  Controlled experimentation, also called A/B testing, is widely adopted to
accelerate product innovations in the online world. However, how fast we
innovate can be limited by how we run experiments. Most experiments go through
a "ramp up" process where we gradually increase the traffic to the new
treatment to 100%. We have seen huge inefficiency and risk in how experiments
are ramped, and it is getting in the way of innovation. This can go both ways:
we ramp too slowly and much time and resource is wasted; or we ramp too fast
and suboptimal decisions are made. In this paper, we build up a ramping
framework that can effectively balance among Speed, Quality and Risk (SQR). We
start out by identifying the top common mistakes experimenters make, and then
introduce the four SQR principles corresponding to the four ramp phases of an
experiment. To truly scale SQR to all experiments, we develop a statistical
algorithm that is embedded into the process of running every experiment to
automatically recommend ramp decisions. Finally, to complete the whole picture,
we briefly cover the auto-ramp engineering infrastructure that can collect
inputs and execute on the recommendations timely and reliably.


  Identifying trendline visualizations with desired patterns is a common and
fundamental data exploration task. Existing visual analytics tools offer
limited flexibility and expressiveness for such tasks, especially when the
pattern of interest is under-specified and approximate, and do not scale well
when the pattern searching needs are ad-hoc, as is often the case. We propose
ShapeSearch, an efficient and flexible pattern-searching tool, that enables the
search for desired patterns via multiple mechanisms: sketch, natural-language,
and visual regular expressions. We develop a novel shape querying algebra, with
a minimal set of primitives and operators that can express a large number of
ShapeSearch queries, and design a natural-language and regex-based parser to
automatically parse and translate user queries to the algebra representation.
To execute these queries within interactive response times, ShapeSearch uses a
fast shape algebra-based execution engine with query-aware optimizations, and
perceptually-aware scoring methodologies. We present a thorough evaluation of
the system, including a general-purpose user study, a case study involving
genomic data analysis, as well as performance experiments, comparing against
state-of-the-art time series shape matching approaches---that together
demonstrate the usability and scalability of ShapeSearch.


  We investigate relations between best selling artists in last decade on
phonographic market and from perspective of listeners by using the Social
Network Analyzes. Starting network is obtained from the matrix of correlations
between the world's best selling artists by considering the synchronous time
evolution of weekly record sales. This method reveals the structure of
phonographic market, but we claim that it has no impact on people who see
relationship between artists and music genres. We compare 'sale' (based on
correlation of record sales) or 'popularity' (based on data mining of the
record charts) networks with 'similarity' (obtained mainly from survey within
music experts opinion) and find no significant relations. We postulate that
non-laminar phenomena on this specific market introduce turbulence to how
people view relations of artists.


  This paper provides a formalization of the energy disaggregation problem for
particle swarm optimization and shows the successful application of particle
swarm optimization for disaggregation in a multi-tenant commercial building.
The developed mathmatical description of the disaggregation problem using a
state changes matrix belongs to the group of non-event based methods for energy
disaggregation. This work includes the development of an objective function in
the power domain and the description of position and velocity of each particle
in a high dimensional state space. For the particle swarm optimization, four
adaptions have been applied to improve the results of disaggregation, increase
the robustness of the optimizer regarding local optima and reduce the
computational time. The adaptions are varying movement constants, shaking of
particles, framing and an early stopping criterion. In this work we use two
unlabelled power datasets with a granularity of 1 s. Therefore, the results are
validated in the power domain in which good results regarding multiple error
measures like root mean squared error or the percentage energy error can be
shown.


  We show that separably closed valued fields of finite imperfection degree
(either with lambda-functions or commuting Hasse derivations) eliminate
imaginaries in the geometric language. We then use this classification of
interpretable sets to study stably dominated types in those structures. We show
that separably closed valued fields of finite imperfection degree are
metastable and that the space of stably dominated types is strict
pro-definable.


  In the present paper we introduce the notion of dilation of a multiparametric
linear stationary dynamical system (systems of this type, in particular
passive, and conservative scattering ones were first introduced in
func-an/9804130). We establish the criterion for existence of a conservative
dilation of a multiparametric passive scattering system. This allows to
distinguish the class of so-called $N$-passive systems preserving the most
important properties of one-parametric passive scattering systems.


  Usually, important parameters of young, low-mass star clusters are very
difficult to obtain by means of photometry, especially when differential
reddening and/or binaries occur in large amounts. We present a semi-analytical
approach that, applied to the Hess diagram of a young star cluster, is able to
retrieve the values of mass, age, star-formation spread, distance modulus,
foreground and differential reddening, and binary fraction. The global
optimisation method known as adaptive simulated annealing (ASA) is used to
minimise the residuals between the observed and simulated Hess diagrams of a
star cluster. The simulations are realistic and take the most relevant
parameters of young clusters into account. Important features of the
simulations are: a normal (Gaussian) differential reddening distribution, a
time-decreasing star-formation rate, the unresolved binaries, and the smearing
effect produced by photometric uncertainties on Hess diagrams. Free parameters
are: cluster mass, age, distance modulus, star-formation spread, foreground and
differential reddening, and binary fraction.


  With the traditional equilibrium molecular simulations, it is usually
difficult to efficiently visit the whole conformational space in complex
systems, which are separated into some metastable conformational regions by
high free energy barriers. The applied non-equilibrium process in simulations
could enhance the transitions among these conformational regions, and the
associated non-equilibrium effects can be removed by employing the Jarzynski
equality (JE), then the global equilibrium distribution can be reproduced.
However, the original JE requires the initial distribution of the
non-equilibrium process is equilibrium, which largely limits the application of
the non-equilibrium method in equilibrium sampling. By extending the previous
method, the reweighted ensemble dynamics (RED), which re-weights many
equilibrium simulation trajectories from arbitrary initial distribution to
reproduce the global equilibrium, to non-equilibrium simulations, we present a
method, named as re-weighted non-equilibrium ensemble dynamics (RNED), to
generalize the JE in the non-equilibrium trajectories started from an arbitrary
initial distribution, thus provide an efficient method to reproduce the
equilibrium distribution based on multiple independent (short) non-equilibrium
trajectories. We have illustrated the validity of the RNED in a one-dimensional
toy model and in a Lennard-Jones system to detect the liquid-solid phase
coexistence.


  In this paper we numerically conduct micromagnetic modelling to optimize
computational boundaries of magnetic thin-film elements applicable to single
and double point contact spin torque nano-oscillators. Different boundary
conditions have been introduced to compensate spin waves reflections at
boundaries that are based on extended layers, absorbing boundaries, and focal
point methods and are compared with a technique based on scattering theory. A
surface roughness boundary model is presented which is modelled according to
the Rayleigh criterion to minimize specular reflections at computational
boundaries. It is shown that the surface roughness model disperses the
reflected spin waves and improves the signal to background noise ratio. The
model is tested in comparison to conventional approaches such as extended layer
systems, variable damping constant and focal point methods for double point
contacts. The surface roughness model gives solutions that are stable in time,
in qualitative agreement with experiments and capable to reproduce phenomena
such as phase locking in double point contacts.


  We discuss hadronic light-by-light scattering contribution to the muon
anomalous magnetic moment a_\mu^{\rm lbl}, paying particular attention to the
consistent matching between the short- and the long-distance behavior of the
light-by-light scattering amplitude. We argue that the short-distance QCD
imposes strong constraints on this amplitude overlooked in previous analyses.
We find that accounting for these constraints leads to approximately 50 per
cent increase in the central value of a_\mu^{\rm lbl}, compared to existing
estimates. The hadronic light-by-light scattering contribution becomes
a_\mu^{\rm lbl}=136(25) \times 10^{-11}, thereby shifting the Standard Model
prediction closer to the experimental value.


  On the basis of nonzero neutrino electromagnetic properties, we consider a
problem of electrically millicharged neutrino energy spectra in a magnetized
matter. It is shown that in this case neutrino energies are quantized. These
phenomena can be important for astrophysical applications.


  In our basic model, we study a stationary Poisson pattern of nodes on a line
embedded in an independent planar Poisson field of interfering nodes. Assuming
slotted Aloha and the signal-to-interference-and-noise ratio capture condition,
with the usual power-law path loss model and Rayleigh fading, we explicitly
evaluate several local and end-to-end performance characteristics related to
the nearest-neighbor packet relaying on this line, and study their dependence
on the model parameters (the density of relaying and interfering nodes, Aloha
tuning and the external noise power). Our model can be applied in two cases:
the first use is for vehicular ad-hoc networks, where vehicles are randomly
located on a straight road. The second use is to study a typical route traced
in a (general) planar ad-hoc network by some routing mechanism. The approach we
have chosen allows us to quantify the non-efficiency of long-distance routing
in pure ad-hoc networks and evaluate a possible remedy for it in the form of
additional fixed relaying nodes, called road-side units in a vehicular network.
It also allows us to consider a more general field of interfering nodes and
study the impact of the clustering of its nodes the routing performance. As a
special case of a field with more clustering than the Poison field, we consider
a Poisson-line field of interfering nodes, in which all the nodes are randomly
located on random straight lines. The comparison to our basic model reveals a
paradox: clustering of interfering nodes decreases the outage probability of a
single (typical) transmission on the route, but increases the mean end-to-end
delay.


  Thermal suppression of quarkonium production in heavy-ion collisions, due to
Debye screening of the quark-antiquark potential, has been proposed as a clear
signature of Quark-Gluon Plasma (QGP) formation. At RHIC energies, the
$\Upsilon$ meson is a clean probe of the early system due to negligible levels
of enhancement from \bbbar recombination and non-thermal suppression from
co-mover absorption. We report on our measurement of the $\Upsilon \to e^+ e^-$
cross section in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV. We compute the
Nuclear Modification Factor by comparing these results to new p+p measurements
from 2009 (21 pb$^{-1}$ in 2009 compared to 7.9 pb$^{-1}$ in 2006). In order to
have a complete assessment of both hot and cold nuclear matter effects on
Upsilon production we also report on results from d+Au collisions.


  This paper proposes a novel framework for multi-label image recognition
without any training data, called data-free framework, which uses knowledge of
pre-trained Large Language Model (LLM) to learn prompts to adapt pretrained
Vision-Language Model (VLM) like CLIP to multilabel classification. Through
asking LLM by well-designed questions, we acquire comprehensive knowledge about
characteristics and contexts of objects, which provides valuable text
descriptions for learning prompts. Then we propose a hierarchical prompt
learning method by taking the multi-label dependency into consideration,
wherein a subset of category-specific prompt tokens are shared when the
corresponding objects exhibit similar attributes or are more likely to
co-occur. Benefiting from the remarkable alignment between visual and
linguistic semantics of CLIP, the hierarchical prompts learned from text
descriptions are applied to perform classification of images during inference.
Our framework presents a new way to explore the synergies between multiple
pre-trained models for novel category recognition. Extensive experiments on
three public datasets (MS-COCO, VOC2007, and NUS-WIDE) demonstrate that our
method achieves better results than the state-of-the-art methods, especially
outperforming the zero-shot multi-label recognition methods by 4.7% in mAP on
MS-COCO.


  In this paper we propose a novel image encryption scheme. The proposed method
is based on the chaos theory. Our cryptosystem uses the chaos theory to define
a dynamic chaotic Look-Up Table (LUT) to compute the new value of the current
pixel to cipher. Applying this process on each pixel of the plain image, we
generate the encrypted image. The results of different experimental tests, such
as Key space analysis, Information Entropy and Histogram analysis, show that
the proposed encryption image scheme seems to be protected against various
attacks. A comparison between the plain and encrypted image, in terms of
correlation coefficient, proves that the plain image is very different from the
encrypted one.


  This paper is concerned with the mathematical analysis of continuous time
Ensemble Kalman Filters (EnKBFs) and their mean field limit in an infinite
dimensional setting. The signal is determined by a nonlinear Stochastic Partial
Differential Equation (SPDE), which is posed in the standard variational
setting. Assuming global one-sided Lipschitz conditions and finite dimensional
observations we first prove the well posedness of both the EnKBF and its
corresponding mean field version. We then investigate the quantitative
convergence of the EnKBF towards its mean field limit, recovering the rates
suggested by the law of large numbers for bounded observation functions. The
main tool hereby are exponential moment estimates for the empirical covariance
of the EnKBF, which may be of independent interest. In the appendix of the
paper we investigate the connection of the mean field EnKBF and the Stochastic
Filtering Problem. In particular we derive the Feedback Particle Filter for
infinite dimensional signals and show that the mean field EnKBF can viewed as
its constant gain approximation.


  Exposure to green space seems to be beneficial for self-reported mental
health. In this study we used an objective health indicator, namely
antidepressant prescription rates. Current studies rely exclusively upon mean
regression models assuming linear associations. It is, however, plausible that
the presence of green space is non-linearly related with different quantiles of
the outcome antidepressant prescription rates. These restrictions may
contribute to inconsistent findings. Our aim was to assess antidepressant
prescription rates in relation to green space, and to analyze how the
relationship varies non-linearly across different quantiles of antidepressant
prescription rates. We used cross-sectional data for the year 2014 at a
municipality level in the Netherlands. Ecological Bayesian geoadditive quantile
regressions were fitted for the 15, 50, and 85 percent quantiles to estimate
green space-prescription rate correlations, controlling for confounders. The
results suggested that green space was overall inversely and non-linearly
associated with antidepressant prescription rates. More important, the
associations differed across the quantiles, although the variation was modest.
Significant non-linearities were apparent: The associations were slightly
positive in the lower quantile and strongly negative in the upper one. Our
findings imply that an increased availability of green space within a
municipality may contribute to a reduction in the number of antidepressant
prescriptions dispensed. Green space is thus a central health and community
asset, whilst a minimum level of 28 percent needs to be established for health
gains. The highest effectiveness occurred at a municipality surface percentage
higher than 79 percent. This inverse dose-dependent relation has important
implications for setting future community-level health and planning policies.


  Causality graphs are routinely estimated in social sciences, natural
sciences, and engineering due to their capacity to efficiently represent the
spatiotemporal structure of multivariate data sets in a format amenable for
human interpretation, forecasting, and anomaly detection. A popular approach to
mathematically formalize causality is based on vector autoregressive (VAR)
models and constitutes an alternative to the well-known, yet usually
intractable, Granger causality. Relying on such a VAR causality notion, this
paper develops two algorithms with complementary benefits to track time-varying
causality graphs in an online fashion. Their constant complexity per update
also renders these algorithms appealing for big-data scenarios. Despite using
data sequentially, both algorithms are shown to asymptotically attain the same
average performance as a batch estimator which uses the entire data set at
once. To this end, sublinear (static) regret bounds are established.
Performance is also characterized in time-varying setups by means of dynamic
regret analysis. Numerical results with real and synthetic data further support
the merits of the proposed algorithms in static and dynamic scenarios.


  MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting
algorithm which, up to today, for many input sizes achieves the best known
upper bound on the number of comparisons. Indeed, it gets extremely close to
the information-theoretic lower bound. While the worst-case behavior is well
understood, only little is known about the average case.
  This work takes a closer look at the average case behavior. In particular, we
establish an upper bound of $n \log n - 1.4005n + o(n)$ comparisons. We also
give an exact description of the probability distribution of the length of the
chain a given element is inserted into and use it to approximate the average
number of comparisons numerically. Moreover, we compute the exact average
number of comparisons for $n$ up to 148.
  Furthermore, we experimentally explore the impact of different decision trees
for binary insertion. To conclude, we conduct experiments showing that a
slightly different insertion order leads to a better average case and we
compare the algorithm to the recent combination with (1,2)-Insertionsort by
Iwama and Teruyama.


  The capacity of a complex and discrete-time memoryless additive white
Gaussian noise (AWGN) channel under three constraints, namely, input average
power, input amplitude and output delivered power is studied. The output
delivered power constraint is modelled as the average of linear combination of
even moments of the channel input being larger than a threshold. It is shown
that the capacity of an AWGN channel under transmit average power and receiver
delivered power constraints is the same as the capacity of an AWGN channel
under an average power constraint. However, depending on the two constraints,
the capacity can be either achieved by a Gaussian distribution or arbitrarily
approached by using time-sharing between a Gaussian distribution and On-Off
Keying. As an application, a simultaneous wireless information and power
transfer (SWIPT) problem is studied, where an experimentally-validated
nonlinear model of the harvester is used. It is shown that the delivered power
depends on higher order moments of the channel input. Two inner bounds, one
based on complex Gaussian inputs and the other based on further restricting the
delivered power are obtained for the Rate-Power (RP) region. For Gaussian
inputs, the optimal inputs are zero mean and a tradeoff between transmitted
information and delivered power is recognized by considering asymmetric power
allocations between inphase and quadrature subchannels. Through numerical
algorithms, it is observed that input distributions (obtained by restricting
the delivered power) attain larger RP region compared to Gaussian input
counterparts.


  An exclusive measurement of the dd -> 3He n \pi 0 reaction was carried at a
beam momentum of p = 1.2 GeV/c using the WASA-at-COSY facility. For the first
time data on the total cross section as well as differential distributions were
obtained. The data are described with a phenomenological approach based on a
combination of a quasi-free model and a partial wave expansion for three-body
reaction. The total cross section is found to be \sigma(tot) = (2.89 +-
0.01(stat) +- 0.06(sys) +- 0.29(norm)) \mu b. The contribution of the
quasi-free processes (with the neutron being target or beam spectator) accounts
for 38% of the total cross section and dominates the differential distributions
in specific regions of the phase space. The remaining part of the cross section
can be described within a partial wave decomposition indicating the
significance of p-wave contributions in the final state.


  The exploitation of interference in a constructive manner has recently been
proposed for the downlink of multiuser, multi-antenna transmitters. This novel
linear precoding technique, herein referred to as constructive interference
zero forcing (CIZF) precoding, has exhibited substantial gains over
conventional approaches; the concept is to cancel, on a symbol-by-symbol basis,
only the interfering users that do not add to the intended signal power. In
this paper, the power allocation problem towards maximizing the performance of
a CIZF system with respect to some metric (throughput or fairness) is
investigated. What is more, it is shown that the performance of the novel
precoding scheme can be further boosted by choosing some of the constructive
multiuser interference terms in the precoder design. Finally, motivated by the
significant effect of user selection on conventional, zero forcing (ZF)
precoding, the problem of user selection for the novel precoding method is
tackled. A new iterative, low complexity algorithm for user selection in CIZF
is developed. Simulation results are provided to display the gains of the
algorithm compared to known user selection approaches.


  Three different elements, Silicon, Selenium, and Tellurium, are ion-implanted
in Gallium arsenide to form a conducting layer that serves as a back-gate to a
molecular beam epitaxy (MBE) overgrown two-dimensional electron gas (2DEG).
While the heavy ion Tellurium creates too many damages in the gallium arsenide
to form a conducting layer, both Silicon and Selenium show promising results
combined with MBE-grown high-quality 2DEGs. Similar 2DEG mobility compared to
non-implanted reference samples is achieved for both Silicon and Selenium
implanted structures. Individual contacts to the back-gate are challenging.
However, Silicon implanted structures, annealed before the MBE growth, result
in a function back-gate, and the electron density of the 2DEG is tuned via the
back-gate.


  A U(3) model proposed by Iachello for superconductivity in cuprate materials
is analyzed. The model consists of s and d pairs (approximated as bosons) in a
two-dimensional Fermi system with a surface. The transition occurs between a
phase in which the system is a condensate of one of the bosons, and a phase
which is a mixture of two types of bosons. In the current work we have
investigated the validity of the Bogoliubov approximation, and we used a
reduced Hamiltonian to determine a phase diagram, the symmetry of the phases
and the temperature dependence of the heat capacity.


  We present for the first time phase-resolved UV spectroscopy of an Of?p star,
namely, HD 191612. The observations were acquired with the Space Telescope
Imaging Spectrograph (STIS) on-board the Hubble Space Telescope (HST). We
report the variability observed in the main photospheric and wind features and
compare the results with previous findings for the Of?p star HD 108. We show
that UV line strengths, H(alpha), and longitudinal magnetic field, vary
coherently according to the rotational period (P = 537.6d), providing
additional support for the magnetic oblique rotator scenario. The stellar and
wind parameters of HD 191612 are obtained based on NLTE expanding atmosphere
models. The peculiar wind line profile variations revealed by the new STIS data
- not reproduced by 1D atmosphere models - are addressed through non-spherical
MHD simulations coupled with radiative transfer. The basic aspects of the UV
variability observed are explained and the structure of the dynamical
magnetosphere of HD 191612 is discussed.


  In the 90s, based on presentations of 3-manifolds by Heegaard diagrams,
Kuperberg associated a scalar invariant of 3-manifolds to each finite
dimensional involutory Hopf algebra over a field. We generalize this
construction to the case of involutory Hopf algebras in arbitrary symmetric
monoidal categories admitting certain pairs of morphisms called good pairs. We
construct examples of such good pairs for involutory Hopf algebras whose
distinguished grouplike elements are central. The generalized construction is
illustrated by an example of an involutory super Hopf algebra.


  Rejoinder to "Statistical Modeling of Spatial Extremes" by A. C. Davison, S.
A. Padoan and M. Ribatet [arXiv:1208.3378].


  Elasticity plays an important role in modern cloud computing systems. Elastic
computing allows virtual machines (i.e., computing nodes) to be preempted when
high-priority jobs arise, and also allows new virtual machines to participate
in the computation. In 2018, Yang et al. introduced Coded Storage Elastic
Computing (CSEC) to address the elasticity using coding technology, with lower
storage and computation load requirements. However, CSEC is limited to certain
types of computations (e.g., linear) due to the coded data storage based on
linear coding. Then Centralized Uncoded Storage Elastic Computing (CUSEC) with
heterogeneous computation speeds was proposed, which directly copies parts of
data into the virtual machines. In all existing works in elastic computing, the
storage assignment is centralized, meaning that the number and identity of all
virtual machines possible used in the whole computation process are known
during the storage assignment. In this paper, we consider Decentralized Uncoded
Storage Elastic Computing (DUSEC) with heterogeneous computation speeds, where
any available virtual machine can join the computation which is not predicted
and thus coordination among different virtual machines' storage assignments is
not allowed. Under a decentralized storage assignment originally proposed in
coded caching by Maddah-Ali and Niesen, we propose a computing scheme with
closed-form optimal computation time. We also run experiments over MNIST
dataset with Softmax regression model through the Tencent cloud platform, and
the experiment results demonstrate that the proposed DUSEC system approaches
the state-of-art best storage assignment in the CUSEC system in computation
time.


  The indirect approach to continuous-time system identification consists in
estimating continuous-time models by first determining an appropriate
discrete-time model. For a zero-order hold sampling mechanism, this approach
usually leads to a transfer function estimate with relative degree 1,
independent of the relative degree of the strictly proper real system. In this
paper, a refinement of these methods is developed. Inspired by indirect PEM, we
propose a method that enforces a fixed relative degree in the continuous-time
transfer function estimate, and show that the resulting estimator is consistent
and asymptotically efficient. Extensive numerical simulations are put forward
to show the performance of this estimator when contrasted with other indirect
and direct methods for continuous-time system identification.


  In this paper we study the relations of Planck-Einstein-de Broglie type for
the wave packets. We assume that the wave packet is a possible model of
particle . When studying the behaviour of the wave packet for standing waves,
in relation to an accelerated observer (i.e. Rindler observer), there can be
demonstrated that the equivalent mass of the packet is the inertial mass. In
our scenario, the waves and of the wave packets are depicted by the strain
induced/produced in the medium. The properties of the waves, of the wave packet
and, generally, of the perturbations in a material medium suggest the existence
of an acoustic world. The acoustic world has mechanical and thermodynamical
properties. The perturbations that are generated and propagated in the medium
are correlated by means of acoustic waves with maximum speed. The observers of
this world of disturbances (namely the acoustic world) have senses that are
based on the perception of mechanical waves (disturbance of any kind) and
apparatus for detecting and acquiring information by means of the same type of
wave. Time and length measurements (and other parameters) are correlated by
Lorentz type transformations, where the maximum speed is the speed of the sound
waves. By applying these transformations to the packet of standing waves, there
results that the energy, mass, linear momentum and the action variable/variable
action undergo relativistic changes. We highlight the fact that the dynamic
relativist relationship between energy and momentum is a consequence of the
wave packet model for a particle. We have also emphasized the existence of
certain limits for the energy of the disturbance and the corresponding action
variable.


  We probe the higher-order clustering of the galaxies in the final data
release (DR12) of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic
Survey (BOSS) using the method of germ-grain Minkowski Functionals (MFs). Our
sample consists of 410,615 BOSS galaxies from the northern Galactic cap in the
redshift range 0.450--0.595. We show the MFs to be sensitive to contributions
up to the six-point correlation function for this data set. We ensure with a
custom angular mask that the results are more independent of boundary effects
than in previous analyses of this type. We extract the higher-order part of the
MFs and quantify the difference to the case without higher-order correlations.
The resulting $\chi^{2}$ value of over 10,000 for a modest number of degrees of
freedom, O(200), indicates a 100-sigma deviation and demonstrates that we have
a highly significant signal of the non-Gaussian contributions to the galaxy
distribution. This statistical power can be useful in testing models with
differing higher-order correlations. Comparing the galaxy data to the QPM and
MultiDark-Patchy mocks, we find that the latter better describes the observed
structure. From an order-by-order decomposition we expect that, for example,
already a reduction of the amplitude of the MD-Patchy mock power spectrum by 5%
would remove the remaining tension.


  Radio sources at the highest redshifts can provide unique information on the
first massive galaxies and black holes, the densest primordial environments,
and the epoch of reionization. The number of astronomical objects identified at
z>6 has increased dramatically over the last few years, but previously only
three radio-loud (R2500>10) sources had been reported at z>6, with the most
distant being a quasar at z=6.18. Here we present the discovery and
characterization of P172+18, a radio-loud quasar at z=6.823. This source has an
MgII-based black hole mass of ~3x10^8 Msun and is one of the fastest accreting
quasars, consistent with super-Eddington accretion. The ionized region around
the quasar is among the largest measured at these redshifts, implying an active
phase longer than the average lifetime of the z>6 quasar population. From
archival data, there is evidence that its 1.4 GHz emission has decreased by a
factor of two over the last two decades. The quasar's radio spectrum between
1.4 and 3.0 GHz is steep (alpha=-1.31) and has a radio-loudness parameter
R2500~90. A second steep radio source (alpha=-0.83) of comparable brightness to
the quasar is only 23.1" away (~120 kpc at z=6.82; projection probability <2%),
but shows no optical or near-infrared counterpart. Further follow-up is
required to establish whether these two sources are physically associated.


  We suggest that physics underlying the recently observed removal of
sublattice and spin degeneracies in graphene in a strong magnetic field
describes a phase transition connected with the generation of an excitonic gap.
The experimental form of the Hall conductivity is reproduced and the main
characteristics of the dynamics are described. Predictions of the behavior of
the gap as a function of temperature and a gate voltage are made.


  The emergent collective motion of active agents - in particular pedestrians -
at a three-way intersection is studied by Langevin simulations of cognitive
intelligent active Brownian particles (iABPs) with directed visual perception
and self-steering avoidance. Depending on the maneuverability $\Omega$, the
goal fixation $K$, and the vision angle $\psi$, different types of pedestrian
motion emerge. At intermediate relative maneuverability $\Delta = \Omega/K$ and
large $\psi$, pedestrians have noisy trajectories due to multiple scattering
events as they encounter other pedestrians in their field of view. For $\psi =
\pi$ and large relative maneuverability $\Delta$, an effectively jammed state
is found, which belongs to the percolation universality class. For small
$\psi$, agents exhibit localised clustering and flocking, while for
intermediate $\psi$ self-organized rotational flows can emerge. The analysis of
mean squared displacement and velocity auto-correlation of the agents reveals
that the motion is well described by fractional Brownian Motion with positively
correlated noise. Finally, despite the rich variety of collective behaviour,
the fundamental flow diagram for the three-way-crossing setup shows a universal
curve for the different vision angles. Our research provides valuable insights
into the importance of vision angle and self-steering avoidance on pedestrian
dynamics in semi-dense crowds.


  Resource sharing within Grid collaborations usually implies specific sharing
mechanisms at participating sites. Challenging policy issues can arise within
virtual organizations (VOs) that integrate participants and resources spanning
multiple physical institutions. Resource owners may wish to grant to one or
more VOs the right to use certain resources subject to local policy and service
level agreements, and each VO may then wish to use those resources subject to
VO policy. Thus, we must address the question of what usage policies (UPs)
should be considered for resource sharing in VOs. As a first step in addressing
this question, we develop and evaluate different UP scenarios within a
specialized context that mimics scientific Grids within which the resources to
be shared are computers. We also present a UP architecture and define roles and
functions for scheduling resources in such grid environments while satisfying
resource owner policies.


  We consider minimization of a smooth nonconvex function with inexact oracle
access to gradient and Hessian (without assuming access to the function value)
to achieve approximate second-order optimality. A novel feature of our method
is that if an approximate direction of negative curvature is chosen as the
step, we choose its sense to be positive or negative with equal probability. We
allow gradients to be inexact in a relative sense and relax the coupling
between inexactness thresholds for the first- and second-order optimality
conditions. Our convergence analysis includes both an expectation bound based
on martingale analysis and a high-probability bound based on concentration
inequalities. We apply our algorithm to empirical risk minimization problems
and obtain improved gradient sample complexity over existing works.


  We study a graded algebra D=D(L,G) defined by a finite lattice L and a subset
G in L, a so-called building set. This algebra is a generalization of the
cohomology algebras of hyperplane arrangement compactifications found in work
of De Concini and Procesi. Our main result is a representation of D, for an
arbitrary atomic lattice L, as the Chow ring of a smooth toric variety that we
construct from L and G. We describe this variety both by its fan and
geometrically by a series of blowups and orbit removal. Also we find a Groebner
basis of the relation ideal of D and a monomial basis of D over Z.


  We develop a phenomenological formalism for mixing effects between the
Standard Model and hidden-sector fields, motivated by dark matter in the
Universe as well as string theories. The scheme includes multiple Higgs-portal
interactions in the scalar sector as well as multiple gauge-kinetic mixings in
the abelian gauge sector. While some of the mixing effects can be cast in
closed form, other elements can be controlled analytically only by means of
perturbative expansions in the ratio of standard scales over large hidden
scales. Higgs and vector-boson masses and mixings are illustrated numerically
for characteristic processes.


  We consider the initial value problem for a new two-component Sasa-Satsuma
equation associated with the fourth-order Lax pair with decaying initial data
on the line. By utilizing the spectral analysis, the solution of the new
two-component Sasa-Satsuma system is transformed into the solution of a
fourth-order matrix Riemann-Hilbert problem. Then the long-time asymptotics of
the solution is obtained by means of the nonlinear steepest descent method of
Deift and Zhou for oscillatory Riemann-Hilbert problems. We show that there are
three main regions in the half-plane, where the asymptotics has qualitatively
different forms: a left fast decaying sector, a central Painleve sector where
the asymptotics is described in terms of the solution of a new coupled Painleve
II equation which is related to a fourth-order matrix Riemann-Hilbert problem,
and a right slowly decaying oscillatory sector.


  Both the Haldane spin chain and a topologically dimerized chain feature
topologically protected edge states that are expected to be robust against some
kind of noise. To elucidate whether it might be feasible to create such edge
states in dimerized chains in a controlled manner in solid states environments,
e.g. as spin chains on surfaces, as has already been successfully achieved with
the Haldane chain, we investigate their robustness with respect to long-range
coupling, anisotropies and finite chain length. The theoretical investigation
is based on an alternating Heisenberg spin chain with spin-1/2, which is
investigated using exact diagonalization. We find that dimerized chains and
Haldane chains have robustness against long-range coupling and anisotropies. In
particular, dimerized spin chains are significantly more robust than Haldane
chains


  In this note, we prove the existence of a tri-graded Khovanov-type bicomplex
(Theorem 1.2). The graded Euler characteristic of the total complex associated
with this bicomplex is the colored Jones polynomial of a link. The first
grading of the bicomplex is a homological one derived from cabling of the link
(i.e., replacing a strand of the link with several parallel strands); the
second grading is related to the homological grading of ordinary Khovanov
homology; finally, the third grading is preserved by the differentials, and
corresponds to the degree of the variable in the colored Jones polynomial. In
particular, we introduce a way to take a small cabling link diagram directly
from a big cabling link diagram (Theorem 3.2). This is a refined version of
arXiv:0907.5247.


  We explore the sparticle and Higgs spectroscopy of an SU(5) inspired
extension of the constrained minimal supersymmetric standard model (CMSSM). The
universal soft parameter m_0 is replaced by m_{\bar 5} and m_{10}, where
m_{\bar 5} and m_{10} denote universal soft scalar masses associated with
fields in the five and ten dimensional representations of SU(5). The special
case m_{\bar 5} << m_{10} yields a rather characteristic sparticle spectroscopy
which can be tested at the LHC. We highlight a few benchmark points in which
the lightest neutralino saturates the WMAP bound on cold dark matter abundance.


  Let $A_{1} := k [t, \partial ]$ be the first algebra over a field $k$ of
characteristic zero. One can associate to each right ideal $I$ of $A_1$ its
Stafford subgroup, which is a subgroup of $\Aut_k(A_1)$, the automorphism group
of the ring $A_1$. In this article we show that each Stafford subgroup is equal
to its normalizer. For that, we study when the Stafford subgroup of a right
ideal of $A_1$ contains a given Stafford subgroup.


  Spike sorting is a class of algorithms used in neuroscience to attribute the
time occurences of particular electric signals, called action potential or
spike, to neurons. We rephrase this problem as a particular optimization
problem : Lasso for convolutional models in high dimension. Lasso (i.e. least
absolute shrinkage and selection operator) is a very generic tool in machine
learning that help us to look for sparse solutions (here the time occurrences).
However, for the size of the problem at hand in this neuroscience context, the
classical Lasso solvers are failing. We present here a new and much faster
algorithm. Making use of biological properties related to neurons, we explain
how the particular structure of the problem allows several optimizations,
leading to an algorithm with a temporal complexity which grows linearly with
respect to the size of the recorded signal and can be performed online.
Moreover the spatial separability of the initial problem allows to break it
into subproblems, further reducing the complexity and making possible its
application on the latest recording devices which comprise a large number of
sensors. We provide several mathematical results: the size and numerical
complexity of the subproblems can be estimated mathematically by using
percolation theory. We also show under reasonable assumptions that the Lasso
estimator retrieves the true time occurrences of the spikes {with large
probability}. Finally the theoretical time complexity of the algorithm is
given. Numerical simulations are also provided in order to illustrate the
efficiency of our approach.


  The hierarchically orthogonal functional decomposition of any measurable
function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into
a sum of increasing dimension functions depending only on a subvector of X.
Even when X_1,..., X_p are assumed to be dependent, this decomposition is
unique if components are hierarchically orthogonal. That is, two of the
components are orthogonal whenever all the variables involved in one of the
summands are a subset of the variables involved in the other. Setting Y=f(X),
this decomposition leads to the definition of generalized sensitivity indices
able to quantify the uncertainty of Y with respect to the dependent inputs X.
In this paper, a numerical method is developed to identify the component
functions of the decomposition using the hierarchical orthogonality property.
Furthermore, the asymptotic properties of the components estimation is studied,
as well as the numerical estimation of the generalized sensitivity indices of a
toy model. Lastly, the method is applied to a model arising from a real-world
problem.


  Metamaterials are composed of periodic subwavelength metal/dielectric
structures that resonantly couple to the electric and/or magnetic components of
the incident electromagnetic fields, exhibiting properties that are not found
in nature. Planar metamaterials with subwavelength thickness, or metasurfaces,
consisting of single-layer or few-layer stacks of planar structures, can be
readily fabricated using lithography and nanoprinting methods, and the
ultrathin thickness in the wave propagation direction can greatly suppress the
undesirable losses. Metasurfaces enable a spatially varying optical response,
mold optical wavefronts into shapes that can be designed at will, and
facilitate the integration of functional materials to accomplish active control
and greatly enhanced nonlinear response. This paper reviews recent progress in
the physics of metasurfaces operating at wavelengths ranging from microwave to
visible. We provide an overview of key metasurface concepts such as anomalous
reflection and refraction, and introduce metasurfaces based on the
Pancharatnam-Berry phase and Huygens' metasurfaces, as well as their use in
wavefront shaping and beam forming applications, followed by a discussion of
polarization conversion in few-layer metasurfaces and their related properties.
An overview of dielectric metasurfaces reveals their ability to realize unique
functionalities coupled with Mie resonances and their low ohmic losses. We also
describe metasurfaces for wave guidance and radiation control, as well as
active and nonlinear metasurfaces. Finally, we conclude by providing our
opinions of opportunities and challenges in this rapidly developing research
field.


  Using the Keldysh nonequilibrium Green function technique, we study the
current and shot noise spectroscopy of a single molecular quantum dot coupled
to a local phonon mode. It is found that in the presence of electron-phonon
coupling, in addition to the resonant peak associated with the single level of
the dot, satellite peaks with the separation set by the frequency of phonon
mode appear in the differential conductance. In the ``single level'' resonant
tunneling region, the differential shot noise power exhibit two split peaks.
However, only single peaks show up in the ``phonon assisted''
resonant-tunneling region. An experimental setup to test these predictions is
also proposed.


  Let $k$ and $l$ be integers, both at least 2. A $(k,l)$-bipartite graph is an
$l$-regular bipartite multigraph with coloured bipartite sets of size $k$.
Define $\chi(k,l)$ and $\mu(k,l)$ to be the minimum and maximum order of
automorphism groups of $(k,l)$-bipartite graphs, respectively. We determine
$\chi(k,l)$ and $\mu(k,l)$ for $k\geq 8$, and analyse the generic situation
when $k$ is fixed and $l$ is large. In particular, we show that almost all such
graphs have automorphism groups which fix the vertices pointwise and have order
far less than $\mu(k,l)$. These graphs are intimately connected with both
integer doubly-stochastic matrices and uniform set partitions; we examine the
uniform distribution on the set of $k\times k$ integer doubly-stochastic
matrices with all line sums $l$, showing that with high probability all entries
stray far from the mean. We also show that the symmetric group acting on
uniform set partitions is non-synchronizing.


  We show that there is a constant $k$ such that when $r \geq 2$ and $m \geq
r^k$, the complete $r$-partite graph $K_{m*r}$ has a non-colorable list
assignment $L$ such that $|L(v)| \geq \frac{7}{750}r\ln m$ for all $v$ and such
that $|L(u) \cap L(v)| \leq \left\lfloor \frac{2r}{r-1} \right\rfloor$ whenever
$u \neq v$. This roughly extends a result of Alon to the context of
"choosability with separation", introduced by Kratochv\'il, Tuza, and Voigt.


  In this paper, the notion of bi-Boolean independence for non-unital pairs of
algebras is introduced thereby extending the notion of Boolean independence to
pairs of algebras. The notion of B-$(\ell, r)$-cumulants is defined via a
bi-Boolean moment-cumulant formula over the lattice of bi-interval partitions,
and it is demonstrated that bi-Boolean independence is equivalent to the
vanishing of mixed B-$(\ell, r)$-cumulants. Furthermore, some of the simplest
bi-Boolean convolutions are considered, and a bi-Boolean partial
$\eta$-transform is constructed for the study of limit theorems and infinite
divisibility with respect to the additive bi-Boolean convolution. In
particular, a bi-Boolean L\'{e}vy-Hin\v{c}in formula is derived in perfect
analogy with the bi-free case, and some Bercovici-Pata type bijections are
provided. Additional topics considered include the additive bi-Fermi
convolution, some relations between the $(\ell, r)$- and B-$(\ell,
r)$-cumulants, and bi-Boolean independence in an amalgamated setting.
  The last section of this paper also includes an errata that will be published
with this copy of the paper.


  We present a framework for the quantum enhanced estimation of multiple
parameters corresponding to non-commuting unitary generators. Our formalism
provides a recipe for the simultaneous estimation of all three components of a
magnetic field. We propose a probe state that surpasses the precision of
estimating the three components individually and discuss measurements that come
close to attaining the quantum limit. Our study also reveals that too much
quantum entanglement may be detrimental to attaining the Heisenberg scaling in
quantum metrology.


  We propose and analyse a new Milstein type scheme for simulating stochastic
differential equations (SDEs) with highly nonlinear coefficients. Our work is
motivated by the need to justify multi-level Monte Carlo simulations for
mean-reverting financial models with polynomial growth in the diffusion term.
We introduce a double implicit Milstein scheme and show that it possesses
desirable properties. It converges strongly and preserves non-negativity for a
rich family of financial models and can reproduce linear and nonlinear
stability behaviour of the underlying SDE without severe restriction on the
time step. Although the scheme is implicit, we point out examples of financial
models where an explicit formula for the solution to the scheme can be found.


  Instead of the Yukawa mechanism for intermediate- and short-range interaction
some new approach based on formation of the symmetric six-quark bag in the
state $|(0s)^6[6]_X,L=0>$ dressed due to strong coupling to $\pi$, $\sigma$ and
$\rho$ fields are suggested. This new mechanism offers both a strong
intermediate-range attraction which replaces the effective $\sigma$-exchange
(or excitation of two isobars in the intermediate state) in traditional force
models and also short-range repulsion. Simple illustrative model is developed
which demonstrates clearly how well the suggested new mechanism can reproduce
$NN$ data.


  The Bose-Einstein condensation of excitons continues to garner immense
attention as a prototypical example for observing emergent properties from
many-body quantum effects. In particular, Titanium Diselenide (TiSe$_2$) is a
promising candidate for realizing exciton condensation and was experimentally
observed only very recently. Surprisingly, the condensate was experimentally
characterized by a soft plasmon mode that only exists near the transition
temperature, $T_c$, of the charge density wave (CDW). Here, we characterize and
analyze the experimental spectra using linear-response time-dependent density
functional theory and find that the soft mode can be attributed to interband
electronic transitions. At the CDW state below $T_c$, the periodic lattice
distortions hamper the spontaneous formation of the exciton by introducing a
CDW gap. The band gap raises the soft mode and merges it into the regular
plasmon. Our surprising results contradict previous simplistic analytical
models commonly used in the scientific literature. In addition, we find that a
finite electronic temperature, $T_e$, introduces a dissipation channel and
prevents the condensation above $T_c$. The combined effect of the CDW and $T_e$
explains the fragile temperature-dependence of the exciton condensation. Taken
together, our work provides the first \textit{ab initio} atomic-level framework
for rationalizing recent experiments and further manipulating exciton
condensates in TiSe$_2$.


  The Cauchy identities play an important role in the theory of symmetric
functions. It is known that Cauchy sums for the $q$-Whittaker and the skew
Schur polynomials produce the same factorized expressions modulo a
$q$-Pochhammer symbol. We consider the sums with restrictions on the length of
the first rows for labels of both polynomials and prove an identity which
relates them. The proof is based on techniques from integrable probability: we
rewrite the identity in terms of two probability measures: the $q$-Whittaker
measure and the periodic Schur measure. The relation follows by comparing their
Fredholm determinant formulas.


  A new model for the high-energy emission from pulsars is developed by
considering charged particle motion in the fields of a spinning, highly
magnetised and conducting sphere in vacuum. A generally applicable
approximation to the particle motion in strong fields is developed and applied
to the numerical modelling, and the radiation emitted by curvature emission is
summed to generate light curves. The model predicts many of the observed
features of pulsar light curves. This paper outlines the basic properties of
the model; a subsequent paper will discuss the statistical properties of a
population of model pulsars and apply the model to the known gamma-ray pulsars.


  The synthesis of transition metals in a two-dimensional (2D) fashion has
attracted growing attention for both fundamental and application-oriented
investigations, such as 2D magnetism, nanoplasmonics and non-linear optics.
However, the large-area synthesis of this class of materials in a single-layer
form poses non-trivial difficulties. Here we present the synthesis of a
large-area 2D gold layer, stabilized in between silicon carbide and monolayer
(ML) graphene. We show that the 2D-Au ML is a semiconductor with the valence
band maximum 50 meV below the Fermi level. The graphene and gold layers are
largely non-interacting, thereby defining a novel class of van der Waals
heterostructure. The 2D-Au bands, exhibit a 225 meV spin-orbit splitting along
the {\Gamma K} direction, making it appealing for spin-related applications. By
tuning the amount of gold at the SiC/graphene interface, we induce a
semiconductor to metal transition in the 2D-Au, which was never observed before
and hosts great interest for fundamental physics.


  Recent measurements at Q-band (43 GHz) have verified the improved performance
of the GBT provided by the updated gravity model that was deployed in the fall
of 2014. The measured gain curve is indistinguishable from 1.0 over an
elevation range from 15 degrees to 80 degrees. This represents a significant
improvement on the previous gain curve from 2009 that showed decreasing
efficiency below 40 degrees and above 65 degrees elevation. The current
estimated surface errors, under good conditions, is 230 microns for the GBT.


  Deadlock-free dynamic network reconfiguration process is usually studied from
the routing algorithm restrictions and resource reservation perspective. The
dynamic nature yielded by the transition process from one routing function to
another is often managed by restricting resource usage in a static predefined
manner, which often limits the supported routing algorithms and/or inactive
link patterns, or either requires additional resources such as virtual
channels. Exploiting compatibility between routing functions by exploring their
associated Channel Dependency Graphs (CDG) can take a great benefit from the
dynamic nature of the reconfiguration process. In this paper, we propose a new
dynamic reconfiguration process called Upstream Progressive Reconfiguration
(UPR). Our algorithm progressively performs dependency addition/removal in a
per channel basis relying on the information provided by the CDG while the
reconfiguration process takes place. This gives us the opportunity to foresee
compatible scenarios where both routing functions coexist, reducing the amount
of resource drainage as well as packet injection halting.


  There is no doubt that the field of Fundamental Constants in Physics and
Their Time Variation is one of the hottest subjects in modern theoretical and
experimental physics, with potential implications in all fundamental areas of
physics research, such as particle physics, gravitation, astrophysics and
cosmology. In this Special Issue, the state-of-the-art in the field is
presented in detail.


  In this paper, we establish the Freidlin-Wentzell type large deviation
principles for porous medium-type equations perturbed by small multiplicative
noise. The porous medium operator $\Delta (|u|^{m-1}u)$ is allowed. Our proof
is based on weak convergence approach.


  The analysis of surrounding media has been a long-standing challenge of
optical fiber sensors. Measurements are difficult due to the confinement of
light to the inner core of standard fibers. Over the last two years, new sensor
concepts have enabled the analysis of liquids outside the cladding boundary,
where light does not reach. Sensing is based on opto-mechanical, forward
stimulated Brillouin scattering interactions between guided light and sound
waves. In most previous works, however, the protective polymer coating of the
fiber had to be removed first. In this work, we report the opto-mechanical
analysis of liquids outside commercially available, standard single-mode fibers
with polyimide coating. The polyimide layer provides mechanical protection but
can also transmit acoustic waves from the fiber cladding towards outside media.
Comprehensive analysis of opto-mechanical coupling in coated fibers that are
immersed in liquid is provided. The model shows that forward stimulated
Brillouin scattering spectra in coated fibers are more complex than those of
bare fibers, and strongly depend on the exact coating diameter and the choice
of acoustic mode. Nevertheless, sensing outside coated fibers is demonstrated
experimentally. Integrated measurements over 100 meters of fiber clearly
distinguish between air, ethanol and water outside polyimide coating. Measured
spectra are in close quantitative agreement with the analytic predictions.
Further, distributed opto-mechanical time-domain reflectometry mapping of water
and ethanol outside coated fiber is reported, with a spatial resolution of 100
meters. The results represent a large step towards practical opto-mechanical
fiber sensors.


  We consider the damped wave equation on a compact manifold. We propose
different ways of measuring decay of the energy (time averages of lower energy
levels, decay for frequency localized data...) and exhibit links with resolvent
estimates on the imaginary axis. As an application we prove a universal
logarithmic lower resolvent bound on the imaginary axis for the damped wave
operator when the Geometric Control Condition (GCC) is not satisfied. This is
to be compared to the uniform boundedness of the resolvent on that set when GCC
holds. The proofs rely on (i) various (re-)formulations of the damped wave
equation as a conservative hyperbolic part perturbed by a lower order damping
term;(ii) a "Plancherel-in-time" argument as in classical proofs of the
Gearhart-Huang-Pr{\"u}ss theorem; and (iii) an idea of Bony-Burq-Ramond of
propagating a coherent state along an undamped trajectory up to Ehrenfest time.


  Two-dimensional (2D) topological insulators (TIs) hold promise for
applications in spintronics based on the fact that the propagation direction of
edge electrons of a 2D TI is robustly linked to their spin origination. Here,
with the use of first-principles calculations, we predict a family of robust 2D
TIs in monolayer square transition metal dichalcogenides (MoS2, MoSe2, MoTe2,
WS2, WSe2, and WTe2). Sizeable intrinsic nontrivial bulk band gaps ranging from
24 to 187 meV are obtained, guarantying the quantum spin Hall (QSH) effect
observable at room temperature in these new 2D TIs. Significantly different
from most known 2D TIs with comparable band gaps, these sizeable energy gaps
originate from the strong spin-orbit interaction related to the pure d
electrons of the Mo/W atoms around the Fermi level. A single pair of
topologically protected helical edge states is established for the edge of
these systems with the Dirac point locating in the middle of the bulk band gap,
and their topologically nontrivial states are also confirmed with nontrivial
topological invariant Z2 = 1. More interestingly, by controlling the applied
strain, a topological quantum phase transition between a QSH phase and a
metallic phase or a trivial insulating phase can be realized in these 2D
materials, and the detailed topological phase diagram is established.


  Epidemiological delays, such as incubation periods, serial intervals, and
hospital lengths of stay, are among key quantities in infectious disease
epidemiology that inform public health policy and clinical practice. This
information is used to inform mathematical and statistical models, which in
turn can inform control strategies. There are three main challenges that make
delay distributions difficult to estimate. First, the data are commonly
censored (e.g., symptom onset may only be reported by date instead of the exact
time of day). Second, delays are often right truncated when being estimated in
real time (not all events that have occurred have been observed yet). Third,
during a rapidly growing or declining outbreak, overrepresentation or
underrepresentation, respectively, of recently infected cases in the data can
lead to bias in estimates. Studies that estimate delays rarely address all
these factors and sometimes report several estimates using different
combinations of adjustments, which can lead to conflicting answers and
confusion about which estimates are most accurate. In this work, we formulate a
checklist of best practices for estimating and reporting epidemiological delays
with a focus on the incubation period and serial interval. We also propose
strategies for handling common biases and identify areas where more work is
needed. Our recommendations can help improve the robustness and utility of
reported estimates and provide guidance for the evaluation of estimates for
downstream use in transmission models or other analyses.


  Finding \cp~violation (\CPV ) in 1964 produced a real revolution in the
fundamental dynamics, although the community did not understand it right away.
The paper by Kobayashi \& Maskawa \cite{KM} appeared in 1973 to describe
\CPV~in classes of three (or more) families of quarks, non-minimal Higgs'
dynamics and/or charged right-handed currents. The Standard Model is defined
now with three families of quarks. It can describe the measured \cp~ \&
\ot~violation in kaon and $B$ mesons at least as the leading source. None has
been found in baryons, charm mesons, top quarks and EDMs -- except from `hot'
news from LHCb data about {\bf T}-odd moment in $\Lambda_b^0 \to p
\pi^-\pi^+\pi^-$ \cite{LHCbtalk}. We have failed the explain our matter vs.
anti-matter huge asymmetry. Even when there is no obvious connections with that
asymmetry, it makes sense to probe \CPV~for the signs of New Dynamics \& their
features. Furthermore we have to measure regional \CPV~in many-body final
states with accuracy. I discuss EDMs, axion's impact on cosmology \& its
connection with Dark Matter; finally I talk about \CPV~in leptonic dynamics.


  We investigate magnetic excitations in iridium insulators with pentavalent
Ir$^{5+}$ ($5d^4$) ions with strong spin-orbit coupling. We obtain a
microscopic model based on the local Ir$^{5+}$ multiplets involving $J=0$
(singlet), $J=1$ (triplet), and $J=2$ (quintet) spin-orbital states. We get
effective interactions between these multiplets on square and
face-centered-cubic (fcc) structures of magnetic ions in the
layered-perovskites and the double-perovkites, in particular Ba$_2$YIrO$_6$.
Further, we derive an effective spin-orbital Hamiltonian in terms of bond
bosons and explore possible instabilities towards magnetic and quadrupole
orderings. Additionally, we study charge excitations with help of the
variational cluster perturbation theory and calculate the electronic charge gap
as a function of hopping and Coulomb interactions. Based on both electronic and
magnetic phase diagrams, we verify the possibility of excitonic magnetism due
to condensation of spin-orbital excitons in Ir$^{5+}$ iridates.


  Reaction delays play an important role in determining the qualitative
dynamical properties of a platoon of vehicles traversing a straight road. In
this paper, we investigate the impact of delayed feedback on the dynamics of
the Classical Car-Following Model (CCFM). Specifically, we analyze the CCFM in
no delay, small delay and arbitrary delay regimes. First, we derive a
sufficient condition for local stability of the CCFM in no-delay and
small-delay regimes using. Next, we derive the necessary and sufficient
condition for local stability of the CCFM for an arbitrary delay. We then
demonstrate that the transition of traffic flow from the locally stable to the
unstable regime occurs via a Hopf bifurcation, thus resulting in limit cycles
in system dynamics. Physically, these limit cycles manifest as back-propagating
congestion waves on highways. In the context of human-driven vehicles, our work
provides phenomenological insight into the impact of reaction delays on the
emergence and evolution of traffic congestion. In the context of self-driven
vehicles, our work has the potential to provide design guidelines for control
algorithms running in self-driven cars to avoid undesirable phenomena.
Specifically, designing control algorithms that avoid jerky vehicular movements
is essential. Hence, we derive the necessary and sufficient condition for
non-oscillatory convergence of the CCFM. Next, we characterize the rate of
convergence of the CCFM, and bring forth the interplay between local stability,
non-oscillatory convergence and the rate of convergence of the CCFM. Further,
to better understand the oscillations in the system dynamics, we characterize
the type of the Hopf bifurcation and the asymptotic orbital stability of the
limit cycles using Poincare normal forms and the center manifold theory. The
analysis is complemented with stability charts, bifurcation diagrams and MATLAB
simulations.


  In the paper, we discuss the studies of mathematical models of diffusion
scattering of waves in the phase space, and relation of these models with
quantum mechanics. In the previous works it is shown that in these models of
classical scattering process of waves, the quantum mechanical description
arises as the asymptotics after a small time. In this respect, the proposed
models can be considered as examples in which the quantum descriptions arise as
approximate ones for certain hypothetical reality. The deviation between the
proposed models and the quantum ones can arise, for example, for processes with
rapidly changing potential function. Under its action the diffusion scattering
process of waves will go out from the states described by quantum mechanics.
  In the paper it is shown that the proposed models of diffusion scattering of
waves possess the property of gauge invariance. This implies that they are
described similarly in all inertial coordinate systems, i.e., they are
invariant under the Galileo transformations.
  We propose a program of further research.


  A system of interacting dipoles is of paramount importance for understanding
of many-body physics. The interaction between dipoles is {\it anisotropic} and
{\it long-range}. While the former allows to observe rich effects due to
different geometries of the system, long-range ($1/r^3$) interactions lead to
strong correlations between dipoles and frustration. In effect, interacting
dipoles in a lattice form a paradigmatic system with strong correlations and
exotic properties with possible applications in quantum information
technologies, and as quantum simulators of condensed matter physics, material
science, etc. Notably, such a system is extremely difficult to model due to a
proliferation of interaction induced multi-band excitations for sufficiently
strong dipole-dipole interactions. In this article we develop a consistent
theoretical model of interacting polar molecules in a lattice by applying the
concepts and ideas of ionization theory which allows us to include highly
excited Bloch bands. Additionally, by involving concepts from quantum optics
(population trapping), we show that one can induce frustration and engineer
exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a
system.


  To study the assumption that the utility maximization hypothesis implicitly
adds to consumer theory, we consider a mathematical representation of
pre-marginal revolution consumer theory based on subjective exchange ratios. We
introduce two axioms on subjective exchange ratio, and show that both axioms
hold if and only if consumer behavior is consistent with the utility
maximization hypothesis. Moreover, we express the process for a consumer to
find the transaction stopping point in terms of differential equations, and
prove that the conditions for its stability are equal to the two axioms
introduced in the above argument. Therefore, the consumer can find his/her
transaction stopping point if and only if his/her behavior is consistent with
the utility maximization hypothesis. In addition to these results, we discuss
equivalence conditions for axioms to evaluate their mathematical strength, and
methods for expressing the theory of subjective exchange ratios in terms of
binary relations.


  We investigate the possibility for a flat Bianchi I brane Universe to
recollaps due to the presence of a negative "dark radiation" and an anisotropic
stress in the form of a homogeneous magnetic field, localized on the brane.


  In this work, we propose a new approach to cosmic ray muon momentum
measurement using multiple pressurized gaseous Cherenkov radiators. Knowledge
of cosmic ray muon momentum has the potential to significantly improve and
expand the use of a variety of recently developed muon-based radiographic
techniques. However, existing muon tomography systems rely only on muon
tracking and have no momentum measurement capabilities which reduces the image
resolution and requires longer measurement times. A fieldable cosmic ray muon
spectrometer with momentum measurement capabilities for use in muon scattering
tomography is currently missing. We address this challenge by optimally varying
the pressure of multiple gaseous Cherenkov radiators and identifying the
radiators that are triggered by muons that have momentum higher than the
Cherenkov threshold momentum. We evaluate the proposed concept through Geant4
simulations and demonstrate that the cosmic ray muon momentum spectrum can be
reconstructed with sufficient accuracy and resolution for two scenarios: (i) a
perfect Cherenkov muon spectrometer and (ii) a practical spectrometer where
noise is introduced in the form of scintillation and transition radiation
photons. To quantify the accuracy of spectrometer, the concept of true and
false classifications are introduced. The fraction of true classification is
investigated for each momentum level in a practical radiator. The average
classification rate for momentum range of 0.2 to 7.0 GeV/c with uncertainty of
1 GeV/c is approximately 85%.


  We present a self-consistent theoretical framework for finite-dimensional
discrete phase spaces that leads us to establish a well-grounded mapping scheme
between Schwinger unitary operators and generators of the special unitary group
$\mathrm{SU(N)}$. This general mathematical construction provides a sound
pathway to the formulation of a genuinely discrete Wigner function for
arbitrary quantum systems described by finite-dimensional state vector spaces.
To illustrate our results, we obtain a general discrete Wigner function for the
group $\mathrm{SU(3)}$ and apply this to the study of a particular three-level
system. Moreover, we also discuss possible extensions to the discrete Husimi
and Glauber-Sudarshan functions, as well as future investigations on
multipartite quantum states.


  A numerical code for solving various Lyman alpha (Lya) radiative transfer
(RT) problems is presented. The code is suitable for an arbitrary,
three-dimensional distribution of Lya emissivity, gas temperature, density, and
velocity field. Capable of handling Lya RT in an adaptively refined grid-based
structure, it enables detailed investigation of the effects of clumpiness of
the interstellar (or intergalactic) medium. The code is tested against various
geometrically and physically idealized configurations for which analytical
solutions exist, and subsequently applied to three "Lyman-break galaxies",
extracted from high-resolution cosmological simulations at redshift z = 3.6.
Proper treatment of the Lya scattering reveals a diversity of surface
brightness (SB) and line profiles. Specifically, for a given galaxy the maximum
observed SB can vary by an order of magnitude, and the total flux by a factor
of 3 - 6, depending on the viewing angle. This may provide an explanation for
differences in observed properties of high-redshift galaxies, and in particular
a possible physical link between Lyman-break galaxies and regular Lya emitters.


  We probe the $\theta$-dependence of QCD at finite isospin chemical potential
$\mu_I$ using the effective chiral Lagrangian approach. The phase diagram in
the $\theta$, $\mu_I$ plane is constructed and described in detail in terms of
chiral and pion condensates. The physics at $\theta ~ \pi$ is investigated in
both the normal and superfluid phase. Finally, the behaviour of the gluon
condensate at finite $\mu_I$ is computed.


  BDAQ53 is a readout system and verification framework for hybrid pixel
detector readout chips of the RD53 family. These chips are designed for the
upgrade of the inner tracking detectors of the ATLAS and CMS experiments.
BDAQ53 is used in applications where versatility and rapid customization are
required, such as in laboratory testing environments, test beam campaigns, and
permanent setups for quality control measurements. It consists of custom and
commercial hardware, a Python-based software framework, and FPGA firmware.
BDAQ53 is developed as open source software with both software and firmware
being hosted in a public repository.


  We study Koopman and quasi-regular representations corresponding to the
action of arbitrary weakly branch group G on the boundary of a rooted tree T.
One of the main results is that in the case of a quasi-invariant Bernoulli
measure on the boundary of T the corresponding Koopman representation of G is
irreducible (under some general conditions). We also show that quasi-regular
representations of G corresponding to different orbits and Koopman
representations corresponding to different Bernoulli measures on the boundary
of T are pairwise disjoint. This gives two continual collections of pairwise
disjoint irreducible representations of a weakly branch group. Another
corollary of our results is triviality of the centralizer of G in various
groups of transformations on the boundary of T.


  A decomposition of a higher order linear differential operator with
polynomial coefficients into a direct sum of two factor operators is obtained.
This leads to a lower echelon matrix representation for operators of the above
mentioned type arising from a finite sequence of elementary operations. As a
consequence, a complete basis of canonical polynomials is generated via a
modified Ortiz' recurrence formula. The approach presented in this paper
enables us to curry out the full and self-operative recursive implementation of
the spectral-tau method. These results can be applied to a variety of operator
equations associated with infinite matrices in lower row echelon form, having
implications for a broad family of discrete and continuous numerical methods,
interpreted as special realizations of the tau method under specific
perturbation terms.


  Recently, Transformers have shown promising performance in various vision
tasks. However, the high costs of global self-attention remain challenging for
Transformers, especially for high-resolution vision tasks. Local self-attention
runs attention computation within a limited region for the sake of efficiency,
resulting in insufficient context modeling as their receptive fields are small.
In this work, we introduce two new attention modules to enhance the global
modeling capability of the hierarchical vision transformer, namely, random
sampling windows (RS-Win) and important region windows (IR-Win). Specifically,
RS-Win sample random image patches to compose the window, following a uniform
distribution, i.e., the patches in RS-Win can come from any position in the
image. IR-Win composes the window according to the weights of the image patches
in the attention map. Notably, RS-Win is able to capture global information
throughout the entire model, even in earlier, high-resolution stages. IR-Win
enables the self-attention module to focus on important regions of the image
and capture more informative features. Incorporated with these designs,
RSIR-Win Transformer demonstrates competitive performance on common vision
tasks.


  In this paper we investigate how the dynamics of a two-level atom is affected
by its interaction with the quantized near field of a plasmonic slab in
relative motion. We demonstrate that for small separation distances and a
relative velocity greater than a certain threshold, this interaction can lead
to a population inversion, such that the probability of the excited state
exceeds the probability of the ground state, corresponding to a negative
spontaneous emission rate. It is shown that the developed theory is intimately
related to a classical problem. The problem of quantum friction is analyzed and
the differences with respect to the corresponding classical effect are
highlighted.


  As we typically teach in an introductory mechanics course, choosing a "good"
reference frame with convenient axes may present a major simplification to a
problem. Additionally, knowing some conserved quantities provides an extremely
powerful problem-solving tool. While the former idea is typically discussed in
the context of Newton's Laws, the latter starts with introducing conservation
of energy even later.
  This work presents an elegant example of implementing both aforementioned
ideas in the kinematical context, thus providing a "warm-up" introduction to
the standard tools used later on in dynamics. Both the choice of the
(non-orthogonal) reference frame and the conserved quantities are rather
non-standard, yet at the same time quite intuitive to the problem at hand. Two
such problems are discussed in detail with two alternative approaches. The
first approach does not even require knowledge of calculus. In the appendix, I
also present the brute-force solution involving a coupled system of
differential equations. In addition, a few exercises and another similar
problem for students' "homework" are provided at the end.


  We describe in detail how a sliding scale is introduced in the
renormalization of a QFT according to integer-dimensional implicit
regularization scheme. We show that since no regulator needs to be specified at
intermediate steps of the calculation, the introduction of a mass scale is a
direct consequence of a set of renormalization conditions. As an illustration
the one loop beta-function for QED and lambda*phi^4 theories are derived. They
are given in terms of derivatives of appropriately systematized functions
(related to definited parts of the amplitudes) with respect to a mass scale mu.
Our formal scheme can be easily generalized to higher loop calculations.


  Gaussian blurring is a well-established method for image data augmentation:
it may generate a large set of images from a small set of pictures for training
and testing purposes for Artificial Intelligence (AI) applications. When we
apply AI for non-imagelike biological data, hardly any related method exists.
Here we introduce the "Newtonian blurring" in human braingraph (or connectome)
augmentation: Started from a dataset of 1053 subjects, we first repeat a
probabilistic weighted braingraph construction algorithm 10 times for
describing the connections of distinct cerebral areas, then take 7 repetitions
in every possible way, delete the lower and upper extremes, and average the
remaining 7-2=5 edge-weights for the data of each subject. This way we augment
the 1053 graph-set to 120 x 1053 = 126,360 graphs. In augmentation techniques,
it is an important requirement that no artificial additions should be
introduced into the dataset. Gaussian blurring and also this Newtonian blurring
satisfy this goal. The resulting dataset of 126,360 graphs, each in 5
resolutions (i.e., 631,800 graphs in total), is freely available at the site
https://braingraph.org/cms/download-pit-group-connectomes/. Augmenting with
Newtonian blurring may also be applicable in other non-image related fields,
where probabilistic processing and data averaging are implemented.


  In his 1916 ground-breaking general relativity paper Einstein had imposed a
restrictive coordinate condition, his field equations were valid for coordinate
systems which are unimodular. Later, Einstein published a paper on
gravitational waves. The solution presented in this paper did not satisfy the
above restrictive condition. In his gravitational waves paper, Einstein
concluded that gravitational fields propagate at the speed of light. The
solution is the Minkowski flat metric plus a small disturbance propagating in a
flat spacetime. Einstein calculated the small deviation from Minkowski metric
in a manner analogous to that of retarded potentials in electrodynamics.
However, in obtaining the above derivation, Einstein made a mathematical error.
This error caused him to obtain three different types of waves compatible with
his approximate field equations: longitudinal waves, transverse waves and a new
type of wave. Einstein added an Addendum in which he suggested that in systems
in unimodular coordinates only waves of the third type occur and these waves
transport energy. He became obsessed with his unimodular coordinates.
Einstein's colleagues demonstrated to him that in the coordinate system in
unimodular coordinates the gravitational wave of a mass point carry no energy,
but Einstein tried to persuade them that he had actually not made a mistake in
his gravitational waves paper. Einstein, however, eventually accepted his
colleagues results and dropped the restrictive unimodular coordinates. This
finally led him to discover plane transverse gravitational waves.


  In order to perform quantum Hamiltonian dynamics minimizing localization
effects, we introduce a quasi-one dimensional tight-binding model whose mean
free path is smaller than the size of the sample. This one, in turn, is smaller
than the localization length. We study the return probability to the starting
layer of the system by means of direct diagonalization of the Hamiltonian. We
create a one dimensional excitation and observe sub-diffusive behavior for
times larger than the Debye time but shorter than the Heisenberg time. The
exponent corresponds to the fractal dimension $d^{*} \sim 0.72$ which is
compared to that calculated from the eigenstates by means of the inverse
participation number.


  Recently Kipping (2021) identified the so-called "exomoon corridor", a
potentially powerful new tool for identifying possible exomoon hosts, enabled
by the observation that fully half of all planets hosting an exomoon will
exhibit transit timing variation (TTV) periodicities of 2-4 epochs. One key
outstanding problem in the search for exomoons, however, is the question of how
well the methods we have developed under the single moon assumption extend to
systems with multiple moons. In this work we use $N$-body simulations to
examine the exomoon corridor effect in the more general case of $N \geq 1$
moons, generating realistic TTVs produced by satellite systems more akin to
those seen in the outer Solar System. We find that indeed the relationship does
hold for systems with up to 5 moons in both resonant and non-resonant chain
configurations. Our results suggest an observational bias against finding
systems with large numbers of massive moons; as the number of moons increases,
total satellite mass ratios are generally required to be significantly lower in
order to maintain stability, or architectures must be more finely tuned to
survive. Moons produced in impact or capture scenarios may therefore dominate
early detections. Finally, we examine the distribution of TTV periods measured
for a large number of Kepler Objects of Interest (KOIs) and find the same
characteristic exomoon corridor distribution in several cases. This could be
dynamical evidence for an abundance of moons in the field, though we caution
against strong inferences based on this result.


  In this work, we describe strategies and provide case-study activities that
can be used to examine the properties of superposition, entanglement, tagging,
complementarity, and measurement in quantum curricula geared for teacher
training. Having a solid foundation in these conceptual ideas is critical for
educators who will be adopting quantum ideas within the classroom. Yet they are
some of the most difficult concepts to master. We show how one can
systematically develop these conceptual foundations with thought experiments on
light and with thought experiments that employ the Stern-Gerlach experiment. We
emphasize the importance of computer animations in aiding the instruction on
these concepts.


  Low-energy reflectivity of electrons from single- and multi-layer graphene is
examined both theoretically and experimentally. A series of minima in the
reflectivity over the energy range of 0 - 8 eV are found, with the number of
minima depending on the number of graphene layers. Using first-principles
computations, it is demonstrated that a free standing n-layer graphene slab
produces n-1 reflectivity minima. This same result is also found experimentally
for graphene supported on SiO2. For graphene bonded onto other substrates it is
argued that a similar series of reflectivity minima is expected, although in
certain cases an additional minimum occurs, at an energy that depends on the
graphene-substrate separation and the effective potential in that space.


  We introduce a new cohomology theory for stacks called elliptic Hochschild
homology, prove some fundamental properties and compute it in some classes of
examples. We then introduce its periodic cyclic version and show that, over the
complex numbers and for a quotient stack, this recovers Grojnowski's
equivariant elliptic cohomology of the analytification.


  Bootstrap percolation on a graph with infection threshold $r\in \mathbb{N}$
is an infection process, which starts from a set of initially infected vertices
and in each step every vertex with at least $r$ infected neighbours becomes
infected. We consider bootstrap percolation on the binomial random graph
$G(n,p)$, which was investigated among others by Janson, \L uczak, Turova and
Valier (2012). We improve their results by strengthening the probability bounds
for the number of infected vertices at the end of the process.


  The upper critical fields, $H_{c2}$($T$), of single crystals of the
superconductor
Ca$_{10}$(Pt$_{4-\delta}$As$_{8}$)((Fe$_{0.97}$Pt$_{0.03}$)$_{2}$As$_{2}$)$_{5}$
($\delta$ $\approx$ 0.246) are determined over a wide range of temperatures
down to $T$ = 1.42 K and magnetic fields of up to $\mu_{0}H$ $\simeq$ 92 T. The
measurements of anisotropic $H_{c2}$($T$) curves are performed in pulsed
magnetic fields using radio-frequency contactless penetration depth
measurements for magnetic field applied both parallel and perpendicular to the
\textbf{ab}-plane. Whereas a clear upward curvature in
$H_{c2}^{\parallel\textbf{c}}$($T$) along \textbf{H}$\parallel$\textbf{c} is
observed with decreasing temperature, the $H_{c2}^{\parallel\textbf{ab}}$($T$)
along \textbf{H}$\parallel$\textbf{ab} shows a flattening at low temperatures.
The rapid increase of the $H_{c2}^{\parallel\textbf{c}}$($T$) at low
temperatures suggests that the superconductivity can be described by two
dominating bands. The anisotropy parameter, $\gamma_{H}$ $\equiv$
$H_{c2}^{\parallel\textbf{ab}}/H_{c2}^{\parallel\textbf{c}}$, is $\sim$7 close
to $T_{c}$ and decreases considerably to $\sim$1 with decreasing temperature,
showing rather weak anisotropy at low temperatures.


  In this work we investigate the electrostatic properties of two dimensional
electron system (2DES) in the integer quantum Hall regime. The alternating
screening properties of compressible and incompressible strips are formed due
to edge effects together with electron-electron interactions. As it is well
known, the Landau quantization emanates from strong perpendicular magnetic
fields. The (Landau) energy levels are broadened due to impurities, which we
embedded their effects in density of states (DOS). In a basic level DOS has two
different forms: the Gaussian and semi-elliptic descriptions. The second form
is calculated within the self consistent Born approximation (SCBA). Having in
hand the density of states, we obtain both the longitudinal and Hall
(transversal) conductivities ($\sigma_{l}, \sigma_{H}$) utilizing
Thomas-Fermi-Poisson approximation to calculate position dependent charge
density profile and use Drude formalism to obtain transport coefficients.
Since, the definition of capacitance is closely related with compressibility
via DOS, (local) screening properties of 2DES is extremely important to
understand local capacitances. Here we numerically simulate a translational
invariant Hall bar subject to high magnetic fields which is perpendicular to
the plane of the 2DES using realistic parameters extracted from the related
experiments. Using the above mentioned approaches the local capacitances are
calculated, numerically. Our findings are in perfect agreement with related
experimental results which are based on a dynamic scanning capacitance
microscopy technique.


  Nuclear charge radii of $^{7,9,10,11}$Be have been determined by
high-precision laser spectroscopy. On-line measurements were performed with
collinear laser spectroscopy in the $2s_{1/2} \to 2p_{1/2}$ transition on a
beam of Be$^{+}$ ions. Collinear and anticollinear laser beams were used
simultaneously and the absolute frequency determination using a frequency comb
yielded an accuracy in the isotope-shift measurements of about
  1 MHz. Combination with accurate calculations of the mass-dependent isotope
shifts yield nuclear charge radii. The charge radius decreases from $^7$Be to
$^{10}$Be and then increases for the halo nucleus $^{11}$Be. When comparing our
results with predictions of {\it ab initio} nuclear structure calculations we
find good agreement. Additionally, the nuclear magnetic moment of $^7$Be was
determined to be $-1.3995(5)\mu_{\rm N}$ and that of $^{11}$Be from a previous
$\beta$-NMR measurement was confirmed.


  We study the Hodge structure of elliptic surfaces which are canonically
defined from bielliptic curves of genus three. We prove that the period map for
the second cohomology has one dimensional fibers, and the period map for the
total cohomology is of degree twelve, and moreover, by adding the information
of the Hodge structure of the canonical divisor, we prove a generic Torelli
theorem for these elliptic surfaces. Finally, we give explicit examples of the
pair of non-isomorphic elliptic surfaces which have the same Hodge structure on
themselves and the same Hodge structure on their canonical divisors.


  We propose that a single mesoscopic ensemble of trapped polar molecules can
support a "holographic quantum computer" with hundreds of qubits encoded in
collective excitations with definite spatial phase variations. Each phase
pattern is uniquely addressed by optical Raman processes with classical optical
fields, while one- and two-qubit gates are accomplished by selectively
transferring the individual qubit states to a stripline microwave cavity field
and a Cooper pair box where controllable two-level unitary dynamics is governed
by classical microwave fields.


  Continuum or discrete polarizable models for the study of optoelectronic
processes in embedded subsystems rely mostly on the restriction of the
surrounding electronic dielectric response to its low frequency limit. Such a
description hinges on the assumption that the electrons in the surrounding
medium react instantaneously to any excitation in the central subsystem,
treating thus the environment in the adiabatic limit. Exploiting a recently
developed embedded $GW$ formalism, with an environment described at the fully
ab initio level, we assess the merits of the adiabatic limit with respect to an
environment where the full dynamics of the dielectric response is considered.
Further, we show how to properly take the static limit of the environment
susceptibility, introducing the so-called Coulomb-hole and screened-exchange
contributions to the reaction field. As a first application, we consider a
C$_{60}$ molecule at the surface of a C$_{60}$ crystal, namely a case where the
dynamics of the embedded and embedding subsystems are similar. The common
adiabatic assumption, when properly treated, generates errors below $10\%$ on
the polarization energy associated with frontier energy levels and associated
energy gaps. Finally, we consider a water molecule inside a metallic nanotube,
the worst case for the environment adiabatic limit. The error on the gap
polarization energy remains below $10\%$, even though the error on the frontier
orbitals polarization energies can reach a few tenths of an electronvolt.


  We show that, when compactified on a circle, N=(2,0),d=6 supergravity coupled
to 1 tensor multiplet and nV vector multiplets is dual to N=(2,0),d=6
supergravity coupled to just nT=nV+1 tensor multiplets and no vector
multiplets. Both theories reduce to the same models of N=2,d=5 supergravity
coupled to nV5=nV+2 vector fields. We derive Buscher rules that relate
solutions of these theories (and of the theory that one obtains by dualizing
the 3-form field strength) admitting an isometry. Since the relations between
the fields of N=2,d=5 supergravity and those of the 6-dimensional theories are
the same with or without gaugings, we construct supersymmetric non-Abelian
solutions of the 6-dimensional gauged theories by uplifting the recently found
5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions
describe the usual superpositions of strings and waves supplemented by a BPST
instanton in the transverse directions. One of the solutions obtained
interpolates smoothly between two AdS3xS3 geometries with different radii.


  Robotic navigation has been approached as a problem of 3D reconstruction and
planning, as well as an end-to-end learning problem. However, long-range
navigation requires both planning and reasoning about local traversability, as
well as being able to utilize general knowledge about global geography, in the
form of a roadmap, GPS, or other side information providing important cues. In
this work, we propose an approach that integrates learning and planning, and
can utilize side information such as schematic roadmaps, satellite maps and GPS
coordinates as a planning heuristic, without relying on them being accurate.
Our method, ViKiNG, incorporates a local traversability model, which looks at
the robot's current camera observation and a potential subgoal to infer how
easily that subgoal can be reached, as well as a heuristic model, which looks
at overhead maps for hints and attempts to evaluate the appropriateness of
these subgoals in order to reach the goal. These models are used by a heuristic
planner to identify the best waypoint in order to reach the final destination.
Our method performs no explicit geometric reconstruction, utilizing only a
topological representation of the environment. Despite having never seen
trajectories longer than 80 meters in its training dataset, ViKiNG can leverage
its image-based learned controller and goal-directed heuristic to navigate to
goals up to 3 kilometers away in previously unseen environments, and exhibit
complex behaviors such as probing potential paths and backtracking when they
are found to be non-viable. ViKiNG is also robust to unreliable maps and GPS,
since the low-level controller ultimately makes decisions based on egocentric
image observations, using maps only as planning heuristics. For videos of our
experiments, please check out our project page
https://sites.google.com/view/viking-release.


  We prove that one of the conditions in M.V. Zaicev's formula for the
PI-exponent and in its natural generalization for the Hopf PI-exponent, can be
weakened. Using the modification of the formula, we prove that if a finite
dimensional semisimple Lie algebra acts by derivations on a finite dimensional
Lie algebra over a field of characteristic $0$, then the differential
PI-exponent coincides with the ordinary one. Analogously, the exponent of
polynomial $G$-identities of a finite dimensional Lie algebra with a rational
action of a connected reductive affine algebraic group $G$ by automorphisms,
coincides with the ordinary PI-exponent. In addition, we provide a simple
formula for the Hopf PI-exponent and prove the existence of the Hopf
PI-exponent itself for $H$-module Lie algebras whose solvable radical is
nilpotent, assuming only the $H$-invariance of the radical, i.e. under weaker
assumptions on the $H$-action, than in the general case. As a consequence, we
show that the analog of Amitsur's conjecture holds for $G$-codimensions of all
finite dimensional Lie $G$-algebras whose solvable radical is nilpotent, for an
arbitrary group $G$.