  The solution of a boundary--value problem formulated for the Kretschmann
configuration shows that the phase speed of a surface--plasmon--polariton (SPP)
wave guided by the planar interface of a sufficiently thin metal film and a
sculptured thin film (STF) depends on the vapor incidence angle used while
fabricating the STF by physical vapor deposition. Furthermore, it may be
possible to engineer the phase speed by periodically varying the vapor
incidence angle. The phase speed of the SPP wave can be set by selecting higher
mean value and/or the modulation amplitude of the vapor incidence angle.


  Let R be a Cohen-Macaulay ring and M a maximal Cohen-Macaulay R-module.
Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and Van
den Bergh we study the question of when the endomorphism ring of M has finite
global dimension via certain conditions about vanishing of $\Ext$ modules. We
are able to strengthen certain results by Iyama on connections between a higher
dimension version of Auslander correspondence and existence of non-commutative
crepant resolutions. We also recover and extend to positive characteristics a
recent Theorem by Burban-Iyama-Keller-Reiten on cluster-tilting objects in the
category of maximal Cohen-Macaulay modules over reduced 1-dimensional
hypersurfaces.


  We apply the probability distribution function method to the study of chiral
properties of QCD with quarks in the exact massless limit. A relation among the
chiral condensate, zeros of the Bessel function and eigenvalue of Dirac
operator is also given. The chiral condensate in this limit can be measured
with small number of eigenvalues of the massless Dirac operator and without any
ambiguous mass extrapolation. Results for SU(3) gauge theory with quenched
Kogut-Susskind quarks on the $10^4$ lattice are shown.


  The classical theorem of F\'{a}ry states that every planar graph can be
represented by an embedding in which every edge is represented by a straight
line segment. We consider generalizations of F\'{a}ry's theorem to surfaces
equipped with Riemannian metrics. In this setting, we require that every edge
is drawn as a shortest path between its two endpoints and we call an embedding
with this property a shortest path embedding. The main question addressed in
this paper is whether given a closed surface S, there exists a Riemannian
metric for which every topologically embeddable graph admits a shortest path
embedding. This question is also motivated by various problems regarding
crossing numbers on surfaces.
  We observe that the round metrics on the sphere and the projective plane have
this property. We provide flat metrics on the torus and the Klein bottle which
also have this property.
  Then we show that for the unit square flat metric on the Klein bottle there
exists a graph without shortest path embeddings. We show, moreover, that for
large g, there exist graphs G embeddable into the orientable surface of genus
g, such that with large probability a random hyperbolic metric does not admit a
shortest path embedding of G, where the probability measure is proportional to
the Weil-Petersson volume on moduli space.
  Finally, we construct a hyperbolic metric on every orientable surface S of
genus g, such that every graph embeddable into S can be embedded so that every
edge is a concatenation of at most O(g) shortest paths.


  Together with the existence of new neutral gauge bosons, models based on
extended gauge groups (rank $> 4$) often predict also new charged fermions. A
mixing of the known fermions with new states with {\it exotic} weak-isospin
assignments (left-handed singlets and right-handed doublets) will induce tree
level flavour changing neutral interactions mediated by $Z$ exchange, while if
the mixing is only with new states with {\it ordinary} weak-isospin
assignments, the flavour changing neutral currents are mainly due to the
exchange of the lightest new neutral gauge boson $Z^\prime$. We show that the
present experimental limits on $\mu-e$ conversion in nuclei give a
nuclear-model-independent bound on the $Z$-$e$-$\mu$ vertex which is twice as
strong as that obtained from $\mu\to e e e$. In the case of E$_6$ models these
limits provide quite stringent constraints on the $Z^\prime$ mass and on the
$Z-Z^\prime$ mixing angle. We point out that the proposed experiments to search
for $\mu-e$ conversion in nuclei have good chances to find evidence of lepton
flavour violation, either in the case that new exotic fermions are present at
the electroweak scale, or if a new neutral gauge boson $Z^\prime$ of E$_6$
origin lighter than a few TeV exists.


  We propose an approach to address two issues that commonly occur during
training of unsupervised GANs. First, since GANs use only a continuous latent
distribution to embed multiple classes or clusters of data, they often do not
correctly handle the structural discontinuity between disparate classes in a
latent space. Second, discriminators of GANs easily forget about past generated
samples by generators, incurring instability during adversarial training. We
argue that these two infamous problems of unsupervised GAN training can be
largely alleviated by a learnable memory network to which both generators and
discriminators can access. Generators can effectively learn representation of
training samples to understand underlying cluster distributions of data, which
ease the structure discontinuity problem. At the same time, discriminators can
better memorize clusters of previously generated samples, which mitigate the
forgetting problem. We propose a novel end-to-end GAN model named memoryGAN,
which involves a memory network that is unsupervisedly trainable and integrable
to many existing GAN models. With evaluations on multiple datasets such as
Fashion-MNIST, CelebA, CIFAR10, and Chairs, we show that our model is
probabilistically interpretable, and generates realistic image samples of high
visual fidelity. The memoryGAN also achieves the state-of-the-art inception
scores over unsupervised GAN models on the CIFAR10 dataset, without any
optimization tricks and weaker divergences.


  Let $M$ be a compact, connected symplectic manifold with a Hamiltonian action
of a compact $n$-dimensional torus $G=T^n$. Suppose that $\sigma$ is an
anti-symplectic involution compatible with the $G$-action. The real locus of
$M$ is $X$, the fixed point set of $\sigma$. Duistermaat uses Morse theory to
give a description of the ordinary cohomology of $X$ in terms of the cohomology
of $M$. There is a residual $\G=(\Zt)^n$ action on $X$, and we can use
Duistermaat's result, as well as some general facts about equivariant
cohomology, to prove an equivariant analogue to Duistermaat's theorem. In some
cases, we can also extend theorems of Goresky-Kottwitz-MacPherson and
Goldin-Holm to the real locus.


  Laser based ranging (LiDAR) - already ubiquitously used in industrial
monitoring, atmospheric dynamics, or geodesy - is key sensor technology.
Coherent laser ranging, in contrast to time-of-flight approaches, is immune to
ambient light, operates continuous wave allowing higher average powers, and
yields simultaneous velocity and distance information. State-of-the-art
coherent single laser-detector architectures reach hundreds of kilopixel per
second rates. While emerging applications such as autonomous driving, robotics,
and augmented reality mandate megapixel per second point sampling to support
real-time video-rate imaging. Yet, such rates of coherent LiDAR have not been
demonstrated. Here we report a swept dual-soliton microcomb technique enabling
coherent ranging and velocimetry at megapixel per second line scan measurement
rates with up to 64 spectrally dispersed optical channels. It is based on
recent advances in photonic chip-based microcombs that offer a solution to
reduce complexity both on the transmitter and receiver sides.
Multi-heterodyning two synchronously frequency-modulated microcombs yields
distance and velocity information of all individual ranging channels on a
single receiver alleviating the need for individual separation, detection, and
digitization. The reported LiDAR implementation is hardware-efficient,
compatible with photonic integration, and demonstrates the significant
advantages of acquisition speed afforded by the convergence of optical
telecommunication and metrology technologies. We anticipate our research will
motivate further investigation of frequency swept microresonator dual-comb
approach in the neighboring fields of linear and nonlinear spectroscopy,
optical coherence tomography.


  Sensitivity analysis measures the influence of a Bayesian network's
parameters on a quantity of interest defined by the network, such as the
probability of a variable taking a specific value. In particular, the so-called
sensitivity value measures the quantity of interest's partial derivative with
respect to the network's conditional probabilities. However, finding such
values in large networks with thousands of parameters can become
computationally very expensive. We propose to use automatic differentiation
combined with exact inference to obtain all sensitivity values in a single
pass. Our method first marginalizes the whole network once using e.g. variable
elimination and then backpropagates this operation to obtain the gradient with
respect to all input parameters. We demonstrate our routines by ranking all
parameters by importance on a Bayesian network modeling humanitarian crises and
disasters, and then show the method's efficiency by scaling it to huge networks
with up to 100'000 parameters. An implementation of the methods using the
popular machine learning library PyTorch is freely available.


  The Spitzer Space Telescope has advanced debris disk science tremendously
with a wealth of information on debris disks around nearby A, F, G, K and M
stars at 24 and 70 microns with the MIPS photometer and at 8-34 microns with
IRS. Here we present 160 micron observations of a small sub-set of these stars.
At this wavelength, the stellar photospheric emission is negligible and any
detected emission corresponds to cold dust in extended Kuiper belt analogs.
However, the Spitzer 160 micron observations are limited in sensitivity by the
large beam size which results in significant ''noise'' due to cirrus and
extragalactic confusion. In addition, the 160 micron measurements suffer from
the added complication of a light leak next to the star's position whose flux
is proportional to the near-infrared flux of the star. We are able to remove
the contamination from the leak and report 160 micron measurements or upper
limits for 24 stars. Three stars (HD 10647, HD 207129, and HD 115617) have
excesses at 160 micron that we use to constrain the properties of the debris
disks around them. A more detailed model of the spectral energy distribution of
HD 10647 reveals that the 70 and 160 micron emission could be due to small
water ice particles at a distance of 100 AU consistent with Hubble Space
Telescope optical imaging of circumstellar material in the system.


  With the advent of evolution of cloud computing, large organizations have
been scaling the on-premise IT infrastructure to the cloud. Although this being
a popular practice, it lacks comprehensive efforts to study the aspects of
automated negotiation of resources among cloud customers and providers. This
paper proposes a full-fledged framework for the multi-party, multi-issue
negotiation system for cloud resources. It introduces a robust cloud
marketplace system to buy and sell cloud resources. The Belief-Desire-Intention
(BDI) model-based cloud customer and provider agents concurrently negotiate on
multiple issues, pursuing a hybrid tactic of time and resource-based dynamic
deadline algorithms to generate offers and counter-offers. The cloud
marketplace-based system is further augmented with the assignment of behavior
norm score and reputation index to the agents to establish trust among them.


  The surfaces of neutron stars are likely sources of strongly polarized soft X
rays due to the presence of strong magnetic fields. Scattering transport in the
surface layers is critical to the determination of the emergent anisotropy of
light intensity, and is strongly influenced by the complicated interplay
between linear and circular polarization information. We have developed a
magnetic Thomson scattering simulation to model the outer layers of
fully-ionized atmospheres in such compact objects. Here we summarize emergent
intensities and polarizations from extended atmospheric simulations, spanning
considerable ranges of magnetic colatitudes. General relativistic propagation
of light from the surface to infinity is fully included. The net polarization
degrees are moderate and not very small when summing over a variety of field
directions. These results provide an important foundation for observations of
magnetars to be acquired by NASA's new IXPE X-ray polarimeter and future X-ray
polarimetry missions.


  In recent years, messages and text posted on the Internet are used in
criminal investigations. Unfortunately, the authorship of many of them remains
unknown. In some channels, the problem of establishing authorship may be even
harder, since the length of digital texts is limited to a certain number of
characters. In this work, we aim at identifying authors of tweet messages,
which are limited to 280 characters. We evaluate popular features employed
traditionally in authorship attribution which capture properties of the writing
style at different levels. We use for our experiments a self-captured database
of 40 users, with 120 to 200 tweets per user. Results using this small set are
promising, with the different features providing a classification accuracy
between 92% and 98.5%. These results are competitive in comparison to existing
studies which employ short texts such as tweets or SMS.


  Let G be a semisimple Lie group without compact factors, \Gamma be an
irreducible lattice in G. In the first part of the article we give the
necessary and sufficient condition under which a sequence of translates of
probability "horospherical measures" is convergent. And the limiting measure is
also determined when it is convergent (see Theorems 1 and 2 for the precise
statements). In the second part, two applications are presented. The first one
is of geometric nature and the second one gives an alternative way to count the
number of rational points on a flag variety.


  We consider the following query answering problem: Given a Boolean
conjunctive query and a theory in the Horn loosely guarded fragment, the aim is
to determine whether the query is entailed by the theory. In this paper, we
present a resolution decision procedure for the loosely guarded fragment, and
use such a procedure to answer Boolean conjunctive queries against the Horn
loosely guarded fragment. The Horn loosely guarded fragment subsumes classes of
rules that are prevalent in ontology-based query answering, such as Horn ALCHOI
and guarded existential rules. Additionally, we identify star queries and cloud
queries, which using our procedure, can be answered against the loosely guarded
fragment.


  Dynamic Fault Trees (DFT) are widely adopted in industry to assess the
dependability of safety-critical equipment. Since many systems are too large to
be studied numerically, DFTs dependability is often analysed using Monte Carlo
simulation. A bottleneck here is that many simulation samples are required in
the case of rare events, e.g. in highly reliable systems where components fail
seldomly. Rare Event Simulation (RES) provides techniques to reduce the number
of samples in the case of rare events. We present a RES technique based on
importance splitting, to study failures in highly reliable DFTs. Whereas RES
usually requires meta-information from an expert, our method is fully
automatic: by cleverly exploiting the fault tree structure we extract the
so-called importance function. We handle DFTs with Markovian and non-Markovian
failure and repair distributions (for which no numerical methods exist) and
show the efficiency of our approach on several case studies.


  We perform direct 3-dimensional numerical simulations for magnetohydrodynamic
(MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform
magnetic fields. We use a pseudo-spectral code with hyperviscosity and
hyperdiffusivity to solve the incompressible MHD equations. We analyze the
structure of the eddies as a function of scale. A straightforward calculation
of anisotropy in wavevector space shows that the anisotropy is scale-{\it
independent}. We discuss why this is {\it not} the true scaling law and how the
curvature of large-scale magnetic fields affects the power spectrum and leads
to the wrong conclusion. When we correct for this effect, we find that the
anisotropy of eddies depends on their size: smaller eddies are more elongated
than larger ones along {\it local} magnetic field lines. The results are
consistent with the scaling law $\tilde{k}_{\parallel} \sim
\tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here
$\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to
the local magnetic field direction. However, we see some systematic deviations
which may be a sign of limitations to the model, or our inability to fully
resolve the inertial range of turbulence in our simulations.


  We show the existence and optimal regularity of the optimal temperature
configuration in a problem in heat conduction with minimal temperature
constraint, interior heating and exterior insulation. Regularity of the two
free boundaries is also studied.


  Designing reinforcement learning (RL) problems that can produce delicate and
precise manipulation policies requires careful choice of the reward function,
state, and action spaces. Much prior work on applying RL to manipulation tasks
has defined the action space in terms of direct joint torques or reference
positions for a joint-space proportional derivative (PD) controller. In
practice, it is often possible to add additional structure by taking advantage
of model-based controllers that support both accurate positioning and control
of the dynamic response of the manipulator. In this paper, we evaluate how the
choice of action space for dynamic manipulation tasks affects the sample
complexity as well as the final quality of learned policies. We compare
learning performance across three tasks (peg insertion, hammering, and
pushing), four action spaces (torque, joint PD, inverse dynamics, and impedance
control), and using two modern reinforcement learning algorithms (Proximal
Policy Optimization and Soft Actor-Critic). Our results lend support to the
hypothesis that learning references for a task-space impedance controller
significantly reduces the number of samples needed to achieve good performance
across all tasks and algorithms.


  We demonstrate that current state-of-the-art approaches to Automated Essay
Scoring (AES) are not well-suited to capturing adversarially crafted input of
grammatical but incoherent sequences of sentences. We develop a neural model of
local coherence that can effectively learn connectedness features between
sentences, and propose a framework for integrating and jointly training the
local coherence model with a state-of-the-art AES model. We evaluate our
approach against a number of baselines and experimentally demonstrate its
effectiveness on both the AES task and the task of flagging adversarial input,
further contributing to the development of an approach that strengthens the
validity of neural essay scoring models.


  Observations indicate that massive stars form in regions of very high surface
density, ~1 g cm^-2. Clusters containing massive stars and globular clusters
have a comparable column density. The total pressure in clouds of such a column
density is P/k~10^8-10^9 K cm^-3, far greater than that in the diffuse ISM or
the average in GMCs. Observations show that massive star-forming regions are
supersonically turbulent, and we show that the molecular cores out of which
individual massive stars form are as well. The protostellar accretion rate in
such a core is approximately equal to the instantaneous mass of the star
divided by the free-fall time of the gas that is accreting onto the star
(Stahler, Shu, & Taam 1980). The star-formation time in this Turbulent Core
model for massive star formation is several mean free-fall timesscales of the
core, but is about equal to that of the region in which the core is embedded.
The typical time for a massive star to form is about 10^5 yr and the accretion
rate is high enough to overcome radiation pressure due to the luminosity of the
star. For the typical case we consider, in which the cores out of which the
stars form have a density structure varying as r^{-1.5}, the protostellar
accretion rate grows linearly with time. We calculate the evolution of the
radius of a protostar and determine the accretion luminosity. At the high
accretion rates that are typical in regions of massive star formation,
protostars join the main sequence at about 20 solar masses. We apply these
results to predict the properties of protostars thought to be powering several
observed hot molecular cores, including the Orion hot core and W3(H2O). In the
Appendixes, we discuss the pressure in molecular clouds and we argue that
``logatropic'' models for molecular clouds are incompatible with observation.


  The death toll for Covid-19 may be reduced by dividing the population into
two classes, the vulnerable and the fit, with different lockdown regimes.
Instead of one reproduction number there now are four parameters. These make it
possible to quantify the effect of the social distancing measures. There is a
simple stochastic model for epidemics in a two type population. Apart from the
size of the population of the vulnerable and the fit, and the initial number of
infected in the two classes, only the four reproduction parameters are needed
to run the two type Reed-Frost model. The program is simple and fast. On a pc
it takes less than five minutes to do a hundred thousand simulations of the
epidemic for a population of the size of the US. Epidemics are non-linear
processes. Results may be counterintuitive. The average number of vulnerable
persons infected by an infectious fit person is a crucial parameter of the
epidemic in the two type population. Intuitively this parameter should be
small. However simulations show that even if this parameter is small the death
toll may be higher than without shielding. Under certain conditions increasing
the value of the parameter may reduce the death toll. The article addresses
these blind spots in our intuition.


  Multi-modal fusion of sensors is a commonly used approach to enhance the
performance of odometry estimation, which is also a fundamental module for
mobile robots. However, the question of \textit{how to perform fusion among
different modalities in a supervised sensor fusion odometry estimation task?}
is still one of challenging issues remains. Some simple operations, such as
element-wise summation and concatenation, are not capable of assigning adaptive
attentional weights to incorporate different modalities efficiently, which make
it difficult to achieve competitive odometry results. Recently, the Transformer
architecture has shown potential for multi-modal fusion tasks, particularly in
the domains of vision with language. In this work, we propose an end-to-end
supervised Transformer-based LiDAR-Inertial fusion framework (namely
TransFusionOdom) for odometry estimation. The multi-attention fusion module
demonstrates different fusion approaches for homogeneous and heterogeneous
modalities to address the overfitting problem that can arise from blindly
increasing the complexity of the model. Additionally, to interpret the learning
process of the Transformer-based multi-modal interactions, a general
visualization approach is introduced to illustrate the interactions between
modalities. Moreover, exhaustive ablation studies evaluate different
multi-modal fusion strategies to verify the performance of the proposed fusion
strategy. A synthetic multi-modal dataset is made public to validate the
generalization ability of the proposed fusion strategy, which also works for
other combinations of different modalities. The quantitative and qualitative
odometry evaluations on the KITTI dataset verify the proposed TransFusionOdom
could achieve superior performance compared with other related works.


  We study the dynamics of massive black hole pairs in clumpy gaseous
circumnuclear disks. We track the orbital decay of the light, secondary black
hole $M_{\bullet2}$ orbiting around the more massive primary at the center of
the disk, using $N$-body/smoothed particle hydrodynamic simulations. We find
that the gravitational interaction of $M_{\bullet2}$ with massive clumps
$M_{\rm cl}$ erratically perturbs the otherwise smooth orbital decay. In close
encounters with massive clumps, gravitational slingshots can kick the secondary
black hole out of the disk plane. The black hole moving on an inclined orbit
then experiences the weaker dynamical friction of the stellar background,
resulting in a longer orbital decay timescale. Interactions between clumps can
also favor orbital decay when the black hole is captured by a massive clump
which is segregating toward the center of the disk. The stochastic behavior of
the black hole orbit emerges mainly when the ratio $M_{\bullet2}/M_{\rm cl}$
falls below unity, with decay timescales ranging from $\sim1$ to $\sim50$ Myr.
This suggests that describing the cold clumpy phase of the inter-stellar medium
in self-consistent simulations of galaxy mergers, albeit so far neglected, is
important to predict the black hole dynamics in galaxy merger remnants.


  The biplanar crossing number of a graph $G$ is the minimum number of
crossings over all possible drawings of the edges of $G$ in two disjoint
planes. We present new bounds on the biplanar crossing number of complete
graphs and complete bipartite graphs. In particular, we prove that the biplanar
crossing number of complete bipartite graphs can be approximated to within a
factor of $3$, improving over the best previously known approximation factor of
$4.03$. For complete graphs, we provide a new approximation factor of $3.17$,
improving over the best previous factor of $4.34$. We provide similar improved
approximation factors for the $k$-planar crossing number of complete graphs and
complete bipartite graphs, for any positive integer $k$. We also investigate
the relation between (ordinary) crossing number and biplanar crossing number of
general graphs in more depth, and prove that any graph with a crossing number
of at most $10$ is biplanar.


  Dimensional flow, the scale dependence of the dimensionality of spacetime, is
a feature shared by many theories of quantum gravity (QG). We present the first
study of the consequences of QG dimensional flow for the luminosity distance
scaling of gravitational waves in the frequency ranges of LIGO and LISA. We
find generic modifications with respect to the standard general-relativistic
scaling, largely independent of specific QG proposals. We constrain these
effects using two examples of multimessenger standard sirens, the binary
neutron-star merger GW170817 and a simulated supermassive black-hole merger
event detectable with LISA. We apply these constraints to various QG
candidates, finding that the quantum geometries of group field theory, spin
foams and loop quantum gravity can give rise to observable signals in the
gravitational-wave spin-2 sector. Our results complement and improve GW
propagation-speed bounds on modified dispersion relations. Under more
model-dependent assumptions, we also show that bounds on quantum geometry can
be strengthened by solar-system tests.


  Recent self-consistent mean-field calculations predict a substantial
depletion of the proton density in the interior of 34Si. In the present study,
we investigate how correlations beyond the mean field modify this finding. The
framework of the calculation is a particle-number and angular-momentum
projected Generator Coordinate Method based on
Hartree-Fock-Bogoliubov+Lipkin-Nogami states with axial quadrupole deformation.
The parametrization SLy4 of the Skyrme energy density functional is used
together with a density-dependent pairing energy functional. For the first
time, the generator coordinate method is applied to the calculation of charge
and transition densities. The impact of pairing correlations, symmetry
restorations and shape mixing on the density profile is analyzed step by step.
All these effects significantly alter the radial density profile, and tend to
bring it closer to a Fermi-type density distribution.


  The emission from a gamma-ray burst (GRB) photosphere can give rise to a
variety of spectral shapes. The spectrum can retain the shape of a Planck
function or it can be broadened and have the shape of a Band function. This
fact is best illustrated by studying GRB090902B: The main gamma-ray spectral
component is initially close to a Planck function, which can only be explained
by emission from the jet photosphere. Later, the same component evolves into a
broader Band function. This burst thus provides observational evidence that the
photosphere can give rise to a non-thermal spectrum. We show that such a
broadening is most naturally explained by subphotospheric dissipation in the
jet. The broadening mainly depends on the strength and location of the
dissipation, on the magnetic field strength, and on the relation between the
energy densities of thermal photons and of the electrons. We suggest that the
evolution in spectral shape observed in GRB090902B is due to a decrease of the
bulk Lorentz factor of the flow, leading to the main dissipation becoming
subphotospheric. Such a change in the flow parameters can also explain the
correlation observed between the peak energy of the spectrum and low-energy
power law slope, alpha, a correlation commonly observed in GRBs. We conclude
that photospheric emission could indeed be a ubiquitous feature during the
prompt phase in GRBs and play a decisive role in creating the diverse spectral
shapes and spectral evolutions that are observed.


  We investigate the (linearized) Morse index of solutions to Hamiltonan
systems, with a focus on convex Hamiltonians functions and sign-changing radial
solutions. For strongly coupled systems, we describe the profile of the radial
solutions and give an estimate of their Morse index.


  In this paper we study how the (normalised) Gagliardo semi-norms
$[u]_{W^{s,p} (\mathbb{R}^n)}$ control translations. In particular, we prove
that $\| u(\cdot + y) - u \|_{L^p (\mathbb{R}^n)} \le C [ u ] _{W^{s,p}
(\mathbb{R}^n)} |y|^s$ for $n\geq1$, $s \in [0,1]$ and $p \in [1,+\infty]$,
where $C$ depends only on $n$. We then obtain a corresponding higher-order
version of this result: we get fractional rates of the error term in the Taylor
expansion. We also present relevant implications of our two results. First, we
obtain a direct proof of several compact embedding of $W^{s,p}(\mathbb{R}^n)$
where the Fr\'echet-Kolmogorov Theorem is applied with known rates. We also
derive fractional rates of convergence of the convolution of a function with
suitable mollifiers. Thirdly, we obtain fractional rates of convergence of
finite-difference discretizations for $W^{s,p} (\mathbb{R}^n))$.


  Lifelong learning agents aim to learn multiple tasks sequentially over a
lifetime. This involves the ability to exploit previous knowledge when learning
new tasks and to avoid forgetting. Modulating masks, a specific type of
parameter isolation approach, have recently shown promise in both supervised
and reinforcement learning. While lifelong learning algorithms have been
investigated mainly within a single-agent approach, a question remains on how
multiple agents can share lifelong learning knowledge with each other. We show
that the parameter isolation mechanism used by modulating masks is particularly
suitable for exchanging knowledge among agents in a distributed and
decentralized system of lifelong learners. The key idea is that the isolation
of specific task knowledge to specific masks allows agents to transfer only
specific knowledge on-demand, resulting in robust and effective distributed
lifelong learning. We assume fully distributed and asynchronous scenarios with
dynamic agent numbers and connectivity. An on-demand communication protocol
ensures agents query their peers for specific masks to be transferred and
integrated into their policies when facing each task. Experiments indicate that
on-demand mask communication is an effective way to implement distributed
lifelong reinforcement learning and provides a lifelong learning benefit with
respect to distributed RL baselines such as DD-PPO, IMPALA, and PPO+EWC. The
system is particularly robust to connection drops and demonstrates rapid
learning due to knowledge exchange.


  Let the pair of operators, $(H, T)$, satisfy the weak Weyl relation:
$Te^{-itH} = e^{-itH}(T + t)$, where $H$ is self-adjoint and $T$ is closed
symmetric. Suppose that g is a realvalued Lebesgue measurable function on $\RR$
such that $g \in C^2(R K)$ for some closed subset $K \subset \RR$ with Lebesgue
measure zero. Then we can construct a closed symmetric operator $D$ such that
$(g(H), D)$ also obeys the weak Weyl relation.


  Software development teams have to face stress caused by deadlines, staff
turnover, or individual differences in commitment, expertise, and time zones.
While students are typically taught the theory of software project management,
their exposure to such stress factors is usually limited. However, preparing
students for the stress they will have to endure once they work in project
teams is important for their own sake, as well as for the sake of team
performance in the face of stress. Team performance has been linked to the
diversity of software development teams, but little is known about how
diversity influences the stress experienced in teams. In order to shed light on
this aspect, we provided students with the opportunity to self-experience the
basics of project management in self-organizing teams, and studied the impact
of six diversity dimensions on team performance, coping with stressors, and
positive perceived learning effects. Three controlled experiments at two
universities with a total of 65 participants suggest that the social background
impacts the perceived stressors the most, while age and work experience have
the highest impact on perceived learnings. Most diversity dimensions have a
medium correlation with the quality of work, yet no significant relation to the
team performance. This lays the foundation to improve students' training for
software engineering teamwork based on their diversity-related needs and to
create diversity-sensitive awareness among educators, employers and
researchers.


This paper has been withdrawn for modification.


  Heterogeneous wireless networks with wireless devices supporting multitude of
radio access technologies are witnessing increasing interest from network
providers and consumers alike. Energy efficiency in such networks has become an
important design consideration due to the limited battery life of mobile
terminals on one side, and the ever increasing operational expenses pertaining
to energy expenditure on the other. In this paper, we present a routing
protocol for multi-radio multi-hop wireless networks, which aims to achieve a
trade-off between energy consumption in the network and routing delay,
considering both the energy consumption at the devices and the link energy
costs. We also present optimum route-path selection strategies by defining a
utility function to minimize the energy consumption in the network while
maximizing the network lifetime. Using simulations, we verify the utility of
the route-path selection strategies and the efficiency of the energy aware
routing algorithm. It turns out that the proposed protocol is energy efficient
in terms of path selection, with a slight compromise in the end-to-end delay.


  The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on
the interplay between the strong electron correlation and the weak
electron-phonon interaction. The slave boson method has been employed in
combination with the large degeneracy expansion (1/N) technique. The charge and
spin susceptibilities and the phonon propagator are obtained in the
approximation scheme where the saddle point configuration and the Gaussian 1/N
fluctuations are taken into account. The spin susceptibility is found not to be
renormalized by electron-phonon interaction, while the charge susceptibility is
renormalized.
  From the renormalized charge susceptibility the Kondo temperature is found to
increase by the electron-phonon interaction. It turns out that the bosonic 1/N
Gaussian fluctuations play a very crucial role, in particular, for the phonon
propagator.


  Getzler-Jones-Petrack introduced $A_\infty$ structures on the equivariant
complex for manifold $M$ with smooth $\mathbb{S}^1$ action, motivated by
geometry of loop spaces. Applying Witten's deformation by Morse functions
followed by homological perturbation we obtained a new set of $A_\infty$
structures. We extend and prove Fukaya's conjecture relating this Witten's
deformed equivariant de Rham complexes, to a new Morse theoretical $A_\infty$
complexes defined by counting gradient trees with jumping which are closely
related to the $\mathbb{S}^1$ equivariant symplectic cohomology proposed by
Siedel.


  Using spatially resolved H-alpha emission line maps of star-forming galaxies,
we study the evolution of gradients in galaxy assembly over a wide range in
redshift ($0.5<z<1.7$). Our $z\sim0.5$ measurements come from deep Hubble Space
Telescope WFC3 G102 grism spectroscopy obtained as part of the CANDELS
Lyman-alpha Emission at Reionization (CLEAR) Experiment. For star-forming
galaxies with Log$(M_{*}/\mathrm{M}_{\odot})\geqslant8.96$, the mean H-alpha
effective radius is $1.2\pm0.1$ times larger than that of the stellar
continuum, implying inside-out growth via star formation. This measurement
agrees within $1\sigma$ with those measured at $z\sim1$ and $z\sim1.7$ from the
3D-HST and KMOS-3D surveys respectively, implying no redshift evolution.
However, we observe redshift evolution in the stellar mass surface density
within 1 kiloparsec ($\Sigma_\mathrm{1kpc}$). Star-forming galaxies at
$z\sim0.5$ with a stellar mass of Log$(M_{*}/\mathrm{M}_{\odot})=9.5$ have a
ratio of $\Sigma_\mathrm{1kpc}$ in H-alpha relative to their stellar continuum
that is lower by $(19\pm2)\%$ compared to $z\sim1$ galaxies.
$\Sigma_{1\mathrm{kpc, H}\alpha}$/$\Sigma_{1\mathrm{kpc,Cont}}$ decreases
towards higher stellar masses. The majority of the redshift evolution in
$\Sigma_{1\mathrm{kpc,H}\alpha}$/$\Sigma_{1\mathrm{kpc,Cont}}$ versus stellar
mass stems from the fact that Log($\Sigma_{1\mathrm{kpc, H}\alpha}$) declines
twice as much as Log($\Sigma_{1\mathrm{kpc, Cont}}$) from $z\sim 1$ to 0.5 (at
a fixed stellar mass of Log$(M_{*}/\mathrm{M}_{\odot})=9.5$). By comparing our
results to the TNG50 cosmological magneto-hydrodynamical simulation, we rule
out dust as the driver of this evolution. Our results are consistent with
inside-out quenching following in the wake of inside-out growth, the former of
which drives the significant drop in $\Sigma_{1\mathrm{kpc, H}\alpha}$ from
$z\sim1$ to $z\sim0.5$.


  We consider a well-known model for micro-electromechanical systems (MEMS)
with variable dielectric permittivity, involving a parabolic equation with
singular nonlinearity. We study the touchdown, or quenching, phenomenon.
Recently, the question whether or not touchdown can occur at zero points of the
premittivity profile f, which had long remained open, was answered negatively
for the case of interior points.
  The first aim of this article is to go further by considering the same
question at points of positive but small permittivity. We show that, in any
bounded domain, touchdown cannot occur at an interior point where the
permittivity profile is suitably small. We also obtain a similar result in the
boundary case, under a smallness assumption on f in a neighborhood of the
boundary. This allows in particular to construct f producing touchdown sets
concentrated near any given sphere.
  Our next aim is to obtain more information on the structure and properties of
the touchdown set. In particular, we show that the touchdown set need not in
general be localized near the maximum points of the premittivity profile f. In
the radial case in a ball, we show the existence of M-shaped profiles for which
the touchdown set is located far away from the maximum points of f and we even
obtain strictly convex f for which touchdown occurs at the unique minimum point
of f. These results show that some kind of smallness condition as above cannot
be avoided in order to rule out touchdown at a point.
  On the other hand, we construct profiles f producing more complex behaviors:
in any bounded domain the touchdown set may be concentrated near two
arbitrarily given points, or two arbitrarily given (n-1)-dimensional spheres in
a ball. These examples are obtained as a consequence of stability results for
the touchdown time and touchdown set under small perturbations of the
permittivity profile.


  The moduli space of solutions to the vortex equations on a Riemann surface
are well known to have a symplectic (in fact K\"{a}hler) structure. We show
this symplectic structure explictly and proceed to show a family of symplectic
(in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space,
parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface.
Next we show that corresponding to these there is a family of prequantum line
bundles ${\mathcal P}_{\Psi_0} $on the moduli space whose curvature is
proportional to the symplectic forms $\Omega_{\Psi_0}$.


  We present a structural and magnetic study on two batches of polycrystalline
LiNi$_{0.8}$Mn$_{0.1}$Co$_{0.1}$O$_2$ (commonly known as Li NMC 811), a Ni-rich
Li ion battery cathode material, using elemental analysis, X-ray and neutron
diffraction, magnetometry, and polarised neutron scattering measurements. We
find that the samples, labelled S1 and S2, have the composition
Li$_{1-x}$Ni$_{0.9+x-y}$Mn$_y$Co$_{0.1}$O$_2$, with $x = 0.025(2)$, $y =
0.120(2)$ for S1 and $x = 0.002(2)$, $y = 0.094(2)$ for S2, corresponding to
different concentrations of magnetic ions and excess Ni$^{2+}$ in the
Li$^+$layers. Both samples show a peak in the zero-field cooled (ZFC) dc
susceptibility at 8.0(2) K but the temperature at which the ZFC and FC
(field-cooled) curves deviate is substantially different: 64(2) K for S1 and
122(2) K for S2. Ac susceptibility measurements show that the transition for S1
shifts with frequency whereas no such shift is observed for S2 within the
resolution of our measurements. Our results demonstrate the sample dependence
of magnetic properties in Li NMC 811, consistent with previous reports on the
parent material LiNiO$_2$. We further establish that a combination of
experimental techniques are necessary to accurately determine the chemical
composition of next generation battery materials with multiple cations.


  Let $f$ be a Hecke-Maass cusp form for the full modular group and let $\chi$
be a primitive Dirichlet character modulo a prime $q$. Let $s_0=\sigma_0+it_0$
with $\frac{1}{2}\leq\sigma_0<1$. We improve the error term for the first
moment of $L(s_0,f\otimes\chi)\overline{L(s_0,\chi)}$ over the family of even
primitive Dirichlet characters. As an application, we show that for any
$t\in\mathbb{R}$, there exists a primitive Dirichlet character $\chi$ modulo
$q$ for which $L(1/2+it,f\otimes\chi)L(1/2+it,\chi)\neq0$ if the prime $q$
satisfies $q\gg (1+|t|)^{\frac{543}{25}+\varepsilon}$.


  Due to the severe multipath effect, no satisfactory device-free methods have
ever been found for indoor speed estimation problem, especially in
non-line-of-sight scenarios, where the direct path between the source and
observer is blocked. In this paper, we present WiSpeed, a universal
low-complexity indoor speed estimation system leveraging radio signals, such as
commercial WiFi, LTE, 5G, etc., which can work in both device-free and
device-based situations. By exploiting the statistical theory of
electromagnetic waves, we establish a link between the autocorrelation function
of the physical layer channel state information and the speed of a moving
object, which lays the foundation of WiSpeed. WiSpeed differs from the other
schemes requiring strong line-of-sight conditions between the source and
observer in that it embraces the rich-scattering environment typical for
indoors to facilitate highly accurate speed estimation. Moreover, as a
calibration-free system, WiSpeed saves the users' efforts from large-scale
training and fine-tuning of system parameters. In addition, WiSpeed could
extract the stride length as well as detect abnormal activities such as falling
down, a major threat to seniors that leads to a large number of fatalities
every year. Extensive experiments show that WiSpeed achieves a mean absolute
percentage error of 4.85% for device-free human walking speed estimation and
4.62% for device-based speed estimation, and a detection rate of 95% without
false alarms for fall detection.


  We consider the universe as a huge $\nu_R$-sphere formed with degenerate
relic neutrinos and suggest that its constant energy density play a role of an
effective cosmological constant. We construct the sphere as a bubble of true
vacuum in a field theory model with a spontaneously broken U(1) global
symmetry, and we interpret the sphere-forming time as the transition time for
recent acceleration of the universe. The coincidence problem may be regarded as
naturally resolved in this model, because the relic neutrinos can make the
$\nu_R$-sphere at the recent past time during the matter-dominated era.


  Bell state measurement is crucial to quantum information protocols, but it is
impossible to unambiguously distinguish all the Bell states encoded in
multi-photon using only linear optics. There is a maximum number of
distinguished Bell states, i.e. distinguising limit which is very important for
increasing the channel capacity of quantum communications. In this paper, we
separate $n$-photon $D$-dimensional hyperentanglement into two groups. For the
first group of $U$ ($G_1$), we obtain the limit ${N_1} = nD - (n - 1)$, which
can be applied for both bosons' and fermions' cases. We further discuss the
limit $N$ for any $nD$ system with the second group of $U$ ($G_2$), inferring
that at least ${D^{n - 1}}$ Bell states can be distinguished due to the
symmetry of Bell states. Obviously, ${N_1} \le {N_2}$ for those systems with
$n>2$. Finally, we theoretically design an optical setup for Bell state
measurement of two-photon eight-dimensional hyperentanglement of spin, path and
orbital angular momentum (OAM) and distinguish 15 classes of 64 Bell states.
Our results provide a theoretical basis and practical reference to increase the
channel capacity of the quantum communication.


  We demonstrate how to identify which physical processes dominate the
low-energy spectral functions of correlated electron systems. We obtain an
unambiguous classification through an analysis of the equation of motion for
the electron self-energy in its charge, spin and particle-particle
representations. Our procedure is then employed to clarify the controversial
physics responsible for the appearance of the pseudogap in correlated systems.
We illustrate our method by examining the attractive and repulsive Hubbard
model in two-dimensions. In the latter, spin fluctuations are identified as the
origin of the pseudogap, and we also explain why $d-$wave pairing fluctuations
play a marginal role in suppressing the low-energy spectral weight, independent
of their actual strength.


  Recent advancements in large-scale pre-trained text-to-image models have led
to remarkable progress in semantic image synthesis. Nevertheless, synthesizing
high-quality images with consistent semantics and layout remains a challenge.
In this paper, we propose the adaPtive LAyout-semantiC fusion modulE (PLACE)
that harnesses pre-trained models to alleviate the aforementioned issues.
Specifically, we first employ the layout control map to faithfully represent
layouts in the feature space. Subsequently, we combine the layout and semantic
features in a timestep-adaptive manner to synthesize images with realistic
details. During fine-tuning, we propose the Semantic Alignment (SA) loss to
further enhance layout alignment. Additionally, we introduce the Layout-Free
Prior Preservation (LFP) loss, which leverages unlabeled data to maintain the
priors of pre-trained models, thereby improving the visual quality and semantic
consistency of synthesized images. Extensive experiments demonstrate that our
approach performs favorably in terms of visual quality, semantic consistency,
and layout alignment. The source code and model are available at
https://github.com/cszy98/PLACE/tree/main.


  We obtained the first long, homogenous time-series of V2104Cyg, consisting of
679 datapoints, with the uvbybeta photometers of Sierra Nevada and San Pedro
Martir Observatories with the aim to detect and subsequently interpret the
intrinsic frequencies of this previously unstudied variable star, which turned
out to be a Be star. We try to figure out its place among the variable B stars
on the upper Main Sequence. In order to obtain additional information on
physical parameters we collected a few spectra with the ELODIE and FIES
instruments. We searched for frequencies in the uvby passbands using 2
different frequency analysis methods and used the S/N>4 criterion to select the
significant periodicities. We obtained an estimate of the physical parameters
of the underlying B star of spectral type between B5 and B7, by correcting for
the presence of a circumstellar disk, using a formalism based on the strenght
of the Halpha line emission. We detected 3 independent frequencies with
amplitudes below 0.01mag, f1 = 4.7126 c/d, f2 = 2.2342 c/d and f3 = 4.671 c/d,
and discovered that V2104Cyg is a Be star. The fast rotation (vsini=290+/-10
km/s, and 27<i<45) hampered the investigation of the associated pulsational
parameters l. Nevertheless, the most plausible explanation for the observed
variability of this mid-late type Be star is a non-radial pulsation model. This
paper is based on observations obtained at the Observatorio Astronomico
Nacional San Pedro Martir (Mexico), Observatorio de Sierra Nevada (Spain),
Observatoire de Haute Provence (France), and on observations made with the
Nordic Optical Telescope, Observatorio Roque de los Muchachos, La Palma, Spain.


  We call a periodic ball packing in d-dimensional Euclidean space periodically
(strictly) jammed with respect to a period lattice if there are no nontrivial
motions of the balls that preserve the period (that maintain some period with
smaller or equal volume). In particular, we call a packing consistently
periodically (strictly) jammed if it is periodically (strictly) jammed on every
one of its periods. After extending a well-known bar framework and stress
condition to strict jamming, we prove that a packing with period Lambda is
consistently strictly jammed if and only if it is strictly jammed with respect
to Lambda and consistently periodically jammed. We next extend a result about
rigid unit mode spectra in crystallography to characterize periodic jamming on
sublattices. After that, we prove that there are finitely many strictly jammed
packings of m unit balls and other similar results. An interesting example
shows that the size of the first sublattice on which a packing is first
periodically unjammed is not bounded. Finally, we find an example of a
consistently periodically jammed packing of low density \delta = \frac{4 \pi}{6
\sqrt{3} + 11} + \epsilon ~ 0.59, where \epsilon is an arbitrarily small
positive number. Throughout the paper, the statements for the closely related
notions of periodic infinitesimal rigidity and affine infinitesimal rigidity
for tensegrity frameworks are also given.


  A new method is proposed to compute connectivity measures on multivariate
time series with gaps. Rather than removing or filling the gaps, the rows of
the joint data matrix containing empty entries are removed and the calculations
are done on the remainder matrix. The method, called measure adapted gap
removal (MAGR), can be applied to any connectivity measure that uses a joint
data matrix, such as cross correlation, cross mutual information and transfer
entropy. MAGR is favorably compared using these three measures to a number of
known gap-filling techniques, as well as the gap closure. The superiority of
MAGR is illustrated on time series from synthetic systems and financial time
series.


  Physics-informed neural networks (PINNs), rooted in deep learning, have
emerged as a promising approach for solving partial differential equations
(PDEs). By embedding the physical information described by PDEs into
feedforward neural networks, PINNs are trained as surrogate models to
approximate solutions without the need for label data. Nevertheless, even
though PINNs have shown remarkable performance, they can face difficulties,
especially when dealing with equations featuring rapidly changing solutions.
These difficulties encompass slow convergence, susceptibility to becoming
trapped in local minima, and reduced solution accuracy. To address these
issues, we propose a binary structured physics-informed neural network (BsPINN)
framework, which employs binary structured neural network (BsNN) as the neural
network component. By leveraging a binary structure that reduces inter-neuron
connections compared to fully connected neural networks, BsPINNs excel in
capturing the local features of solutions more effectively and efficiently.
These features are particularly crucial for learning the rapidly changing in
the nature of solutions. In a series of numerical experiments solving Burgers
equation, Euler equation, Helmholtz equation, and high-dimension Poisson
equation, BsPINNs exhibit superior convergence speed and heightened accuracy
compared to PINNs. From these experiments, we discover that BsPINNs resolve the
issues caused by increased hidden layers in PINNs resulting in over-smoothing,
and prevent the decline in accuracy due to non-smoothness of PDEs solutions.


  Automatic metrics are commonly used as the exclusive tool for declaring the
superiority of one machine translation system's quality over another. The
community choice of automatic metric guides research directions and industrial
developments by deciding which models are deemed better. Evaluating metrics
correlations with sets of human judgements has been limited by the size of
these sets. In this paper, we corroborate how reliable metrics are in contrast
to human judgements on -- to the best of our knowledge -- the largest
collection of judgements reported in the literature. Arguably, pairwise
rankings of two systems are the most common evaluation tasks in research or
deployment scenarios. Taking human judgement as a gold standard, we investigate
which metrics have the highest accuracy in predicting translation quality
rankings for such system pairs. Furthermore, we evaluate the performance of
various metrics across different language pairs and domains. Lastly, we show
that the sole use of BLEU impeded the development of improved models leading to
bad deployment decisions. We release the collection of 2.3M sentence-level
human judgements for 4380 systems for further analysis and replication of our
work.


  In this article, we study local models associated to certain Shimura
varieties. In particular, we present a resoultion of their singularities. As a
consequence, we are able to determine the alternating semisimple trace of the
geometric Frobenius on the sheaf of nearby cycles.


  In this fourth part of the series presenting the Optical Gravitational
Lensing Experiment (OGLE) microlensing studies of the dark matter halo compact
objects (MACHOs) we describe results of the OGLE-III monitoring of the Small
Magellanic Cloud (SMC). Three sound candidates for microlensing events were
found and yielded the optical depth tau_SMC-OIII=1.30+-1.01 10^{-7}, consistent
with the expected contribution from Galactic disk and SMC self-lensing. We
report that event OGLE-SMC-03 is the most likely a thick disk lens candidate,
the first of such type found towards the SMC. In this paper we also combined
all OGLE Large and Small Magellanic Cloud microlensing results in order to
refine the conclusions on MACHOs. All but one of OGLE events are most likely
caused by the lensing by known populations of stars, therefore we concluded
that there is no need for introducing any special dark matter compact objects
in order to explain the observed events rates. Potential black hole event
indicates that similar lenses can contribute only about 2 per cent to the total
mass of the halo, which is still in agreement with the expected number of such
objects.


  In this study, we explore the influence of quark-antiquark confinement on the
deflection angle within the framework of nonlinear electrodynamic (NED) black
holes. To achieve this, we establish the appropriate optical spacetime metric
and subsequently determine the Gaussian optical curvature. Utilizing the
Gauss-Bonnet theorem, we investigate the impact of quark-antiquark confinement
on the deflection angle exhibited by NED black holes. Additionally, we delve
into the effects of a cold non-magnetized plasma medium and also axion-plasmon
on gravitational lensing. Our findings highlight the significance of the
axion-plasmon effect on the optical properties of NED black holes, particularly
its influence on gravitational lensing. This exploration is particularly
relevant in the context of the axion's potential role as a dark matter
candidate. The multifaceted interplay between quark-antiquark confinement,
nonlinear electrodynamics, and plasma dynamics provides a nuanced understanding
of gravitational lensing phenomena. These insights contribute to ongoing
research in dark matter studies and offer avenues for further theoretical and
observational investigations in astrophysics.


  We study the transformation properties of a scalar-tensor theory, coupled to
fermions, under the Weyl rescaling associated with a transition from the Jordan
to the Einstein frame. We give a simple derivation of the corresponding
modification to the gauge couplings. After changing frame, this gives rise to a
direct coupling between the scalar and the gauge fields.


  Real quantum heat engines lack the separation of time and length scales that
is characteristic for classical engines. They must be understood as open
quantum systems in non-equilibrium with time-controlled coupling to thermal
reservoirs as integral part. Here, we present a systematic approach to describe
a broad class of engines and protocols beyond conventional weak coupling
treatments starting from a microscopic modeling. For the four stroke Otto
engine the full dynamical range down to low temperatures is explored and the
crucial role of the work associated with the coupling/decoupling to/from
reservoirs in the energy balance is revealed. Quantum correlations turn out to
be instrumental to enhance the efficiency which opens new ways for optimal
control techniques.


  Any unitary operation in quantum information processing can be implemented
via a sequence of simpler steps - quantum gates. However, actual implementation
of a quantum gate is always imperfect and takes a finite time. Therefore,
seeking for a short sequence of gates - efficient quantum circuit for a given
operation, is an important task. We contribute to this issue by proposing
optimization of the well-known universal procedure proposed by Barenco et.al
[1]. We also created a computer program which realizes both Barenco's
decomposition and the proposed optimization. Furthermore, our optimization can
be applied to any quantum circuit containing generalized Toffoli gates,
including basic quantum gate circuits.


  This paper deals with asymptotics for multiple-set linear canonical analysis
(MSLCA). A definition of this analysis, that adapts the classical one to the
context of Euclidean random variables, is given and properties of the related
canonical coefficients are derived. Then, estimators of the MSLCA's elements,
based on empirical covariance operators, are proposed and asymptotics for these
estimators are obtained. More precisely, we prove their consistency and we
obtain asymptotic normality for the estimator of the operator that gives MSLCA,
and also for the estimator of the vector of canonical coefficients. These
results are then used to obtain a test for mutual non-correlation between the
involved Euclidean random variables.


  Recent surveys of dust continuum emission at sub-mm wavelengths have shown
that filamentary molecular clouds are ubiquitous along the Galactic plane.
These structures are inhomogeneous, with over-densities that are sometimes
associated with infrared emission and active of star formation. To investigate
the connection between filaments and star formation, requires an understanding
of the processes that lead to the fragmentation of filaments and a
determination of the physical properties of the over-densities (clumps). In
this paper, we present a multi-wavelength study of five filamentary molecular
clouds, containing several clumps in different evolutionary stages of star
formation. We analyse the fragmentation of the filaments and derive the
physical properties of their clumps. We find that the clumps in all filaments
have a characteristic spacing consistent with the prediction of the `sausage'
instability theory, regardless of the complex morphology of the filaments or
their evolutionary stage. We also find that most clumps have sufficient mass
and density to form high-mass stars, supporting the idea that high-mass stars
and clusters form within filaments.


  Stellar activity is the major roadblock on the path to finding true
Earth-analogue planets with the Doppler technique. Thus, identifying new
indicators that better trace magnetic activity (i.e. faculae and spots) is
crucial to aid in disentangling these signals from that of a planet's Doppler
wobble. In this work, we investigate activity related features as seen in
disk-integrated spectra from the HARPS-N solar telescope. We divide
high-activity spectral echelle orders by low-activity master templates (as
defined using both log R'HK and images from the Solar Dynamics Observatory,
SDO), creating "relative spectra". With resolved images of the surface of the
Sun (via SDO), the faculae and spot filling factors can be calculated, giving a
measure of activity independent of, and in addition to, log R'HK. We find
pseudo-emission (and pseudo-absorption) features in the relative spectra that
are similar to those reported in our previous work on alpha Cen B. In alpha Cen
B, the features are shown to correlate better to changes in faculae filling
factor than spot filling factor. In this work we more confidently identify
changes in faculae coverage of the visible hemisphere of the Sun as the source
of features produced in the relative spectra. Finally, we produce trailed
spectra to observe the RV component of the features, which show that the
features move in a redward direction as one would expect when tracking active
regions rotating on the surface of a star.


  3D video coding is one of the most popular research area in multimedia. This
paper reviews the recent progress of the coding technologies for multiview
video (MVV) and free view-point video (FVV) which is represented by MVV and
depth maps. We first discuss the traditional multiview video coding (MVC)
framework with different prediction structures. The rate-distortion performance
and the view switching delay of the three main coding prediction structures are
analyzed. We further introduce the joint coding technologies for MVV and depth
maps and evaluate the rate-distortion performance of them. The scalable 3D
video coding technologies are reviewed by the quality and view scalability,
respectively. Finally, we summarize the bit allocation work of 3D video coding.
This paper also points out some future research problems in high efficiency 3D
video coding such as the view switching latency optimization in coding
structure and bit allocation.


  Laman graphs naturally arise in structural mechanics and rigidity theory.
Specifically, they characterize minimally rigid planar bar-and-joint systems
which are frequently needed in robotics, as well as in molecular chemistry and
polymer physics. We introduce three new combinatorial structures for planar
Laman graphs: angular structures, angle labelings, and edge labelings. The
latter two structures are related to Schnyder realizers for maximally planar
graphs. We prove that planar Laman graphs are exactly the class of graphs that
have an angular structure that is a tree, called angular tree, and that every
angular tree has a corresponding angle labeling and edge labeling.
  Using a combination of these powerful combinatorial structures, we show that
every planar Laman graph has an L-contact representation, that is, planar Laman
graphs are contact graphs of axis-aligned L-shapes. Moreover, we show that
planar Laman graphs and their subgraphs are the only graphs that can be
represented this way.
  We present efficient algorithms that compute, for every planar Laman graph G,
an angular tree, angle labeling, edge labeling, and finally an L-contact
representation of G. The overall running time is O(n^2), where n is the number
of vertices of G, and the L-contact representation is realized on the n x n
grid.


  We argue that there is a fundamental problem regarding the analysis that
serves as the foundation for the papers {\it Information theory explanation of
the fluctuation theorem, maximum entropy production and self-organized
criticality in non-equilibrium stationary states} [R. Dewar, J. Phys. A: Math.
Gen. {\bf 36} (2003), 631-641] and {\it Maximum entropy production and the
fluctuation theorem} [R. Dewar, J. Phys. A: Math. Gen. {\bf 38} (2005),
L371-L381]. In particular, we demonstrate that this analysis is based on an
assumption that is physically unrealistic and that, hence, the results obtained
in those papers cannot be regarded as physically meaningful.


  We study spin tunneling in a magnetic nanoparticle with biaxial anisotropy
that is free to rotate about its anisotropy axis. Exact instanton of the
coupled equations of motion is found that connects degenerate classical energy
minima. We show that mechanical freedom of the particle renormalizes magnetic
anisotropy and increases the tunnel splitting.


  We report inelastic neutron scattering measurements of low energy ($\hbar
\omega < 10$ meV) magnetic excitations in the "11" system
Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. The spin correlations are two-dimensional (2D) in
the superconducting samples at low temperature, but appear much more
three-dimensional when the temperature rises well above $T_c \sim 15$ K, with a
clear increase of the (dynamic) spin correlation length perpendicular to the Fe
planes. The spontaneous change of dynamic spin correlations from 2D to 3D on
warming is unexpected and cannot be naturally explained when only the spin
degree of freedom is considered. Our results suggest that the low temperature
physics in the "11" system, in particular the evolution of low energy spin
excitations towards %better satisfying the nesting condition for mediating
superconducting pairing, is driven by changes in orbital correlations.


  We report on ballistic transport over more than 28 \mu m in graphene grown by
chemical vapor deposition (CVD) that is fully encapsulated in hexagonal boron
nitride. The structures are fabricated by an advanced dry van-der-Waals
transfer method and exhibit carrier mobilities of up to three million
cm$^2$/(Vs). The ballistic nature of charge transport is probed by measuring
the bend resistance in cross- and square-shaped devices. Temperature dependent
measurements furthermore prove that ballistic transport is maintained exceeding
1 \mu m up to 200 K.


  We explore the use of galaxy bispectrum induced by the nonlinear
gravitational evolution as a possible probe to test general scalar-tensor
theories with second-order equations of motion. We find that time dependence of
the leading second-order kernel is approximately characterized by one
parameter, the second-order index, which is expected to trace the higher-order
growth history of the Universe. We show that our new parameter can
significantly carry new information about the non-linear growth of structure.
We forecast future constraints on the second-order index as well as the
equation-of-state parameter and the growth index.


  We study translation invariant, real-valued valuations on the class of convex
polytopes in Euclidean space and discuss which continuity properties are
sufficient for an extension of such valuations to all convex bodies. For this
purpose, we introduce flag support measures of convex bodies via a local
Steiner formula and derive some of the properties of these measures.


  The GLR-MQ equation is a nonlinear evolution equation that takes into account
the shadowing effect, which tames the growth of the gluon at small-$x$. In this
study, we analytically solve for the first time the nonlinear GLR-MQ equation
using the homogeneous balance method. The definite solution of the GLR-MQ
equation is obtained by fitting the MSTW2008LO gluon distribution data. We find
that the geometric scaling is an intrinsic property of our analytical solution
and the gluon distribution functions from our solution are able to reproduce
the MSTW2008LO data. These results indicate that our analytical solution from
the homogeneous balance method is valid to describe the gluon behavior at
small-$x$. Moreover, the saturation scale $Q_s$ has been extracted from our
analytical solution, we find that the energy-dependent saturation scale obeys
the exponential law $Q_s^2\,\propto\,Q_0^2 e^{\lambda Y}$.


  Experimental studies were carried out on the motions and transformations of
liquid metal in ionic liquid under applied electric field. The induced vortex
rings and flows of ionic liquid were determined via the photographs taken
sequentially over the experiments. The polarization of electric double layer of
liquid metals was employed to explain the flow of ionic liquid with the
presence of liquid metal. Unlike former observation of liquid metal machine in
conventional solution, no gas bubble was generated throughout the whole
experiments, which makes it possible to encapsulate the liquid system for
fabricating soft robots.


  Switched reluctance machines (SRMs) have recently become popular in the
automotive market as they are a good alternative to the permanent magnet
machines commonly employed for an electric powertrain. Lumped parameter thermal
networks are usually used for thermal analysis of motors due to their low
computational cost and relatively accurate results. A critical aspect to be
modelled is the rotor-stator air-gap heat transfer, and this is particularly
challenging in an SRM due to the salient pole geometry. This work presents
firstly a review of the literature including the most relevant correlations for
this geometry, and secondly, numerical CFD simulations of air-gap heat transfer
for a typical configuration. A new correlation has been derived:
$\mathbf{Nu=0.181\ Ta_m^{0.207}}$


  Network homophily, the tendency of similar nodes to be connected, and
transitivity, the tendency of two nodes being connected if they share a common
neighbor, are conflated properties in network analysis, since one mechanism can
drive the other. Here we present a generative model and corresponding inference
procedure that are capable of distinguishing between both mechanisms. Our
approach is based on a variation of the stochastic block model (SBM) with the
addition of triadic closure edges, and its inference can identify the most
plausible mechanism responsible for the existence of every edge in the network,
in addition to the underlying community structure itself. We show how the
method can evade the detection of spurious communities caused solely by the
formation of triangles in the network, and how it can improve the performance
of edge prediction when compared to the pure version of the SBM without triadic
closure.


  This paper reports on the systematic electromechanical characterization of a
new three-axial force sensor used in dimensional metrology of micro components.
The siliconbased sensor system consists of piezoresistive mechanicalstress
transducers integrated in thin membrane hinges supporting a suspended flexible
cross structure. The mechanical behavior of the fragile micromechanical
structure isanalyzed for both static and dynamic load cases. This work
demonstrates that the silicon microstructure withstands static forces of 1.16N
applied orthogonally to the front-side of the structure. A statistical Weibull
analysis of the measured data shows that these values are significantly reduced
if the normal force is applied to the back of the sensor. Improvements of the
sensor system design for future development cycles are derived from the
measurement results.


  Analytical expressions for the rates of formation and destruction of
gravitationally bound systems are derived assuming that they are originated
from primordial random-Gaussian density fluctuations. The resulting formulae
reproduce the time derivative of the Press-Schechter mass function in a certain
limit. Combining a theoretical model for the evolution of structures with the
formation rate, we can make various cosmological predictions which are to be
compared with observations. As an example to elucidate such applicability, we
evaluate the contribution of clusters of galaxies to the cosmic X-ray
background radiation. With the {\it COBE} normalization, we find that the
significant fraction of the observed soft X-ray background is accounted for by
clusters of galaxies in a cold dark matter universe with $\Omega_0 \sim 0.2$,
$\lambda_0 =1- \Omega_0$ and $h \sim 0.8$.


  In this paper, we derive the optimal centralized dynamic-time-division-duplex
(D-TDD) scheme for a wireless network comprised of $K$ full-duplex nodes
impaired by self-interference and additive white Gaussian noise. As a special
case, we also provide the optimal centralized D-TDD scheme when the nodes are
half-duplex as well as when the wireless network is comprised of both
half-duplex and full-duplex nodes. Thereby, we derive the optimal adaptive
scheduling of the reception, transmission, simultaneous reception and
transmission, and silence at every node in the network in each time slot such
that the rate region of the network is maximized. The performance of the
optimal centralized D-TDD can serve as an upper-bound to any other TDD scheme,
which is useful in qualifying the relative performance of TDD schemes. The
numerical results show that the proposed centralized D-TDD scheme achieves
significant rate gains over existing centralized D-TDD schemes.


  We constructed a model of five-dimensional Lorentz manifold with foliation of
codimension 1 the leaves of which are four-dimensional space-times. The Past of
these space-times can interact in macroscopic scale by means of large quantum
fluctuations. Hence, it is possible that our Human History consists of
"somebody else's" (alien) events.


  The original mixed multiplicity theory considered the class of mixed
multiplicities concerning the terms of highest total degree in the Hilbert
polynomial. This paper defines a broader class of mixed multiplicities that
concern the maximal terms in this polynomial, and gives many results, which are
not only general but also more natural than many results in the original mixed
multiplicity theory.


  Qubit control electronics composed of CMOS circuits are of critical interest
for next generation quantum computing systems. A CMOS-based application
specific integrated circuit (ASIC) fabricated in 14nm FinFET technology was
used to generate and sequence qubit control waveforms and demonstrate a
two-qubit cross resonance gate between fixed frequency transmons. The
controller was thermally anchored to the T = 4K stage of a dilution
refrigerator and the measured power was 23 mW per qubit under active control.
The chip generated single--side banded output frequencies between 4.5 and 5.5
GHz with a maximum power output of -18 dBm. Randomized benchmarking (RB)
experiments revealed an average number of 1.71 instructions per Clifford (IPC)
for single-qubit gates, and 17.51 IPC for two-qubit gates. A single-qubit error
per gate of $\epsilon_{\text{1Q}}$=8e-4 and two-qubit error per gate of
$\epsilon_\text{2Q}$=1.4e-2 is shown. A drive-induced Z-rotation is observed by
way of a rotary echo experiment; this observation is consistent with expected
qubit behavior given measured excess local oscillator (LO) leakage from the
CMOS chip. The effect of spurious drive induced Z-errors is numerically
evaluated with a two-qubit model Hamiltonian, and shown to be in good agreement
with measured RB data. The modeling results suggest the Z-error varies linearly
with pulse amplitude.


  Inspired by [Fehrman, Gess; Invent. Math., 2023], we provide a fine analysis
of the McKean-Vlasov PDE with singular interactions and drift terms of square
root form. As the corresponding skeleton equation of Dean-Kawasaki equation
with singular interactions (a stochastic, conservative PDE), it determines the
rate function of small noise large deviations. By imposing
Ladyzhenskaya-Prodi-Serrin type conditions on the interaction kernel, we
establish the large deviations in the framework of stochastic renormalized
kinetic solution, when the intensity and the correlation of the noise are
simultaneously sent to $0$ under a suitable scaling. This result contributes to
demonstrating the consistency between the macroscopic fluctuation theory
associated with singular interacting mean-field systems and fluctuating
hydrodynamics related to the Dean-Kawasaki equation. As an application, we also
obtain large deviations for the other stochastic conservative PDE called
fluctuating Ising-Kac-Kawasaki dynamics. It is of great importance in exploring
fluctuations of Kawasaki dynamical Ising-Kac model, since they formally
exhibits the same key features in terms of Gaussian fluctuations, large
deviations, and scaling limits near criticality.


  Motivation. While recent studies show high accuracy in the classification of
Alzheimer's disease using deep neural networks, the underlying learned concepts
have not been investigated.
  Goals. To systematically identify changes in brain regions through concepts
learned by the deep neural network for model validation.
  Approach. Using quantitative R2* maps we separated Alzheimer's patients
(n=117) from normal controls (n=219) by using a convolutional neural network
and systematically investigated the learned concepts using Concept Relevance
Propagation and compared these results to a conventional region of
interest-based analysis.
  Results. In line with established histological findings and the region of
interest-based analyses, highly relevant concepts were primarily found in and
adjacent to the basal ganglia.
  Impact. The identification of concepts learned by deep neural networks for
disease classification enables validation of the models and could potentially
improve reliability.


  In this paper the collision of two cosmic string loops is studied. After
collision junctions are formed and the loops are entangled. We show that after
their formation the junctions start to unzip and the loops disentangle. This
analysis provides a theoretical understanding of the unzipping effect observed
in numerical simulations of a network of cosmic strings with more than one type
of cosmic strings. The unzipping phenomena have important effects in the
evolution of cosmic string networks when junctions are formed upon collision,
such as in a network of cosmic superstrings.


  Phase separation of colloid-polymer mixtures, described by the Asakura-Oosawa
(AO) model, confined in a thin slit pore is studied by grand-canonical Monte
Carlo simulation. While one wall is a hard wall for both particles, at the
other wall there acts an additional repulsive potential on the colloids only.
Varying the strength of this potential, a crossover from capillary condensation
to an interface localization transition is found. The latter occurs under
conditions where in the bulk almost complete phase separation has occurred.


  We study line patterns in a free group by considering the topology of the
decomposition space, a quotient of the boundary at infinity of the free group
related to the line pattern. We show that the group of quasi-isometries
preserving a line pattern in a free group acts by isometries on a related space
if and only if there are no cut pairs in the decomposition space.


  Based on the Connes--Kreimer Hopf algebra of rooted trees, the rooted tree
maps are defined as linear maps on noncommutative polynomial algebra in two
indeterminates. It is known that they induce a large class of linear relations
for multiple zeta values. In this paper, we investigate some basic algebraic
properties of rooted tree maps by relating to the harmonic algebra. We also
characterize the antipode maps as the conjugation by the special map $\tau$.


  Commutative Hilbertian Frobenius algebras are those commutative semi-group
objects in the monoidal category of Hilbert spaces, for which the Hilbert
adjoint of the multiplication satisfies the Frobenius compatibility relation,
that is, this adjoint is a bimodule map. In this note we prove that they split
as an orthogonal direct sum of two closed ideals, their Jacobson radical which
in fact is nothing but their annihilator, and the closure of the linear span of
their group-like elements. As a consequence such an algebra is semisimple if,
and only if, its multiplication has a dense range. In particular every
commutative special Hilbertian algebra, that is, with a coisometric
multiplication, is semisimple. Extending a known result in the
finite-dimensional situation, we prove that the structures of such Frobenius
algebras on a given Hilbert space are in one-one correspondence with its
bounded above orthogonal sets. We show, moreover, that the category of
commutative Hilbertian Frobenius algebras is dually equivalent to a category of
pointed sets. Thus, each semigroup morphism between commutative Hilbertian
Frobenius semigroups arises from a unique base-point preserving map (of some
specific kind), from the set of minimal ideals of its codomain to the set of
minimal ideals of its domain, both with zero added. MSC 2010: Primary 46J40,
Secondary 16T15.


  The quasi--equilibrium or maximum entropy approximation is applied in order
to derive constitutive equations from kinetic models of polymer dynamics. It is
shown in general and illustrated for an example how canonical distribution
functions are obtained from the maximum entropy principle, how macroscopic and
constitutive equations are derived therefrom and how these constitutive
equations can be implemented numerically. In addition, a measure for the
accuracy of the quasi--equilibrium approximation is proposed that can be
evaluated while integrating the constitutive equations. In the example
considered, it is confirmed that the accuracy of the approximation is increased
by including more macroscopic variables. In steady elongational flow, it is
found that more macroscopic variables need to be included above the
coil--stretch transition to achieve the same accuracy as below.


  We develop a method to compute the $H^2$-conforming finite element
approximation to planar fourth order elliptic problems without having to
implement $C^1$ elements. The algorithm consists of replacing the original
$H^2$-conforming scheme with pre-processing and post-processing steps that
require only an $H^1$-conforming Poisson type solve and an inner Stokes-like
problem that again only requires at most $H^1$-conformity. We then demonstrate
the method applied to the Morgan-Scott elements with three numerical examples.


  Fractional (hyper-)graph theory is concerned with the specific problems that
arise when fractional analogues of otherwise integer-valued (hyper-)graph
invariants are considered. The focus of this paper is on fractional edge covers
of hypergraphs. Our main technical result generalizes and unifies previous
conditions under which the size of the support of fractional edge covers is
bounded independently of the size of the hypergraph itself. This allows us to
extend previous tractability results for checking if the fractional hypertree
width of a given hypergraph is $\leq k$ for some constant $k$. We also show how
our results translate to fractional vertex covers.


  We present a method for including inelastic scattering in a first-principles
density-functional computational scheme for molecular electronics. As an
application, we study two geometries of four-atom gold wires corresponding to
two different values of strain, and present results for nonlinear differential
conductance vs. device bias. Our theory is in quantitative agreement with
experimental results, and explains the experimentally observed mode
selectivity. We also identify the signatures of phonon heating.


  This paper introduces {\Delta}Breakpad. It extends the Breakpad crash
reporting system to handle software diversity effectively and efficiently by
replicating and patching the debug information of diversified software
versions. Simple adaptations to existing open source compiler tools are
presented that on the one hand introduce significant amounts of diversification
in the code and stack layout of ARMv7 binaries to mitigate the widespread
deployment of code injection and code reuse attacks, while on the other hand
still supporting accurate crash reporting. An evaluation on SPEC2006 benchmarks
demonstrates that the corresponding computational, storage, and communication
overheads are small.


  As part of the SINS/zC-SINF surveys of high-z galaxy kinematics, we derive
the radial distributions of H-alpha surface brightness, stellar mass surface
density, and dynamical mass at ~2 kpc resolution in 19 z~2 star-forming disks
with deep SINFONI AO spectroscopy at the ESO VLT. From these data we infer the
radial distribution of the Toomre Q-parameter for these main-sequence star
forming galaxies (SFGs), covering almost two decades of stellar mass (10^9.6 to
10^11.5 solar masses). In more than half of our SFGs, the H-alpha distributions
cannot be fit by a centrally peaked distribution, such as an exponential, but
are better described by a ring, or the combination of a ring and an
exponential. At the same time the kinematic data indicate the presence of a
mass distribution more centrally concentrated than a single exponential
distribution for 5 of the 19 galaxies. The resulting Q-distributions are
centrally peaked for all, and significantly exceed unity there for three
quarters of the SFGs. The occurrence of H-alpha rings and of large nuclear
Q-values is strongly correlated, and is more common for the more massive SFGs.
While our sample is small and there remain substantial uncertainties and
caveats, our observations are consistent with a scenario in which cloud
fragmentation and global star formation are secularly suppressed in gas rich
high-z disks from the inside out, as the central stellar mass density of the
disks grows.


  Reinforcement learning has made great strides in recent years due to the
success of methods using deep neural networks. However, such neural networks
act as a black box, obscuring the inner workings. While reinforcement learning
has the potential to solve unique problems, a lack of trust and understanding
of reinforcement learning algorithms could prevent their widespread adoption.
Here, we present a library that attaches a "data scraper" to deep reinforcement
learning agents, acting as an observer, and then show how the data collected by
the Atari Data Scraper can be used to understand and interpret deep
reinforcement learning agents. The code for the Atari Data Scraper can be found
here: https://github.com/IRLL/Atari-Data-Scraper


  In this paper, we reconsider the large-$z$ asymptotic expansion of the Lommel
function $S_{\mu,\nu}(z)$ and its derivative. New representations for the
remainder terms of the asymptotic expansions are found and used to obtain sharp
and realistic error bounds. We also give re-expansions for these remainder
terms and provide their error estimates. Applications to the asymptotic
expansions of the Anger--Weber-type functions, the Scorer functions, the Struve
functions and their derivatives are provided. The sharpness of our error bounds
is discussed in detail, and numerical examples are given.


  We have measured star formation histories (SFHs) and stellar masses of
galaxies detected by the Balloon-borne Large Aperture Sub-millimetre Telescope
(BLAST) over approximately 9 square degrees centred on the Chandra Deep Field
South. We have applied the recently developed SFH reconstruction method of Dye
et al. to optical, near-infrared and mid-infrared photometry of 92 BLAST
galaxies. We find significant differences between the SFHs of low mass (<10^11
M_sol) and high mass (>10^11 M_sol) galaxies. On average, low mass galaxies
exhibit a dominant late burst of star formation which creates a large fraction
of their stellar mass. Conversely, high mass systems tend to have a significant
amount of stellar mass that formed much earlier. We also find that the high
mass SFHs evolve more strongly than the low mass SFHs. These findings are
consistent with the phenomenon of downsizing observed in optically selected
samples of galaxies.


  Recent lattice data on $\pi\pi$-scattering phase shifts in the
vector-isovector channel, pseudoscalar meson masses and decay constants for
strange-quark masses smaller or equal to the physical value allow us to study
the strangeness dependence of these observables for the first time. We perform
a global analysis on two kind of lattice trajectories depending on whether the
sum of quark masses or the strange-quark mass is kept fixed to the physical
point. The quark mass dependence of these observables is extracted from
unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis
guides new predictions on the $\rho(770)$ meson properties over trajectories
where the strange-quark mass is lighter than the physical mass, as well as on
the SU(3) symmetric line. As a result, the light- and strange-quark mass
dependence of the $\rho(770)$ meson parameters are discussed and precise values
of the Low Energy Constants present in unitarized one-loop Chiral Perturbation
Theory are given. Finally, the current discrepancy between two- and
three-flavor lattice results for the $\rho(770)$ meson is studied.


  We describe a derivational approach to abstract interpretation that yields
novel and transparently sound static analyses when applied to well-established
abstract machines. To demonstrate the technique and support our claim, we
transform the CEK machine of Felleisen and Friedman, a lazy variant of
Krivine's machine, and the stack-inspecting CM machine of Clements and
Felleisen into abstract interpretations of themselves. The resulting analyses
bound temporal ordering of program events; predict return-flow and
stack-inspection behavior; and approximate the flow and evaluation of by-need
parameters. For all of these machines, we find that a series of well-known
concrete machine refactorings, plus a technique we call store-allocated
continuations, leads to machines that abstract into static analyses simply by
bounding their stores. We demonstrate that the technique scales up uniformly to
allow static analysis of realistic language features, including tail calls,
conditionals, side effects, exceptions, first-class continuations, and even
garbage collection.


  Interaction between dark energy and dark matter is probed through deviation
from the virial equilibrium for two relaxed clusters: A586 and A1689. The
evaluation of the virial equilibrium is performed using realistic density
profiles. The virial ratios found for the more realistic density profiles are
consistent with the absence of interaction.


  We present a quantum Monte Carlo study of the hydrogen-benzene system where
binding is very weak. We demonstrate that the binding is well described at both
variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels by a
Jastrow correlated single determinant geminal wave function with an optimized
compact basis set that includes diffuse orbitals. Agreement between VMC and
fixed-node DMC binding energies is found to be within 0.18 mHa, suggesting the
calculations are well-converged with respect to the basis. Essentially the same
binding is also found in independent DMC calculations using a different trial
wave function of a more conventional Slater-Jastrow form, supporting our
conclusion that the binding energy is accurate and includes all effects of
correlation. We compare with empirical models and previous calculations, and we
discuss the physical mechanisms of the interaction, the role of diffuse basis
functions, and the charge redistribution in the bond.


  We present the analysis of photometric and spectroscopic data of two
classical Cepheids, FN Aquilae and V1344 Aquilae. Based on the joint treatment
of the new and earlier radial velocity data, both Galactic Cepheids have been
found to be a member in a spectroscopic binary system.
  To match the phases of the earlier radial velocity data correctly with the
new ones, we also determined the temporal behaviour of the pulsation period of
these Cepheids based on all available photometric data. The O-C graph covering
about half century shows slight changes in the pulsation period due to stellar
evolution for both Cepheids.


  The quaternary structure of Filamin A (FLNa) 16-23 was recently shown to
exhibit multiple domain-domain interactions that lead to a propeller-like
construction. Here we present single molecule force spectroscopy experiments to
show a wide variety of mechanical responses of this molecule and compare it
with its linear counterpart FLNa 1-8. The compact structure of FLNa 16-23 leads
to a broad distribution of rupture forces and end-to-end lengths in the
force-extension mode and multiple unraveling timescales in the force-clamp
mode. Moreover, a subset of force-extension trajectories reveals a mechanical
hierarchy in which the rupture of domain-domain interactions at high forces
(200 pN) liberates the unfolding of individual domains at low forces (100 pN).
This mechanism may also explain the order of magnitude difference in the rates
of the biexponential fits to the distribution of unfolding dwell times under
force-clamp. Overall, FLNa 16-23 under a force of 100 pN is more compliant than
the linear FLNa 1-8. Since a physiological role of FLNa is to crosslink actin
filaments, this range of responses allows it to accommodate a broad spectrum of
forces exerted by the cell and its environment.


  Let A_q(g) be the quantized algebra of functions associated with simple Lie
algebra g defined by generators obeying the so called RTT relations. We
describe the embedding $A_q(B_2) \hookrightarrow A_q(C_2)$ explicitly. As an
application, a new solution of the Isaev-Kulish 3D reflection equation is
constructed by combining the embedding with the previous solution for A_q(C_2)
by the authors.


  We provide a new paradigm for quantum simulation that is based on path
integration that allows quantum speedups to be observed for problems that are
more naturally expressed using the path integral formalism rather than the
conventional sparse Hamiltonian formalism. We provide two novel quantum
algorithms based on Hamiltonian versions of the path integral formulation and
another for Lagrangians of the form $\frac{m}{2}\dot{x}^2 - V(x)$. This
Lagrangian path integral algorithm is based on a new rigorous derivation of a
discrete version of the Lagrangian path integral. Our first Hamiltonian path
integral method breaks up the paths into short timesteps. It is efficient under
appropriate sparsity assumptions and requires a number of queries to oracles
that give the eigenvalues and overlaps between the eigenvectors of the
Hamiltonian terms that scales as $t^{o(1)}/\epsilon^{o(1)}$ for simulation time
$t$ and error $\epsilon$. The second approach uses long-time path integrals for
near-adiabatic systems and has query complexity that scales as
$O(1/\sqrt{\epsilon})$ if the energy eigenvalue gaps and simulation time is
sufficiently long. Finally, we show that our Lagrangian simulation algorithm
requires a number of queries to an oracle that computes the discrete Lagrangian
that scales, in the continuum limit, as $\widetilde{O}(t^2/\epsilon)$ if $V(x)$
is bounded and finite and the wave function obeys appropriate position and
momentum cutoffs. This shows that Lagrangian dynamics can be efficiently
simulated on quantum computers and opens up the possibility for quantum field
theories for which the Hamiltonian is unknown to be efficiently simulated on
quantum computers.


  We show that the generic solutions of the Lovelock equations with spherical,
planar or hyperbolic symmetry are locally isometric to the corresponding static
Lovelock black hole. As a consequence, these solutions are locally static: they
admit an additional Killing vector that can either be space-like or time-like,
depending on the position. This result also holds in the presence of an abelian
gauge field, in which case the solutions are locally isometric to a charged
static black hole.


  Quantitative and mechanistically-detailed kinetics of the reaction of
hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal
of contemporary chemical kinetics. This fundamental prototype reaction plays an
important role in atmospheric and combustion chemistry, motivating studies for
accurate determination of the reaction rate coefficient and its pressure and
temperature dependence at thermal reaction conditions. This intricate
dependence can be traced directly to details of the underlying dynamics
(formation, isomerization, and dissociation) involving the reactive
intermediates cis- and trans-HOCO, which can only be observed transiently.
Using time-resolved frequency comb spectroscopy, comprehensive mechanistic
elucidation of the kinetics of the isotopic analogue deuteroxyl radical (OD)
with CO has been realized. By monitoring the concentrations of reactants,
intermediates, and products in real-time, the branching and isomerization
kinetics and absolute yields of all species in the OD+CO reaction are
quantified as a function of pressure and collision partner.