  Device independent protocols rely on the violation of Bell inequalities to
certify properties of the resources available. The violation of the
inequalities are meaningless without a few well-known assumptions. One of these
is measurement independence, the property that the source of the states
measured in an inequality is uncorrelated from the measurements selected. Since
this assumption cannot be confirmed, we consider the consequences of relaxing
it and find that the definition chosen is critically important to the observed
behavior. Considering a definition that is a bound on the min-entropy of the
measurement settings, we find lower bounds on the min-entropy of the seed used
to choose the inputs required to deduce any quantum or non-local behavior from
a Bell inequality violation. These bounds are significantly more restrictive
than the ones obtained by endowing the seed with the further structure of a
Santha-Vazirani source. We also outline a procedure for finding tight bounds
and study the set of probabilities that can result from relaxing measurement
dependence.


  Machine learning models produce state-of-the-art results in many MRI images
segmentation. However, most of these models are trained on very large datasets
which come from experts manual labeling. This labeling process is very time
consuming and costs experts work. Therefore finding a way to reduce this cost
is on high demand. In this paper, we propose a segmentation method which
exploits MRI images sequential structure to nearly drop out this labeling task.
Only the first slice needs to be manually labeled to train the model which then
infers the next slice's segmentation. Inference result is another datum used to
train the model again. The updated model then infers the third slice and the
same process is carried out until the last slice. The proposed model is an
combination of two Random Forest algorithms: the classical one and a recent one
namely Mondrian Forests. We applied our method on human left ventricle
segmentation and results are very promising. This method can also be used to
generate labels.


  Measuring dependence between two events, or equivalently between two binary
random variables, amounts to expressing the dependence structure inherent in a
$2\times 2$ contingency table in a real number between $-1$ and $1$. Countless
such dependence measures exist, but there is little theoretical guidance on how
they compare and on their advantages and shortcomings. Thus, practitioners
might be overwhelmed by the problem of choosing a suitable measure. We provide
a set of natural desirable properties that a proper dependence measure should
fulfill. We show that Yule's Q and the little-known Cole coefficient are
proper, while the most widely-used measures, the phi coefficient and all
contingency coefficients, are improper. They have a severe attainability
problem, that is, even under perfect dependence they can be very far away from
$-1$ and $1$, and often differ substantially from the proper measures in that
they understate strength of dependence. The structural reason is that these are
measures for equality of events rather than of dependence. We derive the (in
some instances non-standard) limiting distributions of the measures and
illustrate how asymptotically valid confidence intervals can be constructed. In
a case study on drug consumption we demonstrate how misleading conclusions may
arise from the use of improper dependence measures.


  The U.S. Air Force currently is in the process of developing an Airborne
Network (AN) to provide support to its combat aircrafts on a mission. The
reliability needed for continuous operation of an AN is difficult to achieve
through completely infrastructure-less mobile ad hoc networks. In this paper we
first propose an architecture for an AN where airborne networking platforms
(ANPs - aircrafts, UAVs and satellites) form the backbone of the AN. In this
architecture, the ANPs can be viewed as mobile base stations and the combat
aircrafts on a mission as mobile clients. The combat aircrafts on a mission
move through a space called air corridor. The goal of the AN design is to form
a backbone network with the ANPs with two properties: (i) the backbone network
remains connected at all times, even though the topology of the network changes
with the movement of the ANPs, and (ii) the entire 3D space of the air corridor
is under radio coverage at all times by the continuously moving ANPs.
  In addition to proposing an architecture for an AN, the contributions of the
paper include, development of an algorithm that finds the velocity and
transmission range of the ANPs so that the dynamically changing backbone
network remains connected at all times, development of a routing algorithm that
ensures a connection between the source-destination node pair with the fewest
number of path switching, given the dimensions of the air corridor and the
radius of the coverage sphere associated with an ANP, development of an
algorithm that finds the fewest number of ANPs required to provide complete
coverage of the air corridor at all times, development of an algorithm that
provides connected-coverage to the air corridor at all times, and development
of a visualization tool that depicts the movement patterns of the ANPs and the
resulting dynamic graph and the coverage volume of the backbone network.


  The direct manipulation of spins via light may provide a path toward
ultrafast energy-efficient devices. However, distinguishing the microscopic
processes that can occur during ultrafast laser excitation in magnetic alloys
is challenging. Here, we study the Heusler compound Co2MnGa, a material that
exhibits very strong light-induced spin transfers across the entire M-edge. By
combining the element-specificity of extreme ultraviolet high harmonic probes
with time-dependent density functional theory, we disentangle the competition
between three ultrafast light-induced processes that occur in Co2MnGa:
same-site Co-Co spin transfer, intersite Co-Mn spin transfer, and ultrafast
spin-flips mediated by spin-orbit coupling. By measuring the dynamic magnetic
asymmetry across the entire M-edges of the two magnetic sublattices involved,
we uncover the relative dominance of these processes at different probe energy
regions and times during the laser pulse. Our combined approach enables a
comprehensive microscopic interpretation of laser-induced magnetization
dynamics on timescales shorter than 100 fs.


  In this paper we study the motion of three linked ellipses moving through a
viscous fluid in two dimensions. The angles between the ellipses change with
time in a specified manner (the gait) and the resulting time varying
configuration is similar to the appearance of a swimming leech. We simulate the
motion using the particle method Smoothed Particle Hydrodynamics (SPH) which we
test by convergence studies and by comparison with the inviscid results of
Kanso et al. (2005) and the viscous results of Eldredge (2006, 2007, 2008). We
determine how the average speed and power output depends on the amplitude and
oscillation frequency of the gait. We find that the results fit simple scaling
rules which can related to the analytical results of G. I. Taylor for the
swimming of long narrow animals (1952). We apply our results to estimate the
speed of a swimming leech with reasonable accuracy, and we determine the
minimum power required to propel the bodies at a specified average speed.


  $\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}}
\newcommand{\SetX}{\mathsf{X}} \newcommand{\eps}{\varepsilon}
\newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}}
\newcommand{\IntRange}[1]{[ #1 ]} \newcommand{\Space}{\ovebarline{\mathsf{m}}}
\newcommand{\pth}[2][\!]{#1\left({#2}\right)} \newcommand{\Arr}{{\cal A}}$
  Let $H$ be a set of $n$ planes in three dimensions, and let $r \leq n$ be a
parameter. We give a simple alternative proof of the existence of a
$(1/r)$-cutting of the first $n/r$ levels of $\Arr(H)$, which consists of
$O(r)$ semi-unbounded vertical triangular prisms. The same construction yields
an approximation of the $(n/r)$-level by a terrain consisting of $O(r/\eps^3)$
triangular faces, which lies entirely between the levels $(1\pm\eps)n/r$. The
proof does not use sampling, and exploits techniques based on planar separators
and various structural properties of levels in three-dimensional arrangements
and of planar maps. The proof is constructive, and leads to a simple randomized
algorithm, with expected near-linear running time. An application of this
technique allows us to mimic Matousek's construction of cuttings in the plane,
to obtain a similar construction of "layered" $(1/r)$-cutting of the entire
arrangement $\Arr(H)$, of optimal size $O(r^3)$. Another application is a
simplified optimal approximate range counting algorithm in three dimensions,
competing with that of Afshani and Chan.


  We match the seesaw model for generating neutrino masses onto the Standard
Model Effective Field Theory (SMEFT). We perform this matching at tree level up
to dimension seven in the operator expansion. We explain how some of the
perturbations of the neutrino mass matrix due to operators of mass dimension
greater than five are tied to integrating out the heavy Majorana mass
eigenstates in sequence. We demonstrate that the low energy limit of seesaw
models are well described by the SMEFT, particularly when constructed using a
flavour space expansion. Flavour space expansions of seesaw models are of
interest as the coupling of the heavy states to the Standard Model, that are
integrated out to generate neutrino masses, are through flavour space vectors
$\in \mathbb{C}^3$. We point out that neutrino phenomenology can be
systematically developed as a perturbation around the unknown eigenvectors
diagonalizing the charged lepton mass matrix using the fact that these
eigenvectors also form a basis of $\mathbb{C}^3$. This point holds in seesaw
models and can also be applied to other models of neutrino mass generation to
develop systematic expansions. We develop the algebra for this flavour space
and discuss some phenomenology to illustrate this approach.


  We observed spin injection into silicon through Fe/MgO tunnel barrier by
using non-local magnetoresistance measurement technique. Fe/MgO tunnel barrier
contacts with a lateral spin valve structure were fabricated on phosphorous
doped silicon-on-insulator substrate. Spin injection signals in the non-local
scheme were observed up to 120K, which is the highest value where band
transferred spins in Si have ever been reported, and spin diffusion length was
estimated to be about 2.25um at 8K. Temperature dependence and injection
current dependence of the non-local voltage were also investigated. It is
clarified that MgO tunnel barrier is effective for the spin injection into
silicon.


  A scalar field is a favorite candidate for the particle responsible for dark
energy. However, few theoretical means exist that can simultaneously explain
the observed acceleration of the Universe and evade tests of gravity. The
chameleon mechanism, whereby the properties of a particle depend upon the local
environment, is one possible avenue. We present the results of the Chameleon
Afterglow Search (CHASE) experiment, a laboratory probe for chameleon dark
energy. CHASE marks a significant improvement other searches for chameleons
both in terms of its sensitivity to the photon/chameleon coupling as well as
its sensitivity to the classes of chameleon dark energy models and standard
power-law models. Since chameleon dark energy is virtually indistinguishable
from a cosmological constant, CHASE tests dark energy models in a manner not
accessible to astronomical surveys.


  It is common practice to apply gradient-based optimization algorithms to
numerically solve large-scale ODE constrained optimal control problems.
Gradients of the objective function are most efficiently computed by
approximate adjoint variables. High accuracy with moderate computing time can
be achieved by such time integration methods that satisfy a sufficiently large
number of adjoint order conditions and supply gradients with higher orders of
consistency. In this paper, we upgrade our former implicit two-step Peer
triplets constructed in [Algorithms, 15:310, 2022] to meet those new
requirements. Since Peer methods use several stages of the same high stage
order, a decisive advantage is their lack of order reduction as for
semi-discretized PDE problems with boundary control. Additional order
conditions for the control and certain positivity requirements now intensify
the demands on the Peer triplet. We discuss the construction of $4$-stage
methods with order pairs $(3,3)$ and $(4,3)$ in detail and provide three Peer
triplets of practical interest. We prove convergence of order $s-1$, at least,
for $s$-stage methods if state, adjoint and control satisfy the corresponding
order conditions. Numerical tests show the expected order of convergence for
the new Peer triplets.


  This work presents novel extensions for combining two frameworks for
quantifying both aleatoric (i.e., irreducible) and epistemic (i.e., reducible)
sources of uncertainties in the modeling of engineered systems. The
data-consistent (DC) framework poses an inverse problem and solution for
quantifying aleatoric uncertainties in terms of pullback and push-forward
measures for a given Quantity of Interest (QoI) map. Unfortunately, a
pre-specified QoI map is not always available a priori to the collection of
data associated with system outputs. The data themselves are often polluted
with measurement errors (i.e., epistemic uncertainties), which complicates the
process of specifying a useful QoI. The Learning Uncertain Quantities (LUQ)
framework defines a formal three-step machine-learning enabled process for
transforming noisy datasets into samples of a learned QoI map to enable
DC-based inversion. We develop a robust filtering step in LUQ that can learn
the most useful quantitative information present in spatio-temporal datasets.
The learned QoI map transforms simulated and observed datasets into
distributions to perform DC-based inversion. We also develop a DC-based
inversion scheme that iterates over time as new spatial datasets are obtained
and utilizes quantitative diagnostics to identify both the quality and impact
of inversion at each iteration. Reproducing Kernel Hilbert Space theory is
leveraged to mathematically analyze the learned QoI map and develop a
quantitative sufficiency test for evaluating the filtered data. An illustrative
example is utilized throughout while the final two examples involve the
manufacturing of shells of revolution to demonstrate various aspects of the
presented frameworks.


  Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation
in Euclidean space are considered. It is argued that the complete set of Dirac
matrices is the most appropriate basis to define the partial amplitudes and to
solve numerically the resulting system of equations with realistic interaction
kernels. Other representations can be obtained by performing proper unitary
transformations. A generalization of the iteration method for finding the
energy spectrum of the BS equation is discussed and examples of concrete
calculations are presented. Comparison of relativistic calculations with
available experimental data and with corresponding non relativistic results
together with an analysis of the role of Lorentz boost effects and relativistic
corrections are presented.
  A novel method related to the use of hyperspherical harmonics is considered
for a representation of the vertex functions suitable for numerical
calculations.


  The main goal of concept-oriented programming (COP) is describing how objects
are represented and accessed. It makes references (object locations)
first-class elements of the program responsible for many important functions
which are difficult to model via objects. COP rethinks and generalizes such
primary notions of object-orientation as class and inheritance by introducing a
novel construct, concept, and a new relation, inclusion. An advantage is that
using only a few basic notions we are able to describe many general patterns of
thoughts currently belonging to different programming paradigms: modeling
object hierarchies (prototype-based program-ming), precedence of parent methods
over child methods (inner methods in Beta), modularizing cross-cutting
con-cerns (aspect-oriented programming), value-orientation (functional
programming). Since COP remains backward compatible with object-oriented
programming, it can be viewed as a perspective direction for developing a
simple and natural unified programming model.


  Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to
vertices. We present the first efficient algebraic algorithm to find an
f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with
integral edge weights of maximum absolute value W we find a maximum weight
f-factor in time \tilde{O}(Wf(V)^{\omega}). (The algorithms are randomized,
correct with high probability and Las Vegas; the time bound is worst-case.) We
also present three specializations of these algorithms: For maximum weight
perfect f-matching the algorithm is considerably simpler (and almost identical
to its special case of ordinary weighted matching). For the single-source
shortest-path problem in undirected graphs with conservative edge weights, we
present a generalization of the shortest-path tree, and we compute it in
\tilde{O(Wn^{\omega}) time. For bipartite graphs, we improve the known
complexity bounds for vertex capacitated max-flow and min-cost max-flow on a
subclass of graphs.


  The nature of pulsar-like compact stars is essentially a central question of
the fundamental strong interaction (explained in quantum chromo-dynamics) at
low energy scale, the solution of which still remains a challenge though
tremendous efforts have been tried. This kind of compact objects could actually
be strange quark stars if strange quark matter in bulk may constitute the true
ground state of the strong-interaction matter rather than Fe^56 (the so-called
Witten's conjecture). From astrophysical points of view, however, it is
proposed that strange cluster matter could be absolutely stable and thus those
compact stars could be strange cluster stars in fact. This proposal could be
regarded as a general Witten's conjecture: strange matter in bulk could be
absolutely stable, in which quarks are either free (for strange quark matter)
or localized (for strange cluster matter). Strange cluster with
three-light-flavor symmetry is renamed strangeon, being coined by combining
"strange nucleon" for the sake of simplicity. A strangeon star can then be
thought as a 3-flavored gigantic nucleus, and strangeons are its constituent as
an analogy of nucleons which are the constituent of a normal (micro) nucleus.
The observational consequences of strangeon stars show that different
manifestations of pulsar-like compact stars could be understood in the regime
of strangeon stars, and we are expecting more evidence for strangeon star by
advanced facilities (e.g., FAST, SKA, and eXTP).


  In this paper, we consider a coordination problem for a class of
heterogeneous nonlinear multi-agent systems with a prescribed input-output
behavior which was represented by another input-driven system. In contrast to
most existing multi-agent coordination results with an autonomous (virtual)
leader, this formulation takes possible control inputs of the leader into
consideration. First, the coordination was achieved by utilizing a group of
distributed observers based on conventional assumptions of model matching
problem. Then, a fully distributed adaptive extension was proposed without
using the input of this input-output behavior. An example was given to verify
their effectiveness.


  Intrinsic bugs are bugs for which a bug introducing change can be identified
in the version control system of a software. In contrast, extrinsic bugs are
caused by external changes to a software, such as errors in external APIs;
thereby they do not have an explicit bug introducing change in the version
control system. Although most previous research literature has assumed that all
bugs are of intrinsic nature, in a previous study, we show that not all bugs
are intrinsic. This paper shows an example of how considering extrinsic bugs
can affect software engineering research. Specifically, we study the impact of
extrinsic bugs in Just In Time bug prediction by partially replicating a recent
study by McIntosh and Kamei on JIT models. These models are trained using
properties of earlier bug-introducing changes. Since extrinsic bugs do not have
bug introducing changes in the version control system, we manually curate
McIntosh and Kamei's dataset to distinguish between intrinsic and extrinsic
bugs. Then, we address their original research questions, this time removing
extrinsic bugs, to study whether bug-introducing changes are a moving target in
Just-In-Time bug prediction. Finally, we study whether characteristics of
intrinsic and extrinsic bugs are different. Our results show that intrinsic and
extrinsic bugs are of different nature. When removing extrinsic bugs the
performance is different up to 16 % Area Under the Curve points. This indicates
that our JIT models obtain a more accurate representation of the real world. We
conclude that extrinsic bugs negatively impact Just-In-Time models.
Furthermore, we offer evidence that extrinsic bugs should be further
investigated, as they can significantly impact how software engineers
understand bugs.


  Recent observation of $\sim$ 10 times higher critical temperature in FeSe
monolayer compared with its bulk phase has drawn a great deal of attention
because the electronic structure in the monolayer phase appears to be different
than bulk FeSe. Using a combination of density functional theory and dynamical
mean field theory, we find electronic correlations have important effects on
the predicted atomic-scale geometry and the electronic structure of the
monolayer FeSe on SrTiO$_3$. The electronic correlations are dominantly
controlled by the Se-Fe-Se angle either in the bulk phase or the monolayer
phase. But the angle sensitivity increases and the orbital differentiation
decreases in the monolayer phase compared to the bulk phase. The correlations
are more dependent on Hund's J than Hubbard U. The observed orbital selective
incoherence to coherence crossover with temperature confirms the Hund's
metallic nature of the monolayer FeSe. We also find electron doping by oxygen
vacancies in SrTiO$_3$ increases the correlation strength, especially in the
$d_{xy}$ orbital by reducing the Se-Fe-Se angle.


  We propose a new method for exemplar-free class incremental training of ViTs.
The main challenge of exemplar-free continual learning is maintaining
plasticity of the learner without causing catastrophic forgetting of previously
learned tasks. This is often achieved via exemplar replay which can help
recalibrate previous task classifiers to the feature drift which occurs when
learning new tasks. Exemplar replay, however, comes at the cost of retaining
samples from previous tasks which for many applications may not be possible. To
address the problem of continual ViT training, we first propose gated
class-attention to minimize the drift in the final ViT transformer block. This
mask-based gating is applied to class-attention mechanism of the last
transformer block and strongly regulates the weights crucial for previous
tasks. Importantly, gated class-attention does not require the task-ID during
inference, which distinguishes it from other parameter isolation methods.
Secondly, we propose a new method of feature drift compensation that
accommodates feature drift in the backbone when learning new tasks. The
combination of gated class-attention and cascaded feature drift compensation
allows for plasticity towards new tasks while limiting forgetting of previous
ones. Extensive experiments performed on CIFAR-100, Tiny-ImageNet and
ImageNet100 demonstrate that our exemplar-free method obtains competitive
results when compared to rehearsal based ViT methods.


  Based on the SED, Herbig stars have been categorized into two observational
groups, reflecting their overall disk structure: group I members have disks
with a higher degree of flaring than their group II counterparts. We
investigate the 5-35 um Spitzer IRS spectra of a sample of 13 group I sources
and 20 group II sources. We focus on the continuum emission to study the
underlying disk geometry. We have determined the [30/13.5] and [13.5/7]
continuum flux ratios. The 7-um flux excess with respect to the stellar
photosphere is measured, as a marker for the strength of the near-IR emission
produced by the inner disk. We have compared our data to self-consistent
passive-disk model spectra, for which the same quantities were derived. We
confirm the literature result that the difference in continuum emission between
group I and II sources can largely be explained by a different amount of small
dust grains. However, we report a strong correlation between the [30/13.5] and
[13.5/7] flux ratios for Meeus group II sources. Moreover, the [30/13.5] flux
ratio decreases with increasing 7-um excess for all targets in the sample. To
explain these correlations with the models, we need to introduce an artificial
scaling factor for the inner disk height. In roughly 50% of the Herbig Ae/Be
stars in our sample, the inner disk must be inflated by a factor 2 to 3 beyond
what hydrostatic calculations predict. The total disk mass in small dust grains
determines the degree of flaring. We conclude, however, that for any given disk
mass in small dust grains, the shadowing of the outer (tens of AU) disk is
determined by the scale height of the inner disk (1 AU). The inner disk
partially obscures the outer disk, reducing the disk surface temperature. Here,
for the first time, we prove these effects observationally.


  We introduce a wide category of superspaces, called locally finitely
generated, which properly includes supermanifolds but enjoys much stronger
permanence properties, as are prompted by applications. Namely, it is closed
under taking finite fibre products (i.e. is finitely complete) and thickenings
by spectra of Weil superalgebras. Nevertheless, in this category, morphisms
with values in a supermanifold are still given in terms of coordinates. This
framework gives a natural notion of relative supermanifolds over a locally
finitely generated base. Moreover, the existence of inner homs, whose source is
the spectrum of a Weil superalgebra, is established; they are generalisations
of the Weil functors defined for smooth manifolds.


  Solving Fluid-Structure Interaction (FSI) problems using traditional methods
is a big challenge in the field of numerical simulation. As a powerful
multi-physical field coupled library, preCICE has a bright application prospect
for solving FSI, which supports many open/closed source software and commercial
CFD solvers to solve FSI problems in the form of a black box. However, this
library currently only supports mesh-based coupling schemes. This paper
proposes a critical grid (mesh) as an intermediate medium for the particle
method to connect a bidirectional coupling tool named preCICE. The particle and
critical mesh are used to interpolate the displacement and force so that the
pure Lagrangian Smoothed Particle Hydrodynamic (SPH) method can also solve the
FSI problem. This method is called the particle mesh coupling (PMC) method,
which theoretically solves the mesh mismatch problem based on the particle
method to connect preCICE. In addition, we conduct experiments to verify the
performance of the PMC method, in which the fluid and the structure is
discretized by SPH and the Finite Element Method (FEM), respectively. The
results show that the PMC method given in this paper is effective for solving
FSI problems. Finally, our source code for the SPH fluid adapter is open-source
and available on GitHub for further developing preCICE compatibility with more
meshless methods.


  In response to privacy concerns about collecting and using personal data, the
online advertising industry has been developing privacy-enhancing technologies
(PETs), e.g., under Google's Privacy Sandbox initiative. In this research, we
use the dual-privacy framework, which postulates that consumers have intrinsic
and instrumental preferences for privacy, to understand consumers' perceived
privacy violations (PPVs) for current and proposed online advertising
practices. The key idea is that different practices differ in whether
individual data leaves the consumer's machine or not and in how they track and
target consumers; these affect, respectively, the intrinsic and instrumental
components of privacy preferences differently, leading to different PPVs for
different practices. We conducted online studies focused on consumers in the
United States to elicit PPVs for various advertising practices. Our findings
confirm the intuition that tracking and targeting consumers under the industry
status quo of behavioral targeting leads to high PPV. New technologies or
proposals that ensure that data are kept on the consumer's machine lower PPV
relative to behavioral targeting but, importantly, this decrease is small.
Furthermore, group-level targeting does not differ significantly from
individual-level targeting in reducing PPV. Under contextual targeting, where
there is no tracking, PPV is significantly reduced. Interestingly, with respect
to PPV, consumers are indifferent between seeing untargeted ads and no ads when
they are not being tracked. We find that consumer perceptions of privacy
violations under different tracking and targeting practices may differ from
what technical definitions suggest. Therefore, rather than relying solely on
technical perspectives, a consumer-centric approach to privacy is needed, based
on, for instance, the dual-privacy framework.


  The longer-lived excited nuclear states, referred as nuclear isomers, exist
due to the hindered decays owing to their peculiar nucleonic structural
surroundings. Some of these conditions, being exceptionally rare and limited to
achieve, elevate certain isomers to the status of extreme and unusual isomers
among their kin. For example, the $E5$ coupling of single-particle orbitals is
rare and so are $E5$ decaying isomers. This review delves into some of such
remarkable isomers scattered across the nuclear landscape while highlighting
the possibilities to find more of them. Unique properties of some of them,
harbor the potential for transformative applications in medicine and energy. An
exciting example is that of the lowest energy isomer known so far in
$^{229}$Th, which may help realize the dream of an ultra-precise nuclear clock
in the coming decade. These isomers also offer an insight into the extremes of
nuclear structure associated with them, which leads to their unusual status in
energy, half-life, spin etc. The review attempts to highlight isomers with
high-multipolarities, high-spins, high-energies, longest half-lives, extremely
low energy, etc. A lack of theoretical understanding of the decay rates,
half-lives and moments of these isomers is also pointed out.


  Retrieving images transmitted through multi-mode fibers is of growing
interest, thanks to their ability to confine and transport light efficiently in
a compact system. Here, we demonstrate machine-learning-based decoding of
large-scale digital images (pages), maximizing page capacity for optical
storage applications. Using a millimeter-sized square cross-section waveguide,
we image an 8-bit spatial light modulator, presenting data as a matrix of
symbols. Normally, decoders will incur a prohibitive O(n^2) computational
scaling to decode n symbols in spatially scrambled data. However, by combining
a digital twin of the setup with a U-Net, we can retrieve up to 66 kB using
efficient convolutional operations only. We compare trainable ray-tracing-based
with eigenmode-based twins and show the former to be superior thanks to its
ability to overcome the simulation-to-experiment gap by adjusting to optical
imperfections. We train the pipeline end-to-end using a differentiable
mutual-information estimator based on the von-Mises distribution, generally
applicable to phase-coding channels.


  QED-model for multichain coupled qubit system, proposed in \cite{Part1}, was
confirmed by Raman scattering studies of quasi-1D carbon zigzag-shaped
nanotubes (CZSNTs), produced by high energy ion beam modification of natural
diamond single crystals. Multichain coupled qubit system represents itself
Su-Schriffer-Heeger $\sigma$-polaron lattice, formed in CZSNTs plus quantized
external electromagnetic (EM) field. New quantum optics phenomenon - Rabi
waves, predicted in \cite{Slepyan_Yerchak} has experimentally been identified
for the first time. It is shown, that Raman spectra in quasi-1D CZSNTs are
quite different in comparison with well known Raman spectra in 2D those ones.
They characterized by semiclassical consideration by the only one vibronic mode
of Su-Schriffer-Heeger $\sigma$-polaron lattice instead of longitudinal and
transverse optical phonon $G^+$ and $G^-$modes and the out-of-plane radial
breathing mode, which are observed in Raman spectra of 2D single wall
nanotubes. It is consequence of 2D - 1D transition in all physical properties
of nanotubes. It is shown, that strong electron-photon coupling takes place in
CZSNTs by interaction with EM-field and quantum nature of EM-field has to be
taken into account. It has been done for the first time in stationary
spectroscopy at all. All optical spectra, in particular, Raman spectra are
registered by usual stationary measurement technique in nonequilibrium
conditions, which are the consequence of Rabi wave packets' formation. It leads
in its turn to appearance of additional lines, corresponding to revival part of
inversion dependence of joint EM-field + matter system in frequency
representation.


  The Galactic supernova remnant (SNR) MSH 15-56 is a member of the class of
composite SNRs that consists of the remnant shell and a displaced pulsar wind
nebula (PWN). The earlier X-ray observations reported the comet-like morphology
of the PWN and the ejecta distribution of the SNR. In this work, we present a
study of MSH 15-56 using archival Suzaku data. We investigate the nature of the
emission and spectral parameters of the remnant. The X-ray spectra are well
fitted with a combination of a thermal and non-thermal model with temperature
~0.6 keV and photon index ~2.0. The slightly enhanced abundances of Ne, Mg, S
and enhanced abundance of Si confirm the presence of ejected material.


  In this paper, we propose a deterministic algorithm that approximates the
optimal path cover on weighted undirected graphs. Based on the
1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to
remove the redundant edges as the algorithm progresses. Our optimized algorithm
not only significantly reduces the computation time but also maintains the
theoretical guarantee of the original 1/2-Approximation Path Cover Algorithm.
To test the time complexity, we conduct numerical tests on graphs with various
structures and random weights, from structured ring graphs to random graphs,
such as Erdos-Renyi graphs. The tests demonstrate the effectiveness of our
proposed algorithm on graphs, especially those with high degree nodes, and the
advantages expand as the graph gets larger. Moreover, we also launch tests on
various graphs/networks derived from a wide range of real-world problems to
suggest the effectiveness and applicability of the proposed algorithm.


  Since Deep Learning (DL) backdoor attacks have been revealed as one of the
most insidious adversarial attacks, a number of countermeasures have been
developed with certain assumptions defined in their respective threat models.
However, the robustness of these countermeasures is inadvertently ignored,
which can introduce severe consequences, e.g., a countermeasure can be misused
and result in a false implication of backdoor detection.
  For the first time, we critically examine the robustness of existing backdoor
countermeasures with an initial focus on three influential model-inspection
ones that are Neural Cleanse (S&P'19), ABS (CCS'19), and MNTD (S&P'21).
Although the three countermeasures claim that they work well under their
respective threat models, they have inherent unexplored non-robust cases
depending on factors such as given tasks, model architectures, datasets, and
defense hyper-parameter, which are \textit{not even rooted from delicate
adaptive attacks}. We demonstrate how to trivially bypass them aligned with
their respective threat models by simply varying aforementioned factors.
Particularly, for each defense, formal proofs or empirical studies are used to
reveal its two non-robust cases where it is not as robust as it claims or
expects, especially the recent MNTD. This work highlights the necessity of
thoroughly evaluating the robustness of backdoor countermeasures to avoid their
misleading security implications in unknown non-robust cases.


  In \cite{D3}, Donaldson defines a dynamical system on the space of
Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that
if there exists a balanced metric for the polarization, then this dynamical
system always converges to the balanced metric (\cite{S}). In \cite{DKLR},
Douglas, et. al., conjecture that the same holds in the case of vector bundles.
In this paper, we give an affirmative answer to their conjecture.


  In this paper, we focus on the statistical filtering problem in dynamical
models with jumps. When a particular application relies on physical properties
which are modeled by linear and Gaussian probability density functions with
jumps, an usualmethod consists in approximating the optimal Bayesian estimate
(in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian
Jump Markov State Space System (JMSS). Practical solutions include algorithms
based on numerical approximations or based on Sequential Monte Carlo (SMC)
methods. In this paper, we propose a class of alternative methods which
consists in building statistical models which share the same physical
properties of interest but in which the computation of the optimal MMSE
estimate can be done at a computational cost which is linear in the number of
observations.


  Algorithmic trading is well studied in traditional financial markets.
However, it has received less attention in centralized cryptocurrency
exchanges. The Commodity Futures Trading Commission (CFTC) attributed the
$2010$ flash crash, one of the most turbulent periods in the history of
financial markets that saw the Dow Jones Industrial Average lose $9\%$ of its
value within minutes, to automated order "spoofing" algorithms. In this paper,
we build a set of methodologies to characterize and empirically measure
different algorithmic trading strategies in Binance, a large centralized
cryptocurrency exchange, using a complete data set of historical trades. We
find that a sub-strategy of triangular arbitrage is widespread, where bots
convert between two coins through an intermediary coin, and obtain a favorable
exchange rate compared to the direct one. We measure the profitability of this
strategy, characterize its risks, and outline two strategies that algorithmic
trading bots use to mitigate their losses. We find that this strategy yields an
exchange ratio that is $0.144\%$, or $14.4$ basis points (bps) better than the
direct exchange ratio. $2.71\%$ of all trades on Binance are attributable to
this strategy.


  We investigate the dynamics of a magnetic vortex driven by spin-transfer
torque due to spin current in the adiabatic case. The vortex core represented
by collective coordinate experiences a transverse force proportional to the
product of spin current and gyrovector, which can be interpreted as the
geometric force determined by topological charges. We show that this force is
just a reaction force of Lorentz-type force from the spin current of conduction
electrons. Based on our analyses, we propose analytically and numerically a
possible experiment to check the vortex displacement by spin current in the
case of single magnetic nanodot.


  In this paper we present the implementation of a Control Barrier Function
(CBF) using a quadratic program (QP) formulation that provides obstacle
avoidance for a robotic manipulator arm system. CBF is a control technique that
has emerged and developed over the past decade and has been extensively
explored in the literature on its mathematical foundations, proof of set
invariance and potential applications for a variety of safety-critical control
systems. In this work we will look at the design of CBF for the robotic
manipulator obstacle avoidance, discuss the selection of the CBF parameters and
present a Reinforcement Learning (RL) scheme to assist with finding parameters
values that provide the most efficient trajectory to successfully avoid
different sized obstacles. We then create a data-set across a range of
scenarios used to train a Neural-Network (NN) model that can be used within the
control scheme to allow the system to efficiently adapt to different obstacle
scenarios. Computer simulations (based on Matlab/Simulink) demonstrate the
effectiveness of the proposed algorithm.


  Recent progress and open problems in kaonic atom physics are presented. A
connection between phenomenological deep potentials and the underlying $K^-N$
interaction is established as well as the need for a theory for multinucleon
absorption of kaons. $K^-$ absorption at rest to specific $\Lambda $
hypernuclei states is briefly discussed.


  The hallmark of nematic order in iron-based superconductors is a resistivity
anisotropy but it is unclear to which extent quasiparticle dispersions,
lifetimes and coherence contribute. While the lifted degeneracy of the Fe
$d_{xz}$ and $d_{yz}$ dispersions has been studied extensively, only little is
known about the two other factors. Here, we combine in situ strain tuning with
ARPES and study the nematic response of the spectral weight in BaFe$_2$As$_2$.
The symmetry analysis of the ARPES spectra demonstrates that the $d_{xz}$ band
gains quasiparticle spectral weight compared to the $d_{yz}$ band for negative
antisymmetric strain $\Delta \epsilon_{yy}$ suggesting the same response inside
the nematic phase. Our results are compatible with a different coherence of the
$d_{xz}$ and $d_{yz}$ orbital within a Hund's metal picture. We also discuss
the influence of orbital mixing.


  We reanalyze the extraction of the heavy Higgs boson signal $H\rightarrow
W^+W^-\rightarrow \bar\ell\nu,\ell\bar\nu$ $(\ell=e\hbox{ or }\mu)$ from the
Standard Model background at hadron supercolliders, taking into account revised
estimates of the top quark background. With new acceptance criteria the
detection of the signal remains viable. Requiring a forward jet-tag, a central
jet-veto, and a large relative transverse momentum of the two charged leptons
yields $S/\sqrt B>6$ for one year of running at the SSC or LHC.


  This brief review deals with recent interest in the prospects of observing a
Massive Metastable Charged Particle (MMCP) at the Large Hadron Collider (LHC),
and measuring its properties there. We discuss the motivation for scenarios
with MMCPs in a phenomenological context, focusing on supersymmetric models
that allow us to explore the expected experimental signatures of MMCPs at the
LHC. We review current bounds and give estimates of the LHC reach in terms of
MMCP masses.


  Gradient compression (GC) is a promising approach to addressing the
communication bottleneck in distributed deep learning (DDL). However, it is
challenging to find the optimal compression strategy for applying GC to DDL
because of the intricate interactions among tensors. To fully unleash the
benefits of GC, two questions must be addressed: 1) How to express all
compression strategies and the corresponding interactions among tensors of any
DDL training job? 2) How to quickly select a near-optimal compression strategy?
In this paper, we propose ByteComp to answer these questions. It first designs
a decision tree abstraction to express all the compression strategies and
develops empirical models to timeline tensor computation, communication, and
compression to enable ByteComp to derive the intricate interactions among
tensors. It then designs a compression decision algorithm that analyzes tensor
interactions to eliminate and prioritize strategies and optimally offloads
compression to CPUs. Experimental evaluations show that ByteComp can improve
the training throughput over the start-of-the-art compression-enabled system by
up to 77% for representative DDL training jobs. Moreover, the computational
time needed to select the compression strategy is measured in milliseconds, and
the selected strategy is only a few percent from optimal.


  The premise of massive multiple-input multiple-output (MIMO) is based around
coherent transmission and detection. Majority of the vast literature on massive
MIMO presents performance evaluations over simplified statistical propagation
models. All such models are drop-based and do not ensure continuity of channel
parameters. In this paper, we quantify the impact of spatially consistent (SC)
models on beamforming for massive MIMO systems. We focus on the downlink of a
28GHz multiuser urban microcellular scenario. Using the recently standardized
Third Generation Partnership Project 38.901 SC-I procedure, we evaluate the
signal-to-interference-plus-noise ratio of a user equipment and the system
ergodic sum spectral efficiency with zero-forcing, block diagonalization, and
signal-to-leakage-plus-noise ratio beamforming. Our results disclose that at
practical signal-to-noise ratio levels, SC channels yield a significant
performance loss relative to the case without SC due to substantial spatial
correlation across the channel parameters.


  Recent experimental studies of $^{87}$Rb spinor Bose Einstein condensates
have shown the existence of a magnetic field driven quantum phase transition
accompanied by structure formation on the ferromagnetic side of the transition.
In this theoretical study we examine the dynamics of the unstable modes
following the transition taking into account the effects of the trap,
non-linearities, finite temperature and dipole-dipole interactions. Starting
from an initial state which includes quantum fluctuations, we attempt to make
quantitative comparisons with recent experimental data on this system and
estimate the contribution of quantum zero-point fluctuations to the domain
formation. Finally, using the strong anisotropy of the trap, we propose ways to
observe directly the effects of dipole-dipole interactions on the spinor
condensate dynamics.


  A new density functional theory (DFT) exchange-correlation functional for the
exploration of reaction mechanisms is proposed. This new functional, denoted
BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for
transition state barriers but, unlike previous attempts at such a functional,
this improved accuracy does not come at the expense of equilibrium properties.
This makes it a general-purpose functional whose domain of applicability has
been extended to transition states, rather than a specialized functional for
kinetics. The improvement in BMK rests on the inclusion of the kinetic energy
density together with a large value of the exact exchange mixing coefficient.
For this functional, the kinetic energy density appears to correct `back' the
excess exact exchange mixing for ground-state properties, possibly simulating
variable exchange.


  It is demonstrated that, in the adiabatic approximation, non-Equatorial
circular orbits of particles in the Kerr metric (i.e. orbits of constant
Boyer-Lindquist radius) remain circular under the influence of gravitational
radiation reaction. A brief discussion is given of conditions for breakdown of
adiabaticity and of whether slightly non-circular orbits are stable against the
growth of eccentricity.


  Missing data present challenges in data analysis. Naive analyses such as
complete-case and available-case analysis may introduce bias and loss of
efficiency, and produce unreliable results. Multiple imputation (MI) is one of
the most widely used methods for handling missing data which can be partly
attributed to its ease of use. However, existing MI methods implemented in most
statistical software are not applicable to or do not perform well in
high-dimensional settings where the number of predictors is large relative to
the sample size. To remedy this issue, we develop an MI approach that uses
dimension reduction techniques. Specifically, in constructing imputation models
in the presence of high-dimensional data our approach uses sure independent
screening followed by either sparse principal component analysis (sPCA) or
sufficient dimension reduction (SDR) techniques. Our simulation studies,
conducted for high-dimensional data, demonstrate that using SIS followed by
sPCA to perform MI achieves better performance than the other imputation
methods including several existing imputation approaches. We apply our approach
to analysis of gene expression data from a prostate cancer study.


  We report on the shape dynamics of ice suspended in cold fresh water and
subject to the natural convective flows generated during melting. Experiments
reveal shape motifs for increasing far-field temperature: Sharp pinnacles
directed downward at low temperatures, scalloped waves for intermediate
temperatures between 5 and $7^\circ$C, and upward pointing pinnacles at higher
temperatures. Phase-field simulations reproduce these morphologies, which are
closely linked to the anomalous density-temperature profile of liquid water.
Boundary layer flows yield pinnacles that sharpen with accelerating growth of
tip curvature while scallops emerge from a Kelvin-Helmholtz-like instability
caused by counterflowing currents that roll up to form vortex arrays. By
linking the molecular-scale effects underlying water's density anomaly to the
macro-scale flows that imprint the surface, these results show that the
morphology of melted ice is a sensitive indicator of ambient temperature.


  We analyze the necessary physical conditions to model an open quantum system
as a quantum game. By applying the formalism of Quantum Operations on a
particular system, we use Kraus operators as quantum strategies. The physical
interpretation is a conflict among different configurations of the environment.
The resolution of the conflict displays regimes of minimum loss of information.


  Spray cooling a hot target is characterized by strong heat flux density and
fast change of the temperature of the wall interface. The heat flux density
during spray cooling is determined by the instantaneous substrate temperature,
which is illustrated by boiling curves. The variation of the heat flux density
is especially notable during different thermodynamic regimes: film,
transitional and nucleate boiling. In this study transient boiling curves are
obtained by measurement of the local and instantaneous heat flux density
produced by sprays of variable mass flux, drop diameter and impact velocity.
These spray parameters are accurately characterized using a phase Doppler
instrument and a patternator. The hydrodynamic phenomena of spray impact during
various thermodynamic regimes are observed using a high-speed video system. A
theoretical model has been developed for heat conduction in the thin expanding
thermal boundary layer in the substrate. The theory is able to predict the
evolution of the target temperature in time in the film boiling regime.
Moreover, a remote asymptotic solution for a heat flux density during the fully
developed nucleate boiling regime is developed. The theoretical predictions
agree very well with the experimental data for a wide range of impact
parameters.


  A route to the derivation of the numbers $s$ to the transcendental equation
$\zeta(s)=0$ is presented. The solutions to this equation require the solving
of a geodesic flow in an infinite dimensional manifold. These solutions enable
one approach to a formula generating the prime numbers.


  It is argued that important information on the emergence of space is hidden
at the quark/hadron level. The arguments follow from the acceptance of the
conception that space is an attribute of matter. They involve in particular the
discussion of possibly relevant mass and distance scales, the generalization of
the concept of mass as suggested by the phase-space-based explanation of the
rishon model, and the phenomenological conclusions on the structure of excited
baryons that are implied by baryon spectroscopy. A counterpart of the
Eddington-Weinberg relation concerning Regge towers of hadronic resonances is
noted.


  We investigate the Hoyle-Lyttleton accretion of dusty-gas for the case where
the central source is the black hole accretion disk. By solving the equation of
motion taking into account the radiation force which is attenuated by the dust
absorption, we reveal the steady structure of the flow around the central
object. We find that the mass accretion rate tends to increase with an increase
of the optical thickness of the flow and the gas can accrete even if the disk
luminosity exceeds the Eddington luminosity for the dusty-gas, since the
radiation force is weakened by the attenuation via the dust absorption. When
the gas flows in from the direction of the rotation axis for the disk with
${\Gamma}^{'}=3.0$, the accretion rate is about 93% of the Hoyle-Lyttleton
accretion rate if ${\tau}_{\rm{HL}}=3.3$ and zero for ${\tau}_{\rm{HL}}=1.0$,
where ${\Gamma}^{'}$ is the Eddington ratio for the dusty-gas and
${\tau}_{\rm{HL}}$ is the typical optical thickness of the Hoyle-Lyttleton
radius. Since the radiation flux in the direction of disk plane is small, the
radiation force tends not to prevent gas accretion from the direction near the
disk plane. For ${\tau}_{\rm{HL}}=3.3$ and ${\Gamma}^{'}=3.4$, although the
accretion is impossible in the case of ${\Theta}=0$, the accretion rate is 28%
of the Hoyle-Lyttleton one in the case of ${\Theta}=90$, where ${\Theta}$ is
the angle between the direction the gas is coming from and the rotation axis of
the disk. We also obtain relatively high accretion luminosity that is realized
when the accretion rate of the disk onto the BH is consistent with that via the
Hoyle-Lyttleton mechanism taking into account the effect of radiation. This
implies the intermediate-mass black holes moving in the dense dusty-gas are
identified as luminous objects in the infrared band.


  In this paper, first we have defined a uniform distribution on the boundary
of a regular hexagon, and then investigated the optimal sets of $n$-means and
the $n$th quantization errors for all positive integers $n$. We give an exact
formula to determine them, if $n$ is of the form $n=6k$ for some positive
integer $k$. We further calculate the quantization dimension, the quantization
coefficient, and show that the quantization dimension is equal to the dimension
of the object, and the quantization coefficient exists as a finite positive
number. Then, we define a mixture of two uniform distributions on the boundary
of a semicircular disc, and obtain a sequence and an algorithm, with the help
of which we determine the optimal sets of $n$-means and the $n$th quantization
errors for all positive integers $n$ with respect to the mixed distribution.
Finally, for a uniform distribution defined on an elliptical curve, we
investigate the optimal sets of $n$-means and the $n$th quantization errors for
all positive integers $n$.


  In this paper, we explore the slot tagging with only a few labeled support
sentences (a.k.a. few-shot). Few-shot slot tagging faces a unique challenge
compared to the other few-shot classification problems as it calls for modeling
the dependencies between labels. But it is hard to apply previously learned
label dependencies to an unseen domain, due to the discrepancy of label sets.
To tackle this, we introduce a collapsed dependency transfer mechanism into the
conditional random field (CRF) to transfer abstract label dependency patterns
as transition scores. In the few-shot setting, the emission score of CRF can be
calculated as a word's similarity to the representation of each label. To
calculate such similarity, we propose a Label-enhanced Task-Adaptive Projection
Network (L-TapNet) based on the state-of-the-art few-shot classification model
-- TapNet, by leveraging label name semantics in representing labels.
Experimental results show that our model significantly outperforms the
strongest few-shot learning baseline by 14.64 F1 scores in the one-shot
setting.


  We investigate a model for pattern formation in the presence of Galilean
symmetry proposed by Matthews and Cox [Phys.\ Rev.\ E \textbf{62}, R1473
(2000)], which has the form of coupled generalized Burgers and
Ginzburg-Landau-type equations. With only the system size $L$ as a parameter,
we find distinct "small-$L$" and "large-$L$" regimes exhibiting clear
differences in their dynamics and scaling behavior. The long-time statistically
stationary state contains a single $L$-dependent front, stabilized globally by
spatiotemporally chaotic dynamics localized away from the front. For
sufficiently large domains, the transient dynamics include a state consisting
of several viscous shock-like structures which coarsens gradually, before
collapsing to a single front when one front absorbs the others.


  We consider the complexity of the Independent Set Reconfiguration problem
under the Token Sliding rule. In this problem we are given two independent sets
of a graph and are asked if we can transform one to the other by repeatedly
exchanging a vertex that is currently in the set with one of its neighbors,
while maintaining the set independent. Our main result is to show that this
problem is PSPACE-complete on split graphs (and hence also on chordal graphs),
thus resolving an open problem in this area. We then go on to consider the
$c$-Colorable Reconfiguration problem under the same rule, where the constraint
is now to maintain the set $c$-colorable at all times. As one may expect, a
simple modification of our reduction shows that this more general problem is
PSPACE-complete for all fixed $c\ge 1$ on chordal graphs. Somewhat
surprisingly, we show that the same cannot be said for split graphs: we give a
polynomial time ($n^{O(c)}$) algorithm for all fixed values of $c$, except
$c=1$, for which the problem is PSPACE-complete. We complement our algorithm
with a lower bound showing that $c$-Colorable Reconfiguration is W[2]-hard on
split graphs parameterized by $c$ and the length of the solution, as well as a
tight ETH-based lower bound for both parameters.


  We investigate the Z(2) gauge model on a generalized Bethe lattice with three
plaquette representation of the action. We obtain the cascade of phase
transitions according to Feigenbaum scheme leading to chaotic states for some
values of parameters of the model. The duality between this gauge model and
three site Ising spin model on Husimi tree is shown. The Lyapunov exponent as a
new order parameter for the characterization of the model in the chaotic region
is considered. The line of the second order phase transition, which corresponds
to the points of the first period doubling bifurcation, is also obtained.


  A method based on laser wakefield acceleration with controlled ionization
injection triggered by another frequency-tripled laser is proposed, which can
produce electron bunches with low energy spread. As two color pulses
co-propagate in the background plasma, the peak amplitude of the combined laser
field is modulated in time and space during the laser propagation due to the
plasma dispersion. Ionization injection occurs when the peak amplitude exceeds
certain threshold. The threshold is exceeded for limited duration periodically
at different propagation distances, leading to multiple ionization injections
and separated electron bunches. The method is demonstrated through
multi-dimensional particle-in-cell simulations. Such electron bunches may be
used to generate multi-chromatic X-ray sources for a variety of applications.


  In this paper, we consider Nesterov's Accelerated Gradient method for solving
Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based
iterative method for solving well-posed convex optimization problems, this
method also leads to promising results for ill-posed problems. Here, we provide
a convergence analysis for ill-posed problems of this method based on the
assumption of a locally convex residual functional. Furthermore, we demonstrate
the usefulness of the method on a number of numerical examples based on a
nonlinear diagonal operator and on an inverse problem in auto-convolution.


  We describe an online database of number fields which accompanies this paper
The database centers on complete lists of number fields with prescribed
invariants. Our description here focuses on summarizing tables and connections
to theoretical issues of current interest.


  Stationary points (SPs) of the potential energy landscapes can be classified
by their Morse index, i.e., the number of negative eigenvalues of the Hessian
evaluated at the SPs. In understanding chemical clusters through their
potential energy landscapes, only SPs of a particular Morse index are needed.
We propose a modification of the "fixed-point homotopy" method which can be
used to directly target stationary points of a specified Morse index. We
demonstrate the effectiveness of our approach by applying it to the
Lennard-Jones clusters.


  Renewable generators perturb the electric power grid with heavily
non-Gaussian and time correlated fluctuations. While changes in generated power
on timescales of minutes and hours are compensated by frequency control
measures, we report subsecond distribution grid frequency measurements with
local non-Gaussian fluctuations which depend on the magnitude of wind power
generation in the grid. Motivated by such experimental findings, we simulate
the sub-second grid frequency dynamics by perturbing the power grid, as modeled
by a network of phase coupled nonlinear oscillators, with synthetically
generated wind power feed-in time series. We derive a linear response theory
and obtain analytical results for the variance of frequency increment
distributions. We find that the variance of short-term fluctuations decays, for
large inertia, exponentially with distance to the feed-in node, in agreement
with numerical results both for a linear chain of nodes and the German
transmission grid topology. In sharp contrast, the kurtosis of frequency
increments is numerically found to decay only slowly, not exponentially, in
both systems, indicating that the non-Gaussian shape of frequency fluctuations
persists over long ranges.


  We prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices
that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3}
\rfloor$ contains each tree $T$ with $m$ edges as a subgraph. Our result
confirms, for large $m$, an important special case of a conjecture by Havet,
Reed, Stein, and Wood. The present paper builds on the results of a companion
paper in which we proved the statement for all trees having a vertex that is
adjacent to many leaves.


  In this work we consider the problem of approximating the statistics of a
given Quantity of Interest (QoI) that depends on the solution of a linear
elliptic PDE defined over a random domain parameterized by $N$ random
variables. The random domain is split into large and small variations
contributions. The large variations are approximated by applying a sparse grid
stochastic collocation method. The small variations are approximated with a
stochastic collocation-perturbation method. Convergence rates for the variance
of the QoI are derived and compared to those obtained in numerical experiments.
Our approach significantly reduces the dimensionality of the stochastic
problem. The computational cost of this method increases at most quadratically
with respect to the number of dimensions of the small variations. Moreover, for
the case that the small and large variations are independent the cost increases
linearly.


  Surfaces covered with nanostructures, such as nanowire arrays, have shown to
facilitate a significantly higher absorption of laser energy as compared to
flat surfaces. Due to the efficient coupling of the laser energy, highly
energetic electrons are produced, which in turn can emit intense ultrafast
X-ray pulses. In the present work we use full three dimensional PIC simulations
to analyze the behavior of arrays of carbon nanowires $400 nm$ in diameter,
irradiated by a $\lambda_0 = 400 nm$ laser pulse of $60 fs$ duration at FWHM
and a vector potential of $a_0 = 18$. We analyze the ionization dynamics of the
nanowires. We investigate the difference of the ionization strength and
structure between linearly and circularly polarized laser beam. The nanowires
are found to be fully ionized after about 30 laser cycles. Circularly polarized
light reveals a slightly stronger ionization effect.


  The increasing sensitivity of current experiments, which nowadays routinely
measure the thermal SZ effect within galaxy clusters, provide the hope that
peculiar velocities of individual clusters of galaxies will be measured rather
soon using the kinematic SZ effect. Also next generation of X-ray telescopes
with microcalorimeters, promise first detections of the motion of the intra
cluster medium (ICM) within clusters. We used a large set of cosmological,
hydrodynamical simulations, which cover very large cosmological volume, hosting
a large number of rich clusters of galaxies, as well as moderate volumes where
the internal structures of individual galaxy clusters can be resolved with very
high resolution to investigate, how the presence of baryons and their
associated physical processes like cooling and star-formation are affecting the
systematic difference between mass averaged velocities of dark matter and the
ICM inside a cluster. We, for the first time, quantify the peculiar motion of
galaxy clusters as function of the large scale environment. We also demonstrate
that especially in very massive systems, the relative velocity of the ICM
compared to the cluster peculiar velocity add significant scatter onto the
inferred peculiar velocity, especially when measurements are limited to the
central regions of the cluster. Depending on the aperture used, this scatter
varies between 50% and 20%, when going from the core (e.g. ten percent of the
virial radius) to the full cluster (e.g. the virial radius).


  Most treatments of electron-electron correlations in dense plasmas either
ignore them entirely (random phase approximation) or neglect the role of ions
(jellium approximation). In this work, we go beyond both these approximations
to derive a new formula for the electron-electron static structure factor which
properly accounts for the contributions of both ionic structure and
quantum-mechanical dynamic response in the electrons. The result can be viewed
as a natural extension of the quantum Ornstein-Zernike theory of ionic and
electronic correlations, and it is suitable for dense plasmas in which the ions
are classical and the conduction electrons are quantum-mechanical. The
corresponding electron-electron pair distribution functions are compared with
the results of path integral Monte Carlo simulations, showing good agreement
whenever no strong electron resonance states are present. We construct
approximate potentials of mean force which describe the effective screened
interaction between electrons. Significant deviations from Debye-H\"uckel
screening are present at temperatures and densities relevant to high energy
density experiments involving warm and hot dense plasmas. The presence of
correlations between conduction electrons is likely to influence the
electron-electron contribution to the electron and thermal conductivity. It is
expected that excitation processes involving the conduction electrons (e.g.,
free-free absorption) will also be affected.


  In this work are consider several topics in the Topological Membrane (TM)
approach to string theory. The string dynamics is generated from the bulk
physics, namely from the 3D Topologically Massive Gauge Theory (TMGT) and
Topologically Massive Gravity (TMG). Both (equivalent) path integral and
canonical methods of quantizing TMGT are studied. It is shown that Narain
constraints on toroidal compactification (integer, even, self-dual momentum
lattice) have a natural interpretation in purely three dimensional terms. The
Heterotic string and the block structure of c=1 RCFT are derived from the point
of view of three dimensional field theory. Open and unoriented strings in
TM(GT) theory are also studied through orbifolds of the bulk 3D space. This is
achieved by gauging discrete symmetries of the theory. Open and unoriented
strings can be obtained from all possible realizations of C, P and T
symmetries. The important role of C symmetry to distinguish between Dirichlet
and Neumann boundary conditions is discussed in detail. Future directions of
research in this field are also suggested and discussed.


  We study automorphism groups of real del Pezzo surfaces, concentrating on
finite groups acting minimally on them. As a result, we obtain a vast part of
classification of finite subgroups in the real plane Cremona group.


  The problem of situational awareness (SAW) is investigated from the
probabilistic modeling point of view. Taking the situation as a hidden
variable, we introduce a hidden Markov model (HMM) and an extended state space
model (ESSM) to mathematically express the dynamic evolution law of the
situation and the relationships between the situation and the observable
quantities. We use the Gaussian mixture model (GMM) to formulate expert
knowledge, which is needed in building the HMM and ESSM. We show that the ESSM
model is preferable as compared with HMM, since using ESSM, we can also get a
real time estimate of the pivot variable that connects the situation with the
observable quantities. The effectiveness and efficiency of both models are
tested through a simulated experiment about threat surveillance.


  We study the problem of invisibility for bodies with a mirror surface in the
framework of geometrical optics. We show that for any two given directions it
is possible to construct a two-dimensional fractal body invisible in these
directions. Moreover, there exists a three-dimensional fractal body invisible
in three orthogonal directions. The work continues the previous study in [A.
Aleksenko and A. Plakhov. Bodies of zero resistance and bodies invisible in one
direction. Nonlinearity 22, 1247-1258 (2009)], [A Plakhov and V Roshchina.
Invisibility in billiards. Nonlinearity 24, 847-854 (2011)], where
two-dimensional bodies invisible in one direction and three-dimensional bodies
invisible in one and two orthogonal directions were constructed.


  We construct a highly-symmetric periodic orbit of eight bodies in three
dimensions. In this orbit, each body collides with its three nearest neighbors
in a regular periodic fashion. Regularization of the collisions in the orbit is
achieved by an extension of the Levi-Civita method. Initial conditions for the
orbit are found numerically. Linear stability of the orbit is then shown using
a technique by Roberts. Evidence toward higher-order stability is presented as
an additional result of a numerical calculation.


  We investigate the continuous extension of discrete shift translations on one
dimensional quantum lattice systems. We focus on a specific construction
provided by a quasi-free C*-flow on the one-dimensional fermion lattice system.
This quasi-free C*-flow is heuristically generated by a long-range Hamiltonian
consisting of two-body translation invariant interactions with
$\frac{1}{r}$-decay. We explore statistical-mechanical interpretation of such a
long-range Hamiltonian, which may be more naturally associated with a momentum
operator rather than the Hamiltonian. Through its explicit dynamical formulas,
wherein notably the sinc function appears, the continuous shift translations
reveal violations of causality and locality. Furthermore, we demonstrate that
this quasi-free C*-flow, implementing the shift translations, cannot be
extended to the one-dimensional quantum spin system via the Jordan-Wigner
transformation.


  A generalized propagation matrix method is used to study how scattering off
local Einstein phonons affects resonant electron transmission through quantum
wells. In particular, the parity and the number of the phonon mediated
satellite resonances are found to depend on the available scattering channels.
For a large number of phonon channels, the formation of low-energy impurity
bands is observed. Furthermore, an effective theory is developed which
accurately describes the phonon generated sidebands for sufficiently small
electron-phonon coupling. Finally, the current-voltage characteristics caused
by phonon assisted transmission satellites are discussed for a specific double
barrier geometry.


  A new experiment is proposed with the aim to study eta-mesic nuclei and
low-energy interactions of eta with nuclei. Two decay modes of eta produced by
a photon beam inside a nucleus will be observed, namely a collisional decay
\eta N \to \pi N inside the nucleus and the radiative decay \eta \to \gamma
\gamma outside. In addition, a collisional decay of stopped S_{11}(1535)
resonance inside the nucleus, S_{11}(1535) N \to N N, will be studied. The
experiment can be performed using the tagged photon beam at ESRF with the
end-point energy 1000 MeV and the GRAAL detector which includes a
high-resolution BGO calorimeter and a large acceptance lead-scintillator
time-of-flight wall. Some results of simulation and estimates of yields are
given.


  We estimate the axion properties i.e. its mass, topological susceptibility
and the self-coupling within the framework of Polyakov loop enhanced
Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical
potential. PNJL model, where quarks couple simultaneously to the chiral
condensate and to a background temporal quantum chromodynamics (QCD) gauge
field, includes two important features of QCD phase transition, i.e.
deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model
plays an important role near the critical temperature. We have shown
significant difference in the axion properties calculated in PNJL model
compared to the same obtained using Nambu-Jona-Lasinio (NJL) model. We find
that both the mass of the axion and its self-coupling are correlated with the
chiral transition as well as the confinement-deconfinement transition. We have
also estimated the axion properties at finite chemical potential. Across the
QCD transition temperature and/or quark chemical potential axion mass and its
self-coupling also changes significantly. Since the PNJL model includes both
the fermionic sector and the gauge fields, it can give reliable estimates of
the axion properties, i.e. it's mass and the self-coupling in a hot and dense
QCD medium. We also compare our results with the lattice QCD results whenever
available.


  In this paper, we consider a connected orientable closed Riemannian manifold
$M^{n+1}$ with positive Ricci curvature. Suppose $G$ is a compact Lie group
acting by isometries on $M$ with $3\leq {\rm codim}(G\cdot p)\leq 7$ for all
$p\in M$. Then we show the equivariant min-max $G$-hypersurface $\Sigma$
corresponding to the fundamental class $[M]$ is a multiplicity one minimal
$G$-hypersurface with a $G$-invariant unit normal and $G$-equivariant index
one. As an application, we are able to establish a genus bound for $\Sigma$, a
control on the singular points of $\Sigma/G$, and an upper bound for the
(first) $G$-width of $M$ provided $n+1=3$ and the actions of $G$ are
orientation preserving.


  Nearly two-orders of magnitude increase in room-temperature band-to-band
(1.067 eV) infrared emission from crystalline silicon, coated with erbium-doped
sol-gel films, have been achieved. Phonon-assisted band-to-band emission from
coated and annealed p-Si is strongest for the sample annealed at
700$^{\circ}$C. In this paper, evidence of the origin of the emission band from
the band edge recombination activities is established. Enhancement of radiative
recombination of free carriers is reasoned by stresses at the interface due to
the annealed sol-gel deposited silica. Comparative studies with other strained
silicon samples are presented.


  At low temperatures, the main coolant in primordial gas is molecular
hydrogen, H2. Recent work has shown that primordial gas that is not collapsing
gravitationally but is cooling from an initially ionized state forms hydrogen
deuteride, HD, in sufficient amounts to cool the gas to the temperature of the
cosmic microwave background. This extra cooling can reduce the characteristic
mass for gravitational fragmentation and may cause a shift in the
characteristic masses of population III stars. Motivated by the importance of
the atomic and molecular data for the cosmological question, we assess several
chemical and radiative processes that have hitherto been neglected: the
sensitivity of the low temperature H2 cooling rate to the ratio of ortho-H2 to
para-H2, the uncertainty in the low temperature cooling rate of H2 excited by
collisions with H, the effects of cooling from H2 excited by collisions with H+
and e-, and the large uncertainties in the rates of several of the reactions
responsible for determining the H2 fraction in the gas.
  We show that the most important of the neglected processes is the excitation
of H2 by collisions with protons and electrons. This cools the gas more rapidly
at early times, and so it forms less H2 and HD at late times. This fact, as
well as several of the chemical uncertainties presented here, significantly
affects the thermal evolution of the gas. We anticipate that this may lead to
clear differences in future detailed 3D studies of first structure formation.
Finally, we show that although the thermal evolution of the gas is in principle
sensitive to the ortho-para ratio, in practice the standard assumption of a 3:1
ratio produces results that are almost indistinguishable from those produced by
a more detailed treatment. (abridged)


  The U(1,1) and U(2) transformations realized by three-mode interaction in the
respective parametric approximations are studied in conditional measurement,
and the corresponding non-unitary transformation operators are derived. As an
application, the preparation of single-mode quantum states using an optical
feedback loop is discussed, with special emphasis of Fock state preparation.
For that example, the influence of non-perfect detection and feedback is also
considered.


  In this paper, we develop an $n$ dimensional volumetric stretch energy
($n$-VSE) functional for the volume-/mass-preserving parameterization of the
$n$-manifolds topologically equivalent to $n$-ball. The $n$-VSE has a lower
bound and equal to it if and only if the map is volume-/mass-preserving. This
motivates us to minimize the $n$-VSE to achieve the ideal
volume-/mass-preserving parameterization. In the discrete case, we also
guarantee the relation between the lower bound and the
volume-/mass-preservation, and propose the spherical and ball
volume-/mass-preserving parameterization algorithms. The numerical experiments
indicate the accuracy and robustness of the proposed algorithms. The modified
algorithms are applied to the manifold registration and deformation, showing
the versatility of $n$-VSE.


  We discuss hadroproduction of open charmed mesons ($D^0$, $D^{\pm}$,
$D^{\pm}_{S}$) at the LHC energy $\sqrt{s} = 7$ TeV. The cross section for
inclusive production of $c \bar c$ pairs is calculated within the
$k_{\perp}$-factorization (or high-energy factorization) approach which
effectively includes higher-order corrections. Results of the
$k_{\perp}$-factorization approach are compared to NLO parton model
predictions. The hadronization of charm quarks is included with the help of the
Peterson fragmentation functions. Inclusive differential distributions in
(pseudo)rapidity and transverse momentum for several charmed mesons are
calculated and compared to recent results of the ALICE, ATLAS and LHCb
experiments. We also take into consideration a mechanism of double charm (two
pairs of $c \bar c$) production within a simple formalism of double-parton
scattering (DPS). Surprisingly for LHC energies the DPS cross sections are
found to be larger than those from the standard SPS mechanism. We compare our
predictions for $DD$ meson-meson pair production with recent measurements of
the LHCb collaboration, including correlation observables. Our calculations
clearly confirm the dominance of DPS in the production of double charm, however
some strength seems to be still lacking. Possible missing contribution from the
so-called single-ladder-splitting DPS mechanism is also discussed.


  Syndromic surveillance detects and monitors individual and population health
indicators through sources such as emergency department records. Automated
classification of these records can improve outbreak detection speed and
diagnosis accuracy. Current syndromic systems rely on hand-coded keyword-based
methods to parse written fields and may benefit from the use of modern
supervised-learning classifier models. In this paper we implement two recurrent
neural network models based on long short-term memory (LSTM) and gated
recurrent unit (GRU) cells and compare them to two traditional bag-of-words
classifiers: multinomial naive Bayes (MNB) and a support vector machine (SVM).
The MNB classifier is one of only two machine learning algorithms currently
being used for syndromic surveillance. All four models are trained to predict
diagnostic code groups as defined by Clinical Classification Software, first to
predict from discharge diagnosis, then from chief complaint fields. The
classifiers are trained on 3.6 million de-identified emergency department
records from a single United States jurisdiction. We compare performance of
these models primarily using the F1 score. Using discharge diagnoses, the LSTM
classifier performs best, though all models exhibit an F1 score above 96.00.
The GRU performs best on chief complaints (F1=47.38), and MNB with bigrams
performs worst (F1=39.40). Certain syndrome types are easier to detect than
others. For examples, chief complaints using the GRU model predicts
alcohol-related disorders well (F1=78.91) but predicts influenza poorly
(F1=14.80). In all instances, the RNN models outperformed the bag-of-word
classifiers, suggesting deep learning models could substantially improve the
automatic classification of unstructured text for syndromic surveillance.


  Let X be a K\"ahler manifold, and E be a Hermitian vector bundle on X. We
investigate the space N(X,E) of nearly holomorphic sections in E, which
generalizes the notion of nearly holomorphic functions introduced by Shimura.
If X=U/K is a compact Hermitian symmetric space, and E is U-homogeneous, it
turns out that N(X,E) coincides with the space of $U$-finite vectors in
C^\infty(X,E), and we obtain new results on the U-type decomposition of the
Hilbert space of square integrable sections. As an application, we determine
this decomposition for the holomorphic tangent space of X.


  A multi-channel scattering problem is studied from a point of view of
integral equations system. The system appears while natural one-particle wave
function equation of the electron under action of a potential with
non-intersecting ranges is considered.
  Spherical functions basis expansion of the potentials introduces partial
amplitudes and corresponding radial functions. The approach is generalized to
multi-channel case by a matrix formulation in which a state vector component is
associated with a scattering channel.
  The zero-range potentials naturally enter the scheme when the class of
operators of multiplication is widen to distributions. %Analog of multipolar
expansion is treated. Spin variables, o Oscillations and rotations are
incorporated into the scheme.


  We investigate superfluid properties and strong-coupling effects in a
one-component Fermi gas with an anisotropic p-wave interaction. Within the
framework of the Gaussian fluctuation theory, we determine the superfluid
transition temperature $T_{\rm c}$, as well as the temperature $T_0$ at which
the phase transition from the $p_x$-wave pairing state to the $p_x+ip_y$-wave
state occurs below $T_{\rm c}$. We also show that while the anisotropy of the
p-wave interaction enhances $T_{\rm c}$ in the strong-coupling regime, it
suppresses $T_0$.


  With view to applications in stochastic analysis and geometry, we introduce a
new correspondence for positive definite kernels (p.d.) $K$ and their
associated reproducing kernel Hilbert spaces. With this we establish two kinds
of factorizations: (i) Probabilistic: Starting with a positive definite kernel
$K$ we analyze associated Gaussian processes $V$. Properties of the Gaussian
processes will be derived from certain factorizations of $K$, arising as a
covariance kernel of $V$. (ii) Geometric analysis: We discuss families of
measure spaces arising as boundaries for $K$. Our results entail an analysis of
a partial order on families of p.d. kernels, a duality for operators and
frames, optimization, Karhunen--Lo\`eve expansions, and factorizations.
Applications include a new boundary analysis for the Drury-Arveson kernel, and
for certain fractals arising as iterated function systems; and an
identification of optimal feature spaces in machine learning models.


  There is no theoretical reason to think that the spin-flip component of the
Pomeron is zero. One can measure the spin-flip part using Coulomb-nuclear
interference (CNI). Perturbative QCD calculations show that the spin-flip
component is sensitive to the smallest quark separation in the proton, while
the non-flip part probes the largest separation. According to HERA results on
the proton structure function at very low x the energy dependence of the
cross-section correlates with the size of the color dipole. Analysing the data
from HERA we predict that the ratio of the spin-flip to non-flip amplitude
grows with energy as $r(s)\propto (1/x)^{0.1-0.2}$, violating Regge
factorisation of the Pomeron.


  At linear colliders, the e+e- luminosity is limited by beam-collision
effects, which determine the required emittances of beams in damping rings
(DRs). While in gamma-gamma collisions at the photon collider, these effects
are absent, and so smaller emittances are desirable. In present damping rings
designs, nominal DR parameters correspond to those required for e+e-
collisions. In this note, I would like to stress once again that as soon as we
plan the photon-collider mode of ILC operation, the damping-ring emittances are
dictated by the photon-collider requirements--namely, they should be as small
as possible. This can be achieved by adding more wigglers to the DRs; the
incremental cost is easily justified by a considerable potential improvement of
the gamma-gamma luminosity. No expert analysis exists as of yet, but it seems
realistic to obtain a factor five increase of the gamma-gamma luminosity
compared to the ``nominal'' DR design.


  This article develops a new theoretical basis for decomposing signals that
are formed by the linear superposition of a finite number of modes. Each mode
depends nonlinearly upon several parameters; we seek both these parameters and
the weights within the superposition. The particular focus of this article is
upon solving the decomposition problem when the number of modes is not known in
advance. A sheaf-theoretic formalism is introduced that describes all modal
decomposition problems, and it is shown that minimizing the local consistency
radius within this sheaf is guaranteed to solve them. Since the modes may or
may not be well-separated, a greedy algorithm that identifies the most distinct
modes first may not work reliably. This article introduces a novel mathematical
formalism, aggregation sheaves, and shows how they characterize the behavior of
greedy algorithms that attempt to solve modal decomposition problems.


  We define global Weyl modules for twisted loop algebras and analyze their
high- est weight spaces, which are in fact isomorphic to Laurent polynomial
rings in finitely many variables. We are able to show that the global Weyl
module is a free module of finite rank over these rings. Furthermore we prove,
that there exist injective maps from the global Weyl modules for twisted loop
algebras into a direct sum of global Weyl modules for untwisted loop algebras.
Relations between local Weyl modules for twisted and untwisted generalized
current algebras are known; we provide for the first time a relation on global
Weyl modules.


  There has been increased interest in devising learning techniques that
combine unlabeled data with labeled data ? i.e. semi-supervised learning.
However, to the best of our knowledge, no study has been performed across
various techniques and different types and amounts of labeled and unlabeled
data. Moreover, most of the published work on semi-supervised learning
techniques assumes that the labeled and unlabeled data come from the same
distribution. It is possible for the labeling process to be associated with a
selection bias such that the distributions of data points in the labeled and
unlabeled sets are different. Not correcting for such bias can result in biased
function approximation with potentially poor performance. In this paper, we
present an empirical study of various semi-supervised learning techniques on a
variety of datasets. We attempt to answer various questions such as the effect
of independence or relevance amongst features, the effect of the size of the
labeled and unlabeled sets and the effect of noise. We also investigate the
impact of sample-selection bias on the semi-supervised learning techniques
under study and implement a bivariate probit technique particularly designed to
correct for such bias.


  Periodic variations of the position angle of the inner jet of the blazar S5
0716+71 suggest a helical structure for the jet. The geometrical parameters of
a model helical jet are determined. It is shown that, when the trajectories of
the jet components are non-ballistic, the angle between their velocity vectors
and the line of sight lies in a broader interval than is the case for ballistic
motions of the components, in agreement with available estimates. The
contradictory results for the apparent speeds of components in the inner and
outer jet at epochs 2004 and 2008-2010 can be explained in such a model. The
ratio of the apparent speeds in the inner and outer jet is used to derive a
lower limit for the true speed of the components ($\beta>0.999$) and to
determine the pitch angle of the helical jet ($p=5.5^\circ$). The derived
parameters can give rise to the conditions required to observe high speeds
(right to 37$c$) for individual jet components.


  For most values of parameters $\lambda$ and $\alpha$, the zeros of the Lerch
zeta-function $L(\lambda, \alpha, s)$ are distributed very chaotically. In this
paper we consider the special case of equal parameters $L(\lambda, \lambda, s)$
and show by calculations that the nontrivial zeros either lie extremely close
to the critical line $\sigma = 1/2$ or are distributed almost symmetrically
with respect to the critical line. We also investigate this phenomenon
theoretically.


  The gravitational field of a black hole is strongly localized near its
horizon when the number of dimensions D is very large. In this limit, we can
effectively replace the black hole with a surface in a background geometry (eg
Minkowski or Anti-deSitter space). The Einstein equations determine the
effective equations that this 'black hole surface' (or membrane) must satisfy.
We obtain them up to next-to-leading order in 1/D for static black holes of the
Einstein-(A)dS theory. To leading order, and also to next order in Minkowski
backgrounds, the equations of the effective theory are the same as soap-film
equations, possibly up to a redshift factor. In particular, the Schwarzschild
black hole is recovered as a spherical soap bubble. Less trivially, we find
solutions for 'black droplets', ie black holes localized at the boundary of
AdS, and for non-uniform black strings.


  New results concerning the production of neutral strange particles, $K^0$ and
$\Lambda$ in Ni + Ni collisions at 1.93$A$ GeV, measured with the FOPI detector
at GSI-Darmstadt, are presented. Rapidity density distributions and Boltzmann
slope parameter distributions are measured in nearly the full phase space of
the reaction. The observables are compared to existing $K^+$ and proton data.
While the $K^0$ data agree with previously reported $K^+$ measurements, the
$\Lambda$ distributions show a different behavior relative to that of protons.
The strangeness balance and the production yield per participating nucleon as a
function of the centrality of the reaction are discussed, for the first time at
SIS energies.


  Large real-life complex networks are often modeled by various random graph
constructions and hundreds of further references therein. In many cases it is
not at all clear how the modeling strength of differently generated random
graph model classes relate to each other. We would like to systematically
investigate such issues. Our approach was originally motivated to capture
properties of the random network topology of wireless communication networks.
We started some investigations, but here we elevate it to a more general level
that makes it possible to compare the strength of different classes of random
network models. Specially, we introduce various classes of random graph models
that are significantly more general than the ones that are usually treated in
the literature, and show relationships among them. One of our main results is
that no random graph model can fall in the following three classes at the same
time: (1) random graph models with bounded expected degrees; (2) random graph
models that are asymptotically almost connected; (3) an abstracted version of
geometric random graph models with two mild restrictions that we call locality
and name invariance. In other words, in a mildly restricted, but still very
general, class of generalized geometric-style models the requirements of
bounded expected degrees and asymptotic almost connectivity are incompatible.


  Aims: In view of the substantial uncertainties regarding the possible
dynamics of the dark energy, we aim at constraining the expansion rate of the
universe without reference to a specific Friedmann model and its parameters.
Methods: We show that cosmological observables integrating over the cosmic
expansion rate can be converted into a Volterra integral equation which is
known to have a unique solution in terms of a Neumann series. Expanding
observables such as the luminosity distances to type-Ia supernovae into a
series of orthonormal functions, the integral equation can be solved and the
cosmic expansion rate recovered within the limits allowed by the accuracy of
the data. Results: We demonstrate the performance of the method applying it to
synthetic data sets of increasing complexity, and to the first-year SNLS data.
In particular, we show that the method is capable of reproducing a hypothetical
expansion function containing a sudden transition.


  Stars form in clustered environments, but how they form when the available
resources are shared is still not well understood. A related question is
whether the IMF is in fact universal across galactic environments, a galactic
initial mass function (IGIMF), or whether it is an average of local IMFs. One
of the long-standing problems in resolving this question and in the study of
young clusters is observational: the emission from multiple sources is
frequently seen as blended because at different wavelengths or with different
telescopes the beam sizes are different. The confusion hinders our ability to
fully characterize clustered star formation. Here we present a new method that
uses a genetic algorithm and Bayesian inference to fit the blended SEDs and
images of individual YSOs in confused clusters. We apply this method to the
infrared photometry of a sample comprising 70 Spitzer-selected, low-mass
($M_{\rm{cl}}<100~\rm{M}_{\odot}$) young clusters in the galactic plane, and
use the derived physical parameters to investigate the distributions of masses
and evolutionary stages of clustered YSOs, and the implications of those
distributions for studies of the IMF and the different models of star
formation. We find that for low-mass clusters composed of class I and class II
YSOs, there exists a non-trivial relationship between the total stellar mass of
the cluster ($M_{\rm{cl}}$) and the mass of its most massive member
($m_{\rm{max}}$). The properties of the derived correlation are most compatible
with the random sampling of a Kroupa IMF, with a fundamental high-mass limit of
$150~\rm{M}_{\odot}$. Our results are also compatible with SPH models that
predict a dynamical termination of the accretion in protostars, with massive
stars undergoing this stopping at later times in their evolution.


  When the ground state of a localized ion is a non-Kramers doublet, such
localized ions may carry multipolar moments. For example, Pr$^{3+}$ ions in a
cubic environment would possess quadrupolar and octupolar, but no magnetic
dipole, moments. When such multipolar moments are placed in a metallic host,
unusual interactions between these local moments and conduction electrons
arise, in contrast to the familiar magnetic dipole interactions in the classic
Kondo problem. In this work, we consider the interaction between a single
quadrupolar-octupolar local moment and conduction electrons with $p$-orbital
symmetry as a concrete model for the multipolar Kondo problem. We show that
this model can be written most naturally in the spin-orbital entangled basis of
conduction electrons. Using this basis, the perturbative renormalization group
(RG) fixed points are readily identified. There are two kinds of fixed points,
one for the two-channel Kondo and the other for a novel fixed point. We
investigate the nature of the novel fixed point non-perturbatively using
non-abelian bosonization, current algebra and conformal field theory
approaches. It is shown that the novel fixed point leads to a, previously
unidentified, non-Fermi liquid state with entangled spin and orbital degrees of
freedom, which shows resistivity $\rho \sim T^{\Delta}$ and diverging specific
heat coefficient $C/T \sim T^{-1 + 2\Delta}$ with $\Delta=1/5$. Our results
open up the possibility of myriads of non-Fermi liquid states, depending on the
choices of multipolar moments and conduction electron orbitals, which would be
relevant for many rare-earth metallic systems.