  High-contrast imaging instruments need extreme wavefront control to directly
image exoplanets. This requires highly sensitive wavefront sensors which
optimally make use of the available photons to sense the wavefront. Here, we
propose to numerically optimize Fourier-filtering wavefront sensors using
automatic differentiation. First, we optimize the sensitivity of the wavefront
sensor for different apertures and wavefront distributions. We find sensors
that are more sensitive than currently used sensors and close to the
theoretical limit, under the assumption of monochromatic light. Subsequently,
we directly minimize the residual wavefront error by jointly optimizing the
sensing and reconstruction. This is done by connecting differentiable models of
the wavefront sensor and reconstructor and alternatingly improving them using a
gradient-based optimizer. We also allow for nonlinearities in the wavefront
reconstruction using Convolutional Neural Networks, which extends the design
space of the wavefront sensor. Our results show that optimization can lead to
wavefront sensors that have improved performance over currently used wavefront
sensors. The proposed approach is flexible, and can in principle be used for
any wavefront sensor architecture with free design parameters.


  Here we study the nonnegative solutions of the viscous Hamilton-Jacobi
problem \[ \left\{\begin{array} [c]{c}% u_{t}-\nu\Delta u+|\nabla u|^{q}=0,
u(0)=u_{0}, \end{array} \right. \] in
$Q_{\Omega,T}=\Omega\times\left(0,T\right) ,$ where $q>1,\nu\geqq
0,T\in\left(0,\infty\right] ,$ and $\Omega=\mathbb{R}^{N}$ or $\Omega$ is a
smooth bounded domain, and $u_{0}\in L^{r}(\Omega),r\geqq1,$ or $u_{0}%
\in\mathcal{M}_{b}(\Omega).$ We show $L^{\infty}$ decay estimates, valid for
\textit{any weak solution}, \textit{without any conditions a}s $\left\|
x\right\| \rightarrow\infty,$ and \textit{without uniqueness assumptions}. As a
consequence we obtain new uniqueness results, when $u_{0}\in
\mathcal{M}_{b}(\Omega)$ and $q<(N+2)/(N+1),$ or $u_{0}\in L^{r}(\Omega)$ and
$q<(N+2r)/(N+r).$ We also extend some decay properties to quasilinear equations
of the model type \[ u_{t}-\Delta_{p}u+\left\| u\right\| ^{\lambda-1}u|\nabla
u|^{q}=0 \] where $p>1,\lambda\geqq0,$ and $u$ is a signed solution.


  This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor
gauge fields. The theory describes the propagation of free massless gauge
bosons of integer helicities and their interaction with external currents.
Self-consistency of its equations requires only the traceless part of the
current divergence to vanish. The essence of the theory is given by the fact
that this weaker current conservation is enough to guarantee the unitarity of
the theory. Physically this means that only waves with transverse polarizations
are propagating very far from the sources. The question whether such currents
exist should be answered by a fully interacting theory. We also suggest an
equivalent representation of the corresponding action.


  Observing inversion lines of ammonia (NH3), complemented by rotational lines
of NH3 and other molecular species, provides stringent constraints on potential
variations of the proton-to-electron mass ratio. While a limit of one part per
million is derived for a lookback time of 7 billion years, nearby dark clouds
might show a statistically significant variation of order 20-30 parts per
billion, possibly being related to chameleon fields. The detection of
radio-loud quasars with strong molecular absorption lines at redshifts z > 1 as
well as the identification of a larger sample of nearby dark clouds with
exceptionally narrow lines (<0.2 km/s) would be essential to improve present
limits and to put the acquired results onto a firmer statistical basis.


  The escape of particles through a narrow absorbing gate in confined domains
is a abundant phenomenon in various systems in physics, chemistry and molecular
biophysics. We consider the narrow escape problem in a cellular flow when the
two gates randomly switch between different states with a switching rate k
between the two gates. After briefly deriving the coupled partial differential
equations for the escape time through two gates, we compute the mean escape
time for particles escaping from the gates with different initial states. By
numerical simulation under nonuniform boundary conditions, we quantify how
narrow escape time is affected by the switching rate k between the two gates,
arc length s between two gates, angular velocity w of the cellular flow and
diffusion coefficient D. We reveal that the mean escape time decreases with the
switching rate k between the two gates, angular velocity w and diffusion
coefficient D for fixed arc length, but takes the minimum when the two gates
are evenly separated on the boundary for any given switching rate k between the
two gates. In particular, we find that when the arc length size {\epsilon} for
the gates is sufficiently small, the average narrow escape time is
approximately independent of the gate arc length size. We further indicate
combinations of system parameters (regions located in the parameter space) such
that the mean escape time is the longest or shortest. Our findings provide
mathematical understanding for phenomena such as how ions select ion channels
and how chemicals leak in annulus ring containers, when drift vector fields are
present.


  We study the exclusive photoproduction of a photon-meson pair with a large
invariant mass, working in the QCD factorisation framework. Explicitly, we
consider a $ \rho $-meson or a charged $ \pi $ in the final state. This process
gives access to chiral-even GPDs as well as chiral-odd GPDs. We focus here on
the chiral-even sector. The computation is performed at leading order and
leading twist. We discuss the prospects of measuring them in various
experiments such as JLab 12-GeV, COMPASS, future EIC and LHC (in
ultraperipheral collisions). In particular, the high centre of mass energies
available at collider experiments can be used to probe GPDs at small skewness $
\xi $. We also compute the polarisation asymmetries with respect to the
incoming photon. The results for an alternative distribution amplitude
(`holographic' form) are also compared with the predictions obtained with an
asymptotic distribution amplitude.


  The influence of human activity own the earth's atmospheric composition has
never been more pronounced. Anthropogenic pollution is in fact the largest
effector of the observed evolving atmospheric composition (Wallace, 2006).
PM2.5 is a class of particulate matter pollutants of notable interest due to
their significant driving of chemical, atmospheric change, their wide-scale,
global circulations, and their malignant effects on human health; with a
diameter of less than 2.5 microns; PM2.5s derive from combustion of organic
materials, including fossil fuel combustion (Wallace, 2006) and forest fires
(Newman, 2007). The gases released in these combustion reactions then condense
in the atmosphere, undergoing gas to particle conversion, resulting in the
atmospheric presence of PM2.5s. Particulate matter (PM) pollutants are harmful
to human health in all diameter scales; increasing in recent years global
morbidity and mortality (Araujo, 2011). The health risks of PM2.5 in particular
are troubling due to their small size, which facilities their permeability in
the respiratory system and ready diffusion into the bloodstream, inducing
pathologies like ischaemic heart disease, respiratory infections, and lung
cancers to name a few (Araujo, 2011). Once PM2.5 manifest in the atmosphere,
they circulate on a larger scale due to atmospheric circulation patterns.
Though government-enacted air quality measures have reduced the average PM2.5
levels in North America, pollution episodes still cause localized, acute PM2.5
exposure. The purpose of this project was to analyze PM2.5 mean concentration
across America to identify and quantify any pollution episodes, as well as try
to explain their dynamics using large scale, meteorological processes.


  The complexity in large-scale optimization can lie in both handling the
objective function and handling the constraint set. In this respect, stochastic
Frank-Wolfe algorithms occupy a unique position as they alleviate both
computational burdens, by querying only approximate first-order information
from the objective and by maintaining feasibility of the iterates without using
projections. In this paper, we improve the quality of their first-order
information by blending in adaptive gradients. We derive convergence rates and
demonstrate the computational advantage of our method over the state-of-the-art
stochastic Frank-Wolfe algorithms on both convex and nonconvex objectives. The
experiments further show that our method can improve the performance of
adaptive gradient algorithms for constrained optimization.


  We study fluctuation theorems for open quantum systems with a non-Markovian
heat bath using the approach of quantum master equations and examine the
physical quantities that appear in those fluctuation theorems. The approach of
Markovian quantum master equations to the fluctuation theorems was developed by
Esposito and Mukamel [Phys. Rev. E {\bf73}, 046129 (2006)]. We show that their
discussion can be formally generalized to the case of a non-Markovian heat bath
when the local system is linearly connected to a Gaussian heat bath with the
spectrum distribution of the Drude form. We found by numerically simulating the
spin-boson model in non-Markovian regime that the "detailed balance" condition
is well satisfied except in a strongly non-equilibrium transient situation, and
hence our generalization of the definition of the "entropy production" is
almost always legitimate. Therefore, our generalization of the fluctuation
theorem seems meaningful in wide regions.


  We prove sharp $L^1$ inequalities for the dyadic maximal function $M_T\phi$
when $\phi$ satisfies certain $L^1$ and $L^{\infty}$ conditions


  A computational tool for coarse-graining nonlinear systems of ordinary
differential equations in time is discussed. Three illustrative model examples
are worked out that demonstrate the range of capability of the method. This
includes the averaging of Hamiltonian as well as dissipative microscopic
dynamics whose `slow' variables, defined in a precise sense, can often display
mixed slow-fast response as in relaxation oscillations, and dependence on
initial conditions of the fast variables. Also covered is the case where the
quasi-static assumption in solid mechanics is violated. The computational tool
is demonstrated to capture all of these behaviors in an accurate and robust
manner, with significant savings in time. A practically useful strategy for
initializing short bursts of microscopic runs for the accurate computation of
the evolution of slow variables is also developed.


  We propose a notion of integral Menger curvature for compact, $m$-dimensional
sets in $n$-dimensional Euclidean space and prove that finiteness of this
quantity implies that the set is $C^{1,\alpha}$ embedded manifold with the
H{\"o}lder norm and the size of maps depending only on the curvature. We
develop the ideas introduced by Strzelecki and von der Mosel [Adv. Math.
226(2011)] and use a similar strategy to prove our results.


  Non-autoregressive translation (NAT) models generate multiple tokens in one
forward pass and is highly efficient at inference stage compared with
autoregressive translation (AT) methods. However, NAT models often suffer from
the multimodality problem, i.e., generating duplicated tokens or missing
tokens. In this paper, we propose two novel methods to address this issue, the
Look-Around (LA) strategy and the Vocabulary Attention (VA) mechanism. The
Look-Around strategy predicts the neighbor tokens in order to predict the
current token, and the Vocabulary Attention models long-term token dependencies
inside the decoder by attending the whole vocabulary for each position to
acquire knowledge of which token is about to generate. %We also propose a
dynamic bidirectional decoding approach to accelerate the inference process of
the LAVA model while preserving the high-quality of the generated output. Our
proposed model uses significantly less time during inference compared with
autoregressive models and most other NAT models. Our experiments on four
benchmarks (WMT14 En$\rightarrow$De, WMT14 De$\rightarrow$En, WMT16
Ro$\rightarrow$En and IWSLT14 De$\rightarrow$En) show that the proposed model
achieves competitive performance compared with the state-of-the-art
non-autoregressive and autoregressive models while significantly reducing the
time cost in inference phase.


  The rapid development and reduced barriers to entry for Text-to-Image (T2I)
models have raised concerns about the biases in their outputs, but existing
research lacks a holistic definition and evaluation framework of biases,
limiting the enhancement of debiasing techniques. To address this issue, we
introduce FAIntbench, a holistic and precise benchmark for biases in T2I
models. In contrast to existing benchmarks that evaluate bias in limited
aspects, FAIntbench evaluate biases from four dimensions: manifestation of
bias, visibility of bias, acquired attributes, and protected attributes. We
applied FAIntbench to evaluate seven recent large-scale T2I models and
conducted human evaluation, whose results demonstrated the effectiveness of
FAIntbench in identifying various biases. Our study also revealed new research
questions about biases, including the side-effect of distillation. The findings
presented here are preliminary, highlighting the potential of FAIntbench to
advance future research aimed at mitigating the biases in T2I models. Our
benchmark is publicly available to ensure the reproducibility.


  We classify outer actions (or $\mathscr{G}$-kernels) of discrete amenable
groupoids on injective factors. Our method based on unified approach for
classification of discrete amenable groups actions, and cohomology reduction
theorem of discrete amenable equivalence relations. We do not use
Katayama-Takesaki type resolution group approach.


  Neural interfaces capable of multi-site electrical recording, on-site signal
classification, and closed-loop therapy are critical for the diagnosis and
treatment of neurological disorders. However, deploying machine learning
algorithms on low-power neural devices is challenging, given the tight
constraints on computational and memory resources for such devices. In this
paper, we review the recent developments in embedding machine learning in
neural interfaces, with a focus on design trade-offs and hardware efficiency.
We also present our optimized tree-based model for low-power and
memory-efficient classification of neural signal in brain implants. Using
energy-aware learning and model compression, we show that the proposed oblique
trees can outperform conventional machine learning models in applications such
as seizure or tremor detection and motor decoding.


  Big data has shown its uniquely powerful ability to reveal, model, and
understand driver behaviors. The amount of data affects the experiment cost and
conclusions in the analysis. Insufficient data may lead to inaccurate models
while excessive data waste resources. For projects that cost millions of
dollars, it is critical to determine the right amount of data needed. However,
how to decide the appropriate amount has not been fully studied in the realm of
driver behaviors. This paper systematically investigates this issue to estimate
how much naturalistic driving data (NDD) is needed for understanding driver
behaviors from a statistical point of view. A general assessment method is
proposed using a Gaussian kernel density estimation to catch the underlying
characteristics of driver behaviors. We then apply the Kullback-Liebler
divergence method to measure the similarity between density functions with
differing amounts of NDD. A max-minimum approach is used to compute the
appropriate amount of NDD. To validate our proposed method, we investigated the
car-following case using NDD collected from the University of Michigan Safety
Pilot Model Deployment (SPMD) program. We demonstrate that from a statistical
perspective, the proposed approach can provide an appropriate amount of NDD
capable of capturing most features of the normal car-following behavior, which
is consistent with the experiment settings in many literatures.


  The aim of this paper is to give an explicit formula of the invariant
distribution of a quasi-birth-and-death process in terms of the block entries
of the transition probability matrix using a matrix-valued orthogonal
polynomials approach. We will show that the invariant distribution can be
computed using the squared norms of the corresponding matrix-valued orthogonal
polynomials, no matter if they are or not diagonal matrices. We will give an
example where the squared norms are not diagonal matrices, but nevertheless we
can compute its invariant distribution.


  Recent work has demonstrated the strong qualitative differences between the
dynamics near a glass transition driven by short-ranged repulsion and one
governed by short-ranged attraction. Here, we study in detail the behavior of
non-linear, higher-order correlation functions that measure the growth of
length scales associated with dynamical heterogeneity in both types of systems.
We find that this measure is qualitatively different in the repulsive and
attractive cases with regards to the wave vector dependence as well as the time
dependence of the standard non-linear four-point dynamical susceptibility. We
discuss the implications of these results for the general understanding of
dynamical heterogeneity in glass-forming liquids.


  We show that the L^2-torsion and the von Neumann rho-invariant give rise to
commensurability invariants of knots.


  We calculate the time reversal odd (T-odd) generalized transverse momentum
dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a
light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum
transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We
have incorporated both scalar and axial vector diquarks in the model and
obtained an overlap representation of the GTMDs using the light-front wave
functions (LFWFs). Contribution from the final state interaction is
incorporated at the level of one gluon exchange as a phase factor in the LFWF.
We show that the final state interaction term can be factored out in this model
and this part is the same for both GTMDs. We also present the corresponding
Wigner distributions.


  We study K\"ahler manifolds that are (weak) relatives, that is, K\"ahler
manifolds which share a (locally isometric) submanifold. In particular, we
prove that if two K\"ahler manifolds are weak relatives and one of them is
projective, then they are relatives. Moreover, we introduce the notion of
strict relatives K\"ahler manifolds and provide several nontrivial examples.


  Fast radio bursts (FRBs) are bright radio pulses from the sky with
millisecond durations and Jansky-level flux densities. Their origins are still
largely uncertain. Here we suggest a new model for FRBs. We argue that the
collision of a white dwarf with a black hole can give birth to a transient
accretion disk, from which powerful episodic magnetic blobs will be launched.
The collision between two consecutive magnetic blobs can result in a
catastrophic magnetic reconnection, which releases a large amount of free
magnetic energy and forms a forward shock. The shock propagates through the
cold magnetized plasma within the blob in the collision region, radiating
through synchrotron maser mechanism, which is responsible for a non-repeating
FRB signal. Our calculations show that the theoretical energetics, radiation
frequency, duration timescale, and event rate can be well consistent with the
observational characteristic of FRBs.


  The tidal breakup of binary star systems by the supermassive black hole
(SMBH) in the center of the galaxy has been suggested as the source of both the
observed sample of hypervelocity stars (HVSs) in the halo of the Galaxy and the
S-stars that remain in tight orbits around Sgr A*. Here, we use a
post-Newtonian N-body code to study the dynamics of main-sequence binaries on
highly elliptical bound orbits whose periapses lie close to the SMBH,
determining the properties of ejected and bound stars as well as collision
products. Unlike previous studies, we follow binaries that remain bound for
several revolutions around the SMBH, finding that in the case of relatively
large periapses and highly inclined binaries the Kozai resonance can lead to
large periodic oscillations in the internal binary eccentricity and
inclination. Collisions and mergers of the binary elements are found to
increase significantly for multiple orbits around the SMBH, while HVSs are
primarily produced during a binary's first passage. This process can lead to
stellar coalescence and eventually serve as an important source of young stars
at the galactic center.


  We study the ring of algebraic functions on the space of persistence
barcodes, with applications to pattern recognition.


  This paper presents \textsc{hankel}, a pure-python code for solving
Hankel-type integrals and transforms. Such transforms are common in the
physical sciences, especially appearing as the radial solution to angularly
symmetric Fourier Transforms in arbitrary dimensions. The code harnesses the
advantages of solving such transforms via the one-dimensional Hankel transform
-- an increase in conceptual simplicity and efficiency -- and implements them
in the user-friendly and flexible Python language. We discuss several
limitations of the adopted method, and point to the code's extensive
documentation for further examples.


  Robinsonian matrices arise in the classical seriation problem and play an
important role in many applications where unsorted similarity (or
dissimilarity) information must be reordered. We present a new polynomial time
algorithm to recognize Robinsonian matrices based on a new characterization of
Robinsonian matrices in terms of straight enumerations of unit interval graphs.
The algorithm is simple and is based essentially on lexicographic breadth-first
search (Lex-BFS), using a divide-and-conquer strategy. When applied to a
nonnegative symmetric $n\times n$ matrix with~$m$ nonzero entries and given as
a weighted adjacency list, it runs in $O(d(n+m))$ time, where $d$ is the depth
of the recursion tree, which is at most the number of distinct nonzero entries
of $A$.


  A recently published correlated electron pseudopotentials (CEPPs) method has
been adapted for application to the 3d-transition metals, and to include
relativistic effects. New CEPPs are reported for the atoms Sc$-$Fe, constructed
from atomic quantum chemical calculations that include an accurate description
of correlated electrons. Dissociation energies, molecular geometries, and
zero-point vibrational energies of small molecules are compared with all
electron results, with all quantities evaluated using coupled cluster singles
doubles and triples (CCSD(T)) calculations. The CEPPs give better results in
the correlated-electron calculations than Hartree-Fock-based pseudopotentials
available in the literature.


  We derive two general transformations for certain basic hypergeometric series
from the recurrence formulae for the partial numerators and denominators of two
$q$-continued fractions previously investigated by the authors. By then
specializing certain free parameters in these transformations, and employing
various identities of Rogers-Ramanujan type, we derive \emph{$m$-versions} of
these identities. Some of the identities thus found are new, and some have been
derived previously by other authors, using different methods. By applying
certain transformations due to Watson, Heine and Ramanujan, we derive still
more examples of such $m$-versions of Rogers-Ramanujan-type identities.


  Weighted voting games are frequently used in decision making. Each voter has
a weight and a proposal is accepted if the weight sum of the supporting voters
exceeds a quota. One line of research is the efficient computation of so-called
power indices measuring the influence of a voter. We treat the inverse problem:
Given an influence vector and a power index, determine a weighted voting game
such that the distribution of influence among the voters is as close as
possible to the given target value. We present exact algorithms and
computational results for the Shapley-Shubik and the (normalized) Banzhaf power
index.


  We study the problem of scheduling $n$ independent moldable tasks on $m$
processors that arises in large-scale parallel computations. When tasks are
monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation
algorithm for makespan minimization with a complexity linear in $n$ and
polynomial in $\log{m}$ and $\frac{1}{\epsilon}$ where $\epsilon$ is
arbitrarily small. We propose a new perspective of the existing speedup models:
the speedup of a task $T_{j}$ is linear when the number $p$ of assigned
processors is small (up to a threshold $\delta_{j}$) while it presents
monotonicity when $p$ ranges in $[\delta_{j}, k_{j}]$; the bound $k_{j}$
indicates an unacceptable overhead when parallelizing on too many processors.
The generality of this model is proved to be between the classic monotonic and
linear-speedup models. For any given integer $\delta\geq 5$, let $u=\left\lceil
\sqrt[2]{\delta} \right\rceil-1\geq 2$. In this paper, we propose a
$\frac{1}{\theta(\delta)} (1+\epsilon)$-approximation algorithm for makespan
minimization where $\theta(\delta) = \frac{u+1}{u+2}\left( 1- \frac{k}{m}
\right)$ ($m\gg k$). As a by-product, we also propose a
$\theta(\delta)$-approximation algorithm for throughput maximization with a
common deadline.


  We study the power of the bounded-width consistency algorithm in the context
of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main
technical finding is that the template of every PCSP that is solvable in
bounded width satisfies a certain structural condition implying that its
algebraic closure-properties include weak near unanimity polymorphisms of all
large arities. While this parallels the standard (non-promise) CSP theory, the
method of proof is quite different and applies even to the regime of sublinear
width. We also show that, in contrast with the CSP world, the presence of weak
near unanimity polymorphisms of all large arities does not guarantee
solvability in bounded width. The separating example is even solvable in the
second level of the Sherali-Adams (SA) hierarchy of linear programming
relaxations. This shows that, unlike for CSPs, linear programming can be
stronger than bounded width. A direct application of these methods also show
that the problem of $q$-coloring $p$-colorable graphs is not solvable in
bounded or even sublinear width, for any two constants $p$ and $q$ such that $3
\leq p \leq q$. Turning to algorithms, we note that Wigderson's algorithm for
$O(\sqrt{n})$-coloring $3$-colorable graphs with $n$ vertices is implementable
in width $4$. Indeed, by generalizing the method we see that, for any $\epsilon
> 0$ smaller than $1/2$, the optimal width for solving the problem of
$O(n^\epsilon)$-coloring $3$-colorable graphs with $n$ vertices lies between
$n^{1-3\epsilon}$ and $n^{1-2\epsilon}$. The upper bound gives a simple
$2^{\Theta(n^{1-2\epsilon}\log(n))}$-time algorithm that, asymptotically, beats
the straightforward $2^{\Theta(n^{1-\epsilon})}$ bound that follows from
partitioning the graph into $O(n^\epsilon)$ many independent parts each of size
$O(n^{1-\epsilon})$.


  The Run II physics program of CDF is proceeding with approximately 200 pb-1
of analysis quality data collected at the center-of-mass energy of 1.96 TeV.
The Electroweak measurements are among the first and most important benchmarks
towards the best understanding of the detector and testing of the Standard
Model. We present precision measurements of the W and Z inclusive cross
sections and decay asymmetries, recent results in di-boson physics and their
sensitivity to new physics, and preliminary studies for the W mass measurement.


  Doppler orbitography uses the Doppler shift in a transmitted signal to
determine the orbital parameters of satellites including range and range-rate
(or radial velocity). We describe two techniques for atmospheric-limited
optical Doppler orbitography measurements of range-rate. The first determines
the Doppler shift directly from a heterodyne measurement of the returned
optical signal. The second aims to improve the precision of the first by
suppressing atmospheric phase noise imprinted on the transmitted optical
signal. We demonstrate the performance of each technique over a 2.2 km
horizontal link with a simulated in-line velocity Doppler shift at the far end.
A horizontal link of this length has been estimated to exhibit nearly half the
total integrated atmospheric turbulence of a vertical link to space. Without
stabilisation of the atmospheric effects, we obtained an estimated range rate
precision of 17 um/s at 1 s of integration. With active suppression of
atmospheric phase noise, this improved by three orders-of-magnitude to an
estimated range rate precision of 9.0 nm/s at 1 second of integration, and 1.1
nm/s when integrated over a 60 s. This represents four orders-of-magnitude
improvement over the typical performance of operational ground to space X-Band
systems in terms of range-rate precision at the same integration time.
  The performance of this system is a promising proof of concept for coherent
optical Doppler orbitography. There are many additional challenges associated
with performing these techniques from ground to space, that were not captured
within the preliminary experiments presented here. In the future, we aim to
progress towards a 10 km horizontal link to replicate the expected atmospheric
turbulence for a ground to space link.


  We follow the scenario of formation of second generation stars in globular
clusters by matter processed by hot bottom burning (HBB) in massive asymptotic
giant branch (AGB) stars and Super AGB stars (SAGB). In the cluster NGC 2419 we
assume the presence of an extreme population directly formed from the AGB and
SAGB ejecta, so we can directly compare the yields for a metallicity Z=0.0003
with the chemical inventory of the cluster NGC 2419. At such a low metallicity,
the HBB temperatures (well above 108K) allow a very advanced nucleosynthesis.
Masses of about 6Mo deplete Mg and synthesize Si, going beyond Al, so this
latter element results only moderately enhanced; sodium can not be enhanced.
The models are consistent with the observations, although the predicted Mg
depletion is not as strong as in the observed stars. We predict that the oxygen
abundance must be depleted by a huge factor in the Mg poor stars. The HBB
temperatures are close to the region where other p capture reactions on heavier
nuclei become possible. We show that high potassium abundance found in Mg poor
stars can be achieved during HBB, by p captures on the argon nuclei, if the
relevant cross section(s) are larger than listed in the literature or if the
HBB temperature is higher. Finally, we speculate that some calcium production
is occurring owing to proton capture on potassium. We emphasize the importance
of a strong effort to measure a larger sample of abundances in this cluster.


  The main goal in this paper is to point out that quantity $||\nabla R||^2(p)$
on a harmonic space can not be determined by the spectra of local geodesic
spheres or balls, therefore the main results of [AM-S] (quoted in the title)
are wrong. My strong interest in the above theorem is motivated by the fact
that it contradicts some of my isospectrality examples constructed on geodesic
spheres and balls of certain harmonic manifolds. The authors overlooked that
the Lichnerowicz identity is not determined by the given spectral data, and so
is the final crucial equation obtained by eliminating with the Lichnerowicz
identity. In short, the above theorem has falsely been established by
spectrally undetermined identities which can not be computed (determined) by
the spectra of local geodesic spheres. More complicated spectrally undetermined
functions cause the problems also in case of local geodesic balls. I describe
also a strong physical argument which clearly explains why the manifolds
appearing in my examples are isospectral. It must be pointed out, however, that
a very remarkable new idea, namely, the asymptotic expansion of the heat
invariants $a_k(p,r)$ defined on geodesic spheres, $S_p(r)$, is introduced in
the paper. It can be used for developing both geometric uncertainty theory and
global vs. local spectral investigations. Among my contributions to this
developing field is the following statement: Average volumes, $\int
vol(B_p(r))dp$ resp. $\int vol(S_p(r))dp$, of geodesic balls resp. spheres are
generically not determined by the spectra of compact Riemann manifolds. This
theorem interestingly contrasts the statement asserting that the volume of the
whole manifold can be determined in terms of this global spectrum. We also
have: Music written for local drums can not be played, in general, on the whole
manifold.


  These notes (prepared for the author's lectures at the Cracow Summer School
on Linear Systems organized by S. Mueller-Stach and T. Szemberg, held March
23-27, 2009 at the Pedagogical University of Cracow under the sponsorship of
the Deutsche Forschungsgemeinschaft) present a number of open problems on the
theory of smooth projective algebraic surfaces, and put into historical context
recent work on a range of topics, including Mori dream spaces and the finite
generation of the Cox ring, Seshadri constants, and the resurgence of
homogeneous ideals and the problem of which ordinary powers of homogeneous
ideals contain given symbolic powers of those ideals. These notes include many
exercises, with solutions.


  Consider $d$ dependent change point tests, each based on a CUSUM-statistic.
We provide an asymptotic theory that allows us to deal with the maximum over
all test statistics as both the sample size $n$ and $d$ tend to infinity. We
achieve this either by a consistent bootstrap or an appropriate limit
distribution. This allows for the construction of simultaneous confidence bands
for dependent change point tests, and explicitly allows us to determine the
location of the change both in time and coordinates in high-dimensional time
series. If the underlying data has sample size greater or equal $n$ for each
test, our conditions explicitly allow for the large $d$ small $n$ situation,
that is, where $n/d\to0$. The setup for the high-dimensional time series is
based on a general weak dependence concept. The conditions are very flexible
and include many popular multivariate linear and nonlinear models from the
literature, such as ARMA, GARCH and related models. The construction of the
tests is completely nonparametric, difficulties associated with parametric
model selection, model fitting and parameter estimation are avoided. Among
other things, the limit distribution for $\max_{1\leq h\leq d}\sup_{0\leq
t\leq1}\vert \mathcal{W}_{t,h}-t\mathcal{W}_{1,h}\vert$ is established, where
$\{\mathcal{W}_{t,h}\}_{1\leq h\leq d}$ denotes a sequence of dependent
Brownian motions. As an application, we analyze all S&P 500 companies over a
period of one year.


  Momentum strategies are an important part of alternative investments and are
at the heart of commodity trading advisors (CTAs). These strategies have,
however, been found to have difficulties adjusting to rapid changes in market
conditions, such as during the 2020 market crash. In particular, immediately
after momentum turning points, where a trend reverses from an uptrend
(downtrend) to a downtrend (uptrend), time-series momentum (TSMOM) strategies
are prone to making bad bets. To improve the response to regime change, we
introduce a novel approach, where we insert an online changepoint detection
(CPD) module into a Deep Momentum Network (DMN) [1904.04912] pipeline, which
uses an LSTM deep-learning architecture to simultaneously learn both trend
estimation and position sizing. Furthermore, our model is able to optimise the
way in which it balances 1) a slow momentum strategy which exploits persisting
trends, but does not overreact to localised price moves, and 2) a fast
mean-reversion strategy regime by quickly flipping its position, then swapping
it back again to exploit localised price moves. Our CPD module outputs a
changepoint location and severity score, allowing our model to learn to respond
to varying degrees of disequilibrium, or smaller and more localised
changepoints, in a data driven manner. Back-testing our model over the period
1995-2020, the addition of the CPD module leads to an improvement in Sharpe
ratio of one-third. The module is especially beneficial in periods of
significant nonstationarity, and in particular, over the most recent years
tested (2015-2020) the performance boost is approximately two-thirds. This is
interesting as traditional momentum strategies have been underperforming in
this period.


  We have added some some refrences & given some figures giving results in
parameter space allowed by b \to s \gamma. Conclusions more or less remains
unchanged.


  We study a class of decoherence process which admits a 3 dimensional
holographic bulk. Starting from a thermo-field double dual to a wormhole, we
prepare another thermo-field double which plays the role of environment. By
allowing the energy flow between the original and environment thermo-field
double, the entanglement of the original thermo-field double eventually
decoheres. We model this decoherence by four-boundary wormhole geometries, and
study the time-evolution of the moduli parameters to see the change of the
entanglement pattern among subsystems. A notable feature of this holographic
decoherence processes is that at the end point of the processes, the
correlations of the original thermo-field double are lost completely both
classically and also quantum mechanically. We also discuss distinguishability
between thermo-field double state and thermo mixed double state, which contains
only classical correlations, and construct a code subspace toy model for that.


  Let $\mathcal{L}$ be a completely distributive commutative subspace lattice
or a subspace lattice with two atoms, we use a unified approach to study the
derivations, homomorphisms on $\mathrm{Alg} \mathcal{L}$. We verify that the
multiplier algebra of $\mathrm{Alg} \mathcal{L}\cap \mathcal{K}(\mathcal{H})$
is isomorphic to $\mathrm{Alg} \mathcal{L}$ and $\mathrm{Alg} \mathcal{L}$ is
zero product determined. For $T$ in $M_{n}(\mathbb{C})$, $n\geq 2$, we show
that $\mathcal{A}_{T}$ is zero product determined if and only if every local
derivation from $\mathcal{A}_{T}$ into any Banach $\mathcal{A}_{T}$-bimodule is
a derivation. In addition, we establish some equivalent conditions for an
algebra to be zero product determined. For countable dimensional locally matrix
algebras and triangular UHF algebras, we also show that they are zero Lie
product determined.


  Black hole masses for samples of active galactic nuclei (AGN) are currently
estimated from single-epoch optical spectra using scaling relations anchored in
reverberation mapping results. In particular, the two quantities needed for
calculating black hole masses, namely, the velocity and the radial distance of
the orbiting gas are derived from the widths of the Balmer hydrogen broad
emission lines and the optical continuum luminosity, respectively. We have
recently presented a near-infrared (near-IR) relationship for estimating AGN
black hole masses based on the widths of the Paschen hydrogen broad emission
lines and the total 1 micron continuum luminosity. The near-IR offers several
advantages over the optical: it suffers less from dust extinction, the AGN
continuum is observed only weakly contaminated by the host galaxy and the
strongest Paschen broad emission lines Pa alpha and Pa beta are unblended. Here
we improve the calibration of the near-IR black hole mass relationship by
increasing the sample from 14 to 23 reverberation-mapped AGN using additional
spectroscopy obtained with the Gemini Near-Infrared Spectrograph (GNIRS). The
additional sample improves the number statistics in particular at the high
luminosity end.


  Images of semiconductor `dot in rods' and their small clusters are studied by
measuring the second-order correlation function with a spatially resolving ICCD
camera. This measurement allows one to distinguish between a single dot and a
cluster and, to a certain extent, to estimate the number of dots in a cluster.
A more advanced measurement is proposed, based on higher-order correlations,
enabling more accurate determination of the number of dots in a small cluster.
Nonclassical features of the light emitted by such a cluster are analyzed.


  The Debye-H\"uckel equation is a fundamental physical model in chemical
thermodynamics that describes the free energy (chemical potential, activity) of
an ion in electrolyte solutions at variable salt concentration, temperature,
and pressure. It is based on the linear Poisson-Boltzmann equation that ignores
the steric (finite size), correlation, and polarization effects of ions and
water (or solvent molecules). The Poisson-Fermi theory developed in recent
years takes these effects into account. A generalized Debye-H\"uckel equation
is derived from the Poisson-Fermi theory and is shown to consistently reduce to
the classical equation when these effects vanish in limiting cases. As a
result, a linear fourth-order Poisson-Fermi equation is presented for which
unique solutions are shown to exist for spherically symmetric systems.
Moreover, a generalized Debye length is proposed to include the size effects of
ions and water.


  The non-linear realisation of the semi-direct product of E11 with its vector
representation leads to equation of motions for the fields graviton, three
form, six form, dual graviton and the level four fields which correctly
describe the degree of freedom of eleven dimensional supergravity at the
linearised level. The equations with one derivative generically hold as
equivalence relations and are often duality relations. From these equations, by
taking derivatives, one can derive equations that are equations of motion of
the familiar kind. The entire hierarchy of equations is E11 invariant and the
construction does not require any steps beyond E11. We review these past
developments with an emphasis on the features that have been overlooked in
hep-th:1703.01305, whose alternative approach we also comment on.


  This paper proves the existence of potentials of the first and second kind of
a Frobenius like structure in a frame which encompasses families of
arrangements.
  The frame uses the notion of matroids. For the proof of the existence of the
potentials, a power series ansatz is made. The proof that it works requires
that certain decompositions of tuples of coordinate vector fields are related
by certain elementary transformations. This is shown with a nontrivial result
on matroid partition.


  In this paper, we show how a class of operators used in the analysis of
measures from wavelets and iterated function systems may be understood from a
special family of representations of Cuntz algebras.


  We develop an efficient pricing approach for guaranteed minimum withdrawal
benefits (GMWBs) with continuous withdrawals under a realistic modeling setting
with jump-diffusions and stochastic interest rate. Utilizing an impulse
stochastic control framework, we formulate the no-arbitrage GMWB pricing
problem as a time-dependent Hamilton-Jacobi-Bellman (HJB) Quasi-Variational
Inequality (QVI) having three spatial dimensions with cross derivative terms.
Through a novel numerical approach built upon a combination of a
semi-Lagrangian method and the Green's function of an associated linear partial
integro-differential equation, we develop an $\epsilon$-monotone Fourier
pricing method, where $\epsilon > 0$ is a monotonicity tolerance. Together with
a provable strong comparison result for the HJB-QVI, we mathematically
demonstrate convergence of the proposed scheme to the viscosity solution of the
HJB-QVI as $\epsilon \to 0$. We present a comprehensive study of the impact of
simultaneously considering jumps in the sub-account process and stochastic
interest rate on the no-arbitrage prices and fair insurance fees of GMWBs, as
well as on the holder's optimal withdrawal behaviors.


  The subspaces and subalgebras of B(H) which are hyperreflexive with constant
1 are completely classified. It is shown that there are 1-hyperreflexive
subspaces for which the complete hyperreflexivity constant is strictly greater
than 1. The constants for $\bC T \otimes B(H)$ are analyzed in detail.


  Ferroelectric belongs to an important class of materials showing very
interesting nonlinear optical properties that have a variety of application in
photonic devices In a discrete Hamiltonian, if we consider the space and time
dependence of polarization vectors with an interaction term between two
polarization domains, it gives rise to a nonlinear Klein-Gordon (K-G) equation
that has been shown in some systems [1]. This equation as a governing equation
enables multiple time-scale analysis (MTSA) to be performed on a real
ferroelectric material that reveals new type of information on both linear
(known as soft modes) and the nonlinear parts of frequencies and amplitudes of
oscillations. MTSA was described in a K-G system based on staggered
polarization where more emphasis was given to reveal the presence of intrinsic
localized modes (ILM). Here, detailed results for the first three linear modes
and their frequencies as a 2 function of a wide range of niobium antisite
defects or, impurities in lithium niobate ferroelectric are presented. It is
found that when an external excitation (i.e. the input) is only harmonic in
nature, it could not be ascertained whether the even modes of the solitonic
waves (i.e. the output) will have phase-locking with this type of harmonic
external force.


  We study the richer structures of quasi-one-dimensional Bogoliubov-de Genes
collective excitations of F = 1 spinor Bose-Einstein condensate in a harmonic
trap potential loaded in an optical lattice. Employing a perturbative method we
report general analytical expressions for the confined collective polar and
ferromagnetic Goldstone modes. In both cases the excited eigenfrequencies are
given as function of the 1D effective coupling constants, trap frequency and
optical lattice parameters. It is shown that the main contribution of the
optical lattice laser intensity is to shift the confined phonon frequencies.
Moreover, for high intensities, the excitation spectrum becomes independent of
the self-interaction parameters. We reveal some features of the evolution for
the Goldstone modes as well as the condensate densities from the ferromagnetic
to the polar phases.


  We have used the Monte Carlo (MC) simulation method with Metropolis algorithm
to study the finite temperature phase transition properties of a binary alloy
spherical nanoparticle with radius $r$ of the type $A_{p}B_{1-p}$. The system
consists of two different species of magnetic components, namely, $A$ and $B$,
and the components of the system have been selected $A$ and $B$ to be as
$\sigma = 1/2$ and $S=1$, respectively. A complete picture of phase diagrams,
total magnetizations and susceptibilities in related planes have been
presented, and the main roles of the radius of nanoparticle, active
concentration value of type-$A$ atoms as well as other system parameters on the
thermal and magnetic phase transition features of the considered system have
been discussed in detail. Our MC investigations clearly show that it is
possible to control the critical characteristic behaviors of the system with
the help of adjustable Hamiltonian parameters.


  Motivated by the discovery of floating orbits and the potential to provide
extra constraints on alternative theories, in this paper we derive the
self-force equation for a small compact object moving on an accelerated world
line in a background spacetime which is a solution of the coupled gravitational
and scalar field equations of scalar-tensor theory. In the Einstein frame, the
coupled field equations governing the perturbations sourced by the particle
share the same form as the field equations for perturbations of a scalarvac
spacetime, with both falling under the general class of hyperbolic field
equations studied by Zimmerman and Poisson. Here, we solve the field equations
formally in terms of retarded Green functions, which have explicit
representations as Hadamard forms in the neighbourhood of the world line. Using
a quasi-local expansion of the Hadamard form, we derive the regular solutions
in Fermi normal coordinates according to the Detweiler-Whiting prescription. To
compute the equation of motion, we parameterize the world line in terms of a
mass and "charge", which we define in terms of the original Jordan frame mass,
its derivative, and the parameter which translates the proper time in the
Jordan frame to the Einstein frame. These parameters depend on the value of the
background scalar field and its self-field corrections. The equation of motion
which follows from the regular fields strongly resembles the equation for the
self-force acting on a charged, massive particle in a scalarvac geometry of
general relativity. Unlike the scalar vacuum scenario, the "charge" parameter
in the scalar-tensor self-force equation is time variable and leading to
additional local and tail terms. We also provide evolution equations for the
world line parameters under the influence of the self-fields.


  Basing on the Bohr collective quadrupole Hamiltonian the $A$-dependence of
the Grodzins product is derived and the proportionality coefficient for the
Grodzins relation is evaluated. The result obtained is in a correspondence with
the experimental data.


  This paper begins with an observation that the isospectral leaves of the
signed Toda lattice as well as the Toda flow itself may be constructed from the
Tomei manifolds by cutting and pasting along certain chamber walls inside a
polytope. It is also observed through examples that although there is some
freedom in this procedure of cutting and pasting the manifold and the flow, the
choices that can be made are not arbitrary. We proceed to describe a procedure
that begins with an action of the Weyl group on a set of signs; it uses the
Convexity Theorem in \cite{BFR:90} and combines the resulting polytope with the
chosen Weyl group action to paste together a compact manifold. This manifold
which is obtained carries an action of the Weyl group and a Toda lattice flow
which is related to this action. This construction gives rise to a large family
of compact manifolds which is parametrized by twisted sign actions of the Weyl
group. For example, the trivial action gives rise to Tomei manifolds and the
standard action of the Weyl group on the connected components of a split Cartan
subgroup of a split semisimple real Lie group gives rise to the isospectral
leaves of the signed Toda lattice. This clarifies the connection between the
polytope in the Convexity Theorem and the topology of the compact smooth
manifolds arising from the isospectral leaves of a Toda flow. Furthermore, this
allows us to give a uniform treatment to two very different cases that have
been studied extensively in the literature producing new cases to look at.
Finally we describe the unstable manifolds of the Toda flow for these more
general manifolds and determine which of these give rise to cycles.


  We report the large scale structure and clustering analysis of Ly$\alpha$
emitters (LAEs) and Ly$\alpha$ blobs (LABs) at $z=2.2-2.3$. Using 3,341 LAEs,
117 LABs, and 58 bright (Ly$\alpha$ luminosity $L_{\rm Ly\alpha}>10^{43.4}$ erg
s$^{-1}$) LABs at $z=2.2-2.3$ selected with Subaru/Hyper Suprime-Cam (HSC), we
calculate the LAE overdensity to investigate the large scale structure at
$z=2$. We show that 74% LABs and 78% bright LABs locate in overdense regions,
which is consistent with the trend found by previous studies that LABs
generally locate in overdense regions. We find that one of our 8 fields dubbed
J1349 contains $39/117\approx33\%$ of our LABs and $22/58\approx38\%$ of our
bright LABs. A unique and overdense $24'\times12'$ ($\approx 40\times20$
comoving Mpc$^2$) region in J1349 has 12 LABs (8 bright LABs). By comparing to
SSA22 that is one of the most overdense LAB regions found by previous studies,
we show that the J1349 overdense region contains $\geq 2$ times more bright
LABs than the SSA22 overdense region. We calculate the angular correlation
functions (ACFs) of LAEs and LABs in the unique J1349 field and fit the ACFs
with a power-law function to measure the slopes. The slopes of LAEs and LABs
are similar, while the bright LABs show a $\approx 2$ times larger slope
suggesting that bright LABs are more clustered than faint LABs and LAEs. We
show that the amplitudes of ACFs of LABs are higher than LAEs, which suggests
that LABs have a $\approx 10$ times larger galaxy bias and field-to-field
variance than LAEs. The strong field-to-field variance is consistent with the
large differences of LAB numbers in our 8 fields.


  We report theoretical calculations on the effect of the multiple orbital
contribution in high-order harmonic generation (HHG) from aligned CO$_2$ with
inclusion of macroscopic propagation of harmonic fields in the medium. Our
results show very good agreements with recent experiments for the dynamics of
the minimum in HHG spectra as laser intensity or alignment angle changes.
Calculations are carried out to check how the position of the minimum in HHG
spectra depends on the degrees of molecular alignment, laser focusing
conditions, and the effects of alignment-dependent ionization rates of the
different molecular orbitals. These analyses help to explain why the minima
observed in different experiments may vary.


  We consider effects of motion in cavity quantum electrodynamics experiments
where single cold atoms can now be observed inside the cavity for many Rabi
cycles. We discuss the timescales involved in the problem and the need for good
control of the atomic motion, particularly the heating due to exchange of
excitation between the atom and the cavity, in order to realize nearly unitary
dynamics of the internal atomic states and the cavity mode which is required
for several schemes of current interest such as quantum computing. Using a
simple model we establish ultimate effects of the external atomic degrees of
freedom on the action of quantum gates. The perfomance of the gate is
characterized by a measure based on the entanglement fidelity and the motional
excitation caused by the action of the gate is calculated. We find that schemes
which rely on adiabatic passage, and are not therefore critically dependent on
laser pulse areas, are very much more robust against interaction with the
external degrees of freedom of atoms in the quantum gate.


  In any theory satisfying the no-signaling principle correlations generated
among spatially separated parties in a Bell-type experiment are subject to
certain constraints known as monogamy relations. Recently, in the context of
the black hole information loss problem it was suggested that these monogamy
relations might be violated. This in turn implies that correlations arising in
such a scenario must violate the no-signaling principle and hence can be used
to send classical information between parties. Here, we study the amount of
information that can be sent using such correlations. To this aim, we first
provide a framework associating them with classical channels whose capacities
are then used to quantify the usefulness of these correlations in sending
information. Finally, we determine the minimal amount of information that can
be sent using signaling correlations violating the monogamy relation associated
to the chained Bell inequalities.


  In this work, a study on Variable Neighborhood Search algorithms for
multi-depot dial-a-ride problems is presented. In dial-a-ride problems patients
need to be transported from pre-specified pickup locations to pre-specified
delivery locations, under different considerations. The addressed problem
presents several constraints and features, such as heterogeneous vehicles,
distributed in different depots, and heterogeneous patients. The aim is of
minimizing the total routing cost, while respecting time-window, ride-time,
capacity and route duration constraints. The objective of the study is of
determining the best algorithm configuration in terms of initial solution,
neighborhood and local search procedures. At this aim, two different procedures
for the computation of an initial solution, six different type of neighborhoods
and five local search procedures, where only intra-route changes are made, have
been considered and compared.
  We have also evaluated an "adjusting procedure" that aims to produce feasible
solutions from infeasible solutions with small constraints violations. The
different VNS algorithms have been tested on instances from literature as well
as on random instances arising from a real-world healthcare application.


  The calculations of the p-process in the O/Ne layers of Type II supernovae
are quite successful in reproducung the solar system content of p-nuclides.
They predict, however, a significant underproduction of the rare odd-odd
nuclide 138La. A model for the explosion of a 25 Mo star with solar metallicity
is used to suggest that electron neutrino captures on 138Ba may well be its
most efficient production mechanism. The responsibility of an inadequate
prediction of the 138La and 139La photodisintegration rates in the too low
production of 138La is also examined quantitatively. A detailed discussion of
the theoretical uncertainties in these rates suggest that the required rate
changes are probably too high to be fully plausible. Their measurement would be
most welcome. They would help disentangling the relative contributions of
thermonuclear and neutrino processes to the 138La production.


  In the present work, we study {\alpha} decay and proton emission half-lives
within the modified Gamow-like model, which introduces the effects of the
nucleus's deformation. The calculations show that it is necessary to consider
the deformation in the calculation for nuclei far from the shell. Moreover, we
use the improved model to predict the proton emission half-lives of the nuclei
far from the shell. The calculation results indicate that our model is in good
agreement with most models. Furthermore, the deformed Gamow-like model is used
to find the following neutron magic number. This work is meaningful for future
research on superheavy nuclei.


  The Semi-Parallel Deep Neural Network (SPDNN) idea is explained in this
article and it has been shown that the convergence of the mixed network is very
close to the best network in the set and the generalization of SPDNN is better
than all the parent networks.


  The Ramsey multiplicity problem asks for the minimum asymptotic density of
monochromatic labelled copies of a graph $H$ in a red/blue colouring of the
edges of $K_n$. We introduce an off-diagonal generalization in which the goal
is to minimize a certain weighted sum of the densities of red copies of one
graph and blue copies of another. We build up various properties of this new
notion, including a useful "dual formulation," and use these results to solve
the problem for several pairs of graphs.


  In Effective Field Theory, we describe $\mu\leftrightarrow e$ flavour
changing transitions using an operator basis motivated by experimental
observables. In a six-dimensional subspace probed by $\mu \to e \gamma$, $\mu
\to 3e$ and $\mu\to e$ conversion on nuclei, we derive constraints on the New
Physics scale from past and future experiments, illustrating the
complementarity of the processes in an intuitive way. We also recall that a
precise determination of the scalar quark currents in the nucleon will be
required to distinguish scalar $\mu\to e$ interactions on u-quarks from those
on d-quarks.


  Network Function Virtualization (NFV) has drawn significant attention from
both industry and academia as an important shift in telecommunication service
provisioning. By decoupling Network Functions (NFs) from the physical devices
on which they run, NFV has the potential to lead to significant reductions in
Operating Expenses (OPEX) and Capital Expenses (CAPEX) and facilitate the
deployment of new services with increased agility and faster time-to-value. The
NFV paradigm is still in its infancy and there is a large spectrum of
opportunities for the research community to develop new architectures, systems
and applications, and to evaluate alternatives and trade-offs in developing
technologies for its successful deployment. In this paper, after discussing NFV
and its relationship with complementary fields of Software Defined Networking
(SDN) and cloud computing, we survey the state-of-the-art in NFV, and identify
promising research directions in this area. We also overview key NFV projects,
standardization efforts, early implementations, use cases and commercial
products.


  We present new data obtained with SpIOMM, the imaging Fourier transform
spectrometer attached to the 1.6-m telescope of the Observatoire du
Mont-M\'egantic in Qu\'ebec. Recent technical and data reduction improvements
have significantly increased SpIOMM's capabilities to observe fainter objects
or weaker nebular lines, as well as continuum sources and absorption lines, and
to increase its modulation efficiency in the near ultraviolet. To illustrate
these improvements, we present data on the supernova remnant Cas A, planetary
nebulae M27 and M97, the Wolf-Rayet ring nebula M1-67, spiral galaxies M63 and
NGC 3344, as well as the interacting pair of galaxies Arp 84.


  Enhancement of methane emission measurement techniques is necessary to
address the need for greenhouse gas emissions monitoring. Here we introduce a
gas analyzer designed for remote sensing of atmospheric methane aboard unmanned
aerial vehicles. This device employs the wavelength modulation spectroscopy
approach and quadrature detection of laser radiation scattered from the
underlying surface. Our results demonstrate that the observed correlation
between various signal attributes and the distance to the surface, where laser
radiation scatters, aligns with analytical expectations. Calibrations proved
that the instrument provides reliable methane measurements up to 120 meters
while being lightweight and power efficient. Notably, this device outperforms
its competitors at altitudes exceeding 50 meters, which is safer for piloting.


  Hurwitz algebras are unital composition algebras widely known in algebra and
mathematical physics for their useful applications. In this paper, inspired by
works of Lesenby and Hitzer, we show how to embed all seven Hurwitz algebras
(division and split) in 3D geometric algebras, i.e.
$\mathcal{G}\left(p,q\right)$ with $p+q=3$. This is achieved studying the even
subalgebra, which is always of quaternionic or split-quaternionic type, and the
algebra generated by the pseudoscalar which is always of complex or
split-complex type. Reversion, inversion and Clifford conjugation correspond to
biquaternionic, complex and quaternionic conjugation respectively. Octonionic
algebras, i.e., octonions and split-octonions, are obtained in two ways
introducing two different products, replicating a variation of the
Cayley-Dickson process. Octonionic conjugation is achieved in the geometric
algebra formalism through the involution defined by the full grade inversion.


  The cochlea, the auditory part of the inner ear, is a spiral-shaped organ
with large morphological variability. An individualized assessment of its shape
is essential for clinical applications related to tonotopy and cochlear
implantation. To unambiguously reference morphological parameters, reliable
recognition of the cochlear modiolar axis in computed tomography (CT) images is
required. The conventional method introduces measurement uncertainties, as it
is based on manually selected and difficult to identify landmarks. Herein, we
present an algorithm for robust modiolar axis detection in clinical CT images.
We define the modiolar axis as the rotation component of the kinematic spiral
motion inherent in the cochlear shape. For surface fitting, we use a compact
shape representation in a 7-dimensional kinematic parameter space based on
extended Pl\"ucker coordinates. It is the first time such a kinematic
representation is used for shape analysis in medical images. Robust surface
fitting is achieved with an adapted approximate maximum likelihood method
assuming a Student-t distribution, enabling axis detection even in partially
available surface data. We verify the algorithm performance on a synthetic data
set with cochlear surface subsets. In addition, we perform an experimental
study with four experts in 23 human cochlea CT data sets to compare the
automated detection with the manually found axes. Axes found from co-registered
high resolution micro-CT scans are used for reference. Our experiments show
that the algorithm reduces the alignment error providing more reliable modiolar
axis detection for clinical and research applications.


  The Finite Element Method (FEM) is widely used to solve discrete Partial
Differential Equations (PDEs) in engineering and graphics applications. The
popularity of FEM led to the development of a large family of variants, most of
which require a tetrahedral or hexahedral mesh to construct the basis. While
the theoretical properties of FEM basis (such as convergence rate, stability,
etc.) are well understood under specific assumptions on the mesh quality, their
practical performance, influenced both by the choice of the basis construction
and quality of mesh generation, have not been systematically documented for
large collections of automatically meshed 3D geometries.
  We introduce a set of benchmark problems involving most commonly solved
elliptic PDEs, starting from simple cases with an analytical solution, moving
to commonly used test problem setups, and using manufactured solutions for
thousands of real-world, automatically meshed geometries. For all these cases,
we use state-of-the-art meshing tools to create both tetrahedral and hexahedral
meshes, and compare the performance of different element types for common
elliptic PDEs.
  The goal of his benchmark is to enable comparison of complete FEM pipelines,
from mesh generation to algebraic solver, and exploration of relative impact of
different factors on the overall system performance.


  We study consequences of Lorentz symmetry violation in a z=2 Lifshitz
extension of QED in 3+1 dimensions, and we discuss non-trivial effects of
quantization. Because of the specific power of space momentum in propagators of
the model, dimensional regularization leads to an unusual interpretation of
loop integrals, which are finite even when the space dimension goes to the
integer 3. We check the consistency of the approach by calculating the
(vanishing) corrections to the photon mass and the IR-divergence-free
corrections to the dispersion relation for massless fermions.


  In the field of Judgment Aggrgation, a domain, that is a subset of a
Cartesian power of $\{0,1\}$, is considered to reflect abstract rationality
restrictions on vectors of two-valued judgments on a number of issues. We are
interested in the ways we can aggregate the positions of a set of individuals,
whose positions over each issue form vectors of the domain, by means of
unanimous (idempotent) functions, whose output is again an element of the
domain. Such functions are called non-dictatorial, when their output is not
simply the positions of a single individual. Here, we consider domains
admitting various kinds of non-dictatorial aggregators, which reflect various
properties of majority aggregation: (locally) non-dictatorial, generalized
dictatorships, anonymous, monotone, StrongDem and systematic. We show that
interesting and, in some sense, democratic voting schemes are always provided
by domains that can be described by propositional formulas of specific
syntactic types we define. Furthermore, we show that we can efficiently
recognize such formulas and that, given a domain, we can both efficiently check
if it is described by such a formula and, in case it is, construct it. Our
results fall in the realm of classical results concerning the syntactic
characterization of domains with specific closure properties, like domains
closed under logical AND which are the models of Horn formulas. The techniques
we use to obtain our results draw from judgment aggregation as well as
propositional logic and universal algebra.


  Despite relevance to disparate areas such as cloud microphysics and
tribology, major gaps in the understanding of the structures and phase
transitions of low-dimensional water ice remain. Here we report a first
principles study of confined 2D ice as a function of pressure. We find that at
ambient pressure hexagonal and pentagonal monolayer structures are the two
lowest enthalpy phases identified. Upon mild compression the pentagonal
structure becomes the most stable and persists up to \textit{ca.} 2 GPa at
which point square and rhombic phases are stable. The square phase agrees with
recent experimental observations of square ice confined within graphene sheets.
We also find a double layer AA stacked square ice phase, which clarifies the
difference between experimental observations and earlier force field
simulations. This work provides a fresh perspective on 2D confined ice,
highlighting the sensitivity of the structures observed to both the confining
pressure and width.


  Observations of the B0.2V star tau Scorpii have revealed unusual stellar wind
characteristics: red-shifted absorption in the far-ultraviolet O VI resonance
doublet up to +250 km/s, and extremely hard X-ray emission implying gas at
temperatures in excess of 10^7 K. We describe a phenomenological model to
explain these properties. We assume the wind of tau Sco consists of two
components: ambient gas in which denser clumps are embedded. The clumps are
optically thick in the UV resonance lines primarily responsible for
accelerating the ambient wind. The reduced acceleration causes the clumps to
slow and even infall, all the while being confined by the ram pressure of the
outflowing ambient wind. We calculate detailed trajectories of the clumps in
the ambient stellar wind, accounting for a line radiation driving force and the
momentum deposited by the ambient wind in the form of drag. We show these
clumps will fall back towards the star with velocities of several hundred
km/sec for a broad range of initial conditions. The infalling clumps produce
X-ray emitting plasmas with temperatures in excess of (1-6)x10^7 K in bow
shocks at their leading edge. The infalling material explains the peculiar
red-shifted absorption wings seen in the O VI doublet. The required mass loss
in clumps is 3% - 30% ofthe total mass loss rate. The model developed here can
be generally applied to line-driven outflows with clumps or density
irregularities. (Abstract Abridged)


  We investigate the infrared properties of the IRAS sources not confirmed as
PNe in Van de Steene & Pottasch (1993). We observed 28 objects in the N-band of
which 20 were detected and 5 were resolved. We obtained medium resolution
Br_gamma spectra and we took high resolution JHKL images of these 20 objects.
We critically assessed the identification of the IRAS counterpart in the
images. Of sixteen positively identified objects, seven show Br_gamma in
absorption, another six objects show Br_gamma in emission on top of a
continuum. In another three objects, no clear Br_gamma absorption or emission
was visible. Our detection rate of emission line objects is higher compared to
previous studies. None of the objects with Br_gamma in emission were detected
above a detection limit of 0.6 mJy/beam at 6 cm, while they should have been
easily detected if the radio flux was optically thin and Case B recombination
was applicable. Their SED's are typical for post-AGB stars. We also constructed
various color-color diagrams using the near-infrared and IRAS magnitudes. No
distinction can be made between the objects showing Br_gamma in emission,
absorption, or a flat spectrum in the near and far-infrared color-color
diagrams. The near-infrared color-color diagrams show evidence for a very large
range of extinction, which in part is of circumstellar origin. Near-infrared
versus far-infrared color-color diagrams show trends that are consistent with
the expected evolution of the circumstellar shell. This sample of post-AGB
stars show a larger range in color and are generally closer to the galactic
plane than the ones known so far.


  We compare the results of three binary population synthesis codes to
understand the differences in their results. As a first result we find that
when equalizing the assumptions the results are similar. The main differences
arise from deviating physical input.


  We will reduce the task of creating AI to the task of finding an appropriate
language for description of the world. This will not be a programing language
because programing languages describe only computable functions, while our
language will describe a somewhat broader class of functions. Another
specificity of this language will be that the description will consist of
separate modules. This will enable us look for the description of the world
automatically such that we discover it module after module. Our approach to the
creation of this new language will be to start with a particular world and
write the description of that particular world. The point is that the language
which can describe this particular world will be appropriate for describing any
world.


  We prove several asymptotic vanishing theorems for Frobenius twists of ample
vector bundles in positive characteristic. As an application, we prove a
generalization of the Bott-Danilov-Steenbrink vanishing theorem for ample
vector bundles on toric varieties.


  In magnetic topological insulators, spontaneous time-reversal symmetry
breaking by intrinsic magnetic order can open an energy gap in the topological
surface spectrum. In the resulting state, exotic properties like axion
electrodynamics, the quantum anomalous Hall effect, and other topological
magnetoelectric responses are expected to emerge. A detailed understanding of
the magnetic order and its coupling to the topological surface states is
essential to harness and tune these properties. Here, we leverage near-resonant
electric quadrupole optical second harmonic generation to probe magnetic
fluctuations in the candidate axion insulator EuSn$_2$(As,P)$_2$ across its
antiferromagnetic phase boundary. We observe a pronounced dimensional crossover
in the quantum decoherence induced by magnetic fluctuations, where
two-dimensional in-plane ferromagnetic correlations at high temperatures give
way to three-dimensional long-range order at the N\'eel temperature. We also
observe the breaking of rotational symmetry within the long-range-ordered
antiferromagnetic state and map out the resulting spatial domain structure.
More generally, we demonstrate the unique capabilities of nonlinear optical
spectroscopy to study quantum coherence and fluctuations in magnetic quantum
materials.


  In recent years, the field of implicit neural representation has progressed
significantly. Models such as neural radiance fields (NeRF), which uses
relatively small neural networks, can represent high-quality scenes and achieve
state-of-the-art results for novel view synthesis. Training these types of
networks, however, is still computationally very expensive. We present depth
distribution neural radiance field (DDNeRF), a new method that significantly
increases sampling efficiency along rays during training while achieving
superior results for a given sampling budget. DDNeRF achieves this by learning
a more accurate representation of the density distribution along rays. More
specifically, we train a coarse model to predict the internal distribution of
the transparency of an input volume in addition to the volume's total density.
This finer distribution then guides the sampling procedure of the fine model.
This method allows us to use fewer samples during training while reducing
computational resources.


  EuroCrops contains geo-referenced polygons of agricultural croplands from 16
countries of the European Union (EU) as well as information on the respective
crop species grown there. These semantic annotations are derived from
self-declarations by farmers receiving subsidies under the Common Agriculture
Policy (CAP) of the European Commission (EC). Over the last 1.5 years, the
individual national crop datasets have been manually collected, the crop
classes have been translated into the English language and transferred into the
newly developed Hierarchical Crop and Agriculture Taxonomy (HCAT). EuroCrops is
publicly available under continuous improvement through an active user
community.


  New sharp affine isoperimetric inequalities for volume decomposition
functionals $X_{2}$ and $X_{3}$ in $\mathbb{R}^n$ are established. To fulfil
this task, we prove the recursion formulas for volume decomposition functionals
and find out the connection between the domains of these functionals and
matroid polytopes. Applications of matroid theory to convex geometry are
presented.


  The multilevel Monte Carlo (MLMC) method for continuous-time Markov chains,
first introduced by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1),
2012), is a highly efficient simulation technique that can be used to estimate
various statistical quantities for stochastic reaction networks (SRNs), in
particular for stochastic biological systems. Unfortunately, the robustness and
performance of the multilevel method can be affected by the high kurtosis, a
phenomenon observed at the deep levels of MLMC, which leads to inaccurate
estimates of the sample variance. In this work, we address cases where the
high-kurtosis phenomenon is due to \textit{catastrophic coupling
(characteristic of pure jump processes where coupled consecutive paths are
identical in most of the simulations, while differences only appear in a tiny
proportion) and introduce a pathwise-dependent importance sampling (IS)
technique that improves the robustness and efficiency of the multilevel method.
Our theoretical results, along with the conducted numerical experiments,
demonstrate that our proposed method significantly reduces the kurtosis of the
deep levels of MLMC, and also improves the strong convergence rate from
$\beta=1$ for the standard case (without IS), to $\beta=1+\delta$, where
$0<\delta<1$ is a user-selected parameter in our IS algorithm. Due to the
complexity theorem of MLMC, and given a pre-selected tolerance, $\text{TOL}$,
this results in an improvement of the complexity from
$\mathcal{O}\left(\text{TOL}^{-2} \log(\text{TOL})^2\right)$ in the standard
case to $\mathcal{O}\left(\text{TOL}^{-2}\right)$, which is the optimal
complexity of the MLMC estimator. We achieve all these improvements with a
negligible additional cost since our IS algorithm is only applied a few times
across each simulated path.


  The explicit formulas of operations, in particular addition and
multiplication, of $p $-adic integers are presented. As applications of the
results, at first the explicit formulas of operations of Witt vectors with
coefficients in $\mathbb{F}_{2}$ are given; then, through solving a problem of
Browkin about the transformation between the coefficients of a $p$-adic integer
expressed in the ordinary least residue system and the numerically least
residue system, similar formulas for Witt vectors with coefficients in
$\mathbb{F}_{3}$ are obtained.


  Using geometric properties of the variety $\cV_{r,t}$, the image under the
Grassmannian map of a Desarguesian $(t-1)$-spread of $\PG(rt-1,q)$, we
introduce error correcting codes related to the twisted tensor product
construction, producing several families of constacyclic codes. We exactly
determine the parameters of these codes and characterise the words of minimum
weight.


  The level structure of the transitional nucleus $\mathrm{^{217}Ra}$ has been
extended with the addition of around 20 new transitions. The discrepancies
between the placements of several transitions reported in the earlier studies
are resolved. The newly-established negative-parity sequence at low excitation
energies hints at the expected parity-doublet structures in this nucleus. The
properties of the observed simplex bands are compared with that of similar
bands in neighboring nuclei. Since the presence of parity-doublet structures
reflect octupole correlations, theoretical calculations using
reflection-asymmetric triaxial particle rotor model (RAT-PRM) have been
performed. A comparison of the observed features of the simplex bands with the
predictions of the RAT-PRM calculations suggests that $\mathrm{^{217}Ra}$
exhibits an intermediate the behavior between the extremes of spherical and
octupole-deformed nuclei. The termination of the simplex bands at intermediate
energies and the structures lying above reflect the dominance of the
single-particle excitations at higher excitation energies.


  Topologically protected zero-line modes appear at the interface between two
regions of the monolayer graphene in quantum anomalous Hall phase with
different Chern number. In the presence of staggered sublattice potential, the
band gaps of the two valleys become different, and the phase diagram defined by
the Chern number has an additional regime of topologically trivial phase. The
interface between the topologically trivial and non-trivial regions hosts
zero-line mode in only one valley. By tuning the exchange field, three types of
interface that host zero-line modes in selected valley(s) are formed. The
nano-devices consisted of Y-shape junctions of the three types of interface
exhibit the functions of valley splitting, merging or filtering for the
incident currents.


  We propose an entanglement mean field theory inspired approach for dealing
with interacting classical many-body systems. It involves a coarse-graining
technique that terminates a step before the mean field theory: While mean field
theory deals with only single-body physical parameters, the entanglement mean
field theory deals with single- as well as two-body ones. We improve the theory
to a cluster entanglement mean field, that deals with a fundamental unit of the
lattice of the many-body system. We apply these methods to interacting Ising
spin systems in several lattice geometries and dimensions, and show that the
predictions of the onset of criticality of these models are much better in the
proposed theories as compared to the corresponding ones in mean field theories.


  We investigate the thermodynamics and percolation regimes of model binary
mixtures of patchy colloidal particles. The particles of each species have
three sites of two types, one of which promotes bonding of particles of the
same species while the other promotes bonding of different species. We find up
to four percolated structures at low temperatures and densities: two gels where
only one species percolates, a mixed gel where particles of both species
percolate but neither species percolates separately, and a bicontinuous gel
where particles of both species percolate separately forming two interconnected
networks. The competition between the entropy and the energy of bonding drives
the stability of the different percolating structures. Appropriate mixtures
exhibit one or more connectivity transitions between the mixed and bicontinuous
gels, as the temperature and/or the composition changes.


  Two solvable Hamiltonians for describing the dynamic gamma deformation, are
proposed. The limiting case of each of them is the X(5) Hamiltonian. Analytical
solutions for both energies and wave functions, which are periodic in $\gamma$,
are presented in terms of spheroidal and Mathieu functions, respectively.
Moreover, the gamma depending factors of the transition operator can be
treated.


  Schur's partition theorem states that the number of partitions of n into
distinct parts congruent 1, 2 (mod 3) equals the number of partitions of n into
parts which differ by >= 3, where the inequality is strict if a part is a
multiple of 3. We establish a double bounded refined version of this theorem by
imposing one bound on the parts congruent 0,1 (mod 3) and another on the parts
congruent 2 (mod 3), and by keeping track of the number of parts in each of the
residue classes (mod 3). Despite the long history of Schur's theorem, our
result is new, and extends earlier work of Andrews, Alladi-Gordon and Bressoud.
We give combinatorial and q-theoretic proofs of our result. The special case
L=M leads to a representation of the generating function of the underlying
partitions in terms of the q-trinomial coefficients extending a similar
previous representation of Andrews.


  This paper describes finite dimensionall irreducible representations of both
twisted and untwisted Cartan map Lie superalgebras.


  We study new consistent scalar-tensor theories of gravity recently introduced
by Langlois and Noui with potentially interesting cosmological applications. We
derive the conditions for the existence of a primary constraint that prevents
the propagation of an additional dangerous mode associated with higher order
equations of motion. We then classify the most general, consistent
scalar-tensor theories that are at most quadratic in the second derivatives of
the scalar field. In addition, we investigate the possible connection between
these theories and (beyond) Horndeski through conformal and disformal
transformations. Finally, we point out that these theories can be associated
with new operators in the effective field theory of dark energy, which might
open up new possibilities to test dark energy models in future surveys.


  Decomposition and localization of a supervisor both are reduction methods in
distributed supervisory control of discrete-event systems.Decomposition is
employed to reduce the number of events and localization is used to reduce the
number of states of local controllers.In decomposition of a supervisor both
observation and control scopes are restricted, whereas in localization only
control authority is restricted to the corresponding local controller. In this
paper, we propose a decomposition method by defining coparanormality property,
and by using relative observability property of a monolithic supervisor.
Coparanormality is a coobservation property defined based on paranormality
property for a set of natural projections.It is shown that each supervisor can
be coparanormal, provided a set of appropriate natural projections exist.
Moreover, it is proved that relative observability is a sufficient condition
for decomposition of a supervisor. Furthermore, the supervisor localization
procedure is generalized to find a set of local controllers for any partition
ofthe controllable events set. The implementation of such local controllers may
become easier in industrial systems.


  Graphene is a promising contender to succeed the throne of silicon in
electronics. To this goal, large-scale epitaxial growth of graphene on
substrates should be developed. Among various methods along this line,
epitaxial growth of graphene on SiC substrates by thermal decomposition of
surface layers has proved itself quite satisfactory both in quality and in
process reliability. Even modulation of structural and hence electronic
properties of graphene is possible by tuning the graphene/SiC interface
structure. The challenges for this graphene-on-SiC technology, however, are the
abdication of the well-established Si technologies and the high production cost
of the SiC bulk crystals. Here, we demonstrate that formation of epitaxial
graphene on silicon substrate is possible, by graphitizing epitaxial SiC thin
films formed on silicon substrates. This graphene-on-silicon (GOS) method
enables us to form a large-area film of well-ordered sp2 carbon networks on Si
substrates and to fabricate electronic devices based on the structure.


  Ultra-luminous X-ray sources (ULXs) have been puzzling us with a debate
whether they consist of an intermediate mass black hole or super-Eddington
accretion by a stellar mass black hole. Here we suggest that in the presence of
large scale strong magnetic fields and non-negligible vertical motion, the
luminosity of ULXs, particularly in their hard states, can be explained with
sub-Eddington accretion by stellar mass black holes. In this framework of 2.5D
magnetized advective accretion flows, magnetic tension plays the role of
transporting matter (equivalent to viscous shear via turbulent viscosity) and
we neither require to invoke an intermediate mass black hole nor
super-Eddington accretion. Our model explains the sources, like, NGC 1365
X1/X2, M82 X42.3+59, M99 X1 etc. which are in their hard power-law dominated
states.


  The use of Recurrent Neural Networks (RNNs) for system identification has
recently gathered increasing attention, thanks to their black-box modeling
capabilities.Albeit RNNs have been fruitfully adopted in many applications,
only few works are devoted to provide rigorous theoretical foundations that
justify their use for control purposes. The aim of this paper is to describe
how stable Gated Recurrent Units (GRUs), a particular RNN architecture, can be
trained and employed in a Nonlinear MPC framework to perform offset-free
tracking of constant references with guaranteed closed-loop stability. The
proposed approach is tested on a pH neutralization process benchmark, showing
remarkable performances.


  Deep learning techniques have recently demonstrated broad success in
predicting complex dynamical systems ranging from turbulence to human speech,
motivating broader questions about how neural networks encode and represent
dynamical rules. We explore this problem in the context of cellular automata
(CA), simple dynamical systems that are intrinsically discrete and thus
difficult to analyze using standard tools from dynamical systems theory. We
show that any CA may readily be represented using a convolutional neural
network with a network-in-network architecture. This motivates our development
of a general convolutional multilayer perceptron architecture, which we find
can learn the dynamical rules for arbitrary CA when given videos of the CA as
training data. In the limit of large network widths, we find that training
dynamics are nearly identical across replicates, and that common patterns
emerge in the structure of networks trained on different CA rulesets. We train
ensembles of networks on randomly-sampled CA, and we probe how the trained
networks internally represent the CA rules using an information-theoretic
technique based on distributions of layer activation patterns. We find that CA
with simpler rule tables produce trained networks with hierarchical structure
and layer specialization, while more complex CA produce shallower
representations---illustrating how the underlying complexity of the CA's rules
influences the specificity of these internal representations. Our results
suggest how the entropy of a physical process can affect its representation
when learned by neural networks.


  To see the feasibility of a large-scale quantum computing, it is required to
accurately analyze the performance and the quantum resource. However, most of
the analysis reported so far have focused on the statistical examination, i.e.,
simply calculating the performance and resource based on individual data, and
even worse usually only a few components have been considered. In this work, to
achieve more exact analysis, we propose an integrated analysis method for a
practical quantum computing model with three components (\textit{algorithm},
\textit{error correction} and \textit{device}) under a realistic quantum
computer system architecture. To implement the above method, we develop a
quantum computing framework composed of three functional layers: compile,
system and building block. This framework can support, for the first time, the
mapping of quantum algorithm from physical qubit level to system architecture
level with a given fault-tolerant scheme. Therefore, the proposed method can
measure the effect of dynamic situation when the quantum computer practically
runs. By using our method, we found that Shor algorithm to factorize 512-bit
integer requires $8.78\times 10^ 5$ hours. We also show how the proposed method
can be used for analyzing optimal concatenation level and code distance of
fault-tolerant quantum computing.


  In this paper, we investigate the transmission probabilities in three cases
(depending only on the legitimate receiver, depending only the eavesdropper,
and depending on both legitimate receiver and eavesdropper) in quantum key
distribution (QKD) systems over free-space optical links. To be more realistic,
we consider a generalized pointing error scenario, where the azimuth and
elevation pointing error angles caused by stochastic jitters and vibrations in
the legitimate receiver platform are independently distributed according to a
non-identical normal distribution. Taking these assumptions into account, we
derive approximate expressions of transmission probabilities by using the
Gaussian quadrature method. To simplify the expressions and get some physical
insights, some asymptotic analysis on the transmission probabilities is
presented based on asymptotic expression for the generalized Marcum Q-function
when the telescope gain at the legitimate receiver approaches to infinity.
Moreover, from the asymptotic expression for the generalized Marcum Q-function,
the asymptotic outage probability over Beckmann fading channels (a general
channel model including Rayleigh, Rice, and Hoyt fading channels) can be also
easily derived when the average signal-to-noise ratio is sufficiently large,
which shows the diversity order and array gain.


  We investigate the combined effects of boundaries and topology on the vacuum
expectation values (VEVs) of the charge and current densities for a massive 2D
fermionic field confined on a conical ring threaded by a magnetic flux.
Different types of boundary conditions on the ring edges are considered for
fields realizing two inequivalent irreducible representations of the Clifford
algebra. The related bound states and zero energy fermionic modes are
discussed. The edge contributions to the VEVs of the charge and azimuthal
current densities are explicitly extracted and their behavior in various
asymptotic limits is considered. On the ring edges the azimuthal current
density is equal to the charge density or has an opposite sign. We show that
the absolute values of the charge and current densities increase with
increasing planar angle deficit. Depending on the boundary conditions, the VEVs
are continuous or discontinuous at half-integer values of the ratio of the
effective magnetic flux to the flux quantum. The discontinuity is related to
the presence of the zero energy mode. By combining the results for the fields
realizing the irreducible representations of the Clifford algebra, the charge
and current densities are studied in parity and time-reversal symmetric
fermionic models. If the boundary conditions and the phases in quasiperiodicity
conditions for separate fields are the same the total charge density vanishes.
Applications are given to graphitic cones with edges (conical ribbons).


  We examine the parametrization of the QCD coupling in the Evolution
Equations, including DGLAP. Our conclusion is that the well-known
parametrization, where the argument of the coupling is k^2_{\perp}/\beta or
just k^2_{\perp}, stands only if the lowest integration limit in the transverse
momentum space (the starting point mu^2 of the Q^2 -evolution) obeys the
relation mu >> Lambda_{QCD} \exp {(\pi/2)}, otherwise the coupling should be
replaced by the more complicated expression presented in Eq. (37).


  We develop a simulation procedure for angle-resolved photoemission
spectroscopy (ARPES), where a photoelectron wave function is set to be an
outgoing plane wave in a vacuum associated with the emitted photoelectron wave
packet. ARPES measurements on the transition metal dichalcogenide
$1T$-$\mathrm{Ti}\mathrm{S}_2$ are performed, and our simulations exhibit good
agreement with experiments. Analysis of our calculated final state wave
functions quantitatively visualizes that they include various waves due to the
boundary condition and the uneven crystal potential. These results show that a
more detailed investigation of the photoelectron final states is necessary to
fully explain the photon-energy- and light-polarization-dependent ARPES
spectra.


  Motivated by the sign problem in several systems, we have developed a
geometric simulation algorithm based on the strong coupling expansion which can
be applied to abelian pure gauge models. We have studied the algorithm in the
U(1) model in 3 and 4 dimensions, and seen that it is practical and is
similarly efficient to the standard heat-bath algorithm, but without the
ergodicity problems which comes from the presence of vortices. We have also
applied the algorithm to the Ising gauge model at the critical point, and we
find hints of a better asymptotic behaviour of the autocorrelation time, which
therefore suggests the possibility of a smaller dynamical critical exponent
with respect to the standard heat-bath algorithm.