to understanding the presence of an old metal-rich
population, and of many exoplanetary systems in our neighbourhood. Moreover, a
strong spiral pattern seems to be needed in order to yield such prominent
streams. Since spiral structure is usually baryonic, this would leave very
little room for dark matter. This may be an indication that the era of the
dark-matter paradigm explaining the dynamics of the Galaxy may come to an end,
and is being superseded by modified gravity.


  Payment channel networks (PCNs) are a promising solution to the scalability
problem of cryptocurrencies. Any two users connected by a payment channel in
the network can theoretically send an unbounded number of instant, costless
transactions between them. Users who are not directly connected can also
transact with each other in a multi-hop fashion. In this work, we study the
incentive structure behind the creation of payment channel networks,
particularly from the point of view of a single user that wants to join the
network. We define a utility function for a new user in terms of expected
revenue, expected fees, and the cost of creating channels, and then provide
constant factor approximation algorithms that optimise the utility function
given a certain budget. Additionally, we take a step back from a single user to
the whole network and examine the parameter spaces under which simple graph
topologies form a Nash equilibrium.


  We present results of studying the post-pulse transport properties of single
pores. Single pores exhibit active transport (drift), and not just passive
transport (diffusion) at early post-pulse times. In addition, we suggest
experimental design methods obtained from model parameters that would enable
experimentalists to find localized regions of a few pores.


  The influence of high electric fields on the charge stripe order in
Nd1.67Sr0.33NiO4 was studied by means of simultaneous hard x-ray diffraction
and electrical transport experiments. Direct measurements of the charge stripe
satellite peaks in zero and high electric fields provide no evidence for a
deformation or a sliding of the stripe lattice, which contradicts previous
indications from non-linear conductance effects. By using the order parameter
of a structural phase transition for instant sample temperature measurements,
non-linear transport effects can be attributed to resistive heating.
Implications for the pinning of stripes in the nickelates are discussed.


  Double-exchange system is investigated by the dynamical mean-field theory. We
show that the chemical potential shifts as a function of temperature and
magnetization, which is anomalously large. We also discuss the influences of
dynamic Jahn-Teller effect to the shift of the chemical potential. Measurement
of the shift of the chemical potential casts a constraint to theoretical
approaches for the magnetoresistance phenomena in ($R$,$A$)MnO$_3$ such as
double-exchange effects and dynamic Jahn-Teller effects. We also propose a
method to measure the shift of $\mu$.


  The top quark data in the lepton plus $\tau$ channel offers a viable probe
for the charged Higgs boson signal. We analyse the recent Tevatron collider
data in this channel to obtain a significant limit on the $H^\pm$ mass in the
large $\tan\beta$ region.


  We report a comparative study of magnetic field driven domain wall motion in
thin films made of different magnetic materials for a wide range of field and
temperature. The full thermally activated creep motion, observed below the
depinning threshold, is shown to be described by a unique universal energy
barrier function. Our findings should be relevant for other systems whose
dynamics can be modeled by elastic interfaces moving on disordered energy
landscapes.


  The pair spin-orbit interaction (PSOI) is the spin-orbit component of the
electron-electron interaction that originates from the Coulomb fields of the
electrons. This relativistic component, which has been commonly assumed small
in the low-energy approximation, appears large and very significant in
materials with the strong SOI. The PSOI, being determined by the spins and
momenta of electrons, has highly unusual properties among which of most
interest is the mutual attraction of the electrons in certain spin
configurations. We review the nature of the PSOI in solids and its
manifestations in low-dimensional systems that have been studied to date. The
specific results depend on the configuration of the Coulomb fields in a
particular structure. The main actual structures are considered:
one-dimensional quantum wires and two-dimensional layers, both suspended and
placed in various dielectric media, as well as in the presence of a metallic
gate. We discuss the possible types of the two-electron bound states, the
conditions of their formation, their spectra together with the spin and orbital
structure. In a many-particle system, the PSOI breaks the spin-charge
separation as a result of which spin and charge degrees of freedom are mixed in
the collective excitations. At sufficiently strong PSOI, one of the collective
modes softens. This signals of the instability, which eventually leads to the
reconstruction of the homogeneous state of the system.


  The optical response of metallic nanoparticle arrays is dominated by
localized surface plasmon excitations and is the sum of individual particle
contributions modified by inter-particle coupling depending on specific array
geometry. Here we scrutinize how experimentally measured properties of large
scale (30 mm$^{2}$) amorphous Au nanodisk arrays stem from single particle
properties and their interaction. They give rise to a distinct oscillatory
behavior of the plasmon peak position, full-width at half-maximum, and
extinction efficiency which depends on the minimum particle center-to-center
(CC) distance.


  We study one-dimensional Levy processes with Levy-Khintchine exponent
psi(xi^2), where psi is a complete Bernstein function. These processes are
subordinate Brownian motions corresponding to subordinators, whose Levy measure
has completely monotone density; or, equivalently, symmetric Levy processes
whose Levy measure has completely monotone density on the positive half-line.
Examples include symmetric stable processes and relativistic processes. The
main result is a formula for the generalized eigenfunctions of transition
operators of the process killed after exiting the half-line. A generalized
eigenfunction expansion of the transition operators is derived. As an
application, a formula for the distribution of the first passage time (or the
supremum functional) is obtained.


  Performance and scalability are major concerns for blockchains:
permissionless systems are typically limited by slow proof of X consensus
algorithms and sequential post-order transaction execution on every node of the
network. By introducing a small amount of trust in their participants,
permissioned blockchain systems such as Hyperledger Fabric can benefit from
more efficient consensus algorithms and make use of parallel pre-order
execution on a subset of network nodes. Fabric, in particular, has been shown
to handle tens of thousands of transactions per second. However, this
performance is only achievable for contention-free transaction workloads. If
many transactions compete for a small set of hot keys in the world state, the
effective throughput drops drastically. We therefore propose XOX: a novel
two-pronged transaction execution approach that both minimizes invalid
transactions in the Fabric blockchain and maximizes concurrent execution. Our
approach additionally prevents unintentional denial of service attacks by
clients re-submitting conflicting transactions. Even under fully contentious
workloads, XOX can handle more than 3000 transactions per second, all of which
would be discarded by regular Fabric.


  Some features of old results in the total summation of all logarithmic
contributions of all diagrams in Yukawa theory are presented. We discuss some
lessons from this picture for the description of Pomeron, odderon, etc. in QCD.


  We investigate theoretically how the proximity effect in
superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling
manifests in the density of states and critical temperature. To describe a
general scenario, we allow for both Rashba and Dresselhaus type spin-orbit
coupling. Our results are obtained via the quasiclassical theory of
superconductivity, extended to include spin-orbit coupling in the Usadel
equation and Kupriyanov--Lukichev boundary conditions. Unlike previous works,
we have derived a Riccati parametrization of the Usadel equation with
spin-orbit coupling which allows us to address the full proximity regime.
First, we consider the density of states in both SF bilayers and SFS trilayers,
where the spectroscopic features in the latter case are sensitive to the phase
difference between the two superconductors. We find that the presence of
spin-orbit coupling leaves clear spectroscopic fingerprints in the density of
states due to its role in creating spin-triplet Cooper pairs. Unlike SF and SFS
structures without spin-orbit coupling, the density of states in the present
case depends strongly on the direction of magnetization. We show that the
spin-orbit coupling can stabilize singlet superconductivity even in the
presence of a strong exchange field $h \gg \Delta$. This leads to the
possibility of a magnetically tunable minigap: changing the direction of the
exchange field opens and closes the minigap. We also determine how the critical
temperature $T_c$ of an SF bilayer is affected by spin-orbit coupling and
demonstrate that one can achieve a spin-valve effect with a single ferromagnet.
We find that $T_c$ displays highly non-monotonic behavior both as a function of
the magnetization direction and the type and direction of the spin-orbit
coupling, offering a new way to exert control over the superconductivity of
proximity structures.


  We propose a percolation based M2M networking architecture and its data
transmission method. The proposed network architecture can be server-free and
router-free, which allows us to operate routing efficiently with percolations
based on six degrees of separation theory in small world network modeling. The
data transmission can be divided into two phases: routing and data transmission
phases. In the routing phase, probe packets will be transmitted and forwarded
in the network thus multiple paths are selected and performed based on the
constriction of the maximum hop number. In the second phase, the information
will be encoded, say, with the fountain codes, and transmitted using the paths
generated in the first phase. In such a way, an efficient routing and data
transmission mechanism can be built, which allow us to construct a low-cost,
flexible and ubiquitous network. Such a networking architecture and data
transmission can be used in many M2M communications, such as the stub network
of internet of things, and deep space networking, and so on.


  Static verification techniques leverage Boolean formula satisfiability
solvers such as SAT and SMT solvers that operate on conjunctive normal form and
first order logic formulae, respectively, to validate programs. They force
bounds on variable ranges and execution time and translate the program and its
specifications into a Boolean formula. They are limited to programs of
relatively low complexity for the following reasons. (1) A small increase in
the bounds can cause a large increase in the size of the translated formula.
(2) Boolean satisfiability solvers are restricted to using optimizations that
apply at the level of the formula. Finally, (3) the Boolean formulae often need
to be regenerated with higher bounds to ensure the correctness of the
translation. We present a method that uses sequential circuits, Boolean
formulae with memory elements and hierarchical structure, and sequential
circuit synthesis and verification frameworks to validate programs. (1)
Sequential circuits are much more succinct than Boolean formulae with no memory
elements and preserve the high-level structure of the program. (2) Encoding the
problem as a sequential circuit enables the use of a number of powerful
automated analysis techniques that have no counterparts for other Boolean
formulae. Our method takes an imperative program with a first order logic
specification consisting of a precondition and a postcondition pair, and a
bound on the program variable ranges, and produces a sequential circuit with a
designated output that is true when the program violates the specification.


  The interpretation of experimental measurements at the LHC requires accurate
theoretical predictions for exclusive observables, and in particular the
summation of soft and collinear radiation to all orders in perturbation theory.
We report on recent progress towards the automated calculation of multi-parton
LHC cross sections at next-to-leading order in QCD, including the summation of
next-to-leading logarithmic corrections through the combination with parton
showers.


  We consider the Travelling Salesman Problem with Vertex Requisitions, where
for each position of the tour at most two possible vertices are given. It is
known that the problem is strongly NP-hard. The proposed algorithm for this
problem has less time complexity compared to the previously known one. In
particular, almost all feasible instances of the problem are solvable in O(n)
time using the new algorithm, where n is the number of vertices. The developed
approach also helps in fast enumeration of a neighborhood in the local search
and yields an integer programming model with O(n) binary variables for the
problem.


  The most established method of reconstructing neural circuits from animals
involves slicing tissue very thin, then taking mosaics of electron microscope
(EM) images. To trace neurons across different images and through different
sections, these images must be accurately aligned, both with the others in the
same section and to the sections above and below. Unfortunately, sectioning and
imaging are not ideal processes - some of the problems that make alignment
difficult include lens distortion, tissue shrinkage during imaging, tears and
folds in the sectioned tissue, and dust and other artifacts. In addition the
data sets are large (hundreds of thousands of images) and each image must be
aligned with many neighbors, so the process must be automated and reliable.
This paper discusses methods of dealing with these problems, with numeric
results describing the accuracy of the resulting alignments.


  Self consistent analytic and numeric design for a set of electron guns with a
high beams quality to be used in high power Ka-band klystrons are presented in
this paper. The set of electron guns can be used in the high power Ka-band
klystrons in order to feed linear accelerating structures at 36 GHz with an
estimated 20 MW input power by achieving an effective accelerating electric
field in the (100-150) MV/m range. In the framework of the Compact Light XLS
project, a short Ka-band linearizer by working at 36 GHz able for providing an
integrated voltage of at least 15 MV is proposed for bunch-phase linearization.
In order to optimize the Ka-band klystrons efficiency for achieving 20 MW RF
output power, different electron guns and beam focusing channel designs are
examined and discussed in this paper.


  In this article we give an approach to define continuous functional calculus
for bounded quaternionic normal operators defined on a right quaternionic
Hilbert space.


  We obtain new non-extremal rotating black hole solutions in maximal
five-dimensional gauged supergravity. They are characterised by five
parameters, associated with the mass, the two angular momenta, and two
independently-specifiable charge parameters. Two of the three charges
associated with the U(1)^3 Cartan subgroup of the SO(6) gauge group are equal,
whilst the third can be independently specified. These new solutions generalise
all the previously-known rotating solutions in five-dimensional gauged
supergravity with independent angular momenta. They describe regular black
holes, provided the parameters lie in appropriate ranges so that naked
singularities and closed-timelike curves (CTCs) are avoided. We also construct
the BPS limit, and show that regular supersymmetric black holes or topological
solitons arise if the parameters are further restricted in an appropriate
manner.


  Document-level Relation Extraction (RE) is a more challenging task than
sentence RE as it often requires reasoning over multiple sentences. Yet, human
annotators usually use a small number of sentences to identify the relationship
between a given entity pair. In this paper, we present an embarrassingly simple
but effective method to heuristically select evidence sentences for
document-level RE, which can be easily combined with BiLSTM to achieve good
performance on benchmark datasets, even better than fancy graph neural network
based methods. We have released our code at
https://github.com/AndrewZhe/Three-Sentences-Are-All-You-Need.


  We show that every closed Legendrian submanifold of $S^{2n-1}$ with contact
form induced by a convex embedding into $\mathbb{R}^{2n}$ admits a Reeb chord
with distinct endpoints.


  The problem of sequentially detecting a moving anomaly which affects
different parts of a sensor network with time is studied. Each network sensor
is characterized by a non-anomalous and anomalous distribution, governing the
generation of sensor data. Initially, the observations of each sensor are
generated according to the corresponding non-anomalous distribution. After some
unknown but deterministic time instant, a moving anomaly emerges, affecting
different sets of sensors as time progresses. As a result, the observations of
the affected sensors are generated according to the corresponding anomalous
distribution. Our goal is to design a stopping procedure to detect the
emergence of the anomaly as quickly as possible, subject to constraints on the
frequency of false alarms. The problem is studied in a quickest change
detection framework where it is assumed that the evolution of the anomaly is
unknown but deterministic. To this end, we propose a modification of Lorden's
worst average detection delay metric to account for the trajectory of the
anomaly that maximizes the detection delay of a candidate detection procedure.
We establish that a Cumulative Sum-type test solves the resulting sequential
detection problem exactly when the sensors are homogeneous. For the case of
heterogeneous sensors, the proposed detection scheme can be modified to provide
a first-order asymptotically optimal algorithm. We conclude by presenting
numerical simulations to validate our theoretical analysis.


  This paper concerns the quantisation of a rigid body in the framework of
``covariant quantum mechanics'' on a curved spacetime with absolute time.
  The basic idea is to consider the multi-configuration space, i.e. the
configuration space for $n$ particles, as the $n$-fold product of the
configuration space for one particle. Then we impose a rigid constraint on the
multi-configuration space. The resulting space is then dealt with as a
configuration space of a single abstract `particle'. The same idea is applied
to all geometric and dynamical structures.
  We show that the above configuration space fits into the general framework of
``covariant quantum mechanics''. Hence, the methods of this theory can be
applied to the rigid body.
  Accordingly, we find exactly two inequivalent choices of quantum structures
for the rigid body. Then, we evaluate the quantum energy and momentum operators
and the `rotational part' of their spectra. We provide a new mathematical
interpretation of two-valued wavefunctions on SO(3) in terms of single-valued
sections of a new non-trivial quantum bundle. These results have clear
analogies with spin.


  In this work we present an efficient implementation of Canonical Monte Carlo
simulation for Coulomb many body systems on graphics processing units (GPU).
Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD)
architectures. It adopts the sequential updating scheme of Metropolis
algorithm, and makes no approximation in the computation of energy. It reaches
a remarkable 440-fold speedup, compared with the serial implementation on CPU.
We use this method to simulate primitive model electrolytes. We measure very
precisely all ion-ion pair correlation functions at high concentrations, and
extract renormalized Debye length, renormalized valences of constituent ions,
and renormalized dielectric constants. These results demonstrate unequivocally
physics beyond the classical Poisson-Boltzmann theory.


  We prove that the restricted wreath product ${\mathbb{Z}_n
\mathbin{\mathrm{wr}} \mathbb{Z}^k}$ has the $R_\infty$-property, i. e. every
its automorphism $\varphi$ has infinite Reidemeister number $R(\varphi)$, in
exactly two cases: (1) for any $k$ and even $n$; (2) for odd $k$ and $n$
divisible by 3. In the remaining cases there are automorphisms with finite
Reidemeister number, for which we prove the finite-dimensional twisted
Burnside--Frobenius theorem (TBFT): $R(\varphi)$ is equal to the number of
equivalence classes of finite-dimensional irreducible unitary representations
fixed by the action ${[\rho]\mapsto[\rho\circ\varphi]}$.


  In this paper we describe an elimination process which is a deterministic
rewriting procedure that on each elementary step transforms one system of
equations over free groups into a finitely many new ones. Infinite branches of
this process correspond to cyclic splittings of the coordinate group of the
initial system of equations. This allows us to construct algorithmically
Grushko's decompositions of finitely generated fully residually free groups and
cyclic [abelian] JSJ decompositions of freely indecomposable finitely generated
fully residually free groups. We apply these results to obtain an effective
description of the set of homomorphisms from a given finitely presented group
into a free group, or, more generally, into an NTQ group.


  By using a non-local, quantum mechanical response function we study graphene
plasmons in a one-dimensional superlattice (SL) potential $V_0 \cos G_0x$. The
SL introduces a quantum energy scale $E_G \sim \hbar v_F G_0$ associated to
electronic sub-band transitions. At energies lower than $E_G$, the plasmon
dispersion is highly anisotropic; plasmons propagate perpendicularly to the SL
axis, but become damped by electronic transitions along the SL direction. These
results question the validity of semiclassical approximations for describing
low energy plasmons in periodic structures. At higher energies, the dispersion
becomes isotropic and Drude-like with effective Drude weights related to the
average of the absolute value of the local chemical potential. Full quantum
mechanical treatment of the kinetic energy thus introduces non-local effects
that delocalize the plasmons in the SL, making the system behave as a
meta-material even near singular points where the charge density vanishes.


  V-spin symmetry ($s \leftrightarrow d$ symmetry) forbids the radiative decay
$\Xi_{c2}^{0*} \rightarrow \Xi_{c1}^0 \gamma$ in the SU(3) limit. The quark
mass term breaks V-spin symmetry and the leading nonanalytic contribution to
the radiative decay amplitude is computable in heavy baryon chiral perturbation
theory. The radiative decay branching ratio is determined by the coupling
constant $g_2$ and at leading order in chiral perturbation theory is given by
$Br(\Xi_{c2}^{0*} \rightarrow \Xi_{c1}^0 \gamma) = 1.0\times 10^{-3} g_2^2$.
Measurement of this branching fraction will determine $|g_2|$.


  The dynamics of power grids are governed by a large number of nonlinear
differential and algebraic equations (DAEs). To safely operate the system,
operators need to check that the states described by these DAEs stay within
prescribed limits after various potential faults. However, current numerical
solvers of DAEs are often too slow for real-time system operations. In
addition, detailed system parameters are often not exactly known. Machine
learning approaches have been proposed to reduce computational efforts, but
existing methods generally suffer from overfitting and failures to predict
unstable behaviors.
  This paper proposes a novel framework to predict power system transients by
learning in the frequency domain. The intuition is that although the system
behavior is complex in the time domain, there are relatively few dominant modes
in the frequency domain. Therefore, we learn to predict by constructing neural
networks with Fourier transform and filtering layers. System topology and fault
information are encoded by taking a multi-dimensional Fourier transform,
allowing us to leverage the fact that the trajectories are sparse both in time
and spatial frequencies. We show that the proposed approach does not need
detailed system parameters, greatly speeds up prediction computations and is
highly accurate for different fault types.


  The theoretical maximum time variation in the electronic charge permitted by
the Generalized Second Law of Thermodynamics applied to black holes radiating
and accreting in the cosmic microwave background matches the measured
cosmological variation in the fine structure constant claimed by Webb et al..
Such black holes cannot respond adiabatically to a varying fine structure
constant.


  Data-driven speech enhancement employing deep neural networks (DNNs) can
provide state-of-the-art performance even in the presence of non-stationary
noise. During the training process, most of the speech enhancement neural
networks are trained in a fully supervised way with losses requiring noisy
speech to be synthesized by clean speech and additive noise. However, in a real
implementation, only the noisy speech mixture is available, which leads to the
question, how such data could be advantageously employed in training. In this
work, we propose an end-to-end non-intrusive PESQNet DNN which estimates
perceptual evaluation of speech quality (PESQ) scores, allowing a
reference-free loss for real data. As a further novelty, we combine the PESQNet
loss with denoising and dereverberation loss terms, and train a complex
mask-based fully convolutional recurrent neural network (FCRN) in a "weakly"
supervised way, each training cycle employing some synthetic data, some real
data, and again synthetic data to keep the PESQNet up-to-date. In a subjective
listening test, our proposed framework outperforms the Interspeech 2021 Deep
Noise Suppression (DNS) Challenge baseline overall by 0.09 MOS points and in
particular by 0.45 background noise MOS points.


  Deception plays critical roles in economics and technology, especially in
emerging interactions in cyberspace. Holistic models of deception are needed in
order to analyze interactions and to design mechanisms that improve them. Game
theory provides such models. In particular, existing work models deception
using signaling games. But signaling games inherently model deception that is
undetectable. In this paper, we extend signaling games by including a detector
that gives off probabilistic warnings when the sender acts deceptively. Then we
derive pooling and partially-separating equilibria of the game. We find that 1)
high-quality detectors eliminate some pure-strategy equilibria, 2) detectors
with high true-positive rates encourage more honest signaling than detectors
with low false-positive rates, 3) receivers obtain optimal outcomes for
equal-error-rate detectors, and 4) surprisingly, deceptive senders sometimes
benefit from highly accurate deception detectors. We illustrate these results
with an application to defensive deception for network security. Our results
provide a quantitative and rigorous analysis of the fundamental aspects of
detectable deception.


  We study a dynamic model of relaxor ferroelectrics based on the spherical
random-bond---random-field model and the Langevin equations of motion. The
solution to these equations is obtained in the long-time limit where the system
reaches an equilibrium state in the presence of random local electric fields.
The complex dynamic linear and third-order nonlinear susceptibilities
$\chi_1(\omega)$ and $\chi_3(\omega)$, respectively, are calculated as
functions of frequency and temperature. In analogy with the static case, the
dynamic model predicts a narrow frequency dependent peak in $\chi_3(T,\omega)$,
which mimics a transition into a glass-like state.


  Image quality is the basis of image communication and understanding tasks.
Due to the blur and noise effects caused by imaging, transmission and other
processes, the image quality is degraded. Blind image restoration is widely
used to improve image quality, where the main goal is to faithfully estimate
the blur kernel and the latent sharp image. In this study, based on
experimental observation and research, an adaptively sparse regularized
minimization method is originally proposed. The high-order gradients combine
with low-order ones to form a hybrid regularization term, and an adaptive
operator derived from the image entropy is introduced to maintain a good
convergence. Extensive experiments were conducted on different blur kernels and
images. Compared with existing state-of-the-art blind deblurring methods, our
method demonstrates superiority on the recovery accuracy.


  We revisit the notions of the quantum-mechanical sojourn time in the context
of the quantum clocks to enquire whether the sojourn time be clocked without
the clock affecting the dynamics of the wave motion. Upon recognizing that the
positivity of conditional sojourn time is not ensured even in the case of
physically co-evolving clock mechanisms, we trace its origins to the
non-trivial inadvertent scattering arising from the disparity, however weak,
engendered by the very clock potential. Specifically, our investigations focus
on the Larmor spin rotation-based unitary clock where the alleviation of these
unphysical contributions has been achieved by correcting the mathematical
apparatus of extracting the sojourn times. The corrections have been obtained
for both the spin precession-based and spin alignment-based scenarios. The
sojourn times so obtained are found to have proper high- and low-energy limits
and turn out to be positive definite for an arbitrary potential. The regimen
provided here is general and appeals equivalently for unitary as well as
non-unitary clocks where the clock-induced perturbations couple to the system
Hamiltonian.


  The Riemann surface for polylogarithms of half-integer index, which has the
topology of an infinite dimensional hypercube, is studied in relation to
one-dimensional KPZ universality in finite volume. Known exact results for
fluctuations of the KPZ height with periodic boundaries are expressed in terms
of meromorphic functions on this Riemann surface, summed over all the sheets of
a covering map to an infinite cylinder. Connections to stationary large
deviations, particle-hole excitations and KdV solitons are discussed.


  Deceptive news posts shared in online communities can be detected with NLP
models, and much recent research has focused on the development of such models.
In this work, we use characteristics of online communities and authors -- the
context of how and where content is posted -- to explain the performance of a
neural network deception detection model and identify sub-populations who are
disproportionately affected by model accuracy or failure. We examine who is
posting the content, and where the content is posted to. We find that while
author characteristics are better predictors of deceptive content than
community characteristics, both characteristics are strongly correlated with
model performance. Traditional performance metrics such as F1 score may fail to
capture poor model performance on isolated sub-populations such as specific
authors, and as such, more nuanced evaluation of deception detection models is
critical.


  This paper presents a novel method for face clustering in videos using a
video-centralised transformer. Previous works often employed contrastive
learning to learn frame-level representation and used average pooling to
aggregate the features along the temporal dimension. This approach may not
fully capture the complicated video dynamics. In addition, despite the recent
progress in video-based contrastive learning, few have attempted to learn a
self-supervised clustering-friendly face representation that benefits the video
face clustering task. To overcome these limitations, our method employs a
transformer to directly learn video-level representations that can better
reflect the temporally-varying property of faces in videos, while we also
propose a video-centralised self-supervised framework to train the transformer
model. We also investigate face clustering in egocentric videos, a
fast-emerging field that has not been studied yet in works related to face
clustering. To this end, we present and release the first large-scale
egocentric video face clustering dataset named EasyCom-Clustering. We evaluate
our proposed method on both the widely used Big Bang Theory (BBT) dataset and
the new EasyCom-Clustering dataset. Results show the performance of our
video-centralised transformer has surpassed all previous state-of-the-art
methods on both benchmarks, exhibiting a self-attentive understanding of face
videos.


  Although single-layer transition-metal dichalcogenides with novel valley
functionalities are promising candidate to realize valleytronic devices, the
essential understanding of valley depolarization mechanisms is still
incomplete. Based on pump-probe experiments performed for MoSe2 and WSe2
monolayers and corroborating analysis from density functional calculations, we
demonstrate that coherent phonons at the K-point of the Brillouin zone can
effectively mediate the valley transfer of electron carriers. In the MoSe2
monolayer case, we identify this mode as the flexural acoustic ZA(K) mode,
which has broken inversion symmetry and thus can enable electron spin-flip
during valley transfer. On the other hand, in the monolayer WSe2 case where
spin-preserving inter-valley relaxations are preferred coherent LA(K) phonons
with even inversion symmetry are efficiently generated. These findings
establish that, while the specifics of inter-valley relaxations depend on the
spin alignments of energy bands, the K-point phonons should be taken into
account as an effective valley depolarization pathway in transition metal
dichalcogenide monolayers.


  In this work we disentangle the underlying physical picture of the in-medium
gluon radiation process across its different energy regimes by comparing the
recently obtained fully-resummed -- without any further approximations --
BDMPS-Z in-medium emission spectrum with the extensively used analytical
approaches. We observe that in the high-energy regime the radiation process is
dominated by a single hard scattering, while in the intermediate-energy region
coherence effects among multiple scatterings are crucial. Finally, we prove
that in the low-energy regime the dynamics is again controlled by a single
scattering but where one must include a suppression factor accounting for the
probability of not having any further scatterings.


  Deep learning has come a long way and has enjoyed an unprecedented success.
Despite high accuracy, however, deep models are brittle and are easily fooled
by imperceptible adversarial perturbations. In contrast to common
inference-time attacks, Backdoor (\aka Trojan) attacks target the training
phase of model construction, and are extremely difficult to combat since a) the
model behaves normally on a pristine testing set and b) the augmented
perturbations can be minute and may only affect few training samples. Here, I
propose a new method to tell whether a model has been subject to a backdoor
attack. The idea is to generate adversarial examples, targeted or untargeted,
using conventional attacks such as FGSM and then feed them back to the
classifier. By computing the statistics (here simply mean maps) of the images
in different categories and comparing them with the statistics of a reference
model, it is possible to visually locate the perturbed regions and unveil the
attack.


  An efficient dominating set (or perfect code) in a graph is a set of vertices
the closed neighborhoods of which partition the vertex set of the graph. The
minimum weight efficient domination problem is the problem of finding an
efficient dominating set of minimum weight in a given vertex-weighted graph;
the maximum weight efficient domination problem is defined similarly. We
develop a framework for solving the weighted efficient domination problems
based on a reduction to the maximum weight independent set problem in the
square of the input graph. Using this approach, we improve on several previous
results from the literature by deriving polynomial-time algorithms for the
weighted efficient domination problems in the classes of dually chordal and
AT-free graphs. In particular, this answers a question by Lu and Tang regarding
the complexity of the minimum weight efficient domination problem in strongly
chordal graphs.


  At the core of equilibrium statistical mechanics lies the notion of
statistical ensembles: a collection of microstates, each occurring with a given
a priori probability that depends only on a few macroscopic parameters such as
temperature, pressure, volume, and energy. In this review article, we discuss
recent advances in establishing statistical ensembles for athermal materials.
The broad class of granular and particulate materials is immune from the
effects of thermal fluctuations because the constituents are macroscopic. In
addition, interactions between grains are frictional and dissipative, which
invalidates the fundamental postulates of equilibrium statistical mechanics.
However, granular materials exhibit distributions of microscopic quantities
that are reproducible and often depend on only a few macroscopic parameters. We
explore the history of statistical ensemble ideas in the context of granular
materials, clarify the nature of such ensembles and their foundational
principles, highlight advances in testing key ideas, and discuss applications
of ensembles to analyze the collective behavior of granular materials.


  We present a finite-energy electroweak-monopole solution obtained by
considering non-linear extensions of the hypercharge sector of the Electroweak
Theory, based on logarithmic and exponential versions of electrodynamics. We
find constraints for a class of non-linear extensions and also work out an
estimate for the monopole mass in this scenario. We finally derive a lower
bound for the energy of the monopole and discuss the simpler case of a Dirac
magnetic charge.


  We present detailed timing and spectral analyses of the transient X-ray
pulsar RX J0209.6$-$7427 in the Small Magellanic Cloud during its 2019 giant
outburst. With a better known distance than most galactic X-ray pulsars, its
peak luminosity is determined to be $(1.11\pm0.06)\times 10^{39}\, \rm erg\
s^{-1}$; it is thus a {\it bonda fide} pulsating ultraluminous X-ray source
(PULX). Owing to the broad energy band of \textit{Insight}-HXMT, its pulsed
X-ray emission was detected from 1 keV up to the 130$-$180 keV band, which is
the highest energy emission detected from any PULXs outside the Milky Way. This
allows us to conclude that its main pulsed X-ray emission is from the "fan
beam" of the accretion column, and its luminosity is thus intrinsic. We also
estimate its magnetic field of (4.8$-$8.6)$\times10^{12}$ G or
(1.7$-$2.2)$\times10^{13}$ G, from its spin evolution or transition in the
accretion column structure during the outburst; we suggest that the two values
of the magnetic field strength correspond to the dipole and multipole magnetic
fields of the neutron star, similar to the recent discovery in the Galactic
PULX Swift J0243.6+6124. Therefore, the nature of the neutron star and its ULX
emission can be understood within the current theoretical frame of accreting
neutron stars. This may have implications for understanding the nature of those
farther away extragalactic PULXs.


  We discuss the production of particles in relativistic heavy-ion collisions
through the mechanism of massive bremsstrahlung, in which massive mesons are
emitted during rapid nucleon acceleration. This mechanism is described within
the framework of classical hadrodynamics for extended nucleons, corresponding
to nucleons of finite size interacting with massive meson fields. This new
theory provides a natural covariant microscopic approach to relativistic
heavy-ion collisions that includes automatically spacetime nonlocality and
retardation, nonequilibrium phenomena, interactions among all nucleons, and
particle production. Inclusion of the finite nucleon size cures the
difficulties with preacceleration and runaway solutions that have plagued the
classical theory of self-interacting point particles. For the soft reactions
that dominate nucleon-nucleon collisions, a significant fraction of the
incident center-of-mass energy is radiated through massive bremsstrahlung. In
the present version of the theory, this radiated energy is in the form of
neutral scalar ($\sigma$) and neutral vector ($\omega$) mesons, which
subsequently decay primarily into pions with some photons also. Additional
meson fields that are known to be important from nucleon-nucleon scattering
experiments should be incorporated in the future, in which case the radiated
energy would also contain isovector pseudoscalar ($\pi^+$, $\pi^-$, $\pi^0$),
isovector scalar ($\delta^+$, $\delta^-$, $\delta^0$), isovector vector
($\rho^+$, $\rho^-$, $\rho^0$), and neutral pseudoscalar ($\eta$) mesons.


  The role of cooperative effects (i.e. synergy) in transmission of infection
is investigated analytically and numerically for epidemics following the rules
of Susceptible-Infected-Susceptible (SIS) model defined on random regular
graphs. Non-linear dynamics are shown to lead to bifurcation diagrams for such
spreading phenomena exhibiting three distinct regimes: non-active, active and
bi-stable. The dependence of bifurcation loci on node degree is studied and
interesting effects are found that contrast with the behaviour expected for
non-synergistic epidemics.


  Some years ago, Lovelock showed that a number of apparently unrelated
familiar tensor identities had a common structure, and could all be considered
consequences in n-dimensional space of a pair of fundamental identities
involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's
results, and by using the fact that associated with any tensor in n-dimensional
space there is associated a fundamental tensor identity obtained by
antisymmetrising over n+1 indices, we establish a very general 'master'
identity for all trace-free (k,l)-forms. We then show how various other special
identities are direct and simple consequences of this master identity; in
particular we give direct application to Maxwell, Lanczos, Ricci, Bel and
Bel-Robinson tensors, and also demonstrate how relationships between scalar
invariants of the Riemann tensor can be investigated in a systematic manner.


  We calculate the two-, three- and (for the first time) four-point correlation
functions of the COBE-DMR 4-year sky maps, and search for evidence of
non-Gaussianity by comparing the data to Monte Carlo-simulations of the
functions. The analysis is performed for the 53 and 90 GHz channels, and five
linear combinations thereof. For each map, we simulate an ensemble of 10,000
Gaussian realisations based on an a priori best-fit scale-invariant
cosmological power spectrum, the DMR beam pattern and instrument-specific noise
properties. Each observed COBE-DMR map is compared to the ensemble using a
simple chi^2 statistic, itself calibrated by simulations. In addition, under
the assumption of Gaussian fluctuations, we find explicit expressions for the
expected values of the four-point functions in terms of combinations of
products of the two-point functions, then compare the observed four-point
statistics to those predicted by the observed two-point function, using a
redefined chi^2 statistic. Both tests accept the hypothesis that the DMR maps
are consistent with Gaussian initial perturbations.


  Meta distributions (MDs) are refined performance metrics in wireless networks
modeled using point processes. While there is no known method to directly
calculate MDs, the moments of the underlying conditional distributions (given
the point process) can often be expressed in exact analytical form. The problem
of finding the MD given the moments has several solutions, but the standard
approaches are inefficient and sensitive to the choices of a number of
parameters. Here we propose and explore the use of a method based on binomial
mixtures, which has several key advantages over other methods, since it is
based on a simple linear transform of the moments.


  Floquet engineering of isolated systems is often based on the concept of the
effective time-independent Floquet Hamiltonian, which describes the
stroboscopic evolution of a periodically driven quantum system in steps of the
driving period and which is routinely obtained analytically using
high-frequency expansions. The generalization of these concepts to open quantum
systems described by a Markovian master equation of Lindblad type turns out to
be non-trivial: On the one hand, already for a two-level system two different
phases can be distinguished, where the effective time-independent Floquet
generator (describing the stroboscopic evolution) is either again Markovian and
of Lindblad type or not. On the other hand, even though in the high-frequency
regime a Lindbladian Floquet generator (Floquet Linbladian) is numerically
found to exist, this behaviour is, curiously, not correctly reproduced within
analytical high-frequency expansions. Here, we demonstrate that a proper
Floquet Lindbladian can still be obtained from a high-frequency expansion, when
treating the problem in a suitably chosen rotating frame. Within this approach,
we can then also describe the transition to a phase at lower driving
frequencies, where no Floquet Lindbladian exists, and show that the emerging
non-Markovianity of the Floquet generator can entirely be attributed to the
micromotion of the open driven system.


  The quantum null energy condition (QNEC) is a conjectured relation between a
null version of quantum field theory energy and derivatives of quantum field
theory von Neumann entropy. In some cases, divergences cancel between these two
terms and the QNEC is intrinsically finite. We study the more general case here
where they do not and argue that a QNEC can still hold for bare
(unrenormalized) quantities. While the original QNEC applied only to locally
stationary null congruences in backgrounds that solve semiclassical theories of
quantum gravity, at least in the formal perturbation theory at a small Planck
length, the quantum focusing conjecture can be viewed as the special case of
our bare QNEC for which the metric is on shell.


  We analytically derive the general pseudo-potential operator of an arbitrary
isotropic interaction for particles confined in two-dimensional (2D) systems,
using the frame work developed by Huang and Yang for 3D scattering. We also
analytically derive the low energy dependence of the scattering phase-shift for
an arbitrary interaction with a power-law decaying tail, $V_{\rm
2D}(\rho)\propto \rho^{-\alpha}$ (for $\alpha>2$). We apply our results to the
2D dipolar gases ($\alpha=3$) as an example, calculating the momentum and
dipole moment dependence of the pseudo-potential for both $s$- and p-wave
scattering channels if the two scattering particles are in the same 2D layer.
Results for the s-wave scattering between particles in two different (parallel)
layers are also investigated. Our results can be directly applied to the
systems of dipolar atoms and/or polar molecules in a general 2D geometry.


  This paper presents results from the (to our knowledge) first dynamic
double-directionally resolved measurement campaign at mm-wave frequencies for
an outdoor microcellular scenario. The measurements are performed with USC's
real-time channel sounder equipped with phased array antennas that can steer
beams electrically in microseconds, allowing directional measurements in
dynamic environments. Exploiting the phase coherency of the setup, the
multi-path components can be tracked over time to investigate the temporal
dependencies of the channel characteristics. We present results for
time-varying path-loss, delay spread, mean angles and angular spreads observed
at the transmitter (TX) and receiver (RX) in the presence of moving vehicles
and pedestrians. Additionally, we investigate excess losses observed due to
blockage by vehicles and compare the cases when TX and RX are using fixed beams
or when they are capable of adjusting beam directions dynamically.


  In the framework of the many-electron s-d exchange model and Hubbard model,
self-consistent equations are derived for the one-particle retarded Green's
function in the many-electron Hubbard X-operator representation. We analyze the
general structure of the single-site approximations and their connection with
the coherent potential approximation (CPA) and dynamic effective field theory
(DMFT). Using the self-consistent approximation, we examine in detail the
picture of the evolution of the electron spectrum with the model parameters
(coupling constants, the concentration of charge carriers). The influence of
various factors (Kondo many-electron scattering, smearing due to damping,
dynamics of localized moment subsystem) on the shape of the density of states
N(E) in the interacting system is investigated. It is shown that the use of the
locator representation allows to avoid in some cases the non-analyticity in
approximate expressions for the Green's functions. Our approach enables one to
reproduce, at certain values of the parameters, three-peak structure of N(E)
near the metal-insulator transition.


  The spread of deep learning on embedded devices has prompted the development
of numerous methods to optimise the deployment of deep neural networks (DNN).
Works have mainly focused on: i) efficient DNN architectures, ii) network
optimisation techniques such as pruning and quantisation, iii) optimised
algorithms to speed up the execution of the most computational intensive layers
and, iv) dedicated hardware to accelerate the data flow and computation.
However, there is a lack of research on cross-level optimisation as the space
of approaches becomes too large to test and obtain a globally optimised
solution. Thus, leading to suboptimal deployment in terms of latency, accuracy,
and memory. In this work, we first detail and analyse the methods to improve
the deployment of DNNs across the different levels of software optimisation.
Building on this knowledge, we present an automated exploration framework to
ease the deployment of DNNs. The framework relies on a Reinforcement Learning
search that, combined with a deep learning inference framework, automatically
explores the design space and learns an optimised solution that speeds up the
performance and reduces the memory on embedded CPU platforms. Thus, we present
a set of results for state-of-the-art DNNs on a range of Arm Cortex-A CPU
platforms achieving up to 4x improvement in performance and over 2x reduction
in memory with negligible loss in accuracy with respect to the BLAS
floating-point implementation.


  The conductance through a serial double dot structure for which the inter-dot
tunneling is stronger than the tunneling to the leads is studied using the
numerical density matrix renormalization group method and analytic arguments.
When the dots are occupied by 1 or 3 electrons the usual Kondo peak is
obtained. For the case in which 2 electrons occupy the molecule a singlet is
formed. Nevertheless, the conductance in that case has a constant non-zero
value, and might even be equal to the maximum conductance of $2 e^2/h$ for
certain values of the molecule parameters. We show that this is the result of
the subtle interplay between the symmetric and anti-symmetric orbitals of the
molecule caused by interactions and interference.


  Remarkable recent experiments on the moir\'e structure formed by pentalayer
rhombohedral graphene aligned with a hexagonal Boron-Nitride substrate report
the discovery of a zero field fractional quantum hall effect. These
``(Fractional) Quantum Anomalous Hall" ((F)QAH) phases occur for one sign of a
perpendicular displacement field, and correspond, experimentally, to full or
partial filling of a valley polarized Chern-$1$ band. Such a band is absent in
the non-interacting band structure. Here we show that electron-electron
interactions play a crucial role, and present microscopic theoretical
calculations demonstrating the emergence of a nearly flat, isolated, Chern-$1$
band and FQAH phases in this system. We also study the four and six-layer
analogs and identify parameters where a nearly flat isolated Chern-$1$ band
emerges which may be suitable to host FQAH physics.


  In this work, we study the global existence of strong solutions and
large-time behavior of a two-phase fluid model in a bounded domain. The model
consists of the isothermal Euler equations and the isentropic compressible
Navier--Stokes equations, coupled via the drag force. It was derived in [13[
from a kinetic-fluid model describing the dynamics of particles subject to
local alignment force and Brownian noises immersed in a compressible viscous
fluid. For this system, we extend the local existence theory for strong
solutions developed in [13] to obtain the global existence of strong solutions
to the system. Moreover, we use the Lyapunov functional associated with the
system to get large-time behavior estimates for global classical solutions.


  We recall that, at both the intermittency transitions and at the Feigenbaum
attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics
rigorously obeys the Tsallis statistics. We account for the $q$-indices and the
generalized Lyapunov coefficients $\lambda_{q}$ that characterize the
universality classes of the pitchfork and tangent bifurcations. We identify the
Mori singularities in the Lyapunov spectrum at the edge of chaos with the
appearance of a special value for the entropic index $q$. The physical area of
the Tsallis statistics is further probed by considering the dynamics near
criticality and glass formation in thermal systems. In both cases a close
connection is made with states in unimodal maps with vanishing Lyapunov
coefficients.


  This paper explores the sensitivity of line profiles of H2D+, HCO+ and N2H+,
observed towards the center of L1544, to various kinematic and chemical
parameters. The total width of the H2D+ line can be matched by a static model
and by models invoking ambipolar diffusion and gravitational collapse. The
derived turbulent line width is b=0.15 km/s for the static case and <~ 0.05
km/s for the collapse case. However, line profiles of HC18O+ and N2H+ rule out
the static solution. The double-peaked H2D+ line shape requires either infall
speeds in the center that are much higher than predicted by ambipolar diffusion
models, or a shell-type distribution of H2D+, as is the case for HCO+ and N2H+.
At an offset of ~20 arcsec from the dust peak, the H2D+ abundance drops by a
factor of ~5.


  For G a finite non-Abelian group we write c(G) for the probability that two
randomly chosen elements commute and k(G) for the largest integer such that any
k(G)-colouring of G is guaranteed to contain a monochromatic quadruple
(x,y,xy,yx) with xy not equal to yx. We show that c(G) tends to 0 if and only
if k(G) tends to infinity.


  The evolution of deep learning and artificial intelligence has significantly
reshaped technological landscapes. However, their effective application in
crucial sectors such as medicine demands more than just superior performance,
but trustworthiness as well. While interpretability plays a pivotal role,
existing explainable AI (XAI) approaches often do not reveal {\em Clever Hans}
behavior where a model makes (ungeneralizable) correct predictions using
spurious correlations or biases in data. Likewise, current post-hoc XAI methods
are susceptible to generating unjustified counterfactual examples. In this
paper, we approach XAI with an innovative {\em model debugging} methodology
realized through Jacobian Saliency Map (JSM). To cast the problem into a
concrete context, we employ Alzheimer's disease (AD) diagnosis as the use case,
motivated by its significant impact on human lives and the formidable challenge
in its early detection, stemming from the intricate nature of its progression.
We introduce an interpretable, multimodal model for AD classification over its
multi-stage progression, incorporating JSM as a modality-agnostic tool that
provides insights into volumetric changes indicative of brain abnormalities.
Our extensive evaluation including ablation study manifests the efficacy of
using JSM for model debugging and interpretation, while significantly enhancing
model accuracy as well.


  We study universal chaotic dynamics of a large class of periodically driven
critical systems described by spatially inhomogeneous conformal field theories.
By employing an effective curved spacetime approach, we show that the onset of
quantum chaotic correlations, captured by the Lyapunov exponent of
out-of-time-order correlators (OTOCs), is set by the Hawking temperature of
emergent Floquet horizons. Furthermore, scrambling of quantum information is
shown to be strongly inhomogeneous, leading to transitions from chaotic to
non-chaotic regimes by tuning driving parameters. We finally use our framework
to propose a concrete protocol to simulate and measure OTOCs in quantum
simulators, by designing an efficient stroboscopic backward time evolution.


  Late asymptotic giant branch (AGB) and early post-AGB stars which are
progenitors of planetary nebulae lose mass at extremely high rate, in what is
termed a superwind. We show that the existence of this superwind during the
post-AGB phase cannot be explained with models where the stellar effective
temperature is the sole main physical parameter which determine the mass loss
rate. Instead, we argue that the envelope structure, in particular the entropy
and density gradients, should be among the main parameters which determine the
mass loss rate on the tip of the AGB and the early post-AGB evolutionary
phases. The entropy profile becomes steeper and the density profile becomes
shallower as the star becomes hotter on the early post-AGB phase, until the
star heats-up to about 8000 K. We do not propose a new mass loss mechanism, but
rather mention several mechanisms by which these profiles may influence the
mass loss rate within the popular mechanism for mass loss on the AGB, where
pulsations coupled with radiation pressure on dust cause the high mass loss
rate.


  Using the formal analysis made by Bohm in his book, {\em "Quantum theory"},
Dover Publications Inc. New York (1979), to calculate approximately the phase
time for a transmitted and the reflected wave packets through a potential
barrier, we calculate the phase time for a semiconductor system formed by
different mesoscopic layers. The transmitted and the reflected wave packets are
analyzed and the applicability of this procedure, based on the stationary phase
of a wave packet, is considered in different conditions. For the applicability
of the stationary phase method an expression is obtained in the case of the
transmitted wave depending only on the derivatives of the phase, up to third
order. This condition indicates whether the parameters of the system allow to
define the wave packet by its leading term. The case of a multiple barrier
systems is shown as an illustration of the results. This formalism includes the
use of the Transfer Matrix to describe the central stratum, whether it is
formed by one layer (the single barrier case), or two barriers and an inner
well (the DBRT system), but one can assume that this stratum can be comprise of
any number or any kind of semiconductor layers.


  Recurrent Neural Networks (RNNs) are renowned for their adeptness in modeling
temporal dependencies, a trait that has driven their widespread adoption for
sequential data processing. Nevertheless, vanilla RNNs are confronted with the
well-known issue of gradient vanishing and exploding, posing a significant
challenge for learning and establishing long-range dependencies. Additionally,
gated RNNs tend to be over-parameterized, resulting in poor network
generalization. To address these challenges, we propose a novel Delayed Memory
Unit (DMU) in this paper, wherein a delay line structure, coupled with delay
gates, is introduced to facilitate temporal interaction and temporal credit
assignment, so as to enhance the temporal modeling capabilities of vanilla
RNNs. Particularly, the DMU is designed to directly distribute the input
information to the optimal time instant in the future, rather than aggregating
and redistributing it over time through intricate network dynamics. Our
proposed DMU demonstrates superior temporal modeling capabilities across a
broad range of sequential modeling tasks, utilizing considerably fewer
parameters than other state-of-the-art gated RNN models in applications such as
speech recognition, radar gesture recognition, ECG waveform segmentation, and
permuted sequential image classification.


  Triangle fees are a novel fee structure for AMMs, in which marginal fees are
decreasing in a trade's size. That decline is proportional to the movement in
the AMM's implied price, i.e. for every basis point the trade moves the ratio
of assets, the marginal fee declines by a basis point. These fees create
incentives that protect against price staleness, while still allowing the AMM
to earn meaningful fee revenue. Triangle fees can strictly improve the Pareto
frontier of price accuracy versus losses generated by the status quo of
constant fee mechanisms.


  Behavioural cloning is an imitation learning technique that teaches an agent
how to behave via expert demonstrations. Recent approaches use self-supervision
of fully-observable unlabelled snapshots of the states to decode state pairs
into actions. However, the iterative learning scheme employed by these
techniques is prone to get trapped into bad local minima. Previous work uses
goal-aware strategies to solve this issue. However, this requires manual
intervention to verify whether an agent has reached its goal. We address this
limitation by incorporating a discriminator into the original framework,
offering two key advantages and directly solving a learning problem previous
work had. First, it disposes of the manual intervention requirement. Second, it
helps in learning by guiding function approximation based on the state
transition of the expert's trajectories. Third, the discriminator solves a
learning issue commonly present in the policy model, which is to sometimes
perform a `no action' within the environment until the agent finally halts.


  Mobile devices such as smartphones and autonomous vehicles increasingly rely
on deep neural networks (DNNs) to execute complex inference tasks such as image
classification and speech recognition, among others. However, continuously
executing the entire DNN on mobile devices can quickly deplete their battery.
Although task offloading to cloud/edge servers may decrease the mobile device's
computational burden, erratic patterns in channel quality, network, and edge
server load can lead to a significant delay in task execution. Recently,
approaches based on split computing (SC) have been proposed, where the DNN is
split into a head and a tail model, executed respectively on the mobile device
and on the edge server. Ultimately, this may reduce bandwidth usage as well as
energy consumption. Another approach, called early exiting (EE), trains models
to embed multiple "exits" earlier in the architecture, each providing
increasingly higher target accuracy. Therefore, the trade-off between accuracy
and delay can be tuned according to the current conditions or application
demands. In this paper, we provide a comprehensive survey of the state of the
art in SC and EE strategies by presenting a comparison of the most relevant
approaches. We conclude the paper by providing a set of compelling research
challenges.


  We present an elaborate version of the hadron resonance gas model with the
combined treatment of separate chemical freeze-outs for strange and non-strange
hadrons and with an additional $\gamma_{s}$ factor which accounts for the
remaining strange particle non-equilibration. Within suggested approach the
parameters of two chemical freeze-outs are connected by the conservation laws
of entropy, baryonic charge, third isospin projection and strangeness. The
developed model enables us to perform a high-quality fit of the hadron
multiplicity ratios measured at AGS, SPS and RHIC with $\chi^2/dof \simeq
0.93$. A special attention is paid to a successful description of the
Strangeness Horn. The well-known problem of selective suppression of $\bar
\Lambda $ and $\bar \Xi$ hyperons is also discussed. The main result is that
for all collision energies the $\gamma_{s}$ factor is about 1 within the error
bars, except for the center of mass collision energy 7.6 GeV at which we find
about 20\% enhancement of strangeness. Also we confirm an existence of strong
jumps in pressure, temperature and effective number of degrees of freedom at
the stage of strange particle chemical freeze-out, when the center of mass
collision energy changes from 4.3 to 4.9 GeV. We argue that these
irregularities may signal about the quark-hadron phase transition.


  We study the physical origin of the low-redshift Lyman alpha forest in
hydrodynamic simulations of four CDM cosmologies. Our main conclusions are
insensitive to the cosmological model but depend on our assumption that the UV
background declines at low redshift. We find that the expansion of the universe
drives rapid evolution of dN/dz (the number of absorbers per unit z) at z >
1.7, but that at lower redshift the fading of the UV background counters the
influence of expansion, leading to slow evolution. At every redshift, weaker
lines come primarily from moderate fluctuations of the diffuse, unshocked IGM,
and stronger lines originate in shocked or radiatively cooled gas of higher
overdensity. However, the neutral hydrogen column density associated with
structures of fixed overdensity drops as the universe expands, so an absorber
at z = 0 is dynamically analogous to an absorber with neutral hydrogen column
density 10 to 50 times higher at z = 2-3. We find no clear distinction between
lines arising in "galaxy halos" and lines arising in larger scale structures;
however, galaxies tend to lie near the dense regions of the IGM that produce
strong Lyman alpha lines. The simulations provide a unified physical picture
that accounts for the most distinctive observed properties of the low redshift
Lyman alpha forest: (1) a sharp transition in the evolution of dN/dz at z ~
1.7, (2) stronger evolution for absorbers of higher equivalent width, (3) a
correlation of increasing Lyman alpha equivalent width with decreasing galaxy
impact parameter, and (4) a tendency for stronger lines to arise in close
proximity to galaxies while weaker lines trace more diffuse large scale
structure. (Abridged)


  With the scaling of technology and higher requirements on performance and
functionality, power dissipation is becoming one of the major design
considerations in the development of network processors. In this paper, we use
an assertion-based methodology for system-level power/performance analysis to
study two dynamic voltage scaling (DVS) techniques, traffic-based DVS and
execution-based DVS, in a network processor model. Using the automatically
generated distribution analyzers, we analyze the power and performance
distributions and study their trade-offs for the two DVS policies with
different parameter settings such as threshold values and window sizes. We
discuss the optimal configurations of the two DVS policies under different
design requirements. By a set of experiments, we show that the assertion-based
trace analysis methodology is an efficient tool that can help a designer easily
compare and study optimal architectural configurations in a large design space.


  Typestate systems ensure many desirable properties of imperative programs,
including initialization of object fields and correct use of stateful library
interfaces. Abstract sets with cardinality constraints naturally generalize
typestate properties: relationships between the typestates of objects can be
expressed as subset and disjointness relations on sets, and elements of sets
can be represented as sets of cardinality one. Motivated by these applications,
this paper presents new algorithms and new complexity results for constraints
on sets and their cardinalities. We study several classes of constraints and
demonstrate a trade-off between their expressive power and their complexity.
  Our first result concerns a quantifier-free fragment of Boolean Algebra with
Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for
reducing the satisfiability of sets with symbolic cardinalities to constraints
on constant cardinalities, and give a polynomial-space algorithm for the
resulting problem.
  In a quest for more efficient fragments, we identify several subclasses of
sets with cardinality constraints whose satisfiability is NP-hard. Finally, we
identify a class of constraints that has polynomial-time satisfiability and
entailment problems and can serve as a foundation for efficient program
analysis.


  Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022,
Lott 2019) that three-dimensional complete manifolds with non-negatively
pinched Ricci curvature must be flat or compact, thus confirming a conjecture
of Hamilton. In this paper we generalise our work on the existence of Ricci
flows from non-compact pinched three-manifolds in order to prove a
higher-dimensional analogue. We construct a solution to Ricci flow, for all
time, starting with an arbitrary complete non-compact manifold that is PIC1
pinched. As an application we prove that any complete manifold of non-negative
complex sectional curvature that is PIC1 pinched must be flat or compact.


  Modulation instability, rogue wave and spectral analysis are investigated for
the nonlinear Schrodinger equation with the higher-order terms. The modulation
instability distribution characteristics from the sixth-order to the
eighth-order nonlinear Schrodinger equations are studied. Higher-order
dispersion terms are closely related to the distribution of modulation
stability regime, and n-order dispersion term corresponds to $n-2$ modulation
stability curves in the modulation instability band. Based on the generalized
Darboux transformation method, the higher-order rational solutions are
constructed. Then the compact algebraic expression of the Nth-order rogue wave
is given. Dynamic phenomena of first- to third-order rogue waves are
illustrated, which exhibit meaningful structures. Two arbitrary parameters play
important roles in the rogue wave solution. One can control deflection of crest
of rogue wave and its width, while the other can cause the change of width and
amplitude of rogue wave. When it comes to the third-order rogue wave, three
typical nonlinear wave constructions, namely fundamental, circular and
triangular are displayed and discussed. Through the spectral analysis on
first-order rogue wave, when these parameters satisfy certain conditions, it
occurs a transition between W-shaped soliton and rogue wave.


  The quickly increasing data traffic and the user demand for a full coverage
of mobile services anywhere and anytime are leading mobile networking into a
future of small cell networks. However, due to the high-density and randomness
of small cell networks, there are several technical challenges. In this paper,
we investigate two critical issues: \emph{best signal quality} and
\emph{mobility management}. Under the assumptions that base stations are
uniformly distributed in a ring shaped region and that shadowings are
lognormal, independent and identically distributed, we prove that when the
number of sites in the ring tends to infinity, then (i) the maximum signal
strength received at the center of the ring tends in distribution to a Gumbel
distribution when properly renormalized, and (ii) it is asymptotically
independent of the interference. Using these properties, we derive the
distribution of the best signal quality. Furthermore, an optimized random cell
scanning scheme is proposed, based on the evaluation of the optimal number of
sites to be scanned for maximizing the user data throughput.


  We present stellar population age and metallicity trends for a sample of 59
S0 galaxies based on optical SDSS and NIR J & H photometry. When combined with
optical g and r passband imaging data from the SDSS archive and stellar
population models, we obtain radial age and metallicity trends out to at least
5 effective radii for most of the galaxies in our sample. The sample covers a
range in stellar mass and light concentration. We find an average central
light-weighted age of ~ 4 Gyr and central metallicity [Z/H] ~ 0.2 dex. Almost
all galaxies show a negative metallicity gradient from the center out, with an
average value of Delta[Z/H]/Delta(log(r/Re)) = -0.6. An age increase, decrease,
and minimal change with radius is observed for 58%, 19%, and 23%, respectively,
for a mean age gradient of Delta(age)/Delta(log(r/Re)) = 2.3 Gyr dex^{-1}. For
14 out of 59 galaxies, the light-weighted age of the outer region is greater
than 10 Gyr. We find that galaxies with both lower mass and lower concentration
have younger light-weighted ages and lower light-weighted metallicities. This
mass-metallicity relation extends into the outer regions of our S0 galaxies.
Our results are consistent with the formation of S0 galaxies through the
transformation of spiral galaxy disks. Determining the structural component
that makes up the outer region of galaxies with old outksirts is a necessary
step to understand the formation history of S0 galaxies.


  We present a Bayesian approach to machine learning with probabilistic
programs. In our approach, training on available data is implemented as
inference on a hierarchical model. The posterior distribution of model
parameters is then used to \textit{stochastically condition} a complementary
model, such that inference on new data yields the same posterior distribution
of latent parameters corresponding to the new data as inference on a
hierachical model on the combination of both previously available and new data,
at a lower computation cost. We frame the approach as a design pattern of
probabilistic programming referred to herein as `stump and fungus', and
evaluate realization of the pattern on case studies.


  We prove that for regular Poisson manifolds, the zeroth homology group is
isomorphic to the top foliated cohomology group and we give some applications.
In particular, we show that for regular unimodular Poisson manifolds top
Poisson and foliated cohomology groups are isomorphic. Inspired by the
symplectic setting, we define what is a perfect Poisson manifold. We use these
Poisson homology computations to provide families of perfect Poisson manifolds.


  Blue straggler stars (BSSs) are formed through mass transfer or mergers in
binaries. The recent detections of white dwarf (WD) companions to BSSs in M67
suggested a mass transfer pathway of formation. In search of a close companion
to five BSSs in M67 that are known to be spectroscopic binaries, we study the
light curves from K2 and TESS data. We use PHOEBE to analyse the light curves
and estimate the properties of the companions. We detect variability in WOCS
1007, and the light curve is dominated by ellipsoidal variation. Using the
light curve and radial velocity measurements, we estimate its orbital period to
be 4.212$\pm$0.041 d and $e$ = 0.206$\pm$002. The mass of the companion is
estimated to be 0.22$\pm$0.05 M$_{\odot}$ with a radius of 0.078$\pm$0.027
R$_{\odot}$, confirming it to be a low mass WD with T$_{\rm eff}$ =
14300$\pm$1100 K. The estimated mass of the BSS, 1.95$\pm$0.26 M$_{\odot}$, is
similar to that estimated from isochrones. The BSS in WOCS 1007 shows $\delta$
Scuti pulsations, although it is slightly deformed and likely to be formed
through an efficient mass transfer. Though we detect a light curve for WOCS
4003 showing grazing eclipse with ellipsoidal variation, the estimated
parameters are inconclusive. Apart from the 0.44 d period, we found smaller
eclipses with a period of 1.1 d, suggesting a compact triple system. In the
case of WOCS 4003, WOCS 5005, and WOCS 1025, no eclipses or pulsations are
detected, confirming the absence of any short-period inner binary with high
inclination in these BSSs.


  We consider multi-antenna base stations using orthogonal frequency-division
multiple access (OFDMA) and space division multiple access (SDMA) techniques to
serve single antenna users, where some of those users have minimum rate
requirements and must be served in the current time slot (real time users),
while others do not have strict timing constraints (non real time users) and
are served on a best effort basis. The resource allocation problem is to find
the user assignment to subcarriers and the transmit beamforming vectors that
maximize a linear utility function of the user rates subject to power and
minimum rate constraints. The exact optimal solution to this problem can not be
reasonably obtained for practical parameters values of the communication
system. We thus derive a dual problem formulation whose optimal solution
provides an upper bound to all feasible solutions and can be used to benchmark
the performance of any heuristic method used to solve this problem. We also
derive from this dual optimal solution a primal-feasible dual-based method to
solve the problem and we compare its performance and computation time against a
standard weight adjustment method. We find that our method follows the dual
optimal bound more closely than the weight adjustment method. This off-line
algorithm can serve as the basis to develop more efficient heuristic methods.


  Bianchi type I and type IX ('Mixmaster') geometries are investigated within
the framework of Ho\v{r}ava-Witten cosmology. We consider the models for which
the fifth coordinate is a $S^1/Z_2$ orbifold while the four coordinates are
such that the 3-space is homogeneous and has geometry of Bianchi type I or IX
while the rest six dimensions have already been compactified on a Calabi-Yau
space. In particular, we study Kasner-type solutions of the Bianchi I field
equations and discuss Kasner asymptotics of Bianchi IX field equations. We are
able to recover the isotropic 3-space solutions found by Lukas {\it et al}.
Finally, we discuss if such Bianchi IX configuration can result in chaotic
behaviour of these Ho\v{r}ava-Witten cosmologies.