  Radio occultations of Saturn's main rings by spacecraft suggest a power law
particle size-distribution down to sizes of the order of 1 cm (Marouf et al.,
1983), (Zebker et al., 1985). The lack of optical depth variations between
ultraviolet and near-IR wavelengths indicate a lack of micron-sized particles.
Between these two regimes, the particle-size distribution is largely unknown. A
cutoff where the particle-size distribution turns over must exist, but the
position and shape of it is not clear from existing studies.
  Using a series of solar occultations performed by the VIMS instrument
on-board Cassini in the near-infrared, we are able to measure light forward
scattered by particles in the A and C rings. With a model of diffraction by
ring particles, and the previous radio work as a constraint on the slope of the
particle size distribution, we estimate the minimum particle size using a
truncated power-law size distribution. The C Ring shows a minimum particle size
of $4.1^{+3.8}_{-1.3}$ mm, with an assumed power law index of q=3.1 and a
maximum particle size of 10 m.
  The A Ring signal shows a similar level of scattered flux, but modeling is
complicated by the presence of self-gravity wakes and higher optical depths. If
q<3, our A Ring model requires a minimum particle size below one millimeter (<
0.34 mm for an assumed q=2.75, or $0.56^{+0.35}_{-0.16}$ mm for a steeper
q=2.9) to be consistent with VIMS observations. These results might seem to
contradict previous optical(Dones et al., 1993) and infrared (French and
Nicholson, 2000) work, which implied that there were few particles in the A
Ring smaller than 1 cm. But, because of the shallow power law, relatively
little optical depth (between 0.03 and 0.16 in extinction, or 0.015 - 0.08 in
absorption) is provided by these particles.


  We extend the general formalism of two-photon exchange to elastic
lepton-nucleon scattering by accounting for all lepton mass terms. We then
perform a numerical estimate of the muon-proton scattering at low momentum
transfer in view of the future MUSE experiment. For this purpose, we estimate
the two-photon exchange corrections to muon-proton scattering observables by
considering the contribution of the proton intermediate state, which is
expected to dominate at very low momentum transfers. We find that the
two-photon exchange effect to the unpolarized muon- proton scattering cross
section in the MUSE kinematical region is of the order of 0.5%.


  Most existing slot filling models tend to memorize inherent patterns of
entities and corresponding contexts from training data. However, these models
can lead to system failure or undesirable outputs when being exposed to spoken
language perturbation or variation in practice. We propose a perturbed semantic
structure awareness transferring method for training perturbation-robust slot
filling models. Specifically, we introduce two MLM-based training strategies to
respectively learn contextual semantic structure and word distribution from
unsupervised language perturbation corpus. Then, we transfer semantic knowledge
learned from upstream training procedure into the original samples and filter
generated data by consistency processing. These procedures aim to enhance the
robustness of slot filling models. Experimental results show that our method
consistently outperforms the previous basic methods and gains strong
generalization while preventing the model from memorizing inherent patterns of
entities and contexts.


  Recently, De Lellis and Sz\'ekelyhidi constructed H\"older continuous,
dissipative (weak) solutions to the incompressible Euler equations in the torus
$\mathbb T^3$. The construction consists in adding fast oscillations to the
trivial solution. We extend this result by establishing optimal h-principles in
two and three space dimensions. Specifically, we identify all subsolutions
(defined in a suitable sense) which can be approximated in the $H^{-1}$-norm by
exact solutions. Furthermore, we prove that the flows thus constructed on
$\mathbb T^3$ are genuinely three-dimensional and are not trivially obtained
from solutions on $\mathbb T^2$.


  We present algorithms for the detection of a class of heart arrhythmias with
the goal of eventual adoption by practicing cardiologists. In clinical
practice, detection is based on a small number of meaningful features extracted
from the heartbeat cycle. However, techniques proposed in the literature use
high dimensional vectors consisting of morphological, and time based features
for detection. Using electrocardiogram (ECG) signals, we found smaller subsets
of features sufficient to detect arrhythmias with high accuracy. The features
were found by an iterative step-wise feature selection method. We depart from
common literature in the following aspects: 1. As opposed to a high dimensional
feature vectors, we use a small set of features with meaningful clinical
interpretation, 2. we eliminate the necessity of short-duration
patient-specific ECG data to append to the global training data for
classification 3. We apply semi-parametric classification procedures (in an
ensemble framework) for arrhythmia detection, and 4. our approach is based on a
reduced sampling rate of ~ 115 Hz as opposed to 360 Hz in standard literature.


  Additive isotonic regression attempts to determine the relationship between a
multi-dimensional observation variable and a response, under the constraint
that the estimate is the additive sum of univariate component effects that are
monotonically increasing. In this article, we present a new method for such
regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear
modelling to additive isotonic regression. Thus, it is viable in many
situations with high dimensional predictor variables, where selection of
significant versus insignificant variables are required. We suggest an
algorithm involving a modification of the backfitting algorithm CPAV. We give a
numerical convergence result, and finally examine some of its properties
through simulations. We also suggest some possible extensions that improve
performance, and allow calculation to be carried out when the direction of the
monotonicity is unknown.


  In the fields of finance, engineering and sciences data mining/ machine
learning has held an eminent position in predictive analysis. Complex
algorithms and adaptive decision models have contributed towards streamlining
research as well as improve forecasting. Extensive study in areas surrounding
computation and mathematical sciences has primarily been responsible for the
field's development. Classification based modeling, which holds a prominent
position amongst the different rule-based algorithms, is one of the most widely
used decision making tool. The decision tree has a place of profound
significance in classification modeling. A number of heuristics have been
developed over the years to refine its decision making process. Most heuristics
applied to such tree-based learning algorithms derive their roots from
Shannon's 'Information Theory'. The current application of this theory is
directed towards individual assessment of the attribute-values. The proposed
study takes a look at the effects of combining these values with the aim to
improve the 'Information Gain'. A search-based heuristic tool is applied for
identifying the subsets sharing a better gain value than the ones presented in
the GID3 approach. An application towards the feature selection stage of the
mining process has been tested and presented with statistical analysis.


  In this work, we report observation of strain effect on physical properties
of Sr2IrO4 thin films grown on SrTiO3 (001) and LaAlO3 (001) substrates. It is
found that the film on LaAlO3 with compressive strain has a lower
antiferromagnetic transition temperature (TN~210 K) than the film on SrTiO3
(TN~230 K) with tensile strain, which is probably caused by modified interlayer
coupling. Interestingly, magnetoresistance due to pseudospin-flip of the film
on LaAlO3 is much larger than that of tensile-strained film on SrTiO3, and
robust anisotropic magnetoresistance is observed in the former, but H-driven
reversal behavior is seen in the latter. By performing first principles
calculations, it is revealed that epitaxial strain plays an efficient role in
tuning the canting angle of Jeff=1/2 moments and thus net moment at every IrO2
layer, responsible for the difference in magnetoresistance between the films.
The reversal of anisotropic magnetoresistance in the thin film on SrTiO3 can be
ascribed to stabilization of a metastable stable with smaller bandgap as the
Jeff=1/2 moments are aligned along the diagonal of basal plane by H. However,
theoretical calculations reveal much higher magnetocrystalline anisotropy
energy in the film on LaAlO3. This causes difficulties to drive the Jeff=1/2
moments to reach the diagonal and thereby the metastable state, explaining the
distinct anisotropic magnetoresistance between two samples in a qualitative
sense. Our findings indicate that strain can be a highly efficient mean to
engineer the functionalities of Jeff=1/2 antiferromagnet Sr2IrO4.


  We present a Julia package, DisjunctiveProgramming.jl, that extends the
functionality in JuMP.jl to allow modeling problems via logical propositions
and disjunctive constraints. Such models can then be reformulated into
Mixed-Integer Programs (MIPs) that can be solved with the various MIP solvers
supported by JuMP. To do so, logical propositions are converted to Conjunctive
Normal Form (CNF) and reformulated into equivalent algebraic constraints.
Disjunctions are reformulated into mixed-integer constraints via the
reformulation technique specified by the user (Big-M or Hull reformulations).
The package supports reformulations for disjunctions containing linear,
quadratic, and nonlinear constraints.


  By means of self-consistent semi-empirical LCAO calculations we study the
itinerant magnetism of (Fe_{0.65}Ni_{0.35})_{1-y} Mn_y alloys for y between 0
and 0.22 at T=0 K, neglecting only the transverse spin components. We find that
the magnetic behaviour is quite complicated on a local scale. In addition to
ferromagnetic behaviour, also metastable spin-glass-like configurations are
found. In the same approach, using a direct numerical calculation by the
Kubo-Formalism without any fit parameters, we also calculate the electrical
conductance in the magnetic state and find that the $y$-dependence observed in
the experiments is well reproduced by our calculations, except of an overall
factor of rougly 5, by which our resistivities are too large.


  The brain is intrinsically organized into large-scale networks that
constantly re-organize on multiple timescales, even when the brain is at rest.
The timing of these dynamics is crucial for sensation, perception, cognition
and ultimately consciousness, but the underlying dynamics governing the
constant reorganization and switching between networks are not yet well
understood. Functional magnetic resonance imaging (fMRI) and
electroencephalography (EEG) provide anatomical and temporal information about
the resting-state networks (RSNs), respectively. EEG microstates are brief
periods of stable scalp topography, and four distinct configurations with
characteristic switching patterns between them are reliably identified at rest.
Microstates have been identified as the electrophysiological correlate of
fMRI-defined RSNs, this link could be established because EEG microstate
sequences are scale-free and have long-range temporal correlations. This
property is crucial for any approach to model EEG microstates. This paper
proposes a novel modeling approach for microstates: we consider nonlinear
stochastic differential equations (SDEs) that exhibit a noisy network attractor
between nodes that represent the microstates. Using a single layer network
between four states, we can reproduce the transition probabilities between
microstates but not the heavy tailed residence time distributions. Introducing
a two layer network with a hidden layer gives the flexibility to capture these
heavy tails and their long-range temporal correlations. We fit these models to
capture the statistical properties of microstate sequences from EEG data
recorded inside and outside the MRI scanner and show that the processing
required to separate the EEG signal from the fMRI machine noise results in a
loss of information which is reflected in differences in the long tail of the
dwell-time distributions.


  Motivated by the question whether quantum gravity can "smear out" the
classical singularity we analyze a certain quantum space and its
quantum-mechanical completeness. Classical singularity is understood as a
geodesic incompleteness, while quantum completeness requires a unique unitary
time evolution for test fields propagating on an underlying background. Here
the crucial point is that quantum completeness renders the Hamiltonian (or
spatial part of the wave operator) to be essentially self-adjoint in order to
generate a unique time evolution. We examine a model of quantum space which
consists of a noncommutative BTZ black hole probed by a test scalar field. We
show that the quantum gravity (noncommutative) effect is to enlarge the domain
of BTZ parameters for which the relevant wave operator is essentially
self-adjoint. This means that the corresponding quantum space is quantum
complete for a larger range of BTZ parameters rendering the conclusion that in
the quantum space one observes the effect of "smearing out" the singularity.


  We have obtained the Love number and corresponding tidal deformabilites
($\Lambda$) associated with the relativistic mean-field parametrizations shown
to be consistent (CRMF) with the nuclear matter, pure neutron matter, symmetry
energy and its derivatives [Dutra, et al., Phys. Rev. C 90, 055203 (2014)]. Our
results show that CRMF models present very good agreement with the recent data
from binary neutron star merger event GW170817. They also confirm the strong
correlation between $\Lambda_{1.4}$ and the radius of canonical stars
($R_{1.4}$). When a recently GW170817 constraint on $\Lambda_{1.4}$ and the
corresponding radius $R_{1.4}$ is used, the majority of the models tested are
shown to satisfy it.


  We here confirm the occurrence of spin glass phase transition and extract
estimates of associated critical exponents of a highly monodisperse and densely
compacted system of bare maghemite nanoparticles. This system has earlier been
found to behave like an archetypal spin glass, with e.g. a sharp transition
from paramagnetic to non-equilibrium behavior, suggesting that this system
undergoes a spin-glass phase transition at a relatively high temperature, $T_g$
$\sim$ 140 K.


  We report on observations of the supernova remnant Cassiopeia A in the energy
range from 100 MeV to 100 GeV using 44 months of observations from the Large
Area Telescope on board the Fermi Gamma-ray Space Telescope. We perform a
detailed spectral analysis of this source and report on a low-energy break in
the spectrum at $1.72^{+1.35}_{-0.89}$ GeV. By comparing the results with
models for the gamma-ray emission, we find that hadronic emission is preferred
for the GeV energy range.


  Starting from a (non-associative) quasi-Poisson structure, the derivation of
a Roytenberg-type algebra is presented. From the Jacobi identities of the
latter, the most general form of Bianchi identities for fluxes (H,f,Q,R) is
then derived. It is also explained how this approach is related to the
mathematical theory of quasi-Lie and Courant algebroids.


  Through Monte Carlo Simulation, the well-known majority-vote model has been
studied with noise on directed random graphs. In order to characterize
completely the observed order-disorder phase transition, the critical noise
parameter $q_c$, as well as the critical exponents $beta/nu$, $gamma/nu$ and
$1/nu$ have been calculated as a function of the connectivity $z$ of the random
graph.


  This paper proposes a deep speech enhancement method which exploits the high
potential of residual connections in a wide neural network architecture, a
topology known as Wide Residual Network. This is supported on single
dimensional convolutions computed alongside the time domain, which is a
powerful approach to process contextually correlated representations through
the temporal domain, such as speech feature sequences. We find the residual
mechanism extremely useful for the enhancement task since the signal always has
a linear shortcut and the non-linear path enhances it in several steps by
adding or subtracting corrections. The enhancement capacity of the proposal is
assessed by objective quality metrics and the performance of a speech
recognition system. This was evaluated in the framework of the REVERB Challenge
dataset, including simulated and real samples of reverberated and noisy speech
signals. Results showed that enhanced speech from the proposed method succeeded
for both, the enhancement task with intelligibility purposes and the speech
recognition system. The DNN model, trained with artificial synthesized
reverberation data, was able to deal with far-field reverberated speech from
real scenarios. Furthermore, the method was able to take advantage of the
residual connection achieving to enhance signals with low noise level, which is
usually a strong handicap of traditional enhancement methods.


  We present a multi-wavelength study on three new $z\sim5.6$ quasi stellar
objects (QSOs) selected based on their radio and optical/near-infrared
properties in publicly available surveys and then identified with dedicated
spectroscopic observations. These are among the radio-brightest QSOs currently
known at $z>5.5$, having $\rm R=S_{\rm 5GHz}/S_{\rm 4400A}>100$. In this work
we present their identification and we also discuss their multi-wavelength
properties (from the radio to the X-ray band) based on the detection in public
surveys as well as dedicated radio and X-ray observations. The three sources
present a wide range of properties, in terms of relative intensity and spectral
shape, highlighting the importance of multi-wavelength observations in order to
accurately characterise these high-$z$ objects. In particular, from our
analysis we found one source, at $z=5.61$, that presents clear blazars
properties (strong and flat radio and X-ray emission), making it one of the
most distant currently known in this class. Moreover, from the fit of the
optical/near-infrared photometric measurements with an accretion disc model, as
well as the analysis of the CIV broad emission line in one case, we were able
to estimate the mass and the accretion rate of the central black holes in these
systems, finding $\rm M_{\rm BH}\sim1-10\times10^9$ M$_\odot$ accreting at a
rate $\lambda_{\rm Edd}\sim0.1-0.2$. With this work we increase the number of
very-high redshift radio-powerful QSOs characterised with multi-wavelength
observations, essential in order to understand the evolution and the properties
of this still poorly constrained class of sources.


  This paper introduces a new strategy for setting the regularization parameter
when solving large-scale discrete ill-posed linear problems by means of the
Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy
principle, although no initial knowledge of the norm of the error that affects
the right-hand side is assumed; an increasingly more accurate approximation of
this quantity is recovered during the Arnoldi algorithm. Some theoretical
estimates are derived in order to motivate our approach. Many numerical
experiments, performed on classical test problems as well as image deblurring
are presented.


  Vehicle routing problems (VRPs), which can be found in numerous real-world
applications, have been an important research topic for several decades.
Recently, the neural combinatorial optimization (NCO) approach that leverages a
learning-based model to solve VRPs without manual algorithm design has gained
substantial attention. However, current NCO methods typically require building
one model for each routing problem, which significantly hinders their practical
application for real-world industry problems with diverse attributes. In this
work, we make the first attempt to tackle the crucial challenge of
cross-problem generalization. In particular, we formulate VRPs as different
combinations of a set of shared underlying attributes and solve them
simultaneously via a single model through attribute composition. In this way,
our proposed model can successfully solve VRPs with unseen attribute
combinations in a zero-shot generalization manner. Extensive experiments are
conducted on eleven VRP variants, benchmark datasets, and industry logistic
scenarios. The results show that the unified model demonstrates superior
performance in the eleven VRPs, reducing the average gap to around 5% from over
20% in the existing approach and achieving a significant performance boost on
benchmark datasets as well as a real-world logistics application. The source
code is included in https://github.com/FeiLiu36/MTNCO.


  We develop two methods to calculate the momentum distribution of the
insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard
model with on-site and nearest-neighbor boson-boson repulsions on
$d$-dimensional hypercubic lattices. First we construct the random phase
approximation result, which corresponds to the exact solution for the
infinite-dimensional limit. Then we perform a power-series expansion in the
hopping $t$ via strong-coupling perturbation theory, to evaluate the momentum
distribution in two and three dimensions; we also use the strong-coupling
theory to verify the random phase approximation solution in infinite
dimensions. Finally, we briefly discuss possible implications of our results in
the context of ultracold dipolar Bose gases with dipole-dipole interactions
loaded into optical lattices.


  Motivated by several generalizations of the well--known Mathieu series, the
main object of this paper is to introduce new extension of generalized Mathieu
series and to derive various integral representations of such series. Finally
master bounding inequality is established using the newly derived integral
expression.


  Mapping the environment has been an important task for robot navigation and
Simultaneous Localization And Mapping (SLAM). LIDAR provides a fast and
accurate 3D point cloud map of the environment which helps in map building.
However, processing millions of points in the point cloud becomes a
computationally expensive task. In this paper, a methodology is presented to
generate the segmented surfaces in real time and these can be used in modeling
the 3D objects. At first an algorithm is proposed for efficient map building
from single shot data of spinning Lidar. It is based on fast meshing and
sub-sampling. It exploits the physical design and the working principle of the
spinning Lidar sensor. The generated mesh surfaces are then segmented by
estimating the normal and considering their homogeneity. The segmented surfaces
can be used as proposals for predicting geometrically accurate model of objects
in the robots activity environment. The proposed methodology is compared with
some popular point cloud segmentation methods to highlight the efficacy in
terms of accuracy and speed.


  We present a comparative study of three infrared asteroid surveys based on
the size and albedo data from the Infrared Astronomical Satellite (IRAS), the
Japanese infrared satellite AKARI, and the Wide-field Infrared Survey Explorer
(WISE). Our study showed that: (i) the total number of asteroids detected with
diameter and albedo information with these three surveyors is 138,285, which is
largely contributed by WISE; (ii) the diameters and albedos measured by the
three surveyors for 1,993 commonly detected asteroids are in good agreement,
and within +/-10% in diameter and +/-22% in albedo at 1sigma deviation level.
It is true that WISE offers size and albedo of a large fraction (>20%) of known
asteroids down to a few km bodies, but we would suggest that the IRAS and AKARI
catalogs compensate for larger asteroids up to several hundred km, especially
in the main belt region. We discuss the complementarity of these three catalogs
in order to facilitate the use of these data sets for characterizing the
physical properties of minor planets.


  Contemporary methods for benchmarking noisy quantum processors typically
measure average error rates or process infidelities. However, thresholds for
fault-tolerant quantum error correction are given in terms of worst-case error
rates -- defined via the diamond norm -- which can differ from average error
rates by orders of magnitude. One method for resolving this discrepancy is to
randomize the physical implementation of quantum gates, using techniques like
randomized compiling (RC). In this work, we use gate set tomography to perform
precision characterization of a set of two-qubit logic gates to study RC on a
superconducting quantum processor. We find that, under RC, gate errors are
accurately described by a stochastic Pauli noise model without coherent errors,
and that spatially-correlated coherent errors and non-Markovian errors are
strongly suppressed. We further show that the average and worst-case error
rates are equal for randomly compiled gates, and measure a maximum worst-case
error of 0.0197(3) for our gate set. Our results show that randomized
benchmarks are a viable route to both verifying that a quantum processor's
error rates are below a fault-tolerance threshold, and to bounding the failure
rates of near-term algorithms, if -- and only if -- gates are implemented via
randomization methods which tailor noise.


  Dynamic Neural Radiance Fields (Dynamic NeRF) enhance NeRF technology to
model moving scenes. However, they are resource intensive and challenging to
compress. To address these issues, this paper presents WavePlanes, a fast and
more compact explicit model. We propose a multi-scale space and space-time
feature plane representation using N-level 2-D wavelet coefficients. The
inverse discrete wavelet transform reconstructs feature signals at varying
detail, which are linearly decoded to approximate the color and density of
volumes in a 4-D grid. Exploiting the sparsity of wavelet coefficients, we
compress the model using a Hash Map containing only non-zero coefficients and
their locations on each plane. Compared to the state-of-the-art (SotA)
plane-based models, WavePlanes is up to 15x smaller while being less resource
demanding and competitive in performance and training time. Compared to other
small SotA models WavePlanes preserves details better without requiring custom
CUDA code or high performance computing resources. Our code is available at:
https://github.com/azzarelli/waveplanes/


  We assess the effects on Big Bang Nucleosynthesis (BBN) of lepton number
generation in the early universe resulting from the two-doublet four-neutrino
mass/mixing scheme. It has been argued that this neutrino mass/mixing
arrangement gives the most viable fit to the existing data. We study full 4 x 4
mixing matrices and show how possible symmetries in these can affect the BBN
He-4 abundance yields. Though there is as yet no consensus on the reliability
of BBN calculations with neutrino flavor mixing, we show that, in the case
where the sign of the lepton number asymmetry is unpredictable, BBN
considerations may pick out specific relationships between mixing angles. In
particular, reconciling the observed light element abundances with a
\bar\nu_\mu <-> \bar\nu_e oscillation interpretation of LSND would allow unique
new constraints on the neutrino mixing angles in this model.


  In this paper, we systematically study weak solutions of a linear singular or
degenerate parabolic equation in a mixed divergence form and nondivergence
form, which arises from the linearized fast diffusion equation and the
linearized porous medium equation with the homogeneous Dirichlet boundary
condition. We prove the H\"older regularity of their weak solutions.


  A major outstanding question regarding the formation of planetary systems is
whether wide-orbit giant planets form differently than close-in giant planets.
We aim to establish constraints on two key parameters that are relevant for
understanding the formation of wide-orbit planets: 1) the relative mass
function and 2) the fraction of systems hosting multiple companions. In this
study, we focus on systems with directly imaged substellar companions, and the
detection limits on lower-mass bodies within these systems. First, we uniformly
derive the mass probability distributions of known companions. We then combine
the information contained within the detections and detection limits into a
survival analysis statistical framework to estimate the underlying mass
function of the parent distribution. Finally, we calculate the probability that
each system may host multiple substellar companions. We find that 1) the
companion mass distribution is rising steeply toward smaller masses, with a
functional form of $N\propto M^{-1.3\pm0.3}$, and consequently, 2) many of
these systems likely host additional undetected sub-stellar companions.
Combined, these results strongly support the notion that wide-orbit giant
planets are formed predominantly via core accretion, similar to the better
studied close-in giant planets. Finally, given the steep rise in the relative
mass function with decreasing mass, these results suggest that future deep
observations should unveil a greater number of directly imaged planets.


  We describe a simple setup generating pure valley currents -- valley
transport without charge transport -- in strained graphene nanoribbons with
zigzag edges. The crucial ingredient is a uniaxial strain pattern which couples
to the low-energy Dirac electrons as a uniform pseudomagnetic field.
Remarkably, the resulting pseudo-Landau levels are not flat but disperse
linearly from the Dirac points, with an opposite slope in the two valleys. We
show how this is a natural consequence of an inhomogeneous Fermi velocity
arising in the low-energy theory describing the system, which maps to an
exactly-solvable singular Sturm-Liouville problem. The velocity of the valley
currents can be controlled by tuning the magnitude of strain and by applying
bias voltages across the ribbon. Furthermore, applying an electric field along
the ribbon leads to pumping of charge carriers between the two valleys,
realizing a valley analog of the chiral anomaly in one spatial dimension. These
effects produce unique signatures that can be observed experimentally by
performing ordinary charge transport measurements and spectroscopy.


  We establish a formula relating global diffusion in a space periodic
dynamical system to cycles in the elementary cell which tiles the space under
translations.


  COSY INFINITY uses a beamline coordinate system with a Frenet-Serret frame
relative to the reference particle, and calculates differential algebra-valued
transfer maps by integrating the ODEs of motion in the respective vector space
over a differential algebra (DA).
  We will describe and perform computation of the DA transfer map of an
electrostatic spherical deflector in a laboratory coordinate system using two
conventional methods: (1) by integrating the ODEs of motion using a 4th order
Runge-Kutta integrator and (2) by computing analytically and in closed form the
properties of the respective elliptical orbits from Kepler theory. We will
compare the resulting transfer maps with (3) the DA transfer map of COSY
INFINITY's built-in electrostatic spherical deflector element ESP and (4) the
transfer map of the electrostatic spherical deflector computed using the
program GIOS.
  In addition to the electrostatic spherical deflector, we study an
electrostatic cylindrical deflector, where the Kepler theory is not applicable.
We compute the DA transfer map by the ODE integration method (1), and compare
it with the transfer maps by (3) COSY INFINITY's built-in electrostatic
cylindrical deflector element ECL, and (4) GIOS.
  In addition to the code listings in the appendices, the codes to run the test
cases are available at http://bt.pa.msu.edu/cgi-bin/display.pl?name=ELSPHTM17


  The staggered quark action on anisotropic lattices is studied. We carry out
numerical simulations in the quenched approximation at three values of lattice
spacing ($a_{\sigma}^{-1}=1-2$ GeV) with the anisotropy $\xi=
a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are the spatial and
temporal lattice spacings, respectively. The bare anisotropy $\gamma_F$ in the
quark action is numerically tuned through the ratio of meson masses in the fine
and coarse directions, and through the dispersion relation of a meson, so that
the renormalized fermionic anisotropy coincides with that of the gauge field.
The discrepancy between these two calibration schemes provides an estimate of
the finite lattice artifact, which is found to be sizable in the range of
cutoff explored in this work. We also compute the meson masses using
correlators with the wall source at the tuned anisotropy parameter. The flavor
symmetry breaking effect smoothly decreases as $\beta$ increases. The effect of
uncertainty in $\gamma_F$ on the meson masses are examined. We also discuss a
perspective on dynamical simulations.


  A smart home can be considered a place of residence that enables the
management of appliances and systems to help with day-to-day life by automated
technology. In the current paper is described a prototype that simulates a
context-aware environment, developed in a designed smart home. The smart home
environment has been simulated using three agents and five locations in a
house. The context-aware agents behave based on predefined rules designed for
daily activities. Our proposal aims to reduce operational cost of running
devices. In the future, monitors of health aspects belonging to home residents
will sustain their healthy life daily.


  In the preceding paper we presented empirical results describing the growth
of publicly-traded United States manufacturing firms within the years
1974--1993. Our results suggest that the data can be described by a scaling
approach. Here, we propose models that may lead to some insight into these
phenomena. First, we study a model in which the growth rate of a company is
affected by a tendency to retain an ``optimal'' size. That model leads to an
exponential distribution of the logarithm of the growth rate in agreement with
the empirical results. Then, we study a hierarchical tree-like model of a
company that enables us to relate the two parameters of the model to the
exponent $\beta$, which describes the dependence of the standard deviation of
the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln
z$, where $z$ defines the mean branching ratio of the hierarchical tree and
$\Pi$ is the probability that the lower levels follow the policy of higher
levels in the hierarchy. We also study the distribution of growth rates of this
hierarchical model. We find that the distribution is consistent with the
exponential form found empirically.


  In this paper, a virus optimization algorithm, which is one of the
metaheuristic optimization technique, is employed for the first time to the
problem of finding extremal binary self-dual codes. We present a number of
generator matrices of the form $[I_{36} \ | \ \tau_3(v)],$ where $I_{36}$ is
the $36 \times 36$ identity matrix, $v$ is an element in the group matrix ring
$M_3(\mathbb{F}_2)G$ and $G$ is a finite group of order 12, which we then
employ together with the the virus optimization algorithm and the genetic
algorithm to search for extremal binary self-dual codes of length 72. We obtain
that the virus optimization algorithm finds more extremal binary self-dual
codes than the genetic algorithm. Moreover, by employing the above mentioned
constructions together with the virus optimization algorithm, we are able to
obtain 39 Type I and 19 Type II codes of length 72, with parameters in their
weight enumerators that were not known in the literature before.


  Plasma etching has a potential to be an alternative processing technology for
superconducting radio frequency (SRF) cavities. An apparatus and a method are
developed for plasma etching of the inner surfaces of SRF cavities. To test the
effect of the plasma etching on the cavity rf performance, a 1497 MHz single
cell SRF cavity is used. The single cell cavity is mechanically polished,
buffer chemically etched afterwards and rf tested at cryogenic temperatures for
a baseline test. This cavity is then plasma processed. The processing was
accomplished by moving axially the inner electrode and the gas flow inlet in a
step-wise manner to establish segmented plasma processing. The cavity is rf
tested afterwards at cryogenic temperatures. The rf test and surface condition
results are presented.


  A smooth T-surface can be thought of as a generalization of a surface of
revolution in such a way that the axis of rotation is not fixed at one point
but rather traces a smooth path on the base plane. Furthermore, the action, by
which the aforementioned surface is obtained does not need to be merely
rotation but any ``suitable" planar equiform transformation applied to the
points of a certain smooth profile curve. In analogy to the smooth setting, if
the axis footpoints sweep a polyline on the base plane and if the profile curve
is discretely chosen then a T-hedra (discrete T-surface) with trapezoidal faces
is obtained. The goal of this article is to reconstruct a T-hedron from an
already given point cloud of a T-surface. In doing so, a kinematic approach is
taken into account, where the algorithm at first tries to find the
aforementioned axis direction associated with the point cloud. Then the
algorithm finds a polygonal path through which the axis footpoint moves.
Finally, by properly cutting the point cloud with the planes passing through
the axis and its footpoints, it reconstructs the surface. The presented method
is demonstrated on base of examples. From an applied point of view, the
straightforwardness of the generation of these surfaces predestines them for
building and design processes. In fact, one can find many built objects
belonging to the sub-classes of T-surfaces such as \emph{surfaces of
revolution} and \emph{moulding surfaces}. Furthermore, the planarity of the
faces of the discrete version paves the way for steel/glass construction in
industry. Finally, these surfaces are also suitable for transformable designs
as they allow an isometric deformation.


  We consider large-scale wireless sensor networks with $n$ nodes, out of which
k are in possession, (e.g., have sensed or collected in some other way) k
information packets. In the scenarios in which network nodes are vulnerable
because of, for example, limited energy or a hostile environment, it is
desirable to disseminate the acquired information throughout the network so
that each of the n nodes stores one (possibly coded) packet so that the
original k source packets can be recovered, locally and in a computationally
simple way from any k(1 + \epsilon) nodes for some small \epsilon > 0. We
develop decentralized Fountain codes based algorithms to solve this problem.
Unlike all previously developed schemes, our algorithms are truly distributed,
that is, nodes do not know n, k or connectivity in the network, except in their
own neighborhoods, and they do not maintain any routing tables.


  In this paper, a two-level additive Schwarz preconditioner is proposed for
solving the algebraic systems resulting from the finite element approximations
of space fractional partial differential equations (SFPDEs). It is shown that
the condition number of the preconditioned system is bounded by C(1+H/\delta),
where H is the maximum diameter of subdomains and \delta is the overlap size
among the subdomains. Numerical results are given to support our theoretical
findings.


  Temporally and spatially dependent uncertain parameters are regularly
encountered in engineering applications. Commonly these uncertainties are
accounted for using random fields and processes, which require knowledge about
the appearing probability distributions functions that is not readily
available. In these cases non-probabilistic approaches such as interval
analysis and fuzzy set theory are helpful uncertainty measures. Partial
differential equations involving fuzzy and interval fields are traditionally
solved using the finite element method where the input fields are sampled using
some basis function expansion methods. This approach however is problematic, as
it is reliant on knowledge about the spatial correlation fields. In this work
we utilize physics-informed neural networks (PINNs) to solve interval and fuzzy
partial differential equations. The resulting network structures termed
interval physics-informed neural networks (iPINNs) and fuzzy physics-informed
neural networks (fPINNs) show promising results for obtaining bounded solutions
of equations involving spatially and/or temporally uncertain parameter fields.
In contrast to finite element approaches, no correlation length specification
of the input fields as well as no Monte-Carlo simulations are necessary. In
fact, information about the input interval fields is obtained directly as a
byproduct of the presented solution scheme. Furthermore, all major advantages
of PINNs are retained, i.e. meshfree nature of the scheme, and ease of inverse
problem set-up.


  The Lienard-Wiechert potentials for charged tachyons are deduced in this
note. They turn out to be twice as large as compared to the corresponding
potentials for ordinary particles. Several remarks are made on tachyon
Cherenkov radiation and its intensity. In particular, it follows in a
straightforward way from the derivation of the Lienard-Wiechert potentials that
the tachyon Cherenkov radiation angle obeys the same formula as that for
ordinary particles.


  CuInP2S6 (CIPS) is an emerging layered ferroelectric material with a TC above
room temperature. When synthesized with Cu deficiencies (i.e.,
Cu1-xIn1+x/3P2S6), the material segregates into CIPS and In4/3P2S6 (IPS)
self-assembled heterostructures within the same single crystal. This
segregation results in significant in-plane and out-of-plane strains between
the CIPS and IPS phases as the volume fraction of CIPS (IPS) domains shrink
(grow) with decreasing Cu fraction. Here, we synthesized CIPS with varying
amounts of Cu (x = 0, 0.2, 0.3, 0.4, 0.5, 0.7, 0.8 and 1) and measured the
strains between the CIPS and IPS phases through the evolution of the respective
Raman, infrared, and optical reflectance spectra. Density functional theory
calculations revealed vibrational modes unique to the CIPS and IPS phases,
which can be used to distinguish between the two phases through two-dimensional
Raman mapping. A comparison of the composition-dependent frequencies and
intensities of the CIPS and IPS Raman peaks showed interesting trends with
decreasing CIPS phase fraction (i.e., Cu/In ratio). Our data reveal red- and
blue-shifted Raman and infrared peak frequencies that we correlate to lattice
strains arising from the segregation of the material into CIPS and IPS chemical
domains. The strain is highest for a Cu/In ratio of 0.33 (Cu0.4In1.2P2S6),
which we attribute to equal and opposite strains exerted by the CIPS and IPS
phases on each other. In addition, bandgaps extracted from the optical
reflectance spectra revealed a decrease in values, with the lowest value (~ 2.3
eV) for Cu0.4In1.2P2S6.


  Bulk-boundary correspondence is a concept for topological insulators and
superconductors that determines the existence of topological boundary states
within the tenfold classification table. Contrary to this belief, we
demonstrate that topological domain-wall states can emerge in all forbidden 1D
classes in the classification table using representative generalized
Su-Schrieffer-Heeger and Kitaev models, which manifests as quantized electric
dipole moments and Majorana zero modes, respectively. We first show that a
zero-energy domain-wall state can possess a quantized polarization, even if the
polarization of individual domains is not inherently quantized. A quantized
Berry phase difference between the domains confirms the non-trivial nature of
the domain-wall states, implying a general-bulk-boundary principle, further
confirmed by the tight-binding, topological field, and low-energy effective
theories. Our methodology is then extended to a superconducting system,
resulting in Majorana zero modes on the domain wall of a generalized Kitaev
model. Finally, we suggest potential systems where our results may be realized,
spanning from condensed matter to optical.


  The isoperimetric constant of a graph $G$ on $n$ vertices, $i(G)$, is the
minimum of $\frac{|\partial S|}{|S|}$, taken over all nonempty subsets
$S\subset V(G)$ of size at most $n/2$, where $\partial S$ denotes the set of
edges with precisely one end in $S$. A random graph process on $n$ vertices,
$\widetilde{G}(t)$, is a sequence of $\binom{n}{2}$ graphs, where
$\widetilde{G}(0)$ is the edgeless graph on $n$ vertices, and
$\widetilde{G}(t)$ is the result of adding an edge to $\widetilde{G}(t-1)$,
uniformly distributed over all the missing edges. We show that in almost every
graph process $i(\widetilde{G}(t))$ equals the minimal degree of
$\widetilde{G}(t)$ as long as the minimal degree is $o(\log n)$. Furthermore,
we show that this result is essentially best possible, by demonstrating that
along the period in which the minimum degree is typically $\Theta(\log n)$, the
ratio between the isoperimetric constant and the minimum degree falls from 1 to
1/2, its final value.


  The quasi-two-body $B \to D (R\to) K \pi$ decays are calculated in PQCD
approach based on the $k_T$ factorization by introducing the wave functions of
$K\pi$ pair associated with the resonances $K^*(892)$, $K_0^*(1430)$ and
$K_2^*(1430)$. The results show that most branching fractions are at the order
of $10^{-7}$ or even smaller. However, for $B^0\to D^0(K^*\to)K\pi$ decays
enhanced by the CKM element $V_{cs}$, their branching fractions are at the
order of $10^{-6}$, which are measurable in the current ongoing experiments.
Based on the narrow-width-approximation we also extract the branching fractions
of the corresponding two-body $B \to D K^*$ decays and the results are in good
agreement with previous predictions. Because these decays are only governed by
the tree operators, there are no $CP$ asymmetries in these decays in the
standard model.


  D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where
p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at
most 3n-2 complex zeros. We show that this bound is sharp for all n by proving
a conjecture of Sarason and Crofoot about the existence of holomorphic
polynomials p which map all critical points to their complex conjugates. We
also count the number of equivalence classes of real polynomials solving this
system of equations. The methods employed rely on Thurston's characterization
of post-critically finite rational maps, in particular the results on
polynomials by S. Levy and A. Poirier.


  The Logit lane assignment model has been introduced recently in order to
describe multi-lane traffic flow from a macroscopic point of view. The model is
based on the idea that each available lane has a specific utility for each
driver, who chooses the lane with the highest utility. The model is expressed
by a system of conservation laws with a smooth but implicitly defined flux
function. The first aim of the paper is to explore on two data-sets how traffic
data supports the fact that traffic speed constitutes an explanatory variable
of lane assignment. Second the paper addresses the problem of discretization of
the model. Several numerical schemes are proposed: Lax-Friedrichs,
Euler-lagrange remap, Lagrange, and their convergence properties are
illustrated on the treatment of the Riemann problem. Directions for future
research are outlined.


  We obtain a description of the C*-algebras which can occur as a simple
quotient of the C*-algebra of a locally injective surjection on a compact
metric space of finite covering dimension.


  Many successful applications of computer vision to image or video
manipulation are interactive by nature. However, parameters of such systems are
often trained neglecting the user. Traditionally, interactive systems have been
treated in the same manner as their fully automatic counterparts. Their
performance is evaluated by computing the accuracy of their solutions under
some fixed set of user interactions. This paper proposes a new evaluation and
learning method which brings the user in the loop. It is based on the use of an
active robot user - a simulated model of a human user. We show how this
approach can be used to evaluate and learn parameters of state-of-the-art
interactive segmentation systems. We also show how simulated user models can be
integrated into the popular max-margin method for parameter learning and
propose an algorithm to solve the resulting optimisation problem.


  The prediction of intrinsic spin Hall currents by Murakami \textit{et al.}
and Sinova \textit{et al.} raised many questions about methods of detection and
the effect of disorder. We focus on a contact between a Rashba type spin orbit
coupled region with a normal two-dimensional electron gas and show that the
spin Hall currents, though vanishing in the bulk of the sample, can be
recovered from the edges. We also show that the current induced spin
accumulation in the spin orbit coupled system diffuses into the normal region
and contributes to the spin current in the leads.


  Several Networks of Excellence have been set up in the framework of the
European FP5 research program. Among these Networks of Excellence, the NEMIS
project focuses on the field of Text Mining.
  Within this field, document processing and visualization was identified as
one of the key topics and the WG1 working group was created in the NEMIS
project, to carry out a detailed survey of techniques associated with the text
mining process and to identify the relevant research topics in related research
areas.
  In this document we present the results of this comprehensive survey. The
report includes a description of the current state-of-the-art and practice, a
roadmap for follow-up research in the identified areas, and recommendations for
anticipated technological development in the domain of text mining.


  Causality never gained the status of a "law" or "principle" in physics. Some
recent literature even popularized the false idea that causality is a notion
that should be banned from theory. Such misconception relies on an alleged
universality of reversibility of laws of physics, based either on determinism
of classical theory, or on the multiverse interpretation of quantum theory, in
both cases motivated by mere interpretational requirements for realism of the
theory. Here, I will show that a properly defined unambiguous notion of
causality is a theorem of quantum theory, which is also a falsifiable
proposition of the theory. Such causality notion appeared in the literature
within the framework of operational probabilistic theories. It is a genuinely
theoretical notion, corresponding to establish a definite partial order among
events, in the same way as we do by using the future causal cone on Minkowski
space. The causality notion is logically completely independent of the
misidentified concept of "determinism", and, being a consequence of quantum
theory, is ubiquitous in physics. In addition, as classical theory can be
regarded as a restriction of quantum theory, causality holds also in the
classical case, although the determinism of the theory trivializes it. I then
conclude arguing that causality naturally establishes an arrow of time. This
implies that the scenario of the "Block Universe" and the connected "Past
Hypothesis" are incompatible with causality, and thus with quantum theory: they
both are doomed to remain mere interpretations and, as such, not falsifiable,
similar to the hypothesis of "super-determinism". This article is part of a
discussion meeting issue "Foundations of quantum mechanics and their impact on
contemporary society".


  We consider random walks in a random environment which are generalized
versions of well-known effective models for Mott variable-range hopping. We
study the homogenized diffusion constant of the random walk in the
one-dimensional case. We prove various estimates on the low-temperature
behavior which confirm and extend previous work by physicists.


  Frequencies of the three quasi-periodic oscillation (QPO) modes observed
simultaneously in the accreting black hole GRO J1655-40 are compared with the
predictions of models. Models in which all three QPO signals are produced at
the same radius are considered: these include different versions of
relativistic precession, epicyclic resonance, tidal disruption, and warped disc
models. Models that were originally proposed to interpret only the twin
high-frequency QPOs are generalized here to interpret also the low-frequency
QPO in terms of relativistic nodal precession. Inferred values of the black
hole mass and spin from each QPO model are compared with the mass measured from
optical observations and the spin inferred from X-ray spectroscopy techniques.
We find that along with the relativistic precession model predicting
$M=(5.3\pm0.1)~M_{\odot}, a=0.286\pm0.004$, the so-called total precession
model ($M=(5.5\pm0.1)~M_{\odot}, a=0.276\pm0.003$), and the resonance epicyclic
model with beat frequency ($M=(5.1\pm0.1)~M_{\odot}, a=0.274\pm0.003$) also
satisfy the optical mass test. We compare our results with those inferred from
X-ray spectral measurements.


  We use time-dependent (current) density functional theory to study collective
transitions between the two lowest subbands in GaAs/AlGaAs quantum wells. We
focus on two systems where experimental results are available: a wide single
and a narrow asymmetric double well. The aim is to calculate frequency and
linewidth of collective electronic modes damped via electron-electron
interaction only. Since Landau damping is not effective here, the dominant
damping mechanism involves dynamical exchange-correlation effects such as
multipair production. To capture these effects, one has to go beyond the widely
used adiabatic local density approximation (ALDA) and include retardation. We
perform a comparative study of two approaches which fall in this category: the
dynamical extension of the ALDA by Gross and Kohn, and a more recent method
which treats exchange and correlation beyond the ALDA as viscoelastic stresses
in the electron liquid. We find that the former method is more robust: it
performs similarly for strongly different degrees of collectivity of the
electronic motion. Results for quantum wells compare reasonably to experiment,
with a tendency towards overdamping. By contrast, the viscoelastic approach is
superior for systems where the electron dynamics is predominantly collective,
but breaks down if the local velocity field is too rapidly varying, as in the
case of a single-electron-like behavior such as tunneling through a potential
barrier.


  Supersymmetric scenarios with a very weakly interacting lightest superpartner
(LSP) - like the gravitino or axino - naturally give rise to a long-lived
next-to-LSP (NLSP). If the NLSP is a charged slepton it leaves a very distinct
signature in a collider experiment. At the ILC/CLIC it will be possible to
capture a significant fraction of the produced charged sleptons and observe
their decays. These decays potentially reveal the nature of the LSP and thus
provide a unique possibility to measure the properties of a very weakly
interacting LSP which otherwise is most likely hidden from any other
observation, like direct or indirect dark matter searches. We review the
proposals that have been made to measure the LSP properties at the ILC/CLIC and
compare its potential to the capability of the LHC.


  The concept of fault-tolerant control has extensively been explored with
various mapping of development. It starts from the system characteristic, the
robustness of the controller, estimation methods and optimization, to the
combination of the faults such that it can touch the true observed system. The
mathematical concepts of the scrubber plant taking into account the pressure
parameter along with sensing element and actuator are proposed. The data to
construct the designs derive from the true values in one of Indonesian company.
The performances coming from the simulations depict that the open- and
closed-loop system could be the same as those of the real results. Furthermore,
the observer is proposed to give the estimates of the states of $(\hat{x})$ and
$(\hat{f}_s)$ showing the positive trace on the set-point of the residual fault
followed by designing the fault-tolerant control with sensor fault on
sensitivity. The scenarios are to give the lack of reading in sensor with
$70\%$ and $85\%$ sensitivity and those are contrasted to the system without
FTC (only PI controller). The yields portray that the system with FTC could
deal with those sensor fault scenarios while its counterpart cannot drawing the
faulty performance instead of tracking the set-point. The next project
associated with this paper is also mentioned in the last section.


  Purpose: We previously established an open-access lung sound database,
HF_Lung_V1, and developed deep learning models for inhalation, exhalation,
continuous adventitious sound (CAS), and discontinuous adventitious sound (DAS)
detection. The amount of data used for training contributes to model accuracy.
Herein, we collected larger quantities of data to further improve model
performance. Moreover, the issues of noisy labels and sound overlapping were
explored. Methods: HF_Lung_V1 was expanded to HF_Lung_V2 with a 1.45x increase
in the number of audio files. Convolutional neural network-bidirectional gated
recurrent unit network models were trained separately using the HF_Lung_V1
(V1_Train) and HF_Lung_V2 (V2_Train) training sets and then tested using the
HF_Lung_V1 (V1_Test) and HF_Lung_V2 (V2_Test) test sets, respectively. Segment
and event detection performance was evaluated using the F1 scores. Label
quality was assessed. Moreover, the overlap ratios between inhalation,
exhalation, CAS, and DAS labels were computed. Results: The model trained using
V2_Train exhibited improved F1 scores in inhalation, exhalation, and CAS
detection on both V1_Test and V2_Test but not in DAS detection. Poor CAS
detection was attributed to the quality of CAS labels. DAS detection was
strongly influenced by the overlapping of DAS labels with inhalation and
exhalation labels. Conclusion: Collecting greater quantities of lung sound data
is vital for developing more accurate lung sound analysis models. To build real
ground-truth labels, the labels must be reworked; this process is ongoing.
Furthermore, a method for addressing the sound overlapping problem in DAS
detection must be formulated.


  It has been recently pointed out that local volume fluctuations in granular
packings follow remarkably well a shifted and rescaled Gamma distribution named
the kGamma distribution [T. Aste, T. Di Matteo, Phys. Rev. E 77 (2008) 021309].
In this paper we confirm, extend and discuss this finding by supporting it with
additional experimental and simulation data.


  We present a theory of modified reduced dynamics in the presence of counting
fields. Reduced dynamics techniques are useful for describing open quantum
systems at long emergent timescales when the memory timescales are short.
However, they can be difficult to formulate for observables spanning the system
and its environment, such as those characterizing transport properties. A large
variety of mixed system--environment observables, as well as their statistical
properties, can be evaluated by considering counting fields. Given a numerical
method able to simulate the field-modified dynamics over the memory timescale,
we show that the long-lived full counting statistics can be efficiently
obtained from the reduced dynamics. We demonstrate the utility of the technique
by computing the long-time current in the nonequilibrium Anderson impurity
model from short-time Monte Carlo simulations.


  Due to the sparsity and irregularity of the point cloud data, methods that
directly consume points have become popular. Among all point-based models,
graph convolutional networks (GCN) lead to notable performance by fully
preserving the data granularity and exploiting point interrelation. However,
point-based networks spend a significant amount of time on data structuring
(e.g., Farthest Point Sampling (FPS) and neighbor points querying), which limit
the speed and scalability. In this paper, we present a method, named Grid-GCN,
for fast and scalable point cloud learning. Grid-GCN uses a novel data
structuring strategy, Coverage-Aware Grid Query (CAGQ). By leveraging the
efficiency of grid space, CAGQ improves spatial coverage while reducing the
theoretical time complexity. Compared with popular sampling methods such as
Farthest Point Sampling (FPS) and Ball Query, CAGQ achieves up to 50X speed-up.
With a Grid Context Aggregation (GCA) module, Grid-GCN achieves
state-of-the-art performance on major point cloud classification and
segmentation benchmarks with significantly faster runtime than previous
studies. Remarkably, Grid-GCN achieves the inference speed of 50fps on ScanNet
using 81920 points per scene as input.


  This paper narrows the gap between previous literature on quantum linear
algebra and practical data analysis on a quantum computer, formalizing quantum
procedures that speed-up the solution of eigenproblems for data representations
in machine learning. The power and practical use of these subroutines is shown
through new quantum algorithms, sublinear in the input matrix's size, for
principal component analysis, correspondence analysis, and latent semantic
analysis. We provide a theoretical analysis of the run-time and prove tight
bounds on the randomized algorithms' error. We run experiments on multiple
datasets, simulating PCA's dimensionality reduction for image classification
with the novel routines. The results show that the run-time parameters that do
not depend on the input's size are reasonable and that the error on the
computed model is small, allowing for competitive classification performances.


  Determining the nature -Dirac or Majorana- of massive neutrinos is one of the
most pressing and challenging problems in the field of neutrino physics. We
discuss how one can possibly extract information on the couplings, if any,
which might be involved in neutrinoless double beta-decay using a multi-isotope
approach. We investigate as well the potential of combining data on the
half-lives of nuclides which largely different Nuclear Matrix Elements such as
$^{136}$Xe and of one or more of the four nuclei $^{76}$Ge, $^{82}$Se,
$^{100}$Mo and $^{130}$Te, for discriminating between different pairs of
non-interfering or interfering mechanisms of neutrinoless double beta-decay.
The case studies do not extend to the evaluation of the theoretical
uncertainties of the results, due to the nuclear matrix elements calculations
and other causes.


  In this paper, we consider a two-way relay network where two sources can
communicate only through an untrusted intermediate relay, and investigate the
physical layer security issue of this two-way relay scenario. Specifically, we
treat the intermediate relay as an eavesdropper from which the information
transmitted by the sources needs to be kept secret, despite the fact that its
cooperation in relaying this information is essential. We indicate that a
non-zero secrecy rate is indeed achievable in this two-way relay network even
without external friendly jammers. As for the system with friendly jammers,
after further analysis, we can obtain that the secrecy rate of the sources can
be effectively improved by utilizing proper jamming power from the friendly
jammers. Then, we formulate a Stackelberg game model between the sources and
the friendly jammers as a power control scheme to achieve the optimized secrecy
rate of the sources, in which the sources are treated as the sole buyer and the
friendly jammers are the sellers. In addition, the optimal solutions of the
jamming power and the asking prices are given and a distributed updating
algorithm to obtain the Stakelberg equilibrium is provided for the proposed
game. Finally, the simulations results verify the properties and the efficiency
of the proposed Stackelberg game based scheme.


  Starting from a successful model of the pi-meson electromagnetic form factor,
we calculate the similar form factor, f_K(Q^2), of the charged K meson for a
wide range of the momentum transfer squared, Q^2. The only remaining free
parameter is to be determined from the measurements of the K-meson charge
radius, r_K. We fit this single parameter to the published data of the NA-7
experiment which measured f_K(Q^2) at Q^2->0 and determine our preferred range
of r_K, which happens to be close to recent lattice results. Still, the
accuracy in the determination of r_K is poor. However, future measurements of
the K-meson electromagnetic form factor at Q^2<~5.5 GeV^2, scheduled in
Jefferson Laboratory for 2017, will test our approach and will reduce the
uncertainty in r_K significantly.


  Under dynamic traffic, service function chain (SFC) migration is considered
as an effective way to improve resource utilization. However, the lack of
future network information leads to non-optimal solutions, which motivates us
to study reinforcement learning based SFC migration from a long-term
perspective. In this paper, we formulate the SFC migration problem as a
minimization problem with the objective of total network operation cost under
constraints of users' quality of service. We firstly design a deep Q-network
based algorithm to solve single SFC migration problem, which can adjust
migration strategy online without knowing future information. Further, a novel
multi-agent cooperative framework, called MSDF, is proposed to address the
challenge of considering multiple SFC migration on the basis of single SFC
migration. MSDF reduces the complexity thus accelerates the convergence speed,
especially in large scale networks. Experimental results demonstrate that MSDF
outperforms typical heuristic algorithms under various scenarios.


  We calculate the effects of velocity-dependent dark matter annihilation cross
sections on the intensity of the extragalactic gamma-ray background. Our
formalism does not assume a locally thermal distribution of dark matter
particles in phase space, and is valid for arbitrary velocity-dependent
annihilation. As concrete examples, we calculate the effects of p-wave
annihilation (with the $v$-weighted cross section of $\sigma v=a+bv^2$) on the
mean intensity of extragalactic gamma rays produced in cosmological dark matter
halos. This velocity variation makes the shape of the energy spectrum harder,
but this change in the shape is too small to see unless $b/a\agt 10^6$. While
we find no such models in the parameter space of the Minimal Supersymmetric
Standard Model (MSSM), we show that it is possible to find $b/a\agt 10^6$ in
the extension MSSM$\otimes U(1)_{B-L}$. However, we find that the most dominant
effect of the p-wave annihilation is the suppression of the amplitude of the
gamma-ray background. A non-zero $b$ at the dark matter freeze-out epoch
requires a smaller value of $a$ in order for the relic density constraint to be
satisfied, suppressing the amplitude by a factor as low as $10^{-6}$ for a
thermal relic. Non-thermal relics will have weaker amplitude suppression. As
another velocity-dependent effect, we calculate the spectrum for s-wave
annihilation into fermions enhanced by the attractive Sommerfeld effect.
Resonances associated with this effect result in significantly enhanced
intensities, with a slightly softer energy spectrum.


  We studied the process $\gamma\gamma \to t\bar{c}+c\bar{t}$ in a $R_{p}$
violating supersymmetric Model with the effects from both B- and L-violating
interactions. The calculation shows that it is possible to detect a $R_{p}$
violating signal at the Next Linear Collider. Information about the B-violating
interaction in this model could be obtained under very clean background, if we
take the present upper bounds for the parameters in the supersymmetric $\rlap/
R_{p}$ interactions. Even if we can not detect a signal of $\rlap/R_{p}$ in the
experiment, we may get more stringent constraints on the heavy-flavor
$\rlap/R_{p}$ couplings.


  We propose a discussion on the synthesis and scattering analysis of nonlinear
metasurfaces. For simplicity, we investigate the case of a second-order
nonlinear isotropic metasurface possessing both electric and magnetic linear
and nonlinear susceptibility components. We next find the synthesis expressions
relating the susceptibilities to the specified fields, which leads to the
definition of the nonlinear metasurface conditions for no reflection,
themselves revealing the nonreciprocal nature of such structures. Finally, we
provide the approximate expressions of the scattered fields based on
perturbation theory and compare the corresponding results to finite-difference
time-domain simulations.


  The behavior of the network and its stability are governed by both dynamics
of individual nodes as well as their topological interconnections. Attention
mechanism as an integral part of neural network models was initially designed
for natural language processing (NLP), and so far, has shown excellent
performance in combining dynamics of individual nodes and the coupling
strengths between them within a network. Despite undoubted impact of attention
mechanism, it is not yet clear why some nodes of a network get higher attention
weights. To come up with more explainable solutions, we tried to look at the
problem from stability perspective. Based on stability theory, negative
connections in a network can create feedback loops or other complex structures
by allowing information to flow in the opposite direction. These structures
play a critical role in the dynamics of a complex system and can contribute to
abnormal synchronization, amplification, or suppression. We hypothesized that
those nodes that are involved in organizing such structures can push the entire
network into instability modes and therefore need higher attention during
analysis. To test this hypothesis, attention mechanism along with spectral and
topological stability analyses was performed on a real-world numerical problem,
i.e., a linear Multi Input Multi Output state-space model of a piezoelectric
tube actuator. The findings of our study suggest that the attention should be
directed toward the collective behaviour of imbalanced structures and
polarity-driven structural instabilities within the network. The results
demonstrated that the nodes receiving more attention cause more instability in
the system. Our study provides a proof of concept to understand why perturbing
some nodes of a network may cause dramatic changes in the network dynamics.


  Recent work has shown that neutrino oscillations in matter can be greatly
enhanced by flips between mass eigenstates if the medium is fluctuating with a
period equal to the neutrino oscillation length. Here we investigate the effect
of the primordial fluctuations on the neutrino oscillations in the early
universe. We calculate the oscillation probability in the case of a general
power law fluctuation spectrum and for a more realistic spectrum predicted by
inflation. We also include the effect of the amplification of fluctuations
resulting from the QCD phase transition. We find that there is a region of
parameter space where this mechanism would be the dominant mechanism for
producing sterile neutrinos. However this conclusion does not take account of
the damping of fluctuations on the neutrino oscillation scale when the
neutrinos decouple from the plasma. We find that this reduces the probability
of flips between the mass eigenstates to an unobservable level.


  We classify vertex operator algebras (VOAs) of OZ-type generated by Ising
vectors of $\sigma$-type. As a consequence of the classification, we also prove
that such VOAs are simple, rational, $C_2$-cofinite and unitary, that is, they
have compact real forms generated by Ising vectors of $\sigma$-type over the
real numbers.


  Using non-LTE time-dependent radiative-transfer calculations, we study the
impact of mixing and non-thermal processes associated with radioactive decay on
SN IIb/Ib/Ic light curves (LCs) and spectra. Starting with short-period binary
models of \leq5Msun He-rich stars (18-25Msun on the main-sequence), we produce
1.2B ejecta which we artificially mix to alter the chemical stratification.
While the total 56Ni mass influences the LC peak, the spatial distribution of
56Ni, controlled by mixing processes, impacts both the multi-band LCs and
spectra. With enhanced mixing, our synthetic LCs start their post-breakout
re-brightening phase earlier, follow a more gradual rise to peak, appear
redder, and fade faster after peak due to enhanced gamma-ray escape.
Non-thermal electrons, crucial for the production of HeI lines, deposit a
dominant fraction of their energy as heat. Because energy deposition is
generally local well after the LC peak, the broad HeI lines characteristic of
maximum-light SN IIb/Ib spectra require mixing that places 56Ni and helium
nuclei to within a gamma-ray mean-free-path. This requirement indicates that
SNe IIb and Ib most likely arise from the explosion of stripped-envelope
massive stars (main-sequence masses \leq25Msun) that have evolved through
mass-transfer in a binary system, rather than from more massive single WR
stars. In contrast, the lack of HeI lines in SNe Ic may result from a variety
of causes: A genuine helium deficiency; strongly-asymmetric mixing; weak
mixing; or a more massive, perhaps single, progenitor characterized by a larger
oxygen-rich core. Our models, subject to different mixing magnitudes, can
produce a variety of SN types, including IIb, IIc, Ib, and Ic. As it is poorly
constrained by explosion models, mixing challenges our ability to infer the
progenitor and explosion properties of SNe IIb/Ib/Ic.


  Aims: We investigate the influence of high-energy stellar radiation at
close-in orbits on atmospheric mass loss during stellar evolution of a G-type
star. Methods: High-energy stellar luminosity varies over a wide range for G
field stars. The temporal evolution of the distribution of stellar X-ray
luminosity and its influence on the evolution of close-in exoplanets is
investigated. X-ray luminosity distributions from the Pleiades, the Hyades and
the field are used to derive a scaling law for the evolution of the stellar
X-ray luminosity distribution. A modified energy-limited escape approach is
used to calculate atmospheric mass loss for a broad range of planetary
parameters. Results: We show that the evolution of close-in exoplanets strongly
depends on the detailed X-ray luminosity history of their host stars, which
varies over several orders-of-magnitude for G stars. Stars located at the
high-energy tail of the luminosity distribution can evaporate most of its
planets within 0.5 AU, while for a moderate luminosity a significant fraction
of planets can survive. We show the change on an initial planetary mass
distribution caused by atmospheric escape.


  In this paper, the performance of indoor Terahertz (THz) communication
systems with one-bit digital-to-analog converters (DACs) is investigated.
Array-of-subarrays architecture is assumed for the antennas at the access
points, where each RF chain uniquely activates a disjoint subset of antennas,
each of which is connected to an exclusive phase shifter. Hybrid precoding,
including maximum ratio transmission (MRT) and zero-forcing (ZF) precoding, is
considered. The best beamsteering direction for the phase shifter in the large
subarray antenna regime is first proved to be the direction of the
line-of-sight (LOS) path. Subsequently, the closed-form expression of the
lower-bound of the achievable rate in the large subarray antenna regime is
derived, which is the same for both MRT and ZF and is independent of the
transmit power. Numerical results validating the analysis are provided as well.


  This paper discusses the ATLAS potential to study Supersymmetry for the
"Focus-Point" region of the parameter space of mSUGRA models. The potential to
discovery a deviation from Standard Model expectations with the first few
${fb}^{-1}$ of LHC data was studied using the parametrized simulation of the
ATLAS detector. Several signatures were considered, involving hard jets, large
missing energy, and either $b$-tagged jets, opposite-sign isolated electron or
muon pairs, or top quarks reconstructed exploiting their fully hadronic decays.
With only 1 ${fb}^{-1}$ of data each of these signatures may allow to observe
an excess of events over Standard Model expectation with a statistical
significance exceeding 5 standard deviations. An analytical expression was
derived for the shape of the distribution of the dilepton invariant mass
arising from the three-body leptonic decay of the neutralinos under the
hypothesis of heavy scalars, which is appropriate for the focus-point scenario.
The resulting function was used to fit the distribution of the dilepton
invariant mass obtained with simulated LHC data, and to extract the value of
two kinematic endpoints measuring the $\tilde \chi^0_2 - \tilde \chi^0_1$ and
the $\tilde \chi^0_3 - \tilde \chi^0_1$ mass differences. This information was
used to constrain the MSSM parameter space compatible with the data.


  When a plate is withdrawn from a liquid bath, either a static meniscus forms
in the transition region between the bath and the substrate or a liquid film of
finite thickness (a Landau-Levich film) is transferred onto the moving
substrate. If the substrate is inhomogeneous, e.g., has a prestructure
consisting of stripes of different wettabilities, the meniscus can be deformed
or show a complex dynamic behavior. Here we study the free surface shape and
dynamics of a dragged meniscus occurring for striped prestructures with two
orientations, parallel and perpendicular to the transfer direction. A thin film
model is employed that accounts for capillarity through a Laplace pressure and
for the spatially varying wettability through a Derjaguin (or disjoining)
pressure. Numerical continuation is used to obtain steady free surface profiles
and corresponding bifurcation diagrams in the case of substrates with different
homogeneous wettabilities. Direct numerical simulations are employed in the
case of the various striped prestructures. The final part illustrates the
importance of our findings for particular applications that involve complex
liquids by modeling a Langmuir-Blodgett transfer experiment. There, one
transfers a monolayer of an insoluble surfactant that covers the surface of the
bath onto the moving substrate. The resulting pattern formation phenomena can
be crucially influenced by the hydrodynamics of the liquid meniscus that itself
depends on the prestructure on the substrate. In particular, we show how
prestructure stripes parallel to the transfer direction lead to the formation
of bent stripes in the surfactant coverage after transfer and present similar
experimental results.


  We investigate large changes, bursts, of the continuous stochastic signals,
when the exponent of multiplicativity is higher than one. Earlier we have
proposed a general nonlinear stochastic model which can be transformed into
Bessel process with known first hitting (first passage) time statistics. Using
these results we derive PDF of burst duration for the proposed model. We
confirm analytical expressions by numerical evaluation and discuss bursty
behavior of return in financial markets in the framework of modeling by
nonlinear SDE.


  Optical transitions of an Er$_2$O$_3$ film on a Si substrate grown by using a
metal-organic chemical vapor deposition technique were investigated in a wide
temperature (300 K $\sim$ 5 K) and spectral (500 nm and 850 nm) ranges.
Numerous sharp transitions corresponding to the Er$^{3+}$ ionic levels were
observed, which show Stark shifts induced by the crystal field. With decreasing
temperature from 300 K to 5 K, all transition peaks exhibit spectral red-shift.
We believe that such red-shift behavior is due to the change of the crystal
field together with the change of strain field induced by the film and the
substrate in varying temperature. An interesting result is the total amount of
red-shifts between 300 K and 5 K. We obtain that the higher transition energy
peaks show bigger red-shifts. This is very consistent to all transition peaks.
This is because the dipole moments between the transition levels are different
that lead to different amounts of Stark shifts.


  Plasma facing components (PFCs) in the next generation of tokamak devices
will operate in challenging environments, with heat loads predicted to exceed
10 MWm$^{-2}$. The magnitude of these heat loads is set by the width of the
channel, the "scrape-off layer" (SOL), into which heat is exhausted, and can be
characterised by an e-folding length scale for the decay of heat flux across
the channel. It is expected this channel will narrow as tokamaks move towards
reactor relevant conditions. Understanding the processes involved in setting
the SOL heat flux width is imperative to be able to predict the heat loads PFCs
must handle in future devices. Measurements of the SOL width are performed on
the high-field spherical tokamak, ST40, using a newly commissioned infrared
thermography system. With its high on-axis toroidal magnetic field ($\geq$1.5
T) ST40 is uniquely positioned to investigate the influence of toroidal field
on the heat flux width in spherical tokamaks, whilst also extending
measurements of the SOL width in spherical tokamaks to increased poloidal field
($\geq$0.3 T). Due to the divertor on ST40 having a low degree of axisymmetry,
it is necessary for a set of radial measurements of the heat flux to be taken
across the divertor, made possible using an automated toolchain that fully
incorporates its 3D geometry. These radial profiles are combined with the
magnetic topology of the plasma to infer the width of the SOL, with both single
and double exponential profiles of heat flux observed. A reduction in the heat
flux is observed toroidally across part of the divertor, with preliminary
investigations indicating that partial shadowing occurs, resulting from the
separation between magnetic field lines and trailing edges upstream of the
observed region becoming comparable to the ion gyro-radius.


  The statistics of multi-field inflation are investigated using the stochastic
approach. We analytically obtain the probability distribution function of
fields with the scaling approximation by extending the previous work by
Amendola. The non-Gaussian nature of the probability distribution function is
investigated decomposing the fields into the adiabatic and isocurvature
components. We find that the non-Gaussianity of the isocurvature component can
be large compared with that of the adiabatic component. The adiabatic and
isocurvature components may be correlated at nonlinear order in the skewness
and kurtosis even if uncorrelated at linear level.


  We present a theoretical study of the mesoscopic fluctuations of $g$-tensors
in a metal nanoparticle. The calculations were performed using a semi-realistic
tight-binding model, which contains both spin and orbital contributions to the
$g$-tensors. The results depend on the product of the spin-orbit scattering
time $\tau_{\textrm{\small so}}$ and the mean-level spacing $\delta$, but are
otherwise weakly affected by the specific shape of a {\it generic}
nanoparticle. We find that the spin contribution to the $g$-tensors agrees with
Random Matrix Theory (RMT) predictions. On the other hand, in the strong
spin-orbit coupling limit $\delta \tau_{\textrm{\small so}}/\hbar \to 0$, the
orbital contribution depends crucially on the space character of the
quasi-particle wavefunctions: it levels off at a small value for states of $d$
character but is strongly enhanced for states of $sp$ character. Our numerical
results demonstrate that when orbital coupling to the field is included, RMT
predictions overestimate the typical $g$-factor of orbitals that have dominant
$d$-character. This finding points to a possible source of the puzzling
discrepancy between theory and experiment.


  In this paper we revise the theory of turnpikes in discounted Markov decision
processes, prove the turnpike theorem for the undiscounted model and apply the
results to the specific random walk.


  Fault-tolerant quantum computation requires non-destructive quantum
measurements with classical feed-forward. Many experimental groups are actively
working towards implementing such capabilities and so they need to be
accurately evaluated. As with unitary channels, an arbitrary imperfect
implementation of a quantum instrument is difficult to analyze. In this paper,
we define a class of quantum instruments that correspond to stochastic errors
and thus are amenable to standard analysis methods. We derive efficiently
computable upper- and lower-bounds on the diamond distance between two quantum
instruments. Furthermore, we show that, for the special case of uniform
stochastic instruments, the diamond distance and the natural generalization of
the process infidelity to quantum instruments coincide and are equal to a
well-defined probability of an error occurring during the measurement.


  The neutron dose distributions on observation distances and on observation
angles were measured using a Wendi-II neutron dose-meter at the deep tumor
therapy terminal at HIRFL (Heavy Ion Research Facility in Lanzhou) as 12C ions
with energies from 165 to 350 MeV/u bombarding on thick solid water targets
with different thickness according to the ion energies. The experimental
results were compared with those calculated by FLUKA code. It is found that the
experimental data was in good agreement with the calculated results. The
neutron energy spectra were also studied by using the FLUKA code. The results
are valuable for the shielding design of high energy heavy ion medical machines
and for the individual dose assessment.


  Nonlocal entanglement between two quantum dots can be generated through
Majorana fermions. The two Majorana fermions at the ends of an one-dimensional
topological superconductor form a nonlocal fermion level, coupling to the
occupation states of two quantum dots put close to the two ends, and the entire
system will come into an entangled state. After introducing a charging energy
by a capacitor, entanglement of the entire system can manifest itself through
the nonlocal entanglement between the two quantum dots. That is, when measuring
the electron occupations of the quantum dots, the measurement result of one
quantum dot will influence the measurement result of the other quantum dot.
This nonlocal entanglement between the two quantum dots is a strong evidence of
the nonlocal nature of the fermion level constructed by two Majorana fermions.


  We study the problem of pathwise stochastic optimal control, where the
optimization is performed for each fixed realisation of the driving noise, by
phrasing the problem in terms of the optimal control of rough differential
equations. We investigate the degeneracy phenomenon induced by directly
controlling the coefficient of the noise term, and propose a simple procedure
to resolve this degeneracy whilst retaining dynamic programming. As an
application, we use pathwise stochastic control in the context of stochastic
filtering to construct filters which are robust to parameter uncertainty,
demonstrating an original application of rough path theory to statistics.


  The problem of determining the smallest number of edges,
$h(n;\bar{\kappa}\geq r)$, which guarantees that any graph with $n$ vertices
and $h(n;\bar{\kappa}\geq r)$ edges will contain a pair of vertices joined by
$r$ internally disjoint paths was posed by Erd\"{o}s and Gallai. Bollob\'{a}s
considered the problem of determining the largest number of edges
$f(n;\bar{\kappa}\leq \ell)$ for graphs with $n$ vertices and local
connectivity at most $\ell$. One can see that $f(n;\bar{\kappa}\leq \ell)=
h(n;\bar{\kappa}\geq \ell+1)-1$. These two problems had received a wide
attention of many researchers in the last few decades. In the above problems,
only pairs of vertices connected by internally disjoint paths are considered.
In this paper, we study the number of internally disjoint Steiner trees
connecting sets of vertices with cardinality at least 3.


  The double exponential formula was introduced for calculating definite
integrals with singular point oscillation functions and Fourier-integrals. The
double exponential transformation is not only useful for numerical computations
but it is also used in different methods of Sinc theory. In this paper we use
double exponential transformation for calculating particular improper
integrals. By improving integral estimates having singular final points. By
comparison between double exponential transformations and single exponential
transformations it is proved that the error margin of double exponential
transformations is smaller. Finally Fourier-integral and double exponential
transformations are discussed.


  The current generation of surgeons requires extensive training in
teleoperation to develop specific dexterous skills, which are independent of
medical knowledge. Training curricula progress from manipulation tasks to
simulated surgical tasks but are limited in time. To tackle this, we propose to
integrate surgical robotic training together with Haptic Feedback (HF) to
improve skill acquisition. This paper present the initial but promising results
of our haptic device designed to support in the training of surgical gestures.
Our ongoing work is related to integrate the HF in the RAVEN II platform.


  This work presents an application of Reinforcement Learning (RL) for the
complete control of real soccer robots of the IEEE Very Small Size Soccer
(VSSS), a traditional league in the Latin American Robotics Competition (LARC).
In the VSSS league, two teams of three small robots play against each other. We
propose a simulated environment in which continuous or discrete control
policies can be trained, and a Sim-to-Real method to allow using the obtained
policies to control a robot in the real world. The results show that the
learned policies display a broad repertoire of behaviors that are difficult to
specify by hand. This approach, called VSSS-RL, was able to beat the
human-designed policy for the striker of the team ranked 3rd place in the 2018
LARC, in 1-vs-1 matches.


  The dimension of a poset $P$, denoted $\dim(P)$, is the least positive
integer $d$ for which $P$ is the intersection of $d$ linear extensions of $P$.
The maximum dimension of a poset $P$ with $|P|\le 2n+1$ is $n$, provided
$n\ge2$, and this inequality is tight when $P$ contains the standard example
$S_n$. However, there are posets with large dimension that do not contain the
standard example $S_2$. Moreover, for each fixed $d\ge2$, if $P$ is a poset
with $|P|\le 2n+1$ and $P$ does not contain the standard example $S_d$, then
$\dim(P)=o(n)$. Also, for large $n$, there is a poset $P$ with $|P|=2n$ and
$\dim(P)\ge (1-o(1))n$ such that the largest $d$ so that $P$ contains the
standard example $S_d$ is $o(n)$. In this paper, we will show that for every
integer $c\ge1$, there is an integer $f(c)=O(c^2)$ so that for large enough
$n$, if $P$ is a poset with $|P|\le 2n+1$ and $\dim(P)\ge n-c$, then $P$
contains a standard example $S_d$ with $d\ge n-f(c)$. From below, we show that
$f(c)=\Omega(c^{4/3})$. On the other hand, we also prove an analogous result
for fractional dimension, and in this setting $f(c)$ is linear in $c$. Here the
result is best possible up to the value of the multiplicative constant.


  We embark on a tour that takes us through four closely related topics: the
dual concepts of independence and spanning in finite abelian groups and the
analogous dual concepts of designs and distance sets on spheres. We review some
of the main known results in each area, mention several open questions, and
discuss some connections among these four interesting topics.


  Discrete time hedging in a complete diffusion market is considered. The hedge
portfolio is rebalanced when the absolute difference between delta of the hedge
portfolio and the derivative contract reaches a threshold level. The rate of
convergence of the expected squared hedging error as the threshold level
approaches zero is analyzed. The results hinge to a great extent on a theorem
stating that the difference between the hedge ratios normalized by the
threshold level tends to a triangular distribution as the threshold level tends
to zero.


  If G is a Lie group, let D(G) be the space of compactly supported smooth
functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |->
f*g which takes a pair of test functions to their convolution. We show that B
is continuous if and only if G is sigma-compact. More generally, let r,s,t be
non-negative integers (or infinity) with t <= r+s. Let E_1, E_2 be locally
convex spaces and b : E_1 x E_2 -> F be a continuous bilinear map to a complete
locally convex space F. The main result is a characterization of those
(G,r,s,t,b) for which the convolution map C^r_c(G,E_1) x C^s_c(G,E_2) ->
C^t_c(G,F) associated with b is continuous. Convolution of compactly supported
continuous functions on a locally compact group is also discussed, as well as
convolution of compactly supported L^1-functions and convolution of compactly
supported Radon measures.


  The Peterson variety is a subvariety of the flag manifold $G/B$ equipped with
an action of a one-dimensional torus, and a torus invariant paving by affine
cells, called Peterson cells. We prove that the equivariant pull-backs of
Schubert classes indexed by arbitrary Coxeter elements are dual (up to an
intersection multiplicity) to the fundamental classes of Peterson cell
closures. Dividing these classes by the intersection multiplicities yields a
$\mathbb Z$-basis for the equivariant cohomology of the Peterson variety. We
prove several properties of this basis, including a Graham positivity property
for its structure constants, and stability with respect to inclusion in a
larger Peterson variety. We also find formulae for intersection multiplicities
with Peterson classes. This explains geometrically, in arbitrary Lie type,
recent positivity statements proved in type A by Goldin and Gorbutt.


  Stan is a probabilistic programming language that has been increasingly used
for real-world scalable projects. However, to make practical inference
possible, the language sacrifices some of its usability by adopting a block
syntax, which lacks compositionality and flexible user-defined functions.
Moreover, the semantics of the language has been mainly given in terms of
intuition about implementation, and has not been formalised.
  This paper provides a formal treatment of the Stan language, and introduces
the probabilistic programming language SlicStan --- a compositional,
self-optimising version of Stan. Our main contributions are: (1) the
formalisation of a core subset of Stan through an operational density-based
semantics; (2) the design and semantics of the Stan-like language SlicStan,
which facilities better code reuse and abstraction through its compositional
syntax, more flexible functions, and information-flow type system; and (3) a
formal, semantic-preserving procedure for translating SlicStan to Stan.


  X-ray activity of Anomalous X-ray Pulsars and Soft Gamma-Ray Repeaters may
result from the heating of their magnetic corona by direct currents dissipated
by magnetic reconnection. We investigate the possibility that X-ray flares and
bursts observed from AXPs and SGRs result from magnetospheric reconnection
events initiated by development of tearing mode in magnetically-dominated
relativistic plasma. We formulate equations of resistive force-free
electrodynamics, discuss its relation to ideal electrodynamics, and give
examples of both ideal and resistive equilibria. Resistive force-free current
layers are unstable toward the development of small-scale current sheets where
resistive effects become important. Thin current sheets are found to be
unstable due to the development of resistive force-free tearing mode. The
growth rate of tearing mode is intermediate between the short \Alfven time
scale $ \tau_A$ and a long resistive time scale $\tau_R$: $\Gamma \sim
1/(\tau_R \tau_A)^{1/2}$, similar to the case of non-relativistic
non-force-free plasma. We propose that growth of tearing mode is related to the
typical rise time of flares, $\sim 10$ msec. Finally, we discuss how
reconnection may explain other magnetar phenomena and ways to test the model.


  We give a Thurston-like definition for laminations on higher Teichmuller
spaces associated to a surface $S$ and a semi-simple group $G$ for $G-SL_m$ and
$PGL_m$. The case $G=SL_2$ or $PGL_2$ corresponds to the classical theory of
laminations. Our construction involves positive configurations of points in the
affine building. We show that these laminations are parameterized by the
tropical points of the spaces $\X_{G,S}$ and $\A_{G,S}$ of Fock and Goncharov.
Finally, we explain how these laminations give a compactification of higher
Teichmuller spaces.


  In supersymmetric quantum mechanics the emergence of a singularity may lead
to the breakdown of isospectrality between partner potentials. One of the
regularization recipes is based on a topologically nontrivial, multisheeted
complex deformations of the line of coordinate $x$ giving the so called quantum
toboggan models (QTM). The consistent theoretical background of this recipe is
briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional
and reducible to doublets of non-singular ordinary differential equations
a.k.a. Sturm-Schr\"odinger equations containing a weighted energy $E\to EW(x)$
and living in single complex plane.